,,history ,,of ,,the ,,inductive ,,sciences4 ,,volume ,i4 ,,history ,,of ,,the ,,inductive ,,sciences1 ,,from ,,the ,,earliest ,,to ,,the ,,present ,,time4 ,,by ,,william ,,whewell1 ,d4 ,d41 ,,master ,,of ,,trinity ,,college1 ,,cambridge4 ,,the ,,third ,,edition1 ,,with ,,additions4 ,,in ,,two ,,volumes4 ,,volume ,i4 ,,new ,,york3 ,d4 ,,appleton ,,and ,,company1 #edi #eea ,,broadway4 #ahge4 ,,to ,,sir ,,john ,,frederick ,,william ,,herschel1 ,k4,g4,h4 ,,my ,,dear ,,herschel1 ,,it is with no common pleasure that ,i take up my pen to dedicate these volumes to you4 ,they are the result of trains of thought which have often been the subject of our conversation1 and of which the origin goes back to the period of our early companionship at the ,university4 ,and if ,i had ever wavered in my purpose of combining such reflections and researches into a whole1 ,i should have derived a renewed impulse and increased animation from your delightful ,discourse on a kindred subject4 ,for ,i could not have read it without finding this portion of philosophy invested with a fresh charm2 and though ,i might be well aware that ,i could not aspire to that large share of popularity which your work so justly gained1 ,i should still have reflected1 that something was due to the subject itself1 and should have hoped that my own aim was so far similar to yours1 that the present work might have a chance of exciting an interest in some of your readers4 ,that it will interest you1 ,i do not at all hesitate to believe4 ,if you were now in ,england ,i should stop here3 but when a friend is removed for years to a far distant land1 we seem to acquire a right to speak openly of his good qualities4 ,i cannot1 therefore1 prevail upon myself to lay down my pen without alluding to the affectionate admiration of your moral and social1 as well as intellectual excellencies1 which springs up in the hearts of your friends1 whenever you are thought of4 ,they are much delighted to look upon the halo of deserved fame which plays round your head but still more1 to recollect1 #f as one of them said1 that your head is far from being the best part about you4 ,may your sojourn in the southern hemisphere be as happy and successful as its object is noble and worthy of you2 and may your return home be speedy and prosperous1 as soon as your purpose is attained4 ,ever1 my dear ,herschel1 yours1 ,w4 ,,whewell4 ,march #bb1 #ahcg4 ,p4,s4 ,so ,i wrote nearly ten years ago1 when you were at the ,cape of ,good ,hope1 employed in your great task of making a complete standard survey of the nebul and double stars visible to man4 ,now that you are1 as ,i trust1 in a few weeks about to put the crowning stone upon your edifice by the publication of your ,observations in the ,southern ,hemisphere1 ,i cannot refrain from congratulating you upon having had your life ennobled by the conception and happy execution of so great a design1 and once more offering you my wishes that you may long enjoy the glory you have so well won4 ,w4 ,w4 ,,trinity ,,college1 ,,nov4 #bb1 #ahdf4 #g ,,preface ,,to ,,the ,,third ,,edition4 ,,in the ,prefaces to the previous ,editions of this work1 several remarks were made which it is not necessary now to repeat to the same extent4 ,that a ,history of the ,sciences1 executed as this is1 has some value in the eyes of the ,public1 is sufficiently proved by the circulation which it has obtained4 ,i am still able to say that ,i have seen no objection urged against the plan of the work1 and scarcely any against the details4 ,the attempt to throw the history of each science into ,,epochs at which some great and cardinal discovery was made1 and to arrange the subordinate events of each history as belonging to the ,,preludes and the ,,sequels of such ,epochs1 appears to be assented to1 as conveniently and fairly exhibiting the progress of scientific truth4 ,such a view being assumed1 as it was a constant light and guide to the writer in his task1 so will it also1 ,i think1 make the view of the reader far more clear and comprehensive than it could otherwise be4 ,with regard to the manner in which this plan has been carried into effect with reference to particular writers and their researches1 as ,i have said1 ,i have seen scarcely any objection made4 ,i was aware1 as ,i stated at the outset1 of the difficulty and delicacy of the office which ,i had undertaken2 but ,i had various considerations to encourage me to go through it2 and ,i had a trust1 which ,i #h have as yet seen nothing to disturb1 that ,i should be able to speak impartially of the great scientific men of all ages1 even of our own4 ,i have already said1 in the ,introduction1 that the work aimed at being1 not merely a narration of the facts in the history of ,science1 but a basis for the ,philosophy of ,science4 ,it seemed to me that our study of the modes of discovering truth ought to be based upon a survey of the truths which have been discovered4 ,this maxim1 so stated1 seems sufficiently self-evident2 yet it has1 even up to the present time1 been very rarely acted on4 ,those who discourse concerning the nature of ,truth and the mode of its discovery1 still1 commonly1 make for themselves examples of truths1 which for the most part are utterly frivolous and unsubstantial 7as in most ,treatises on ,logic72 or else they dig up1 over and over1 the narrow and special field of mathematical truth1 which certainly cannot1 of itself1 exemplify the general mode by which man has attained to the vast body of certain truth which he now possesses4 ,yet it must not be denied that the ,ideas which form the basis of ,mathematical ,truth are concerned in the formation of ,scientific ,truth in general2 and discussions concerning these ,ideas are by no means necessarily barren of advantage4 ,but it must be borne in mind that1 besides these ,ideas1 there are also others1 which no less lie at the root of ,scientific ,truth2 and concerning which there have been1 at various periods1 discussions which have had an important bearing on the progress of ,scientific ,truth2--such as discussions concerning the nature and necessary attributes of ,matter1 of ,force1 of ,atoms1 of ,mediums1 of ,kinds1 of ,organization4 ,the controversies which have taken place concerning these have an important place in the history of ,natural ,science in #i its most extended sense4 ,yet it appeared convenient to carry on the history of ,science1 so far as it depends on ,observation1 in a line separate from these discussions concerning ,ideas4 ,the account of these discussions and the consequent controversies1 therefore1 though it be thoroughly historical1 and1 as appears to me1 a very curious and interesting history1 is reserved for the other work1 the ,philosophy of the ,inductive ,sciences4 ,such a history has1 in truth1 its natural place in the ,philosophy of ,science2 for the ,philosophy of ,science at the present day must contain the result and summing up of all the truth which has been disentangled from error and confusion during these past controversies4 ,i have made a few ,additions to the present ,edition2 partly1 with a view of bringing up the history1 at least of some of the ,sciences1 to the present time1--so far as those larger features of the ,history of ,science are concerned1 with which alone ,i have here to deal1--and partly also1 especially in the ,first ,volume1 in order to rectify and enlarge some of the earlier portions of the history4 ,several works which have recently appeared suggested reconsideration of various points2 and ,i hoped that my readers might be interested in the reflections so suggested4 ,i will add a few sentences from the ,preface to the ,first ,edition4 ,as will easily be supposed1 ,i have borrowed largely from other writers1 both of the histories of special sciences and of philosophy in general4#a,p ,i have done this without #aj scruple1 since the novelty of my work was intended to consist1 not in its superiority as a collection of facts1 but in the point of view in which the facts were placed4 ,i have1 however1 in all cases1 given references to my authorities1 and there are very few instances in which ,i have not verified the references of previous historians1 and studied the original authors4 ,according to the plan which ,i have pursued1 the history of each science forms a whole in itself1 divided into distinct but connected members1 by the ,epochs of its successive advances4 ,if ,i have satisfied the competent judges in each science by my selection of such epochs1 the scheme of the work must be of permanent value1 however imperfect may be the execution of any of its portions4 ,note #a,p3 ,among these1 ,i may mention as works to which ,i have peculiar obligations1 ,tennemann's ,geschichte der ,philosophie2 ,degerando's ,histoire ,compare des ,systmes de ,philosophie2 ,montucla's ,histoire des ,mathmatiques1 with ,delalande's continuation of it2 ,delambre's ,astronomie ,ancienne1 ,astronomie du ,moyen ,age1 ,astronomie ,moderne1 and ,astronomie du ,dix-huitime ,sicle2 ,bailly's ,histoire d',astronomie ,ancienne1 and ,histoire d',astronomie ,moderne2 ,voiron's ,histoire d',astronomie 7published as a continuation of ,bailly71 ,fischer's ,geschichte der ,physik1 ,gmelin's ,geschichte der ,chemie1 ,thomson's ,history of ,chemistry1 ,sprengel's ,history of ,medicine1 his ,history of ,botany1 and in all branches of ,natural ,history and ,physiology1 ,cuvier's works2 in their historical1 as in all other portions1 most admirable and instructive4 ,with all these grounds of hope1 it is still impossible not to see that such an undertaking is1 in no small degree1 arduous1 and its event obscure4 ,but all who venture upon such tasks must gather trust and encouragement from reflections like those by which their great forerunner prepared himself for his endeavors2--by recollecting that they are aiming to advance the best interests and privileges of man2 and that they may expect all the best and wisest of men to join them in their aspirations and to aid them in their labors4 ',concerning ourselves we speak not2 but as touching the matter which we have in hand1 this we ask2--that men deem it not to be the setting up of an ,opinion1 but the performing of a ,work2 and that they receive this as a certainty--that we are not laying the foundations of any sect or doctrine1 but of the profit and dignity of mankind3--,furthermore1 #aa that being well disposed to what shall advantage themselves1 and putting off factions and prejudices1 they take common counsel with us1 to the end that being by these our aids and appliances freed and defended from wanderings and impediments1 they may lend their hands also to the labors which remain to be performed3--,and yet1 further1 that they be of good hope2 neither feign and imagine to themselves this our ,reform as something of infinite dimension and beyond the grasp of mortal man1 when1 in truth1 it is1 of infinite error1 the end and true limit2 and is by no means unmindful of the condition of mortality and humanity1 not confiding that such a thing can be carried to its perfect close in the space of one single day1 but assigning it as a task to a succession of generations4'--,,bacon--,,instauratio ,,magna1 ,prf4 ad fin4 ',if there be any man who has it at heart1 not merely to take his stand on what has already been discovered1 but to profit by that1 and to go on to something beyond2--not to conquer an adversary by disputing1 but to conquer nature by working2--not to opine probably and prettily1 but to know certainly and demonstrably2--let such1 as being true sons of nature 7if they will consent to do so71 join themselves to us2 so that1 leaving the porch of nature which endless multitudes have so long trod1 we may at last open a way to the inner courts4 ,and that we may mark the two ways1 that old one1 and our new one1 by familiar names1 we have been wont to call the one the ,anticipation of the ,mind1 the other1 the ,interpretation of ,nature4'--,,inst4 ,,mag4 ,prf4 ad ,part4 ii4 #ac ,,contents ,,of ,,the ,,first ,,volume4 ,,page ,preface to the ,third ,edition4 #g ,index of ,proper ,names4 #bc ,index of ,technical ,terms4 #cc ,,introduction4 #da ,,book ,i4 ,,history ,,of ,,the ,,greek ,,school ,,philosophy1 ,,with ,,reference ,,to ,,physical ,,science4 ,,chapter ,i4--,,prelude ,,to ,,the ,,greek ,,school ,,philosophy4 ,sect4 #a4 ,first ,attempts of the ,speculative ,faculty in ,physical ,inquiries4 #ee ,sect4 #b4 ,primitive ,mistake in ,greek ,physical ,philosophy4 #fj ,,chapter ,,ii4--,,the ,,greek ,,school ,,philosophy4 ,sect4 #a4 ,the ,general ,foundation of the ,greek ,school ,philosophy4 #fc ,sect4 #b4 ,the ,aristotelian ,physical ,philosophy4 #fg ,sect4 #c4 ,technical ,forms of the ,greek ,schools4 #gc #a4 ,technical ,forms of the ,aristotelian ,philosophy4 #gc #b4 ,platonists4 #ge #c4 ,pythagoreans4 #gg #d4 ,atomists and ,others4 #gh ,,chapter ,,iii4--,,failure ,,of ,,the ,,physical ,,philosophy ,,of ,,the ,,greek ,,schools4 ,sect4 #a4 ,result of the ,greek ,school ,philosophy4 #hj ,sect4 #b4 ,cause of the ,failure of the ,greek ,physical ,philosophy4 #hc #ad ,,book ,,ii4 ,,history ,,of ,,the ,,physical ,,sciences ,,in ,,ancient ,,greece4 ,introduction4 #ie ,,chapter ,i4--,,earliest ,,stages ,,of ,,mechanics ,,and ,,hydrostatics4 ,sect4 #a4 ,mechanics4 #if ,sect4 #b4 ,hydrostatics4 #ih ,,chapter ,,ii4--,,earliest ,,stages ,,of ,,optics4 #ajj ,,chapter ,,iii4--,,earliest ,,stages ,,of ,,harmonics4 #aje ,,book ,,iii4 ,,history ,,of ,,greek ,,astronomy4 ,introduction4 #aaa ,,chapter ,i4--,,earliest ,,stages ,,of ,,astronomy4 ,sect4 #a4 ,formation of the ,notion of a ,year4 #aab ,sect4 #b4 ,fixation of the ,civil ,year4 #aac ,sect4 #c4 ,correction of the ,civil ,year 7,julian ,calendar74 #aag ,sect4 #d4 ,attempts at the ,fixation of the ,month4 #aah ,sect4 #e4 ,invention of ,lunisolar ,years4 #abj ,sect4 #f4 ,the ,constellations4 #abd ,sect4 #g4 ,the ,planets4 #abf ,sect4 #h4 ,the ,circles of the ,sphere4 #abh ,sect4 #i4 ,the ,globular ,form of the ,earth4 #acb ,sect4 #aj4 ,the ,phases of the ,moon4 #acd ,sect4 #aa4 ,eclipses4 #ace ,sect4 #ab4 ,sequel to the ,early ,stages of ,astronomy4 #acf ,,chapter ,,ii4--,,prelude ,,to ,,the ,,inductive ,,epoch ,,of ,,hipparchus4 #ach #ae ,,chapter ,,iii4--,,inductive ,,epoch ,,of ,,hipparchus4 ,sect4 #a4 ,establishment of the ,theory of ,epicycles and ,eccentrics4 #ade ,sect4 #b4 ,estimate of the ,value of the ,theory of ,eccentrics and ,epicycles4 #aea ,sect4 #c4 ,discovery of the ,precession of the ,equinoxes4 #aee ,,chapter ,,iv4--,,sequel ,,to ,,the ,,inductive ,,epoch ,,of ,,hipparchus4 ,sect4 #a4 ,researches which verified the ,theory4 #aeg ,sect4 #b4 ,researches which did not verify the ,theory4 #aei ,sect4 #c4 ,methods of ,observation of the ,greek ,astronomers4 #afa ,sect4 #d4 ,period from ,hipparchus to ,ptolemy4 #aff ,sect4 #e4 ,measures of the ,earth4 #afi ,sect4 #f4 ,ptolemy's ,discovery of ,evection4 #agj ,sect4 #g4 ,conclusion of the ,history of ,greek ,astronomy4 #age ,sect4 #h4 ,arabian ,astronomy4 #agf ,,book ,,iv4 ,,history ,,of ,,physical ,,science ,,in ,,the ,,middle ,,ages4 ,introduction4 #ahe ,,chapter ,i4--,,on ,,the ,,indistinctness ,,of ,,ideas ,,of ,,the ,,middle ,,ages4 #a4 ,collections of ,opinions4 #ahg #b4 ,indistinctness of ,ideas in ,mechanics4 #ahh #c4 shown in ,architecture4 #aia #d4 in ,astronomy4 #aib #e4 shown by ,skeptics4 #aib #f4 ,neglect of ,physical ,reasoning in ,christendom4 #aie #g4 ,question of ,antipodes4 #aie #h4 ,intellectual ,condition of the ,religious ,orders4 #aig #i4 ,popular ,opinions4 #aii ,,chapter ,,ii4--,,the ,,commentatorial ,,spirit ,,of ,,the ,,middle ,,ages4 #bja #a4 ,natural ,bias to ,authority4 #bjb #b4 ,character of ,commentators4 #bjd #c4 ,greek ,commentators of ,aristotle4 #bje #af #d4 ,greek ,commentators of ,plato and ,others4 #bjg #e4 ,arabian ,commentators of ,aristotle4 #bjh ,,chapter ,,iii4--,,of ,,the ,,mysticism ,,of ,,the ,,middle ,,ages4 #baa #a4 ,neoplatonic ,theosophy4 #bab #b4 ,mystical ,arithmetic4 #baf #c4 ,astrology4 #bah #d4 ,alchemy4 #bbd #e4 ,magic4 #bbe ,,chapter ,,iv4--,,of ,,the ,,dogmatism ,,of ,,the ,,stationary ,,period4 #a4 ,origin of the ,scholastic ,philosophy4 #bbh #b4 ,scholastic ,dogmas4 #bcj #c4 ,scholastic ,physics4 #bce #d4 ,authority of ,aristotle among the ,schoolmen4 #bcf #e4 ,subjects omitted4 ,civil ,law4 ,medicine4 #bch ,,chapter ,v4--,,progress ,,of ,,the ,,arts ,,in ,,the ,,middle ,,ages4 #a4 ,art and ,science4 #bci #b4 ,arabian ,science4 #bdb #c4 ,experimental ,philosophy of the ,arabians4 #bdc #d4 ,roger ,bacon4 #bde #e4 ,architecture of the ,middle ,ages4 #bdf #f4 ,treatises on ,architecture4 #bdh ,,book ,v4 ,,history ,,of ,,formal ,,astronomy ,,after ,,the ,,stationary ,,period4 ,introduction4 #bee ,,chapter ,i4--,,prelude ,,to ,,the ,,inductive ,,epoch ,,of ,,copernicus4 #beg ,,chapter ,,ii4--,,induction ,,of ,,copernicus4 ,,the ,,heliocentric ,,theory ,,asserted ,,on ,,formal ,,grounds4 #bfb #ag ,,chapter ,,iii--,,sequel ,,to ,,copernicus4 ,,the ,,reception ,,and ,,development ,,of ,,the ,,copernican ,,theory4 ,sect4 #a4 ,first ,reception of the ,copernican ,theory4 #bfi ,sect4 #b4 ,diffusion of the ,copernican ,theory4 #bgb ,sect4 #c4 ,the ,heliocentric ,theory confirmed by ,facts4 ,galileo's ,astronomical ,discoveries4 #bgf ,sect4 #d4 ,the ,copernican ,system opposed on ,theological ,grounds4 #bhf ,sect4 #e4 ,the ,heliocentric ,theory confirmed on ,physical ,considerations4 7,prelude to ,kepler's ,astronomical ,discoveries47 #bhg ,,chapter ,,iv4--,,inductive ,,epoch ,,of ,,kepler4 ,sect4 #a4 ,intellectual ,character of ,kepler4 #bij ,sect4 #b4 ,kepler's ,discovery of his ,third ,law4 #bic ,sect4 #c4 ,kepler's ,discovery of his ,first and ,second ,laws4 ,elliptical ,theory of the ,planets4 #bif ,,chapter ,v4--,,sequel ,,to ,,the ,,epoch ,,of ,,kepler4 ,,reception1 ,,verification1 ,,and ,,extension ,,of ,,the ,,elliptical ,,theory4 ,sect4 #a4 ,application of the ,elliptical ,theory to the ,planets4 #cjb ,sect4 #b4 ,moon4 #cjc ,sect4 #c4 ,causes of the further ,progress of ,astronomy4 #cje ,,the ,,mechanical ,,sciences4 ,,book ,,vi4 ,,history ,,of ,,mechanics1 ,,including ,,fluid ,,mechanics4 ,introduction4 #caa ,,chapter ,i4--,,prelude ,,to ,,the ,,epoch ,,of ,,galileo4 ,sect4 #a4 ,prelude to the ,science of ,statics4 #cab ,sect4 #b4 ,revival of the ,scientific ,idea of ,pressure4 --,stevinus4--,equilibrium of ,oblique ,forces4 #caf ,sect4 #c4 ,prelude to the ,science of ,dynamics4--,attempts at the ,first ,law of ,motion4 #cai #ah ,,chapter ,,ii4--,,inductive ,,epoch ,,of ,,galileo4--,,discovery ,,of ,,the ,,laws ,,of ,,motion ,,in ,,simple ,,cases4 ,sect4 #a4 ,establishment of the ,first ,law of ,motion4 #cbb ,sect4 #b4 ,formation and ,application of the ,motion of ,accelerating ,force4 ,laws of ,falling ,bodies4 #cbd ,sect4 #c4 ,establishment of the ,second ,law of ,motion4--,curvilinear ,motions4 #ccj ,sect4 #d4 ,generalization of the ,laws of ,equilibrium4--,principle of ,virtual ,velocities4 #cca ,sect4 #e4 ,attempts at the ,third ,law of ,motion4--,notion of ,momentum4 #ccd ,,chapter ,,iii4--,,sequel ,,to ,,the ,,epoch ,,of ,,galileo4--,,period ,,of ,,verification ,,and ,,deduction4 #cdj ,,chapter ,,iv4--,,discovery ,,of ,,the ,,mechanical ,,principles ,,of ,,fluids4 ,sect4 #a4 ,rediscovery of the ,laws of ,equilibrium of ,fluids4 #cde ,sect4 #b4 ,discovery of the ,laws of ,motion of ,fluids4 #cdh ,,chapter ,v4--,,generalization ,,of ,,the ,,principles ,,of ,,mechanics4 ,sect4 #a4 ,generalization of the ,second ,law of ,motion4--,central ,forces4 #ceb ,sect4 #b4 ,generalization of the ,third ,law of ,motion4--,centre of ,oscillation4--,huyghens4 #cef ,,chapter ,,vi4--,,sequel ,,to ,,the ,,generalization ,,of ,,the ,,principles ,,of ,,mechanics4--,,period ,,of ,,mathematical ,,deduction4--,,analytical ,,mechanics4 #cfb #a4 ,geometrical ,mechanics4--,newton1 c4 #cfc #b4 ,analytical ,mechanics4--,euler4 #cfc #c4 ,mechanical ,problems4 #cfd #d4 ,d',alembert's ,principle4 #cfe #e4 ,motion in ,resisting ,media4--,ballistics4 #cfe #f4 ,constellation of ,mathematicians4 #cff #g4 ,the ,problem of ,three ,bodies4 #cfg #h4 ,mcanique ,cleste1 c4 #cga #i4 ,precession4--,motion of ,rigid ,bodies4 #cgd #aj4 ,vibrating ,strings4 #cge #aa4 ,equilibrium of ,fluids4--,figure of the ,earth4--,tides4 #cgf #ab4 ,capillary ,action4 #cgg #ac4 ,motion of ,fluids4 #cgh #ad4 ,various ,general ,mechanical ,principles4 #chj #ae4 ,analytical ,generality4--,connection of ,statics and ,dynamics4 #cha #ai ,,book ,,vii4 ,,history ,,of ,,physical ,,astronomy4 ,,chapter ,i4--,,prelude ,,to ,,the ,,inductive ,,epoch ,,of ,,newton4 #che ,,chapter ,,ii4--,,the ,,inductive ,,epoch ,,of ,,newton4--,,discovery ,,of ,,the ,,universal ,,gravitation ,,of ,,matter1 ,,according ,,to ,,the ,,law ,,of ,,the ,,inverse ,,square ,,of ,,the ,,distance4 #cii #a4 ,sun's ,force on ,different ,planets4 #cii #b4 ,force in ,different ,points of an ,orbit4 #djj #c4 ,moon's ,gravity to the ,earth4 #djb #d4 ,mutual ,attraction of all the ,celestial ,bodies4 #djf #e4 ,particles of ,matter4 #daa ,reflections on the ,discovery4 #dad ,character of ,newton4 #daf ,,chapter ,,iii4--,,sequel ,,to ,,the ,,epoch ,,of ,,newton4--,,reception ,,of ,,the ,,newtonian ,,theory4 ,sect4 #a4 ,general ,remarks4 #dbj ,sect4 #b4 ,reception of the ,newtonian ,theory in ,england4 #dba ,sect4 #c4 ,abroad4 #dbi ,,chapter ,,iv4--,,sequel ,,to ,,the ,,epoch ,,of ,,newton1 ,,continued4 ,,verification ,,and ,,completion ,,of ,,the ,,newtonian ,,theory4 ,sect4 #a4 ,division of the ,subject4 #dcc ,sect4 #b4 ,application of the ,newtonian ,theory to the ,moon4 #dcd ,sect4 #c4 ,planets1 ,satellites1 and ,earth4 #dch ,sect4 #d4 ,application of the ,newtonian ,theory to ,secular ,inequalities4 #ddd ,sect4 #e4 to the new ,planets4#ddf ,sect4 #f4 to ,comets4 #ddi ,sect4 #g4 to the ,figure of the ,earth4 #deb ,sect4 #h4 ,confirmation of the ,newtonian ,theory by ,experiments on ,attraction4 #def ,sect4 #i4 ,application of the ,newtonian ,theory to the ,tides4 #deg ,,chapter ,v4--,,discoveries ,,added ,,to ,,the ,,newtonian ,,theory4 ,sect4 #a4 ,tables of ,astronomical ,refraction4 #dfb ,sect4 #b4 ,discovery of the ,velocity of ,light4--,rmer4 #dfc #bj ,sect4 #c4 ,discovery of ,aberration4--,bradley4 #dfd ,sect4 #d4 ,discovery of ,nutation4 #dfe ,sect4 #e4 ,discovery of the ,laws of ,double ,stars4--,the ,two ,herschels4 #dfg ,,chapter ,,vi4--,,the ,,instruments ,,and ,,aids ,,of ,,astronomy ,,during ,,the ,,newtonian ,,period4 ,sect4 #a4 ,instruments4 #dgj ,sect4 #b4 ,observatories4 #dgf ,sect4 #c4 ,scientific ,societies4 #dgh ,sect4 #d4 ,patrons of ,astronomy4 #dgi ,sect4 #e4 ,astronomical ,expeditions4 #dhj ,sect4 #f4 ,present ,state of ,astronomy4 #dha ,,additions ,,to ,,the ,,third ,,edition4 ,,introduction #dhi ,,book ,i4--,,the ,,greek ,,school ,,philosophy4 ,,the ,,greek ,,schools4 ,the ,platonic ,doctrine of ,ideas4 #dia ,,failure ,,of ,,the ,,greek ,,physical ,,philosophy4 ,bacon's ,remarks on the ,greeks4 #did ,aristotle's ,account of the ,rainbow4 #die ,,book ,,ii4--,,the ,,physical ,,sciences ,,in ,,ancient ,,greece4 ,plato's ,timus and ,republic4 #dig ,hero of ,alexandria4 #eja ,,book ,,iii4--,,the ,,greek ,,astronomy4 ,introduction4 #ejc ,,earliest ,,stages ,,of ,,astronomy4 ,the ,globular ,form of the ,earth4 #eje ,the ,heliocentric ,system among the ,ancients4 #ejf ,the ,eclipse of ,thales4 #ejh #ba ,,book ,,iv4--,,physical ,,science ,,in ,,the ,,middle ,,ages4 ,general ,remarks4 #eaa ,,progress ,,in ,,the ,,middle ,,ages4 ,thomas ,aquinas4 #eab ,roger ,bacon4 #eab ,,book ,v4--,,formal ,,astronomy4 ,,prelude ,,to ,,copernicus4 ,nicolas of ,cus4 #ebc ,,the ,,copernican ,,theory4 ,the ,moon's ,rotation4 #ebd ,m4 ,foucault's ,experiments4 #ebe ,,sequel ,,to ,,copernicus4 ,english ,copernicans4 #ebf ,giordano ,bruno4 #ecj ,did ,francis ,bacon reject the ,copernican ,doctrine8 #ecj ,kepler persecuted4 #ecb ,the ,papal ,edicts against the ,copernican ,system repealed4 #ecd ,,book ,,vi4--,,mechanics4 ,,principles ,,and ,,problems4 ,significance of ,analytical ,mechanics4 #ecf ,strength of ,materials4 #ech ,roofs--,arches--,vaults4 #eda ,,book ,,vii4--,,physical ,,astronomy4 ,,prelude ,,to ,,newton4 ,the ,ancients4 #edd ,jeremiah ,horrox4 #ede ,newton's ,discovery of ,gravitation4 #edf #bb ,,the ,,principia4 ,reception of the ,principia4 #edh ,is ,gravitation proportional to ,quantity of ,matter8 #edi ,,verification ,,and ,,completion ,,of ,,the ,,newtonian ,,theory4 ,tables of the ,moon and ,planets4 #eej ,the ,discovery of ,neptune4 #eed ,the ,minor ,planets4 #eeg ,anomalies in the ,action of ,gravitation4 #efj ,the ,earth's ,density4 #efa ,tides4 #efb ,double ,stars4 #efc ,,instruments4 ,clocks4 #efe #bc ,,index ,,of ,,proper ,,names4 ,the letters a1 b1 indicate vol4 ,i41 vol4 ,,ii41 respectively4 ,abdollatif1 b4 #ddc4 ,aboazen1 a4 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,elliptical polarization1 b4 #abb1 #abc4 ,empiric school 7of medicine71 b4 #dci4 ,empyrean1 a4 #hb4 ,enneads1 a4 #bac4 ,entelechy1 a4 #gd4 ,eocene1 b4 #ebi4 ,epicycles1 a4 #adj1 #ade ,epochs1 a4 #df4 ,equant1 a4 #age4 ,equation of time1 a4 #aei4 ,equator1 a4 #acj4 ,equinoctial points1 a4 #aca4 ,escarpment1 b4 #ecg4 ,evection1 a4 #aga1 #agb4 ,exchanges of heat1 ,theory of1 b4 #adc4 ,facts and ideas1 a4 #dc4 ,faults 7in strata71 b4 #ecg4 ,final causes1 b4 #ddb1 #dib4 ,finite intervals 7hypothesis of71 b4 #abf4 ,first law of motion1 a4 #cbb4 ,fits of easy transmission1 b4 #gg1 #hi4 ,fixed air1 b4 #bgb4 ,fixity of the stars1 a4 #aeh4 #ce ,formal optics1 b4 #eb4 ,franklinism1 b4 #bjb4 ,fresnel's rhomb1 b4 #aje4 ,fringes of shadows1 b4 #gi1 #abe4 ,fuga vacui1 a4 #cdg4 ,full months1 a4 #abb4 ,function 7in ,physiology71 b4 #dce4 ,galvanism1 b4 #bci4 ,galvanometer1 b4 #bea4 ,ganglionic system1 b4 #dfc4 ,ganglions1 b4 #dfc4 ,generalization1 a4 #df4 ,geocentric theory1 a4 #beh4 ,gnomon1 a4 #afb4 ,gnomonic1 a4 #acg4 ,golden number1 a4 #abc4 ,grave harmonics1 b4 #ch4 ,gravitate1 a4 #djf4 ,habitations 7of plants71 b4 #efb4 ,hcceity1 a4 #bcc4 ,hakemite tables1 a4 #agg4 ,halogenes1 b4 #cjh4 ,haloide1 b4 #ceb4 ,harmonics1 ,acute1 b4 #cg4 ,grave1 b4 #ch4 ,heat1 b4 #aci4 ,latent1 b4 #afj4 ,heccdecateris1 a4 #aba4 ,height of a homogeneous atmosphere1 b4 #cd4 ,heliacal rising and setting1 a4 #aca4 ,heliocentric theory1 a4 #beh4 ,hemisphere of ,berosus1 a4 #afb4 ,hollow months1 a4 #abb4 ,homoiomeria1 a4 #gh4 ,horizon1 a4 #aca4 ,horoscope1 a4 #bbb4 ,horror of a vacuum1 a4 #cdf4 ,houses 7in ,astrology71 a4 #bbb4 ,hydracids1 b4 #bhc4 ,hygrometer1 b4 #agg4 ,hygrometry1 b4 #ach4 ,hypostatical principles1 b4 #bfb4 ,iatro-chemists1 b4 #bfc4 ,ideas of the ,platonists1 a4 #ge4 ,ilchanic tables1 a4 #agh4 ,impressed forces1 a4 #cei4 ,inclined plane1 a4 #cac4 ,induction 7electric71 b4 #aig4 7logical71 a4 #dc4 ,inductive1 a4 #db4 charts1 a4 #dg4 epochs1 a4 #df4 ,inflammable air1 b4 #bgc4 ,influences1 a4 #bai4 ,intercalation1 a4 #aah4 ,interferences1 b4 #hf1 #ic4 ,ionic school1 a4 #ef4 ,isomorphism1 b4 #ccd4 ,isothermal lines1 b4 #adf1 #ech4 ,italic school1 a4 #ef4 ,joints 7in rocks71 b4 #ecg4 ,judicial astrology1 a4 #bbb4 ,julian calendar1 a4 #aah4 ,lacteals1 b4 #dec4 ,latent heat1 b4 #afj4 ,laws of motion1 first1 a4 #cbb4 second1 a4 #ccj4 third1 a4 #ccd4 ,leap year1 a4 #aah4 ,leyden phial1 b4 #aif4 ,librations 7of planets71 a4 #big4 ,libration of ,jupiter's ,satellites1 a4 #dda4 ,limb of an instrument1 a4 #afb4 ,longitudinal vibrations1 b4 #dd4 ,lunisolar year1 a4 #abj4 ,lymphatics1 b4 #dec4 ,magnetic elements1 b4 #bbb4 equator1 b4 #bai4 ,magnetism1 b4 #bag4 ,magneto-electric induction1 b4 #bef4 ,matter and form1 a4 #gc4 ,mean temperature1 b4 #adf4 ,mechanical mixture of gases1 b4 #agb4 ,mechanico-chemical sciences1 b4 #aia4 ,meiocene1 b4 #ebi4 ,meridian line1 a4 #afd4 ,metals1 b4 #cjf1 #cjg4 ,meteorology1 b4 #ach4 ,meteors1 a4 #hf4 ,methodic school 7of medicine71 b4 #dci4 #cf ,metonic cycle1 a4 #abb4 ,mineral alkali1 b4 #bfd4 ,mineralogical axis1 b4 #ecg4 ,minutes1 a4 #afc4 ,miocene1 b4 #ebi4 ,mollusca1 b4 #dgh4 ,moment of inertia1 a4 #cef4 ,momentum1 a4 #ccg1 #cch4 ,moon's libration1 a4 #cge4 ,morphology1 b4 #dfi1 #dgd4 ,movable polarization1 b4 #aje4 ,multiple proportions 7in ,chemistry71 b4 #bhe4 ,music of the spheres1 a4 #hb4 ,mysticism1 a4 #bji1 #baa4 ,nadir1 a4 9999#ahb4 ,nebular hypothesis1 b4 #eja4 ,neoplatonists1 a4 #bjg4 ,neutral axes1 b4 #ha4 ,neutralization 7in ,chemistry71 b4 #bfc4 ,newton's rings1 b4 #gg1 #abd4 scale of color1 b4 #gg4 ,nitrous air1 b4 #bgc4 ,nomenclature1 b4 #chi4 ,nominalists1 a4 #bch4 ,non-electrics1 b4 #aid4 ,numbers of the ,pythagoreans1 a4 #hb1 #baf4 ,nutation1 a4 #dfe4 ,nycthemer1 a4 #aei4 ,octateris1 a4 #aba4 ,octants1 a4 #ahj4 ,oolite1 b4 #ebi4 ,optics1 b4 #ea1 c4 ,organical sciences1 b4 #dce4 ,organic molecules1 b4 #dfj4 ,organization1 b4 #dce4 ,oscillation1 ,centre of1 a4 #cef4 ,outcrop 7of strata71 b4 #eab4 ,oxide1 b4 #bhb4 ,oxyd1 b4 #bhb4 ,oxygen1 b4 #bgf4 ,palontology1 b4 #eai4 ,paltiological sciences1 b4 #dii4 ,parallactic instrument1 a4 #afe4 ,parallax1 a4 #aei4 ,percussion1 ,centre of1 a4 #ceg4 ,perfectihabia1 a4 #ge4 ,perigee1 a4 #adf4 ,perijove1 a4 #ddf4 ,periodical colors1 b4 #ic4 ,phases of the moon1 a4 #acd4 ,philolaic tables1 a4 #cjd4 ,phlogisticated air1 b4 #bgc4 ,phlogiston1 b4 #bfh4 ,phthongometer1 b4 #dg4 ,physical optics1 b4 #eb4 ,piston1 a4 #cdf4 ,plagihedral faces1 b4 #hb4 ,plane of maximum areas1 b4 #chj4 ,pleiocene1 b4 #ebi4 ,plesiomorphous1 b4 #cce4 ,plumb line1 a4 #afd4 ,pneumatic trough1 b4 #bgc4 ,poikilite1 b4 #ecj4 ,polar decompositions1 b4 #bic4 ,polarization1 b4 #gb1 #gd4 ,circular1 b4 #hb1 #aai4 ,elliptical1 b4 #abb1 #abd4 ,movable1 b4 #aje4 ,plane1 b4 #abj4 of heat1 b4 #aec4 ,poles 7voltaic71 b4 #bih4 of maximum cold1 b4 #adf4 ,potential levers1 a4 #cah4 ,power and act1 a4 #gd4 ,precession of the equinoxes1 a4 #aee4 ,predicables1 a4 #bje4 ,predicaments1 a4 #bjf4 ,preludes of epochs1 a4 #df4 ,primary rocks1 b4 #eac4 ,primitive rocks1 b4 #eac4 ,primum calidum1 a4 #gg4 ,principal plane 7of a rhomb71 b4 #gc4 ,principle of least action1 a4 #chj4 ,prosthapheresis1 a4 #adf4 ,provinces 7of plants and animals71 b4 #efb4 ,prutenic tables1 a4 #bgj4 ,pulses1 b4 #cc4 ,pyrites1 b4 #ceb4 ,quadrant1 a4 #afd ,quadrivium1 a4 #aii4 ,quiddity1 a4 #bcd4 #cg ,quinary division 7in ,natural ,history71 b4 #dah4 ,quintessence1 a4 #gc4 ,radiata1 b4 #dgh4 ,radiation1 b4 #aci4 ,rays1 b4 #eh4 ,realists1 a4 #bch4 ,refraction1 b4 #ed4 of heat1 b4 #aee4 ,remora1 a4 #aij4 ,resinous electricity1 b4 #aie4 ,rete mirabile1 b4 #dfc4 ,retrograde motion of planets1 a4 #aci4 ,roman calendar1 a4 #abc4 ,rotatory vibrations1 b4 #dd4 ,rudolphine tables1 a4 #bgj1 #cjb4 ,saros1 a4 #acf4 ,scholastic philosophy1 a4 #bcj4 ,school philosophy1 a4 #ej4 ,science1 a4 #db4 ,secondary rocks1 b4 #eac4 mechanical sciences1 b4 #bc4 ,second law of motion1 a4 #ccj4 ,seconds1 a4 #afc4 ,secular inequalities1 a4 #cgj4 ,segregation1 b4 #eeh4 ,seminal contagion1 b4 #dei4 proportions1 a4 #gi4 ,sequels of epochs1 a4 #dg4 ,silicides1 b4 #ceb4 ,silurian rocks1 b4 #ecj4 ,simples1 b4 #cfg4 ,sine1 a4 #aha4 ,solar heat1 b4 #ade4 ,solstitial points1 a4 #aca4 ,solution of water in air1 b4 #aff4 ,sothic period1 a4 #aah4 ,spagiric art1 b4 #bfb4 ,specific heat1 b4 #aei4 ,sphere1 a4 #acj4 ,spontaneous generation1 b4 #deg4 ,statical electricity1 b4 #bjh4 ,stationary periods1 a4 #dh4 planets1 a4 #aci4 ,stations 7of plants71 b4 #efb4 ,sympathetic sounds1 b4 #cg4 ,systematic ,botany1 b4 #ceg4 ,systematic ,zoology1 b4 #dab4 ,systems of crystallization1 b4 #cbh4 ,tables1 ,solar1 7of ,ptolemy71 a4 #adf4 ,hakemite1 a4 #agg4 ,toletan1 a4 #agg4 ,ilchanic1 a4 #agh4 ,alphonsine1 a4 #agh4 ,prutenic1 a4 #bgj4 ,rudolphine1 a4 #cjb4 ,perpetual 7of ,lansberg71 a4 #cjb4 ,philolaic1 a4 #cjd4 ,carolinian1 a4 #cjd4 ,tangential vibrations1 b4 #de4 ,tautochronous curves1 a4 #cgb4 ,technical terms1 b4 #chi4 ,temperament1 b4 #dg4 ,temperature1 b4 #aci4 ,terminology1 b4 #chi4 ,tertiary rocks1 b4 #eac4 ,tetractys1 a4 #gg4 ,theory of analogues1 b4 #dhc4 ,thermomultiplier1 b4 #aed4 ,thermotics1 b4 #acg4 ,thick plates4 ,colors of1 b4 #gi4 ,thin plates4 ,colors of1 b4 #gg4 ,third law of motion1 a4 #ccd4 ,three principles 7in ,chemistry71 b4 #bfa4 ,toletan tables1 a4 #agg4 ,transition rocks1 b4 #ecj4 ,transverse vibrations1 b4 #dd1 #ic1 #aja4 ,travertin1 b4 #edf4 ,trepidation of the fixed stars1 a4 #agi4 ,trigonometry1 a4 #afg4 ,trivial names1 b4 #cib4 ,trivium1 a4 #aii4 ,tropics1 a4 #aca4 ,truncation 7of crystals71 b4 #cai4 ,type 7in ,comparative ,anatomy71 b4 #dgf4 ,uniform force1 a4 #cbg4 ,unity of ,composition 7in ,comparative ,anatomy71 b4 #dhc4 ,unity of plan 7in ,comparative ,anatomy71 b4 #dhc4 ,variation of the moon1 a4 #agi1 #cjc4 #ch ,vegetable alkali1 b4 #bfd4 ,vertebrata1 b4 #dgh4 ,vibrations1 b4 #dd4 ,vicarious elements1 b4 #ccd4 solicitations1 a4 #cei4 ,virtual velocities1 a4 #ccc4 ,vitreous electricity1 b4 #aie4 ,volatile alkali1 b4 #bfd4 ,volta-electrometer1 b4 #bii4 ,voltaic electricity1 b4 #bci4 pile1 b4 #bci4 ,volumes1 ,theory of1 b4 #bij4 ,voluntary1 violent1 and natural motion1 a4 #cai4 ,vortices1 a4 #chh4 ,week1 a4 #abg4 ,year1 a4 #aab4 ,zenith1 a4 #aha4 ,zodiac1 a4 #aca4 ,zones1 a4 #acf4 #ci ,a ,,history ,,of ,,the ,,inductive ,,sciences4 ,,introduction4 ,a just story of learning1 containing the antiquities and originals of ,,knowledges1 and their sects2 their inventions1 their diverse administrations and managings2 their flourishings1 their oppositions1 decays1 depressions1 oblivions1 removes2 with the causes and occasions of them1 and all other events concerning learning1 throughout all ages of the world2 ,i may truly affirm to be wanting4 ,the use and end of which work ,i do not so much design for curiosity1 or satisfaction of those that are the lovers of learning3 but chiefly for a more serious and grave purpose2 which is this1 in few words--that it will make learned men more wise in the use and administration of learning4 ,,bacon1 ,advancement of ,learning1 book ii4 #da ,,introduction4 ,,it is my purpose to write the ,history of some of the most important of the ,physical ,sciences1 from the earliest to the most recent periods4 ,i shall thus have to trace some of the most remarkable branches of human knowledge1 from their first germ to their growth into a vast and varied assemblage of undisputed truths2 from the acute1 but fruitless1 essays of the early ,greek ,philosophy1 to the comprehensive systems1 and demonstrated generalizations1 which compose such sciences as the ,mechanics1 ,astronomy1 and ,chemistry1 of modern times4 ,the completeness of historical view which belongs to such a design1 consists1 not in accumulating all the details of the cultivation of each science1 but in marking the larger features of its formation4 ,the historian must endeavor to point out how each of the important advances was made1 by which the sciences have reached their present position2 and when and by whom each of the valuable truths was obtained1 of which the aggregate now constitutes a costly treasure4 ,such a task1 if fitly executed1 must have a well-founded interest for all those who look at the existing condition of human knowledge with complacency and admiration4 ,the present generation finds itself the heir of a vast patrimony of science2 and it must needs concern us to know the steps by which these possessions were acquired1 and the documents by which they are secured to us and our heirs forever4 ,our species1 from the time of its creation1 has been travelling onwards in pursuit of truth2 and now that we have reached a lofty and commanding position1 with the broad light of day around us1 it must be grateful to look back on the line of our vast progress2--to review the journey1 begun in early twilight amid primeval wilds2 for a long time continued with slow advance and obscure prospects2 and gradually and in later days followed along more open and lightsome paths1 in a wide and fertile region4 ,the historian of science1 from early periods to the present times1 may hope for favor on the score of the mere subject of his narrative1 and in virtue of the curiosity which the men #db of the present day may naturally feel respecting the events and persons of his story4 ,but such a survey may possess also an interest of another kind2 it may be instructive as well as agreeable2 it may bring before the reader the present form and extent1 the future hopes and prospects of science1 as well as its past progress4 ,the eminence on which we stand may enable us to see the land of promise1 as well as the wilderness through which we have passed4 ,the examination of the steps by which our ancestors acquired our intellectual estate1 may make us acquainted with our expectations as well as our possessions2--may not only remind us of what we have1 but may teach us how to improve and increase our store4 ,it will be universally expected that a ,history of ,inductive ,science should point out to us a philosophical distribution of the existing body of knowledge1 and afford us some indication of the most promising mode of directing our future efforts to add to its extent and completeness4 ,to deduce such lessons from the past history of human knowledge1 was the intention which originally gave rise to the present work4 ,nor is this portion of the design in any measure abandoned2 but its execution1 if it take place1 must be attempted in a separate and future treatise1 ,on the ,philosophy of the ,inductive ,sciences4 ,an essay of this kind may1 ,i trust1 from the progress already made in it1 be laid before the public at no long interval after the present history4#aa ,note #aa3 ,the ,philosophy of the ,inductive ,sciences was published shortly after the present work4 ,though1 therefore1 many of the principles and maxims of such a work will disclose themselves with more or less of distinctness in the course of the history on which we are about to enter1 the systematic and complete exposition of such principles must be reserved for this other treatise4 ,my attempts and reflections have led me to the opinion1 that justice cannot be done to the subject without such a division of it4 ,to this future work1 then1 ,i must refer the reader who is disposed to require1 at the outset1 a precise explanation of the terms which occur in my title4 ,it is not possible1 without entering into this philosophy1 to explain adequately how science which is ,,inductive differs from that which is not so2 or why some portions of knowledge may properly be selected from the general mass and termed ,,science4 ,it will be sufficient at present to say1 that the sciences of which we have #dc here to treat1 are those which are commonly known as the ,physical ,sciences2 and that by ,induction is to be understood that process of collecting general truths from the examination of particular facts1 by which such sciences have been formed4 ,there are1 however1 two or three remarks1 of which the application will occur so frequently1 and will tend so much to give us a clearer view of some of the subjects which occur in our history1 that ,i will state them now in a brief and general manner4 ,facts and ,ideas4#ba--;,in the first place then1 ,i remark1 that1 to the formation of science1 two things are requisite2--,facts and ,ideas2 observation of ,things without1 and an inward effort of ,thought2 or1 in other words1 ,sense and ,reason4 ,neither of these elements1 by itself can constitute substantial general knowledge4 ,the impressions of sense1 unconnected by some rational and speculative principle1 can only end in a practical acquaintance with individual objects2 the operations of the rational faculties1 on the other hand1 if allowed to go on without a constant reference to external things1 can lead only to empty abstraction and barren ingenuity4 ,real speculative knowledge demands the combination of the two ingredients2--right reason1 and facts to reason upon4 ,it has been well said1 that true knowledge is the interpretation of nature2 and therefore it requires both the interpreting mind1 and nature for its subject2 both the document1 and the ingenuity to read it aright4 ,thus invention1 acuteness1 and connection of thought1 are necessary on the one hand1 for the progress of philosophical knowledge2 and on the other hand1 the precise and steady application of these faculties to facts well known and clearly conceived4 ,it is easy to point out instances in which science has failed to advance1 in consequence of the absence of one or other of these requisites2 indeed1 by far the greater part of the course of the world1 the history of most times and most countries1 exhibits a condition thus stationary with respect to knowledge4 ,the facts1 the impressions on the senses1 on which the first successful attempts at physical knowledge proceeded1 were as well known long before the time when they were thus turned to account1 as at that period4 ,the motions of the stars1 and the effects of weight1 were familiar to man before the rise of the ,greek ,astronomy and ,mechanics3 but the diviner mind was still absent2 the act of thought had not been exerted1 by which these facts were bound together under the form of laws and principles4 ,and even at #dd this day1 the tribes of uncivilized and half-civilized man1 over the whole face of the earth1 have before their eyes a vast body of facts1 of exactly the same nature as those with which ,europe has built the stately fabric of her physical philosophy2 but1 in almost every other part of the earth1 the process of the intellect by which these facts become science1 is unknown4 ,the scientific faculty does not work4 ,the scattered stones are there1 but the builder's hand is wanting4 ,and again1 we have no lack of proof that mere activity of thought is equally inefficient in producing real knowledge4 ,almost the whole of the career of the ,greek schools of philosophy2 of the schoolmen of ,europe in the middle ages2 of the ,arabian and ,indian philosophers2 shows us that we may have extreme ingenuity and subtlety1 invention and connection1 demonstration and method2 and yet that out of these germs1 no physical science may be developed4 ,we may obtain1 by such means1 ,logic and ,metaphysics1 and even ,geometry and ,algebra2 but out of such materials we shall never form ,mechanics and ,optics1 ,chemistry and ,physiology4 ,how impossible the formation of these sciences is without a constant and careful reference to observation and experiment2--how rapid and prosperous their progress may be when they draw from such sources the materials on which the mind of the philosopher employs itself2--the history of those branches of knowledge for the last three hundred years abundantly teaches us4 ,note #ba3 ,for the ,antithesis of ,facts and ,ideas1 see the ,philosophy1 book i4 ch4 #a1 #b1 #d1 #e4 ,accordingly1 the existence of clear ,ideas applied to distinct ,facts will be discernible in the ,history of ,science1 whenever any marked advance takes place4 ,and1 in tracing the progress of the various provinces of knowledge which come under our survey1 it will be important for us to see that1 at all such epochs1 such a combination has occurred2 that whenever any material step in general knowledge has been made1--whenever any philosophical discovery arrests our attention1--some man or men come before us1 who have possessed1 in an eminent degree1 a clearness of the ideas which belong to the subject in question1 and who have applied such ideas in a vigorous and distinct manner to ascertained facts and exact observations4 ,we shall never proceed through any considerable range of our narrative1 without having occasion to remind the reader of this reflection4 ,successive ,steps in ,science4#ca--;,but there is another remark which we must also make4 ,such sciences as we have here to do with are1 #de commonly1 not formed by a single act2--they are not completed by the discovery of one great principle4 ,on the contrary1 they consist in a long-continued advance2 a series of changes2 a repeated progress from one principle to another1 different and often apparently contradictory4 ,now1 it is important to remember that this contradiction is apparent only4 ,the principles which constituted the triumph of the preceding stages of the science1 may appear to be subverted and ejected by the later discoveries1 but in fact they are 7so far as they were true7 taken up in the subsequent doctrines and included in them4 ,they continue to be an essential part of the science4 ,the earlier truths are not expelled but absorbed1 not contradicted but extended2 and the history of each science1 which may thus appear like a succession of revolutions1 is1 in reality1 a series of developments4 ,in the intellectual1 as in the material world1 ,omnia mutantur nil interit 4 4 4 4 4 ,nec manet ut fuerat nec formas servat easdem1 ,sed tamen ipsa eadem est4 ,all changes1 naught is lost2 the forms are changed1 ,and that which has been is not what it was1 ,yet that which has been is4 ,nothing which was done was useless or unessential1 though it ceases to be conspicuous and primary4 ,note #ca3 ,concerning ,successive ,generalizations in ,science see the ,philosophy1 book i4 ch4 #b1 sect4 #aa4 ,thus the final form of each science contains the substance of each of its preceding modifications2 and all that was at any antecedent period discovered and established1 ministers to the ultimate development of its proper branch of knowledge4 ,such previous doctrines may require to be made precise and definite1 to have their superfluous and arbitrary portions expunged1 to be expressed in new language1 to be taken up into the body of science by various processes2--but they do not on such accounts cease to be true doctrines1 or to form a portion of the essential constituents of our knowledge4 ,terms record ,discoveries4#da--,the modes in which the earlier truths of science are preserved in its later forms1 are indeed various4 ,from being asserted at first as strange discoveries1 such truths come at last to be implied as almost self-evident axioms4 ,they are recorded by some familiar maxim1 or perhaps by some new word or phrase1 which becomes part of the current language of the philosophical world2 and thus asserts a principle1 while it appears merely to indicate a transient #df notion2--preserves as well as expresses a truth2--and1 like a medal of gold1 is a treasure as well as a token4 ,we shall frequently have to notice the manner in which great discoveries thus stamp their impress upon the terms of a science2 and1 like great political revolutions1 are recorded by the change of the current coin which has accompanied them4 ,note #da3 ,concerning ,technical ,terms1 see ,philosophy1 book i4 ch4 #c4 ,generalization4--,the great changes which thus take place in the history of science1 the revolutions of the intellectual world1 have1 as a usual and leading character1 this1 that they are steps of generalization2 transitions from particular truths to others of a wider extent1 in which the former are included4 ,this progress of knowledge1 from individual facts to universal laws1--from particular propositions to general ones1--and from these to others still more general1 with reference to which the former generalizations are particular1--is so far familiar to men's minds1 that1 without here entering into further explanation1 its nature will be understood sufficiently to prepare the reader to recognize the exemplifications of such a process1 which he will find at every step of our advance4 ,inductive ,epochs2 ,preludes2 ,sequels4--,in our history1 it is the progress of knowledge only which we have to attend to4 ,this is the main action of our drama2 and all the events which do not bear upon this1 though they may relate to the cultivation and the cultivators of philosophy1 are not a necessary part of our theme4 ,our narrative will therefore consist mainly of successive steps of generalization1 such as have just been mentioned4 ,but among these1 we shall find some of eminent and decisive importance1 which have more peculiarly influenced the fortunes of physical philosophy1 and to which we may consider the rest as subordinate and auxiliary4 ,these primary movements1 when the ,inductive process1 by which science is formed1 has been exercised in a more energetic and powerful manner1 may be distinguished as the ,inductive ,epochs of scientific history2 and they deserve our more express and pointed notice4 ,they are1 for the most part1 marked by the great discoveries and the great philosophical names which all civilized nations have agreed in admiring4 ,but1 when we examine more clearly the history of such discoveries1 we find that these epochs have not occurred suddenly and without preparation4 ,they have been preceded by a period1 which we may call their ,prelude during which the ideas and facts on which they turned were called into action2--were gradually evolved into clearness and connection1 permanency and certainty2 till at last the discovery which marks the epoch1 seized and fixed forever the truth which had till then been obscurely and #dg doubtfully discerned4 ,and again1 when this step has been made by the principal discoverers1 there may generally be observed another period1 which we may call the ,sequel of the ,epoch1 during which the discovery has acquired a more perfect certainty and a more complete development among the leaders of the advance2 has been diffused to the wider throng of the secondary cultivators of such knowledge1 and traced into its distant consequences4 ,this is a work1 always of time and labor1 often of difficulty and conflict4 ,to distribute the ,history of science into such ,epochs1 with their ,preludes and ,sequels1 if successfully attempted1 must needs make the series and connections of its occurrences more distinct and intelligible4 ,such periods form resting-places1 where we pause till the dust of the confused march is laid1 and the prospect of the path is clear4 ,inductive ,charts4#ea--,since the advance of science consists in collecting by induction true general laws from particular facts1 and in combining several such laws into one higher generalization1 in which they still retain their truth2 we might form a ,chart1 or ,table1 of the progress of each science1 by setting down the particular facts which have thus been combined1 so as to form general truths1 and by marking the further union of these general truths into others more comprehensive4 ,the ,table of the progress of any science would thus resemble the ,map of a ,river1 in which the waters from separate sources unite and make rivulets1 which again meet with rivulets from other fountains1 and thus go on forming by their junction trunks of a higher and higher order4 ,the representation of the state of a science in this form1 would necessarily exhibit all the principal doctrines of the science2 for each general truth contains the particular truths from which it was derived1 and may be followed backwards till we have these before us in their separate state4 ,and the last and most advanced generalization would have1 in such a scheme1 its proper place and the evidence of its validity4 ,hence such an ,inductive ,table of each science would afford a criterion of the correctness of our distribution of the inductive ,epochs1 by its coincidence with the views of the best judges1 as to the substantial contents of the science in question4 ,by forming1 therefore1 such ,inductive ,tables of the principal sciences of which ,i have here to speak1 and by regulating by these tables1 my views of the history of the sciences1 ,i conceive that ,i have secured the distribution of my #dh history from material error2 for no merely arbitrary division of the events could satisfy such conditions4 ,but though ,i have constructed such charts to direct the course of the present history1 ,i shall not insert them in the work1 reserving them for the illustration of the philosophy of the subject2 for to this they more properly belong1 being a part of the ,logic of ,induction4 ,note #ea3 ,inductive charts of the ,history of ,astronomy and of ,optics1 such as are here referred to1 are given in the ,philosophy1 book xi4 ch4 #f4 ,stationary ,periods4--,by the lines of such maps the real advance of science is depicted1 and nothing else4 ,but there are several occurrences of other kinds1 too interesting and too instructive to be altogether omitted4 ,in order to understand the conditions of the progress of knowledge1 we must attend1 in some measure1 to the failures as well as the successes by which such attempts have been attended4 ,when we reflect during how small a portion of the whole history of human speculations1 science has really been1 in any marked degree1 progressive1 we must needs feel some curiosity to know what was doing in these stationary periods2 what field could be found which admitted of so wide a deviation1 or at least so protracted a wandering4 ,it is highly necessary to our purpose1 to describe the baffled enterprises as well as the achievements of human speculation4 ,deduction4--,during a great part of such stationary periods1 we shall find that the process which we have spoken of as essential to the formation of real science1 the conjunction of clear ,ideas with distinct ,facts1 was interrupted2 and1 in such cases1 men dealt with ideas alone4 ,they employed themselves in reasoning from principles1 and they arranged1 and classified1 and analyzed their ideas1 so as to make their reasonings satisfy the requisitions of our rational faculties4 ,this process of drawing conclusions from our principles1 by rigorous and unimpeachable trains of demonstration1 is termed ,deduction4 ,in its due place1 it is a highly important part of every science2 but it has no value when the fundamental principles1 on which the whole of the demonstration rests1 have not first been obtained by the induction of facts1 so as to supply the materials of substantial truth4 ,without such materials1 a series of demonstrations resembles physical science only as a shadow resembles a real object4 ,to give a real significance to our propositions1 ,induction must provide what ,deduction cannot supply4 ,from a pictured hook we can hang only a pictured chain4 ,distinction of common ,notions and ,scientific ,ideas4#fa--,when the #di notions with which men are conversant in the common course of practical life1 which give meaning to their familiar language1 and employment to their hourly thoughts1 are compared with the ,ideas on which exact science is founded1 we find that the two classes of intellectual operations have much that is common and much that is different4 ,without here attempting fully to explain this relation 7which1 indeed1 is one of the hardest problems of our philosophy71 we may observe that they have this in common1 that both are acquired by acts of the mind exercised in connecting external impressions1 and may be employed in conducting a train of reasoning2 or1 speaking loosely 7for we cannot here pursue the subject so as to arrive at philosophical exactness71 we may say1 that all notions and ideas are obtained by an inductive1 and may be used in a deductive process4 ,but scientific ,ideas and common ,notions differ in this1 that the former are precise and stable1 the latter vague and variable2 the former are possessed with clear insight1 and employed in a sense rigorously limited1 and always identically the same2 the latter have grown up in the mind from a thousand dim and diverse suggestions1 and the obscurity and incongruity which belong to their origin hang about all their applications4 ,scientific ,ideas can often be adequately exhibited for all the purposes of reasoning1 by means of ,definitions and ,axioms2 all attempts to reason by means of ,definitions from common ,notions1 lead to empty forms or entire confusion4 ,note #fa3 ,scientific ,ideas depend upon certain ,fundamental ,ideas1 which are enumerated in the ,philosophy1 book i4 ch4 #h4 ,such common ,notions are sufficient for the common practical conduct of human life3 but man is not a practical creature merely2 he has within him a speculative tendency1 a pleasure in the contemplation of ideal relations1 a love of knowledge as knowledge4 ,it is this speculative tendency which brings to light the difference of common ,notions and scientific ,ideas1 of which we have spoken4 ,the mind analyzes such ,notions1 reasons upon them1 combines and connects them2 for it feels assured that intellectual things ought to be able to bear such handling4 ,even practical knowledge1 we see clearly1 is not possible without the use of the reason2 and the speculative reason is only the reason satisfying itself of its own consistency4 ,the speculative faculty cannot be controlled from acting4 ,the mind cannot but claim a right to speculate concerning all its own acts and creations2 yet1 when it exercises this right upon its common practical notions1 we find that it runs into barren abstractions and ever-recurring cycles of subtlety4 ,such ,notions are like waters naturally stagnant2 however much we urge and agitate them1 they only revolve in stationary #ej whirlpools4 ,but the mind is capable of acquiring scientific ,ideas1 which are better fitted to undergo discussion and impulsion4 ,when our speculations are duly fed from the springheads of ,observation1 and frequently drawn off into the region of ,applied ,science1 we may have a living stream of consistent and progressive knowledge4 ,that science may be both real as to its import1 and logical as to its form1 the examples of many existing sciences sufficiently prove4 ,school ,philosophy4--,so long1 however1 as attempts are made to form sciences1 without such a verification and realization of their fundamental ideas1 there is1 in the natural series of speculation1 no self-correcting principle4 ,a philosophy constructed on notions obscure1 vague1 and unsubstantial1 and held in spite of the want of correspondence between its doctrines and the actual train of physical events1 may long subsist1 and occupy men's minds4 ,such a philosophy must depend for its permanence upon the pleasure which men feel in tracing the operations of their own and other men's minds1 and in reducing them to logical consistency and systematical arrangement4 ,in these cases the main subjects of attention are not external objects1 but speculations previously delivered2 the object is not to interpret nature1 but man's mind4 ,the opinions of the ,masters are the facts which the ,disciples endeavor to reduce to unity1 or to follow into consequences4 ,a series of speculators who pursue such a course1 may properly be termed a ,school1 and their philosophy a ,school ,philosophy2 whether their agreement in such a mode of seeking knowledge arise from personal communication and tradition1 or be merely the result of a community of intellectual character and propensity4 ,the two great periods of ,school ,philosophy 7it will be recollected that we are here directing our attention mainly to physical science7 were that of the ,greeks and that of the ,middle ,ages2--the period of the first waking of science1 and that of its midday slumber4 ,what has been said thus briefly and imperfectly1 would require great detail and much explanation1 to give it its full significance and authority4 ,but it seemed proper to state so much in this place1 in order to render more intelligible and more instructive1 at the first aspect1 the view of the attempted or effected progress of science4 ,it is1 perhaps1 a disadvantage inevitably attending an undertaking like the present1 that it must set out with statements so abstract2 and must present them without their adequate development and proof4 ,such an ,introduction1 both in its character and its scale of execution1 may be compared to the geographical sketch of a country1 with which #ea the historian of its fortunes often begins his narration4 ,so much of ,metaphysics is as necessary to us as such a portion of ,geography is to the ,historian of an ,empire2 and what has hitherto been said1 is intended as a slight outline of the ,geography of that ,intellectual ,world1 of which we have here to study the ,history4 ,the name which we have given to this ,history--,a ,,history ,,of ,,the ,,inductive ,,sciences--has the fault of seeming to exclude from the rank of ,inductive ,sciences those which are not included in the ,history2 as ,ethnology and ,glossology1 ,political ,economy1 ,psychology4 ,this exclusion ,i by no means wish to imply2 but ,i could find no other way of compendiously describing my subject1 which was intended to comprehend those ,sciences in which1 by the observation of facts and the use of reason1 systems of doctrine have been established which are universally received as truths among thoughtful men2 and which may therefore be studied as examples of the manner in which truth is to be discovered4 ,perhaps a more exact description of the work would have been1 ,a ,history of the principal ,sciences hitherto established by ,induction4 ,i may add that ,i do not include in the phrase ,inductive ,sciences1 the branches of ,pure ,mathematics 7,geometry1 ,arithmetic1 ,algebra1 and the like71 because1 as ,i have elsewhere stated 7,phil4 ,ind4 ,sc41 book ii4 c4 #a71 these are not ,inductive but ,deductive ,sciences4 ,they do not infer true theories from observed facts1 and more general from more limited laws3 but they trace the conditions of all theory1 the properties of space and number2 and deduce results from ideas without the aid of experience4 ,the ,history of these ,sciences is briefly given in ,chapters #ac and #ad of the ,second ,book of the ,philosophy just referred to4 ,i may further add that the other work to which ,i refer1 the ,philosophy of the ,inductive ,sciences1 is in a great measure historical1 no less than the present ,history4 ,that work contains the history of the ,sciences so far as it depends on ,ideas2 the present work contains the history so far as it depends upon ,observation4 ,the two works resulted simultaneously from the same examination of the principal writers on science in all ages1 and may serve to supplement each other4 #ec ,,book ,i4 ,,history ,,of ,,the ,,greek ,,school ,,philosophy1 ,,with ,,reference ,,to ,,physical ,,science4 2 2 4 4 4 4 4 4 ' 1 1 ' 1 ' 1 4 ,,pindar4 ,pyth4 iv4 #abd1 #cdi4 ,whence came their voyage8 them what peril held ,with adamantine rivets firmly bound8 99 99 99 99 99 99 ,but soon as on the vessel's bow ,the anchor was hung up1 ,then took the ,leader on the prow ,in hands a golden cup1 ,and on great ,father ,jove did call1 ,and on the ,winds and ,waters all1 ,swept by the hurrying blast2 ,and on the ,nights1 and ,ocean ,ways1 ,and on the fair auspicious ,days1 ,and loved return at last4 #ee ,,book ,i4 ,,history ,,of ,,the ,,greek ,,school ,,philosophy1 ,,with ,,reference ,,to ,,physical ,,science4 ,,chapter ,i4 ,,prelude ,,to ,,the ,,greek ,,school ,,philosophy4 ,sect4 #a4--;,first ,attempts of the ,speculative ,faculty in ,physical ,inquiries4 ,,at an early period of history there appeared in men a propensity to pursue speculative inquiries concerning the various parts and properties of the material world4 ,what they saw excited them to meditate1 to conjecture1 and to reason3 they endeavored to account for natural events1 to trace their causes1 to reduce them to their principles4 ,this habit of mind1 or1 at least that modification of it which we have here to consider1 seems to have been first unfolded among the ,greeks4 ,and during that obscure introductory interval which elapsed while the speculative tendencies of men were as yet hardly disentangled from the practical1 those who were most eminent in such inquiries were distinguished by the same term of praise which is applied to sagacity in matters of action1 and were called wise men--4 ,but when it came to be clearly felt by such persons that their endeavors were suggested by the love of knowledge1 a motive different from the motives which lead to the wisdom of active life1 a name was adopted of a more appropriate1 as well as of a more modest signification1 and they were termed philosophers1 or lovers of wisdom4 ,this appellation is said#ga to have been first assumed by ,pythagoras4 ,yet he1 in ,herodotus1 instead of having this title1 is called a powerful sophist-- 2#ha the historian using this word1 as it would seem1 without intending to imply that misuse of reason which the term afterwards came to denote4 ,the historians of literature #ef placed ,pythagoras at the origin of the ,italic ,school1 one of the two main lines of succession of the early ,greek philosophers3 but the other1 the ,ionic ,school1 which more peculiarly demands our attention1 in consequence of its character and subsequent progress1 is deduced from ,thales1 who preceded the age of ,philosophy1 and was one of the sophi1 or wise men of ,greece4 ,note #ga3 ,cic4 ,tusc4 v4 #c4 ,note #ha3 ,herod4 iv4 #ie4 ,the ,ionic ,school was succeeded in ,greece by several others2 and the subjects which occupied the attention of these schools became very extensive4 ,in fact1 the first attempts were1 to form systems which should explain the laws and causes of the material universe2 and to these were soon added all the great questions which our moral condition and faculties suggest4 ,the physical philosophy of these schools is especially deserving of our study1 as exhibiting the character and fortunes of the most memorable attempt at universal knowledge which has ever been made4 ,it is highly instructive to trace the principles of this undertaking2 for the course pursued was certainly one of the most natural and tempting which can be imagined2 the essay was made by a nation unequalled in fine mental endowments1 at the period of its greatest activity and vigor2 and yet it must be allowed 7for1 at least so far as physical science is concerned1 none will contest this71 to have been entirely unsuccessful4 ,we cannot consider otherwise than as an utter failure1 an endeavor to discover the causes of things1 of which the most complete results are the ,aristotelian physical treatises2 and which1 after reaching the point which these treatises mark1 left the human mind to remain stationary1 at any rate on all such subjects1 for nearly two thousand years4 ,the early philosophers of ,greece entered upon the work of physical speculation in a manner which showed the vigor and confidence of the questioning spirit1 as yet untamed by labors and reverses4 ,it was for later ages to learn that man must acquire1 slowly and patiently1 letter by letter1 the alphabet in which nature writes her answers to such inquiries4 ,the first students wished to divine1 at a single glance1 the whole import of her book4 ,they endeavored to discover the origin and principle of the universe2 according to ,thales1 water was the origin of all things1 according to ,anaximenes1 air2 and ,heraclitus considered fire as the essential principle of the universe4 ,it has been conjectured1 with great plausibility1 that this tendency to give to their ,philosophy the form of a ,cosmogony1 was owing to the influence of the poetical ,cosmogonies and ,theogonies which had been produced and admired at a still earlier age4 ,indeed1 such wide and ambitious #eg doctrines as those which have been mentioned1 were better suited to the dim magnificence of poetry1 than to the purpose of a philosophy which was to bear the sharp scrutiny of reason4 ,when we speak of the principles of things1 the term1 even now1 is very ambiguous and indefinite in its import1 but how much more was that the case in the first attempts to use such abstractions6 ,the term which is commonly used in this sense 771 signified at first the beginning2 and in its early philosophical applications implied some obscure mixed reference to the mechanical1 chemical1 organic1 and historical causes of the visible state of things1 besides the theological views which at this period were only just beginning to be separated from the physical4 ,hence we are not to be surprised if the sources from which the opinions of this period appear to be derived are rather vague suggestions and casual analogies1 than any reasons which will bear examination4 ,aristotle conjectures1 with considerable probability1 that the doctrine of ,thales1 according to which water was the universal element1 resulted from the manifest importance of moisture in the support of animal and vegetable life4#ia ,but such precarious analyses of these obscure and loose dogmas of early antiquity are of small consequence to our object4 ,note #ia3 ,metaph4 i4 #c4 ,in more limited and more definite examples of inquiry concerning the causes of natural appearances1 and in the attempts made to satisfy men's curiosity in such cases1 we appear to discern a more genuine prelude to the true spirit of physical inquiry4 ,one of the most remarkable instances of this kind is to be found in the speculations which ,herodotus records1 relative to the cause of the floods of the ,nile4 ,concerning the nature of this river1 says the father of history1#aja ,i was not able to learn any thing1 either from the priests or from any one besides1 though ,i questioned them very pressingly4 ,for the ,nile is flooded for a hundred days1 beginning with the summer solstice2 and after this time it diminishes1 and is1 during the whole winter1 very small4 ,and on this head ,i was not able to obtain any thing satisfactory from any one of the ,egyptians1 when ,i asked what is the power by which the ,nile is in its nature the reverse of other rivers4 ,note #aja3 ,herod4 ii4 #ai4 ,we may see1 ,i think1 in the historian's account1 that the ,grecian mind felt a craving to discover the reasons of things which other nations did not feel4 ,the ,egyptians1 it appears1 had no theory1 and felt no want of a theory4 ,not so the ,greeks2 they had their reasons to render1 though they were not such as satisfied ,herodotus4 ,some #eh of the ,greeks1 he says1 who wish to be considered great philosophers 7 71 have propounded three ways of accounting for these floods4 ,two of them1 he adds1 ,i do not think worthy of record1 except just so far as to mention them4 ,but as these are some of the earliest ,greek essays in physical philosophy1 it will be worth while1 even at this day1 to preserve the brief notice he has given of them1 and his own reasonings upon the same subject4 ,one of these opinions holds that the ,etesian winds which blew from the north are the cause of these floods1 by preventing the ,nile from flowing into the sea4 ,against this the historian reasons very simply and sensibly4 ,very often when the ,etesian winds do not blow1 the ,nile is flooded nevertheless4 ,and moreover1 if the ,etesian winds were the cause1 all other rivers1 which have their course opposite to these winds1 ought to undergo the same changes as the ,nile2 which the rivers of ,syria and ,libya so circumstanced do not4 ,the next opinion is still more unscientific 771 and is1 in truth1 marvellous for its folly4 ,this holds that the ocean flows all round the earth1 and that the ,nile comes out of the ocean1 and by that means produces its effects4 ,now1 says the historian1 the man who talks about this ocean-river1 goes into the region of fable1 where it is not easy to demonstrate that he is wrong4 ,i know of no such river4 ,but ,i suppose that ,homer and some of the earlier poets invented this fiction and introduced it into their poetry4 ,he then proceeds to a third account1 which to a modern reasoner would appear not at all unphilosophical in itself1 but which he1 nevertheless1 rejects in a manner no less decided than the others4 ,the third opinion1 though much the most plausible1 is still more wrong than the others2 for it asserts an impossibility1 namely1 that the ,nile proceeds from the melting of the snow4 ,now the ,nile flows out of ,libya1 and through ,ethiopia1 which are very hot countries1 and thus comes into ,egypt1 which is a colder region4 ,how then can it proceed from snow8 ,he then offers several other reasons to show1 as he says1 to any one capable of reasoning on such subjects 7 71 that the assertion cannot be true4 ,the winds which blow from the southern regions are hot2 the inhabitants are black2 the swallows and kites 77 stay in the country the whole year2 the cranes fly the colds of ,scythia1 and seek their warm winter-quarters there2 which would not be if it snowed ever so little4 ,he adds another reason1 founded apparently upon #ei some limited empirical maxim of weather-wisdom taken from the climate of ,greece4 ,libya1 he said1 has neither rain nor ice1 and therefore no snow2 for1 in five days after a fall of snow there must be a fall of rain2 so that if it snowed in those regions it must rain too4 ,i need not observe that ,herodotus was not aware of the difference between the climate of high mountains and plains in a torrid region2 but it is impossible not to be struck both with the activity and the coherency of thought displayed by the ,greek mind in this primitive physical inquiry4 ,but ,i must not omit the hypothesis which ,herodotus himself proposes1 after rejecting those which have been already given4 ,it does not appear to me easy to catch his exact meaning1 but the statement will still be curious4 ,if1 he says1 one who has condemned opinions previously promulgated may put forward his own opinion concerning so obscure a matter1 ,i will state why it seems to me that the ,nile is flooded in summer4 ,this opinion he propounds at first with an oracular brevity1 which it is difficult to suppose that he did not intend to be impressive4 ,in winter the sun is carried by the seasons away from his former course1 and goes to the upper parts of ,libya4 ,and there1 in short1 is the whole account2 for that region to which this divinity 7the sun7 is nearest1 must naturally be most scant of water1 and the river-sources of that country must be dried up4 ,but the lively and garrulous ,ionian immediately relaxes from this apparent reserve4 ,to explain the matter more at length1 he proceeds1 it is thus4 ,the sun when he traverses the upper parts of ,libya1 does what he commonly does in summer2--he draws the water to him 7 ' 71 and having thus drawn it1 he pushes it to the upper regions 7of the air probably71 and then the winds take it and disperse it till they dissolve in moisture4 ,and thus the winds which blow from those countries1 ,libs and ,notus1 are the most moist of all winds4 ,now when the winter relaxes and the sun returns to the north1 he still draws water from all the rivers1 but they are increased by showers and rain torrents so that they are in flood till the summer comes2 and then1 the rain falling and the sun still drawing them1 they become small4 ,but the ,nile1 not being fed by rains1 yet being drawn by the sun1 is1 alone of all rivers1 much more scanty in the winter than in the summer4 ,for in summer it is drawn like all other rivers1 but in winter it alone has its supplies shut up4 ,and in this way1 ,i have been led to think the sun is the cause of the occurrence in question4 ,we may remark that the historian here appears to #fj ascribe the inequality of the ,nile at different seasons to the influence of the sun upon its springs alone1 the other cause of change1 the rains being here excluded2 and that1 on this supposition1 the same relative effects would be produced whether the sun increase the sources in winter by melting the snows1 or diminish them in summer by what he calls drawing them upwards4 ,this specimen of the early efforts of the ,greeks in physical speculations1 appears to me to speak strongly for the opinion that their philosophy on such subjects was the native growth of the ,greek mind1 and owed nothing to the supposed lore of ,egypt and the ,east2 an opinion which has been adopted with regard to the ,greek ,philosophy in general by the most competent judges on a full survey of the evidence4#aaa ,indeed1 we have no evidence whatever that1 at any period1 the ,african or ,asiatic nations 7with the exception perhaps of the ,indians7 ever felt this importunate curiosity with regard to the definite application of the idea of cause and effect to visible phenomena2 or drew so strong a line between a fabulous legend and a reason rendered2 or attempted to ascend to a natural cause by classing together phenomena of the same kind4 ,we may be well excused1 therefore1 for believing that they could not impart to the ,greeks what they themselves did not possess2 and so far as our survey goes1 physical philosophy has its origin1 apparently spontaneous and independent1 in the active and acute intellect of ,greece4 ,note #aaa3 ,thirlwall1 ,hist4 ,gr41 ii4 #acj2 and1 as there quoted1 ,ritter1 ,geschichte der ,philosophie1 i4 #aei-agc4 ,sect4 #b4--,primitive ,mistake in ,greek ,physical ,philosophy4 ,,we now proceed to examine with what success the ,greeks followed the track into which they had thus struck4 ,and here we are obliged to confess that they very soon turned aside from the right road to truth1 and deviated into a vast field of error1 in which they and their successors have wandered almost to the present time4 ,it is not necessary here to inquire why those faculties which appear to be bestowed upon us for the discovery of truth1 were permitted by ,providence to fail so signally in answering that purpose2 whether1 like the powers by which we seek our happiness1 they involve a responsibility on our part1 and may be defeated by rejecting the guidance of a higher faculty2 or whether these endowments1 though they did not #fa immediately lead man to profound physical knowledge1 answered some nobler and better purpose in his constitution and government4 ,the fact undoubtedly was1 that the physical philosophy of the ,greeks soon became trifling and worthless2 and it is proper to point out1 as precisely as we can1 in what the fundamental mistake consisted4 ,to explain this1 we may in the first place return for a moment to ,herodotus's account of the cause of the floods of the ,nile4 ,the reader will probably have observed a remarkable phrase used by ,herodotus1 in his own explanation of these inundations4 ,he says that the sun draws1 or attracts1 the water2 a metaphorical term1 obviously intended to denote some more general and abstract conception than that of the visible operation which the word primarily signifies4 ,this abstract notion of drawing is1 in the historian1 as we see1 very vague and loose2 it might1 with equal propriety1 be explained to mean what we now understand by mechanical or by chemical attraction1 or pressure1 or evaporation4 ,and in like manner1 all the first attempts to comprehend the operations of nature1 led to the introduction of abstract conceptions1 often vague1 indeed1 but not1 therefore1 unmeaning2 such as motion and velocity1 force and pressure1 impetus and momentum 774 ,and the next step in philosophizing1 necessarily was to endeavor to make these vague abstractions more clear and fixed1 so that the logical faculty should be able to employ them securely and coherently4 ,but there were two ways of making this attempt2 the one1 by examining the words only1 and the thoughts which they call up2 the other1 by attending to the facts and things which bring these abstract terms into use4 ,the latter1 the method of real inquiry1 was the way to success2 but the ,greeks followed the former1 the verbal or notional course1 and failed4 ,if ,herodotus1 when the notion of the sun's attracting the waters of rivers had entered into his mind1 had gone on to instruct himself1 by attention to facts1 in what manner this notion could be made more definite1 while it still remained applicable to all the knowledge which could be obtained1 he would have made some progress towards a true solution of his problem4 ,if1 for instance1 he had tried to ascertain whether this ,attraction which the sun exerted upon the waters of rivers1 depended on his influence at their fountains only1 or was exerted over their whole course1 and over waters which were not parts of rivers1 he would have been led to reject his hypothesis2 for he would have found1 by observations sufficiently obvious1 that the sun's ,attraction1 as shown in such cases1 is a tendency to lessen all expanded and #fb open collections of moisture1 whether flowing from a spring or not2 and it would then be seen that this influence1 operating on the whole surface of the ,nile1 must diminish it as well as other rivers1 in summer1 and therefore could not be the cause of its overflow4 ,he would thus have corrected his first loose conjecture by a real study of nature1 and might1 in the course of his meditations1 have been led to available notions of ,evaporation1 or other natural actions4 ,and1 in like manner1 in other cases1 the rude attempts at explanation1 which the first exercise of the speculative faculty produced1 might have been gradually concentrated and refined1 so as to fall in1 both with the requisitions of reason and the testimony of sense4 ,but this was not the direction which the ,greek speculators took4 ,on the contrary2 as soon as they had introduced into their philosophy any abstract and general conceptions1 they proceeded to scrutinize these by the internal light of the mind alone1 without any longer looking abroad into the world of sense4 ,they took for granted that philosophy must result from the relations of those notions which are involved in the common use of language1 and they proceeded to seek their philosophical doctrines by studying such notions4 ,they ought to have reformed and fixed their usual conceptions by ,observation2 they only analyzed and expanded them by ,reflection3 they ought to have sought by trial1 among the ,notions which passed through their minds1 some one which admitted of exact application to ,facts2 they selected arbitrarily1 and1 consequently1 erroneously1 the ,notions according to which ,facts should be assembled and arranged3 they ought to have collected clear ,fundamental ,ideas from the world of things by inductive acts of thought2 they only derived results by ,deduction from one or other of their familiar ,conceptions4#aba ,note #aba3 ,the course by which the ,sciences were formed1 and which is here referred to as that which the ,greeks did not follow1 is described in detail in the ,philosophy1 book xi41 ,of the ,construction of ,science4 ,when this false direction had been extensively adopted by the ,greek philosophers1 we may treat of it as the method of their ,schools4 ,under that title we must give a further account of it4 #fc ,,chapter ,,ii4 ,,the ,,greek ,,school ,,philosophy4 ,sect4 #a4--,the general ,foundation of the ,greek ,school ,philosophy4 ,,the physical philosophy of the ,greek ,schools was formed by looking at the material world through the medium of that common language which men employ to answer the common occasions of life2 and by adopting1 arbitrarily1 as the grounds of comparison of facts1 and of inference from them1 notions more abstract and large than those with which men are practically familiar1 but not less vague and obscure4 ,such a philosophy1 however much it might be systematized1 by classifying and analyzing the conceptions which it involves1 could not overcome the vices of its fundamental principle4 ,but before speaking of these defects1 we must give some indications of its character4 ,the propensity to seek for principles in the common usages of language may be discerned at a very early period4 ,thus we have an example of it in a saying which is reported of ,thales1 the founder of ,greek philosophy4#aca ,when he was asked1 ,what is the greatest thing8 he replied1 ,place2 for all other things are in the world1 but the world is in it4 ,in ,aristotle we have the consummation of this mode of speculation4 ,the usual point from which he starts in his inquiries is1 that we say thus or thus in common language4 ,thus1 when he has to discuss the question1 whether there be1 in any part of the universe1 a ,void1 or space in which there is nothing1 he inquires first in how many senses we say that one thing is in another4 ,he enumerates many of these2#ada we say the part is in the whole1 as the finger is in the hand2 again we say1 the species is in the genus1 as man is included in animal2 again1 the government of ,greece is in the king2 and various other senses are described or exemplified1 but of all these the most proper is when we say a thing is in a vessel1 and generally1 in place4 ,he next examines what place is1 and comes to this conclusion1 that if about a body there be another body including it1 it is in place1 and if not1 not4 ,a body moves when it changes its place2 but #fd he adds1 that if water be in a vessel1 the vessel being at rest1 the parts of the water may still move1 for they are included by each other2 so that while the whole does not change its place1 the parts may change their places in a circular order4 ,proceeding then to the question of a void1 he1 as usual1 examines the different senses in which the term is used1 and adopts1 as the most proper1 place without matter2 with no useful result1 as we shall soon see4 ,note #aca3 ,plut4 ,conv4 ,sept4 ,sap4 ,diog4 ,laert4 i4 #ce4 ,note #ada3 ,physic4 ,ausc4 iv4 #c4 ,again1#aea in a question concerning mechanical action1 he says1 ,when a man moves a stone by pushing it with a stick1 we say both that the man moves the stone1 and that the stick moves the stone1 but the latter more properly4 ,note #aea3 ,physic4 ,ausc4 viii4 #e4 ,again1 we find the ,greek philosophers applying themselves to extract their dogmas from the most general and abstract notions which they could detect2 for example1--from the conception of the ,universe as ,one or as ,many things4 ,they tried to determine how far we may1 or must1 combine with these conceptions that of a whole1 of parts1 of number1 of limits1 of place1 of beginning or end1 of full or void1 of rest or motion1 of cause and effect1 and the like4 ,the analysis of such conceptions with such a view1 occupies1 for instance1 almost the whole of ,aristotle's ,treatise on the ,heavens4 ,the ,dialogue of ,plato1 which is entitled ,parmenides1 appears at first as if its object were to show the futility of this method of philosophizing2 for the philosopher whose name it bears1 is represented as arguing with an ,athenian named ,aristotle1#afa and1 by a process of metaphysical analysis1 reducing him at least to this conclusion1 that whether ,one exist1 or do not exist1 it follows that both it and other things1 with reference to themselves and to each other1 all and in all respects1 both are and are not1 both appear and appear not4 ,yet the method of ,plato1 so far as concerns truths of that kind with which we are here concerned1 was little more efficacious than that of his rival4 ,it consists mainly1 as may be seen in several of the dialogues1 and especially in the ,timus1 in the application of notions as loose as those of the ,peripatetics2 for example1 the conceptions of the ,good1 the ,beautiful1 the ,perfect2 and these are rendered still more arbitrary1 by assuming an acquaintance with the views of the ,creator of the universe4 ,the philosopher is thus led to maxims which agree with those #fe of the ,aristotelians1 that there can be no void1 that things seek their own place1 and the like4#aga ,note #afa3 ,this ,aristotle is not the ,stagirite1 who was forty-five years younger than ,plato1 but one of the thirty tyrants1 as they were called4 ,note #aga3 ,timus1 p4 #hj4 ,another mode of reasoning1 very widely applied in these attempts1 was the doctrine of contrarieties1 in which it was assumed1 that adjectives or substantives which are in common language1 or in some abstract mode of conception1 opposed to each other1 must point at some fundamental antithesis in nature1 which it is important to study4 ,thus ,aristotle#aha says1 that the ,pythagoreans1 from the contrasts which number suggests1 collected ten principles1--,limited and ,unlimited1 ,odd and ,even1 ,one and ,many1 ,right and ,left1 ,male and ,female1 ,rest and ,motion1 ,straight and ,curved1 ,light and ,darkness1 ,good and ,evil1 ,square and ,oblong4 ,we shall see hereafter1 that ,aristotle himself deduced the doctrine of ,four ,elements1 and other dogmas1 by oppositions of the same kind4 ,note #aha3 ,metaph4 #a4 #e4 ,the physical speculator of the present day will learn without surprise1 that such a mode of discussion as this1 led to no truths of real or permanent value4 ,the whole mass of the ,greek philosophy1 therefore1 shrinks into an almost imperceptible compass1 when viewed with reference to the progress of physical knowledge4 ,still the general character of this system1 and its fortunes from the time of its founders to the overthrow of their authority1 are not without their instruction1 and1 it may be hoped1 not without their interest4 ,i proceed1 therefore1 to give some account of these doctrines in their most fully developed and permanently received form1 that in which they were presented by ,aristotle4 ,sect4 #b4--,the ,aristotelian ,physical ,philosophy4 ,,the principal physical treatises of ,aristotle are1 the eight ,books of ,physical ,lectures1 the four ,books ,of the ,heavens1 the two ,books ,of ,production and ,destruction3 for the ,book ,of the ,world is now universally acknowledged to be spurious2 and the ,meteorologies1 though full of physical explanations of natural phenomena1 does not exhibit the doctrines and reasonings of the school in so general a form2 the same may be said of the ,mechanical ,problems4 ,the treatises on the various subjects of ,natural ,history1 ,on ,animals1 ,on the ,parts of ,animals1 ,on ,plants1 ,on ,physiognomonics1 ,on ,colors1 ,on ,sound1 contain an extraordinary #ff accumulation of facts1 and manifest a wonderful power of systematizing2 but are not works which expound principles1 and therefore do not require to be here considered4 ,the ,physical ,lectures are possibly the work concerning which a well-known anecdote is related by ,simplicius1 a ,greek commentator of the sixth century1 as well as by ,plutarch4 ,it is said1 that ,alexander the ,great wrote to his former tutor to this effect2 ,you have not done well in publishing these lectures2 for how shall we1 your pupils1 excel other men1 if you make that public to all1 which we learnt from you8 ,to this ,aristotle is said to have replied3 ,my ,lectures are published and not published2 they will be intelligible to those who heard them1 and to none besides4 ,this may very easily be a story invented and circulated among those who found the work beyond their comprehension2 and it cannot be denied1 that to make out the meaning and reasoning of every part1 would be a task very laborious and difficult1 if not impossible4 ,but we may follow the import of a large portion of the ,physical ,lectures with sufficient clearness to apprehend the character and principles of the reasoning2 and this is what ,i shall endeavor to do4 ,the author's introductory statement of his view of the nature of philosophy falls in very closely with what has been said1 that he takes his facts and generalizations as they are implied in the structure of language4 ,we must in all cases proceed1 he says1 from what is known to what is unknown4 ,this will not be denied2 but we can hardly follow him in his inference4 ,he adds1 ,we must proceed1 therefore1 from universal to particular4 ,and something of this1 he pursues1 may be seen in language2 for names signify things in a general and indefinite manner1 as circle1 and by defining we unfold them into particulars4 ,he illustrates this by saying1 thus children at first call all men father1 and all women mother1 but afterwards distinguish4 ,in accordance with this view1 he endeavors to settle several of the great questions concerning the universe1 which had been started among subtle and speculative men1 by unfolding the meaning of the words and phrases which are applied to the most general notions of things and relations4 ,we have already noticed this method4 ,a few examples will illustrate it further3--,whether there was or was not a void1 or place without matter1 had already been debated among rival sects of philosophers4 ,the antagonist arguments were briefly these3--,there must be a void1 because a body cannot move into a space except it is #fg empty1 and therefore without a void there could be no motion3--and1 on the other hand1 there is no void1 for the intervals between bodies are filled with air1 and air is something4 ,these opinions had even been supported by reference to experiment4 ,on the one hand1 ,anaxagoras and his school had shown1 that air1 when confined1 resisted compression1 by squeezing a blown bladder1 and pressing down an inverted vessel in the water2 on the other hand1 it was alleged that a vessel full of fine ashes held as much water as if the ashes were not there1 which could only be explained by supposing void spaces among the ashes4 ,aristotle decides that there is no void1 on such arguments as this3#aia--;,in a void there could be no difference of up and down2 for as in nothing there are no differences1 so there are none in a privation or negation2 but a void is merely a privation or negation of matter2 therefore1 in a void1 bodies could not move up and down1 which it is in their nature to do4 ,it is easily seen that such a mode of reasoning1 elevates the familiar forms of language and the intellectual connections of terms1 to a supremacy over facts2 making truth depend upon whether terms are or are not privative1 and whether we say that bodies fall naturally4 ,in such a philosophy every new result of observation would be compelled to conform to the usual combinations of phrases1 as these had become associated by the modes of apprehension previously familiar4 ,note #aia3 ,physic4 ,ausc4 iv4 #g1 p4 #bae4 ,it is not intended here to intimate that the common modes of apprehension1 which are the basis of common language1 are limited and casual4 ,they imply1 on the contrary1 universal and necessary conditions of our perceptions and conceptions2 thus all things are necessarily apprehended as existing in ,time and ,space1 and as connected by relations of ,cause and ,effect2 and so far as the ,aristotelian philosophy reasons from these assumptions1 it has a real foundation1 though even in this case the conclusions are often insecure4 ,we have an example of this reasoning in the eighth ,book1#bja where he proves that there never was a time in which change and motion did not exist2 ,for if all things were at rest1 the first motion must have been produced by some change in some of these things2 that is1 there must have been a change before the first change2 and again1 ,how can before and after apply when time is not8 or how can time be when motion is not8 ,if1 he adds1 time is a numeration of motion1 and if time be eternal1 motion must be eternal4 ,but he sometimes #fh introduces principles of a more arbitrary character2 and besides the general relations of thought1 takes for granted the inventions of previous speculators2 such1 for instance1 as the then commonly received opinions concerning the frame of the world4 ,from the assertion that motion is eternal1 proved in the manner just stated1 ,aristotle proceeds by a curious train of reasoning1 to identify this eternal motion with the diurnal motion of the heavens4 ,there must1 he says1 be something which is the ,first ,mover3#baa this follows from the relation of causes and effects4 ,again1 ,motion must go on constantly1 and1 therefore1 must be either continuous or successive4 ,now what is continuous is more properly said to take place constantly1 than what is successive4 ,also the continuous is better2 but we always suppose that which is better to take place in nature1 if it be possible4 ,the motion of the ,first ,mover will1 therefore1 be continuous1 if such an eternal motion be possible4 ,we here see the vague judgment of better and worse introduced1 as that of natural and unnatural was before1 into physical reasonings4 ,note #bja3 ,ib4 viii4 #a1 p4 #beh4 ,note #baa3 ,physic4 ,ausc4 viii4 #f4 p4 #beh4 ,i proceed with ,aristotle's argument4#bba ,we have now1 therefore1 to show that there may be an infinite single1 continuous motion1 and that this is circular4 ,this is1 in fact1 proved1 as may readily be conceived1 from the consideration that a body may go on perpetually revolving uniformly in a circle4 ,and thus we have a demonstration1 on the principles of this philosophy1 that there is and must be a ,first ,mover1 revolving eternally with a uniform circular motion4 ,note #bba3 ,ib4 viii4 #h4 ,though this kind of philosophy may appear too trifling to deserve being dwelt upon1 it is important for our purpose so far as to exemplify it1 that we may afterwards advance1 confident that we have done it no injustice4 ,i will now pass from the doctrines relating to the motions of the heavens1 to those which concern the material elements of the universe4 ,and here it may be remarked that the tendency 7of which we are here tracing the development7 to extract speculative opinions from the relations of words1 must be very natural to man2 for the very widely accepted doctrine of the ,four ,elements which appears to be founded on the opposition of the adjectives hot and cold1 wet and dry1 is much older than ,aristotle1 and was probably one of the earliest of philosophical dogmas4 ,the great master of this philosophy1 however1 puts the opinion in a more systematic manner than his predecessors4 #fi ,we seek1 he says1#bca the principles of sensible things1 that is1 of tangible bodies4 ,we must take1 therefore1 not all the contrarieties of quality1 but those only which have reference to the touch4 ,thus black and white1 sweet and bitter1 do not differ as tangible qualities1 and therefore must be rejected from our consideration4 ,note #bca3 ,de ,gen4 et ,corrupt4 ii4 #b4 ,now the contrarieties of quality which refer to the touch are these3 hot1 cold2 dry1 wet2 heavy1 light2 hard1 soft2 unctuous1 meagre2 rough1 smooth2 dense1 rare4 ,he then proceeds to reject all but the four first of these1 for various reasons2 heavy and light1 because they are not active and passive qualities2 the others1 because they are combinations of the four first1 which therefore he infers to be the four elementary qualities4 #bda ,now in four things there are six combinations of two2 but the combinations of two opposites1 as hot and cold1 must be rejected2 we have1 therefore1 four elementary combinations1 which agree with the four apparently elementary bodies4 ,fire is hot and dry2 air is hot and wet 7for steam is air72 water is cold and wet1 earth is cold and dry4 ,note #bda3 ,ib4 iii4 #h4 ,it may be remarked that this disposition to assume that some common elementary quality must exist in the cases in which we habitually apply a common adjective1 as it began before the reign of the ,aristotelian philosophy1 so also survived its influence4 ,not to mention other cases1 it would be difficult to free ,bacon's ,inquisitio in naturam calidi1 ,examination of the nature of heat1 from the charge of confounding together very different classes of phenomena under the cover of the word hot4 ,the correction of these opinions concerning the elementary composition of bodies belongs to an advanced period in the history of physical knowledge1 even after the revival of its progress4 ,but there are some of the ,aristotelian doctrines which particularly deserve our attention1 from the prominent share they had in the very first beginnings of that revival2 ,i mean the doctrines concerning motion4 ,these are still founded upon the same mode of reasoning from adjectives2 but in this case1 the result follows1 not only from the opposition of the words1 but also from the distinction of their being absolutely or relatively true4 ,former writers1 says ,aristotle1 have considered heavy and light relatively only1 taking cases1 where both things have weight1 but one is lighter than the other2 and they imagined that1 in #gj this way1 they defined what was absolutely 77 heavy and light4 ,we now know that things which rise by their lightness do so only because they are pressed upwards by heavier surrounding bodies2 and this assumption of absolute levity1 which is evidently gratuitous1 or rather merely nominal1 entirely vitiated the whole of the succeeding reasoning4 ,the inference was1 that fire must be absolutely light1 since it tends to take its place above the other three elements2 earth absolutely heavy1 since it tends to take its place below fire1 air1 and water4 ,the philosopher argued also1 with great acuteness1 that air1 which tends to take its place below fire and above water1 must do so by its nature1 and not in virtue of any combination of heavy and light elements4 ,for if air were composed of the parts which give fire its levity1 joined with other parts which produce gravity1 we might assume a quantity of air so large1 that it should be lighter than a small quantity of fire1 having more of the light parts4 ,it thus follows that each of the four elements tends to its own place1 fire being the highest1 air the next1 water the next1 and earth the lowest4 ,the whole of this train of errors arises from fallacies which have a verbal origin2--from considering light as opposite to heavy2 and from considering levity as a quality of a body1 instead of regarding it as the effect of surrounding bodies4 ,it is worth while to notice that a difficulty which often embarrasses persons on their entrance upon physical speculations1--the difficulty of conceiving that up and down are different directions in different places1--had been completely got over by ,aristotle and the ,greek philosophers4 ,they were steadily convinced of the roundness of the earth1 and saw that this truth led to the conclusion that all heavy bodies tend in converging directions to the centre4 ,and1 they added1 as the heavy tends to the centre1 the light tends to the exterior1 for ,exterior is opposite to ,centre as heavy is to light4#bea ,note #bea3 ,de ,clo1 iv4 #d4 ,the tendencies of bodies downwards and upwards1 their weight1 their fall1 their floating or sinking1 were thus accounted for in a manner which1 however unsound1 satisfied the greater part of the speculative world till the time of ,galileo and ,stevinus1 though ,archimedes in the mean time published the true theory of floating bodies1 which is very different from that above stated4 ,other parts of the doctrines of motion were delivered by the ,stagirite in the same spirit and with the same success4 ,the motion of a body which is thrown along the #ga ground diminishes and finally ceases2 the motion of a body which falls from a height goes on becoming quicker and quicker2 this was accounted for on the usual principle of opposition1 by saying that the former is a violent1 the latter a natural motion4 ,and the later writers of this school expressed the characters of such motions in verse4 ,the rule of natural motion was#bfa ,principium tepeat1 medium cum fine calebit4 ,cool at the first1 it warm and warmer glows4 ,and of violent motion1 the law was-- ,principium fervet1 medium calet1 ultima friget4 ,hot at the first1 then barely warm1 then cold4 ,note #bfa3 ,alsted4 ,encyc4 tom4 i4 p4 #fhg4 ,it appears to have been considered by ,aristotle a difficult problem to explain why a stone thrown from the hand continues to move for some time1 and then stops4 ,if the hand was the cause of the motion1 how could the stone move at all when left to itself8 if not1 why does it ever stop8 ,and he answers this difficulty by saying1#bga that there is a motion communicated to the air1 the successive parts of which urge the stone onwards2 and that each part of this medium continues to act for some while after it has been acted on1 and the motion ceases when it comes to a particle which cannot act after it has ceased to be acted on4 ,it will be readily seen that the whole of this difficulty1 concerning a body which moves forward and is retarded till it stops1 arises from ascribing the retardation1 not to the real cause1 the surrounding resistances1 but to the body itself4 ,note #bga3 ,phys4 ,ausc4 viii4 #aj4 ,one of the doctrines which was the subject of the warmest discussion between the defenders and opposers of ,aristotle1 at the revival of physical knowledge1 was that in which he asserts1#bha ,that body is heavier than another which in an equal bulk moves downward quicker4 ,the opinion maintained by the 9999,aristotelians at the time of ,galileo was1 that bodies fall quicker exactly in proportion to their weight4 ,the master himself asserts this in express terms1 and reasons upon it4#bia ,yet in another passage he appears to distinguish between weight and actual motion downwards4#cja ,in physics1 we call bodies heavy and light from their power of motion2 but these names are not applied to their actual operations 77 except any one thinks #gb momentum 77 to be a word of both applications4 ,but heavy and light are1 as it were1 the embers or sparks of motion1 and therefore proper to be treated of here4 ,note #bha3 ,de ,clo1 iv4 #a1 p4 #cjh4 ,note #bia3 ,ib4 iii4 #b4 ,note #cja3 ,ib4 iv4 #a1 p4 #cjg4 ,the distinction just alluded to1 between ,power or ,faculty of ,action1 and actual ,operation or ,energy1 is one very frequently referred to by ,aristotle2 and though not by any means useless1 may easily be so used as to lead to mere verbal refinements instead of substantial knowledge4 ,the ,aristotelian distinction of ,causes has not any very immediate bearing upon the parts of physics of which we have here mainly spoken2 but it was so extensively accepted1 and so long retained1 that it may be proper to notice it4#caa ,one kind of ,cause is the matter of which any thing is made1 as bronze of a statue1 and silver of a vial2 another is the form and pattern1 as the ,cause of an octave is the ratio of two to one2 again1 there is the ,cause which is the origin of the production1 as the father of the child2 and again1 there is the ,end1 or that for the sake of which any thing is done1 as health is the cause of walking4 ,these four kinds of ,cause1 the material1 the formal1 the efficient1 and the final1 were long leading points in all speculative inquiries2 and our familiar forms of speech still retain traces of the influence of this division4 ,note #caa3 ,phys4 ii4 #c4 ,it is my object here to present to the reader in an intelligible shape1 the principles and mode of reasoning of the ,aristotelian philosophy1 not its results4 ,if this were not the case1 it would be easy to excite a smile by insulating some of the passages which are most remote from modern notions4 ,i will only mention1 as specimens1 two such passages1 both very remarkable4 ,in the beginning of the book ,on the ,heavens1 he proves#cba the world to be perfect1 by reasoning of the following kind3 ,the bodies of which the world is composed are solids1 and therefore have three dimensions3 now three is the most perfect number2 it is the first of numbers1 for of one we do not speak as a number2 of two we say both2 but three is the first number of which we say all2 moreover1 it has a beginning1 a middle1 and an end4 ,note #cba3 ,de ,clo1 i4 #a4 ,the reader will still perceive the verbal foundations of opinions thus supported4 ,the simple elements must have simple motions1 and thus fire and air have their natural motions upwards1 and water and earth have #gc their natural motions downwards2 but besides these motions1 there is motion in a circle1 which is unnatural to these elements1 but which is a more perfect motion than the other1 because a circle is a perfect line1 and a straight line is not2 and there must be something to which this motion is natural4 ,from this it is evident1 he adds1 with obvious animation1 that there is some essence of body different from those of the four elements1 more divine than those1 and superior to them4 ,if things which move in a circle move contrary to nature1 it is marvellous1 or rather absurd1 that this1 the unnatural motion1 should alone be continuous and eternal2 for unnatural motions decay speedily4 ,and so1 from all this1 we must collect1 that besides the four elements which we have here and about us1 there is another removed far off1 and the more excellent in proportion as it is more distant from us4 ,this fifth element was the quinta essentia1 of after writers1 of which we have a trace in our modern literature1 in the word quintessence4 ,sect4 #c4--,technical ,forms of the ,greek ,schools4 ,,we have hitherto considered only the principle of the ,greek ,physics2 which was1 as we have seen1 to deduce its doctrines by an analysis of the notions which common language involves4 ,but though the ,grecian philosopher began by studying words in their common meanings1 he soon found himself led to fix upon some special shades or applications of these meanings as the permanent and standard notion1 which they were to express2 that is1 he made his language technical4 ,the invention and establishment of technical terms is an important step in any philosophy1 true or false2 we must1 therefore1 say a few words on this process1 as exemplified in the ancient systems4 #a4 ,technical ,forms of the ,aristotelian ,philosophy4--,we have already had occasion to cite some of the distinctions introduced by ,aristotle1 which may be considered as technical2 for instance1 the classification of ,causes as material1 formal1 efficient1 and final2 and the opposition of ,qualities as absolute and relative4 ,a few more of the most important examples may suffice4 ,an analysis of objects into ,matter and ,form1 when metaphorically extended from visible objects to things conceived in the most general manner1 became an habitual hypothesis of the ,aristotelian school4 ,indeed this metaphor is even yet one of the most significant of those which we can employ1 to suggest one of the most comprehensive and fundamental antitheses with which philosophy has to do2--the opposition of sense and reason1 of #gd impressions and laws4 ,in this application1 the ,german philosophers have1 up to the present time1 rested upon this distinction a great part of the weight of their systems2 as when ,kant says1 that ,space and ,time are the ,forms of ,sensation4 ,even in our own language1 we retain a trace of the influence of this ,aristotelian notion1 in the word ,information1 when used for that knowledge which may be conceived as moulding the mind into a definite shape1 instead of leaving it a mere mass of unimpressed susceptibility4 ,another favorite ,aristotelian antithesis is that of ,power and ,act 71 74 ,this distinction is made the basis of most of the physical philosophy of the school2 being1 however1 generally introduced with a peculiar limitation4 ,thus1 ,light is defined to be the ,act of what is lucid1 as being lucid4 ,and if1 it is added1 the lucid be so in power but not in act1 we have darkness4 ,the reason of the limitation1 as being lucid1 is1 that a lucid body may act in other ways2 thus a torch may move as well as shine1 but its moving is not its act as being a lucid body4 ,aristotle appears to be well satisfied with this explanation1 for he goes on to say1 ,thus light is not ,fire1 nor any body whatever1 or the emanation of any body 7for that would be a kind of body71 but it is the presence of something like ,fire in the body2 it is1 however1 impossible that two bodies should exist in the same place1 so that it is not a body2 and this reasoning appears to leave him more satisfied with his doctrine1 that ,light is an ,energy or ,act4 ,but we have a more distinctly technical form given to this notion4 ,aristotle introduced a word formed by himself to express the act which is thus opposed to inactive power3 this is the celebrated word 4 ,thus the noted definition of ,motion in the third book of the ,physics1#cca is that it is the ,entelechy1 or ,act1 of a movable body in respect of being movable2 and the definition of the ,soul is#cda that it is the ,entelechy of a natural body which has life by reason of its power4 ,this word has been variously translated by the followers of ,aristotle1 and some of them have declared it untranslatable4 ,act and ,action are held to be inadequate substitutes2 the very act1 ipse cursus actionis1 is employed by some2 primus actus is employed by many1 but another school use primus actus of a non-operating form4 ,budus uses efficacia4 ,cicero#cea translates it quasi quandam continuatam motionem1 et perennem2 but this paraphrase1 though it may #ge fall in with the description of the soul1 which is the subject with which ,cicero is concerned1 does not appear to agree with the general applications of the term4 ,hermolaus ,barbarus is said to have been so much oppressed with this difficulty of translation1 that he consulted the evil spirit by night1 entreating to be supplied with a more common and familiar substitute for this word3 the mocking fiend1 however1 suggested only a word equally obscure1 and the translator1 discontented with this1 invented for himself the word perfectihabia4 ,note #cca3 ,phys4 iii4 #a4 ,note #cda3 ,de ,anim1 ii4 #a4 ,note #cea3 ,tusc4 i4 #aj4 ,we need not here notice the endless apparatus of technicalities which was1 in later days1 introduced into the ,aristotelian philosophy2 but we may remark1 that their long continuance and extensive use show us how powerful technical phraseology is1 for the perpetuation either of truth or error4 ,the ,aristotelian terms1 and the metaphysical views which they tend to preserve1 are not yet extinct among us4 ,in a very recent age of our literature it was thought a worthy employment by some of the greatest writers of the day1 to attempt to expel this system of technicalities by ridicule4 ,crambe regretted extremely that substantial forms1 a race of harmless beings1 which had lasted for many years1 and afforded a comfortable subsistence to many poor philosophers1 should now be hunted down like so many wolves1 without a possibility of retreat4 ,he considered that it had gone much harder with them than with essences1 which had retired from the schools into the apothecaries' shops1 where some of them had been advanced to the degree of quintessences49999#cfa ,note #cfa3 ,martinus ,scriblerus1 cap4 vii4 ,we must now say a few words on the technical terms which others of the ,greek philosophical sects introduced4 #b4 ,technical ,forms of the ,platonists4--,the other sects of the ,greek philosophy1 as well as the ,aristotelians1 invented and adopted technical terms1 and thus gave fixity to their tenets and consistency to their traditionary systems2 of these ,i will mention a few4 ,a technical expression of a contemporary school has acquired perhaps greater celebrity than any of the terms of ,aristotle4 ,i mean the ,ideas of ,plato4 ,the account which ,aristotle gives of the origin of these will serve to explain their nature4#cga ,plato1 says he1 who1 in his youth1 was in habits of communication first with ,cratylus and the ,heraclitean opinions1 which represent all the objects of sense as being in a perpetual flux1 so that concerning these no science nor certain #gf knowledge can exist1 entertained the same opinions at a later period also4 ,when1 afterwards1 ,socrates treated of moral subjects1 and gave no attention to physics1 but1 in the subjects which he did discuss1 arrived at universal truths1 and before any man1 turned his thoughts to definitions1 ,plato adopted similar doctrines on this subject also2 and construed them in this way1 that these truths and definitions must be applicable to something else1 and not to sensible things3 for it was impossible1 he conceived1 that there should be a general common definition of any sensible object1 since such were always in a state of change4 ,the things1 then1 which were the subjects of universal truths he called ,ideas2 and held that objects of sense had their names according to ,ideas and after them2 so that things participated in that ,idea which had the same name as was applied to them4 ,note #cga3 ,arist4 ,metaph4 i4 #f4 ,the same account is repeated1 and the subject discussed1 ,metaph4 xii4 #d4 ,in agreement with this1 we find the opinions suggested in the ,parmenides of ,plato1 the dialogue which is considered by many to contain the most decided exposition of the doctrine of ,ideas4 ,in this dialogue1 ,parmenides is made to say to ,socrates1 then a young man1#cha ,o ,socrates1 philosophy has not yet claimed you for her own1 as1 in my judgment1 she will claim you1 and you will not dishonor her4 ,as yet1 like a young man as you are1 you look to the opinions of men4 ,but tell me this3 it appears to you1 as you say1 that there are certain ,kinds or ,ideas 77 of which things partake and receive applications according to that of which they partake3 thus those things which partake of ,likeness are called like2 those things which partake of ,greatness are called great2 those things which partake of ,beauty and ,justice are called beautiful and just4 ,to this ,socrates assents4 ,and in another part of the dialogue he shows that these ,ideas are not included in our common knowledge1 from whence he infers that they are objects of the ,divine mind4 ,note #cha3 ,parmenid4 p4 #aca4 ,in the ,phdo the same opinion is maintained1 and is summed up in this way1 by a reporter of the last conversation of ,socrates1#cia 1 ' 2 that each ,kind has an existence1 and that other things partake of these ,kinds1 and are called according to the ,kind of which they partake4 ,note #cia3 ,phdo1 p4 #ajb4 ,the inference drawn from this view was1 that in order to obtain true and certain knowledge1 men must elevate themselves1 as much as possible1 to these ,ideas of the qualities which they have to consider3 #gg and as things were thus called after the ,ideas1 the ,ideas had a priority and pre-eminence assigned them4 ,the ,idea of ,good1 ,beautiful1 and ,wise was the ,first ,good1 the ,first ,beautiful1 the ,first ,wise4 ,this dignity and distinction were ultimately carried to a large extent4 ,those ,ideas were described as eternal and self-subsisting1 forming an ,intelligible ,world1 full of the models or archetypes of created things4 ,but it is not to our purpose here to consider the ,platonic ,ideas in their theological bearings4 ,in physics they were applied in the same form as in morals4 ,the primum calidum1 primum frigidum were those ,ideas of fundamental ,principles by participation of which1 all things were hot or cold4 ,this school did not much employ itself in the development of its principles as applied to physical inquiries3 but we are not without examples of such speculations4 ,plutarch's ,treatise 1 ,on the ,first ,cold1 may be cited as one4 ,it is in reality a discussion of a question which has been agitated in modern times also2--whether cold be a positive quality or a mere privation4 ,is there1 ,o ,favorinus1 he begins1 a ,first ,power and ,essence of the ,cold1 as ,fire is of the ,hot2 by a certain presence and participation of which all other things are cold3 or is rather coldness a privation of heat1 as darkness is of light1 and rest of motion8 #c4 ,technical ,forms of the ,pythagoreans4--,the ,numbers of the ,pythagoreans1 when propounded as the explanation of physical phenomena1 as they were1 are still more obscure than the ,ideas of the ,platonists4 ,there were1 indeed1 considerable resemblances in the way in which these two kinds of notions were spoken of4 ,plato called his ,ideas unities1 monads2 and as1 according to him1 ,ideas1 so1 according to the ,pythagoreans1 ,numbers1 were the causes of things being what they are4#dja ,but there was this difference1 that things shared the nature of the ,platonic ,ideas by participation1 while they shared the nature of ,pythagorean ,numbers by imitation4 ,moreover1 the ,pythagoreans followed their notion out into much greater development than any other school1 investing particular numbers with extraordinary attributes1 and applying them by very strange and forced analogies4 ,thus the number ,four1 to which they gave the name of ,tetractys1 was held to be the most perfect number1 and was conceived to correspond to the human soul1 in some way which appears to be very imperfectly understood by the commentators of this philosophy4 #gh ,note3 #dja3 ,arist4 ,metaph4 i4 #f4 ,it has been observed by a distinguished modern scholar1#daa that the place which ,pythagoras ascribed to his numbers is intelligible only by supposing that he confounded1 first a numerical unit with a geometrical point1 and then this with a material atom4 ,but this criticism appears to place systems of physical philosophy under requisitions too severe4 ,if all the essential properties and attributes of things were fully represented by the relations of number1 the philosophy which supplied such an explanation of the universe1 might well be excused from explaining also that existence of objects which is distinct from the existence of all their qualities and properties4 ,the ,pythagorean love of numerical speculations might have been combined with the doctrine of atoms1 and the combination might have led to results well worth notice4 ,but so far as we are aware1 no such combination was attempted in the ancient schools of philosophy2 and perhaps we of the present day are only just beginning to perceive1 through the disclosures of chemistry and crystallography1 the importance of such a line of inquiry4 ,note #daa3 ,thirlwall's ,hist4 ,gr4 ii4 #adb4 #d4 ,technical ,forms of the ,atomists and ,others4--,the atomic doctrine1 of which we have just spoken1 was one of the most definite of the physical doctrines of the ancients1 and was applied with most perseverance and knowledge to the explanation of phenomena4 ,though1 therefore1 it led to no success of any consequence in ancient times1 it served to transmit1 through a long series of ages1 a habit of really physical inquiry2 and1 on this account1 has been thought worthy of an historical disquisition by ,bacon4#dba ,note #dba3 ,parmenidis et ,telesii et prcipue ,democriti ,philosophia1 c41 ,works1 vol4 ix4 #cag4 ,the technical term1 ,atom1 marks sufficiently the nature of the opinion4 ,according to this theory1 the world consists of a collection of simple particles1 of one kind of matter1 and of indivisible smallness 7as the name indicates71 and by the various configurations and motions of these particles1 all kinds of matter and all material phenomena are produced4 ,to this1 the ,atomic ,doctrine of ,leucippus and ,democritus1 was opposed the ,homoiomeria of ,anaxagoras2 that is1 the opinion that material things consist of particles which are homogeneous in each kind of body1 but various in different kinds3 thus for example1 since by food the flesh and blood and bones of man increase1 the author of this doctrine held that there are in food particles of flesh1 and blood1 #gi and bone4 ,as the former tenet points to the corpuscular theories of modern times1 so the latter may be considered as a dim glimpse of the idea of chemical analysis4 ,the ,stoics also1 who were1 especially at a later period1 inclined to materialist views1 had their technical modes of speaking on such subjects4 ,they asserted that matter contained in itself tendencies or dispositions to certain forms1 which dispositions they called 99991 seminal proportions1 or seminal reasons4 ,whatever of sound view1 or right direction1 there might be in the notions which suggested these and other technical expressions1 was1 in all the schools of philosophy 7so far as physics was concerned7 quenched and overlaid by the predominance of trifling and barren speculations2 and by the love of subtilizing and commenting upon the works of earlier writers1 instead of attempting to interpret the book of nature4 ,hence these technical terms served to give fixity and permanence to the traditional dogmas of the sect1 but led to no progress of knowledge4 ,the advances which were made in physical science proceeded1 not from these schools of philosophy 7if we except1 perhaps1 the obligations of the science of ,harmonics to the ,pythagoreans71 but from reasoners who followed an independent path4 ,the sequel of the ambitious hopes1 the vast schemes1 the confident undertakings of the philosophers of ancient ,greece1 was an entire failure in the physical knowledge of which it is our business to trace the history4 ,yet we are not1 on that account1 to think slightingly of these early speculators4 ,they were men of extraordinary acuteness1 invention1 and range of thought2 and1 above all1 they had the merit of first completely unfolding the speculative faculty--of starting in that keen and vigorous chase of knowledge out of which all the subsequent culture and improvement of man's intellectual stores have arisen4 ,the sages of early ,greece form the heroic age of science4 ,like the first navigators in their own mythology1 they boldly ventured their untried bark in a distant and arduous voyage1 urged on by the hopes of a supernatural success2 and though they missed the imaginary golden prize which they sought1 they unlocked the gates of distant regions1 and opened the seas to the keels of the thousands of adventurers who1 in succeeding times1 sailed to and fro1 to the indefinite increase of the mental treasures of mankind4 ,but inasmuch as their attempts1 in one sense1 and at first1 failed1 we must proceed to offer some account of this failure1 and of its nature and causes4 #hj ,,chapter ,,iii4 ,,failure ,,of ,,the ,,physical ,,philosophy ,,of ,,the ,,greek ,,schools4 ,sect4 #a4--,result of the ,greek ,school ,philosophy4 ,,the methods and forms of philosophizing which we have described as employed by the ,greek ,schools1 failed altogether in their application to physics4 ,no discovery of general laws1 no explanation of special phenomena1 rewarded the acuteness and boldness of these early students of nature4 ,astronomy1 which made considerable progress during the existence of the sects of ,greek philosophers1 gained perhaps something by the authority with which ,plato taught the supremacy and universality of mathematical rule and order2 and the truths of ,harmonics1 which had probably given rise to the ,pythagorean passion for numbers1 were cultivated with much care by that school4 ,but after these first impulses1 the sciences owed nothing to the philosophical sects2 and the vast and complex accumulations and apparatus of the ,stagirite do not appear to have led to any theoretical physical truths4 ,this assertion hardly requires proof1 since in the existing body of science there are no doctrines for which we are indebted to the ,aristotelian ,school4 ,real truths1 when once established1 remain to the end of time a part of the mental treasure of man1 and may be discerned through all the additions of later days4 ,but we can point out no physical doctrine now received1 of which we trace the anticipation in ,aristotle1 in the way in which we see the ,copernican system anticipated by ,aristarchus1 the resolution of the heavenly appearances into circular motions suggested by ,plato1 and the numerical relations of musical intervals ascribed to ,pythagoras4 ,but it may be worth while to look at this matter more closely4 ,among the works of ,aristotle are thirty-eight chapters of ,problems1 which may serve to exemplify the progress he had really made in the reduction of phenomena to laws and causes4 ,of these ,problems1 a large proportion are physiological1 and these ,i here pass by1 as not illustrative of the state of physical knowledge4 ,but those which are properly physical are1 for the most part1 questions concerning such #ha facts and difficulties as it is the peculiar business of theory to explain4 ,now it may be truly said1 that in scarcely any one instance are the answers1 which ,aristotle gives to his questions1 of any value4 ,for the most part1 indeed1 he propounds his answer with a degree of hesitation or vacillation which of itself shows the absence of all scientific distinctness of thought2 and the opinions so offered never appear to involve any settled or general principle4 ,we may take1 as examples of this1 the problems of the simplest kind1 where the principles lay nearest at hand--the mechanical ones4 ,why1 he asks1#dca do small forces move great weights by means of a lever1 when they have thus to move the lever added to the weight8 ,is it1 he suggests1 because a greater radius moves faster8 ,why does a small wedge split great weights8#dda ,is it because the wedge is composed of two opposite levers8 ,why1#dea when a man rises from a chair1 does he bend his leg and his body to acute angles with his thigh8 ,is it because a right angle is connected with equality and rest8 ,why#dfa can a man throw a stone further with a sling than with his hand8 ,is it that when he throws with his hand he moves the stone from rest1 but when he uses the sling he throws it already in motion8 ,why1#dga if a circle be thrown on the ground1 does it first describe a straight line and then a spiral1 as it falls8 ,is it that the air first presses equally on the two sides and supports it1 and afterwards presses on one side more8 ,why#dha is it difficult to distinguish a musical note from the octave above8 ,is it that proportion stands in the place of equality8 ,it must be allowed that these are very vague and worthless surmises2 for even if we were1 as some commentators have done1 to interpret some of them so as to agree with sound philosophy1 we should still be unable to point out1 in this author's works1 any clear or permanent apprehension of the general principles which such an interpretation implies4 ,note #dca3 ,mech4 ,prob4 #d4 ,note #dda3 ,ib4 #ah4 ,note #dea3 ,ib4 #ca4 ,note #dfa3 ,ib4 #ac4 ,note #dga3 4 #aa4 ,note #dha3 4 #ad4 ,thus the ,aristotelian physics cannot be considered as otherwise than a complete failure4 ,it collected no general laws from facts2 and consequently1 when it tried to explain facts1 it had no principles which were of any avail4 ,the same may be said of the physical speculations of the other schools of philosophy4 ,they arrived at no doctrines from which they could deduce1 by sound reasoning1 such facts as they saw2 though they #hb often venture so far to trust their principles as to infer from them propositions beyond the domain of sense4 ,thus1 the principle that each element seeks its own place1 led to the doctrine that1 the place of fire being the highest1 there is1 above the air1 a ,sphere of ,fire--of which doctrine the word ,empyrean1 used by our poets1 still conveys a reminiscence4 ,the ,pythagorean tenet that ten is a perfect number1#dia led some persons to assume that the heavenly bodies are in number ten2 and as nine only were known to them1 they asserted that there was an antichthon1 or counter-earth1 on the other side of the sun1 invisible to us4 ,their opinions respecting numerical ratios1 led to various other speculations concerning the distances and positions of the heavenly bodies3 and as they had1 in other cases1 found a connection between proportions of distance and musical notes1 they assumed1 on this suggestion1 the music of the spheres4 ,note #dia3 ,arist4 ,metaph4 i4 #e4 ,although we shall look in vain in the physical philosophy of the ,greek ,schools for any results more valuable than those just mentioned1 we shall not be surprised to find1 recollecting how much an admiration for classical antiquity has possessed the minds of men1 that some writers estimate their claims much more highly than they are stated here4 ,among such writers we may notice ,dutens1 who1 in #agff1 published his ,origin of the ,discoveries attributed to the ,moderns2 in which it is shown that our most celebrated ,philosophers have received the greatest part of their knowledge from the ,works of the ,ancients4 ,the thesis of this work is attempted to be proved1 as we might expect1 by very large interpretations of the general phrases used by the ancients4 ,thus1 when ,timus1 in ,plato's dialogue1 says of the ,creator of the world1#eja that he infused into it two powers1 the origins of motions1 both of that of the same thing and of that of different things2 ,dutens#eaa finds in this a clear indication of the projectile and attractive forces of modern science4 ,and in some of the common declamation of the ,pythagoreans and ,platonists concerning the general prevalence of numerical relations in the universe1 he discovers their acquaintance with the law of the inverse square of the distance by which gravitation is regulated1 though he allows#eba that it required all the penetration of ,newton and his followers to detect this law in the scanty fragments by which it is transmitted4 ,note #eja3 ,tim4 #if4 ,note #eaa3 #c;d ed4 p4 #hc4 ,note #eba3 ,ib4 p4 #hh4 ,argument of this kind is palpably insufficient to cover the failure of the ,greek attempts at a general physical philosophy2 or rather we #hc may say1 that such arguments1 since they are as good as can be brought in favor of such an opinion1 show more clearly how entire the failure was4 ,i proceed now to endeavor to point out its causes4 ,sect4 #b4--;,cause of the ,failure of the ,greek ,physical ,philosophy4 ,,the cause of the failure of so many of the attempts of the ,greeks to construct physical science is so important1 that we must endeavor to bring it into view here2 though the full development of such subjects belongs rather to the ,philosophy of ,induction4 ,the subject must1 at present1 be treated very briefly4 ,i will first notice some errors which may naturally occur to the reader's mind1 as possible causes of failure1 but which1 we shall be able to show1 were not the real reasons in this case4 ,the cause of failure was not the neglect of facts4 ,it is often said that the ,greeks disregarded experience1 and spun their philosophy out of their own thoughts alone2 and this is supposed by many to be their essential error4 ,it is1 no doubt1 true1 that the disregard of experience is a phrase which may be so interpreted as to express almost any defect of philosophical method2 since coincidence with experience is requisite to the truth of all theory4 ,but if we fix a more precise sense on our terms1 ,i conceive it may be shown that the ,greek philosophy did1 in its opinions1 recognize the necessity and paramount value of observations2 did1 in its origin1 proceed upon observed facts2 and did employ itself to no small extent in classifying and arranging phenomena4 ,we must endeavor to illustrate these assertions1 because it is important to show that these steps alone do not necessarily lead to science4 #a4 ,the acknowledgment of experience as the main ground of physical knowledge is so generally understood to be a distinguishing feature of later times1 that it may excite surprise to find that ,aristotle1 and other ancient philosophers1 not only asserted in the most pointed manner that all our knowledge must begin from experience1 but also stated in language much resembling the habitual phraseology of the most modern schools of philosophizing1 that particular facts must be collected2 that from these1 general principles must be obtained by induction2 and that these principles1 when of the most general kind1 are axioms4 ,a few passages will show this4 ,the way#eca must be the same1 says ,aristotle1 in speaking of the rules of reasoning1 with respect to philosophy1 as it is with respect to #hd any art or science whatever2 we must collect the facts1 and the things to which the facts happen1 in each subject1 and provide as large a supply of these as possible4 ,he then proceeds to say that we are not to look at once at all this collected mass1 but to consider small and definite portions 4 4 4 ,and thus it is the office of observation to supply principles in each subject2 for instance1 astronomical observation supplies the principles of astronomical science4 ,for the phenomena being properly assumed1 the astronomical demonstrations were from these discovered4 ,and the same applies to every art and science4 ,so that if we take the facts 7 7 belonging to each subject1 it is our task to mark out clearly the course of the demonstrations4 ,for if in our natural history 7 7 we have omitted nothing of the facts and properties which belong to the subject1 we shall learn what we can demonstrate and what we cannot4 ,note #eca3 ,anal4 ,prior4 i4 #cj4 ,these facts1 1 he1 at other times1 includes in the term sensation4 ,thus1 he says1#eda ,it is obvious that if any sensation is wanting1 there must be also some knowledge wanting which we are thus prevented from having1 since we arrive at knowledge either by induction or by demonstration4 ,demonstration proceeds from universal propositions1 ,induction from particulars4 ,but we cannot have universal theoretical propositions except from induction2 and we cannot make inductions without having sensation2 for sensation has to do with particulars4 ,note #eda3 ,anal4 ,post4 i4 #ah4 ,in another place1#eea after stating that principles must be prior to1 and better known than conclusions1 he distinguishes such principles into absolutely prior1 and prior relative to us3 ,the prior principles1 relative to us1 are those which are nearer to the sensation2 but the principles absolutely prior are those which are more remote from the sensation4 ,the most general principles are the more remote1 the more particular are nearer4 ,the general principles which are necessary to knowledge are axioms4 ,note #eea3 ,ib4 i4 #b4 ,we may add to these passages1 that in which he gives an account of the way in which ,leucippus was led to the doctrine of atoms4 ,after describing the opinions of some earlier philosophers1 he says1#efa ,thus1 proceeding in violation of sensation1 and disregarding it1 because1 as they held1 they must follow reason1 some came to the conclusion that the universe was one1 and infinite1 and at rest4 ,as it appeared1 however1 that though this ought to be by reasoning1 it #he would go near to madness to hold such opinions in practice 7for no one was ever so mad as to think fire and ice to be one71 ,leucippus1 therefore1 pursued a line of reasoning which was in accordance with sensation1 and which was not irreconcilable with the production and decay1 the motion and multitude of things4 ,it is obvious that the school to which ,leucippus belonged 7the ,eclectic7 must have been1 at least in its origin1 strongly impressed with the necessity of bringing its theories into harmony with the observed course of nature4 ,note #efa3 ,de ,gen4 et ,cor4 i4 #h4 #b4 ,nor was this recognition of the fundamental value of experience a mere profession4 ,the ,greek philosophy did1 in its beginning1 proceed upon observation4 ,indeed it is obvious that the principles which it adopted were1 in the first place1 assumed in order to account for some classes of facts1 however imperfectly they might answer their purpose4 ,the principle of things seeking their own places1 was invented in order to account for the falling and floating of bodies4 ,again1 ,aristotle says1 that heat is that which brings together things of the same kind1 cold is that which brings together things whether of the same or of different kinds3 it is plain that in this instance he intended by his principle to explain some obvious facts1 as the freezing of moist substances1 and the separation of heterogeneous things by fusion2 for1 as he adds1 if fire brings together things which are akin1 it will separate those which are not akin4 ,it would be easy to illustrate the remark further1 but its truth is evident from the nature of the case2 for no principles could be accepted for a moment1 which were the result of an arbitrary caprice of the mind1 and which were not in some measure plausible1 and apparently confirmed by facts4 ,but the works of ,aristotle show1 in another way1 how unjust it would be to accuse him of disregarding facts4 ,many large treatises of his consist almost entirely of collections of facts1 as for instance1 those ,on ,colors1 ,on ,sounds1 and the collection of ,problems to which we have already referred2 to say nothing of the numerous collection of facts bearing on natural history and physiology1 which form a great portion of his works1 and are even now treasuries of information4 ,a moment's reflection will convince us that the physical sciences of our own times1 for example4 ,mechanics and ,hydrostatics1 are founded almost entirely upon facts with which the ancients were as familiar as we are4 ,the defect of their philosophy1 therefore1 wherever it may lie1 consists neither in the speculative depreciation of the value of facts1 nor in the practical neglect of their use4 #c4 ,nor again1 should we hit upon the truth1 if we were to say that #hf ,aristotle1 and other ancient philosophers1 did indeed collect facts2 but that they took no steps in classifying and comparing them2 and that thus they failed to obtain from them any general knowledge4 ,for1 in reality1 the treatises of ,aristotle which we have mentioned1 are as remarkable for the power of classifying and systematizing which they exhibit1 as for the industry shown in the accumulation4 ,but it is not classification of facts merely which can lead us to knowledge1 except we adopt that special arrangement1 which1 in each case1 brings into view the principles of the subject4 ,we may easily show how unprofitable an arbitrary or random classification is1 however orderly and systematic it may be4 ,for instance1 for a long period all unusual fiery appearances in the sky were classed together as meteors4 ,comets1 shooting-stars1 and globes of fire1 and the aurora borealis in all its forms1 were thus grouped together1 and classifications of considerable extent and minuteness were proposed with reference to these objects4 ,but this classification was of a mixed and arbitrary kind4 ,figure1 color1 motion1 duration1 were all combined as characters1 and the imagination lent its aid1 transforming these striking appearances into fiery swords and spears1 bears and dragons1 armies and chariots4 ,the facts so classified were1 notwithstanding1 worthless2 and would not have been one jot the less so1 had they and their classes been ten times as numerous as they were4 ,no rule or law that would stand the test of observation was or could be thus discovered4 ,such classifications have1 therefore1 long been neglected and forgotten4 ,even the ancient descriptions of these objects of curiosity are unintelligible1 or unworthy of trust1 because the spectators had no steady conception of the usual order of such phenomena4 ,for1 however much we may fear to be misled by preconceived opinions1 the caprices of imagination distort our impressions far more than the anticipations of reason4 ,in this case men had1 indeed we may say with regard to many of these meteors1 they still have1 no science3 not for want of facts1 nor even for want of classification of facts2 but because the classification was one in which no real principle was contained4 #d4 ,since1 as we have said before1 two things are requisite to science1--,facts and ,ideas2 and since1 as we have seen4 ,facts were not wanting in the physical speculations of the ancients1 we are naturally led to ask1 ,were they then deficient in ,ideas8 ,was there a want among them of mental activity1 and logical connection of thought8 ,but it is so obvious that the answer to this inquiry must be in the negative1 that we need not dwell upon it4 ,no one who knows any thing of the #hg history of the ancient ,greek mind1 can question1 that in acuteness1 in ingenuity1 in the power of close and distinct reasoning1 they have never been surpassed4 ,the common opinion1 which considers the defect of their philosophical character to reside rather in the exclusive activity of such qualities1 than in the absence of them1 is at least so far just4 #e4 ,we come back again1 therefore1 to the question1 ,what was the radical and fatal defect in the physical speculations of the ,greek philosophical schools8 ,to this ,i answer3 ,the defect was1 that though they had in their possession ,facts and ,ideas1 the ,ideas were not distinct and appropriate to the ,facts4 ,the peculiar characteristics of scientific ideas1 which ,i have endeavored to express by speaking of them as distinct and appropriate to the facts1 must be more fully and formally set forth1 when we come to the philosophy of the subject4 ,in the mean time1 the reader will probably have no difficulty in conceiving that1 for each class of ,facts1 there is some special set of ,ideas1 by means of which the facts can be included in general scientific truths2 and that these ,ideas1 which may thus be termed appropriate1 must be possessed with entire distinctness and clearness1 in order that they may be successfully applied4 ,it was the want of ,ideas having this reference to material phenomena1 which rendered the ancient philosophers1 with very few exceptions1 helpless and unsuccessful speculators on physical subjects4 ,this must be illustrated by one or two examples4 ,one of the facts which ,aristotle endeavors to explain is this2 that when the sun's light passes through a hole1 whatever be the form of the hole1 the bright image1 if formed at any considerable distance from the hole1 is round1 instead of imitating the figure of the hole1 as shadows resemble their objects in form4 ,we shall easily perceive this appearance to be a necessary consequence of the circular figure of the sun1 if we conceive light to be diffused from the luminary by means of straight rays proceeding from every point of the sun's disk and passing through every point within the boundary of the hole4 ,by attending to the consequences of this mode of conception1 it will be seen that each point of the hole will be the vertex of a double cone of rays which has the sun's disk for its base on one side and an image of the sun on the other2 and the figure of the image of the hole will be determined by supposing a series of equal bright circles1 images of the sun1 to be placed along the boundary of an image equal to the hole itself4 ,the figure of the image thus determined will partake of the form of the hole1 and #hh of the circular form of the sun's image3 but these circular images become larger and larger as they are further from the hole1 while the central image of the hole remains always of the original size2 and thus at a considerable distance from the hole1 the trace of the hole's form is nearly obliterated1 and the image is nearly a perfect circle4 ,instead of this distinct conception of a cone of rays which has the sun's disk for its basis1 ,aristotle has the following loose conjecture4#ega ,is it because light is emitted in a conical form2 and of a cone1 the base is a circle2 so that on whatever the rays of the sun fall1 they appear more circular8 ,and thus though he applies the notion of rays to this problem1 he possesses this notion so indistinctly that his explanation is of no value4 ,he does not introduce into his explanation the consideration of the sun's circular figure1 and is thus prevented from giving a true account of this very simple optical phenomenon4 ,note #ega3 ,problem4 #ae1 1 c4 #f4 ,again1 to pass to a more extensive failure3 why was it that ,aristotle1 knowing the property of the lever1 and many other mechanical truths1 was unable to form them into a science of mechanics1 as ,archimedes afterwards did8 ,the reason was1 that1 instead of considering rest and motion directly1 and distinctly1 with reference to the ,idea of ,cause1 that is ,force1 he wandered in search of reasons among other ideas and notions1 which could not be brought into steady connection with the facts2--the ideas of properties of circles1 of proportions of velocities1--the notions of strange and common1 of natural and unnatural4 ,thus1 in the ,proem to his ,mechanical ,problems1 after stating some of the difficulties which he has to attack1 he says1 ,of all such cases1 the circle contains the principle of the cause4 ,and this is what might be looked for2 for it is nothing absurd1 if something wonderful is derived from something more wonderful still4 ,now the most wonderful thing is1 that opposites should be combined2 and the circle is constituted of such combinations of opposites4 ,for it is constructed by a stationary point and a moving line1 which are contrary to each other in nature2 and hence we may the less be surprised at the resulting contrarieties4 ,and in the first place1 the circumference of the circle1 though a line without breadth1 has opposite qualities2 for it is both convex and concave4 ,in the next place1 it has1 at the same time1 opposite motions1 for it moves forward and backward at the same time4 ,for the circumference1 setting out from any point1 comes to the same point again1 so #hi that by a continuous progression1 the last point becomes the first4 ,so that1 as was before stated1 it is not surprising that the circle should be the principle of all wonderful properties4 ,aristotle afterwards proceeds to explain more specially how he applies the properties of the circle in this case4 ,the reason1 he says1 in his fourth ,problem1 why a force1 acting at a greater distance from the fulcrum1 moves a weight more easily1 is1 that it describes a greater circle4 ,he had already asserted that when a body at the end of a lever is put in motion1 it may be considered as having two motions2 one in the direction of the tangent1 and one in the direction of the radius2 the former motion is1 he says1 according to nature1 the latter1 contrary to nature4 ,now in the smaller circle1 the motion1 contrary to nature1 is more considerable than it is in the larger circle4 ,therefore1 he adds1 the mover or weight at the larger arm will be transferred further by the same force than the weight moved1 which is at the extremity of the shorter arm4 ,these loose and inappropriate notions of natural and unnatural motions1 were unfit to lead to any scientific truths2 and1 with the habits of thought which dictated these speculations a perception of the true grounds of mechanical properties was impossible4 #g4 ,thus1 in this instance1 the error of ,aristotle was the neglect of the ,idea appropriate to the facts1 namely1 the ,idea of ,mechanical ,cause1 which is ,force2 and the substitution of vague or inapplicable notions involving only relations of space or emotions of wonder4 ,the errors of those who failed similarly in other instances1 were of the same kind4 ,to detail or classify these would lead us too far into the philosophy of science2 since we should have to enumerate the ,ideas which are appropriate1 and the various classes of ,facts on which the different sciences are founded1--a task not to be now lightly undertaken4 ,but it will be perceived1 without further explanation1 that it is necessary1 in order to obtain from facts any general truth1 that we should apply to them that appropriate ,idea1 by which permanent and definite relations are established among them4 ,in such ,ideas the ancients were very poor1 and the stunted and deformed growth of their physical science was the result of this penury4 ,the ,ideas of ,space and ,time1 ,number and ,motion1 they did indeed possess distinctly2 and so far as these went1 their science was tolerably healthy4 ,they also caught a glimpse of the ,idea of a ,medium by which the qualities of bodies1 as colors and sounds1 are perceived4 ,but the idea of ,substance remained barren in their hands2 #ij in speculating about elements and qualities1 they went the wrong way1 assuming that the properties of ,compounds must resemble those of the ,elements which determine them2 and their loose notions of ,contrariety never approached the form of those ideas of ,polarity1 which1 in modern times1 regulate many parts of physics and chemistry4 ,if this statement should seem to any one to be technical or arbitrary1 we must refer1 for the justification of it1 to the ,philosophy of ,science1 of which we hope hereafter to treat4 ,but it will appear1 even from what has been here said1 that there are certain ,ideas or ,forms of mental apprehension1 which may be applied to ,facts in such a manner as to bring into view fundamental principles of science2 while the same ,facts1 however arrayed or reasoned about1 so long as these appropriate ideas are not employed1 cannot give rise to any exact or substantial knowledge4 #b;d ,ed4 ,this account of the cause of failure in the physical speculations of the ancient ,greek philosophers has been objected to as unsatisfactory4 ,i will offer a few words in explanation of it4 ,the mode of accounting for the failure of the ,greeks in physics is1 in substance2--that the ,greeks in their physical speculations fixed their attention upon the wrong aspects and relations of the phenomena2 and that the aspects and relations in which phenomena are to be viewed in order to arrive at scientific truths may be arranged under certain heads1 which ,i have termed ,ideas2 such as ,space1 ,time1 ,number1 ,cause1 ,likeness4 ,in every case1 there is an ,idea to which the phenomena may be referred1 so as to bring into view the ,laws by which they are governed2 this ,idea ,i term the appropriate ,idea in such case2 and in order that the reference of the phenomena to the ,law may be clearly seen1 the ,idea must be distinctly possessed4 ,thus the reason of ,aristotle's failure in his attempts at ,mechanical ,science is1 that he did not refer the facts to the appropriate ,idea1 namely ,force1 the ,cause of ,motion1 but to relations of ,space and the like2 that is1 he introduces ,geometrical instead of ,mechanical ,ideas4 ,it may be said that we learn little by being told that ,aristotle's failure in this and the like cases arose from his referring to the wrong class of ,ideas2 or1 as ,i have otherwise expressed it1 fixing his attention upon the wrong aspects and relations of the facts2 since1 it may be said1 this is only to state in other words that he did fail4 ,but this criticism is1 ,i think1 ill-founded4 ,the account which ,i have given is not only a statement that ,aristotle1 and others who took a like course1 did fail2 but also1 that they failed in one certain point out of several #ia which are enumerated4 ,they did not fail because they neglected to observe facts2 they did not fail because they omitted to class facts2 they did not fail because they had not ideas to reason from2 but they failed because they did not take the right ideas in each case4 ,and so long as they were in the wrong in this point1 no industry in collecting facts1 or ingenuity in classing them and reasoning about them1 could lead them to solid truth4 ,nor is this account of the nature of their mistake without its instruction for us2 although we are not to expect to derive from the study of their failure any technical rule which shall necessarily guide us to scientific discovery4 ,for their failure teaches us that1 in the formation of science1 an ,error in the ,ideas is as fatal to the discovery of ,truth as an ,error in the ,facts2 and may as completely impede the progress of knowledge4 ,i have in ,books ,,ii4 to ,x4 of the ,philosophy1 shown historically how large a portion of the progress of ,science consists in the establishment of ,appropriate ,ideas as the basis of each science4 ,of the two main processes by which science is constructed1 as stated in ,book ,,xi4 of that work1 namely the ,explication of ,conceptions and the ,colligation of ,facts1 the former must precede the latter4 ,in ,book ,,xii4 chap4 #e1 of the ,philosophy1 ,i have stated the maxim concerning appropriate ,ideas in this form1 that the ,idea and the ,facts must be homogeneous4 ,when ,i say that the failure of the ,greeks in physical science arose from their not employing appropriate ,ideas to connect the facts1 ,i do not use the term appropriate in a loose popular sense2 but ,i employ it as a somewhat technical term1 to denote the appropriate ,idea1 out of that series of ,ideas which have been made 7as ,i have shown in the ,philosophy7 the foundation of sciences2 namely1 ,space1 ,time1 ,number1 ,cause1 ,likeness1 ,substance1 and the rest4 ,it appears to me just to say that ,aristotle's failure in his attempts to deal with problems of equilibrium1 arose from his referring to circles1 velocities1 notions of natural and unnatural1 and the like1--conceptions depending upon ,ideas of ,space1 of ,nature1 c4--which are not appropriate to these problems1 and from his missing the ,idea of ,mechanical ,force or ,pressure1 which is the appropriate ,idea4 ,i give this1 not as an account of all failures in attempts at science1 but only as the account of such radical and fundamental failures as this of ,aristotle2 who1 with a knowledge of the facts1 failed to connect them into a really scientific view4 ,if ,i had to compare rival theories of a more complex kind1 ,i should not necessarily say that one involved #ib an appropriate ,idea and the other did not1 though ,i might judge one to be true and the other to be false4 ,for instance1 in comparing the emissive and the undulatory theory of light1 we see that both involve the same ,idea2--the ,idea of a ,medium acting by certain mechanical properties4 ,the question there is1 ,what is the true view of the mechanism of the ,medium8 ,it may be remarked1 however1 that the example of ,aristotle's failure in physics1 given in p4 #hg1 namely1 his attempted explanation of the round image of a square hole1 is a specimen rather of indistinct than of inappropriate ideas4 ,the geometrical explanation of this phenomenon1 which ,i have there inserted1 was given by ,maurolycus1 and before him1 by ,leonardo da ,vinci4 ,we shall1 in the next ,book1 see the influence of the appropriate general ,ideas1 in the formation of various sciences4 ,it need only be observed1 before we proceed1 that1 in order to do full justice to the physical knowledge of the ,greek ,schools of philosophy1 it is not necessary to study their course after the time of their founders4 ,their fortunes1 in respect of such acquisitions as we are now considering1 were not progressive4 ,the later chiefs of the ,schools followed the earlier masters2 and though they varied much1 they added little4 ,the ,romans adopted the philosophy of their ,greek subjects2 but they were always1 and1 indeed1 acknowledged themselves to be1 inferior to their teachers4 ,they were as arbitrary and loose in their ideas as the ,greeks1 without possessing their invention1 acuteness1 and spirit of system4 ,in addition to the vagueness which was combined with the more elevated trains of philosophical speculation among the ,greeks1 the ,romans introduced into their treatises a kind of declamatory rhetoric1 which arose probably from their forensic and political habits1 and which still further obscured the waning gleams of truth4 ,yet we may also trace in the ,roman philosophers to whom this charge mostly applies 7,lucretius1 ,pliny1 ,seneca71 the national vigor and ambition4 ,there is something ,roman in the public spirit and anticipation of universal empire which they display1 as citizens of the intellectual republic4 ,though they speak sadly or slightingly of the achievements of their own generation1 they betray a more abiding and vivid belief in the dignity and destined advance of human knowledge as a whole1 than is obvious among the ,greeks4 ,we must1 however1 turn back1 in order to describe steps of more definite value to the progress of science than those which we have hitherto noticed4 #ic ,,book ,,ii4 ,,history ,,of ,,the ,,physical ,,sciences ,,in ,,ancient ,,greece4 1 4 ,prom4 ,vinct4 #aji4 ,i brought to earth the spark of heavenly fire1 ,concealed at first1 and small1 but spreading soon ,among the sons of men1 and burning on1 ,teacher of art and use1 and fount of power4 #ie ,,introduction4 ,,in order to the acquisition of any such exact and real knowledge of nature as that which we properly call ,physical ,science1 it is requisite1 as has already been said1 that men should possess ,ideas both distinct and appropriate1 and should apply them to ascertained ,facts4 ,they are thus led to propositions of a general character1 which are obtained by ,induction1 as will elsewhere be more fully explained4 ,we proceed now to trace the formation of ,sciences among the ,greeks by such processes4 ,the provinces of knowledge which thus demand our attention are1 ,astronomy1 ,mechanics and ,hydrostatics1 ,optics and ,harmonics2 of which ,i must relate1 first1 the earliest stages1 and next1 the subsequent progress4 ,of these portions of human knowledge1 ,astronomy is1 beyond doubt or comparison1 much the most ancient and the most remarkable2 and probably existed1 in somewhat of a scientific form1 in ,chaldea and ,egypt1 and other countries1 before the period of the intellectual activity of the ,greeks4 ,but ,i will give a brief account of some of the other ,sciences before ,i proceed to ,astronomy1 for two reasons2 first1 because the origin of ,astronomy is lost in the obscurity of a remote antiquity2 and therefore we cannot exemplify the conditions of the first rise of science so well in that subject as we can in others which assumed their scientific form at known periods2 and next1 in order that ,i may not have to interrupt1 after ,i have once begun it1 the history of the only progressive ,science which the ancient world produced4 ,it has been objected to the arrangement here employed that it is not symmetrical2 and that ,astronomy1 as being one of the ,physical ,sciences1 ought to have occupied a chapter in this ,second ,book1 instead of having a whole ,book to itself 7,book ,,iii74 ,i do not pretend that the arrangement is symmetrical1 and have employed it only on the ground of convenience4 ,the importance and extent of the history of ,astronomy are such that this science could not1 with a view to our purposes1 be made co-ordinate with ,mechanics or ,optics4 #if ,,chapter ,i4 ,,earliest ,,stages ,,of ,,mechanics ,,and ,,hydrostatics4 ,sect4 #a4--,mechanics4 ,,astronomy is a science so ancient that we can hardly ascend to a period when it did not exist2 ,mechanics1 on the other hand1 is a science which did not begin to be till after the time of ,aristotle2 for ,archimedes must be looked upon as the author of the first sound knowledge on this subject4 ,what is still more curious1 and shows remarkably how little the continued progress of science follows inevitably from the nature of man1 this department of knowledge1 after the right road had been fairly entered upon1 remained absolutely stationary for nearly two thousand years2 no single step was made1 in addition to the propositions established by ,archimedes1 till the time of ,galileo and ,stevinus4 ,this extraordinary halt will be a subject of attention hereafter2 at present we must consider the original advance4 ,the great step made by ,archimedes in ,mechanics was the establishing1 upon true grounds1 the general proposition concerning a straight lever1 loaded with two heavy bodies1 and resting upon a fulcrum4 ,the proposition is1 that two bodies so circumstanced will balance each other1 when the distance of the smaller body from the fulcrum is greater than the distance of the other1 in exactly the same proportion in which the weight of the body is less4 ,this proposition is proved by ,archimedes in a work which is still extant1 and the proof holds its place in our treatises to this day1 as the simplest which can be given4 ,the demonstration is made to rest on assumptions which amount in effect to such ,definitions and ,axioms as these3 ,that those bodies are of equal weight which balance each other at equal arms of a straight lever2 and that in every heavy body there is a definite point called a ,centre of ,gravity1 in which point we may suppose the weight of the body collected4 ,the principle1 which is really the foundation of the validity of the demonstration thus given1 and which is the condition of all experimental knowledge on the subject1 is this3 that when two equal weights are supported on a lever1 they act on the fulcrum of the lever with the #ig same effect as if they were both together supported immediately at that point4 ,or more generally1 we may state the principle to be this3 that the pressure by which a heavy body is supported continues the same1 however we alter the form or position of the body1 so long as the magnitude and material continue the same4 ,the experimental truth of this principle is a matter of obvious and universal experience4 ,the weight of a basket of stones is not altered by shaking the stones into new positions4 ,we cannot make the direct burden of a stone less by altering its position in our hands2 and if we try the effect on a balance or a machine of any kind1 we shall see still more clearly and exactly that the altered position of one weight1 or the altered arrangement of several1 produces no change in their effect1 so long as their point of support remains unchanged4 ,this general fact is obvious1 when we possess in our minds the ideas which are requisite to apprehend it clearly4 ,but when we are so prepared1 the truth appears to be manifest1 even independent of experience1 and is seen to be a rule to which experience must conform4 ,what1 then1 is the leading idea which thus enables us to reason effectively upon mechanical subjects8 ,by attention to the course of such reasonings1 we perceive that it is the idea of ,pressure2 ,pressure being conceived as a measurable effect of heavy bodies at rest1 distinguishable from all other effects1 such as motion1 change of figure1 and the like4 ,it is not here necessary to attempt to trace the history of this idea in our minds2 but it is certain that such an idea may be distinctly formed1 and that upon it the whole science of statics may be built4 ,pressure1 load1 weight1 are names by which this idea is denoted when the effect tends directly downwards2 but we may have pressure without motion1 or dead pull1 in other cases1 as at the critical instant when two nicely-matched wrestlers are balanced by the exertion of the utmost strength of each4 ,pressure in any direction may thus exist without any motion whatever4 ,but the causes which produce such pressure are capable of producing motion1 and are generally seen producing motion1 as in the above instance of the wrestlers1 or in a pair of scales employed in weighing2 and thus men come to consider pressure as the exception1 and motion as the rule3 or perhaps they image to themselves the motion which might or would take place2 for instance1 the motion which the arms of a lever would have if they did move4 ,they turn away from the case really before them1 which is that of bodies at rest1 and balancing each other1 and pass to another case1 which is arbitrarily #ih assumed to represent the first4 ,now this arbitrary and capricious evasion of the question we consider as opposed to the introduction of the distinct and proper idea of ,pressure1 by means of which the true principles of this subject can be apprehended4 ,we have already seen that ,aristotle was in the number of those who thus evaded the difficulties of the problem of the lever1 and consequently lost the reward of success4 ,he failed1 as has before been stated1 in consequence of his seeking his principles in notions1 either vague and loose1 as the distinction of natural and unnatural motions1 or else inappropriate1 as the circle which the weight would describe1 the velocity which it would have if it moved2 circumstances which are not part of the fact under consideration4 ,the influence of such modes of speculation was the main hindrance to the prosecution of the true ,archimedean form of the science of ,mechanics4 ,the mechanical doctrine of ,equilibrium1 is ,statics4 ,it is to be distinguished from the mechanical doctrine of ,motion1 which is termed ,dynamics1 and which was not successfully treated till the time of ,galileo4 ,sect4 #b4--;,hydrostatics4 ,,archimedes not only laid the foundations of the ,statics of solid bodies1 but also solved the principal problem of ,hydrostatics1 or the ,statics of ,fluids2 namely1 the conditions of the floating of bodies4 ,this is the more remarkable1 since not only did the principles which ,archimedes established on this subject remain unpursued till the revival of science in modern times1 but1 when they were again put forward1 the main proposition was so far from obvious that it was termed1 and is to this day called1 the hydrostatic paradox4 ,the true doctrine of ,hydrostatics1 however1 assuming the ,idea of ,pressure1 which it involves1 in common with the ,mechanics of solid bodies1 requires also a distinct ,idea of a ,fluid1 as a body of which the parts are perfectly movable among each other by the slightest partial pressure1 and in which all pressure exerted on one part is transferred to all other parts4 ,from this idea of ,fluidity1 necessarily follows that multiplication of pressure which constitutes the hydrostatic paradox2 and the notion being seen to be verified in nature1 the consequences were also realized as facts4 ,this notion of ,fluidity is expressed in the postulate which stands at the head of ,archimedes' ,treatise on ,floating ,bodies4 ,and from this principle are deduced the solutions1 not only of the simple problems of the science1 but of some problems of considerable complexity4 #ii ,the difficulty of holding fast this ,idea of ,fluidity so as to trace its consequences with infallible strictness of demonstration1 may be judged of from the circumstance that1 even at the present day1 men of great talents1 not unfamiliar with the subject1 sometimes admit into their reasonings an oversight or fallacy with regard to this very point4 ,the importance of the ,idea when clearly apprehended and securely held1 may be judged of from this1 that the whole science of ,hydrostatics in its most modern form is only the development of the ,idea4 ,and what kind of attempts at science would be made by persons destitute of this ,idea1 we may see in the speculations of ,aristotle concerning light and heavy bodies1 which we have already quoted2 where1 by considering light and heavy as opposite qualities1 residing in things themselves1 and by an inability to apprehend the effect of surrounding fluids in supporting bodies1 the subject was made a mass of false or frivolous assertions1 which the utmost ingenuity could not reconcile with facts1 and could still less deduce from the asserted doctrines any new practical truths4 ,in the case of ,statics and ,hydrostatics1 the most important condition of their advance was undoubtedly the distinct apprehension of these two appropriate ,ideas--,statical ,pressure1 and ,hydrostatical ,pressure as included in the idea of ,fluidity4 ,for the ,ideas being once clearly possessed1 the experimental laws which they served to express 7that the whole pressure of a body downwards was always the same2 and that water1 and the like1 were fluids according to the above idea of fluidity71 were so obvious1 that there was no doubt nor difficulty about them4 ,these two ideas lie at the root of all mechanical science2 and the firm possession of them is1 to this day1 the first requisite for a student of the subject4 ,after being clearly awakened in the mind of ,archimedes1 these ideas slept for many centuries1 till they were again called up in ,galileo1 and more remarkably in ,stevinus4 ,this time1 they were not destined again to slumber2 and the results of their activity have been the formation of two ,sciences1 which are as certain and severe in their demonstrations as geometry itself and as copious and interesting in their conclusions2 but which1 besides this recommendation1 possess one of a different order1--that they exhibit the exact impress of the laws of the physical world1 and unfold a portion of the rules according to which the phenomena of nature take place1 and must take place1 till nature herself shall alter4 #ajj ,,chapter ,,ii4 ,,earliest ,,stages ,,of ,,optics4 ,,the progress made by the ancients in ,optics was nearly proportional to that which they made in ,statics4 ,as they discovered the true grounds of the doctrine of ,equilibrium1 without obtaining any sound principles concerning ,motion1 so they discovered the law of the ,reflection of light1 but had none but the most indistinct notions concerning ,refraction4 ,the extent of the principles which they really possessed is easily stated4 ,they knew that vision is performed by rays which proceed in straight lines1 and that these rays are reflected by certain surfaces 7mirrors7 in such manner that the angles which they make with the surface on each side are equal4 ,they drew various conclusions from these premises by the aid of geometry2 as1 for instance1 the convergence of rays which fall on a concave speculum4 ,it may be observed that the ,idea which is here introduced1 is that of visual rays1 or lines along which vision is produced and light carried4 ,this idea once clearly apprehended1 it was not difficult to show that these lines are straight lines1 both in the case of light and of sight4 ,in the beginning of ,euclid's ,treatise on ,optics1 some of the arguments are mentioned by which this was established4 ,we are told in the ,proem1 ,in explaining what concerns the sight1 he adduced certain arguments from which he inferred that all light is carried in straight lines4 ,the greatest proof of this is shadows1 and the bright spots which are produced by light coming through windows and cracks1 and which could not be1 except the rays of the sun were carried in straight lines4 ,so in fires1 the shadows are greater than the bodies if the fire be small1 but less than the bodies if the fire be greater4 ,a clear comprehension of the principle would lead to the perception of innumerable proofs of its truth on every side4 ,the ,law of ,equality of ,angles of ,incidence and ,reflection was not quite so easy to verify2 but the exact resemblance of the object and its image in a plane mirror1 7as the surface of still water1 for instance71 which is a consequence of this law1 would afford convincing evidence of its truth in that case1 and would be confirmed by the examination of other cases4 #aja ,with these true principles was mixed much error and indistinctness1 even in the best writers4 ,euclid1 and the ,platonists1 maintained that vision is exercised by rays proceeding from the eye1 not to it2 so that when we see objects1 we learn their form as a blind man would do1 by feeling it out with his staff4 ,this mistake1 however1 though ,montucla speaks severely of it1 was neither very discreditable nor very injurious2 for the mathematical conclusions on each supposition are necessarily the same4 ,another curious and false assumption is1 that those visual rays are not close together1 but separated by intervals1 like the fingers when the hand is spread4 ,the motive for this invention was the wish to account for the fact1 that in looking for a small object1 as a needle1 we often cannot see it when it is under our nose2 which it was conceived would be impossible if the visual rays reached to all points of the surface before us4 ,these errors would not have prevented the progress of the science4 ,but the ,aristotelian physics1 as usual1 contained speculations more essentially faulty4 ,aristotle's views led him to try to describe the kind of causation by which vision is produced1 instead of the laws by which it is exercised2 and the attempt consisted1 as in other subjects1 of indistinct principles1 and ill-combined facts4 ,according to him1 vision must be produced by a ,medium1--by something between the object and the eye1--for if we press the object on the eye1 we do not see it2 this ,medium is ,light1 or the transparent in action2 darkness occurs when the transparency is potential1 not actual2 color is not the absolute visible1 but something which is on the absolute visible2 color has the power of setting the transparent in action2 it is not1 however1 all colors that are seen by means of light1 but only the proper color of each object2 for some things1 as the heads1 and scales1 and eyes of fish1 are seen in the dark2 but they are not seen with their proper color49999#ab ,note #ab3 ,de ,anim4 ii4 9999#g4 ,in all this there is no steady adherence either to one notion1 or to one class of facts4 ,the distinction of ,power and ,act is introduced to modify the ,idea of ,transparency1 according to the formula of the school2 then ,color is made to be something unknown in addition to ,visibility2 and the distinction of proper and improper colors is assumed1 as sufficient to account for a phenomenon4 ,such classifications have in them nothing of which the mind can take steady hold2 nor is it difficult to see that they do not come under those #ajb conditions of successful physical speculation1 which we have laid down4 ,it is proper to notice more distinctly the nature of the ,geometrical ,propositions contained in ,euclid's work4 ,the ,optica contains ,propositions concerning ,vision and ,shadows1 derived from the principle that the rays of light are rectilinear3 for instance1 the ,proposition that the shadow is greater than the object1 if the illuminating body be less and vice versa4 ,the ,catoptrica contains ,propositions concerning the effects of ,reflection1 derived from the principle that the ,angles of ,incidence and ,reflection are equal3 as1 that in a convex mirror the object appears convex1 and smaller than the object4 ,we see here an example of the promptitude of the ,greeks in deduction4 ,when they had once obtained a knowledge of a principle1 they followed it to its mathematical consequences with great acuteness4 ,the subject of concave mirrors is pursued further in ,ptolemy's ,optics4 ,the ,greek writers also cultivated the subject of ,perspective speculatively1 in mathematical treatises1 as well as practically1 in pictures4 ,the whole of this theory is a consequence of the principle that vision takes place in straight lines drawn from the object to the eye4 ,the ancients were in some measure acquainted with the ,refraction as well as the ,reflection of ,light1 as ,i have shown in ,book ,,ix4 ,chap4 #b #b;d ,ed4 of the ,philosophy4 ,the current knowledge on this subject must have been very slight and confused2 for it does not appear to have enabled them to account for one of the simplest results of ,refraction1 the magnifying effect of convex transparent bodies4 ,i have noticed in the passage just referred to1 ,seneca's crude notions on this subject2 and in like manner ,ptolemy in his ,optics asserts that an object placed in water must always appear larger then when taken out4 ,aristotle uses the term 7,meteorol4 iii4 #b71 but apparently in a very vague manner4 ,it is not evident that he distinguished ,refraction from ,reflection4 ,his ,commentators however do distinguish these as and 4 ,see ,olympiodorus in ,schneider's ,eclog ,physic1 vol4 i4 p4 #cig4 ,and ,refraction had been the subject of special attention among the ,greek ,mathematicians4 ,archimedes had noticed 7as we learn from the same writer7 that in certain cases1 a ring which cannot be seen over the edge of the empty vessel in which it is placed1 becomes visible when the vessel is filled with water4 ,the same fact is stated in the ,optics of ,euclid4 ,we do not find this fact explained in that work as we now have it2 but in ,ptolemy's ,optics the fact is explained by a flexure of the visual ray3 it is #ajc noticed that this flexure is different at different angles from the perpendicular1 and there is an elaborate collection of measures of the flexure at different angles1 made by means of an instrument devised for the purpose4 ,there is also a collection of similar measures of the refraction when the ray passes from air to glass1 and when it passes from glass to water4 ,this part of ,ptolemy's work is1 ,i think1 the oldest extant example of a collection of experimental measures in any other subject than astronomy2 and in astronomy our measures are the result of observation rather than of experiment4 ,as ,delambre says 7,astron4 ,anc4 vol4 ii4 p4 #dbg71 ,on y voit des expriences de physique bien faites1 ce qui est sans exemple chez les anciens4 ,ptolemy's ,optical work was known only by ,roger ,bacon's references to it 7,opus ,majus1 p4 #bhf1 c47 till #ahaf2 but copies of ,latin translations of it were known to exist in the ,royal ,library at ,paris1 and in the ,bodleian at ,oxford4 ,delambre has given an account of the contents of the ,paris copy in his ,astron4 ,anc4 ii4 #dad1 and in the ,connoissance des ,temps for #ahaf2 and ,prof4 ,rigaud's account of the ,oxford copy is given in the article ,optics1 in the ,encyclopdia ,britannica4 ,ptolemy shows great sagacity in applying the notion of ,refraction to the explanation of the displacement of astronomical objects which is produced by the atmosphere1--,astronomical ,refraction1 as it is commonly called4 ,he represents the visual ray as refracted in passing from the ether1 which is above the air1 into the air2 the air being bounded by a spherical surface which has for its centre the centre of all the elements1 the centre of the earth2 and the refraction being a flexure towards the line drawn perpendicular to this surface4 ,he thus constructs1 says ,delambre1 the same figure on which ,cassini afterwards founded the whole of his theory2 and gives a theory more complete than that of any astronomer previous to him4 ,tycho1 for instance1 believed that astronomical refraction was caused only by the vapors of the atmosphere1 and did not exist above the altitude of #de4 ,cleomedes1 about the time of ,augustus1 had guessed at ,refraction1 as an explanation of an eclipse in which the sun and moon are both seen at the same time4 ,is it not possible1 he says1 that the ray which proceeds from the eye and traverses moist and cloudy air may bend downwards to the sun1 even when he is below the horizon8 ,and ,sextus ,empiricus1 a century later1 says1 ,the air being dense1 by the refraction of the visual ray1 a constellation may be seen above the horizon when it is yet below the horizon4 ,but from what follows1 it #ajd appears doubtful whether he clearly distinguished ,refraction and ,reflection4 ,in order that we may not attach too much value to the vague expressions of ,cleomedes and ,sextus ,empiricus1 we may remark that ,cleomedes conceives such an eclipse as he describes not to be possible1 though he offers an explanation of it if it be3 7the fact must really occur whenever the moon is seen in the horizon in the middle of an eclipse37 and that ,sextus ,empiricus gives his suggestion of the effect of refraction as an argument why the ,chaldean astrology cannot be true1 since the constellation which appears to be rising at the moment of a birth is not the one which is truly rising4 ,the ,chaldeans might have answered1 says ,delambre1 that the star begins to shed its influence1 not when it is really in the horizon1 but when its light is seen4 7,ast4 ,anc4 vol4 i4 p4 #bca1 and vol4 ii4 p4 #edh47 ,it has been said that ,vitellio1 or ,vitello1 whom we shall hereafter have to speak of in the history of ,optics1 took his ,tables of ,refractions from ,ptolemy4 ,this is contrary to what ,delambre states4 ,he says that ,vitello may be accused of plagiarism from ,alhazen1 and that ,alhazen did not borrow his ,tables from ,ptolemy4 ,roger ,bacon had said 7,opus ,majus1 p4 #bhh71 ,ptolemus in libro de ,opticis1 id est1 de ,aspectibus1 seu in ,perspectiv su1 qui prius quam ,alhazen dedit hanc sententiam1 quam a ,ptolemo acceptam ,alhazen exposuit4 ,this refers only to the opinion that visual rays proceed from the eye4 ,but this also is erroneous2 for ,alhazen maintains the contrary3 ,visio fit radiis a visibili extrinsecus ad visum manantibus4 7,opt4 ,lib4 i4 cap4 #e47 ,vitello says of his ,table of ,refractions1 ,acceptis instrumentaliter1 prout potuimus propinquius1 angulis omnium refractionum 4 4 4 invenimus quod semper iidem sunt anguli refractionum3 4 4 4 secundum hoc fecimus has tabulas4 ,having measured1 by means of instruments1 as exactly as we could1 the whole range of the angles of refraction1 we found that the refraction is always the same for the same angle2 and hence we have constructed these ,tables4 #aje ,,chapter ,,iii4 ,,earliest ,,stages ,,of ,,harmonics4 ,,among the ancients1 the science of ,music was an application of ,arithmetic1 as ,optics and ,mechanics were of ,geometry4 ,the story which is told concerning the origin of their arithmetical music1 is the following1 as it stands in the ,arithmetical ,treatise of ,nicomachus4 ,pythagoras1 walking one day1 meditating on the means of measuring musical notes1 happened to pass near a blacksmith's shop1 and had his attention arrested by hearing the hammers1 as they struck the anvil1 produce the sounds which had a musical relation to each other4 ,on listening further1 he found that the intervals were a ,fourth1 a ,fifth1 and an ,octave2 and on weighing the hammers1 it appeared that the one which gave the ,octave was one-half the heaviest1 the one which gave the ,fifth was two-thirds1 and the one which gave the ,fourth was three-quarters4 ,he returned home1 reflected upon this phenomenon1 made trials1 and finally discovered1 that if he stretched musical strings of equal lengths1 by weights which have the proportion of one-half1 two-thirds1 and three-fourths1 they produced intervals which were an ,octave1 a ,fifth1 and a ,fourth4 ,this observation gave an arithmetical measure of the principal ,musical ,intervals1 and made ,music an arithmetical subject of speculation4 ,this story1 if not entirely a philosophical fable1 is undoubtedly inaccurate2 for the musical intervals thus spoken of would not be produced by striking with hammers of the weights there stated4 ,but it is true that the notes of strings have a definite relation to the forces which stretch them2 and this truth is still the groundwork of the theory of musical concords and discords4 ,nicomachus says that ,pythagoras found the weights to be1 as ,i have mentioned1 in the proportion of #ab1 #f1 #h1 #i2 and the intervals1 an ,octave1 corresponding to the proportion #ab to #f1 or #b to #a2 a ,fifth1 corresponding to the proportion #ab to #h1 or #c to #b2 and a ,fourth1 corresponding to the proportion #ab to #i1 or #d to #c4 ,there is no doubt that this statement of the ancient writer is inexact as to the physical fact1 for the rate of vibration of a string1 on which its note depends1 is1 #ajf other things being equal1 not as the weight1 but as the square root of the weight4 ,but he is right as to the essential point1 that those ratios of #b to #a1 #c to #b1 and #d to #c1 are the characteristic ratios of the ,octave1 ,fifth1 and ,fourth4 ,in order to produce these intervals1 the appended weights must be1 not as #ab1 #i1 #h1 and #f1 but as #ab1 #f1 #e1 and #c4 ,the numerical relations of the other intervals of the musical scale1 as well as of the ,octave1 ,fifth1 and ,fourth1 were discovered by the ,greeks4 ,thus they found that the proportion in a ,major ,third was #e to #d2 in a ,minor ,third1 #f to #e2 in a ,major ,tone1 #i to #h2 in a ,semitone or ,diesis1 #af to #ae4 ,they even went so far as to determine the ,comma1 in which the interval of two notes is so small that they are in the proportion of #ha to #hj4 ,this is the interval between two notes1 each of which may be called the ,seventeenth above the key-note2--the one note being obtained by ascending a ,fifth four times over2 the other being obtained by ascending through two ,octaves and a ,major ,third4 ,the want of exact coincidence between these two notes is an inherent arithmetical imperfection in the musical scale1 of which the consequences are very extensive4 ,the numerical properties of the musical scale were worked out to a very great extent by the ,greeks1 and many of their ,treatises on this subject remain to us4 ,the principal ones are the seven authors published by ,meibomius4#bb ,these arithmetical elements of ,music are to the present day important and fundamental portions of the ,science of ,harmonics4 ,note #bb3 ,antiqu ,music ,scriptores septem1 #afeb4 ,it may at first appear that the truth1 or even the possibility of this history1 by referring the discovery to accident1 disproves our doctrine1 that this1 like all other fundamental discoveries1 required a distinct and well-pondered ,idea as its condition4 ,in this1 however1 as in all cases of supposed accidental discoveries in science1 it will be found1 that it was exactly the possession of such an ,idea which made the accident possible4 ,pythagoras1 assuming the truth of the tradition1 must have had an exact and ready apprehension of those relations of musical sounds1 which are called respectively an ,octave1 a ,fifth1 and a ,fourth4 ,if he had not been able to conceive distinctly this relation1 and to apprehend it when heard1 the sounds of the anvil would have struck his ears to no more purpose than they did those of the smiths themselves4 ,he #ajg must have had1 too1 a ready familiarity with numerical ratios2 and1 moreover 7that in which1 probably1 his superiority most consisted71 a disposition to connect one notion with the other--the musical relation with the arithmetical1 if it were found possible4 ,when the connection was once suggested1 it was easy to devise experiments by which it might be confirmed4 ,the philosophers of the ,pythagorean ,school1#cb and in particular1 ,lasus of ,hermione1 and ,hippasus of ,metapontum1 made many such experiments upon strings2 varying both their lengths and the weights which stretched them2 and also upon vessels filled with water1 in a greater or less degree4 ,and thus was established that connection of the ,idea with the ,fact1 which this ,science1 like all others1 requires4 ,note #cb3 ,montucla1 iii4 #aj4 ,i shall quit the ,physical ,sciences of ,ancient ,greece1 with the above brief statement of the discovery of the fundamental principles which they involved2 not only because such initial steps must always be the most important in the progress of science1 but because1 in reality1 the ,greeks made no advances beyond these4 ,there took place among them no additional inductive processes1 by which new facts were brought under the dominion of principles1 or by which principles were presented in a more comprehensive shape than before4 ,their advance terminated in a single stride4 ,archimedes had stirred the intellectual world1 but had not put it in progressive motion3 the science of ,mechanics stopped where he left it4 ,and though1 in some objects1 as in ,harmonics1 much was written1 the works thus produced consisted of deductions from the fundamental principles1 by means of arithmetical calculations2 occasionally modified1 indeed1 by reference to the pleasures which music1 as an art1 affords1 but not enriched by any new scientific truths4 #c;d ,ed4 ,we should1 however1 quit the philosophy of the ancient ,greeks without a due sense of the obligations which ,physical ,science in all succeeding ages owes to the acute and penetrating spirit in which their inquiries in that region of human knowledge were conducted1 and to the large and lofty aspirations which were displayed1 even in their failure1 if we did not bear in mind both the multifarious and comprehensive character of their attempts1 and some of the causes which limited their progress in positive science4 ,they speculated and #ajh theorized under a lively persuasion that a ,science of every part of nature was possible1 and was a fit object for the exercise of man's best faculties2 and they were speedily led to the conviction that such a science must clothe its conclusions in the language of mathematics4 ,this conviction is eminently conspicuous in the writings of ,plato4 ,in the ,republic1 in the ,epinomis1 and above all in the ,timus1 this conviction makes him return1 again and again1 to a discussion of the laws which had been established or conjectured in his time1 respecting ,harmonics and ,optics1 such as we have seen1 and still more1 respecting ,astronomy1 such as we shall see in the next ,book4 ,probably no succeeding step in the discovery of the ,laws of ,nature was of so much importance as the full adoption of this pervading conviction1 that there must be ,mathematical ,laws of ,nature1 and that it is the business of ,philosophy to discover these ,laws4 ,this conviction continues1 through all the succeeding ages of the history of science1 to be the animating and supporting principle of scientific investigation and discovery4 ,and1 especially in ,astronomy1 many of the erroneous guesses which the ,greeks made1 contain1 if not the germ1 at least the vivifying life-blood1 of great truths1 reserved for future ages4 ,moreover1 the ,greeks not only sought such theories of special parts of nature1 but a general ,theory of the ,universe4 ,an essay at such a theory is the ,timus of ,plato2 too wide and too ambitious an attempt to succeed at that time2 or1 indeed1 on the scale on which he unfolds it1 even in our time2 but a vigorous and instructive example of the claim which man's ,intellect feels that it may make to understand the universal frame of things1 and to render a reason for all that is presented to it by the outward senses4 ,further2 we see in ,plato1 that one of the grounds of the failure in this attempt1 was the assumption that the reason why every thing is what it is and as it is1 must be that so it is best1 according to some view of better or worse attainable by man4 ,socrates1 in his dying conversation1 as given in the ,phdo1 declares this to have been what he sought in the philosophy of his time2 and tells his friends that he turned away from the speculations of ,anaxagoras because they did not give him such reasons for the constitution of the world2 and ,plato's ,timus is1 in reality1 an attempt to supply this deficiency1 and to present a ,theory of the ,universe1 in which every thing is accounted for by such reasons4 ,though this is a failure1 it is a noble as well as an instructive failure4 #aji ,,book ,,iii4 ,,history ,,of ,,greek ,,astronomy4 1 1 1 ' 1 1 4--,,plato1 ,epinomis1 p4 #ihh4 ,nor should any ,greek have any misgiving of this kind2 that it is not fitting for us to inquire narrowly into the operations of ,superior ,powers1 such as those by which the motions of the heavenly bodies are produced3 but1 on the contrary1 men should consider that the ,divine ,powers never act without purpose1 and that they know the nature of man3 they know that by their guidance and aid1 man may follow and comprehend the lessons which are vouchsafed him on such subjects4 #aaa ,,introduction4 ,,the earliest and fundamental conceptions of men respecting the objects with which ,astronomy is concerned1 are formed by familiar processes of thought1 without appearing to have in them any thing technical or scientific4 ,days1 ,years1 ,months1 the ,sky1 the ,constellations1 are notions which the most uncultured and incurious minds possess4 ,yet these are elements of the ,science of ,astronomy4 ,the reasons why1 in this case alone1 of all the provinces of human knowledge1 men were able1 at an early and unenlightened period1 to construct a science out of the obvious facts of observation1 with the help of the common furniture of their minds1 will be more apparent in the course of the philosophy of science3 but ,i may here barely mention two of these reasons4 ,they are1 first1 that the familiar act of thought1 exercised for the common purposes of life1 by which we give to an assemblage of our impressions such a unity as is implied in the above notions and terms1 a ,month1 a ,year1 the ,sky1 and the like1 is1 in reality1 an inductive act1 and shares the nature of the processes by which all sciences are formed2 and1 in the next place1 that the ideas appropriate to the induction in this case1 are those which1 even in the least cultivated minds1 are very clear and definite2 namely1 the ideas of ,space and ,figure1 ,time and ,number1 ,motion and ,recurrence4 ,hence1 from their first origin1 the modifications of those ideas assume a scientific form4 ,we must now trace in detail the peculiar course which1 in consequence of these causes1 the knowledge of man respecting the heavenly bodies took1 from the earliest period of his history4 #aab ,,chapter ,i4 ,,earliest ,,stages ,,of ,,astronomy4 ,sect4 #a4--;,formation of the ,notion of a ,year4 ,,the notion of a ,day is early and obviously impressed upon man in almost any condition in which we can imagine him4 ,the recurrence of light and darkness1 of comparative warmth and cold1 of noise and silence1 of the activity and repose of animals2--the rising1 mounting1 descending1 and setting of the sun2--the varying colors of the clouds1 generally1 notwithstanding their variety1 marked by a daily progression of appearances2--the calls of the desire of food and of sleep in man himself1 either exactly adjusted to the period of this change1 or at least readily capable of being accommodated to it2--the recurrence of these circumstances at intervals1 equal1 so far as our obvious judgment of the passage of time can decide2 and these intervals so short that the repetition is noticed with no effort of attention or memory2--this assemblage of suggestions makes the notion of a ,day necessarily occur to man1 if we suppose him to have the conception of ,time1 and of ,recurrence4 ,he naturally marks by a term such a portion of time1 and such a cycle of recurrence2 he calls each portion of time1 in which this series of appearances and occurrences come round1 a ,day2 and such a group of particulars are considered as appearing or happening in the same day4 ,a ,year is a notion formed in the same manner2 implying in the same way the notion of recurring facts2 and also the faculty of arranging facts in time1 and of appreciating their recurrence4 ,but the notion of a ,year1 though undoubtedly very obvious1 is1 on many accounts1 less so than that of a ,day4 ,the repetition of similar circumstances1 at equal intervals1 is less manifest in this case1 and the intervals being much longer1 some exertion of memory becomes requisite in order that the recurrence may be perceived4 ,a child might easily be persuaded that successive years were of unequal length2 or1 if the summer were cold1 and the spring and autumn warm1 might be made to believe1 if all who spoke in its hearing agreed to support the delusion1 that one year was two4 ,it would be impossible to practise such a deception with regard to the day1 without the use of some artifice beyond mere words4 #aac ,still1 the recurrence of the appearances which suggest the notion of a ,year is so obvious1 that we can hardly conceive man without it4 ,but though1 in all climes and times1 there would be a recurrence1 and at the same interval in all1 the recurring appearances would be extremely different in different countries2 and the contrasts and resemblances of the seasons would be widely varied4 ,in some places the winter utterly alters the face of the country1 converting grassy hills1 deep leafy woods of various hues of green1 and running waters1 into snowy and icy wastes1 and bare snow-laden branches2 while in others1 the field retains its herbage1 and the tree its leaves1 all the year2 and the rains and the sunshine alone1 or various agricultural employments quite different from ours1 mark the passing seasons4 ,yet in all parts of the world the yearly cycle of changes has been singled out from all others1 and designated by a peculiar name4 ,the inhabitant of the equatorial regions has the sun vertically over him at the end of every period of six months1 and similar trains of celestial phenomena fill up each of these intervals1 yet we do not find years of six months among such nations4 ,the ,arabs alone1#ac who practise neither agriculture nor navigation1 have a year depending upon the moon only2 and borrow the word from other languages1 when they speak of the solar year4 ,note #ac3 ,ideler1 ,berl4 ,trans4 #ahac1 p4 #ea4 ,in general1 nations have marked this portion of time by some word which has a reference to the returning circle of seasons and employments4 ,thus the ,latin annus signified a ring1 as we see in the derivative annulus3 the ,greek term implies something which returns into itself3 and the word as it exists in ,teutonic languages1 of which our word year is an example1 is said to have its origin in the word yra which means a ring in ,swedish1 and is perhaps connected with the ,latin gyrus4 ,sect4 #b4--;,fixation of the ,civil ,year4 ,,the year1 considered as a recurring cycle of seasons and of general appearances1 must attract the notice of man as soon as his attention and memory suffice to bind together the parts of a succession of the length of several years4 ,but to make the same term imply a certain fixed number of days1 we must know how many days the cycle of the seasons occupies2 a knowledge which requires faculties and artifices beyond what we have already mentioned4 ,for instance1 men cannot reckon as far as any number at all approaching the number of days in the year1 without possessing a system of numeral terms1 and methods #aad of practical numeration on which such a system of terms is always founded4#bc ,the ,south ,american ,indians1 the ,koussa ,caffres and ,hottentots1 and the natives of ,new ,holland1 all of whom are said to be unable to reckon further than the fingers of their hands and feet1#cc cannot1 as we do1 include in their notion of a year the fact of its consisting of #cfe days4 ,this fact is not likely to be known to any nation except those which have advanced far beyond that which may be considered as the earliest scientific process which we can trace in the history of the human race1 the formation of a method of designating the successive numbers to an indefinite extent1 by means of names1 framed according to the decimal1 quinary1 or vigenary scale4 ,note #bc3 ,arithmetic in ,encyc4 ,metrop4 7by ,dr4 ,peacock71 ,art4 #h4 ,note #cc3 ,ibid4 ,art4 #cb4 ,but even if we suppose men to have the habit of recording the passage of each day1 and of counting the score thus recorded1 it would be by no means easy for them to determine the exact number of days in which the cycle of the seasons recurs2 for the indefiniteness of the appearances which mark the same season of the year1 and the changes to which they are subject as the seasons are early or late1 would leave much uncertainty respecting the duration of the year4 ,they would not obtain any accuracy on this head1 till they had attended for a considerable time to the motions and places of the sun2 circumstances which require more precision of notice than the general facts of the degrees of heat and light4 ,the motions of the sun1 the succession of the places of his rising and setting at different times of the year1 the greatest heights which he reaches1 the proportion of the length of day and night1 would all exhibit several cycles4 ,the turning back of the sun1 when he had reached the greatest distance to the south or to the north1 as shown either by his rising or by his height at noon1 would perhaps be the most observable of such circumstances4 ,accordingly the 1 the turnings of the sun1 are used repeatedly by ,hesiod as a mark from which he reckons the seasons of various employments4 ,fifty days1 he says1 after the turning of the sun1 is a seasonable time for beginning a voyage4#dc ,note #dc3 4--,op4 et ,dies1 #ffa4 ,the phenomena would be different in different climates1 but the recurrence would be common to all4 ,any one of these kinds of phenomena1 noted with moderate care for a year1 would show what was the number of days of which a year consisted2 and if several years #aae were included in the interval through which the scrutiny extended1 the knowledge of the length of the year so acquired would be proportionally more exact4 ,besides those notices of the sun which offered exact indications of the seasons1 other more indefinite natural occurrences were used2 as the arrival of the swallow 77 and the kite 771 ,the birds1 in ,aristophanes' play of that name1 mention it as one of their offices to mark the seasons2 ,hesiod similarly notices the cry of the crane as an indication of the departure of winter4#ec ,note #ec3 ,ideler1 i4 #bdj4 ,among the ,greeks the seasons were at first only summer and winter 7 and 71 the latter including all the rainy and cold portion of the year4 ,the winter was then subdivided into the and 7winter proper and spring71 and the summer1 less definitely1 into and 7summer and autumn74 ,tacitus says that the ,germans knew neither the blessings nor the name of autumn1 ,autumni perinde nomen ac bona ignorantur4 ,yet harvest1 herbst1 is certainly an old ,german word4#fc ,note #fc3 ,ib4 i4 #bdc4 ,in the same period in which the sun goes through his cycle of positions1 the stars also go through a cycle of appearances belonging to them2 and these appearances were perhaps employed at as early a period as those of the sun1 in determining the exact length of the year4 ,many of the groups of fixed stars are readily recognized1 as exhibiting always the same configuration2 and particular bright stars are singled out as objects of attention4 ,these are observed1 at particular seasons1 to appear in the west after sunset2 but it is noted that when they do this1 they are found nearer and nearer to the sun every successive evening1 and at last disappear in his light4 ,it is observed also1 that at a certain interval after this1 they rise visibly before the dawn of day renders the stars invisible2 and after they are seen to do this1 they rise every day at a longer interval before the sun4 ,the risings and settings of the stars under these circumstances1 or under others which are easily recognized1 were1 in countries where the sky is usually clear1 employed at an early period to mark the seasons of the year4 ,eschylus#gc makes ,prometheus mention this among the benefits of which #aaf he1 the teacher of arts to the earliest race of men1 was the communicator4 ,note #gc3 1 ' 1 ' 1 1 4--,prom4 ,v4 #ded4 ,thus1 for instance1 the rising#hc of the ,pleiades in the evening was a mark of the approach of winter4 ,the rising of the waters of the ,nile in ,egypt coincided with the heliacal rising of ,sirius1 which star the ,egyptians called ,sothis4 ,even without any artificial measure of time or position1 it was not difficult to carry observations of this kind to such a degree of accuracy as to learn from them the number of days which compose the year2 and to fix the precise season from the appearance of the stars4 ,note #hc3 ,ideler 7,chronol4 i4 #bdb7 says that this rising of the ,pleiades took place at a time of the year which corresponds to our #aath ,may1 and the setting to the #bjth ,october2 but this does not agree with the forty days of their being concealed1 which1 from the context1 must mean1 ,i conceive1 the interval between their setting and rising4 ,pliny1 however1 says1 ,vergiliarum exortu stas incipit1 occasu hiems2 semestri spatio intra se messes vindemiasque et omnium maturitatem complex4 7,h4 ,n4 xviii4 #fi47 ,the autumn of the ,greeks1 1 was earlier than our autumn1 for ,homer calls ,sirius 1 which rose at the end of ,july4 ,a knowledge concerning the stars appears to have been first cultivated with the last-mentioned view1 and makes its first appearance in literature with this for its object4 ,thus ,hesiod directs the husbandman when to reap by the rising1 and when to plough by the setting of the ,pleiades4#ic ,in like manner ,sirius1#ajc ,arcturus1#aac the ,hyades and ,orion1#abc are noticed4 #aag ,note #ic3 4 ' 1 4 1 4 ,op4 et ,dies1 l4 #cha4 ,note #ajc3 ,ib4 l4 #dac4 ,note #aac3 ' ' '1 1 ' 1 4 ,op4 et ,dies1 l4 #efb4 ' ' 1 ' 4 ,ib4 #fjg4 ,note #abc3 4 4 4 4 4 4 4 4 ,ib4 #fab4 ,these methods were employed to a late period1 because the ,greek months1 being lunar1 did not correspond to the seasons4 ,tables of such motions were called 4--,ideler1 ,hist4 ,untersuchungen1 p4 #bji4 ,by such means it was determined that the year consisted1 at least1 nearly1 of #cfe days4 ,the ,egyptians1 as we learn from ,herodotus1#acc claimed the honor of this discovery4 ,the priests informed him1 he says1 that the ,egyptians were the first men who discovered the year1 dividing it into twelve equal parts2 and this they asserted that they discovered from the stars4 ,each of these parts or months consisted of #cj days1 and they added #e days more at the end of the year1 and thus the circle of the seasons come round4 ,it seems1 also1 that the ,jews1 at an early period1 had a similar reckoning of time1 for the ,deluge which continued #aej days 7,gen4 vii4 #bd71 is stated to have lasted from the #agth day of the second month 7,gen4 vii4 #aa7 to the #agth day of the seventh month 7,gen4 viii4 #d71 that is1 #e months of #cj days4 ,note #acc3 ,ib4 ii4 #d4 ,a year thus settled as a period of a certain number of days is called a ,civil ,year4 ,it is one of the earliest discoverable institutions of ,states possessing any germ of civilization2 and one of the earliest portions of human systematic knowledge is the discovery of the length of the civil year1 so that it should agree with the natural year1 or year of the seasons4 ,sect4 #c4--;,correction of the ,civil ,year4 7,julian ,calendar47 ,,in reality1 by such a mode of reckoning as we have described1 the circle of the seasons would not come round exactly4 ,the real length of the year is very nearly #cfe days and a quarter4 ,if a year of #cfe days were used1 in four years the year would begin a day too soon1 when considered with reference to the sun and stars2 and in #fj years it would begin #ae days too soon3 a quantity perceptible to the loosest degree of attention4 ,the civil year would be found not to coincide with the year of the seasons2 the beginning of the former would take place at different periods of the latter2 it would wander into various seasons1 instead of remaining fixed to the same season2 the term year1 and any number of years1 would become ambiguous3 some correction1 at least some comparison1 would be requisite4 ,we do not know by whom the insufficiency of the year of #cfe days was first discovered2#adc we find this knowledge diffused among all civilized nations1 and various artifices used in making the correction4 ,the method which we employ1 and which consists in reckoning an #aah additional day at the end of ,february every fourth or leap year1 is an example of the principle of intercalation1 by which the correction was most commonly made4 ,methods of intercalation for the same purpose were found to exist in the new world4 ,the ,mexicans added #ac days at the end of every #eb years4 ,the method of the ,greeks was more complex 7by means of the octateris or cycle of #h years72 but it had the additional object of accommodating itself to the motions of the moon1 and therefore must be treated of hereafter4 ,the ,egyptians1 on the other hand1 knowingly permitted their civil year to wander1 at least so far as their religious observances were concerned4 ,they do not wish1 says ,geminus1#aec the same sacrifices of the gods to be made perpetually at the same time of the year1 but that they should go through all the seasons1 so that the same feast may happen in summer and winter1 in spring and autumn4 ,the period in which any festival would thus pass through all the seasons of the year is #adfa years2 for #adfj years of #cfe days are equal to #adfa years of #cfe days4 ,this period of #adfa years is called the ,sothic ,period1 from ,sothis1 the name of the ,dog-star1 by which their fixed year was determined2 and for the same reason it is called the ,canicular ,period4#afc ,note #adc3 ,syncellus 7,chronographia1 p4 #abc7 says that according to the legend1 it was ,king ,aseth who first added the #e additional days to #cfj1 for the year1 in the eighteenth century1 ,b4 ,c4 ,note #aec3 ,uranol4 p4 #cc4 ,note #afc3 ,censorinus de ,die ,natali1 c4 #ah4 ,other nations did not regulate their civil year by intercalation at short intervals1 but rectified it by a reform when this became necessary4 ,the ,persians are said to have added a month of #cj days every #abj years4 ,the ,roman calendar1 at first very rude in its structure1 was reformed by ,numa1 and was directed to be kept in order by the perpetual interposition of the augurs4 ,this1 however1 was1 from various causes1 not properly done2 and the consequence was1 that the reckoning fell into utter disorder1 in which state it was found by ,julius ,csar1 when he became dictator4 ,by the advice of ,sosigenes1 he adopted the mode of intercalation of one day in #d years1 which we still retain2 and in order to correct the derangement which had already been produced1 he added #ij days to a year of the usual length1 which thus became what was called the year of confusion4 ,the ,julian ,calendar1 thus reformed1 came into use1 ,january #a1 ,b4 ,c4 #de4 ,sect4 #d4--;,attempts at the ,fixation of the ,month4 ,,the circle of changes through which the moon passes in about thirty days1 is marked1 in the earliest stages of language1 by a word which implies the space of time which one such circle occupies2 just #aai as the circle of changes of the seasons is designated by the word year4 ,the lunar changes are1 indeed1 more obvious to the sense1 and strike a more careless person1 than the annual2 the moon1 when the sun is absent1 is almost the sole natural object which attracts our notice2 and we look at her with a far more tranquil and agreeable attention than we bestow on any other celestial object4 ,her changes of form and place are definite and striking to all eyes2 they are uninterrupted1 and the duration of their cycle is so short as to require no effort of memory to embrace it4 ,hence it appears to be more easy1 and in earlier stages of civilization more common1 to count time by moons than by years4 ,the words by which this period of time is designated in various languages1 seem to refer us to the early history of language4 ,our word month is connected with the word moon1 and a similar connection is noticeable in the other branches of the ,teutonic4 ,the ,greek word in like manner is related to 1 which though not the common word for the moon1 is found in ,homer with that signification4 ,the ,latin word mensis is probably connected with the same group4#agc ,note #agc3 ,cicero derives this word from the verb to measure3 quia mensa spatia conficiunt1 menses nominantur2 and other etymologists1 with similar views1 connect the above-mentioned words with the ,hebrew manah1 to measure 7with which the ,arabic word almanach is connected74 ,such a derivation would have some analogy with that of annus1 c41 noticed above3 but if we are to attempt to ascend to the earliest condition of language1 we must conceive it probable that men would have a name for a most conspicuous visible object1 the moon1 before they would have a verb denoting the very abstract and general notion1 to measure4 ,the month is not any exact number of days1 being more than #bi1 and less than #cj4 ,the latter number was first tried1 for men more readily select numbers possessing some distinction of regularity4 ,it existed for a long period in many countries4 ,a very few months of #cj days1 however1 would suffice to derange the agreement between the days of the months and the moon's appearance4 ,a little further trial would show that months of #bi and #cj days alternately1 would preserve1 for a considerable period1 this agreement4 ,the ,greeks adopted this calendar1 and1 in consequence1 considered the days of their month as representing the changes of the moon3 the last day of the month was called 1 the old and new as belonging to both the waning and the reappearing moon3#ahc and their #abj festivals and sacrifices1 as determined by the calendar1 were conceived to be necessarily connected with the same periods of the cycles of the sun and moon4 ,the laws and the oracles1 says ,geminus1 which directed that they should in sacrifices observe three things1 months1 days1 years1 were so understood4 ,with this persuasion1 a correct system of intercalation became a religious duty4 ,note #ahc3 ,aratus says of the moon1 in a passage quoted by ,geminus1 p4 #cc3 ' 1 ,as still her shifting visage changing turns1 ,by her we count the monthly round of morns4 ,the above rule of alternate months of #bi and #cj days1 supposes the length of the months #bi days and a half1 which is not exactly the length of a lunar month4 ,accordingly the ,months and the ,moon were soon at variance4 ,aristophanes1 in ,the ,clouds1 makes the ,moon complain of the disorder when the calendar was deranged4 1 ' ' ' 4 ,nubes1 #fae-ai4 ,,chorus ,,of ,,clouds4 ,the ,moon by us to you her greeting sends1 ,but bids us say that she's an ill-used moon1 ,and takes it much amiss that you should still ,shuffle her days1 and turn them topsy-turvy3 ,and that the gods 7who know their feast-days well7 ,by your false count are sent home supperless1 ,and scold and storm at her for your neglect4#aic ,note #aic3 ,this passage is supposed by the commentators to be intended as a satire upon those who had introduced the cycle of ,meton 7spoken of in ,sect4 #e71 which had been done at ,athens a few years before ,the ,clouds was acted4 ,the correction of this inaccuracy1 however1 was not pursued separately1 but was combined with another object1 the securing a correspondence between the lunar and solar years1 the main purpose of all early cycles4 ,sect4 #e4--;,invention of ,lunisolar ,years4 ,,there are #ab complete lunations in a year2 which according to the above rule 7of #bi days to a lunation7 would make #ced days1 leaving #ab days of difference between such a lunar year and a solar year4 ,it is said that1 at an early period1 this was attempted to be corrected by interpolating a month of #cj days every alternate year2 and ,herodotus#bjc relates a conversation of ,solon1 implying a still ruder mode of #aba intercalation4 ,this can hardly be considered as an improvement in the ,greek calendar already described4 ,note #bjc3 ,b4 i4 c4 #ae4 ,the first cycle which produced any near correspondence of the reckoning of the moon and the sun1 was the ,octateris1 or period of #h years3 #h years of #ced days1 together with #c months of #cj days each1 making up 7in #ii lunations7 #bibb days2 which is exactly the amount of #h years of #cfe days each4 ,hence this period would answer its purpose1 so far as the above lengths of the lunar and solar cycles are exact2 and it might assume various forms1 according to the manner in which the three intercalary months were distributed4 ,the customary method was to add a thirteenth month at the end of the third1 fifth1 and eighth year of the cycle4 ,this period is ascribed to various persons and times2 probably different persons proposed different forms of it4 ,dodwell places its introduction in the #eith ,olympiad1 or in the #fth century1 ,b4 ,c43 but ,ideler thinks the astronomical knowledge of the ,greeks of that age was too limited to allow of such a discovery4 ,this cycle1 however1 was imperfect4 ,the duration of #ii lunations is something more than #bibb days2 it is more nearly #bibc2 hence in #af years there was a deficiency of #c days1 with regard to the motions of the moon4 ,this cycle of #af years 7,heccdecateris71 with #c interpolated days at the end1 was used1 it is said1 to bring the calculation right with regard to the moon2 but in this way the origin of the year was displaced with regard to the sun4 ,after #aj revolutions of this cycle1 or #afj years1 the interpolated days would amount to #cj1 and hence the end of the lunar year would be a month in advance of the end of the solar4 ,by terminating the lunar year at the end of the preceding month1 the two years would again be brought into agreement3 and we have thus a cycle of #afj years4#bac ,note #bac3 ,geminus4 ,ideler4 ,this cycle of #afj years1 however1 was calculated from the cycle of #af years2 and it was probably never used in civil reckoning2 which the others1 or at least that of #h years1 appear to have been4 ,the cycles of #af and #afj years were corrections of the cycle of #h years2 and were readily suggested1 when the length of the solar and lunar periods became known with accuracy4 ,but a much more exact cycle1 independent of these1 was discovered and introduced by ,meton1#bbc #dcb years ,b4 ,c4 ,this cycle consisted of #ai years1 and is so correct and convenient1 that it is in use among ourselves to this day4 ,the time occupied by #ai years1 and by #bce lunations1 is very nearly the same2 #abb 7the former time is less than #fidj days by #i hours1 the latter1 by #g hours74 ,hence1 if the #ai years be divided into #bce months1 so as to agree with the changes of the moon1 at the end of that period the same succession may begin again with great exactness4 ,note #bbc3 ,ideler1 ,hist4 ,unters4 p4 #bjh4 ,in order that #bce months1 of #cj and #bi days1 may make up #fidj days1 we must have #abe of the former1 which were called full months1 and #aaj of the latter1 which were termed hollow4 ,an artifice was used in order to distribute #aaj hollow months among #fidj days4 ,it will be found that there is a hollow month for each #fc days nearly4 ,hence if we reckon #cj days to every month1 but at every #fc;d day leap over a day in the reckoning1 we shall1 in the #ai years1 omit #aaj days2 and this accordingly was done4 ,thus the #c;d day of the #c;d month1 the #fth day of the #eth month1 the #ith day of the #gth1 must be omitted1 so as to make these months hollow4 ,of the #ai years1 seven must consist of #ac months2 and it does not appear to be known according to what order these seven years were selected4 ,some say they were the #c;d1 #fth1 #hth1 #aath1 #adth1 #agth1 and #aith2 others1 the #c;d1 #eth1 #hth1 #aath1 #acth1 #afth1 and #aith4 ,the near coincidence of the solar and lunar periods in this cycle of #ai years1 was undoubtedly a considerable discovery at the time when it was first accomplished4 ,it is not easy to trace the way in which such a discovery was made at that time2 for we do not even know the manner in which men then recorded the agreement or difference between the calendar day and the celestial phenomenon which ought to correspond to it4 ,it is most probable that the length of the month was obtained with some exactness by the observation of eclipses1 at considerable intervals of time from each other2 for eclipses are very noticeable phenomena1 and must have been very soon observed to occur only at new and full moon4#bcc ,note #bcc3 ,thucyd4 vii4 #ej4 4 iv4 #eb1 4 ii4 #bh4 7 7 1 4 ,the exact length of a certain number of months being thus known1 the discovery of a cycle which should regulate the calendar with sufficient accuracy would be a business of arithmetical skill1 and would depend1 in part1 on the existing knowledge of arithmetical methods2 but in making the discovery1 a natural arithmetical sagacity was probably more efficacious than method4 ,it is very possible that the ,cycle of ,meton is correct more nearly than its author was aware1 and #abc nearly than he could ascertain from any evidence and calculation known to him4 ,it is so exact that it is still used in calculating the new moon for the time of ,easter2 and the ,golden ,number1 which is spoken of in stating such rules1 is the number of this ,cycle corresponding to the current year4#bdc ,note #bdc3 ,the same cycle of #ai years has been used by the ,chinese for a very great length of time2 their civil year consisting1 like that of the ,greeks1 of months of #bi and #cj days4 ,the ,siamese also have this period4 7,astron4 ,lib4 ,u4 ,k47 ,meton's ,cycle was corrected a hundred years later 7#ccj ,b4 ,c471 by ,calippus1 who discovered the error of it by observing an eclipse of the moon six years before the death of ,alexander4#bec ,in this corrected period1 four cycles of #ai years were taken1 and a day left out at the end of the #gf years1 in order to make allowance for the hours by which1 as already observed1 #fidj days are greater than #ai years1 and than #bce lunations3 and this ,calippic period is used in ,ptolemy's ,almagest1 in stating observations of eclipses4 ,note #bec3 ,delamb4 ,a4 ,a4 p4 #ag4 ,the ,metonic and ,calippic periods undoubtedly imply a very considerable degree of accuracy in the knowledge which the astronomers1 to whom they are due1 had of the length of the month2 and the first is a very happy invention for bringing the solar and lunar calendars into agreement4 ,the ,roman ,calendar1 from which our own is derived1 appears to have been a much less skilful contrivance than the ,greek2 though scholars are not agreed on the subject of its construction1 we can hardly doubt that months1 in this as in other cases1 were intended originally to have a reference to the moon4 ,in whatever manner the solar and lunar motions were intended to be reconciled1 the attempt seems altogether to have failed1 and to have been soon abandoned4 ,the ,roman months1 both before and after the ,julian correction1 were portions of the year1 having no reference to full and new moons2 and we1 having adopted this division of the year1 have thus1 in our common calendar1 the traces of one of the early attempts of mankind to seize the law of the succession of celestial phenomena1 in a case where the attempt was a complete failure4 ,considered as a part of the progress of our astronomical knowledge1 improvements in the calendar do not offer many points to our observation1 but they exhibit a few very important steps4 ,calendars which1 belonging apparently to unscientific ages and nations1 possess a great degree of accordance with the true motions of the sun and moon 7like #abd the solar calendar of the ,mexicans1 and the lunar calendar of the ,greeks71 contain the only record now extant of discoveries which must have required a great deal of observation1 of thought1 and probably of time4 ,the later improvements in calendars1 which take place when astronomical observation has been attentively pursued1 are of little consequence to the history of science2 for they are generally founded on astronomical determinations1 and are posterior in time1 and inferior in accuracy1 to the knowledge on which they depend4 ,but cycles of correction1 which are both short and close to exactness1 like that of ,meton1 may perhaps be the original form of the knowledge which they imply2 and certainly require both accurate facts and sagacious arithmetical reasonings4 ,the discovery of such a cycle must always have the appearance of a happy guess1 like other discoveries of laws of nature4 ,beyond this point1 the interest of the study of calendars1 as bearing on our subject1 ceases3 they may be considered as belonging rather to ,art than to ,science2 rather as an application of a part of our knowledge to the uses of life1 than a means or an evidence of its extension4 ,sect4 #f4--,the ,constellations4 ,,some tendency to consider the stars as formed into groups1 is inevitable when men begin to attend to them2 but how men were led to the fanciful system of names of ,stars and of ,constellations1 which we find to have prevailed in early times1 it is very difficult to determine4 ,single stars1 and very close groups1 as the ,pleiades1 were named in the time of ,homer and ,hesiod1 and at a still earlier period1 as we find in the book of ,job4#bfc ,note #bfc3 ,job xxxviii4 #ca4 ,canst thou bind the sweet influences of ,chima 7the ,pleiades71 or loose the bands of ,kesil 7,orion78 ,canst thou bring forth ,mazzaroth 7,sirius7 in his season8 or canst thou guide ,ash 7or ,aisch7 7,arcturus7 with his sons8 ,and ix4 #i4 ,which maketh ,arcturus1 ,orion1 and ,pleiades1 and the chambers of the south4 ,dupuis1 vi4 #ede1 thinks that ,aisch was 1 the goat and kids4 ,see ,hyde1 ,ulughbeigh4 ,two remarkable circumstances with respect to the ,constellations are1 first1 that they appear in most cases to be arbitrary combinations2 the artificial figures which are made to include the stars1 not having any resemblance to their obvious configurations2 and second1 that these figures1 in different countries1 are so far similar1 as to imply some communication4 ,the arbitrary nature of these figures shows that they #abe were rather the work of the imaginative and mythological tendencies of man1 than of mere convenience and love of arrangement4 ,the constellations1 says an astronomer of our own time1#bgc seem to have been almost purposely named and delineated to cause as much confusion and inconvenience as possible4 ,innumerable snakes twine through long and contorted areas of the heavens1 where no memory can follow them3 bears1 lions1 and fishes1 large and small1 northern and southern1 confuse all nomenclature4 ,a better system of constellations might have been a material help as an artificial memory4 ,when men indicate the stars by figures1 borrowed from obvious resemblances1 they are led to combinations quite different from the received constellations4 ,thus the common people in our own country find a wain or wagon1 or a plough1 in a portion of the great bear4#bhc ,note #bgc3 ,sir ,j4 ,herschel4 ,note #bhc3 ,so also the ,greeks1 ,homer1 ,il4 ,,xviii4 #dhg4 4 ,the ,northern ,bear which oft the ,wain they call4 was the traditional name2 1 that suggested by the form4 ,the similarity of the constellations recognized in different countries is very remarkable4 ,the ,chaldean1 the ,egyptian1 and the ,grecian skies have a resemblance which cannot be overlooked4 ,some have conceived that this resemblance may be traced also in the ,indian and ,arabic constellations1 at least in those of the zodiac4#bic ,but while the figures are the same1 the names and traditions connected with them are different1 according to the histories and localities of each country2#cjc the river among the stars which the ,greeks called the ,eridanus1 the ,egyptians asserted to be the ,nile4 ,some conceive that the ,signs of the ,zodiac1 or path along which the sun and moon pass1 had its divisions marked by signs which had a reference to the course of the seasons1 to the motion of the sun1 or the employments of the husbandman4 ,if we take the position of the heavens1 which1 from the knowledge we now possess1 we are sure they must have had #ae1jjj years ago1 the significance of the signs of the zodiac1 in which the sun was1 as referred to the ,egyptian year1 becomes very marked1#cac and has led some to suppose that the zodiac was invented at such a period4 ,others have rejected this as an improbably great antiquity1 and have thought it more likely that the constellation assigned to each season was that which1 at that season1 rose at the beginning of the night3 #abf thus the balance 7which is conceived to designate the equality of days and nights7 was placed among the stars which rose in the evening when the spring began3 this would fix the origin of these signs #bejj years before our era4 ,note #bic3 ,dupuis1 vi4 #edh4 ,the ,indian zodiac contains1 in the place of our ,capricorn1 a ram and a fish1 which proves the resemblance without chance of mistake4 ,bailly1 i4 p4 #aeg4 ,note #cjc3 ,dupuis1 vi4 #edi4 ,note #cac3 ,laplace1 ,hist4 ,astron4 p4 #h4 ,it is clear1 as has already been said1 that ,fancy1 and probably ,superstition1 had a share in forming the collection of constellations4 ,it is certain that1 at an early period1 superstitious notions were associated with the stars4#cbc ,astrology is of very high antiquity in the ,east4 ,the stars were supposed to influence the character and destiny of man1 and to be in some way connected with superior natures and powers4 ,note #cbc3 ,dupuis1 vi4 #edf4 ,we may1 ,i conceive1 look upon the formation of the constellations1 and the notions thus connected with them1 as a very early attempt to find a meaning in the relations of the stars2 and as an utter failure4 ,the first effort to associate the appearances and motions of the skies by conceptions implying unity and connection1 was made in a wrong direction1 as may very easily be supposed4 ,instead of considering the appearances only with reference to space1 time1 number1 in a manner purely rational1 a number of other elements1 imagination1 tradition1 hope1 fear1 awe of the supernatural1 belief in destiny1 were called into action4 ,man1 still young1 as a philosopher at least1 had yet to learn what notions his successful guesses on these subjects must involve1 and what they must exclude4 ,at that period1 nothing could be more natural or excusable than this ignorance2 but it is curious to see how long and how obstinately the belief lingered 7if indeed it be yet extinct7 that the motions of the stars1 and the dispositions and fortunes of men1 may come under some common conceptions and laws1 by which a connection between the one and the other may be established4 ,we cannot1 therefore1 agree with those who consider ,astrology in the early ages as only a degraded ,astronomy1 the abuse of a more ancient science4#ccc ,it was the first step to astronomy by leading to habits and means of grouping phenomena2 and1 after a while1 by showing that pictorial and mythological relations among the stars had no very obvious value4 ,from that time1 the inductive process went on steadily in the true road1 under the guidance of ideas of space1 time1 and number4 ,note #ccc3 ,ib4 vi4 #edf4 ,sect4 #g4--,the ,planets4 ,,while men were becoming familiar with the fixed stars1 the planets must have attracted their notice4 ,venus1 from her brightness1 and #abg from her accompanying the sun at no great distance1 and thus appearing as the morning and evening star1 was very conspicuous4 ,pythagoras is said to have maintained that the evening and morning star are the same body1 which certainly must have been one of the earliest discoveries on this subject2 and indeed we can hardly conceive men noticing the stars for a year or two without coming to this conclusion4 ,jupiter and ,mars1 sometimes still brighter than ,venus1 were also very noticeable4 ,saturn and ,mercury were less so1 but in fine climates they and their motion would soon be detected by persons observant of the heavens4 ,to reduce to any rule the movements of these luminaries must have taken time and thought2 probably before this was done1 certainly very early1 these heavenly bodies were brought more peculiarly under those views which we have noticed as leading to astrology4 ,at a time beyond the reach of certain history1 the planets1 along with the sun and moon1 had been arranged in a certain recognized order by the ,egyptians or some other ancient nation4 ,probably this arrangement had been made according to the slowness of their motions among the stars2 for though the motion of each is very variable1 the gradation of their velocities is1 on the whole1 very manifest2 and the different rate of travelling of the different planets1 and probably other circumstances of difference1 led1 in the ready fancy of early times1 to the attribution of a peculiar character to each luminary4 ,thus ,saturn was held to be of a cold and gelid nature2 ,jupiter1 who1 from his more rapid motion1 was supposed to be lower in place1 was temperate2 ,mars1 fiery1 and the like4#cdc ,note #cdc3 ,achilles ,tatius 7,uranol4 pp4 #ace1 #acf71 gives the ,grecian and ,egyptian names of the planets4 ,egyptian4 ,greek4 ,saturn ,jupiter ,mars ,venus ,mercury ,it is not necessary to dwell on the details of these speculations1 but we may notice a very remarkable evidence of their antiquity and generality in the structure of one of the most familiar of our measures of time1 the ,week4 ,this distribution of time according to periods of seven days1 comes down to us1 as we learn from the ,jewish scriptures1 from the beginning of man's existence on the earth4 ,the same usage is found over all the ,east2 it existed among the ,arabians1 ,assyrians1 #abh ,egyptians4#cec ,the same week is found in ,india among the ,bramins2 it has there1 also1 its days marked by those of the heavenly bodies2 and it has been ascertained that the same day has1 in that country1 the name corresponding with its designation in other nations4 ,note #cec3 ,laplace1 ,hist4 ,astron4 p4 #af4 ,the notion which led to the usual designations of the days of the week is not easily unravelled4 ,the days each correspond to one of the heavenly bodies1 which were1 in the earliest systems of the world1 conceived to be the following1 enumerating them in the order of their remoteness from the earth3#cfc ,saturn1 ,jupiter1 ,mars1 the ,sun1 ,venus1 ,mercury1 the ,moon4 ,at a later period1 the received systems placed the seven luminaries in the seven spheres4 ,the knowledge which was implied in this view1 and the time when it was obtained1 we must consider hereafter4 ,the order in which the names are assigned to the days of the week 7beginning with ,saturday7 is1 ,saturn1 the ,sun1 the ,moon1 ,mars1 ,mercury1 ,jupiter1 ,venus2 and various accounts are given of the manner in which one of these orders is obtained from the other2 all the methods proceeding upon certain arbitrary arithmetical processes1 connected in some way with astrological views4 ,it is perhaps not worth our while here to examine further the steps of this process2 it would be difficult to determine with certainty why the former order of the planets was adopted1 and how and why the latter was deduced from it4 ,but there is something very remarkable in the universality of the notions1 apparently so fantastic1 which have produced this result2 and we may probably consider the ,week1 with ,laplace1#cgc as the most ancient monument of astronomical knowledge4 ,this period has gone on without interruption or irregularity from the earliest recorded times to our own days1 traversing the extent of ages and the revolutions of empires2 the names of the ancient deities which were associated with the stars have been replaced by those of the objects of the worship of our ,teutonic ancestors1 according to their views of the correspondence of the two mythologies2 and the ,quakers1 in rejecting these names of days1 have cast aside the most ancient existing relic of astrological as well as idolatrous superstition4 ,note #cfc3 ,philol4 ,mus4 ,no4 #a4 ,note #cgc3 ,hist4 ,ast4 p4 #ag4 ,sect4 #h4--,the ,circles of the ,sphere4 ,,the inventions hitherto noticed1 though undoubtedly they were steps in astronomical knowledge1 can hardly be considered as purely abstract and scientific speculations2 for the exact reckoning of time is one of #abi the wants1 even of the least civilized nations4 ,but the distribution of the places and motions of the heavenly bodies by means of a celestial sphere with imaginary lines drawn upon it1 is a step in speculative astronomy1 and was occasioned and rendered important by the scientific propensities of man4 ,it is not easy to say with whom this notion originated4 ,some parts of it are obvious4 ,the appearance of the sky naturally suggests the idea of a concave ,sphere1 with the stars fixed on its surface4 ,their motions during any one night1 it would be readily seen1 might be represented by supposing this ,sphere to turn round a ,pole or ,axis2 for there is a conspicuous star in the heavens which apparently stands still 7the ,pole-star72 all the others travel round this in circles1 and keep the same positions with respect to each other4 ,this stationary star is every night the same1 and in the same place2 the other stars also have the same relative position2 but their general position at the same time of night varies gradually from night to night1 so as to go through its cycle of appearances once a year4 ,all this would obviously agree with the supposition that the sky is a concave sphere or dome1 that the stars have fixed places on this sphere1 and that it revolves perpetually and uniformly about the ,pole or fixed point4 ,but this supposition does not at all explain the way in which the appearances of different nights succeed each other4 ,this1 however1 may be explained1 it appears1 by supposing the sun also to move among the stars on the surface of the concave sphere4 ,the sun by his brightness makes the stars invisible which are on his side of the heavens3 this we can easily believe2 for the moon1 when bright1 also puts out all but the largest stars2 and we see the stars appearing in the evening1 each in its place1 according to their degree of splendor1 as fast as the declining light of day allows them to become visible4 ,and as the sun brings day1 and his absence night1 if he move through the circuit of the stars in a year1 we shall have1 in the course of that time1 every part of the starry sphere in succession presented to us as our nocturnal sky4 ,this notion1 that the sun moves round among the stars in a year1 is the basis of astronomy1 and a considerable part of the science is only the development and particularization of this general conception4 ,it is not easy to ascertain either the exact method by which the path of the sun among the stars was determined1 or the author and date of the discovery4 ,that there is some difficulty in tracing the course of the sun among the stars will be clearly seen1 when it is considered that no #acj star can ever be seen at the same time with the sun4 ,if the whole circuit of the sky be divided into twelve parts or signs1 it is estimated by ,autolycus1 the oldest writer on these subjects whose works remain to us1#chc that the stars which occupy one of these parts are absorbed by the solar rays1 so that they cannot be seen4 ,hence the stars which are seen nearest to the place of the setting and the rising sun in the evening and in the morning1 are distant from him by the half of a sign3 the evening stars being to the west1 and the morning stars to the east of him4 ,if the observer had previously obtained a knowledge of the places of all the principal stars1 he might in this way determine the position of the sun each night1 and thus trace his path in a year4 ,note #chc3 ,delamb4 ,a4 ,a4 p4 xiii4 ,in this1 or some such way1 the sun's path was determined by the early astronomers of ,egypt4 ,thales1 who is mentioned as the father of ,greek astronomy1 probably learnt among the ,egyptians the results of such speculations1 and introduced them into his own country4 ,his knowledge1 indeed1 must have been a great deal more advanced than that which we are now describing1 if it be true1 as is asserted1 that he predicted an eclipse4 ,but his having done so is not very consistent with what we are told of the steps which his successors had still to make4 ,the ,circle of the ,signs1 in which the sun moves among the stars1 is obliquely situated with regard to the circles in which the stars move about the poles4 ,pliny#cic states that ,anaximander1#djc a scholar of ,thales1 was the first person who pointed out this obliquity1 and thus1 as he says1 opened the gate of nature4 ,certainly1 the person who first had a clear view of the nature of the sun's path in the celestial sphere1 made that step which led to all the rest2 but it is difficult to conceive that the ,egyptians and ,chaldeans had not already advanced so far4 ,note #cic3 ,lib4 ii4 c4 7viii47 ,note #djc3 ,plutarch1 ,de ,plac4 ,phil4 lib4 ii4 cap4 xii4 says ,pythagoras was the author of this discovery4 ,the diurnal motion of the celestial sphere1 and the motion of the moon in the circle of the signs1 gave rise to a mathematical science1 the ,doctrine of the ,sphere1 which was one of the earliest branches of applied mathematics4 ,a number of technical conceptions and terms were soon introduced4 ,the ,sphere of the heavens was conceived to be complete1 though we see but a part of it2 it was supposed to turn about the visible pole and another pole opposite to this1 and these poles were connected by an imaginary ,axis4 ,the circle which divided the sphere exactly midway between these poles was called the ,equator 774 #aca ,the two circles parallel to this which bounded the sun's path among the stars were called ,tropics 771 because the sun turns back again towards the equator when he reaches them4 ,the stars which never set are bounded by a circle called the ,arctic ,circle 71 from 1 the ,bear1 the constellation to which some of the principal stars within that circle belong47 ,a circle about the opposite pole is called ,antarctic1 and the stars which are within it can never rise to us4#dac ,the sun's path or circle of the signs is called the ,zodiac1 or circle of animals2 the points where this circle meets the equator are the ,equinoctial ,points1 the days and nights being equal when the sun is in them2 the ,solstitial ,points are those where the sun's path touches the tropics2 his motion to the south or to the north ceases when he is there1 and he appears in that respect to stand still4 ,the ,colures 71 mutilated7 are circles which pass through the poles and through the equinoctial and solstitial points2 they have their name because they are only visible in part1 a portion of them being below the horizon4 ,note #dac3 ,the ,arctic and ,antarctic ,circles of modern astronomers are different from these4 ,the ,horizon 77 is commonly understood as the boundary of the visible earth and heaven4 ,in the doctrine of the sphere1 this boundary is a great circle1 that is1 a circle of which the plane passes through the centre of the sphere2 and1 therefore1 an entire hemisphere is always above the horizon4 ,the term occurs for the first time in the work of ,euclid1 called ,phnomena 774 ,we possess two treatises written by ,autolycus#dbc 7who lived about #cjj ,b4 ,c47 which trace deductively the results of the doctrine of the sphere4 ,supposing its diurnal motion to be uniform1 in a work entitled 1 ,on the ,moving ,sphere1 he demonstrates various properties of the diurnal risings1 settings1 and motions of the stars4 ,in another work1 1 ,on ,risings and ,settings1#dcc tacitly assuming the sun's motion in his circle to be uniform1 he proves certain propositions1 with regard to those risings and settings of the stars1 which take place at the same time when the sun rises and sets1#ddc or vice vers2#dec and also their apparent risings and settings when they cease to be visible after sunset1 or begin to be visible after sunrise4#dfc #acb ,several of the propositions contained in the former of these treatises are still necessary to be understood1 as fundamental parts of astronomy4 ,note #dbc3 ,delambre1 ,astron4 ,ancienne1 p4 #ai4 ,note #dcc3 ,delambre1 ,astron4 ,anc4 p4 #be4 ,note #ddc3 ,cosmical rising and setting4 ,note #dec3 ,acronycal rising and setting2 71 happening at the extremity of the night47 ,note #dfc3 ,heliacal rising and setting4 ,the work of ,euclid1 just mentioned1 is of the same kind4 ,delambre#dgc finds in it evidence that ,euclid was merely a book-astronomer1 who had never observed the heavens4 ,note #dgc3 ,ast4 ,anc4 p4 #ec4 ,we may here remark the first instance of that which we shall find abundantly illustrated in every part of the history of science2 that man is prone to become a deductive reasoner2--that as soon as he obtains principles which can be traced to details by logical consequence1 he sets about forming a body of science1 by making a system of such reasonings4 ,geometry has always been a favorite mode of exercising this propensity3 and that science1 along with ,trigonometry1 ,plane and ,spherical1 to which the early problems of astronomy gave rise1 have1 up to the present day1 been a constant field for the exercise of mathematical ingenuity2 a few simple astronomical truths being assumed as the basis of the reasoning4 ,sect4 #i4--,the ,globular ,form of the ,earth4 ,,the establishment of the globular form of the earth is an important step in astronomy1 for it is the first of those convictions1 directly opposed to the apparent evidence of the senses1 which astronomy irresistibly proves4 ,to make men believe that up and down are different directions in different places2 that the sea1 which seems so level1 is1 in fact1 convex2 that the earth1 which appears to rest on a solid foundation1 is1 in fact1 not supported at all2 are great triumphs both of the power of discovering and the power of convincing4 ,we may readily allow this1 when we recollect how recently the doctrine of the antipodes1 or the existence of inhabitants of the earth1 who stand on the opposite side of it1 with their feet turned towards ours1 was considered both monstrous and heretical4 ,yet the different positions of the horizon at different places1 necessarily led the student of spherical astronomy towards this notion of the earth as a round body4 ,anaximander#dhc is said by some to have held the earth to be globular1 and to be detached or suspended2 he is also stated to have constructed a sphere1 on which were shown the extent of land and water4 ,as1 however1 we do not know the arguments upon which he maintained the earth's globular form1 we cannot judge of the #acc value of his opinion2 it may have been no better founded than a different opinion ascribed to him by ,laertius1 that the earth had the shape of a pillar4 ,probably1 the authors of the doctrine of the globular form of the earth were led to it1 as we have said1 by observing the different height of the pole at different places4 ,they would find that the space which they passed over from north to south on the earth1 was proportional to the change of place of the horizon in the celestial sphere2 and as the horizon is1 at every place1 in the direction of the earth's apparently level surface1 this observation would naturally suggest to them the opinion that the earth is placed within the celestial sphere1 as a small globe in the middle of a much larger one4 ,note #dhc3 ,see ,brucker1 ,hist4 ,phil4 vol4 i4 p4 #dhf4 ,we find this doctrine so distinctly insisted on by ,aristotle1 that we may almost look on him as the establisher of it4#dic ,as to the figure of the earth1 it must necessarily be spherical4 ,this he proves1 first by the tendency of things1 in all places1 downwards4 ,he then adds1#ejc ,and1 moreover1 from the phenomena according to the sense3 for if it were not so1 the eclipses of the moon would not have such sections as they have4 ,for in the configurations in the course of a month1 the deficient part takes all different shapes2 it is straight1 and concave1 and convex2 but in eclipses it always has the line of division convex2 wherefore1 since the moon is eclipsed in consequence of the interposition of the earth1 the periphery of the earth must be the cause of this by having a spherical form4 ,and again1 from the appearances of the stars1 it is clear1 not only that the earth is round1 but that its size is not very large3 for when we make a small removal to the south or the north1 the circle of the horizon becomes palpably different1 so that the stars overhead undergo a great change1 and are not the same to those that travel to the north and to the south4 ,for some stars are seen in ,egypt or at ,cyprus1 but are not seen in the countries to the north of these2 and the stars that in the north are visible while they make a complete circuit1 there undergo a setting4 ,so that from this it is manifest1 not only that the form of the earth is round1 but also that it is a part of not a very large sphere3 for otherwise the difference would not be so obvious to persons making so small a change of place4 ,wherefore we may judge that those persons who connect the region in the neighborhood of the pillars of ,hercules with that towards ,india1 and who assert that in this way the sea is ,,one1 do not assert things very improbable4 ,they confirm this conjecture moreover by the #acd elephants1 which are said to be of the same species 77 towards each extreme2 as if this circumstance was a consequence of the conjunction of the extremes4 ,the mathematicians1 who try to calculate the measure of the circumference1 make it amount to #djj1jjj stadia2 whence we collect that the earth is not only spherical1 but is not large compared with the magnitude of the other stars4 ,note #dic3 ,arist4 de ,clo1 lib4 ii4 cap4 xiv4 ed4 ,casaub4 p4 #bij4 ,note #ejc3 p4 #bia ,c4 ,when this notion was once suggested1 it was defended and confirmed by such arguments as we find in later writers3 for instance1#eac that the tendency of all things was to fall to the place of heavy bodies1 and that this place being the centre of the earth1 the whole earth had no such tendency2 that the inequalities on the surface were so small as not materially to affect the shape of so vast a mass2 that drops of water naturally form themselves into figures with a convex surface2 that the end of the ocean would fall if it were not rounded off2 that we see ships1 when they go out to sea1 disappearing downwards1 which shows the surface to be convex4 ,these are the arguments still employed in impressing the doctrines of astronomy upon the student of our own days2 and thus we find that1 even at the early period of which we are now speaking1 truths had begun to accumulate which form a part of our present treasures4 ,note #eac3 ,pliny1 ,nat4 ,hist4 ii4 ,,lxv4 ,sect4 #aj4--,the ,phases of the ,moon4 ,,when men had formed a steady notion of the ,moon as a solid body1 revolving about the earth1 they had only further to conceive it spherical1 and to suppose the sun to be beyond the region of the moon1 and they would find that they had obtained an explanation of the varying forms which the bright part of the moon assumes in the course of a month4 ,for the convex side of the crescent-moon1 and her full edge when she is gibbous1 are always turned towards the sun4 ,and this explanation1 once suggested1 would be confirmed1 the more it was examined4 ,for instance1 if there be near us a spherical stone1 on which the sun is shining1 and if we place ourselves so that this stone and the moon are seen in the same direction 7the moon appearing just over the top of the stone71 we shall find that the visible part of the stone1 which is then illuminated by the sun1 is exactly similar in form to the moon1 at whatever period of her changes she may be4 ,the stone and the moon being in the same position with respect to us1 and both being enlightened by the sun1 the bright parts are the same in figure2 #ace the only difference is1 that the dark part of the moon is usually not visible at all4 ,this doctrine is ascribed to ,anaximander4 ,aristotle was fully aware of it4#ebc ,it could not well escape the ,chaldeans and ,egyptians1 if they speculated at all about the causes of the appearances in the heavens4 ,note #ebc3 ,probl4 ,cap4 ,,xv4 ,art4 #g4 ,sect4 #aa4--;,eclipses4 ,,eclipses of the sun and moon were from the earliest tunes regarded with a peculiar interest4 ,the notions of superhuman influences and relations1 which1 as we have seen1 were associated with the luminaries of the sky1 made men look with alarm at any sudden and striking change in those objects2 and as the constant and steady course of the celestial revolutions was contemplated with a feeling of admiration and awe1 any marked interruption and deviation in this course1 was regarded with surprise and terror4 ,this appears to be the case with all nations at an early stage of their civilization4 ,this impression would cause ,eclipses to be noted and remembered2 and accordingly we find that the records of ,eclipses are the earliest astronomical information which we possess4 ,when men had discovered some of the laws of succession of other astronomical phenomena1 for instance1 of the usual appearances of the moon and sun1 it might then occur to them that these unusual appearances also might probably be governed by some rule4 ,the search after this rule was successful at an early period4 ,the ,chaldeans were able to predict ,eclipses of the ,moon4 ,this they did1 probably1 by means of their ,cycle of #bbc months1 or about #ah years2 for at the end of this time1 the eclipses of the moon begin to return1 at the same intervals and in the same order as at the beginning4#ecc ,probably this was the first instance of the prediction of peculiar astronomical phenomena4 ,the ,chinese have1 indeed1 a legend1 in which it is related that a solar eclipse happened in the reign of ,tchongkang1 above #bjjj years before ,christ1 and that the emperor was so much irritated against two great officers of state1 who had neglected to predict this eclipse1 that he put them to death4 ,but this cannot be accepted as a real event3 for1 during the next ten centuries1 we find no single observation or fact connected with astronomy in the ,chinese #acf histories2 and their astronomy has never advanced beyond a very rude and imperfect condition4 ,note #ecc3 ,the eclipses of the sun are more difficult to calculate2 since they depend upon the place of the spectator on the earth4 ,we can only conjecture the mode in which the ,chaldeans discovered their ,period of #ah years2 and we may make very different suppositions with regard to the degree of science by which they were led to it4 ,we may suppose1 with ,delambre1#edc that they carefully recorded the eclipses which happened1 and then1 by the inspection of their registers1 discovered that those of the moon recurred after a certain period4 ,or we may suppose1 with other authors1 that they sedulously determined the motions of the moon1 and having obtained these with considerable accuracy1 sought and found a period which should include cycles of these motions4 ,this latter mode of proceeding would imply a considerable degree of knowledge4 ,note #edc3 ,a4 ,a4 p4 #bab4 ,it appears probable rather that such a period was discovered by noticing the recurrence of eclipses1 than by studying the moon's motions4 ,after #fehe days1 or #bbc lunations1 the same eclipses nearly will recur4 ,it is not contested that the ,chaldeans were acquainted with this period1 which they called ,saros2 or that they calculated eclipses by means of it4 ,sect4 #ab4--,sequel to the ,early ,stages of ,astronomy4 ,,every stage of science has its train of practical applications and systematic inferences1 arising both from the demands of convenience and curiosity1 and from the pleasure which1 as we have already said1 ingenuous and active-minded men feel in exercising the process of deduction4 ,the earliest condition of astronomy1 in which it can be looked upon as a science1 exhibits several examples of such applications and inferences1 of which we may mention a few4 ,prediction of ,eclipses4--,the ,cycles which served to keep in order the ,calendar of the early nations of antiquity1 in some instances enabled them also1 as has just been stated1 to predict ,eclipses2 and this application of knowledge necessarily excited great notice4 ,cleomedes1 in the time of ,augustus1 says1 ,we never see an eclipse happen which has not been predicted by those who made use of the ,tables4 7 47 ,terrestrial ,zones4--,the globular form of the earth being assented to1 the doctrine of the sphere was applied to the earth as well as the heavens2 and the earth's surface was divided by various imaginary #acg circles2 among the rest1 the equator1 the tropics1 and circles1 at the same distance from the poles as the tropics are from the equator4 ,one of the curious consequences of this division was the assumption that there must be some marked difference in the stripes or zones into which the earth's surface was thus divided4 ,in going to the south1 ,europeans found countries hotter and hotter1 in going to the north1 colder and colder2 and it was supposed that the space between the tropical circles must be uninhabitable from heat1 and that within the polar circles1 again1 uninhabitable from cold4 ,this fancy was1 as we now know1 entirely unfounded4 ,but the principle of the globular form of the earth1 when dealt with by means of spherical geometry1 led to many true and important propositions concerning the lengths of days and nights at different places4 ,these propositions still form a part of our ,elementary ,astronomy4 ,gnomonic4--,another important result of the doctrine of the sphere was ,gnomonic or ,dialling4 ,anaximenes is said by ,pliny to have first taught this art in ,greece2 and both he and ,anaximander are reported to have erected the first dial at ,lacedemon4 ,many of the ancient dials remain to us2 some of these are of complex forms1 and must have required great ingenuity and considerable geometrical knowledge in their construction4 ,measure of the ,sun's ,distance4--,the explanation of the phases of the moon led to no result so remarkable as the attempt of ,aristarchus of ,samos to obtain from this doctrine a measure of the ,distance of the ,sun as compared with that of the ,moon4 ,if the moon was a perfectly smooth sphere1 when she was exactly midway between the new and full in position 7that is1 a quadrant from the sun71 she would be somewhat more than a half moon2 and the place when she was dichotomized1 that is1 was an exact semicircle1 the bright part being bounded by a straight line1 would depend upon the sun's distance from the earth4 ,aristarchus endeavored to fix the exact place of this ,dichotomy2 but the irregularity of the edge which bounds the bright part of the moon1 and the difficulty of measuring with accuracy1 by means then in use1 either the precise time when the boundary was most nearly a straight line1 or the exact distance of the moon from the sun at that time1 rendered his conclusion false and valueless4 ,he collected that the sun is at #ah times the distance of the moon from us2 we now know that he is at #djj times the moon's distance4 ,it would be easy to dwell longer on subjects of this kind2 but we have already perhaps entered too much in detail4 ,we have been #ach tempted to do this by the interest which the mathematical spirit of the ,greeks gave to the earliest astronomical discoveries1 when these were the subjects of their reasonings2 but we must now proceed to contemplate them engaged in a worthier employment1 namely1 in adding to these discoveries4 ,,chapter ,,ii4 ,,prelude ,,to ,,the ,,inductive ,,epoch ,,of ,,hipparchus4 ,,without pretending that we have exhausted the consequences of the elementary discoveries which we have enumerated1 we now proceed to consider the nature and circumstances of the next great discovery which makes an ,epoch in the history of ,astronomy2 and this we shall find to be the ,theory of ,epicycles and ,eccentrics4 ,before1 however1 we relate the establishment of this theory1 we must1 according to the general plan we have marked out1 notice some of the conjectures and attempts by which it was preceded1 and the growing acquaintance with facts1 which made the want of such an explanation felt4 ,in the steps previously made in astronomical knowledge1 no ingenuity had been required to devise the view which was adopted4 ,the motions of the stars and sun were most naturally and almost irresistibly conceived as the results of motion in a revolving sphere2 the indications of position which we obtain from different places on the earth's surface1 when clearly combined1 obviously imply a globular shape4 ,in these cases1 the first conjectures1 the supposition of the simplest form1 of the most uniform motion1 required no after-correction4 ,but this manifest simplicity1 this easy and obvious explanation1 did not apply to the movement of all the heavenly bodies4 ,the ,planets1 the wandering stars1 could not be so easily understood2 the motion of each1 as ,cicero says1 undergoing very remarkable changes in its course1 going before and behind1 quicker and slower1 appearing in the evening1 but gradually lost there1 and emerging again in the morning4#eec ,a continued attention to these stars would1 however1 #aci detect a kind of intricate regularity in their motions1 which might naturally be described as a dance4 ,the ,chaldeans are stated by ,diodorus#efc to have observed assiduously the risings and settings of the planets1 from the top of the temple of ,belus4 ,by doing this1 they would find the times in which the forward and backward movements of ,saturn1 ,jupiter1 and ,mars recur2 and also the time in which they come round to the same part of the heavens4#egc ,venus and ,mercury never recede far from the sun1 and the intervals which elapse while either of them leaves its greatest distance from the sun and returns again to the greatest distance on the same side1 would easily be observed4 ,note #eec3 ,cic4 de ,nat4 ,d4 lib4 ii4 p4 #dej4 ,ea qu ,saturni stella dicitur1 que a ,grcis nominatur1 qu a terra abest plurimum1 xxx fere annis cursum suum conficit2 in quo cursu multa mirabiliter efficiens1 tum antecedendo1 tum retardando1 tum vespertinis temporibus delitescendo1 tum matutinis se rursum aperiendo1 nihil immutat sempiternis sculorum tatibus1 quin eadem iisdem temporibus efficiat4 ,and so of the other planets4 ,note #efc3 ,a4 ,a4 i4 p4 #d4 ,note #egc3 ,plin4 ,h4 ,n4 ii4 p4 #bjd4 ,probably the manner in which the motions of the planets were originally reduced to rule was something like the following3--,in about #cj of our years1 ,saturn goes #bi times through his ,anomaly1 that is1 the succession of varied motions by which he sometimes goes forwards and sometimes backwards among the stars4 ,during this time1 he goes once round the heavens1 and returns nearly to the same place4 ,this is the cycle of his apparent motions4 ,perhaps the eastern nations contented themselves with thus referring these motions to cycles of time1 so as to determine their recurrence4 ,something of this kind was done at an early period1 as we have seen4 ,but the ,greeks soon attempted to frame to themselves a sensible image of the mechanism by which these complex motions were produced2 nor did they find this difficult4 ,venus1 for instance1 who1 upon the whole1 moves from west to east among the stars1 is seen1 at certain intervals1 to return or move retrograde a short way back from east to west1 then to become for a short time stationary1 then to turn again and resume her direct motion westward1 and so on4 ,now this can be explained by supposing that she is placed in the rim of a wheel1 which is turned edgeways to us1 and of which the centre turns round in the heavens from west to east1 while the wheel1 carrying the planet in its motion1 moves round its own centre4 ,in this way the motion of the wheel about its centre1 would1 in some situations1 counterbalance the general motion of the centre1 and make the planet retrograde1 while1 on the whole1 the westerly motion would prevail4 ,just as if we suppose that a person1 holding a lamp in his hand in the dark1 and at a #adj distance1 so that the lamp alone is visible1 should run on turning himself round2 we should see the light sometimes stationary1 sometimes retrograde1 but on the whole progressive4 ,a mechanism of this kind was imagined for each of the planets1 and the wheels of which we have spoken were in the end called ,epicycles4 ,the application of such mechanism to the planets appears to have arisen in ,greece about the time of ,aristotle4 ,in the works of ,plato we find a strong taste for this kind of mechanical speculation4 ,in the tenth book of the ,polity1 we have the apologue of ,alcinus the ,pamphylian1 who1 being supposed to be killed in battle1 revived when he was placed on the funeral pyre1 and related what he had seen during his trance4 ,among other revelations1 he beheld the machinery by which all the celestial bodies revolve4 ,the axis of these revolutions is the adamantine distaff which ,destiny holds between her knees2 on this are fixed1 by means of different sockets1 flat rings1 by which the planets are carried4 ,the order and magnitude of these spindles are minutely detailed4 ,also1 in the ,epilogue to the ,laws 7,epinomis71 he again describes the various movements of the sky1 so as to show a distinct acquaintance with the general character of the planetary motions2 and1 after speaking of the ,egyptians and ,syrians as the original cultivators of such knowledge1 he adds some very remarkable exhortations to his countrymen to prosecute the subject4 ,whatever we ,greeks1 he says1 receive from the barbarians1 we improve and perfect2 there is good hope and promise1 therefore1 that ,greeks will carry this knowledge far beyond that which was introduced from abroad4 ,to this task1 however1 he looks with a due appreciation of the qualities and preparation which it requires4 ,an astronomer must be1 he says1 the wisest of men2 his mind must be duly disciplined in youth2 especially is mathematical study necessary2 both an acquaintance with the doctrine of number1 and also with that other branch of mathematics1 which1 closely connected as it is with the science of the heavens1 we very absurdly call geometry1 the measurement of the earth4#ehc ,note #ehc3 ,epinomis1 pp4 #ihh1 #iij4 ,those anticipations were very remarkably verified in the subsequent career of the ,greek ,astronomy4 ,the theory1 once suggested1 probably made rapid progress4 ,simplicius#eic relates1 that ,eudoxus of ,cnidus introduced the hypothesis of revolving circles or spheres4 ,calippus of ,cyzicus1 having visited #ada ,polemarchus1 an intimate friend of ,eudoxus1 they went together to ,athens1 and communicated to ,aristotle the invention of ,eudoxus1 and with his help improved and corrected it4 ,note #eic3 ,lib4 ii4 de ,clo4 ,bullialdus1 p4 #ah4 ,probably at first this hypothesis was applied only to account for the general phenomena of the progressions1 retrogradations1 and stations of the planet2 but it was soon found that the motions of the sun and moon1 and the circular motions of the planets1 which the hypothesis supposed1 had other anomalies or irregularities1 which made a further extension of the hypothesis necessary4 ,the defect of uniformity in these motions of the sun and moon1 though less apparent than in the planets1 is easily detected1 as soon as men endeavor to obtain any accuracy in their observations4 ,we have already stated 7,chap4 ,i47 that the ,chaldeans were in possession of a period of about eighteen years1 which they used in the calculation of eclipses1 and which might have been discovered by close observation of the moon's motions2 although it was probably rather hit upon by noting the recurrence of eclipses4 ,the moon moves in a manner which is not reducible to regularity without considerable care and time4 ,if we trace her path among the stars1 we find that1 like the path of the sun1 it is oblique to the equator1 but it does not1 like that of the sun1 pass over the same stars in successive revolutions4 ,thus its latitude1 or distance from the equator1 has a cycle different from its revolution among the stars2 and its ,nodes1 or the points where it cuts the equator1 are perpetually changing their position4 ,in addition to this1 the moon's motion in her own path is not uniform2 in the course of each lunation1 she moves alternately slower and quicker1 passing gradually through the intermediate degrees of velocity2 and goes through the cycle of these changes in something less than a month2 this is called a revolution of ,anomaly4 ,when the moon has gone through a complete number of revolutions of ,anomaly1 and has1 in the same time1 returned to the same position with regard to the sun1 and also with regard to her ,nodes1 her motions with respect to the sun will thenceforth be the same as at the first1 and all the circumstances on which lunar eclipses depend being the same1 the eclipses will occur in the same order4 ,in #fehe days there are #bci revolutions of anomaly1 #bda revolutions with regard to one of the ,nodes1 and1 as we have said1 #bbc lunations or revolutions with regard to the sun4 ,hence this ,period will bring about a succession of the same lunar eclipses4 ,if the ,chaldeans observed the moon's motion among the stars with any considerable accuracy1 so as to detect this period by that means1 #adb they could hardly avoid discovering the anomaly or unequal motion of the moon2 for in every revolution1 her daily progression in the heavens varies from about twenty-two to twenty-six times her own diameter4 ,but there is not1 in their knowledge of this ,period1 any evidence that they had measured the amount of this variation2 and ,delambre#fjc is probably right in attributing all such observations to the ,greeks4 ,note #fjc3 ,astronomie ,ancienne1 i4 #bab4 ,the sun's motion would also be seen to be irregular as soon as men had any exact mode of determining the lengths of the four seasons1 by means of the passage of the sun through the equinoctial and solstitial points4 ,for spring1 summer1 autumn1 and winter1 which would each consist of an equal number of days if the motions were uniform1 are1 in fact1 found to be unequal in length4 ,it was not very difficult to see that the mechanism of epicycles might be applied so as to explain irregularities of this kind4 ,a wheel travelling round the earth1 while it revolved upon its centre1 might produce the effect of making the sun or moon fixed in its rim go sometimes faster and sometimes slower in appearance1 just in the same way as the same suppositions would account for a planet going sometimes forwards and sometimes backwards3 the epicycles of the sun and moon would1 for this purpose1 be less than those of the planets4 ,accordingly1 it is probable that1 at the time of ,plato and ,aristotle1 philosophers were already endeavoring to apply the hypothesis to these cases1 though it does not appear that any one fully succeeded before ,hipparchus4 ,the problem which was thus present to the minds of astronomers1 and which ,plato is said to have proposed to them in a distinct form1 was1 ,to reconcile the celestial phenomena by the combination of equable circular motions4 ,that the circular motions should be equable as well as circular1 was a condition1 which1 if it had been merely tried at first1 as the most simple and definite conjecture1 would have deserved praise4 ,but this condition1 which is1 in reality1 inconsistent with nature1 was1 in the sequel1 adhered to with a pertinacity which introduced endless complexity into the system4 ,the history of this assumption is one of the most marked instances of that love of simplicity and symmetry which is the source of all general truths1 though it so often produces and perpetuates error4 ,at present we can easily see how fancifully the notion of simplicity and perfection was interpreted1 in the arguments by which the opinion was defended1 that the #adc real motions of the heavenly bodies must be circular and uniform4 ,the ,pythagoreans1 as well as the ,platonists1 maintained this dogma4 ,according to ,geminus1 ,they supposed the motions of the sun1 and the moon1 and the five planets1 to be circular and equable3 for they would not allow of such disorder among divine and eternal things1 as that they should sometimes move quicker1 and sometimes slower1 and sometimes stand still2 for no one would tolerate such anomaly in the movements1 even of a man1 who was decent and orderly4 ,the occasions of life1 however1 are often reasons for men going quicker or slower1 but in the incorruptible nature of the stars1 it is not possible that any cause can be alleged of quickness and slowness4 ,whereupon they propounded this question1 how the phenomena might be represented by equable and circular motions4 ,these conjectures and assumptions led naturally to the establishment of the various parts of the ,theory of ,epicycles4 ,it is probable that this theory was adopted with respect to the ,planets at or before the time of ,plato4 ,and ,aristotle gives us an account of the system thus devised4#fac ,eudoxus1 he says1 attributed four spheres to each ,planet3 the first revolved with the fixed stars 7and this produced the diurnal motion72 the second gave the planet a motion along the ecliptic 7the mean motion in longitude72 the third had its axis perpendicular#fbc to the ecliptic 7and this gave the inequality of each planetary motion1 really arising from its special motion about the sun72 the fourth produced the oblique motion transverse to this 7the motion in latitude74 ,he is also said to have attributed a motion in latitude and a corresponding sphere to the ,sun as well as to the ,moon1 of which it is difficult to understand the meaning1 if ,aristotle has reported rightly of the theory2 for it would be absurd to ascribe to ,eudoxus a knowledge of the motions by which the sun deviates from the ecliptic4 ,calippus conceived that two additional spheres must be given to the sun and to the moon1 in order to explain the phenomena3 probably he was aware of the inequalities of the motions of these luminaries4 ,he also proposed an additional sphere for each planet1 to account1 we may suppose1 for the results of the eccentricity of the orbits4 ,note #fac3 ,metaph4 xi4 #h4 ,note #fbc3 ,aristotle says has its poles in the ecliptic1 but this must be a mistake of his4 ,he professes merely to receive these opinions from the mathematical astronomers1 4 ,the hypothesis1 in this form1 does not appear to have been reduced to measure1 and was1 moreover1 unnecessarily complex4 ,the resolution #add of the oblique motion of the moon into two separate motions1 by ,eudoxus1 was not the simplest way of conceiving it2 and ,calippus imagined the connection of these spheres in some way which made it necessary nearly to double their number2 in this manner his system had no less than #ee spheres4 ,such was the progress which the ,idea of the hypothesis of epicycles had made in men's minds1 previously to the establishment of the theory by ,hipparchus4 ,there had also been a preparation for this step1 on the other side1 by the collection of ,facts4 ,we know that observations of the ,eclipses of the ,moon were made by the ,chaldeans #cfg ,b4 ,c4 at ,babylon1 and were known to the ,greeks2 for ,hipparchus and ,ptolemy founded their ,theory of the ,moon on these observations4 ,perhaps we cannot consider1 as equally certain1 the story that1 at the time of ,alexander's conquest1 the ,chaldeans possessed a series of observations1 which went back #aijc years1 and which ,aristotle caused ,callisthenes to bring to him in ,greece4 ,all the ,greek observations which are of any value1 begin with the school of ,alexandria4 ,aristyllus and ,timocharis appear1 by the citations of ,hipparchus1 to have observed the ,places of ,stars and ,planets1 and the ,times of the ,solstices1 at various periods from ,b4 ,c4 #bie to ,b4 ,c4 #bfi4 ,without their observations1 indeed1 it would not have been easy for ,hipparchus to establish either the ,theory of the ,sun or the ,precession of the ,equinoxes4 ,in order that observations at distant intervals may be compared with each other1 they must be referred to some common era4 ,the ,chaldeans dated by the era of ,nabonassar1 which commenced #gdi ,b4 ,c4 ,the ,greek observations were referred to the ,calippic periods of #gf years1 of which the first began #cca ,b4 ,c4 ,these are the dates used by ,hipparchus and ,ptolemy4 #ade ,,chapter ,,iii4 ,,inductive ,,epoch ,,of ,,hipparchus4 ,sect4 #a4--;,establishment of the ,theory of ,epicycles and ,eccentrics4 ,,although1 as we have already seen1 at the time of ,plato1 the ,idea of ,epicycles had been suggested1 and the problem of its general application proposed1 and solutions of this problem offered by his followers2 we still consider ,hipparchus as the real discoverer and founder of that theory2 inasmuch as he not only guessed that it might1 but showed that it must1 account for the phenomena1 both as to their nature and as to their quantity4 ,the assertion that he only discovers who proves1 is just2 not only because1 until a theory is proved to be the true one1 it has no pre-eminence over the numerous other guesses among which it circulates1 and above which the proof alone elevates it2 but also because he who takes hold of the theory so as to apply calculation to it1 possesses it with a distinctness of conception which makes it peculiarly his4 ,in order to establish the ,theory of ,epicycles1 it was necessary to assign the magnitudes1 distances1 and positions of the circles or spheres in which the heavenly bodies were moved1 in such a manner as to account for their apparently irregular motions4 ,we may best understand what was the problem to be solved1 by calling to mind what we now know to be the real motions of the heavens4 ,the true motion of the earth round the sun1 and therefore the apparent annual motion of the sun1 is performed1 not in a circle of which the earth is the centre1 but in an ellipse or oval1 the earth being nearer to one end than to the other2 and the motion is most rapid when the sun is at the nearer end of this oval4 ,but instead of an oval1 we may suppose the sun to move uniformly in a circle1 the earth being now1 not in the centre1 but nearer to one side2 for on this supposition1 the sun will appear to move most quickly when he is nearest to the earth1 or in his ,perigee1 as that point is called4 ,such an orbit is called an ,eccentric1 and the distance of the earth from the centre of the circle is called the ,eccentricity4 ,it may easily be shown by geometrical reasoning1 that the inequality of apparent motion so produced1 is exactly the same in #adf detail1 as the inequality which follows from the hypothesis of a small ,epicycle1 turning uniformly on its axis1 and carrying the sun in its circumference1 while the centre of this epicycle moves uniformly in a circle of which the earth is the centre4 ,this identity of the results of the hypothesis of the ,eccentric and the ,epicycle is proved by ,ptolemy in the third book of the ,almagest4 ,the ,sun's ,eccentric4--,when ,hipparchus had clearly conceived these hypotheses1 as possible ways of accounting for the sun's motion1 the task which he had to perform1 in order to show that they deserved to be adopted1 was to assign a place to the ,perigee1 a magnitude to the ,eccentricity1 and an ,epoch at which the sun was at the perigee2 and to show that1 in this way1 he had produced a true representation of the motions of the sun4 ,this1 accordingly1 he did2 and having thus determined1 with considerable exactness1 both the law of the solar irregularities1 and the numbers on which their amount depends1 he was able to assign the motions and places of the sun for any moment of future time with corresponding exactness2 he was able1 in short1 to construct ,solar ,tables1 by means of which the sun's place with respect to the stars could be correctly found at any time4 ,these tables 7as they are given by ,ptolemy7#fcc give the ,anomaly1 or inequality of the sun's motion2 and this they exhibit by means of the ,prosthapheresis1 the quantity of which1 at any distance of the sun from the ,apogee1 it is requisite to add to or subtract from the arc1 which he would have described if his motion had been equable4 ,note #fcc3 ,syntax4 #a4 iii4 ,the reader might perhaps expect that the calculations which thus exhibited the motions of the sun for an indefinite future period must depend upon a considerable number of observations made at all seasons of the year4 ,that1 however1 was not the case2 and the genius of the discoverer appeared1 as such genius usually does appear1 in his perceiving how small a number of facts1 rightly considered1 were sufficient to form a foundation for the theory4 ,the number of days contained in two seasons of the year sufficed for this purpose to ,hipparchus4 ,having ascertained1 says ,ptolemy1 that the time from the vernal equinox to the summer tropic is #id days1 and the time from the summer tropic to the autumnal equinox #ib days1 from these phenomena alone he demonstrates that the straight line joining the centre of the sun's eccentric path with the centre of the zodiac 7the spectator's eye7 is nearly the #bdth part of the radius of the eccentric path2 and that #adg its apogee precedes the summer solstice by #bd degrees nearly1 the zodiac containing #cfj4 ,the exactness of the ,solar ,tables1 or ,canon1 which was founded on these data1 was manifested1 not only by the coincidence of the sun's calculated place with such observations as the ,greek astronomers of this period were able to make 7which were indeed very rude71 but by its enabling them to calculate solar and lunar eclipses2 phenomena which are a very precise and severe trial of the accuracy of such tables1 inasmuch as a very minute change in the apparent place of the sun or moon would completely alter the obvious features of the eclipse4 ,though the tables of this period were by no means perfect1 they bore with tolerable credit this trying and perpetually recurring test2 and thus proved the soundness of the theory on which the tables were calculated4 ,the ,moon's ,eccentric4--,the moon's motions have many irregularities2 but when the hypothesis of an ,eccentric or an ,epicycle had sufficed in the case of the sun1 it was natural to try to explain1 in the same way1 the motions of the moon2 and it was shown by ,hipparchus that such hypotheses would account for the more obvious anomalies4 ,it is not very easy to describe the several ways in which these hypotheses were applied1 for it is1 in truth1 very difficult to explain in words even the mere facts of the moon's motion4 ,if she were to leave a visible bright line behind her in the heavens wherever she moved1 the path thus exhibited would be of an extremely complex nature2 the circle of each revolution slipping away from the preceding1 and the traces of successive revolutions forming a sort of band of net-work running round the middle of the sky4#fdc ,in each revolution1 the motion in longitude is affected by an anomaly of the same nature as the sun's anomaly already spoken of2 but besides this1 the path of the moon deviates from the ecliptic to the north and to the south of the ecliptic1 and thus she has a motion in latitude4 ,this motion in latitude would be sufficiently known if we knew the period of its restoration1 that is1 the time which the moon occupies in moving from any latitude till she is restored to the same latitude2 as1 for instance1 from the ecliptic on one side of the heavens to the ecliptic on the same side of the heavens again4 ,but it is found that the period of the restoration of the latitude is not the same as the period of the restoration of the longitude1 that is1 as the period of the moon's revolution among the #adh stars2 and thus the moon describes a different path among the stars in every successive revolution1 and her path1 as well as her velocity1 is constantly variable4 ,note #fdc3 ,the reader will find an attempt to make the nature of this path generally intelligible in the ,companion to the ,british ,almanac for #ahad4 ,hipparchus1 however1 reduced the motions of the moon to rule and to ,tables1 as he did those of the sun1 and in the same manner4 ,he determined1 with much greater accuracy than any preceding astronomer1 the mean or average equable motions of the moon in longitude and in latitude2 and he then represented the anomaly of the motion in longitude by means of an eccentric1 in the same manner as he had done for the sun4 ,but here there occurred still an additional change1 besides those of which we have spoken4 ,the ,apogee of the ,sun was always in the same place in the heavens2 or at least so nearly so1 that ,ptolemy could detect no error in the place assigned to it by ,hipparchus #bej years before4 ,but the ,apogee of the ,moon was found to have a motion among the stars4 ,it had been observed before the time of ,hipparchus1 that in #fehe days1 there are #bda revolutions of the moon with regard to the stars1 but only #bci revolutions with regard to the anomaly4 ,this difference could be suitably represented by supposing the eccentric1 in which the moon moves1 to have itself an angular motion1 perpetually carrying its apogee in the same direction in which the moon travels2 but this supposition being made1 it was necessary to determine1 not only the eccentricity of the orbit1 and place of the apogee at a certain time1 but also the rate of motion of the apogee itself1 in order to form tables of the moon4 ,this task1 as we have said1 ,hipparchus executed2 and in this instance1 as in the problem of the reduction of the sun's motion to tables1 the data which he found it necessary to employ were very few4 ,he deduced all his conclusions from six eclipses of the moon4#fec ,three of these1 the records of which were brought from ,babylon1 where a register of such occurrences was kept1 happened in the #cffth and #cfgth years from the era of ,nabonassar1 and enabled ,hipparchus to determine the eccentricity and apogee of the moon's orbit at that time4 ,the three others were observed at ,alexandria1 in the #edgth year of ,nabonassar1 which gave him another position of the orbit at an interval of #ahj years2 and he thus became acquainted with the motion of the orbit itself1 as well as its form4#ffc #adi ,note #fec3 ,ptol4 ,syn4 iv4 #aj4 ,note #ffc3 ,ptolemy uses the hypothesis of an epicycle for the moon's first inequality2 but ,hipparchus employs an eccentric4 ,the moon's motions are really affected by several other inequalities1 of very considerable amount1 besides those which were thus considered by ,hipparchus2 but the lunar paths1 constructed on the above data1 possessed a considerable degree of correctness1 and especially when applied1 as they were principally1 to the calculation of eclipses2 for the greatest of the additional irregularities which we have mentioned disappear at new and full moon1 which are the only times when eclipses take place4 ,the numerical explanation of the motions of the sun and moon1 by means of the ,hypothesis of ,eccentrics1 and the consequent construction of tables1 was one of the great achievements of ,hipparchus4 ,the general explanation of the motions of the planets1 by means of the hypothesis of epicycles1 was in circulation previously1 as we have seen4 ,but the special motions of the planets1 in their epicycles1 are1 in reality1 affected by anomalies of the same kind as those which render it necessary to introduce eccentrics in the cases of the sun and moon4 ,hipparchus determined1 with great exactness1 the ,mean ,motions of the ,planets2 but he was not able1 from want of data1 to explain the planetary ,irregularities by means of ,eccentrics4 ,the whole mass of good observations of the planets which he received from preceding ages1 did not contain so many1 says ,ptolemy1 as those which he has transmitted to us of his own4 ,hence#fgc it was1 he adds1 that while he labored1 in the most assiduous manner to represent the motions of the sun and moon by means of equable circular motions2 with respect to the planets1 so far as his works show1 he did not even make the attempt1 but merely put the extant observations in order1 added to them himself more than the whole of what he received from preceding ages1 and showed the insufficiency of the hypothesis current among astronomers to explain the phenomena4 ,it appears that preceding mathematicians had already pretended to construct a ,perpetual ,canon1 that is1 ,tables which should give the places of the planets at any future time2 but these being constructed without regard to the eccentricity of the orbits1 must have been very erroneous4 ,note #fgc3 ,synt4 ix4 #b4 ,ptolemy declares1 with great reason1 that ,hipparchus showed his usual love of truth1 and his right sense of the responsibility of his task1 in leaving this part of it to future ages4 ,the ,theories of the ,sun and ,moon1 which we have already described1 constitute him a great astronomical discoverer1 and justify the reputation he has always #aej possessed4 ,there is1 indeed1 no philosopher who is so uniformly spoken of in terms of admiration4 ,ptolemy1 to whom we owe our principal knowledge of him1 perpetually couples with his name epithets of praise3 he is not only an excellent and careful observer1 but a#fhc most truth-loving and labor-loving person1 one who had shown extraordinary sagacity and remarkable desire of truth in every part of science4 ,pliny1 after mentioning him and ,thales1 breaks out into one of his passages of declamatory vehemence3 ,great men6 elevated above the common standard of human nature1 by discovering the laws which celestial occurrences obey1 and by freeing the wretched mind of man from the fears which eclipses inspired--,hail to you and to your genius1 interpreters of heaven1 worthy recipients of the laws of the universe1 authors of principles which connect gods and men6 ,modern writers have spoken of ,hipparchus with the same admiration2 and even the exact but severe historian of astronomy1 ,delambre1 who bestows his praise so sparingly1 and his sarcasm so generally2--who says#fic that it is unfortunate for the memory of ,aristarchus that his work has come to us entire1 and who cannot refer#gjc to the statement of an eclipse rightly predicted by ,halicon of ,cyzicus without adding1 that if the story be true1 ,halicon was more lucky than prudent2--loses all his bitterness when he comes to ,hipparchus4#gac ,in ,hipparchus1 says he1 we find one of the most extraordinary men of antiquity2 the very greatest1 in the sciences which require a combination of observation with geometry4 ,delambre adds1 apparently in the wish to reconcile this eulogium with the depreciating manner in which he habitually speaks of all astronomers whose observations are inexact1 a long period and the continued efforts of many industrious men are requisite to produce good instruments1 but energy and assiduity depend on the man himself4 ,note #fhc3 ,synt4 ix4 #b4 ,note #fic3 ,astronomie ,ancienne1 i4 #ge4 ,note #gjc3 ,ib4 i4 #ag4 ,note #gac3 ,ib4 i4 #ahf4 ,hipparchus was the author of other great discoveries and improvements in astronomy1 besides the establishment of the ,doctrine of ,eccentrics and ,epicycles2 but this1 being the greatest advance in the theory of the celestial motions which was made by the ancients1 must be the leading subject of our attention in the present work2 our object being to discover in what the progress of real theoretical knowledge consists1 and under what circumstances it has gone on4 #aea ,sect4 #b4--;,estimate of the ,value of the ,theory of ,eccentrics and ,epicycles4 ,,it may be useful here to explain the value of the theoretical step which ,hipparchus thus made2 and the more so1 as there are1 perhaps1 opinions in popular circulation1 which might lead men to think lightly of the merit of introducing or establishing the ,doctrine of ,epicycles4 ,for1 in the first place1 this doctrine is now acknowledged to be false2 and some of the greatest men in the more modern history of astronomy owe the brightest part of their fame to their having been instrumental in overturning this hypothesis4 ,and1 moreover1 in the next place1 the theory is not only false1 but extremely perplexed and entangled1 so that it is usually looked upon as a mass of arbitrary and absurd complication4 ,most persons are familiar with passages in which it is thus spoken of4#gbc 4 4 4 4 4 ,he his fabric of the heavens ,hath left to their disputes1 perhaps to move ,his laughter at their quaint opinions wide2 ,hereafter1 when they come to model heaven ,and calculate the stars1 how will they wield ,the mighty frame6 how build1 unbuild1 contrive1 ,to save appearances6 how gird the sphere ,with centric and eccentric scribbled o'er1 ,cycle in epicycle1 orb in orb6 ,and every one will recollect the celebrated saying of ,alphonso ,x41 king of ,castile1#gcc when this complex system was explained to him2 that if ,god had consulted him at the creation1 the universe should have been on a better and simpler plan4 ,in addition to this1 the system is represented as involving an extravagant conception of the nature of the orbs which it introduces2 that they are crystalline spheres1 and that the vast spaces which intervene between the celestial luminaries are a solid mass1 formed by the fitting together of many masses perpetually in motion2 an imagination which is presumed to be incredible and monstrous4 ,note #gbc3 ,paradise ,lost1 viii4 ,note #gcc3 ,a4 ,d4 #abeb4 ,we must endeavor to correct or remove these prejudices1 not only in order that we may do justice to the ,hipparchian1 or1 as it is usually called1 ,ptolemaic system of astronomy1 and to its founder2 but for another reason1 much more important to the purpose of this work2 #aeb namely1 that we may see how theories may be highly estimable1 though they contain false representations of the real state of things1 and may be extremely useful1 though they involve unnecessary complexity4 ,in the advance of knowledge1 the value of the true part of a theory may much outweigh the accompanying error1 and the use of a rule may be little impaired by its want of simplicity4 ,the first steps of our progress do not lose their importance because they are not the last2 and the outset of the journey may require no less vigor and activity than its close4 ,that which is true in the ,hipparchian theory1 and which no succeeding discoveries have deprived of its value1 is the ,resolution of the apparent motions of the heavenly bodies into an assemblage of circular motions4 ,the test of the truth and reality of this ,resolution is1 that it leads to the construction of theoretical ,tables of the motions of the luminaries1 by which their places are given at any time1 agreeing nearly with their places as actually observed4 ,the assumption that these circular motions1 thus introduced1 are all exactly uniform1 is the fundamental principle of the whole process4 ,this assumption is1 it may be said1 false2 and we have seen how fantastic some of the arguments were1 which were originally urged in its favor4 ,but some assumption is necessary1 in order that the motions1 at different points of a revolution1 may be somehow connected1 that is1 in order that we may have any theory of the motions2 and no assumption more simple than the one now mentioned can be selected4 ,the merit of the theory is this2--that obtaining the amount of the eccentricity1 the place of the apogee1 and1 it may be1 other elements1 from few observations1 it deduces from these1 results agreeing with all observations1 however numerous and distant4 ,to express an inequality by means of an epicycle1 implies1 not only that there is an inequality1 but further1--that the inequality is at its greatest value at a certain known place1--diminishes in proceeding from that place by a known law1--continues its diminution for a known portion of the revolution of the luminary1--then increases again2 and so on3 that is1 the introduction of the epicycle represents the inequality of motion1 as completely as it can be represented with respect to its quantity4 ,we may further illustrate this1 by remarking that such a ,resolution of the unequal motions of the heavenly bodies into equable circular motions1 is1 in fact1 equivalent to the most recent and improved processes by which modern astronomers deal with such motions4 ,their universal method is to resolve all unequal motions into a series of #aec terms1 or expressions of partial motions2 and these terms involve sines and cosines1 that is1 certain technical modes of measuring circular motion1 the circular motion having some constant relation to the time4 ,and thus the problem of the resolution of the celestial motions into equable circular ones1 which was propounded above two thousand years ago in the school of ,plato1 is still the great object of the study of modern astronomers1 whether observers or calculators4 ,that ,hipparchus should have succeeded in the first great steps of this resolution for the sun and moon1 and should have seen its applicability in other cases1 is a circumstance which gives him one of the most distinguished places in the roll of great astronomers4 ,as to the charges or the sneers against the complexity of his system1 to which we have referred1 it is easy to see that they are of no force4 ,as a system of calculation1 his is not only good1 but1 as we have just said1 in many cases no better has yet been discovered4 ,if1 when the actual motions of the heavens are calculated in the best possible way1 the process is complex and difficult1 and if we are discontented at this1 nature1 and not the astronomer1 must be the object of our displeasure4 ,this plea of the astronomers must be allowed to be reasonable4 ,we must not be repelled1 says ,ptolemy1#gdc by the complexity of the hypotheses1 but explain the phenomena as well as we can4 ,if the hypotheses satisfy each apparent inequality separately1 the combination of them will represent the truth2 and why should it appear wonderful to any that such a complexity should exist in the heavens1 when we know nothing of their nature which entitles us to suppose that any inconsistency will result8 ,note #gdc3 ,synt4 xiii4 #b4 ,but it may be said1 we now know that the motions are more simple than they were thus represented1 and that the ,theory of ,epicycles was false1 as a conception of the real construction of the heavens4 ,and to this we may reply1 that it does not appear that the best astronomers of antiquity conceived the cycles and epicycles to have a material existence4 ,though the dogmatic philosophers1 as the ,aristotelians1 appear to have taught that the celestial spheres were real solid bodies1 they are spoken of by ,ptolemy as imaginary2#gec and it is clear1 from his proof of the identity of the results of the hypothesis of an eccentric and an epicycle1 that they are intended to pass for no more than geometrical conceptions1 in which view they are true representations of the apparent motions4 #aed ,note #gec3 ,ibid4 iii4 #c4 ,it is true1 that the real motions of the heavenly bodies are simpler than the apparent motions2 and that we1 who are in the habit of representing to our minds their real arrangement1 become impatient of the seeming confusion and disorder of the ancient hypotheses4 ,but this real arrangement never could have been detected by philosophers1 if the apparent motions had not been strictly examined and successfully analyzed4 ,how far the connection between the facts and the true theory is from being obvious or easily traced1 any one may satisfy himself by endeavoring1 from a general conception of the moon's real motions1 to discover the rules which regulate the occurrences of eclipses2 or even to explain to a learner1 of what nature the apparent motions of the moon among the stars will be4 ,the unquestionable evidence of the merit and value of the ,theory of ,epicycles is to be found in this circumstance2--that it served to embody all the most exact knowledge then extant1 to direct astronomers to the proper methods of making it more exact and complete1 to point out new objects of attention and research2 and that1 after doing this at first1 it was also able to take in1 and preserve1 all the new results of the active and persevering labors of a long series of ,greek1 ,latin1 ,arabian1 and modern ,european astronomers1 till a new theory arose which could discharge this office4 ,it may1 perhaps1 surprise some readers to be told1 that the author of this next great step in astronomical theory1 ,copernicus1 adopted the theory of epicycles2 that is1 he employed that which we have spoken of as its really valuable characteristic4 ,we#gfc must confess1 he says1 that the celestial motions are circular1 or compounded of several circles1 since their inequalities observe a fixed law and recur in value at certain intervals1 which could not be1 except that they were circular2 for a circle alone can make that which has been1 recur again4 ,note #gfc3 ,copernicus4 ,de ,rev4 #a4 i4 c4 #d4 ,in this sense1 therefore1 the ,hipparchian theory was a real and indestructible truth1 which was not rejected1 and replaced by different truths1 but was adopted and incorporated into every succeeding astronomical theory2 and which can never cease to be one of the most important and fundamental parts of our astronomical knowledge4 ,a moment's reflection will show that1 in the events just spoken of1 the introduction and establishment of the ,theory of ,epicycles1 those characteristics were strictly exemplified1 which we have asserted to be the conditions of every real advance in progressive science2 namely1 #aee the application of distinct and appropriate ,ideas to a real series of ,facts4 ,the distinctness of the geometrical conceptions which enabled ,hipparchus to assign the ,orbits of the ,sun and ,moon1 requires no illustration2 and we have just explained how these ideas combined into a connected whole the various motions and places of those luminaries4 ,to make this step in astronomy1 required diligence and care1 exerted in collecting observations1 and mathematical clearness and steadiness of view1 exercised in seeing and showing that the theory was a successful analysis of them4 ,sect4 #c4--;,discovery of the ,precession of the ,equinoxes4 ,,the same qualities which we trace in the researches of ,hipparchus already examined1--diligence in collecting observations1 and clearness of idea in representing them1--appear also in other discoveries of his1 which we must not pass unnoticed4 ,the ,precession of the ,equinoxes1 in particular1 is one of the most important of these discoveries4 ,the circumstance here brought into notice was a ,change of ,longitude of the ,fixed ,stars4 ,the longitudes of the heavenly bodies1 being measured from the point where the sun's annual path cuts the equator1 will change if that path changes4 ,whether this happens1 however1 is not very easy to decide2 for the sun's path among the stars is made out1 not by merely looking at the heavens1 but by a series of inferences from other observable facts4 ,hipparchus used for this purpose eclipses of the moon2 for these1 being exactly opposite to the sun1 afford data in marking out his path4 ,by comparing the eclipses of his own time with those observed at an earlier period by ,timocharis1 he found that the bright star1 ,spica ,virginis1 was six degrees behind the equinoctial point in his own time1 and had been eight degrees behind the same point at an earlier epoch4 ,the suspicion was thus suggested1 that the longitudes of all the stars increase perpetually2 but ,hipparchus had too truly philosophical a spirit to take this for granted4 ,he examined the places of ,regulus1 and those of other stars1 as he had done those of ,spica2 and he found1 in all these instances1 a change of place which could be explained by a certain alteration of position in the circles to which the stars are referred1 which alteration is described as the ,precession of the ,equinoxes4 ,the distinctness with which ,hipparchus conceived this change of relation of the heavens1 is manifested by the question which1 as we are told by ,ptolemy1 he examined and decided2--that this motion of the #aef heavens takes place about the poles of the ecliptic1 and not about those of the equator4 ,the care with which he collected this motion from the stars themselves1 may be judged of from this1 that having made his first observations for this purpose on ,spica and ,regulus1 zodiacal stars1 his first suspicion was that the stars of the zodiac alone changed their longitude1 which suspicion he disproved by the examination of other stars4 ,by his processes1 the idea of the nature of the motion1 and the evidence of its existence1 the two conditions of a discovery1 were fully brought into view4 ,the scale of the facts which ,hipparchus was thus able to reduce to law1 may be in some measure judged of by recollecting that the precession1 from his time to ours1 has only carried the stars through one sign of the zodiac2 and that1 to complete one revolution of the sky by the motion thus discovered1 would require a period of #be1jjj years4 ,thus this discovery connected the various aspects of the heavens at the most remote periods of human history2 and1 accordingly1 the novel and ingenious views which ,newton published in his chronology1 are founded on this single astronomical fact1 the ,precession of the ,equinoxes4 ,the two discoveries which have been described1 the mode of constructing ,solar and ,lunar ,tables1 and the ,precession1 were advances of the greatest importance in astronomy1 not only in themselves1 but in the new objects and undertakings which they suggested to astronomers4 ,the one discovery detected a constant law and order in the midst of perpetual change and apparent disorder2 the other disclosed mutation and movement perpetually operating where every thing had been supposed fixed and stationary4 ,such discoveries were well adapted to call up many questionings in the minds of speculative men2 for1 after this1 nothing could be supposed constant till it had been ascertained to be so by close examination2 and no apparent complexity or confusion could justify the philosopher in turning away in despair from the task of simplification4 ,to answer the inquiries thus suggested1 new methods of observing the facts were requisite1 more exact and uniform than those hitherto employed4 ,moreover1 the discoveries which were made1 and others which could not fail to follow in their train1 led to many consequences1 required to be reasoned upon1 systematized1 completed1 enlarged4 ,in short1 the ,epoch of ,induction led1 as we have stated that such epochs must always lead1 to a ,period of ,development1 of ,verification1 ,application1 and ,extension4 #aeg ,,chapter ,,iv4 ,,sequel ,,to ,,the ,,inductive ,,epoch ,,of ,,hipparchus4 ,sect4 #a4--,researches which verified the ,theory4 ,,the discovery of the leading ,laws of the ,solar and ,lunar ,motions1 and the detection of the ,precession1 may be considered as the great positive steps in the ,hipparchian astronomy2--the parent discoveries1 from which many minor improvements proceeded4 ,the task of pursuing the collateral and consequent researches which now offered themselves1--of bringing the other parts of astronomy up to the level of its most improved portions1--was prosecuted by a succession of zealous observers and calculators1 first1 in the school of ,alexandria1 and afterwards in other parts of the world4 ,we must notice the various labors of this series of astronomers2 but we shall do so very briefly2 for the ulterior development of doctrines once established is not so important an object of contemplation for our present purpose1 as the first conception and proof of those fundamental truths on which systematic doctrines are founded4 ,yet ,periods of ,verification1 as well as ,epochs of ,induction1 deserve to be attended to2 and they can nowhere be studied with so much advantage as in the history of astronomy4 ,in truth1 however1 ,hipparchus did not leave to his successors the task of pursuing into detail those views of the heavens to which his discoveries led him4 ,he examined with scrupulous care almost every part of the subject4 ,we must briefly mention some of the principal points which were thus settled by him4 ,the verification of the laws of the changes which he assigned to the skies1 implied that the condition of the heavens was constant1 except so far as it was affected by those changes4 ,thus1 the doctrine that the changes of position of the stars were rightly represented by the precession of the equinoxes1 supposed that the stars were fixed with regard to each other2 and the doctrine that the unequal number of days1 in certain subdivisions of months and years1 was adequately explained by the theory of epicycles1 assumed that years and days were always of constant lengths4 ,but ,hipparchus was not content with assuming these bases of his theory1 he endeavored to prove them4 #aeh #a4 ,fixity of the ,stars4--,the question necessarily arose after the discovery of the precession1 even if such a question had never suggested itself before1 whether the stars which were called fixed1 and to which the motions of the other luminaries are referred1 do really retain constantly the same relative position4 ,in order to determine this fundamental question1 ,hipparchus undertook to construct a ,map of the heavens2 for though the result of his survey was expressed in words1 we may give this name to his ,catalogue of the positions of the most conspicuous stars4 ,these positions are described by means of alineations2 that is1 three or more such stars are selected as can be touched by an apparent straight line drawn in the heavens4 ,thus ,hipparchus observed that the southern claw of ,cancer1 the bright star in the same constellation which precedes the head of the ,hydra1 and the bright star ,procyon1 were nearly in the same line4 ,ptolemy quotes this and many other of the configurations which ,hipparchus had noted1 in order to show that the positions of the stars had not changed in the intermediate time2 a truth which the catalogue of ,hipparchus thus gave astronomers the means of ascertaining4 ,it contained #ajhj stars4 ,the construction of this catalogue of the stars by ,hipparchus is an event of great celebrity in the history of astronomy4 ,pliny1#ggc who speaks of it with admiration as a wonderful and superhuman task 7ausus rem etiam ,deo improbam1 annumerare posteris stellas71 asserts the undertaking to have been suggested by a remarkable astronomical event1 the appearance of a new star2 novam stellam et alium in vo suo genitam deprehendit2 ejusque motu1 qua die fulsit1 ad dubitationem est adductus anne hoc spius fieret1 moverenturque et e quas putamus affixas4 ,there is nothing inherently improbable in this tradition1 but we may observe1 with ,delambre1#ghc that we are not informed whether this new star remained in the sky1 or soon disappeared again4 ,ptolemy makes no mention of the star or the story2 and his catalogue contains no bright star which is not found in the ,catasterisms of ,eratosthenes4 ,these ,catasterisms were an enumeration of #dge of the principal stars1 according to the constellations in which they are1 and were published about sixty years before ,hipparchus4 ,note #ggc3 ,nat4 ,hist4 lib4 ii4 7xxvi47 ,note #ghc3 ,a4 ,a4 i4 #bij4 #b4 ,constant ,length of ,years4--,hipparchus also attempted to ascertain whether successive years are all of the same length2 and though1 with his scrupulous love of accuracy1#gic he does not appear to have #aei thought himself justified in asserting that the years were always exactly equal1 he showed1 both by observations of the time when the sun passed the equinoxes1 and by eclipses1 that the difference of successive years1 if there were any difference1 must be extremely slight4 ,the observations of succeeding astronomers1 and especially of ,ptolemy1 confirmed this opinion1 and proved1 with certainty1 that there is no progressive increase or diminution in the duration of the year4 ,note #gic3 ,ptolem4 ,synt4 iii4 #b4 #c4 ,constant ,length of ,days4 ,equation of ,time4--,the equality of days was more difficult to ascertain than that of years2 for the year is measured1 as on a natural scale1 by the number of days which it contains2 but the day can be subdivided into hours only by artificial means2 and the mechanical skill of the ancients did not enable them to attain any considerable accuracy in the measure of such portions of time2 though clepsydras and similar instruments were used by astronomers4 ,the equality of days could only be proved1 therefore1 by the consequences of such a supposition2 and in this manner it appears to have been assumed1 as the fact really is1 that the apparent revolution of the stars is accurately uniform1 never becoming either quicker or slower4 ,it followed1 as a consequence of this1 that the solar days 7or rather the nycthemers1 compounded of a night and a day7 would be unequal1 in consequence of the sun's unequal motion1 thus giving rise to what we now call the ,equation of ,time1--the interval by which the time1 as marked on a dial1 is before or after the time1 as indicated by the accurate timepieces which modern skill can produce4 ,this inequality was fully taken account of by the ancient astronomers2 and they thus in fact assumed the equality of the sidereal days4 ,sect4 #b4--,researches which did not verify the ,theory4 ,,some of the researches of ,hipparchus and his followers fell upon the weak parts of his theory2 and if the observations had been sufficiently exact1 must have led to its being corrected or rejected4 ,among these we may notice the researches which were made concerning the ,parallax of the heavenly bodies1 that is1 their apparent displacement by the alteration of position of the observer from one part of the earth's surface to the other4 ,this subject is treated of at length by ,ptolemy2 and there can be no doubt that it was well examined by ,hipparchus1 who invented a parallactic instrument for that purpose4 ,the idea of parallax1 as a geometrical possibility1 was indeed too obvious to be overlooked by geometers at any time2 and when the doctrine of the sphere was established1 it must have appeared strange #afj to the student1 that every place on the earth's surface might alike be considered as the centre of the celestial motions4 ,but if this was true with respect to the motions of the fixed stars1 was it also true with regard to those of the sun and moon8 ,the displacement of the sun by parallax is so small1 that the best observers among the ancients could never be sure of its existence2 but with respect to the moon1 the case is different4 ,she may be displaced by this cause to the amount of twice her own breadth1 a quantity easily noticed by the rudest process of instrumental observation4 ,the law of the displacement thus produced is easily obtained by theory1 the globular form of the earth being supposed known2 but the amount of the displacement depends upon the distance of the moon from the earth1 and requires at least one good observation to determine it4 ,ptolemy has given a table of the effects of parallax1 calculated according to the apparent altitude of the moon1 assuming certain supposed distances2 these distances1 however1 do not follow the real law of the moon's distances1 in consequence of their being founded upon the ,hypothesis of the ,eccentric and ,epicycle4 ,in fact this ,hypothesis1 though a very close representation of the truth1 so far as the positions of the luminaries are concerned1 fails altogether when we apply it to their distances4 ,the radius of the epicycle1 or the eccentricity of the eccentric1 are determined so as to satisfy the observations of the apparent motions of the bodies2 but1 inasmuch as the hypothetical motions are different altogether from the real motions1 the ,hypothesis does not1 at the same time1 satisfy the observations of the distances of the bodies1 if we are able to make any such observations4 ,parallax is one method by which the distances of the moon1 at different times1 may be compared2 her ,apparent ,diameters afford another method4 ,neither of these modes1 however1 is easily capable of such accuracy as to overturn at once the ,hypothesis of epicycles2 and1 accordingly1 the ,hypothesis continued to be entertained in spite of such measures2 the measures being1 indeed1 in some degree falsified in consequence of the reigning opinion4 ,in fact1 however1 the imperfection of the methods of measuring parallax and magnitude1 which were in use at this period1 was such1 their results could not lead to any degree of conviction deserving to be set in opposition to a theory which was so satisfactory with regard to the more certain observations1 namely1 those of the motions4 ,the ,eccentricity1 or the ,radius of the ,epicycle1 which would satisfy #afa the inequality of the motions of the moon1 would1 in fact1 double the inequality of the distances4 ,the ,eccentricity of the moon's orbit is determined by ,ptolemy as #a_/ab of the radius of the orbit2 but its real amount is only half as great2 this difference is a necessary consequence of the supposition of uniform circular motions1 on which the ,epicyclic ,hypothesis proceeds4 ,we see1 therefore1 that this part of the ,hipparchian theory carries in itself the germ of its own destruction4 ,as soon as the art of celestial measurement was so far perfected1 that astronomers could be sure of the apparent diameter of the moon within #a_/cj or #a_/dj of the whole1 the inconsistency of the theory with itself would become manifest4 ,we shall see1 hereafter1 the way in which this inconsistency operated2 in reality a very long period elapsed before the methods of observing were sufficiently good to bring it clearly into view4 ,sect4 #c4--,methods of ,observation of the ,greek ,astronomers4 ,,we must now say a word concerning the ,methods above spoken of4 ,since one of the most important tasks of verification is to ascertain with accuracy the magnitude of the quantities which enter1 as elements1 into the theory which occupies men during the period2 the improvement of instruments1 and the methods of observing and experimenting1 are principal features in such periods4 ,we shall1 therefore1 mention some of the facts which bear upon this point4 ,the estimation of distances among the stars by the eye1 is an extremely inexact process4 ,in some of the ancient observations1 however1 this appears to have been the method employed2 and stars are described as being a cubit or two cubits from other stars4 ,we may form some notion of the scale of this kind of measurement1 from what ,cleomedes remarks1#hjc that the sun appears to be about a foot broad2 an opinion which he confutes at length4 ,note #hjc3 ,del4 ,a4 ,a4 i4 #bbb4 ,a method of determining the positions of the stars1 susceptible of a little more exactness than the former1 is the use of alineations1 already noticed in speaking of ,hipparchus's catalogue4 ,thus1 a straight line passing through two stars of the ,great ,bear passes also through the pole-star2 this is1 indeed1 even now a method usually employed to enable us readily to fix on the pole-star2 and the two stars and of ,ursa ,major1 are hence often called the pointers4 #afb ,but nothing like accurate measurements of any portions of the sky were obtained1 till astronomers adopted the method of making visual coincidences of the objects with the instruments1 either by means of shadows or of sights4 ,probably the oldest and most obvious measurements of the positions of the heavenly bodies were those in which the elevation of the sun was determined by comparing the length of the shadow of an upright staff or gnomon1 with the length of the staff itself4 ,it appears1#hac from a memoir of ,gautil1 first printed in the ,connaissance des ,temps for #ahji1 that1 at the lower town of ,loyang1 now called ,hon-anfou1 ,tchon-kong found the length of the shadow of the gnomon1 at the summer solstice1 equal to one foot and a half1 the gnomon itself being eight feet in length4 ,this was about #aajj ,b4 ,c4 ,the ,greeks1 at an early period1 used the same method4 ,strabo says#hbc that ,byzantium and ,marseilles are on the same parallel of latitude1 because the shadows at those places have the same proportion to the gnomon1 according to the statement of ,hipparchus1 who follows ,pytheas4 ,note #hac3 ,lib4 ,u4 ,k4 ,hist4 ,ast4 p4 #e4 ,note #hbc3 ,del4 ,a4 ,a4 i4 #beg4 ,but the relations of position which astronomy considers1 are1 for the most part1 angular distances2 and these are most simply expressed by the intercepted portion of a circumference described about the angular point4 ,the use of the gnomon might lead to the determination of the angle by the graphical methods of geometry2 but the numerical expression of the circumference required some progress in trigonometry2 for instance1 a table of the tangents of angles4 ,instruments were soon invented for measuring angles1 by means of circles1 which had a border or limb1 divided into equal parts4 ,the whole circumference was divided into #cfj degrees3 perhaps because the circles1 first so divided1 were those which represented the sun's annual path2 one such degree would be the sun's daily advance1 more nearly than any other convenient aliquot part which could be taken4 ,the position of the sun was determined by means of the shadow of one part of the instrument upon the other4 ,the most ancient instrument of this kind appears to be the ,hemisphere of ,berosus4 ,a hollow hemisphere was placed with its rim horizontal1 and a style was erected in such a manner that the extremity of the style was exactly at the centre of the sphere4 ,the shadow of this extremity1 on the concave surface1 had the same position with regard to the lowest point of the sphere which the sun had with regard to the highest point of the heavens4 #afc ,but this instrument was in fact used rather for dividing the day into portions of time than for determining position4 ,eratosthenes#hcc observed the amount of the obliquity of the sun's path to the equator3 we are not informed what instruments he used for this purpose2 but he is said to have obtained1 from the munificence of ,ptolemy ,euergetes1 two ,armils1 or instruments composed of circles1 which were placed in the portico at ,alexandria1 and long used for observations4 ,if a circular rim or hoop were placed so as to coincide with the plane of the equator1 the inner concave edge would be enlightened by the sun's rays which came under the front edge1 when the sun was south of the equator1 and by the rays which came over the front edge1 when the sun was north of the equator3 the moment of the transition would be the time of the equinox4 ,such an instrument appears to be referred to by ,hipparchus1 as quoted by ,ptolemy4#hdc ,the circle of copper1 which stands at ,alexandria in what is called the ,square ,porch1 appears to mark1 as the day of the equinox1 that on which the concave surface begins to be enlightened from the other side4 ,such an instrument was called an equinoctial armil4 ,note #hcc3 ,delambre1 ,a4 ,a4 i4 #hf4 ,note #hdc3 ,ptol4 ,synt4 iii4 #b4 ,a solstitial armil is described by ,ptolemy1 consisting of two circular rims1 one sliding round within the other1 and the inner one furnished with two pegs standing out from its surface at right angles1 and diametrically opposite to each other4 ,these circles being fixed in the plane of the meridian1 and the inner one turned1 till1 at noon1 the shadow of the peg in front falls upon the peg behind1 the position of the sun at noon would be determined by the degrees on the outer circle4 ,in calculation1 the degree was conceived to be divided into #fj minutes1 the minute into #fj seconds1 and so on4 ,but in practice it was impossible to divide the limb of the instrument into parts so small4 ,the armils of ,alexandria were divided into no parts smaller than sixths of degrees1 or divisions of #aj minutes4 ,the angles1 observed by means of these divisions1 were expressed as a fraction of the circumference4 ,thus ,eratosthenes stated the interval between the tropics to be #aa_/hc of the circumference4#hec ,note #hec3 ,delambre1 ,a4 ,a4 i4 #hg4 ,it is probable that his observation gave him #dg degrees4 ,the fraction #dg_/cfj #adc_/ajhj #aa #ac_/ajhj #aa_/7hca_/ac71 which is very nearly #aa_/hc4 ,it was soon remarked that the whole circumference of the circle #afd was not wanted for such observations4 ,ptolemy#hfc says that he found it more convenient to observe altitudes by means of a square flat piece of stone or wood1 with a quadrant of a circle described on one of its flat faces1 about a centre near one of the angles4 ,a peg was placed at the centre1 and one of the extreme radii of the quadrant being perpendicular to the horizon1 the elevation of the sun above the horizon was determined by observing the point of the arc of the quadrant on which the shadow of the peg fell4 ,note #hfc3 ,synt4 i4 #a4 ,as the necessity of accuracy in the observations was more and more felt1 various adjustments of such instruments were practised4 ,the instruments were placed in the meridian by means of a meridian line drawn by astronomical methods on the floor on which they stood4 ,the plane of the instrument was made vertical by means of a plumb-line3 the bounding radius1 from which angles were measured1 was also adjusted by the plumb-line4#hgc ,note #hgc3 ,the curvature of the plane of the circle1 by warping1 was noticed4 ,ptol4 iii4 #b4 p4 #aee1 observes that his equatorial circle was illuminated on the hollow side twice in the same day4 7,he did not know that this might arise from refraction47 ,in this manner1 the places of the sun and of the moon could be observed by means of the shadows which they cast4 ,in order to observe the stars1#hhc the observer looked along the face of the circle of the armil1 so as to see its two edges apparently brought together1 and the star apparently touching them4#hic ,note #hhc3 ,delamb4 ,a4 ,a4 i4 #ahe4 ,note #hic3 ,ptol4 ,synt4 i4 #a4 ' 4 ,it was afterwards found important to ascertain the position of the sun with regard to the ecliptic3 and1 for this purpose1 an instrument1 called an astrolabe1 was invented1 of which we have a description in ,ptolemy4#ijc ,this also consisted of circular rims1 movable within one another1 or about poles2 and contained circles which were to be brought into the position of the ecliptic1 and of a plane passing through the sun and the poles of the ecliptic4 ,the position of the moon with regard to the ecliptic1 and its position in longitude with regard to the sun or a star1 were thus determined4 ,note #ijc3 ,synt4 v4 #a4 ,the astrolabe continued long in use1 but not so long as the quadrant described by ,ptolemy2 this1 in a larger form1 is the mural quadrant1 which has been used up to the most recent times4 ,it may be considered surprising1#iac that ,hipparchus1 after having #afe observed1 for some time1 right ascensions and declinations1 quitted equatorial armils for the astrolabe1 which immediately refers the stars to the ecliptic4 ,he probably did this because1 after the discovery of precession1 he found the latitudes of the stars constant1 and wanted to ascertain their motion in longitude4 ,note #iac3 ,del4 ,a4 ,a4 #aha4 ,to the above instruments1 may be added the dioptra1 and the parallactic instrument of ,hipparchus and ,ptolemy4 ,in the latter1 the distance of a star from the zenith was observed by looking through two sights fixed in a rule1 this being annexed to another rule1 which was kept in a vertical position by a plumb-line2 and the angle between the two rules was measured4 ,the following example of an observation1 taken from ,ptolemy1 may serve to show the form in which the results of the instruments1 just described1 were usually stated4#ibc ,note #ibc3 ,del4 ,a4 ,a4 ii4 #bdh4 ,in the #b;d year of ,antoninus1 the #ith day of ,pharmouthi1 the sun being near setting1 the last division of ,taurus being on the meridian 7that is1 #e equinoctial hours after noon71 the moon was in #c degrees of ,pisces1 by her distance from the sun 7which was #ib degrees1 #h minutes72 and half an hour after1 the sun being set1 and the quarter of ,gemini on the meridian1 ,regulus appeared1 by the other circle of the astrolabe1 #eg degrees more forwards than the moon in longitude4 ,from these data the longitude of ,regulus is calculated4 ,from what has been said respecting the observations of the ,alexandrian astronomers1 it will have been seen that their instrumental observations could not be depended on for any close accuracy4 ,this defect1 after the general reception of the ,hipparchian theory1 operated very unfavorably on the progress of the science4 ,if they could have traced the moon's place distinctly from day to day1 they must soon have discovered all the inequalities which were known to ,tycho ,brahe2 and if they could have measured her parallax or her diameter with any considerable accuracy1 they must have obtained a confutation of the epicycloidal form of her orbit4 ,by the badness of their observations1 and the imperfect agreement of these with calculation1 they not only were prevented making such steps1 but were led to receive the theory with a servile assent and an indistinct apprehension1 instead of that rational conviction and intuitive clearness which would have given a progressive impulse to their knowledge4 #aff ,sect4 #d4--,period from ,hipparchus to ,ptolemy4 ,,we have now to speak of the cultivators of astronomy from the time of ,hipparchus to that of ,ptolemy1 the next great name which occurs in the history of this science2 though even he holds place only among those who verified1 developed1 and extended the theory of ,hipparchus4 ,the astronomers who lived in the intermediate time1 indeed1 did little1 even in this way2 though it might have been supposed that their studies were carried on under considerable advantages1 inasmuch as they all enjoyed the liberal patronage of the kings of ,egypt4#icc ,the divine school of ,alexandria1 as it is called by ,synesius1 in the fourth century1 appears to have produced few persons capable of carrying forwards1 or even of verifying1 the labors of its great astronomical teacher4 ,the mathematicians of the school wrote much1 and apparently they observed sometimes2 but their observations are of little value2 and their books are expositions of the theory and its geometrical consequences1 without any attempt to compare it with observation4 ,for instance1 it does not appear that any one verified the remarkable discovery of the precession1 till the time of ,ptolemy1 #bej years after2 nor does the statement of this motion of the heavens appear in the treatises of the intermediate writers2 nor does ,ptolemy quote a single observation of any person made in this long interval of time2 while his references to those of ,hipparchus are perpetual2 and to those of ,aristyllus and ,timocharis1 and of others1 as ,conon1 who preceded ,hipparchus1 are not unfrequent4 ,note #icc3 ,delamb4 ,a4 ,a4 ii4 #bdj4 ,this ,alexandrian period1 so inactive and barren in the history of science1 was prosperous1 civilized1 and literary2 and many of the works which belong to it are come down to us1 though those of ,hipparchus are lost4 ,we have the ,uranologion of ,geminus1#idc a systematic treatise on ,astronomy1 expounding correctly the ,hipparchian ,theories and their consequences1 and containing a good account of the use of the various ,cycles1 which ended in the adoption of the ,calippic ,period4 ,we have likewise ,the ,circular ,theory of the ,celestial ,bodies of ,cleomedes1#iec of which the principal part is a development of the doctrine of the sphere1 including the consequences of the globular form of the earth4 ,we have also another work on ,spherics by ,theodosius of ,bithynia1#ifc which contains some of the most important propositions of the subject1 and has been used as a book of #afg instruction even in modern times4 ,another writer on the same subject is ,menelaus1 who lived somewhat later1 and whose ,three ,books on ,spherics still remain4 ,note #idc3 ,b4 ,c4 #gj4 ,note #iec3 ,b4 ,c4 #fj4 ,note #ifc3 ,b4 ,c4 #ej4 ,one of the most important kinds of deduction from a geometrical theory1 such as that of the doctrine of the sphere1 or that of epicycles1 is the calculation of its numerical results in particular cases4 ,with regard to the latter theory1 this was done in the construction of ,solar and ,lunar ,tables1 as we have already seen2 and this process required the formation of a ,trigonometry1 or system of rules for calculating the relations between the sides and angles of triangles4 ,such a science had been formed by ,hipparchus1 who appears to be the author of every great step in ancient astronomy4#igc ,he wrote a work in twelve books1 ,on the ,construction of the ,tables of ,chords of ,arcs2 such a table being the means by which the ,greeks solved their triangles4 ,the ,doctrine of the ,sphere required1 in like manner1 a ,spherical ,trigonometry1 in order to enable mathematicians to calculate its results2 and this branch of science also appears to have been formed by ,hipparchus1#ihc who gives results that imply the possession of such a method4 ,hypsicles1 who was a contemporary of ,ptolemy1 also made some attempts at the solution of such problems3 but it is extraordinary that the writers whom we have mentioned as coming after ,hipparchus1 namely1 ,theodosius1 ,cleomedes1 and ,menelaus1 do not even mention the calculation of triangles1#iic either plain or spherical2 though the latter writer#ajjc is said to have written on the ,table of ,chords1 a work which is now lost4 ,note #igc3 ,delamb4 ,a4 ,a4 ii4 #cg4 ,note #ihc3 ,a4 ,a4 i4 #aag4 ,note #iic3 ,a4 ,a4 i4 #bdi4 ,note #ajjc3 ,a4 ,a4 ii4 #cg4 ,we shall see1 hereafter1 how prevalent a disposition in literary ages is that which induces authors to become commentators4 ,this tendency showed itself at an early period in the school of ,alexandria4 ,aratus1#ajac who lived #bgj ,b4 ,c4 at the court of ,antigonus1 king of ,macedonia1 described the celestial constellations in two poems1 entitled ,phnomena1 and ,prognostics4 ,these poems were little more than a versification of the treatise of ,eudoxus on the acronycal and heliacal risings and settings of the stars4 ,the work was the subject of a comment by ,hipparchus1 who perhaps found this the easiest way of giving connection and circulation to his knowledge4 ,three ,latin translations of this poem gave the ,romans the means of becoming acquainted with it3 the first is by ,cicero1 of which we have numerous fragments #afh extant2#ajbc ,germanicus ,csar1 one of the sons-in-law of ,augustus1 also translated the poem1 and this translation remains almost entire4 ,finally1 we have a complete translation by ,avienus4#ajcc ,the ,astronomica of ,manilius1 the ,poeticon ,astronomicon of ,hyginus1 both belonging to the time of ,augustus1 are1 like the work of ,aratus1 poems which combine mythological ornament with elementary astronomical exposition2 but have no value in the history of science4 ,we may pass nearly the same judgment upon the explanations and declamations of ,cicero1 ,seneca1 and ,pliny1 for they do not apprise us of any additions to astronomical knowledge2 and they do not always indicate a very clear apprehension of the doctrines which the writers adopt4 ,note #ajac3 ,a4 ,a4 i4 #gd4 ,note #ajbc3 ,two copies of this translation1 illustrated by drawings of different ages1 one set ,roman1 and the other ,saxon1 according to ,mr4 ,ottley1 are described in the ,archologia1 vol4 xviii4 ,note #ajcc3 ,montucla1 i4 #bba4 ,perhaps the most remarkable feature in the two last-named writers1 is the declamatory expression of their admiration for the discoverers of physical knowledge2 and in one of them1 ,seneca1 the persuasion of a boundless progress in science to which man was destined4 ,though this belief was no more than a vague and arbitrary conjecture1 it suggested other conjectures in detail1 some of which1 having been verified1 have attracted much notice4 ,for instance1 in speaking of comets1#ajdc ,seneca says1 ,the time will come when those things which are now hidden shall be brought to light by time and persevering diligence4 ,our posterity will wonder that we should be ignorant of what is so obvious4 ,the motions of the planets1 he adds1 complex and seemingly confused1 have been reduced to rule2 and some one will come hereafter1 who will reveal to us the paths of comets4 ,such convictions and conjectures are not to be admired for their wisdom2 for ,seneca was led rather by enthusiasm1 than by any solid reasons1 to entertain this opinion2 nor1 again1 are they to be considered as merely lucky guesses1 implying no merit2 they are remarkable as showing how the persuasion of the universality of law1 and the belief of the probability of its discovery by man1 grow up in men's minds1 when speculative knowledge becomes a prominent object of attention4 ,note #ajdc3 ,seneca1 ,qu4 ,n4 vii4 #be4 ,an important practical application of astronomical knowledge was made by ,julius ,csar1 in his correction of the calendar1 which we have already noticed2 and this was strictly due to the ,alexandrian ,school3 ,sosigenes1 an astronomer belonging to that school1 came from ,egypt to ,rome for the purpose4 #afi ,sect4 #e4--,measures of the ,earth4 ,,there were1 as we have said1 few attempts made1 at the period of which we are speaking1 to improve the accuracy of any of the determinations of the early ,alexandrian astronomers4 ,one question naturally excited much attention at all times1 the magnitude of the earth1 its figure being universally acknowledged to be a globe4 ,the ,chaldeans1 at an earlier period1 had asserted that a man1 walking without stopping1 might go round the circuit of the earth in a year2 but this might be a mere fancy1 or a mere guess4 ,the attempt of ,eratosthenes to decide this question went upon principles entirely correct4 ,syene was situated on the tropic2 for there1 on the day of the solstice1 at noon1 objects cast no shadow2 and a well was enlightened to the bottom by the sun's rays4 ,at ,alexandria1 on the same day1 the sun was1 at noon1 distant from the zenith by a fiftieth part of the circumference4 ,those two cities were north and south from each other3 and the distance had been determined1 by the royal overseers of the roads1 to be #ejjj stadia4 ,this gave a circumference of #bej1jjj stadia to the earth1 and a radius of about #dj1jjj4 ,aristotle#ajec says that the mathematicians make the circumference #djj1jjj stadia4 ,hipparchus conceived that the measure of ,eratosthenes ought to be increased by about one-tenth4#ajfc ,posidonius1 the friend of ,cicero1 made another attempt of the same kind4 ,at ,rhodes1 the star ,canopus but just appeared above the horizon2 at ,alexandria1 the same star rose to an altitude of #a_/dhth of the circumference2 the direct distance on the meridian was #ejjj stadia1 which gave #bdj1jjj for the whole circuit4 ,we cannot look upon these measures as very precise2 the stadium employed is not certainly known2 and no peculiar care appears to have been bestowed on the measure of the direct distance4 ,note #ajec3 ,de ,clo1 ii4 ad fin4 ,note #ajfc3 ,plin4 ii4 7cviii47 ,when the ,arabians1 in the ninth century1 came to be the principal cultivators of astronomy1 they repeated this observation in a manner more suited to its real importance and capacity of exactness4 ,under the ,caliph ,almamon1#ajgc the vast plain of ,singiar1 in ,mesopotamia1 was the scene of this undertaking4 ,the ,arabian astronomers there divided themselves into two bands1 one under the direction of ,chalid ben ,abdolmalic1 and the other having at its head ,alis ben ,isa4 ,these two parties proceeded1 the one north1 the other south1 determining the distance by the actual application of their measuring-rods to the ground1 #agj till each was found1 by astronomical observation1 to be a degree from the place at which they started4 ,it then appeared that these terrestrial degrees were respectively #ef miles1 and #ef miles and two-thirds1 the mile being #djjj cubits4 ,in order to remove all doubt concerning the scale of this measure1 we are informed that the cubit is that called the black cubit1 which consists of #bg inches1 each inch being the thickness of six grains of barley4 ,note #ajgc3 ,montu4 #ceg4 ,sect4 #f4--,ptolemy's ,discovery of ,evection4 ,,by referring1 in this place1 to the last-mentioned measure of the earth1 we include the labors of the ,arabian as well as the ,alexandrian astronomers1 in the period of mere detail1 which forms the sequel to the great astronomical revolution of the ,hipparchian epoch4 ,and this period of verification is rightly extended to those later times2 not merely because astronomers were then still employed in determining the magnitude of the earth1 and the amount of other elements of the theory1--for these are some of their employments to the present day1--but because no great intervening discovery marks a new epoch1 and begins a new period2--because no great revolution in the theory added to the objects of investigation1 or presented them in a new point of view4 ,this being the case1 it will be more instructive for our purpose to consider the general character and broad intellectual features of this period1 than to offer a useless catalogue of obscure and worthless writers1 and of opinions either borrowed or unsound4 ,but before we do this1 there is one writer whom we cannot leave undistinguished in the crowd2 since his name is more celebrated even than that of ,hipparchus2 his works contain ninety-nine hundredths of what we know of the ,greek astronomy2 and though he was not the author of a new theory1 he made some very remarkable steps in the verification1 correction1 and extension of the theory which he received4 ,i speak of ,ptolemy1 whose work1 ,the ,mathematical ,construction 7of the heavens71 contains a complete exposition of the state of astronomy in his time1 the reigns of ,adrian and ,antonine4 ,this book is familiarly known to us by a term which contains the record of our having received our first knowledge of it from the ,arabic writers4 ,the ,megiste ,syntaxis1 or ,great ,construction1 gave rise1 among them1 to the title ,al ,magisti1 or ,almagest1 by which the work is commonly described4 ,as a mathematical exposition of the ,theory of ,epicycles and ,eccentrics1 of the observations and calculations which were employed in #aga order to apply this theory to the sun1 moon1 and planets1 and of the other calculations which are requisite1 in order to deduce the consequences of this theory1 the work is a splendid and lasting monument of diligence1 skill1 and judgment4 ,indeed1 all the other astronomical works of the ancients hardly add any thing whatever to the information we obtain from the ,almagest2 and the knowledge which the student possesses of the ancient astronomy must depend mainly upon his acquaintance with ,ptolemy4 ,among other merits1 ,ptolemy has that of giving us a very copious account of the manner in which ,hipparchus established the main points of his theories2 an account the more agreeable1 in consequence of the admiration and enthusiasm with which this author everywhere speaks of the great master of the astronomical school4 ,in our present survey of the writings of ,ptolemy1 we are concerned less with his exposition of what had been done before him1 than with his own original labors4 ,in most of the branches of the subject1 he gave additional exactness to what ,hipparchus had done2 but our main business1 at present1 is with those parts of the ,almagest which contain new steps in the application of the ,hipparchian hypothesis4 ,there are two such cases1 both very remarkable1--that of the moon's ,evection1 and that of the ,planetary ,motions4 ,the law of the moon's anomaly1 that is1 of the leading and obvious inequality of her motion1 could be represented1 as we have seen1 either by an eccentric or an epicycle2 and the amount of this inequality had been collected by observations of eclipses4 ,but though the hypothesis of an epicycle1 for instance1 would bring the moon to her proper place1 so far as eclipses could show it1 that is1 at new and full moon1 this hypothesis did not rightly represent her motions at other points of her course4 ,this appeared1 when ,ptolemy set about measuring her distances from the sun at different times4 ,these1 he#ajhc says1 sometimes agreed1 and sometimes disagreed4 ,but by further attention to the facts1 a rule was detected in these differences4 ,as my knowledge became more complete and more connected1 so as to show the order of this new inequality1 ,i perceived that this difference was small1 or nothing1 at new and full moon2 and that at both the dichotomies 7when the moon is half illuminated7 it was small1 or nothing1 if the moon was at the apogee or perigee of the epicycle1 and was greatest when she was in the middle of the interval1 and therefore when the first #agb inequality was greatest also4 ,he then adds some further remarks on the circumstances according to which the moon's place1 as affected by this new inequality1 is before or behind the place1 as given by the epicyclical hypothesis4 ,note #ajhc3 ,synth4 v4 #b4 ,such is the announcement of the celebrated discovery of the moon's second inequality1 afterwards called 7by ,bullialdus7 the ,evection4 ,ptolemy soon proceeded to represent this inequality by a combination of circular motions1 uniting1 for this purpose1 the hypothesis of an epicycle1 already employed to explain the first inequality1 with the hypothesis of an eccentric1 in the circumference of which the centre of the epicycle was supposed to move4 ,the mode of combining these was somewhat complex2 more complex we may1 perhaps1 say1 than was absolutely requisite2#ajic the apogee of the eccentric moved backwards1 or contrary to the order of the signs1 and the centre of the epicycle moved forwards nearly twice as fast upon the circumference of the eccentric1 so as to reach a place nearly1 but not exactly1 the same1 as if it had moved in a concentric instead of an eccentric path4 ,thus the centre of the epicycle went twice round the eccentric in the course of one month3 and in this manner it satisfied the condition that it should vanish at new and full moon1 and be greatest when the moon was in the quarters of her monthly course4#aajc ,note #ajic3 ,if ,ptolemy had used the hypothesis of an eccentric instead of an epicycle for the first inequality of the moon1 an epicycle would have represented the second inequality more simply than his method did4 ,note #aajc3 ,i will insert here the explanation which my ,german translator1 the late distinguished astronomer ,littrow1 has given of this point4 ,the ,rule of this ,inequality1 the ,evection1 may be most simply expressed thus4 ,if a denote the excess of the ,moon's ,longitude over the ,sun's1 and b the ,anomaly of the ,moon reckoned from her ,perigee1 the ,evection is equal to #a4 #c4 sin 7#b;a - b74 ,at ,new and ,full ,moon1 a is #j or #ahj1 and thus the ,evection is - #a4c4sin b4 ,at both quarters1 or dichotomies1 a is #ij or #bgj1 and consequently the ,evection is #a4c 4 sin b4 ,the ,moon's ,elliptical ,equation of the centre is at all points of her orbit equal to #f4c4sin b4 ,the ,greek ,astronomers before ,ptolemy observed the moon only at the time of eclipses2 and hence they necessarily found for the sum of these two greatest inequalities of the moon's motion the quantity #f4c4 sin b - #a4c4sin b1 or #e4sin b3 and as they took this for the moon's equation of the centre1 which depends upon the eccentricity of the moon's orbit1 we obtain from this too small equation of the centre1 an eccentricity also smaller than the truth4 ,ptolemy1 who first observed the moon in her quarters1 found for the sum of those ,inequalities at those points the quantity #f4c4sin b #a4c4sin b1 or #g4f4sin b2 and thus made the eccentricity of the moon as much too great at the quarters as the observers of eclipses had made it too small4 ,he hence concluded that the eccentricity of the ,moon's orbit is variable1 which is not the case4 ,the discovery of the ,evection1 and the reduction of it to the #agc epicyclical theory1 was1 for several reasons1 an important step in astronomy2 some of these reasons may be stated4 #a4 ,it obviously suggested1 or confirmed1 the suspicion that the motions of the heavenly bodies might be subject to many inequalities3--that when one set of anomalies had been discovered and reduced to rule1 another set might come into view2--that the discovery of a rule was a step to the discovery of deviations from the rule1 which would require to be expressed in other rules2--that in the application of theory to observation1 we find1 not only the stated phenomena1 for which the theory does account1 but also residual phenomena1 which remain unaccounted for1 and stand out beyond the calculation2--that thus nature is not simple and regular1 by conforming to the simplicity and regularity of our hypotheses1 but leads us forwards to apparent complexity1 and to an accumulation of rules and relations4 ,a fact like the ,evection1 explained by an ,hypothesis like ,ptolemy's1 tended altogether to discourage any disposition to guess at the laws of nature from mere ideal views1 or from a few phenomena4 #b4 ,the discovery of ,evection had an importance which did not come into view till long afterwards1 in being the first of a numerous series of inequalities of the moon1 which results from the ,disturbing ,force of the sun4 ,these inequalities were successfully discovered2 and led finally to the establishment of the law of universal gravitation4 ,the moon's first inequality arises from a different cause2--from the same cause as the inequality of the sun's motion2--from the motion in an ellipse1 so far as the central attraction is undisturbed by any other4 ,this first inequality is called the ,elliptic ,inequality1 or1 more usually1 the ,equation of the ,centre4#aaac ,all the planets have such inequalities1 but the ,evection is peculiar to the moon4 ,the discovery of other inequalities of the moon's motion1 the ,variation and ,annual ,equation1 made an immediate sequel in the order of the subject to #agd the discoveries of ,ptolemy1 although separated by a long interval of time2 for these discoveries were only made by ,tycho ,brahe in the sixteenth century4 ,the imperfection of astronomical instruments was the great cause of this long delay4 ,note #aaac3 ,the ,equation of the ,centre is the difference between the place of the ,planet in its elliptical orbit1 and that place which a ,planet would have1 which revolved uniformly round the ,sun as a centre in a circular orbit in the same time4 ,an imaginary ,planet moving in the manner last described1 is called the mean ,planet1 while the actual ,planet which moves in the ellipse is called the true ,planet4 ,the ,longitude of the mean ,planet at a given time is easily found1 because its motion is uniform4 ,by adding to it the ,equation of the ,centre1 we find the ,longitude of the true ,planet1 and thus1 its place in its orbit4--,littrow's ,note4 ,i may add that the word ,equation1 used in such cases1 denotes in general a quantity which must be added to or subtracted from a mean quantity1 to make it equal to the true quantity2 or rather1 a quantity which must be added to or subtracted from a variably increasing quantity to make it increase equably4 #c4 ,the ,epicyclical ,hypothesis was found capable of accommodating itself to such new discoveries4 ,these new inequalities could be represented by new combinations of eccentrics and epicycles3 all the real and imaginary discoveries by astronomers1 up to ,copernicus1 were actually embodied in these hypotheses2 ,copernicus1 as we have said1 did not reject such hypotheses2 the lunar inequalities which ,tycho detected might have been similarly exhibited2 and even ,newton#aabc represents the motion of the moon's apogee by means of an epicycle4 ,as a mode of expressing the law of the irregularity1 and of calculating its results in particular cases1 the epicyclical theory was capable of continuing to render great service to astronomy1 however extensive the progress of the science might be4 ,it was1 in fact1 as we have already said1 the modern process of representing the motion by means of a series of circular functions4 ,note #aabc3 ,principia1 lib4 iii4 prop4 xxxv4 #d4 ,but though the doctrine of eccentrics and epicycles was thus admissible as an ,hypothesis1 and convenient as a means of expressing the laws of the heavenly motions1 the successive occasions on which it was called into use1 gave no countenance to it as a ,theory2 that is1 as a true view of the nature of these motions1 and their causes4 ,by the steps of the progress of this ,hypothesis1 it became more and more complex1 instead of becoming more simple1 which1 as we shall see1 was the course of the true ,theory4 ,the notions concerning the position and connection of the heavenly bodies1 which were suggested by one set of phenomena1 were not confirmed by the indications of another set of phenomena2 for instance1 those relations of the epicycles which were adopted to account for the ,motions of the heavenly bodies1 were not found to fall in with the consequences of their apparent ,diameters and ,parallaxes4 ,in reality1 as we have said1 if the relative distances of the sun and moon at different times could have been accurately determined1 the ,theory of ,epicycles must have been forthwith overturned4 ,the insecurity of such measurements alone maintained the theory to later times4#aacc #age ,note #aacc3 ,the alteration of the apparent diameter of the moon is so great that it cannot escape us1 even with very moderate instruments4 ,this apparent diameter contains1 when the moon is nearest the earth1 #bjaj seconds2 when she is furthest off #agfb seconds2 that is1 #bdh seconds1 or #d minutes #h seconds1 less than in the former case4 ,the two quantities are in the proportion of #h to #g1 nearly4--,littrow's ,note4 ,sect4 #g4--;,conclusion of the ,history of ,greek ,astronomy4 ,i ,,might now proceed to give an account of ,ptolemy's other great step1 the determination of the ,planetary ,orbits2 but as this1 though in itself very curious1 would not illustrate any point beyond those already noticed1 ,i shall refer to it very briefly4 ,the planets all move in ellipses about the sun1 as the moon moves about the earth2 and as the sun apparently moves about the earth4 ,they will therefore each have an ,elliptic ,inequality or ,equation of the centre1 for the same reason that the sun and moon have such inequalities4 ,and this inequality may be represented1 in the cases of the planets1 just as in the other two1 by means of an eccentric2 the epicycle1 it will be recollected1 had already been used in order to represent the more obvious changes of the planetary motions4 ,to determine the amount of the ,eccentricities and the places of the ,apogees of the planetary orbits1 was the task which ,ptolemy undertook2 ,hipparchus1 as we have seen1 having been destitute of the observations which such a process required4 ,the determination of the ,eccentricities in these cases involved some peculiarities which might not at first sight occur to the reader4 ,the 9999elcliptical motion of the planets takes place about the sun2 but ,ptolemy considered their movements as altogether independent of the sun1 and referred them to the earth alone2 and thus the apparent eccentricities which he had to account for1 were the compound result of the ,eccentricity of the earth's orbit1 and of the proper eccentricity of the orbit of the ,planet4 ,he explained this result by the received mechanism of an eccentric ,deferent1 carrying an ,epicycle2 but the motion in the ,deferent is uniform1 not about the centre of the circle1 but about another point1 the ,equant4 ,without going further into detail1 it may be sufficient to state that1 by a combination of ,eccentrics and ,epicycles1 he did account for the leading features of these motions2 and by using his own observations1 compared with more ancient ones 7for instance1 those of ,timocharis for ,venus71 he was able to determine the ,dimensions and ,positions of the orbits4#aadc #agf ,note #aadc3 ,ptolemy determined the ,radius and the ,periodic ,time of his two circles for each ,planet in the following manner3 ,for the inferior ,planets1 that is1 ,mercury and ,venus1 he took the ,radius of the ,deferent equal to the ,radius of the ,earth's orbit1 and the ,radius of the ,epicycle equal to that of the ,planet's orbit4 ,for these ,planets1 according to his assumption1 the ,periodic ,time of the ,planet in its ,epicycle was to the ,periodic ,time of the ,epicyclical ,centre on the ,deferent1 as the synodical ,revolution of the ,planet to the tropical ,revolution of the ,earth above the ,sun4 ,for the three superior ,planets1 ,mars1 ,jupiter1 and ,saturn1 the ,radius of the ,deferent was equal to the ,radius of the ,planet's orbit1 and the ,radius of the ,epicycle was equal to the ,radius of the ,earth's orbit2 the ,periodic ,time on the ,planet in its ,epicycle was to the ,periodic ,time of the ,epicyclical ,centre on the ,deferent1 as the synodical ,revolution of the ,planet to the tropical ,revolution of the same ,planet4 ,ptolemy might obviously have made the geometrical motions of all the ,planets correspond with the observations by one of these two modes of construction2 but he appears to have adopted this double form of the theory1 in order that in the inferior1 as well as in the superior ,planets1 he might give the smaller of the two ,radii to the ,epicycle3 that is1 in order that he might make the smaller circle move round the larger1 not vice vers4--,littrow's ,notes4 ,i shall here close my account of the astronomical progress of the ,greek ,school4 ,my purpose is only to illustrate the principles on which the progress of science depends1 and therefore ,i have not at all pretended to touch upon every part of the subject4 ,some portion of the ancient theories1 as1 for instance1 the mode of accounting for the motions of the moon and planets in latitude1 are sufficiently analogous to what has been explained1 not to require any more especial notice4 ,other parts of ,greek astronomical knowledge1 as1 for instance1 their acquaintance with refraction1 did not assume any clear or definite form1 and can only be considered as the prelude to modern discoveries on the same subject4 ,and before we can with propriety pass on to these1 there is a long and remarkable1 though unproductive interval1 of which some account must be given4 ,sect4 #h4--;,arabian ,astronomy4 ,,the interval to which ,i have just alluded may be considered as extending from ,ptolemy to ,copernicus2 we have no advance in ,greek astronomy after the former2 no signs of a revival of the power of discovery till the latter4 ,during this interval of #acej years1#aaec the principal cultivators of astronomy were the ,arabians1 who adopted this science from the ,greeks whom they conquered1 and from whom the conquerors of western ,europe again received back their treasure1 when the love of science and the capacity for it had been awakened in their minds4 ,in the intervening time1 the precious deposit had undergone little change4 ,the ,arab astronomer had been the scrupulous but unprofitable servant1 who kept his talent without apparent danger of loss1 but also without prospect of increase4 ,there is little in #agg ,arabic literature which bears upon the progress of astronomy2 but as the little that there is must be considered as a sequel to the ,greek science1 ,i shall notice one or two points before ,i treat of the stationary period in general4 ,note #aaec3 ,ptolemy died about ,a4 ,d4 #aej4 ,copernicus was living ,a4 ,d4 #aejj4 ,when the sceptre of western ,asia had passed into the hands of the ,abasside caliphs1#aafc ,bagdad1 the city of peace1 rose to splendor and refinement1 and became the metropolis of science under the successors of ,almansor the ,victorious1 as ,alexandria had been under the successors of ,alexander the ,great4 ,astronomy attracted peculiarly the favor of the powerful as well as the learned2 and almost all the culture which was bestowed upon the science1 appears to have had its source in the patronage1 often also in the personal studies1 of ,saracen princes4 ,under such encouragement1 much was done1 in those scientific labors which money and rank can command4 ,translations of ,greek works were made1 large instruments were erected1 observers were maintained2 and accordingly as observation showed the defects and imperfection of the extant tables of the celestial motions1 new ones were constructed4 ,thus under ,almansor1 the ,grecian works of science were collected from all quarters1 and many of them translated into ,arabic4#aagc ,the translation of the ,megiste ,syntaxis of ,ptolemy1 which thus became the ,almagest1 is ascribed to ,isaac ben ,homain in this reign4 ,note #aafc3 ,gibbon1 x4 #ca4 ,note #aagc3 ,id4 x4 #cf4 ,the greatest of the ,arabian ,astronomers comes half a century later4 ,this is ,albategnius1 as he is commonly called2 or more exactly1 ,mohammed ben ,geber ,albatani1 the last appellation indicating that he was born at ,batan1 a city of ,mesopotamia4#aahc ,he was a ,syrian prince1 whose residence was at ,aracte or ,racha in ,mesopotamia3 a part of his observations were made at ,antioch4 ,his work still remains to us in ,latin4 ,after having read1 he says1 the ,syntaxis of ,ptolemy1 and learnt the methods of calculation employed by the ,greeks1 his observations led him to conceive that some improvements might be made in their results4 ,he found it necessary to add to ,ptolemy's observations as ,ptolemy had added to those of ,abrachis 7,hipparchus74 ,he then published ,tables of the motions of the sun1 moon1 and planets1 which long maintained a high reputation4 ,note #aahc3 ,del4 ,astronomie du ,moyen ,age1 #d4 ,these1 however1 did not prevent the publication of others4 ,under the ,caliph ,hakem 7about ,a4 ,d4 #ajjj7 ,ebon ,iounis published ,tables of the ,sun1 ,moon1 and ,planets1 which were hence called the ,hakemite ,tables4 ,not long after1 ,arzachel of ,toledo published the ,toletan #agh ,tables4 ,in the #acth century1 ,nasir ,eddin published ,tables of the ,stars1 dedicated to ,ilchan1 a ,tartar prince1 and hence termed the ,ilchanic ,tables4 ,two centuries later1 ,ulugh ,beigh1 the grandson of ,tamerlane1 and prince of the countries beyond the ,oxus1 was a zealous practical astronomer2 and his ,tables1 which were published in ,europe by ,hyde in #affe1 are referred to as important authority by modern astronomers4 ,the series of ,astronomical ,tables which we have thus noticed1 in which1 however1 many are omitted1 leads us to the ,alphonsine ,tables1 which were put forth in #adhh1 and in succeeding years1 under the auspices of ,alphonso1 king of ,castile2 and thus brings us to the verge of modern astronomy4 ,for all these ,tables1 the ,ptolemaic hypotheses were employed2 and1 for the most part1 without alteration4 ,the ,arabs sometimes felt the extreme complexity and difficulty of the doctrine which they studied2 but their minds did not possess that kind of invention and energy by which the philosophers of ,europe1 at a later period1 won their way into a simpler and better system4 ,thus ,alpetragius states1 in the outset of his ,planetarum ,theorica1 that he was at first astonished and stupefied with this complexity1 but that afterwards ,god was pleased to open to him the occult secret in the theory of his orbs1 and to make known to him the truth of their essence and the rectitude of the quality of their motion4 ,his system consists1 according to ,delambre1#aaic in attributing to the planets a spiral motion from east to west1 an idea already refuted by ,ptolemy4 ,geber of ,seville criticises ,ptolemy very severely1#abjc but without introducing any essential alteration into his system4 ,the ,arabian observations are in many cases valuable2 both because they were made with more skill and with better instruments than those of the ,greeks2 and also because they illustrate the permanence or variability of important elements1 such as the obliquity of the ecliptic and the inclination of the moon's orbit4 ,note #aaic3 ,delambre1 ,m4 ,a4 p4 #g4 ,note #abjc3 ,m4 ,a4 p4 #ahj1 c4 ,we must1 however1 notice one or two peculiar ,arabian doctrines4 ,the most important of these is the discovery of the ,motion of the ,son's ,apogee by ,albategnius4 ,he found the ,apogee to be in longitude #hb degrees2 ,ptolemy had placed it in longitude #fe degrees4 ,the difference of #ag degrees was beyond all limit of probable error of calculation1 though the process is not capable of great precision2 and the inference of the ,motion of the ,apogee was so obvious1 that we cannot #agi agree with ,delambre1 in doubting or extenuating the claim of ,albategnius to this discovery1 on the ground of his not having expressly stated it4 ,in detecting this motion1 the ,arabian astronomers reasoned rightly from facts well observed3 they were not always so fortunate4 ,arzachel1 in the #aath century1 found the apogee of the sun to be less advanced than ,albategnius had found it1 by some degrees2 he inferred that it had receded in the intermediate time2 but we now know1 from an acquaintance with its real rate of moving1 that the true inference would have been1 that ,albategnius1 whose method was less trustworthy than that of ,arzachel1 had made an error to the amount of the difference thus arising4 ,a curious1 but utterly false hypothesis was founded on observations thus erroneously appreciated2 namely1 the ,trepidation of the fixed stars4 ,arzachel conceived that a uniform ,precession of the equinoctial points would not account for the apparent changes of position of the stars1 and that for this purpose1 it was necessary to conceive two circles of about eight degrees radius described round the equinoctial points of the immovable sphere1 and to suppose the first points of ,aries and ,libra to describe the circumference of these circles in about #hjj years4 ,this would produce1 at one time a progression1 and at another a regression1 of the apparent equinoxes1 and would moreover change the latitude of the stars4 ,such a motion is entirely visionary2 but the doctrine made a sect among astronomers1 and was adopted in the first edition of the ,alphonsine ,tables1 though afterwards rejected4 ,an important exception to the general unprogressive character of ,arabian science has been pointed out recently by ,m4 ,sedillot4#abac ,it appears that ,mohammed-,aboul ,wefa-al-,bouzdjani1 an ,arabian astronomer of the tenth century1 who resided at ,cairo1 and observed at ,bagdad in #ige1 discovered a third inequality of the moon1 in addition to the two expounded by ,ptolemy1 the ,equation of the ,centre1 and the ,evection4 ,this third inequality1 the ,variation1 is usually supposed to have been discovered by ,tycho ,brahe1 six centuries later4 ,it is an inequality of the moon's motion1 in virtue of which she moves quickest when she is at new or full1 and slowest at the first and third quarter2 in consequence of this1 from the first quarter to the full1 she is behind her mean place2 at the full1 she does not differ from her mean place2 from the full to the third quarter1 she is before her true #ahj place2 and so on2 and the greatest effect of the inequality is in the octants1 or points half-way between the four quarters4 ,in an ,almagest of ,aboul ,wefa1 a part of which exists in the ,royal ,library at ,paris1 after describing the two inequalities of the moon1 he has a ,section ix41 ,of the ,third ,anomaly of the moon called ,muhazal or ,prosneusis4 ,he there says1 that taking cases when the moon was in apogee or perigee1 and when1 consequently1 the effect of the two first inequalities vanishes1 he found1 by observation of the moon1 when she was nearly in trine and in sextile with the sun1 that she was a degree and a quarter from her calculated place4 ,and hence1 he adds1 ,i perceived that this anomaly exists independently of the two first3 and this can only take place by a declination of the diameter of the epicycle with respect to the centre of the zodiac4 ,note #abac3 ,sedillot1 ,nouvelles ,rech4 sur l',hist4 de l',astron4 chez les ,arabes4 ,nouveau ,journal ,asiatique4 #ahcf4 ,we may remark that we have here this inequality of the moon made out in a really philosophical manner2 a residual quantity in the moon's longitude being detected by observation1 and the cases in which it occurs selected and grouped by an inductive effort of the mind4 ,the advance is not great2 for ,aboul ,wefa appears only to have detected the existence1 and not to have fixed the law or the exact quantity of the inequality2 but still it places the scientific capacity of the ,arabs in a more favorable point of view than any circumstance with which we were previously acquainted4 ,but this discovery of ,aboul ,wefa appears to have excited no notice among his contemporaries and followers3 at least it had been long quite forgotten when ,tycho ,brahe rediscovered the same lunar inequality4 ,we can hardly help looking upon this circumstance as an evidence of a servility of intellect belonging to the ,arabian period4 ,the learned ,arabians were so little in the habit of considering science as progressive1 and looking with pride and confidence at examples of its progress1 that they had not the courage to believe in a discovery which they themselves had made1 and were dragged back by the chain of authority1 even when they had advanced beyond their ,greek masters4 ,as the ,arabians took the whole of their theory 7with such slight exceptions as we have been noticing7 from the ,greeks1 they took from them also the mathematical processes by which the consequences of the theory were obtained4 ,arithmetic and ,trigonometry1 two main branches of these processes1 received considerable improvements at their hands4 ,in the former1 especially1 they rendered a service to the world which it is difficult to estimate too highly1 in abolishing the #aha cumbrous ,sexagesimal ,arithmetic of the ,greeks1 and introducing the notation by means of the digits #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i1 #j1 which we now employ4#abbc ,these numerals appear to be of ,indian origin1 as is acknowledged by the ,arabs themselves2 and thus form no exception to the sterility of the ,arabian genius as to great scientific inventions4 ,another improvement1 of a subordinate kind1 but of great utility1 was ,arabian1 being made by ,albategnius4 ,he introduced into calculation the sine1 or half-chord of the double arc1 instead of the chord of the arc itself1 which had been employed by the ,greek astronomers4 ,there have been various conjectures concerning the origin of the word sine2 the most probable appears to be that sinus is the ,latin translation of the ,arabic word gib1 which signifies a fold1 the two halves of the chord being conceived to be folded together4 ,note #abbc3 ,mont4 i4 #cgf4 ,the great obligation which ,science owes to the ,arabians1 is to have preserved it during a period of darkness and desolation1 so that ,europe might receive it back again when the evil days were past4 ,we shall see hereafter how differently the ,european intellect dealt with this hereditary treasure when once recovered4 ,before quitting the subject1 we may observe that ,astronomy brought back1 from her sojourn among the ,arabs1 a few terms which may still be perceived in her phraseology4 ,such are the zenith1 and the opposite imaginary point1 the nadir2--the circles of the sphere termed almacantars and azimuth circles4 ,the alidad of an instrument is its index1 which possesses an angular motion4 ,some of the stars still retain their ,arabic names2 ,aldebran1 ,rigel1 ,fomalhaut2 many others were known by such appellations a little while ago4 ,perhaps the word almanac is the most familiar vestige of the ,arabian period of astronomy4 ,it is foreign to my purpose to note any efforts of the intellectual faculties among other nations1 which may have taken place independently of the great system of progressive ,european culture1 from which all our existing science is derived4 ,otherwise ,i might speak of the astronomy of some of the ,orientals1 for example1 the ,chinese1 who are said1 by ,montucla 7i4 #dfe71 to have discovered the first equation of the moon1 and the proper motion of the fixed stars 7the ,precession71 in the third century of our era4 ,the ,greeks had made these discoveries #ejj years earlier4 #ahc ,,book ,,iv4 ,,history ,,of ,,physical ,,science ,,in ,,the ,,middle ,,ages2 ,,or1 ,,view ,,of ,,the ,,stationary ,,period ,,of ,,inductive ,,science4 ,in vain1 in vain6 the all-composing hour ,resistless falls 4 4 4 4 4 4 4 4 4 ,as one by one1 at dread ,medea's strain1 ,the sickening stars fade off th' ethereal plain2 ,as ,argus' eyes1 by ,hermes' wand opprest1 ,closed one by one to everlasting rest2 ,thus at her felt approach and secret might1 ,art after art goes out1 and all is night4 ,see skulking ,truth to her old cavern fled1 ,mountains of casuistry heaped on her head2 ,philosophy1 that reached the heavens before1 ,shrinks to her hidden cause1 and is no more4 ,physic of ,metaphysic begs defence1 ,and ,metaphysic calls for aid to ,sense3 ,see ,mystery to ,mathematics fly6 ,in vain6 they gaze1 turn giddy1 rave1 and die4 ,dunciad1 ,b4 iv4 #ahe ,,introduction4 ,,we have now to consider more especially a long and barren period1 which intervened between the scientific activity of ancient ,greece and that of modern ,europe2 and which we may1 therefore1 call the ,stationary ,period of ,science4 ,it would be to no purpose to enumerate the various forms in which1 during these times1 men reproduced the discoveries of the inventive ages2 or to trace in them the small successes of ,art1 void of any principle of genuine ,philosophy4 ,our object requires rather that we should point out the general and distinguishing features of the intellect and habits of those times4 ,we must endeavor to delineate the character of the ,stationary ,period1 and1 as far as possible1 to analyze its defects and errors2 and thus obtain some knowledge of the causes of its barrenness and darkness4 ,we have already stated1 that real scientific progress requires distinct general ,ideas1 applied to many special and certain ,facts4 ,in the period of which we now have to speak1 men's ,ideas were obscured2 their disposition to bring their general views into accordance with ,facts was enfeebled4 ,they were thus led to employ themselves unprofitably1 among indistinct and unreal notions4 ,and the evil of these tendencies was further inflamed by moral peculiarities in the character of those times2--by an abjectness of thought on the one hand1 which could not help looking towards some intellectual superior1 and by an impatience of dissent on the other4 ,to this must be added an enthusiastic temper1 which1 when introduced into speculation1 tends to subject the mind's operations to ideas altogether distorted and delusive4 ,these characteristics of the stationary period1 its obscurity of thought1 its servility1 its intolerant disposition1 and its enthusiastic temper1 will be treated of in the four following chapters1 on the ,indistinctness of ,ideas1 the ,commentatorial ,spirit1 the ,dogmatism1 and the ,mysticism of the ,middle ,ages4 #ahf ,,chapter ,i4 ,,on ,,the ,,indistinctness ,,of ,,ideas ,,of ,,the ,,middle ,,ages4 ,,that firm and entire possession of certain clear and distinct general ideas which is necessary to sound science1 was the character of the minds of those among the ancients who created the several sciences which arose among them4 ,it was indispensable that such inventors should have a luminous and steadfast apprehension of certain general relations1 such as those of space and number1 order and cause2 and should be able to apply these notions with perfect readiness and precision to special facts and cases4 ,it is necessary that such scientific notions should be more definite and precise than those which common language conveys2 and in this state of unusual clearness1 they must be so familiar to the philosopher1 that they are the language in which he thinks4 ,the discoverer is thus led to doctrines which other men adopt and follow out1 in proportion as they seize the fundamental ideas1 and become acquainted with the leading facts4 ,thus ,hipparchus1 conceiving clearly the motions and combinations of motion which enter into his theory1 saw that the relative lengths of the seasons were sufficient data for determining the form of the sun's orbit2 thus ,archimedes1 possessing a steady notion of mechanical pressure1 was able1 not only to deduce the properties of the lever and of the centre of gravity1 but also to see the truth of those principles respecting the distribution of pressure in fluids1 on which the science of hydrostatics depends4 ,with the progress of such distinct ideas1 the inductive sciences rise and flourish2 with the decay and loss of such distinct ideas1 these sciences become stationary1 languid1 and retrograde4 ,when men merely repeat the terms of science1 without attaching to them any clear conceptions2--when their apprehensions become vague and dim2--when they assent to scientific doctrines as a matter of tradition1 rather than of conviction1 on trust rather than on sight2--when science is considered as a collection of opinions1 rather than a record of laws by which the universe is really governed2--it must inevitably happen1 that men will lose their hold on the knowledge which the great discoverers who preceded them have brought to light4 ,they are not able to push forwards the truths on which they lay so #ahg feeble and irresolute a hand2 probably they cannot even prevent their sliding back towards the obscurity from which they had been drawn1 or from being lost altogether4 ,such indistinctness and vacillation of thought appear to have prevailed in the stationary period1 and to be1 in fact1 intimately connected with its stationary character4 ,i shall point out some indications of the intellectual peculiarity of which ,i speak4 #a4 ,collections of ,opinions4--,the fact1 that mere ,collections of the opinions of physical philosophers came to hold a prominent place in literature1 already indicated a tendency to an indistinct and wandering apprehension of such opinions4 ,i speak of such works as ,plutarch's five ,books on the ,opinions of ,philosophers1 or the physical opinions which ,diogenes ,lartius gives in his ,lives of the ,philosophers4 ,at an earlier period still1 books of this kind appear2 as for instance1 a large portion of ,pliny's ,natural ,history1 a work which has very appropriately been called the ,encyclopdia of ,antiquity2 even ,aristotle himself is much in the habit of enumerating the opinions of those who had preceded him4 ,to present such statements as an important part of physical philosophy1 shows an erroneous and loose apprehension of its nature4 ,for the only proof of which its doctrines admit1 is the possibility of applying the general theory to each particular case2 the authority of great men1 which in moral and practical matters may or must have its weight1 is here of no force2 and the technical precision of ideas which the terms of a sound physical theory usually demand1 renders a mere statement of the doctrines very imperfectly intelligible to readers familiar with common notions only4 ,to dwell upon such collections of opinions1 therefore1 both implies1 and produces1 in writers and readers1 an obscure and inadequate apprehension of the full meaning of the doctrines thus collected2 supposing there be among them any which really possess such a clearness1 solidity1 and reality1 as to make them important in the history of science4 ,such diversities of opinion convey no truth2 such a multiplicity of statements of what has been said1 in no degree teaches us what is2 such accumulations of indistinct notions1 however vast and varied1 do not make up one distinct idea4 ,on the contrary1 the habit of dwelling upon the verbal expressions of the views of other persons1 and of being content with such an apprehension of doctrines as a transient notice can give us1 is fatal to firm and clear thought3 it indicates wavering and feeble conceptions1 which are inconsistent with speculation4 #ahh ,we may1 therefore1 consider the prevalence of ,collections of the kind just referred to1 as indicating a deficiency of philosophical talent in the ages now under review4 ,as evidence of the same character1 we may add the long train of publishers of ,abstracts1 ,epitomes1 ,bibliographical ,notices1 and similar writers4 ,all such writers are worthless for all purposes of science1 and their labors may be considered as dead works2 they have in them no principle of philosophical vitality2 they draw their origin and nutriment from the death of true physical knowledge2 and resemble the swarms of insects that are born from the perishing carcass of some noble animal4 #b4 ,indistinctness of ,ideas in ,mechanics4--,but the indistinctness of thought which is so fatal a feature in the intellect of the stationary period1 may be traced more directly in the works1 even of the best authors1 of those times4 ,we find that they did not retain steadily the ideas on which the scientific success of the previous period had depended4 ,for instance1 it is a remarkable circumstance in the history of the science of ,mechanics1 that it did not make any advance from the time of ,archimedes to that of ,stevinus and ,galileo4 ,archimedes had established the doctrine of the lever2 several persons tried1 in the intermediate time1 to prove the property of the inclined plane1 and none of them succeeded4 ,but let us look to the attempts2 for example1 that of ,pappus1 in the eighth ,book of his ,mathematical ,collections1 and we may see the reason of the failure4 ,his ,problem shows1 in the very terms in which it is propounded1 the want of a clear apprehension of the subject4 ,having given the power which will draw a given weight along the horizontal plane1 to find the additional power which will draw the same weight along a given inclined plane4 ,this is proposed without previously defining how ,powers1 producing such effects1 are to be measured2 and as if the speed with which the body were drawn1 and the nature of the surface of the plane1 were of no consequence4 ,the proper elementary ,problem is1 ,to find the force which will support a body on a smooth inclined plane2 and no doubt the solution of ,pappus has more reference to this problem than to his own4 ,his reasoning is1 however1 totally at variance with mechanical ideas on any view of the problem4 ,he supposes the weight to be formed into a sphere2 and this sphere being placed in contact with the inclined plane1 he assumes that the effect will be the same as if the weight were supported on a horizontal lever1 the fulcrum being the point of contact of the sphere with the plane1 and the power acting at the circumference of the sphere4 ,such an assumption implies an entire #ahi absence of those distinct ideas of force and mechanical pressure1 on which our perception of the identity or difference of different modes of action must depend2--of those ideas by the help of which ,archimedes had been able to demonstrate the properties of the lever1 and ,stevinus afterwards discovered the true solution of the problem of the inclined plane4 ,the motive to ,pappus's assumption was probably no more than this2--he perceived that the additional power1 which he thus obtained1 vanished when the plane became horizontal1 and increased as the inclination became greater4 ,thus his views were vague2 he had no clear conception of mechanical action1 and he tried a geometrical conjecture4 ,this is not the way to real knowledge4 ,pappus 7who lived about ,a4 ,d4 #djj7 was one of the best mathematicians of the ,alexandrian school2 and1 on subjects where his ideas were so indistinct1 it is not likely that any much clearer were to be found in the minds of his contemporaries4 ,accordingly1 on all subjects of speculative mechanics1 there appears to have been an entire confusion and obscurity of thought till modern times4 ,men's minds were busy in endeavoring to systematize the distinctions and subtleties of the ,aristotelian school1 concerning ,motion and ,power2 and1 being thus employed among doctrines in which there was involved no definite meaning capable of real exemplification1 they1 of course1 could not acquire sound physical knowledge4 ,we have already seen that the physical opinions of ,aristotle1 even as they came from him1 had no proper scientific precision4 ,his followers1 in their endeavors to perfect and develop his statements1 never attempted to introduce clearer ideas than those of their master2 and as they never referred1 in any steady manner1 to facts1 the vagueness of their notions was not corrected by any collision with observation4 ,the physical doctrines which they extracted from ,aristotle were1 in the course of time1 built up into a regular system2 and though these doctrines could not be followed into a practical application without introducing distinctions and changes1 such as deprived the terms of all steady signification1 the dogmas continued to be repeated1 till the world was persuaded that they were self-evident2 and when1 at a later period1 experimental philosophers1 such as ,galileo and ,boyle1 ventured to contradict these current maxims1 their new principles sounded in men's ears as strange as they now sound familiar4 ,thus ,boyle promulgated his opinions on the mechanics of fluids1 as ,hydrostatical ,paradoxes1 proved and illustrated by experiments4 ,and the opinions which he there opposes1 are those which the ,aristotelian philosophers habitually propounded as certain #aij and indisputable2 such1 for instance1 as that in fluids the upper parts do not gravitate on the lower2 that a lighter fluid will not gravitate on a heavier2 that levity is a positive quality of bodies as well as gravity4 ,so long as these assertions were left uncontested and untried1 men heard and repeated them1 without perceiving the incongruities which they involved3 and thus they long evaded refutation1 amid the vague notions and undoubting habits of the stationary period4 ,but when the controversies of ,galileo's time had made men think with more acuteness and steadiness1 it was discovered that many of these doctrines were inconsistent with themselves1 as well as with experiment4 ,we have an example of the confusion of thought to which the ,aristotelians were liable1 in their doctrine concerning falling bodies4 ,heavy bodies1 said they1 must fall quicker than light ones2 for weight is the cause of their fall1 and the weight of the greater bodies is greater4 ,they did not perceive that1 if they considered the weight of the body as a power acting to produce motion1 they must consider the body itself as offering a resistance to motion2 and that the effect must depend on the proportion of the power to the resistance2 in short1 they had no clear idea of accelerating force4 ,this defect runs through all their mechanical speculations1 and renders them entirely valueless4 ,we may exemplify the same confusion of thought on mechanical subjects in writers of a less technical character4 ,thus1 if men had any distinct idea of mechanical action1 they could not have accepted for a moment the fable of the ,echineis or ,remora1 a little fish which was said to be able to stop a large ship merely by sticking to it4#ad ,lucan refers to this legend in a poetical manner1 and notices this creature only in bringing together a collection of monstrosities2 but ,pliny relates the tale gravely1 and moralizes upon it after his manner4 ,what1 he cries1#bd is more violent than the sea and the winds8 what a greater work of art than a ship8 ,yet one little fish 7the ,echineis7 can hold back all these when they all strain the same way4 ,the winds may #aia blow1 the waves may rage2 but this small creature controls their fury1 and stops a vessel1 when chains and anchors would not hold it3 and this it does1 not by hard labor1 but merely by adhering to it4 ,alas1 for human vanity6 when the turreted ships which man has built1 that he may fight from castle-walls1 at sea as well as at land1 are held captive and motionless by a fish a foot and a half long6 ,such a fish is said to have stopped the admiral's ship at the battle of ,actium1 and compelled ,antony to go into another4 ,and in our own memory1 one of these animals held fast the ship of ,caius1 the emperor1 when he was sailing from ,astura to ,antium4 ,the stopping of this ship1 when all the rest of the fleet went on1 caused surprise2 but this did not last long1 for some of the men jumped into the water to look for the fish1 and found it sticking to the rudder2 they showed it to ,caius1 who was indignant that this animal should interpose its prohibition to his progress1 when impelled by four hundred rowers4 ,it was like a slug2 and had no power1 after it was taken into the ship4 ,note #ad3 ,lucan is describing one of the poetical compounds produced in incantations4 ,huc quicquid ftu genuit ,natura sinistro ,miscetur3 non spuma canum quibus unda timori est1 ,viscera non lyncis1 non dur nodus hyn ,defuit1 et cervi pasti serpente medull2 ,in mediis ,echineis aquis1 oculique draconum4 ,etc4 ,pharsalia1 9999vi4 #fgj4 ,note #bd3 ,plin4 ,hist4 ,n4 xxxii4 #e4 ,a very little advance in the power of thinking clearly on the force which it exerted in pulling1 would have enabled the ,romans to see that the ship and its rowers must pull the adhering fish by the hold the oars had upon the water2 and that1 except the fish had a hold equally strong on some external body1 it could not resist this force4 #c4 ,indistinctness of ,ideas shown in ,architecture4--,perhaps it may serve to illustrate still further the extent to which1 under the ,roman empire1 men's notions of mechanical relations became faint1 wavered1 and disappeared1 if we observe the change which took place in architecture4 ,all architecture1 to possess genuine beauty1 must be mechanically consistent4 ,the decorative members must represent a structure which has in it a principle of support and stability4 ,thus the ,grecian colonnade was a straight horizontal beam1 resting on vertical props2 and the pediment imitated a frame like a roof1 where oppositely inclined beams support each other4 ,these forms of building were1 therefore1 proper models of art1 because they implied supporting forces4 ,but to be content with colonnades and pediments1 which1 though they imitated the forms of the ,grecian ones1 were destitute of their mechanical truth1 belonged to the decline of art2 and showed that men had lost the idea of force1 and retained only that of shape4 ,yet this was what the architects of the ,roman empire did4 ,under their hands1 the pediment was severed at its vertex1 and divided into separate halves1 so that it was no longer a mechanical possibility4 ,the entablature no longer lay straight from pillar to pillar1 but1 projecting over each #aib column1 turned back to the wall1 and adhered to it in the intervening space4 ,the splendid remains of ,palmyra1 ,balbec1 ,petra1 exhibit endless examples of this kind of perverse inventiveness2 and show us1 very instructively1 how the decay of art and of science alike accompany this indistinctness of ideas which we are now endeavoring to illustrate4 #d4 ,indistinctness of ,ideas in ,astronomy4--,returning to the sciences1 it may be supposed1 at first sight1 that1 with regard to astronomy1 we have not the same ground for charging the stationary period with indistinctness of ideas on that subject1 since they were able to acquire and verify1 and1 in some measure1 to apply1 the doctrines previously established4 ,and1 undoubtedly1 it must be confessed that men's notions of the relations of space and number are never very indistinct4 ,it appears to be impossible for these chains of elementary perception ever to be much entangled4 ,the later ,greeks1 the ,arabians1 and the earliest modern astronomers1 must have conceived the hypotheses of the ,ptolemaic system with tolerable completeness4 ,and yet1 we may assert1 that during the stationary period1 men did not possess the notions1 even of space and number1 in that vivid and vigorous manner which enables them to discover new truths4 ,if they had perceived distinctly that the astronomical theorist had merely to do with relative motions1 they must have been led to see the possibility1 at least1 of the ,copernican system2 as the ,greeks1 at an earlier period1 had already perceived it4 ,we find no trace of this4 ,indeed1 the mode in which the ,arabian mathematicians present the solutions of their problems1 does not indicate that clear apprehension of the relations of space1 and that delight in the contemplation of them1 which the ,greek geometrical speculations imply4 ,the ,arabs are in the habit of giving conclusions without demonstrations1 precepts without the investigations by which they are obtained2 as if their main object were practical rather than speculative1--the calculation of results rather than the exposition of theory4 ,delambre#cd has been obliged to exercise great ingenuity1 in order to discover the method by which ,ibn ,iounis proved his solution of certain difficult problems4 ,note #cd3 ,delamb4 ,m4 ,a4 p4 #abe-h4 #e4 ,indistinctness of ,ideas shown by ,skeptics4--,the same unsteadiness of ideas which prevents men from obtaining clear views1 and steady and just convictions1 on special subjects1 may lead them to despair of or deny the possibility of acquiring certainty at all1 and may thus make them skeptics with regard to all knowledge4 ,such skeptics #aic are themselves men of indistinct views1 for they could not otherwise avoid assenting to the demonstrated truths of science2 and1 so far as they may be taken as specimens of their contemporaries1 they prove that indistinct ideas prevail in the age in which they appear4 ,in the stationary period1 moreover1 the indefinite speculations and unprofitable subtleties of the schools might further impel a man of bold and acute mind to this universal skepticism1 because they offered nothing which could fix or satisfy him4 ,and thus the skeptical spirit may deserve our notice as indicative of the defects of a system of doctrine too feeble in demonstration to control such resistance4 ,the most remarkable of these philosophical skeptics is ,sextus ,empiricus2 so called1 from his belonging to that medical sect which was termed the empirical1 in contradistinction to the rational and methodical sects4 ,his works contain a series of treatises1 directed against all the divisions of the science of his time4 ,he has chapters against the ,geometers1 against the ,arithmeticians1 against the ,astrologers1 against the ,musicians1 as well as against ,grammarians1 ,rhetoricians1 and ,logicians2 and1 in short1 as a modern writer has said1 his skepticism is employed as a sort of frame-work which embraces an encyclopedical view of human knowledge4 ,it must be stated1 however1 that his objections are rather to the metaphysical grounds1 than to the details of the sciences2 he rather denies the possibility of speculative truth in general1 than the experimental truths which had been then obtained4 ,thus his objections to geometry and arithmetic are founded on abstract cavils concerning the nature of points1 letters1 unities1 c4 ,and when he comes to speak against astrology1 he says1 ,i am not going to consider that perfect science which rests upon geometry and arithmetic2 for ,i have already shown the weakness of those sciences3 nor that faculty of prediction 7of the motions of the heavens7 which belongs to the pupils of ,eudoxus1 and ,hipparchus1 and the rest1 which some call ,astronomy2 for that is an observation of phenomena1 like agriculture or navigation3 but against the ,art of ,prediction from the time of birth1 which the ,chaldeans exercise4 ,sextus1 therefore1 though a skeptic by profession1 was not insensible to the difference between experimental knowledge and mystical dogmas1 though even the former had nothing which excited his admiration4 ,the skepticism which denies the evidence of the truths of which the best established physical sciences consist1 must necessarily involve a very indistinct apprehension of those truths2 for such truths1 properly exhibited1 contain their own evidence1 and are the best antidote #aid to this skepticism4 ,but an incredulity or contempt towards the asserted truths of physical science may arise also from the attention being mainly directed to the certainty and importance of religious truths4 ,a veneration for revealed religion may thus assume the aspect of a skepticism with regard to natural knowledge4 ,such appears to be the case with ,algazel or ,algezeli1 who is adduced by ,degerando#dd as an example of an ,arabian skeptic4 ,he was a celebrated teacher at ,bagdad in the eleventh century1 and he declared himself the enemy1 not only of the mixed ,peripatetic and ,platonic philosophy of the time1 but of ,aristotle himself4 ,his work entitled ,the ,destructions of the ,philosophers1 is known to us by the refutation of it which ,averrhoes published1 under the title of ,destruction of ,algazel's ,destructions of the ,philosophers4 ,it appears that he contested the fundamental principles both of the ,platonic and of the ,aristotelian schools1 and denied the possibility of a known connection between cause and effect2 thus making a prelude1 says ,degerando1 to the celebrated argumentation of ,hume4 ,note #dd3 ,degerando1 ,hist4 ,comp4 de ,systmes1 iv4 #bbd4 #b;d ,ed4 ,since the publication of my first edition1 an account of ,algazel or ,algazzali and his works has been published under the title of ,essai sur les ,ecoles ,philosophiques chez les ,arabes1 et notamment sur la ,doctrine d',algazzali1 par ,august ,schmlders4 ,paris4 #ahdb4 ,from this book it appears that ,degerando's account of ,algazzali is correct1 when he says#ed that his skepticism seems to have essentially for its object to destroy all systems of merely rational theology1 in order to open an indefinite career1 not only to faith guided by revelation1 but also to the free exaltation of a mystical enthusiasm4 ,it is remarked by ,dr4 ,schmlders1 following ,m4 de ,hammer-,purgstall1 that the title of the work referred to in the text ought rather to be ,mutual ,refutation of the ,philosophers3 and that its object is to show that ,philosophy consists of a mass of systems1 each of which overturns the others4 ,the work of ,algazzali which ,dr4 ,schmlders has published1 ,on the ,errors of ,sects1 c41 contains a kind of autobiographical account of the way in which the author was led to his views4 ,he does not reject the truths of science1 but he condemns the mental habits which are caused by laying too much stress upon science4 ,religious men1 he says1 are1 by such a course1 led to reject all science1 even what relates to eclipses of the moon and sun2 and men of science are led to hate religion4#fd #aie ,note #ed3 ,hist4 ,comp4 iv4 p4 #bbg4 ,note #fd3 ,essai1 p4 #cc4 #f4 ,neglect of ,physical ,reasoning in ,christendom4--,if the ,arabians1 who1 during the ages of which we are speaking1 were the most eminent cultivators of science1 entertained only such comparatively feeble and servile notions of its doctrines1 it will easily be supposed1 that in the ,christendom of that period1 where physical knowledge was comparatively neglected1 there was still less distinctness and vividness in the prevalent ideas on such subjects4 ,indeed1 during a considerable period of the history of the ,christian ,church1 and by many of its principal authorities1 the study of natural philosophy was not only disregarded but discommended4 ,the great practical doctrines which were presented to men's minds1 and the serious tasks1 of the regulation of the will and affections1 which religion impressed upon them1 made inquiries of mere curiosity seem to be a reprehensible misapplication of human powers2 and many of the fathers of the ,church revived1 in a still more peremptory form1 the opinion of ,socrates1 that the only valuable philosophy is that which teaches us our moral duties and religious hopes4#gd ,thus ,eusebius says1#hd ,it is not through ignorance of the things admired by them1 but through contempt of their useless labor1 that we think little of these matters1 turning our souls to the exercise of better things4 ,when the thoughts were thus intentionally averted from those ideas which natural philosophy involves1 the ideas inevitably became very indistinct in their minds2 and they could not conceive that any other persons could find1 on such subjects1 grounds of clear conviction and certainty4 ,they held the whole of their philosophy to be1 as ,lactantius#id asserts it to be1 empty and false4 ,to search1 says he1 for the causes of natural things2 to inquire whether the sun be as large as he seems1 whether the moon is convex or concave1 whether the stars are fixed in the sky or float freely in the air2 of what size and of what material are the heavens2 whether they be at rest or in motion2 what is the magnitude of the earth2 on what foundations it is suspended and balanced2--to dispute and conjecture on such matters1 is just as if we chose to discuss what we think of a city in a remote country1 of which we never heard but the name4 ,it is impossible to express more forcibly that absence of any definite notions on physical subjects which led to this tone of thought4 ,note #gd3 ,brucker1 iii4 #cag4 ,note #hd3 ,prp4 ,ev4 xv4 #fa4 ,note #id3 ,inst4 #a4 iii4 init4 #g4 ,question of ,antipodes4--,with such habits of thought1 we are not to be surprised if the relations resulting from the best established theories were apprehended in an imperfect and incongruous manner4 #aif ,we have some remarkable examples of this2 and a very notable one is the celebrated question of the existence of ,antipodes1 or persons inhabiting the opposite side of the globe of the earth1 and consequently having the soles of their feet directly opposed to ours4 ,the doctrine of the globular form of the earth results1 as we have seen1 by a geometrical necessity1 from a clear conception of the various points of knowledge which we obtain1 bearing upon that subject4 ,this doctrine was held distinctly by the ,greeks2 it was adopted by all astronomers1 ,arabian and ,european1 who followed them2 and was1 in fact1 an inevitable part of every system of astronomy which gave a consistent and intelligible representation of phenomena4 ,but those who did not call before their minds any distinct representation at all1 and who referred the whole question to other relations than those of space1 might still deny this doctrine2 and they did so4 ,the existence of inhabitants on the opposite side of the terraqueous globe1 was a fact of which experience alone could teach the truth or falsehood2 but the religious relations1 which extend alike to all mankind1 were supposed to give the ,christian philosopher grounds for deciding against the possibility of such a race of men4 ,lactantius1#ajd in the fourth century1 argues this matter in a way very illustrative of that impatience of such speculations1 and consequent confusion of thought1 which we have mentioned4 ,is it possible1 he says1 that men can be so absurd as to believe that the crops and trees on the other side of the earth hang downwards1 and that men there have their feet higher than their heads8 ,if you ask of them how they defend these monstrosities--how things do not fall away from the earth on that side--they reply1 that the nature of things is such that heavy bodies tend towards the centre1 like the spokes of a wheel1 while light bodies1 as clouds1 smoke1 fire1 tend from the centre towards the heavens on all sides4 ,now ,i am really at a loss what to say of those who1 when they have once gone wrong1 steadily persevere in their folly1 and defend one absurd opinion by another4 ,it is obvious that so long as the writer refused to admit into his thoughts the fundamental conception of their theory1 he must needs be at a loss what to say to their arguments without being on that account in any degree convinced of their doctrines4 ,note #ajd3 ,inst4 #a4 iii4 #bc4 ,in the sixth century1 indeed1 in the reign of ,justinian1 we find a writer 7,cosmas ,indicopleustes#aad7 who does not rest in this obscurity of #aig representation2 but in this case1 the distinctness of the pictures only serves to show his want of any clear conception as to what suppositions would explain the phenomena4 ,he describes the earth as an oblong floor1 surrounded by upright walls1 and covered by a vault1 below which the heavenly bodies perform their revolutions1 going round a certain high mountain1 which occupies the northern parts of the earth1 and makes night by intercepting the light of the sun4 ,in ,augustin#abd 7who flourished ,a4 ,d4 #djj7 the opinion is treated on other grounds2 and without denying the globular form of the earth1 it is asserted that there are no inhabitants on the opposite side1 because no such race is recorded by ,scripture among the descendants of ,adam4#acd ,considerations of the same kind operated in the well-known instance of ,virgil1 ,bishop of ,salzburg1 in the eighth century4 ,when he was reported to ,boniface1 ,archbishop of ,mentz1 as holding the existence of ,antipodes1 the prelate was shocked at the assumption1 as it seemed to him1 of a world of human beings1 out of the reach of the conditions of salvation2 and application was made to ,pope ,zachary for a censure of the holder of this dangerous doctrine4 ,it does not1 however1 appear that this led to any severity2 and the story of the deposition of ,virgil from his bishopric1 which is circulated by ,kepler and by more modern writers1 is undoubtedly altogether false4 ,the same scruples continued to prevail among ,christian writers to a later period2 and ,tostatus#add notes the opinion of the rotundity of the earth as an unsafe doctrine1 only a few years before ,columbus visited the other hemisphere4 ,note #aad3 ,montfaucon1 ,collectio ,nova ,patrum1 t4 ii4 p4 #aac4 ,cosmas ,indicopleustes4 ,christianorum ,opiniones de ,mundo1 sive ,topographia ,christiana4 ,note #abd3 ,civ4 ,d4 xvi4 #i4 ,note #acd3 ,it appears1 however1 that scriptural arguments were found on the other side4 ,st4 ,jerome says 7,comm4 in ,ezech4 i4 #f71 speaking of the two cherubims with four faces1 seen by the prophet1 and the interpretation of the vision3 ,alii vero qui philosophorum stultam sequuntur sapientiam1 duo hemispheria in duobus templi cherubim1 nos et antipodes1 quasi supinos et cadentes homines suspicantur4 ,note #add3 ,montfauc4 ,patr4 t4 ii4 #h4 ,intellectual ,condition of the ,religious ,orders4--,it must be recollected1 however1 that though these were the views and tenets of many religious writers1 and though they may be taken as indications of the prevalent and characteristic temper of the times of which we speak1 they never were universal4 ,such a confusion of thought affects the minds of many persons1 even in the most enlightened times2 and in what we call the ,dark ,ages1 though clear views on such subjects might be more rare1 those who gave their minds to science1 entertained the true opinion of the figure of the earth4 ,thus ,bothius#aed 7in the sixth century7 urges the smallness of the globe of the earth1 #aih compared with the heavens1 as a reason to repress our love of glory4 ,this work1 it will be recollected1 was translated into the ,anglo-,saxon by our own ,alfred4 ,it was also commented on by ,bede1 who1 in what he says on this passage1 assents to the doctrine1 and shows an acquaintance with ,ptolemy and his commentators1 both ,arabian and ,greek4 ,gerbert1 in the tenth century1 went from ,france to ,spain to study astronomy with the ,arabians1 and soon surpassed his masters4 ,he is reported to have fabricated clocks1 and an astrolabe of peculiar construction4 ,gerbert afterwards 7in the last year of the first thousand from the birth of ,christ7 became pope1 by the name of ,sylvester ,,ii4 ,among other cultivators of the sciences1 some of whom1 from their proficiency1 must have possessed with considerable clearness and steadiness the elementary ideas on which it depends1 we may here mention1 after ,montucla1#afd ,adelbold1 whose work ,on the ,sphere was addressed to ,pope ,sylvester1 and whose geometrical reasonings are1 according to ,montucla1#agd vague and chimerical2 ,hermann ,contractus1 a monk of ,st ,gall1 who1 in #ajej1 published astronomical works2 ,william of ,hirsaugen1 who followed his example in #ajhj2 ,robert of ,lorraine1 who was made ,bishop of ,hereford by ,william the ,conqueror1 in consequence of his astronomical knowledge4 ,in the next century1 ,adelhard ,goth1 an ,englishman1 travelled among the ,arabs for purposes of study1 as ,gerbert had done in the preceding age2 and on his return1 translated the ,elements of ,euclid1 which he had brought from ,spain or ,egypt4 ,robert ,grostte1 ,bishop of ,lincoln1 was the author of an ,epitome on the ,sphere2 ,roger ,bacon1 in his youth the contemporary of ,robert1 and of his brother ,adam ,marsh1 praises very highly their knowledge in mathematics4 ,note #aed3 ,bothius1 ,cons4 ii4 pr4 #g4 ,note #afd3 ,mont4 i4 #ejb4 ,note #agd3 ,ib4 i4 #ejc4 ,and here1 says the ,french historian of mathematics1 whom ,i have followed in the preceding relation1 it is impossible not to reflect that all those men who1 if they did not augment the treasure of the sciences1 at least served to transmit it1 were monks1 or had been such originally4 ,convents were1 during these stormy ages1 the asylum of sciences and letters4 ,without these religious men1 who1 in the silence of their monasteries1 occupied themselves in transcribing1 in studying1 and in imitating the works of the ancients1 well or ill1 those works would have perished2 perhaps not one of them would have come down to us4 ,the thread which connects us with the ,greeks and ,romans would have been snapt asunder2 the precious productions of #aii ancient literature would no more exist for us1 than the works1 if any there were1 published before the catastrophe that annihilated that highly scientific nation1 which1 according to ,bailly1 existed in remote ages in the centre of ,tartary1 or at the roots of ,caucasus4 ,in the sciences we should have had all to create2 and at the moment when the human mind should have emerged from its stupor and shaken off its slumbers1 we should have been no more advanced than the ,greeks were after the taking of ,troy4 ,he adds1 that this consideration inspires feelings towards the religious orders very different from those which1 when he wrote1 were prevalent among his countrymen4 ,except so far as their religious opinions interfered1 it was natural that men who lived a life of quiet and study1 and were necessarily in a great measure removed from the absorbing and blinding interests with which practical life occupies the thoughts1 should cultivate science more successfully than others1 precisely because their ideas on speculative subjects had time and opportunity to become clear and steady4 ,the studies which were cultivated under the name of the ,seven ,liberal ,arts1 necessarily tended to favor this effect4 ,the ,trivium1#ahd indeed1 which consisted of ,grammar1 ,logic1 and ,rhetoric1 had no direct bearing upon those ideas with which physical science is concerned2 but the ,quadrivium1 ,music1 ,arithmetic1 ,geometry1 ,astronomy1 could not be pursued with any attention1 without a corresponding improvement of the mind for the purposes of sound knowledge4#aid ,note #ahd3 ,bruck4 iii4 #eig4 ,note #aid3 ,roger ,bacon1 in his ,specula ,mathematica1 cap4 i41 says ,harum scientiarum porta et clavis est mathematica1 quam sancti a principio mundi invenerunt1 etc4 ,cujus negligentia jam per triginta vel quadraginta annos destruxit totum studium ,latinorum4 ,i do not know on what occasion this neglect took place4 #i4 ,popular ,opinions4--,that1 even in the best intellects1 something was wanting to fit them for scientific progress and discovery1 is obvious from the fact that science was so long absolutely stationary4 ,and ,i have endeavored to show that one part of this deficiency was the want of the requisite clearness and vigor of the fundamental scientific ideas4 ,if these were wanting1 even in the most powerful and most cultivated minds1 we may easily conceive that still greater confusion and obscurity prevailed in the common class of mankind4 ,they actually adopted the belief1 however crude and inconsistent1 that the form of the earth and heavens really is what at any place it appears to be2 that the earth is flat1 and the waters of the sky sustained above a material floor1 through which in showers they descend4 ,yet the true doctrines of #bjj astronomy appear to have had some popular circulation4 ,for instance1 a ,french poem of the time of ,edward the ,second1 called ,ymage du ,monde1 contains a metrical account of the earth and heavens1 according to the ,ptolemaic views2 and in a manuscript of this poem1 preserved in the library of the ,university of ,cambridge1 there are representations1 in accordance with the text1 of a spherical earth1 with men standing upright upon it on every side2 and by way of illustrating the tendency of all things to the centre1 perforations of the earth1 entirely through its mass1 are described and depicted2 and figures are exhibited dropping balls down each of these holes1 so as to meet in the interior4 ,and1 as bearing upon the perplexity which attends the motions of up and down1 when applied to the globular earth1 and the change of the direction of gravity which would occur in passing the centre1 the readers of ,dante will recollect the extraordinary manner in which the poet and his guide emerge from the bottom of the abyss2 and the explanation which ,virgil imparts to him of what he there sees4 ,after they have crept through the aperture in which ,lucifer is placed1 the poet says1 ,io levai gli occhi e credetti vedere ,lucifero com' io l' avea lasciato1 ,e vidile le gambe in su tenere4 4 4 4 4 4 ,questi come fitto ,si sottasopra6 4 4 4 4 4 ,quando mi volsi1 tu passast' il punto ,al qual si traggon d' ogni parte i pesi4 ,inferno1 xxxiv4 4 4 4 4 4 ,i raised mine eyes1 ,believing that ,i ,lucifer should see ,where he was lately left1 but saw him now ,with legs held upward4 4 4 4 4 4 ,how standeth he in posture thus reversed8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ,thou wast on the other side so long as ,i ,descended2 when ,i turned1 thou didst o'erpass ,that point to which from every part is dragged ,all heavy substance4 ,,cary4 ,this is more philosophical than ,milton's representation1 in a more scientific age1 of ,uriel sliding to the earth on a sunbeam1 and sliding back again1 when the sun had sunk below the horizon4 4 4 4 4 4 ,uriel to his charge ,returned on that bright beam whose point now raised1 ,bore him slope downward to the sun1 now fallen ,beneath the ,azores4 ,par4 ,lost1 ,b4 iv4 #bja ,the philosophical notions of up and down are too much at variance with the obvious suggestions of our senses1 to be held steadily and justly by minds undisciplined in science4 ,perhaps it was some misunderstood statement of the curved surface of the ocean1 which gave rise to the tradition of there being a part of the sea directly over the earth1 from which at times an object has been known to fall or an anchor to be let down4 ,even such whimsical fancies are not without instruction1 and may serve to show the reader what that vagueness and obscurity of ideas is1 of which ,i have been endeavoring to trace the prevalence in the dark ages4 ,we now proceed to another of the features which appears to me to mark1 in a very prominent manner1 the character of the stationary period4 ,,chapter ,,ii4 ,,the ,,commentatorial ,,spirit ,,of ,,the ,,middle ,,ages4 ,,we have already noticed1 that1 after the first great achievements of the founders of sound speculation1 in the different departments of human knowledge1 had attracted the interest and admiration which those who became acquainted with them could not but give to them1 there appeared a disposition among men to lean on the authority of some of these teachers2--to study the opinions of others as the only mode of forming their own2--to read nature through books2--to attend to what had been already thought and said1 rather than to what really is and happens4 ,this tendency of men's minds requires our particular consideration4 ,its manifestations were very important1 and highly characteristic of the stationary period2 it gave1 in a great degree1 a peculiar bias and direction to the intellectual activity of many centuries2 and the kind of labor with which speculative men were occupied in consequence of this bias1 took the place of that examination of realities which must be their employment1 in order that real knowledge may make any decided progress4 ,in some subjects1 indeed1 as1 for instance1 in the domains of morals1 poetry1 and the arts1 whose aim is the production of beauty1 this opposition between the study of former opinion and present reality1 may not be so distinct2 inasmuch as it may be said by some1 that1 in these subjects1 opinions are realities2 that the thoughts and feelings which #bjb prevail in men's minds are the material upon which we must work1 the particulars from which we are to generalize1 the instruments which we are to use2 and that1 therefore1 to reject the study of antiquity1 or even its authority1 would be to show ourselves ignorant of the extent and mutual bearing of the elements with which we have to deal2--would be to cut asunder that which we ought to unite into a vital whole4 ,yet even in the provinces of history and poetry1 the poverty and servility of men's minds during the middle ages1 are shown by indications so strong as to be truly remarkable2 for instance1 in the efforts of the antiquarians of almost every ,european country to assimilate the early history of their own state to the poet's account of the foundation of ,rome1 by bringing from the sack of ,troy1 ,brutus to ,england1 ,bavo to ,flanders1 and so on4 ,but however this may be1 our business at present is1 to trace the varying spirit of the physical philosophy of different ages2 trusting that1 hereafter1 this prefatory study will enable us to throw some light upon the other parts of philosophy4 ,and in physics the case undoubtedly was1 that the labor of observation1 which is one of the two great elements of the progress of knowledge1 was in a great measure superseded by the collection1 the analysis1 the explanation1 of previous authors and opinions2 experimenters were replaced by commentators2 criticism took the place of induction2 and instead of great discoverers we had learned men4 #a4 ,natural ,bias to ,authority4--,it is very evident that1 in such a bias of men's studies1 there is something very natural2 however strained and technical this erudition may have been1 the propensities on which it depends are very general1 and are easily seen4 ,deference to the authority of thoughtful and sagacious men1 a disposition which men in general neither reject nor think they ought to reject in practical matters1 naturally clings to them1 even in speculation4 ,it is a satisfaction to us to suppose that there are1 or have been1 minds of transcendent powers1 of wide and wise views1 superior to the common errors and blindness of our nature4 ,the pleasure of admiration1 and the repose of confidence1 are inducements to such a belief4 ,there are also other reasons why we willingly believe that there are in philosophy great teachers1 so profound and sagacious1 that1 in order to arrive at truth1 we have only to learn their thoughts1 to understand their writings4 ,there is a peculiar interest which men feel in dealing with the thoughts of their fellow-men1 rather than with brute matter4 ,matter feels and excites no sympathies3 in seeking for mere laws of nature1 there is nothing of mental intercourse with the great spirits of the past1 as there is in #bjc studying ,aristotle or ,plato4 ,moreover1 a large portion of this employment is of a kind the most agreeable to most speculative minds2 it consists in tracing the consequences of assumed principles3 it is deductive like geometry3 and the principles of the teachers being known1 and being undisputed1 the deduction and application of their results is an obvious1 self-satisfying1 and inexhaustible exercise of ingenuity4 ,these causes1 and probably others1 make criticism and commentation flourish1 when invention begins to fail1 oppressed and bewildered by the acquisitions it has already made2 and when the vigor and hope of men's minds are enfeebled by civil and political changes4 ,accordingly1#bjd the ,alexandrian school was eminently characterized by a spirit of erudition1 of literary criticism1 of interpretation1 of imitation4 ,these practices1 which reigned first in their full vigor in the ,museum1 are likely to be1 at all times1 the leading propensities of similar academical institutions4 ,note #bjd3 ,degerando1 ,hist4 des ,syst4 de ,philos4 iii4 p4 #acd4 ,how natural it is to select a great writer as a paramount authority1 and to ascribe to him extraordinary profundity and sagacity1 we may see1 in the manner in which the ,greeks looked upon ,homer2 and the fancy which detected in his poems traces of the origin of all arts and sciences1 has1 as we know1 found favor even in modern times4 ,to pass over earlier instances of this feeling1 we may observe1 that ,strabo begins his ,geography by saying that he agrees with ,hipparchus1 who had declared ,homer to be the first author of our geographical knowledge2 and he does not confine the application of this assertion to the various and curious topographical information which the ,iliad and ,odyssey contain1 concerning the countries surrounding the ,mediterranean2 but in phrases which1 to most persons1 might appear the mere play of a poetical fancy1 or a casual selection of circumstances1 he finds unquestionable evidence of a correct knowledge of general geographical truths4 ,thus1#bad when ,homer speaks of the sun rising from the soft and deep-flowing ocean1 of his splendid blaze plunging in the ocean2 of the northern constellation ,alone unwashen by the ocean wave2 and of ,jupiter1 who goes to the ocean to feast with the blameless ,ethiopians2 ,strabo is satisfied from these passages that ,homer knew the dry land to be surrounded with water3 and he reasons in like manner with respect to other points of geography4 #bjd ,note #bad3 ,strabo1 i4 p4 #e4 #b4 ,character of ,commentators4--,the spirit of commentation1 as has already been suggested1 turns to questions of taste1 of metaphysics1 of morals1 with far more avidity than to physics4 ,accordingly1 critics and grammarians were peculiarly the growth of this school2 and1 though the commentators sometimes chose works of mathematical or physical science for their subject 7as ,proclus1 who commented on ,euclid's ,geometry1 and ,simplicius1 on ,aristotle's ,physics71 these commentaries were1 in fact1 rather metaphysical than mathematical4 ,it does not appear that the commentators have1 in any instance1 illustrated the author by bringing his assertions of facts to the test of experiment4 ,thus1 when ,simplicius comments on the passage concerning a vacuum1 which we formerly adduced1 he notices the argument which went upon the assertion1 that a vessel full of ashes would contain as much water as an empty vessel2 and he mentions various opinions of different authors1 but no trial of the fact4 ,eudemus had said1 that the ashes contained something hot1 as quicklime does1 and that by means of this1 a part of the water was evaporated2 others supposed the water to be condensed1 and so on4#bbd ,note #bbd3 ,simplicius1 p4 #agj4 ,the ,commentator's professed object is to explain1 to enforce1 to illustrate doctrines assumed as true4 ,he endeavors to adapt the work on which he employs himself to the state of information and of opinion in his own time2 to elucidate obscurities and technicalities2 to supply steps omitted in the reasoning2 but he does not seek to obtain additional truths or new generalizations4 ,he undertakes only to give what is virtually contained in his author2 to develop1 but not to create4 ,he is a cultivator of the thoughts of others3 his labor is not spent on a field of his own2 he ploughs but to enrich the granary of another man4 ,thus he does not work as a freeman1 but as one in a servile condition2 or rather1 his is a menial1 and not a productive service3 his office is to adorn the appearance of his master1 not to increase his wealth4 ,yet though the ,commentator's employment is thus subordinate and dependent1 he is easily led to attribute to it the greatest importance and dignity4 ,to elucidate good books is1 indeed1 a useful task2 and when those who undertake this work execute it well1 it would be most unreasonable to find fault with them for not doing more4 ,but the critic1 long and earnestly employed on one author1 may easily underrate the relative value of other kinds of mental exertion4 ,he may #bje ascribe too large dimensions to that which occupies the whole of his own field of vision4 ,thus he may come to consider such study as the highest aim1 and best evidence of human genius4 ,to understand ,aristotle1 or ,plato1 may appear to him to comprise all that is possible of profundity and acuteness4 ,and when he has travelled over a portion of their domain1 and satisfied himself that of this he too is master1 he may look with complacency at the circuit he has made1 and speak of it as a labor of vast effort and difficulty4 ,we may quote1 as an expression of this temper1 the language of ,sir ,henry ,savile1 in concluding a course of lectures on ,euclid1 delivered at ,oxford4#bcd ,by the grace of ,god1 gentlemen hearers1 ,i have performed my promise2 ,i have redeemed my pledge4 ,i have explained1 according to my ability1 the definitions1 postulates1 axioms1 and first eight propositions of the ,elements of ,euclid4 ,here1 sinking under the weight of years1 ,i lay down my art and my instruments4 ,note #bcd3 ,exolvi per ,dei gratiam1 ,domini auditores1 promissum2 liberavi fldem meam2 explicavi pro meo modulo1 definitiones1 petitiones1 communes sententias1 et octo priores propositiones ,elementorum ,euclidis4 ,hic1 annis fessus1 cyclos artemque repono4 ,we here speak of the peculiar province of the ,commentator2 for undoubtedly1 in many instances1 a commentary on a received author has been made the vehicle of conveying systems and doctrines entirely different from those of the author himself2 as1 for instance1 when the ,new ,platonists wrote1 taking ,plato for their text4 ,the labors of learned men in the stationary period1 which came under this description1 belong to another class4 #c4 ,greek ,commentators on ,aristotle4--,the commentators or disciples of the great philosophers did not assume at once their servile character4 ,at first their object was to supply and correct1 as well as to explain their teacher4 ,thus among the earlier commentators of ,aristotle1 ,theophrastus invented five moods of syllogism in the first figure1 in addition to the four invented by ,aristotle1 and stated with additional accuracy the rules of hypothetical syllogisms4 ,he also not only collected much information concerning animals1 and natural events1 which ,aristotle had omitted1 but often differed with his master2 as1 for instance1 concerning the saltness of the sea3 this1 which the ,stagirite attributed to the effect of the evaporation produced by the sun's rays1 was ascribed by ,theophrastus to beds of salt at the bottom4 ,porphyry1#bdd who flourished in the third century1 wrote a book on the ,predicables1 which was found to be so suitable a complement #bjf to the ,predicaments or ,categories of ,aristotle1 that it was usually prefixed to that treatise2 and the two have been used as an elementary work together1 up to modern times4 ,the ,predicables are the five steps which the gradations of generality and particularity introduce2--genus1 species1 difference1 individual1 accident3--the ,categories are the ten heads under which assertions or predications may be arranged3--substance1 quantity1 relation1 quality1 place1 time1 position1 habit1 action1 passion4 ,note #bdd3 ,buhle1 ,arist4 i4 #bhd4 ,at a later period1 the ,aristotelian commentators became more servile1 and followed the author step by step1 explaining1 according to their views1 his expressions and doctrines2 often1 indeed1 with extreme prolixity1 expanding his clauses into sentences1 and his sentences into paragraphs4 ,alexander ,aphrodisiensis1 who lived at the end of the second century1 is of this class2 sometimes useful1 as one of the recent editors of ,aristotle says2#bed but by the prolixity of his interpretation1 by his perverse itch for himself discussing the argument expounded by ,aristotle1 for defending his opinions1 and for refuting or reconciling those of others1 he rather obscures than enlightens4 ,at various times1 also1 some of the commentators1 and especially those of the ,alexandrian school1 endeavored to reconcile1 or combined without reconciling1 opposing doctrines of the great philosophers of the earlier times4 ,simplicius1 for instance1 and1 indeed1 a great number of the ,alexandrian ,philosophers1#bfd as ,alexander1 ,ammonius1 and others1 employed themselves in the futile task of reconciling the doctrines of the ,pythagoreans1 of the ,eleatics1 of ,plato1 and of the ,stoics1 with those of ,aristotle4 ,boethius#bgd entertained the design of translating into ,latin the whole of ,aristotle's and ,plato's works1 and of showing their agreement2 a gigantic plan1 which he never executed4 ,others employed themselves in disentangling the confusion which such attempts produced1 as ,john the ,grammarian1 surnamed ,philoponus1 the ,labor-loving2 who1 towards the end of the seventh century1 maintained that ,aristotle was entirely misunderstood by ,porphyry and ,proclus1#bhd who had pretended to incorporate his doctrines into those of the ,new ,platonic school1 or even to reconcile him with ,plato himself on the subject of ideas4 ,others1 again1 wrote ,epitomes1 ,compounds1 ,abstracts2 and endeavored to throw the works of the philosopher into some simpler and more obviously regular form1 as ,john of ,damascus1 in #bjg the middle of the eighth century1 who made abstracts of some of ,aristotle's works1 and introduced the study of the author into theological education4 ,these two writers lived under the patronage of the ,arabs2 the former was favored by ,amrou1 the conqueror of ,egypt2 the latter was at first secretary to the ,caliph1 but afterwards withdrew to a monastery4#bid ,note #bed3 ,ib4 i4 #bhh4 ,note #bfd3 ,ib4 i4 #caa4 ,note #bgd3 ,degerando1 ,hist4 des ,syst4 iv4 #ajj4 ,note #bhd3 ,ib4 iv4 #aee4 ,note #bid3 ,deg4 iv4 #aej4 ,at this period the ,arabians became the fosterers and patrons of philosophy1 rather than the ,greeks4 ,justinian had1 by an edict1 closed the school of ,athens1 the last of the schools of heathen philosophy4 ,leo1 the ,isaurian1 who was a zealous ,iconoclast1 abolished also the schools where general knowledge had been taught1 in combination with ,christianity1#cjd yet the line of the ,aristotelian commentators was continued1 though feebly1 to the later ages of the ,greek empire4 ,anna ,comnena#cad mentions a ,eustratus who employed himself upon the dialectic and moral treatises1 and whom she does not hesitate to elevate above the ,stoics and ,platonists1 for his talent in philosophical discussions4 ,nicephorus ,blemmydes wrote logical and physical epitomes for the use of ,john ,ducas2 ,george ,pachymerus composed an epitome of the philosophy of ,aristotle1 and a compend of his logic2 ,theodore ,metochytes1 who was famous in his time alike for his eloquence and his learning1 has left a paraphrase of the books of ,aristotle on ,physics1 on the ,soul1 the ,heavens1#cbd c4 ,fabricius states that this writer has a chapter1 the object of which is to prove1 that all philosophers1 and ,aristotle and ,plato in particular1 have disdained the authority of their predecessors4 ,he could hardly help remarking in how different a spirit philosophy had been pursued since their time4 ,note #cjd3 ,ib4 iv4 #afc4 ,note #cad3 ,ib4 #afg4 ,note #cbd3 ,ib4 #afh4 #d4 ,greek ,commentators of ,plato and others4--,i have spoken principally of the commentators of ,aristotle1 for he was the great subject of the commentators proper2 and though the name of his rival1 ,plato1 was graced by a list of attendants1 hardly less numerous1 these1 the ,neoplatonists1 as they are called1 had introduced new elements into the doctrines of their nominal master1 to such an extent that they must be placed in a different class4 ,we may observe here1 however1 how1 in this school as in the ,peripatetic1 the race of commentators multiplied itself4 ,porphyry1 who commented on ,aristotle1 was commented on by ,ammonius2 ,plotinus's ,enneads were commented on by ,proclus and ,dexippus4 ,psellus#ccd the elder was a paraphrast of #bjh ,aristotle2 ,psellus the younger1 in the eleventh century1 attempted to restore the ,new ,platonic school4 ,the former of these two writers had for his pupils two men1 the emperor ,leo1 surnamed the ,philosopher1 and ,photius the patriarch1 who exerted themselves to restore the study of literature at ,constantinople4 ,we still possess the ,collection of ,extracts of ,photius1 which1 like that of ,stobus and others1 shows the tendency of the age to compilations1 abstracts1 and epitomes1--the extinction of philosophical vitality4 ,note #ccd3 ,deg4 iv4 #afi4 #e4 ,arabian ,commentators of ,aristotle4--,the reader might perhaps have expected1 that when the philosophy of the ,greeks was carried among a new race of intellects1 of a different national character and condition1 the train of this servile tradition would have been broken2 that some new thoughts would have started forth2 that some new direction1 some new impulse1 would have been given to the search for truth4 ,it might have been anticipated that we should have had schools among the ,arabians which should rival the ,peripatetic1 ,academic1 and ,stoic among the ,greeks2--that they would preoccupy the ground on which ,copernicus and ,galileo1 ,lavoisier and ,linnus1 won their fame2--that they would make the next great steps in the progressive sciences4 ,nothing of this1 however1 happened4 ,the ,arabians cannot claim1 in science or philosophy1 any really great names2 they produced no men and no discoveries which have materially influenced the course and destinies of human knowledge2 they tamely adopted the intellectual servitude of the nation which they conquered by their arms2 they joined themselves at once to the string of slaves who were dragging the car of ,aristotle and ,plotinus4 ,nor1 perhaps1 on a little further reflection1 shall we be surprised at this want of vigor and productive power1 in this period of apparent national youth4 ,the ,arabians had not been duly prepared rightly to enjoy and use the treasures of which they became possessed4 ,they had1 like most uncivilized nations1 been passionately fond of their indigenous poetry2 their imagination had been awakened1 but their rational powers and speculative tendencies were still torpid4 ,they received the ,greek philosophy without having passed through those gradations of ardent curiosity and keen research1 of obscurity brightening into clearness1 of doubt succeeded by the joy of discovery1 by which the ,greek mind had been enlarged and exercised4 ,nor had the ,arabians ever enjoyed1 as the ,greeks had1 the individual consciousness1 the independent volition1 the intellectual freedom1 arising from the freedom of political institutions4 ,they had not felt the contagious mental activity of a small city1--the elation arising from the general #bji sympathy in speculative pursuits diffused through an intelligent and acute audience2 in short1 they had not had a national education such as fitted the ,greeks to be disciples of ,plato and ,hipparchus4 ,hence1 their new literary wealth rather encumbered and enslaved1 than enriched and strengthened them3 in their want of taste for intellectual freedom1 they were glad to give themselves up to the guidance of ,aristotle and other dogmatists4 ,their military habits had accustomed them to look to a leader2 their reverence for the book of their law had prepared them to accept a philosophical ,koran also4 ,thus the ,arabians1 though they never translated the ,greek poetry1 translated1 and merely translated1 the ,greek philosophy2 they followed the ,greek philosophers without deviation1 or1 at least1 without any philosophical deviations4 ,they became for the most part ,aristotelians2--studied not only ,aristotle1 but the commentators of ,aristotle2 and themselves swelled the vast and unprofitable herd4 ,the philosophical works of ,aristotle had1 in some measure1 made their way in the ,east1 before the growth of the ,saracen power4 ,in the sixth century1 a ,syrian1 ,uranus1#cdd encouraged by the love of philosophy manifested by ,cosroes1 had translated some of the writings of the ,stagirite2 about the same time1 ,sergius had given some translations in ,syriac4 ,in the seventh century1 ,jacob of ,edessa translated into this language the ,dialectics1 and added ,notes to the work4 ,such labors became numerous2 and the first ,arabic translations of ,aristotle were formed upon these ,persian or ,syriac texts4 ,in this succession of transfusions1 some mistakes must inevitably have been introduced4 ,note #cdd3 ,deg4 iv4 #aif4 ,the ,arabian interpreters of ,aristotle1 like a large portion of the ,alexandrian ones1 gave to the philosopher a tinge of opinions borrowed from another source1 of which ,i shall have to speak under the head of ,mysticism4 ,but they are1 for the most part1 sufficiently strong examples of the peculiar spirit of commentation1 to make it fitting to notice them here4 ,at the head of them stands#ced ,alkindi1 who appears to have lived at the court of ,almamon1 and who wrote commentaries on the ,organon of ,aristotle4 ,but ,alfarabi was the glory of the school of ,bagdad2 his knowledge included mathematics1 astronomy1 medicine1 and philosophy4 ,born in an elevated rank1 and possessed of a rich patrimony1 he led an austere life1 and devoted himself altogether to study and meditation4 ,he employed himself particularly in unfolding the import of ,aristotle's treatise ,on the ,soul4#cfd ,avicenna 7,ebn ,sina7 #baj was at once the ,hippocrates and the ,aristotle of the ,arabians2 and certainly the most extraordinary man that the nation produced4 ,in the course of an unfortunate and stormy life1 occupied by politics and by pleasures1 he produced works which were long revered as a sort of code of science4 ,in particular1 his writings on medicine1 though they contain little besides a compilation of ,hippocrates and ,galen1 took the place of both1 even in the universities of ,europe2 and were studied as models at ,paris and ,montpelier1 till the end of the seventeenth century1 at which period they fell into an almost complete oblivion4 ,avicenna is conceived1 by some modern writers1#cgd to have shown some power of original thinking in his representations of the ,aristotelian ,logic and ,metaphysics4 ,averroes 7,ebn ,roshd7 of ,cordova1 was the most illustrious of the ,spanish ,aristotelians1 and became the guide of the schoolmen1#chd being placed by them on a level with ,aristotle himself1 or above him4 ,he translated ,aristotle from the first ,syriac version1 not being able to read the ,greek text4 ,he aspired to1 and retained for centuries1 the title of the ,commentator2 and he deserves this title by the servility with which he maintains that ,aristotle#cid carried the sciences to the highest possible degree1 measured their whole extent1 and fixed their ultimate and permanent boundaries2 although his works are conceived to exhibit a trace of the ,new ,platonism4 ,some of his writings are directed against an ,arabian skeptic1 of the name of ,algazel1 whom we have already noticed4 ,note #ced3 ,ib4 iv4 #ahg4 ,note #cfd3 ,ib4 iv4 #bje4 ,note #cgd3 ,deg4 iv4 #bjf4 ,note #chd3 ,ib4 iv4 #bdg4 ,averroes died ,a4 ,d4 #abjf4 ,note #cid3 ,ib4 iv4 #bdh4 ,when the schoolmen had adopted the supremacy of ,aristotle to the extent in which ,averroes maintained it1 their philosophy went further than a system of mere commentation1 and became a system of dogmatism2 we must1 therefore1 in another chapter1 say a few words more of the ,aristotelians in this point of view1 before we proceed to the revival of science2 but we must previously consider some other features in the character of the ,stationary ,period4 #baa ,,chapter ,,iii4 ,,of ,,the ,,mysticism ,,of ,,the ,,middle ,,ages4 ,,it has been already several times hinted1 that a new and peculiar element was introduced into the ,greek philosophy which occupied the attention of the ,alexandrian school2 and that this element tinged a large portion of the speculations of succeeding ages4 ,we may speak of this peculiar element as ,mysticism2 for1 from the notion usually conveyed by this term1 the reader will easily apprehend the general character of the tendency now spoken of2 and especially when he sees its effect pointed out in various subjects4 ,thus1 instead of referring the events of the external world to space and time1 to sensible connection and causation1 men attempted to reduce such occurrences under spiritual and supersensual relations and dependencies2 they referred them to superior intelligences1 to theological conditions1 to past and future events in the moral world1 to states of mind and feelings1 to the creatures of an imaginary mythology or demonology4 ,and thus their physical ,science became ,magic1 their ,astronomy became ,astrology1 the study of the ,composition of bodies became ,alchemy1 ,mathematics became the contemplation of the ,spiritual ,relations of number and figure1 and ,philosophy became ,theosophy4 ,the examination of this feature in the history of the human mind is important for us1 in consequence of its influence upon the employments and the thoughts of the times now under our notice4 ,this tendency materially affected both men's speculations and their labours in the pursuit of knowledge4 ,by its direct operation1 it gave rise to the newer ,platonic philosophy among the ,greeks1 and to corresponding doctrines among the ,arabians2 and by calling into a prominent place astrology1 alchemy1 and magic1 it long occupied most of the real observers of the material world4 ,in this manner it delayed and impeded the progress of true science2 for we shall see reason to believe that human knowledge lost more by the perversion of men's minds and the misdirection of their efforts1 than it gained by any increase of zeal arising from the peculiar hopes and objects of the mystics4 ,it is not our purpose to attempt any general view of the progress and fortunes of the various forms of ,mystical ,philosophy2 but only to exhibit some of its characters1 in so far as they illustrate those #bab tendencies of thought which accompanied the retrogradation of inductive science4 ,and of these1 the leading feature which demands our notice is that already alluded to2 namely1 the practice of referring things and events1 not to clear and distinct relations1 obviously applicable to such cases2--not to general rules capable of direct verification2 but to notions vague1 distant1 and vast1 which we cannot bring into contact with facts1 because they belong to a different region from the facts2 as when we connect natural events with moral or historical causes1 or seek spiritual meanings in the properties of number and figure4 ,thus the character of ,mysticism is1 that it refers particulars1 not to generalizations homogeneous and immediate1 but to such as are heterogeneous and remote2 to which we must add1 that the process of this reference is not a calm act of the intellect1 but is accompanied with a glow of enthusiastic feeling4 #a4 ,neoplatonic ,theosophy4--,the ,newer ,platonism is the first example of this ,mystical ,philosophy which ,i shall consider4 ,the main points which here require our notice are1 the doctrine of an ,intellectual ,world resulting from the act of the ,divine ,mind1 as the only reality2 and the aspiration after the union of the human soul with this ,divine ,mind1 as the object of human existence4 ,the ,ideas of ,plato were ,forms of our knowledge2 but among the ,neoplatonists they became really existing1 indeed the only really existing1 ,objects2 and the inaccessible scheme of the universe which these ideas constitute1 was offered as the great subject of philosophical contemplation4 ,the desire of the human mind to approach towards its ,creator and ,preserver1 and to obtain a spiritual access to ,him1 leads to an employment of the thoughts which is well worth the notice of the religious philosopher2 but such an effort1 even when founded on revelation and well regulated1 is not a means of advance in physics2 and when it is the mere result of natural enthusiasm1 it may easily obtain such a place in men's minds as to unfit them for the successful prosecution of natural philosophy4 ,the temper1 therefore1 which introduces such supernatural communion into the general course of its speculations1 may be properly treated as mystical1 and as one of the causes of the decline of science in the ,stationary ,period4 ,the ,neoplatonic philosophy requires our notice as one of the most remarkable forms of this ,mysticism4 ,though ,ammonius ,saccas1 who flourished at the end of the second century1 is looked upon as the beginner of the ,neoplatonists1 his disciple ,plotinus is1 in reality1 the great founder of the school1 both by his #bac works1 which still remain to us1 and by the enthusiasm which his character and manners inspired among his followers4 ,he lived a life of meditation1 gentleness1 and self-denial1 and died in the second year of the reign of ,claudius 7,a4 ,d4 #bgj74 ,his disciple1 ,porphyry1 has given us a ,life of him1 from which we may see how well his habitual manners were suited to make his doctrines impressive4 ,plotinus1 the philosopher of our time1 ,porphyry thus begins his biography1 appeared like a person ashamed that he was in the body4 ,in consequence of this disposition1 he could not bear to talk concerning his family1 or his parents1 or his country4 ,he would not allow himself to be represented by a painter or statuary2 and once1 when ,aurelius entreated him to permit a likeness of him to be taken1 he said1 ',is it not enough for us to carry this image in which nature has enclosed us1 but we must also try to leave a more durable image of this image1 as if it were so great a sight8' ,and he retained the same temper to the last4 ,when he was dying1 he said1 ',i am trying to bring the divinity which is in us to the divinity which is in the universe4' ,he was looked upon by his successors with extraordinary admiration and reverence2 and his disciple ,porphyry collected from his lips1 or from fragmental notes1 the six ,enneads of his doctrines 7that is1 parts each consisting of nine ,books71 which he arranged and annotated4 ,we have no difficulty in finding in this remarkable work examples of mystical speculation4 ,the ,intelligible ,world of realities or essences corresponds to the world of sense#djd in the classes of things which it includes4 ,to the ,intelligible ,world1 man's mind ascends1 by a triple road which ,plotinus figuratively calls that of the ,musician1 the ,lover1 the ,philosopher4#dad ,the activity of the human soul is identified by analogy with the motion of the heavens4 ,this activity is about a middle point1 and thus it is circular2 but a middle point is not the same in body and in the soul3 in that1 the middle point is local2 in this1 it is that on which the rest depends4 ,there is1 however1 an analogy2 for as in one case1 so in the other1 there must be a middle point1 and as the sphere revolves about its centre1 the soul revolves about ,god through its affections4 ,note #djd3 vi4 ,ennead1 iii4 #a4 ,note #dad3 ii4 ,e4 ii4 #b4 ,the conclusion of the work is1#dbd as might be supposed1 upon the approach to1 union with1 and fruition of ,god4 ,the author refers again to the analogy between the movements of the soul and those of the heavens4 ,we move round him like a choral dance2 even when we #bad look from him we revolve about him3 we do not always look at him1 but when we do1 we have satisfaction and rest1 and the harmony which belongs to that divine movement4 ,in this movement1 the mind beholds the fountain of life1 the fountain of mind1 the origin of being1 the cause of good1 the root of the soul4#dcd ,there will be a time when this vision shall be continual2 the mind being no more interrupted1 nor suffering any perturbation from the body4 ,yet that which beholds is not that which is disturbed2 and when this vision becomes dim1 it does not obscure the knowledge which resides in demonstration1 and faith1 and reasoning2 but the vision itself is not reason1 but greater than reason1 and before reason4#ddd ,note #dbd3 vi4 ,enn4 ix4 #h4 ,note #dcd3 vi4 ,enn4 ix4 #i4 ,note #ddd3 vi4 ,enn4 ix4 #aj4 ,the fifth book of the third ,ennead has for its subject the ,dmon which belongs to each man4 ,it is entitled ,concerning ,love2 and the doctrine appears to be1 that the ,love1 or common source of the passions which is in each man's mind1 is the ,dmon which they say accompanies each man4#ded ,these dmons were1 however 7at least by later writers71 invested with a visible aspect and with a personal character1 including a resemblance of human passions and motives4 ,it is curious thus to see an untenable and visionary generalization falling back into the domain of the senses and the fancy1 after a vain attempt to support itself in the region of the reason4 ,this imagination soon produced pretensions to the power of making these dmons or genii visible2 and the ,treatise on the ,mysteries of the ,egyptians1 which is attributed to ,iamblichus1 gives an account of the secret ceremonies1 the mysterious words1 the sacrifices and expiations1 by which this was to be done4 ,note #ded3 ,ficinus1 ,comm4 in v4 ,enn4 iii4 ,it is unnecessary for us to dwell on the progress of this school2 to point out the growth of the ,theurgy which thus arose2 or to describe the attempts to claim a high antiquity for this system1 and to make ,orpheus1 the poet1 the first promulgator of its doctrines4 ,the system1 like all mystical systems1 assumed the character rather of religion than of a theory4 ,the opinions of its disciples materially influenced their lives4 ,it gave the world the spectacle of an austere morality1 a devotional exaltation1 combined with the grossest superstitions of ,paganism4 ,the successors of ,iamblichus appeared rather to hold a priesthood1 than the chair of a philosophical school4#dfd ,they were persecuted by ,constantine and ,constantius1 as opponents of ,christianity4 ,sopater1 a #bae ,syrian philosopher of this school1 was beheaded by the former emperor on a charge that he had bound the winds by the power of magic4#dgd ,but ,julian1 who shortly after succeeded to the purple1 embraced with ardor the opinions of ,iamblichus4 ,proclus 7who died ,a4 ,d4 #dhg7 was one of the greatest of the teachers of this school2#dhd and was1 both in his life and doctrines1 a worthy successor of ,plotinus1 ,porphyry1 and ,iamblichus4 ,we possess a biography1 or rather a panegyric of him1 by his disciple ,marinus1 in which he is exhibited as a representation of the ideal perfection of the philosophic character1 according to the views of the ,neoplatonists4 ,his virtues are arranged as physical1 moral1 purificatory1 theoretic1 and theurgic4 ,even in his boyhood1 ,apollo and ,minerva visited him in his dreams3 he studied oratory at ,alexandria1 but it was at ,athens that ,plutarch and ,lysianus initiated him in the mysteries of the ,new ,platonists4 ,he received a kind of consecration at the hands of the daughter of ,plutarch1 the celebrated ,asclepigenia1 who introduced him to the traditions of the ,chaldeans1 and the practices of theurgy2 he was also admitted to the mysteries of ,eleusis4 ,he became celebrated for his knowledge and eloquence2 but especially for his skill in the supernatural arts which were connected with the doctrines of his sect4 ,he appears before us rather as a hierophant than a philosopher4 ,a large portion of his life was spent in evocations1 purifications1 fastings1 prayers1 hymns1 intercourse with apparitions1 and with the gods1 and in the celebration of the festivals of ,paganism1 especially those which were held in honor of the ,mother of the ,gods4 ,his religious admiration extended to all forms of mythology4 ,the philosopher1 said he1 is not the priest of a single religion1 but of all the religions of the world4 ,accordingly1 he composed hymns in honor of all the divinities of ,greece1 ,rome1 ,egypt1 ,arabia2--,christianity alone was excluded from his favor4 ,note #dfd3 ,deg4 iii4 #djg ,note #dgd3 ,gibbon1 iii4 #ceb4 ,note #dhd3 ,deg4 iii4 #dai4 ,the reader will find an interesting view of the ,school of ,alexandria1 in ,m4 ,barthelemy ,saint-,hilaire's ,rapport on the ,mmoires sent to the ,academy of ,moral and ,political ,sciences at ,paris1 in consequence of its having1 in #ahda1 proposed this as the subject of a prize1 which was awarded in #ahdd4 ,m4 ,saint-,hilaire has prefixed to this ,rapport a dissertation on the ,mysticism of that school4 ,he1 however1 uses the term ,mysticism in a wider sense than my purpose1 which regarded mainly the bearing of the doctrines of this school upon the progress of the ,inductive ,sciences1 has led me to do4 ,although he finds much to #baf admire in the ,alexandrian philosophy1 he declares that they were incapable of treating scientific questions4 ,the extent to which this is true is well illustrated by the extract which he gives from ,plotinus1 on the question1 ,why objects appear smaller in proportion as they are more distant4 ,plotinus denies that the reason of this is that the angles of vision become smaller4 ,his reason for this denial is curious enough4 ,if it were so1 he says1 how could the heaven appear smaller than it is1 since it occupies the whole of the visual angle8 #b4 ,mystical ,arithmetic4--,it is unnecessary further to exemplify1 from ,proclus1 the general mystical character of the school and time to which he belonged2 but we may notice more specially one of the forms of this mysticism1 which very frequently offers itself to our notice1 especially in him2 and which we may call ,mystical ,arithmetic4 ,like all the kinds of ,mysticism1 this consists in the attempt to connect our conceptions of external objects by general and inappropriate notions of goodness1 perfection1 and relation to the divine essence and government2 instead of referring such conceptions to those appropriate ideas1 which1 by due attention1 become perfectly distinct1 and capable of being positively applied and verified4 ,the subject which is thus dealt with1 in the doctrines of which we now speak1 is ,number2 a notion which tempts men into these visionary speculations more naturally than any other4 ,for number is really applicable to moral notions--to emotions and feelings1 and to their objects--as well as to the things of the material world4 ,moreover1 by the discovery of the principle of musical concords1 it had been found1 probably most unexpectedly1 that numerical relations were closely connected with sounds which could hardly be distinguished from the expression of thought and feeling2 and a suspicion might easily arise1 that the universe1 both of matter and of thought1 might contain many general and abstract truths of some analogous kind4 ,the relations of number have so wide a bearing1 that the ramifications of such a suspicion could not easily be exhausted1 supposing men willing to follow them into darkness and vagueness2 which it is precisely the mystical tendency to do4 ,accordingly1 this kind of speculation appeared very early1 and showed itself first among the ,pythagoreans1 as we might have expected1 from the attention which they gave to the theory of harmony3 and this1 as well as some other of the doctrines of the ,pythagorean philosophy1 was adopted by the later ,platonists1 and1 indeed1 by ,plato himself1 whose speculations concerning number have decidedly a mystical character4 ,the mere mathematical relations of numbers1--as odd and even1 perfect and imperfect1 #bag abundant and defective1--were1 by a willing submission to an enthusiastic bias1 connected with the notions of good and beauty1 which were suggested by the terms expressing their relations2 and principles resulting from such a connection were woven into a wide and complex system4 ,it is not necessary to dwell long on this subject2 the mere titles of the works which treated of it show its nature4 ,archytas#did is said to have written a treatise on the number ten3 ,telaug1 the daughter of ,pythagoras1 wrote on the number four4 ,this number1 indeed1 which was known by the name of the ,tetractys1 was very celebrated in the school of ,pythagoras4 ,it is mentioned in the ,golden ,verses1 which are ascribed to him3 the pupil is conjured to be virtuous1 4 4 4 4 ,by him who stampt ,the ,four upon the mind1-- ,the ,four1 the fount of nature's endless stream4 ,note #did3 ,mont4 ii4 #abc4 ,in ,plato's works1 we have evidence of a similar belief in religious relations of ,number2 and in the new ,platonists1 this doctrine was established as a system4 ,proclus1 of whom we have been speaking1 founds his philosophy1 in a great measure1 on the relation of ,unity and ,multiple2 from this1 he is led to represent the causality of the ,divine ,mind by three ,triads of abstractions2 and in the development of one part of this system1 the number seven is introduced4#ejd ,the intelligible and intellectual gods produce all things triadically2 for the monads in these latter are divided according to number2 and what the monad was in the former1 the number is in these latter4 ,and the intellectual gods produce all things hebdomically2 for they evolve the intelligible1 and at the same time intellectual triads1 into intellectual hebdomads1 and expand their contracted powers into intellectual variety4 ,seven is what is called by arithmeticians a prime number1 that is1 it cannot be produced by the multiplication of other numbers4 ,in the language of the ,new ,platonists1 the number seven is said to be a virgin1 and without a mother1 and it is therefore sacred to ,minerva4 ,the number six is a perfect number1 and is consecrated to ,venus4 ,note #ejd3 ,procl4 v4 #c1 ,taylor's translation4 ,the relations of space were dealt with in like manner1 the ,geometrical properties being associated with such physical and metaphysical notions as vague thought and lively feeling could anyhow connect with them4 ,we may consider1 as an example of this1#ead ,plato's opinion #bah concerning the particles of the four elements4 ,he gave to each kind of particle one of the five regular solids1 about which the geometrical speculations of himself and his pupils had been employed4 ,the particles of fire were pyramids1 because they are sharp1 and tend upwards2 those of earth are cubes1 because they are stable1 and fill space2 the particles of air are octahedral1 as most nearly resembling those of fire2 those of water are the icositetrahedron1 as most nearly spherical4 ,the dodecahedron is the figure of the element of the heavens1 and shows its influence in other things1 as in the twelve signs of the zodiac4 ,in such examples we see how loosely space and number are combined or confounded by these mystical visionaries4 ,note #ead3 ,stanley1 ,hist4 ,phil4 ,these numerical dreams of ancient philosophers have been imitated by modern writers2 for instance1 by ,peter ,bungo and ,kircher1 who have written ,de ,mysteriis ,numerorum4 ,bungo treats of the mystical properties of each of the numbers in order1 at great length4 ,and such speculations have influenced astronomical theories4 ,in the first edition of the ,alphonsine ,tables1#ebd the precession was represented by making the first point of ,aries move1 in a period of #gjjj years1 through a circle of which the radius was #ah degrees1 while the circle moved round the ecliptic in #di1jjj years2 and these numbers1 #gjjj and #di1jjj1 were chosen probably by ,jewish calculators1 or with reference to ,jewish ,sabbatarian notions4 ,note #ebd3 ,montucla1 i4 #eaa4 #c4 ,astrology4--,of all the forms which mysticism assumed1 none was cultivated more assiduously than astrology4 ,although this art prevailed most universally and powerfully during the stationary period1 its existence1 even as a detailed technical system1 goes back to a very early age4 ,it probably had its origin in the ,east2 it is universally ascribed to the ,babylonians and ,chaldeans2 the name ,chaldean was1 at ,rome1 synonymous with mathematicus1 or astrologer2 and we read repeatedly that this class of persons were expelled from ,italy by a decree of the senate1 both during the times of the republic and of the empire4#ecd ,the recurrence of this act of legislation shows that it was not effectual3 ,it is a class of men1 says ,tacitus1 which1 in our city1 will always be prohibited1 and will always exist4 ,in ,greece1 it does not appear that the state showed any hostility to the professors of this art4 ,they undertook1 it would seem1 then1 as at a later period1 to determine the course of a man's character and life from the configuration of the stars at the moment of his birth4 ,we do not possess any of the #bai speculations of the early astrologers2 and we cannot therefore be certain that the notions which operated in men's minds when the art had its birth1 agreed with the views on which it was afterwards defended1 when it became a matter of controversy4 ,but it appears probable1 that1 though it was at later periods supported by physical analogies1 it was originally suggested by mythological belief4 ,the ,greeks spoke of the influences or effluxes 77 which proceeded from the stars2 but the ,chaldeans had probably thought rather of the powers which they exercised as deities4 ,in whatever manner the sun1 moon1 and planets came to be identified with gods and goddesses1 it is clear that the characters ascribed to these gods and goddesses regulate the virtues and powers of the stars which bear their names4 ,this association1 so manifestly visionary1 was retained1 amplified1 and pursued1 in an enthusiastic spirit1 instead of being rejected for more distinct and substantial connections2 and a pretended science was thus formed1 which bears the obvious stamp of mysticism4 ,note #ecd3 ,tacit4 ,ann4 ii4 #cb4 xii4 #eb4 ,hist4 ,i4 #bb1 ,,ii4 #fb4 ,that common sense of mankind which teaches them that theoretical opinions are to be calmly tried by their consequences and their accordance with facts1 appears to have counteracted the prevalence of astrology in the better times of the human mind4 ,eudoxus1 as we are informed by ,cicero1#edd rejected the pretensions of the ,chaldeans2 and ,cicero himself reasons against them with arguments as sensible and intelligent as could be adduced by a writer of the present day2 such as the different fortunes and characters of persons born at the same time2 and the failure of the predictions1 in the case of ,pompey1 ,crassus1 ,csar1 to whom the astrologers had foretold glorious old age and peaceful death4 ,he also employs an argument which the reader would perhaps not expect from him1--the very great remoteness of the planets as compared with the distance of the moon4 ,what contagion can reach us1 he asks1 from a distance almost infinite8 ,note #edd3 ,cic4 de ,div4 ii4 #db4 ,pliny argues on the same side1 and with some of the same arguments4#eed ,homer1 he says1 tells us that ,hector and ,polydamus were born the same night2--men of such different fortune4 ,and every hour1 in every part of the world1 are born lords and slaves1 kings and beggars4 ,note #eed3 ,hist4 ,nat4 vii4 #di4 ,the impression made by these arguments is marked in an anecdote told concerning ,publius ,nigidius ,figulus1 a ,roman of the time of ,julius ,csar1 whom ,lucan mentions as a celebrated astrologer4 ,it is #bbj said1 that when an opponent of the art urged as an objection the different fates of persons born in two successive instants1 ,nigidius bade him make two contiguous marks on a potter's wheel1 which was revolving rapidly near them4 ,on stopping the wheel1 the two marks were found to be really far removed from each other2 and ,nigidius is said to have received the name of ,figulus 7the potter71 in remembrance of this story1 ,his argument1 says ,st4 ,augustine1 who gives us the narrative1 was as fragile as the ware which the wheel manufactured4 ,as the darkening times of the ,roman empire advanced1 even the stronger minds seem to have lost the clear energy which was requisite to throw off this delusion4 ,seneca appears to take the influence of the planets for granted2 and even ,tacitus#efd seems to hesitate4 ,for my own part1 says he1 ,i doubt2 but certainly the majority of mankind cannot be weaned from the opinion1 that1 at the birth of each man1 his future destiny is fixed2 though some things may fall out differently from the predictions1 by the ignorance of those who profess the art2 and that thus the art is unjustly blamed1 confirmed as it is by noted examples in all ages4 ,the occasion which gives rise to these reflections of the historian is the mention of ,thrasyllus1 the favorite astrologer of the ,emperor ,tiberius1 whose skill is exemplified in the following narrative4 ,those who were brought to ,tiberius on any important matter1 were admitted to an interview in an apartment situated on a lofty cliff in the island of ,capre4 ,they reached this place by a narrow path1 accompanied by a single freedman of great bodily strength2 and on their return1 if the emperor had conceived any doubts of their trustworthiness1 a single blow buried the secret and its victim in the ocean below4 ,after ,thrasyllus had1 in this retreat1 stated the results of his art as they concerned the emperor1 ,tiberius asked him whether he had calculated how long he himself had to live4 ,the astrologer examined the aspect of the stars1 and while he did this1 as the narrative states1 showed hesitation1 alarm1 increasing terror1 and at last declared that1 the present hour was for him critical1 perhaps fatal4 ,tiberius embraced him1 and told him he was right in supposing he had been in danger1 but that he should escape it2 and made him thenceforth his confidential counsellor4 ,note #efd3 ,ann4 vi4 #bb4 ,the belief in the power of astrological prediction which thus obtained dominion over the minds of men of literary cultivation and practical energy1 naturally had a more complete sway among the speculative #bba but unstable minds of the later philosophical schools of ,alexandria1 ,athens1 and ,rome4 ,we have a treatise on astrology by ,proclus1 which will serve to exemplify the mystical principle in this form4 ,it appears as a commentary on a work on the same subject called ,tetrabiblos1 ascribed to ,ptolemy2 though we may reasonably doubt whether the author of the ,megale ,syntaxis was also the writer of the astrological work4 ,a few notices of the commentary of ,proclus will suffice4#egd ,the science is defended by urging how powerful we know the physical effects of the heavenly bodies to be4 ,the sun regulates all things on earth2--the birth of animals1 the growth of fruits1 the flowing of waters1 the change of health1 according to the seasons3 he produces heat1 moisture1 dryness1 cold1 according to his approach to our zenith4 ,the moon1 which is the nearest of all bodies to the earth1 gives out much influence2 and all things1 animate and inanimate1 sympathize with her3 rivers increase and diminish according to her light2 the advance of the sea1 and its recess1 are regulated by her rising and setting2 and along with her1 fruits and animals wax and wane1 either wholly or in part4 ,it is easy to see that by pursuing this train of associations 7some real and some imaginary7 very vaguely and very enthusiastically1 the connections which astrology supposes would receive a kind of countenance4 ,proclus then proceeds to state#ehd the doctrines of the science4 ,the sun1 he says1 is productive of heat and dryness2 this power is moderate in its nature1 but is more perceived than that of the other luminaries1 from his magnitude1 and from the change of seasons4 ,the nature of the moon is for the most part moist2 for being the nearest to the earth1 she receives the vapors which rise from moist bodies1 and thus she causes bodies to soften and rot4 ,but by the illumination she receives from the sun1 she partakes in a moderate degree of heat4 ,saturn is cold and dry1 being most distant both from the heating power of the sun1 and the moist vapors of the earth4 ,his cold1 however1 is most prevalent1 his dryness is more moderate4 ,both he and the rest receive additional powers from the configurations which they make with respect to the sun and moon4 ,in the same manner it is remarked that ,mars is dry and caustic1 from his fiery nature1 which1 indeed1 his color shows4 ,jupiter is well compounded of warm and moist1 as is ,venus4 ,mercury is variable in his character4 ,from these notions were derived others concerning the beneficial or hurtful effect of these stars4 ,heat and #bbb moisture are generative and creative elements2 hence the ancients1 says ,proclus1 deemed ,jupiter1 and ,venus1 and the ,moon to have a good power2 ,saturn and ,mercury1 on the other hand1 had an evil nature4 ,note #egd3 ,i4 #b4 ,note #ehd3 ,i4 #d4 ,other distinctions of the character of the stars are enumerated1 equally visionary1 and suggested by the most fanciful connections4 ,some are masculine1 and some feminine3 the ,moon and ,venus are of the latter kind4 ,this appears to be merely a mythological or etymological association4 ,some are diurnal1 some nocturnal3 the ,moon and ,venus are of the latter kind1 the ,sun and ,jupiter of the former2 ,saturn and ,mars are both4 ,the fixed stars1 also1 and especially those of the zodiac1 had especial influences and subjects assigned to them4 ,in particular1 each sign was supposed to preside over a particular part of the body2 thus ,aries had the head assigned to it1 ,taurus the neck1 and so on4 ,the most important part of the sky in the astrologer's consideration1 was that sign of the zodiac which rose at the moment of the child's birth2 this was1 properly speaking1 the horoscope1 the ascendant1 or the first house2 the whole circuit of the heavens being divided into twelve houses1 in which life and death1 marriage and children1 riches and honors1 friends and enemies1 were distributed4 ,we need not attempt to trace the progress of this science4 ,it prevailed extensively among the ,arabians1 as we might expect from the character of that nation4 ,albumasar1 of ,balkh in ,khorasan1 who flourished in the ninth century1 who was one of their greatest astronomers1 was also a great astrologer2 and his work on the latter subject1 ,de ,magnis ,conjunctionibus1 ,annorum ,revolutionibus ac eorum ,perfectionibus1 was long celebrated in ,europe4 ,aboazen ,haly 7the writer of a treatise ,de ,judiciis ,astrorum71 who lived in ,spain in the thirteenth century1 was one of the classical authors on this subject4 ,it will easily be supposed that when this apotelesmatic or judicial astrology obtained firm possession of men's minds1 it would be pursued into innumerable subtle distinctions and extravagant conceits2 and the more so1 as experience could offer little or no check to such exercises of fancy and subtlety4 ,for the correction of rules of astrological divination by comparison with known events1 though pretended to by many professors of the art1 was far too vague and fallible a guidance to be of any real advantage4 ,even in what has been called ,natural ,astrology1 the dependence of the weather on the heavenly bodies1 it is easy to see what a vast accumulation of well-observed facts is requisite to establish #bbc any true rule2 and it is well known how long1 in spite of facts1 false and groundless rules 7as the dependence of the weather on the moon7 may keep their hold on men's minds4 ,when the facts are such loose and many-sided things as human characters1 passions1 and happiness1 it was hardly to be expected that even the most powerful minds should be able to find a footing sufficiently firm1 to enable them to resist the impression of a theory constructed of sweeping and bold assertions1 and filled out into a complete system of details4 ,accordingly1 the connection of the stars with human persons and actions was1 for a long period1 undisputed4 ,the vague1 obscure1 and heterogeneous character of such a connection1 and its unfitness for any really scientific reasoning1 could1 of course1 never be got rid of2 and the bewildering feeling of earnestness and solemnity1 with which the connection of the heavens with man was contemplated1 never died away4 ,in other respects1 however1 the astrologers fell into a servile commentatorial spirit2 and employed themselves in annotating and illustrating the works of their predecessors to a considerable extent1 before the revival of true science4 ,it may be mentioned1 that astrology has long been1 and probably is1 an art held in great esteem and admiration among other eastern nations besides the ,mohammedans2 for instance1 the ,jews1 the ,indians1 the ,siamese1 and the ,chinese4 ,the prevalence of vague1 visionary1 and barren notions among these nations1 cannot surprise us2 for with regard to them we have no evidence1 as with regard to ,europeans we have1 that they are capable1 on subjects of physical speculation1 of originating sound and rational general principles4 ,the ,arts may have had their birth in all parts of the globe2 but it is only ,europe1 at particular favored periods of its history1 which has ever produced ,sciences4 ,we are1 however1 now speaking of a long period1 during which this productive energy was interrupted and suspended4 ,during this period ,europe descended1 in intellectual character1 to the level at which the other parts of the world have always stood4 ,her ,science was then a mixture of ,art and ,mysticism2 we have considered several forms of this ,mysticism1 but there are two others which must not pass unnoticed1 ,alchemy and ,magic4 ,we may observe1 before we proceed1 that the deep and settled influence which ,astrology had obtained among them1 appears perhaps most strongly in the circumstance1 that the most vigorous and clear-sighted minds which were concerned in the revival of science1 did not1 for a long period1 shake off the persuasion that there was1 in this art1 some element of truth4 ,roger ,bacon1 ,cardan1 ,kepler1 ,tycho ,brahe1 #bbd ,francis ,bacon1 are examples of this4 ,these1 or most of them1 rejected all the more obvious and extravagant absurdities with which the subject had been loaded2 but still conceived that some real and valuable truth remained when all these were removed4 ,thus ,campanella1#eid whom we shall have to speak of as one of the first opponents of ,aristotle1 wrote an ,astrology purified from all the ,superstitions of the ,jews and ,arabians1 and treated physiologically4 ,note #eid3 ,bacon1 ,de ,aug4 iii4 #d4 #d4 ,alchemy4--,like other kinds of ,mysticism1 ,alchemy seems to have grown out of the notions of moral1 personal1 and mythological qualities1 which men associated with terms1 of which the primary application was to physical properties4 ,this is the form in which the subject is presented to us in the earliest writings which we possess on the subject of chemistry2--those of ,geber#fjd of ,seville1 who is supposed to have lived in the eighth or ninth century4 ,the very titles of ,geber's works show the notions on which this pretended science proceeds4 ,they are1 ,of the ,search of ,perfection2 ,of the ,sum of ,perfection1 or of the ,perfect ,magistery2 ,of the ,invention of ,verity1 or ,perfection4 ,the basis of this phraseology is the distinction of metals into more or less perfect2 gold being the most perfect1 as being the most valuable1 most beautiful1 most pure1 most durable2 silver the next2 and so on4 ,the ,search of ,perfection was1 therefore1 the attempt to convert other metals into gold2 and doctrines were adopted which represented the metals as all compounded of the same elements1 so that this was theoretically possible4 ,but the mystical trains of association were pursued much further than this2 gold and silver were held to be the most noble of metals2 gold was their ,king1 and silver their ,queen4 ,mythological associations were called in aid of these fancies1 as had been done in astrology4 ,gold was ,sol1 silver was ,luna1 the moon2 copper1 iron1 tin1 lead1 were assigned to ,venus1 ,mars1 ,jupiter1 ,saturn4 ,the processes of mixture and heat were spoken of as personal actions and relations1 struggles and victories4 ,some elements were conquerors1 some conquered2 there existed preparations which possessed the power of changing the whole of a body into a substance of another kind3 these were called magisteries4#fad ,when gold and quicksilver are combined1 the king and the queen are married1 to produce children of their own kind4 ,it will easily be conceived1 that when chemical operations were described in phraseology of this sort1 the enthusiasm of the #bbe fancy would be added to that of the hopes1 and observation would not be permitted to correct the delusion1 or to suggest sounder and more rational views4 ,note #fjd3 ,thomson's ,hist4 of ,chem4 i4 #aag4 ,note #fad3 ,boyle1 ,thomson's ,hist4 ,ch4 i4 #be4 ,carolus ,musitanus4 ,the exaggeration of the vague notion of perfection and power in the object of the alchemist's search1 was carried further still4 ,the same preparation which possessed the faculty of turning baser metals into gold1 was imagined to be also a universal medicine1 to have the gift of curing or preventing diseases1 prolonging life1 producing bodily strength and beauty3 the philosophers' stone was finally invested with every desirable efficacy which the fancy of the philosophers could devise4 ,it has been usual to say that ,alchemy was the mother of ,chemistry2 and that men would never have made the experiments on which the real science is founded1 if they had not been animated by the hopes and the energy which the delusive art inspired4 ,to judge whether this is truly said1 we must be able to estimate the degree of interest which men feel in purely speculative truth1 and in the real and substantial improvement of art to which it leads4 ,since the fall of ,alchemy1 and the progress of real ,chemistry1 these motives have been powerful enough to engage in the study of the science1 a body far larger than the ,alchemists ever were1 and no less zealous4 ,there is no apparent reason why the result should not have been the same1 if the progress of true science had begun sooner4 ,astronomy was long cultivated without the bribe of ,astrology4 ,but1 perhaps1 we may justly say this2--that1 in the stationary period1 men's minds were so far enfeebled and degraded1 that pure speculative truth had not its full effect upon them2 and the mystical pursuits in which some dim and disfigured images of truth were sought with avidity1 were among the provisions by which the human soul1 even when sunk below its best condition1 is perpetually directed to something above the mere objects of sense and appetite2--a contrivance of compensation1 as it were1 in the intellectual and spiritual constitution of man4 #e4 ,magic4--,magical ,arts1 so far as they were believed in by those who professed to practise them1 and so far as they have a bearing in science1 stand on the same footing as astrology2 and1 indeed1 a close alliance has generally been maintained between the two pursuits4 ,incapacity and indisposition to perceive natural and philosophical causation1 an enthusiastic imagination1 and such a faith as can devise and maintain supernatural and spiritual connexions1 are the elements of this1 as of other forms of ,mysticism4 ,and thus1 that temper which led men to aim at the magician's supposed authority over the elements1 #bbf is an additional exemplification of those habits of thought which prevented the progress of real science1 and the acquisition of that command over nature which is founded on science1 during the interval now before us4 ,but there is another aspect under which the opinions connected with this pursuit may serve to illustrate the mental character of the ,stationary ,period4 ,the tendency1 during the middle ages1 to attribute the character of ,magician to almost all persons eminent for great speculative or practical knowledge1 is a feature of those times1 which shows how extensive and complete was the inability to apprehend the nature of real science4 ,in cultivated and enlightened periods1 such as those of ancient ,greece1 or modern ,europe1 knowledge is wished for and admired1 even by those who least possess it3 but in dark and degraded periods1 superior knowledge is a butt for hatred and fear4 ,in the one case1 men's eyes are open2 their thoughts are clear2 and1 however high the philosopher may be raised above the multitude1 they can catch glimpses of the intervening path1 and see that it is free to all1 and that elevation is the reward of energy and labor4 ,in the other case1 the crowd are not only ignorant1 but spiritless2 they have lost the pleasure in knowledge1 the appetite for it1 and the feeling of dignity which it gives3 there is no sympathy which connects them with the learned man3 they see him above them1 but know not how he is raised or supported3 he becomes an object of aversion and envy1 of vague suspicion and terror2 and these emotions are embodied and confirmed by association with the fancies and dogmas of superstition4 ,to consider superior knowledge as ,magic1 and ,magic as a detestable and criminal employment1 was the form which these feelings of dislike assumed2 and at one period in the history of ,europe1 almost every one who had gained any eminent literary fame1 was spoken of as a magician4 ,naudus1 a learned ,frenchman1 in the seventeenth century1 wrote ,an ,apology for all the ,wise ,men who have been unjustly reported ,magicians1 from the ,creation to the present ,age4 ,the list of persons whom he thus thinks it necessary to protect1 are of various classes and ages4 ,alkindi1 ,geber1 ,artephius1 ,thebit1 ,raymund ,lully1 ,arnold de ,vill ,nov1 ,peter of ,apono1 and ,paracelsus1 had incurred the black suspicion as physicians or alchemists4 ,thomas ,aquinas1 ,roger ,bacon1 ,michael ,scott1 ,picus of ,mirandula1 and ,trithemius1 had not escaped it1 though ministers of religion4 ,even dignitaries1 such as ,robert ,grosteste1 ,bishop of ,lincoln1 ,albertus ,magnus1 ,bishop of ,ratisbon1 #bbg ,popes ,sylvester the ,second1 and ,gregory the ,seventh1 had been involved in the wide calumny4 ,in the same way in which the vulgar confounded the eminent learning and knowledge which had appeared in recent times1 with skill in dark and supernatural arts1 they converted into wizards all the best-known names in the rolls of fame2 as ,aristotle1 ,solomon1 ,joseph1 ,pythagoras2 and1 finally1 the poet ,virgil was a powerful and skilful necromancer1 and this fancy was exemplified by many strange stories of his achievements and practices4 ,the various results of the tendency of the human mind to mysticism1 which we have here noticed1 form prominent features in the intellectual character of the world1 for a long course of centuries4 ,the theosophy and theurgy of the ,neoplatonists1 the mystical arithmetic of the ,pythagoreans and their successors1 the predictions of the astrologers1 the pretences of alchemy and magic1 represent1 not unfairly1 the general character and disposition of men's thoughts1 with reference to philosophy and science4 ,that there were stronger minds1 which threw off in a greater or less degree this train of delusive and unsubstantial ideas1 is true2 as1 on the other hand1 ,mysticism1 among the vulgar or the foolish1 often went to an extent of extravagance and superstition1 of which ,i have not attempted to convey any conception4 ,the lesson which the preceding survey teaches us is1 that during the ,stationary ,period1 ,mysticism1 in its various forms1 was a leading character1 both of the common mind1 and of the speculations of the most intelligent and profound reasoners2 and that this ,mysticism was the opposite of that habit of thought which we have stated ,science to require2 namely1 clear ,ideas1 distinctly employed to connect well-ascertained ,facts2 inasmuch as the ,ideas in which it dealt were vague and unstable1 and the temper in which they were contemplated was an urgent and aspiring enthusiasm1 which could not submit to a calm conference with experience upon even terms4 ,the fervor of thought in some degree supplied the place of reason in producing belief2 but opinions so obtained had no enduring value2 they did not exhibit a permanent record of old truths1 nor a firm foundation for new4 ,experience collected her stores in vain1 or ceased to collect them1 when she had only to pour them into the flimsy folds of the lap of ,mysticism2 who was1 in truth1 so much absorbed in looking for the treasures which were to fall from the skies1 that she heeded little how scantily she obtained1 or how loosely she held1 such riches as might be found near her4 #bbh ,,chapter ,,iv4 ,,of ,,the ,,dogmatism ,,of ,,the ,,stationary ,,period4 ,,in speaking of the character of the age of commentators1 we noticed principally the ingenious servility which it displays2--the acuteness with which it finds ground for speculation in the expression of other men's thoughts2--the want of all vigor and fertility in acquiring any real and new truths4 ,such was the character of the reasoners of the stationary period from the first2 but1 at a later day1 this character1 from various causes1 was modified by new features4 ,the servility which had yielded itself to the yoke1 insisted upon forcing it on the necks of others3 the subtlety which found all the truth it needed in certain accredited writings1 resolved that no one should find there1 or in any other region1 any other truths2 speculative men became tyrants without ceasing to be slaves2 to their character of ,commentators they added that of ,dogmatists4 #a4 ,origin of the ,scholastic ,philosophy4--,the causes of this change have been very happily analyzed and described by several modern writers4#fbd ,the general nature of the process may be briefly stated to have been the following4 ,note #fbd3 ,dr4 ,hampden1 in the ,life of ,thomas ,aquinas1 in the ,encyc4 ,metrop4 ,degerando1 ,hist4 ,compare1 vol4 iv4 ,also ,tennemann1 ,hist4 of ,phil4 vol4 viii4 ,introduction4 ,the tendencies of the later times of the ,roman empire to a commenting literature1 and a second-hand philosophy1 have already been noticed4 ,the loss of the dignity of political freedom1 the want of the cheerfulness of advancing prosperity1 and the substitution of the less philosophical structure of the ,latin language for the delicate intellectual mechanism of the ,greek1 fixed and augmented the prevalent feebleness and barrenness of intellect4 ,men forgot1 or feared1 to consult nature1 to seek for new truths1 to do what the great discoverers of other times had done2 they were content to consult libraries1 to study and defend old opinions1 to talk of what great geniuses had said4 ,they sought their philosophy in accredited treatises1 and dared not question such doctrines as they there found4 ,the character of the philosophy to which they were thus led1 was determined by this want of courage and originality4 ,there are various #bbi antagonist principles of opinion1 which seem alike to have their root in the intellectual constitution of man1 and which are maintained and developed by opposing sects1 when the intellect is in vigorous action4 ,such principles are1 for instance1--the claims of ,authority and of ,reason to our assent2--the source of our knowledge in ,experience or in ,ideas2--the superiority of a ,mystical or of a ,skeptical turn of thought4 ,such oppositions of doctrine were found in writers of the greatest fame2 and two of those1 who most occupied the attention of students1 ,plato and ,aristotle1 were1 on several points of this nature1 very diverse from each other in their tendency4 ,the attempt to reconcile these philosophers by ,bothius and others1 we have already noticed2 and the attempt was so far successful1 that it left on men's minds the belief in the possibility of a great philosophical system which should be based on both these writers1 and have a claim to the assent of all sober speculators4 ,but1 in the mean time1 the ,christian ,religion had become the leading subject of men's thoughts2 and divines had put forward its claims to be1 not merely the guide of men's lives1 and the means of reconciling them to their heavenly ,master1 but also to be a ,philosophy in the widest sense in which the term had been used2--a consistent speculative view of man's condition and nature1 and of the world in which he is placed4 ,these claims had been acknowledged2 and1 unfortunately1 from the intellectual condition of the times1 with no due apprehension of the necessary ministry of ,observation1 and ,reason dealing with observation1 by which alone such a system can be embodied4 ,it was held without any regulating principle1 that the philosophy which had been bequeathed to the world by the great geniuses of heathen antiquity1 and the ,philosophy which was deduced from1 and implied by1 the ,revelations made by ,god to man1 must be identical2 and1 therefore1 that ,theology is the only true philosophy4 ,indeed1 the ,neoplatonists had already arrived1 by other roads1 at the same conviction4 ,john ,scot ,erigena1 in the reign of ,alfred1 and consequently before the existence of the ,scholastic ,philosophy1 properly so called1 had reasserted this doctrine4#fcd ,anselm1 in the eleventh century1 again brought it forward2#fdd and ,bernard de ,chartres1 in the thirteenth4#fed ,note #fcd3 ,deg4 iv4 #cea4 ,note #fdd3 ,ib4 iv4 #chh4 ,note #fed3 ,ib4 iv4 #dah4 ,this view was confirmed by the opinion which prevailed1 concerning the nature of philosophical truth2 a view supported by the theory #bcj of ,plato1 the practice of ,aristotle1 and the general propensities of the human mind3 ,i mean the opinion that all science may be obtained by the use of reasoning alone2--that by analysing and combining the notions which common language brings before us1 we may learn all that we can know4 ,thus ,logic came to include the whole of ,science2 and accordingly this ,abelard expressly maintained4#ffd ,i have already explained1 in some measure1 the fallacy of this belief1 which consists1 as has been well said1#fgd in mistaking the universality of the theory of language for the generalization of facts4 ,but on all accounts this opinion is readily accepted2 and it led at once to the conclusion1 that the ,theological ,philosophy which we have described1 is complete as well as true4 ,note #ffd3 ,deg4 iv4 #djg4 ,note #fgd3 ,enc4 ,met4 #hjg4 ,thus a ,universal ,science was established1 with the authority of a ,religious ,creed4 ,its universality rested on erroneous views of the relation of words and truths2 its pretensions as a science were admitted by the servile temper of men's intellects2 and its religious authority was assigned it1 by making all truth part of religion4 ,and as ,religion claimed assent within her own jurisdiction under the most solemn and imperative sanctions1 ,philosophy shared in her imperial power1 and dissent from their doctrines was no longer blameless or allowable4 ,error became wicked1 dissent became heresy2 to reject the received human doctrines1 was nearly the same as to doubt the ,divine declarations4 ,the ,scholastic ,philosophy claimed the assent of all believers4 ,the external form1 the details1 and the text of this philosophy1 were taken1 in a great measure1 from ,aristotle2 though1 in the spirit1 the general notions1 and the style of interpretation1 ,plato and the ,platonists had no inconsiderable share4 ,various causes contributed to the elevation of ,aristotle to this distinction4 ,his ,logic had early been adopted as an instrument of theological disputation2 and his spirit of systematization1 of subtle distinction1 and of analysis of words1 as well as his disposition to argumentation1 afforded the most natural and grateful employment to the commentating propensities4 ,those principles which we before noted as the leading points of his physical philosophy1 were selected and adopted2 and these1 presented in a most technical form1 and applied in a systematic manner1 constitute a large portion of the philosophy of which we now speak1 so far as it pretends to deal with physics4 #b4 ,scholastic ,dogmas4--,but before the complete ascendancy of ,aristotle was thus established1 when something of an intellectual waking #bca took place after the darkness and sleep of the ninth and tenth centuries1 the ,platonic doctrines seem to have had1 at first1 a strong attraction for men's minds1 as better falling in with the mystical speculations and contemplative piety which belonged to the times4 ,john ,scot ,erigena#fhd may be looked upon as the reviver of the ,new ,platonism in the tenth century4 ,towards the end of the eleventh1 ,peter ,damien1#fid in ,italy1 reproduced1 involved in a theological discussion1 some ,neoplatonic ideas4 ,godefroy#gjd also1 censor of ,st4 ,victor1 has left a treatise1 entitled ,microcosmus2 this is founded on a mystical analogy1 often afterwards again brought forward1 between ,man and the ,universe4 ,philosophers and theologians1 says the writer1 agree in considering man as a little world2 and as the world is composed of four elements1 man is endowed with four faculties1 the senses1 the imagination1 reason1 and understanding4 ,bernard of ,chartres1#gad in his ,megascosmus and ,microcosmus1 took up the same notions4 ,hugo1 abbot of ,st4 ,victor1 made a contemplative life the main point and crown of his philosophy2 and is said to have been the first of the scholastic writers who made psychology his special study4#gbd ,he says the faculties of the mind are the senses1 the imagination1 the reason1 the memory1 the understanding1 and the intelligence4 ,note #fhd3 ,deg4 iv4 #ce4 ,note #fid3 ,ib4 iv4 #cfg4 ,note #gjd3 ,ib4 iv4 #dac4 ,note #gad3 ,ib4 iv4 #dai4 ,note #gbd3 ,ib4 iv4 #dae4 ,physics does not originally and properly form any prominent part of the ,scholastic ,philosophy1 which consists mainly of a series of questions and determinations upon the various points of a certain technical divinity4 ,of this kind is the ,book of ,sentences of ,peter the ,lombard 7bishop of ,paris71 who is1 on that account1 usually called ,magister ,sententiarum2 a work which was published in the twelfth century1 and was long the text and standard of such discussions4 ,the questions are decided by the authority of ,scripture and of the ,fathers of the ,church1 and are divided into four ,books1 of which the first contains questions concerning ,god and the doctrine of the ,trinity in particular2 the second is concerning the ,creation2 the third1 concerning ,christ and the ,christian ,religion2 and the fourth treats of ,religious and ,moral ,duties4 ,in the second book1 as in many of the writers of this time1 the nature of ,angels is considered in detail1 and the ,orders of their ,hierarchy1 of which there were held to be nine4 ,the physical discussions enter only as bearing upon the scriptural history of the creation1 and cannot be taken as a specimen of the work2 but ,i may observe1 that in speaking of the division of the waters above the #bcb firmament1 he gives one opinion1 that of ,bede1 that the former waters are the solid crystalline heavens in which the stars are fixed1#gcd for crystal1 which is so hard and transparent1 is made of water4 ,but he mentions also the opinion of ,st4 ,augustine1 that the waters above the heavens are in a state of vapor1 7vaporaliter7 and in minute drops2 if1 then1 water can1 as we see in clouds1 be so minutely divided that it may be thus supported as vapor on air1 which is naturally lighter than water2 why may we not believe that it floats above that lighter celestial element in still minuter drops and still lighter vapors8 ,but in whatever manner the waters are there1 we do not doubt that they are there4 ,note #gcd3 ,lib4 ii4 ,distinct4 xiv4 ,de opere secund diei4 ,the celebrated ,summa ,theologic of ,thomas ,aquinas is a work of the same kind2 and anything which has a physical bearing forms an equally small part of it4 ,thus1 of the #eab ,questions of the ,summa1 there is only one 7,part ,i41 ,quest4 #aae71 on ,corporeal ,action1 or on any part of the material world2 though there are several concerning the celestial ,hierarchies1 as on the ,act of ,angels1 on the ,speaking of ,angels1 on the ,subordination of ,angels1 on ,guardian ,angels1 and the like4 ,this1 of course1 would not be remarkable in a treatise on ,theology1 except this ,theology were intended to constitute the whole of ,philosophy4 ,we may observe1 that in this work1 though ,plato1 ,avecibron1 and many other heathen as well as ,christian philosophers1 are adduced as authority1 ,aristotle is referred to in a peculiar manner as the philosopher4 ,this is noticed by ,john of ,salisbury1 as attracting attention in his time 7he died ,a4,d4 #aahb74 ,the various ,masters of ,dialectic1 says he1#gdd shine each with his peculiar merit2 but all are proud to worship the footsteps of ,aristotle2 so much so1 indeed1 that the name of philosopher1 which belongs to them all1 has been pre-eminently appropriated to him4 ,he is called the philosopher autonomatice1 that is1 by excellence4 ,note #gdd3 ,metalogicus1 lib4 ii4 cap4 #af4 ,the ,question concerning ,corporeal ,action1 in ,aquinas1 is divided into six ,articles2 and the conclusion delivered upon the first is1#ged that ,body being compounded of power and act1 is active as well as passive4 ,against this it is urged1 that quantity is an attribute of body1 and that quantity prevents action2 that this appears in fact1 since a larger body is more difficult to move4 ,the author replies1 that #bcc quantity does not prevent corporeal form from action altogether1 but prevents it from being a universal agent1 inasmuch as the form is individualized1 which1 in matter subject to quantity1 it is4 ,moreover1 the illustration deduced from the ponderousness of bodies is not to the purpose2 first1 because the addition of quantity is not the cause of gravity1 as is proved in the fourth book1 ,de ,clo and ,de ,mundo 7we see that he quotes familiarly the physical treatises of ,aristotle72 second1 because it is false that ponderousness makes motion slower2 on the contrary1 in proportion as any thing is heavier1 the more does it move with its proper motion2 thirdly1 because action does not take place by local motion1 as ,democritus asserted2 but by this1 that something is drawn from power into act4 ,note #ged3 9999,summa1 ,p4 i4 ,q4 #aae4 ,art4 #a4 ,it does not belong to our purpose to consider either the theological or the metaphysical doctrines which form so large a portion of the treatises of the schoolmen4 ,perhaps it may hereafter appear1 that some light is thrown on some of the questions which have occupied metaphysicians in all ages1 by that examination of the history of the ,progressive ,sciences in which we are now engaged2 but till we are able to analyze the leading controversies of this kind1 it would be of little service to speak of them in detail4 ,it may be noticed1 however1 that many of the most prominent of them refer to the great question1 ,what is the relation between actual things and general terms8 ,perhaps in modern times1 the actual things would be more commonly taken as the point to start from2 and men would begin by considering how classes and universals are obtained from individuals4 ,but the schoolmen1 founding their speculations on the received modes of considering such subjects1 to which both ,aristotle and ,plato had contributed1 travelled in the opposite direction1 and endeavored to discover how individuals were deduced from genera and species2--what was the ,principle of ,individuation4 ,this was variously stated by different reasoners4 ,thus ,bonaventura#gfd solves the difficulty by the aid of the ,aristotelian distinction of ,matter and ,form4 ,the individual derives from the ,form the property of being something1 and from the ,matter the property of being that particular thing4 ,duns ,scotus1#ggd the great adversary of ,thomas ,aquinas in theology1 placed the principle of ,individuation in a certain determining positive entity1 which his school called ,hcceity or thisness4 ,thus an individual man is ,peter1 because his humanity is combined with ,petreity4 ,the force #bcd of abstract terms is a curious question1 and some remarkable experiments in their use had been made by the ,latin ,aristotelians before this time4 ,in the same way in which we talk of the quantity and quality of a thing1 they spoke of its quiddity4#ghd ,note #gfd3 ,deg4 iv4 #egc4 ,note #ggd3 ,ib4 iv4 #ebc4 ,note #ghd3 ,deg4 iv4 #did4 ,we may consider the reign of mere disputation as fully established at the time of which we are now speaking2 and the only kind of philosophy henceforth studied was one in which no sound physical science had or could have a place4 ,the wavering abstractions1 indistinct generalizations1 and loose classifications of common language1 which we have already noted as the fountain of the physics of the ,greek ,schools of philosophy1 were also the only source from which the ,schoolmen of the middle ages drew their views1 or rather their arguments3 and though these notional and verbal relations were invested with a most complex and pedantic technicality1 they did not1 on that account1 become at all more precise as notions1 or more likely to lead to a single real truth4 ,instead of acquiring distinct ideas1 they multiplied abstract terms2 instead of real generalizations1 they had recourse to verbal distinctions4 ,the whole course of their employments tended to make them1 not only ignorant of physical truth1 but incapable of conceiving its nature4 ,having thus taken upon themselves the task of raising and discussing questions by means of abstract terms1 verbal distinctions1 and logical rules alone1 there was no tendency in their activity to come to an end1 as there was no progress4 ,the same questions1 the same answers1 the same difficulties1 the same solutions1 the same verbal subtleties1--sought for1 admired1 cavilled at1 abandoned1 reproduced1 and again admired1--might recur without limit4 ,john of ,salisbury#gid observes of the ,parisian teachers1 that1 after several years' absence1 he found them not a step advanced1 and still employed in urging and parrying the same arguments2 and this1 as ,mr4 ,hallam remarks1#hjd was equally applicable to the period of centuries4 ,the same knots were tied and #bce untied2 the same clouds were formed and dissipated4 ,the poet's censure of the ,sons of ,aristotle1 is just as happily expressed3 ,they stand ,locked up together hand in hand ,every one leads as he is led1 ,the same bare path they tread1 ,and dance like ,fairies a fantastic round1 ,but neither change their motion nor their ground4 ,note #gid3 ,he studied logic at ,paris1 at ,st4 ,genevive1 and then left them4 ,duodecennium mihi elapsum est diversis studiis occupatum4 ,jucundum itaque visum est veteres quos reliqueram1 et quos adhuc ,dialectica detinebat in monte1 7,sanct ,genovef7 revisere socios1 conferre cum eis super ambiguitatibus pristinis2 ut nostrm invicem collatione mutu commetiremur profectum4 ,inventi sunt1 qui fuerant1 et ubi2 neque enim ad palmam visi sunt processisse ad qustiones pristinis dirimendas1 neque propositiunculam unam adjecerant4 ,quibus urgebant stimulis eisdem et ipsi urgebantur1 c4 ,metalogicus1 lib4 ii4 cap4 #aj4 ,note #hjd3 ,middle ,ages1 iii4 #ecg4 ,it will therefore be unnecessary to go into any detail respecting the history of the ,school ,philosophy of the thirteenth1 fourteenth1 and fifteenth centuries4 ,we may suppose it to have been1 during the intermediate time1 such as it was at first and at last4 ,an occasion to consider its later days will be brought before us by the course of our subject4 ,but1 even during the most entire ascendency of the scholastic doctrines1 the elements of change were at work4 ,while the doctors and the philosophers received all the ostensible homage of men1 a doctrine and a philosophy of another kind were gradually forming3 the practical instincts of man1 their impatience of tyranny1 the progress of the useful arts1 the promises of alchemy1 were all disposing men to reject the authority and deny the pretensions of the received philosophical creed4 ,two antagonist forms of opinion were in existence1 which for some time went on detached1 and almost independent of each other2 but1 finally1 these came into conflict1 at the time of ,galileo2 and the war speedily extended to every part of civilized ,europe4 #c4 ,scholastic ,physics4--,it is difficult to give briefly any appropriate examples of the nature of the ,aristotelian physics which are to be found in the works of this time4 ,as the gravity of bodies was one of the first subjects of dispute when the struggle of the rival methods began1 we may notice the mode in which it was treated4#had ,zabarella maintains that the proximate cause of the motion of elements is the form1 in the ,aristotelian sense of the term3 but to this sentence we1 says ,keckerman1 cannot agree2 for in all other things the form is the proximate cause1 not of the act1 but of the power or faculty from which the act flows4 ,thus in man1 the rational soul is not the cause of the act of laughing1 but of the risible faculty or power4 ,keckerman's system was at one time a work of considerable authority3 it was published in #afad4 ,by comparing and systematizing what he finds in ,aristotle1 he is led to state his results in the form of definitions #bcf and theorems4 ,thus1 gravity is a motive quality1 arising from cold1 density1 and bulk1 by which the elements are carried downwards4 ,water is the lower1 intermediate element1 cold and moist4 ,the first theorem concerning water is1 ,the moistness of the water is controlled by its coldness1 so that it is less than the moistness of the air2 though1 according to the sense of the vulgar1 water appears to moisten more than air4 ,it is obvious that the two properties of fluids1 to have their parts easily moved1 and to wet other bodies1 are here confounded4 ,i may1 as a concluding specimen of this kind1 mention those propositions or maxims concerning fluids1 which were so firmly established1 that1 when ,boyle propounded the true mechanical principles of fluid action1 he was obliged to state his opinions as hydrostatical paradoxes4 ,these were1--that fluids do not gravitate in proprio loco2 that is1 that water has no gravity in or on water1 since it is in its own place2--that air has no gravity on water1 since it is above water1 which is its proper place2--that earth in water tends to descend1 since its place is below water2--that the water rises in a pump or siphon1 because nature abhors a vacuum2--that some bodies have a positive levity in others1 as oil in water2 and the like4 ,note #had3 ,keckerman1 p4 #adbh4 #d4 ,authority of ,aristotle among the ,schoolmen4--,the authority of ,aristotle1 and the practice of making him the text and basis of the system1 especially as it regarded physics1 prevailed during the period of which we speak4 ,this authority was not1 however1 without its fluctuations4 ,launoy has traced one part of its history in a book ,on the various ,fortune of ,aristotle in the ,university of ,paris4 ,the most material turns of this fortune depend on the bearing which the works of ,aristotle were supposed to have upon theology4 ,several of ,aristotle's works1 and more especially his metaphysical writings1 had been translated into ,latin1 and were explained in the schools of the ,university of ,paris1 as early as the beginning of the thirteenth century4#hbd ,at a council held at ,paris in #abji1 they were prohibited1 as having given occasion to the heresy of ,almeric 7or ,amauri71 and because they might give occasion to other heresies not yet invented4 ,the ,logic of ,aristotle recovered its credit some years after this1 and was publicly taught in the ,university of ,paris in the year #abae2 but the ,natural ,philosophy and ,metaphysics were prohibited by a decree of ,gregory the ,ninth1 in #abca4 ,the ,emperor ,frederic the ,second employed a number of learned men to translate into ,latin1 from the ,greek and #bcg ,arabic1 certain books of ,aristotle1 and of other ancient sages2 and we have a letter of ,peter de ,vineis1 in which they are recommended to the attention of the ,university of ,bologna3 probably the same recommendation was addressed to other ,universities4 ,both ,albertus ,magnus and ,thomas ,aquinas wrote commentaries on ,aristotle's works2 and as this was done soon after the decree of ,gregory the ,ninth1 ,launoy is much perplexed to reconcile the fact with the orthodoxy of the two doctors4 ,campanella1 who was one of the first to cast off the authority of ,aristotle1 says1 ,we are by no means to think that ,st4 ,thomas aristotelized2 he only expounded ,aristotle1 that he might correct his errors2 and ,i should conceive he did this with the license of the ,pope4 ,this statement1 however1 by no means gives a just view of the nature of ,albertus's and ,aquinas's commentaries4 ,both have followed their author with profound deference4#hcd ,for instance1 ,aquinas#hdd attempts to defend ,aristotle's assertion1 that if there were no resistance1 a body would move through a space in no time2 and the same defence is given by ,scotus4 ,note #hbd3 ,mosheim1 iii4 #aeg4 ,note #hcd3 ,deg4 ,n4 #dge4 ,note #hdd3 ,f4 ,piccolomini1 ii4 #hce4 ,we may imagine the extent of authority and admiration which ,aristotle would attain1 when thus countenanced1 both by the powerful and the learned4 ,in universities1 no degree could be taken without a knowledge of the philosopher4 ,in #adeb1 ,cardinal ,totaril established this rule in the ,university of ,paris4#hed ,when ,ramus1 in #aedc1 published an attack upon ,aristotle1 it was repelled by the power of the court1 and the severity of the law4 ,francis the ,first published an edict1 in which he states that he had appointed certain judges1 who had been of opinion1#hfd que le dit ,ramus avoit t tmraire1 arrogant et impudent2 et que parcequ'en son livre des animadversions il reprenait ,aristotle1 estait videmment connue et manifeste son ignorance4 ,the books are then declared to be suppressed4 ,it was often a complaint of pious men1 that theology was corrupted by the influence of ,aristotle and his commentators4 ,petrarch says1#hgd that one of the ,italian learned men conversing with him1 after expressing much contempt for the apostles and fathers1 exclaimed1 ,utinam tu ,averroen pati posses1 ut videres quanto ille tuis his nugatoribus major sit6 ,note #hed3 ,launoy1 pp4 #ajh1 #abh4 ,note #hfd3 ,launoy1 p4 #acb4 ,note #hgd3 ,hallam1 ,m4 ,a4 iii4 #ecf4 ,when the revival of letters began to take place1 and a number of men of ardent and elegant minds1 susceptible to the impressions of beauty of style and dignity of thought1 were brought into contact with ,greek literature1 ,plato had naturally greater charms for them4 ,a #bch powerful school of ,platonists 7not ,neoplatonists7 was formed in ,italy1 including some of the principal scholars and men of genius of the time2 as ,picus of ,mirandula in the middle1 ,marsilius ,ficinus at the end1 of the fifteenth century4 ,at one time1 it appeared as if the ascendency of ,aristotle was about to be overturned2 but1 in physics at least1 his authority passed unshaken through this trial4 ,it was not by disputation that ,aristotle could be overthrown2 and the ,platonists were not persons whose doctrines led them to use the only decisive method in such cases1 the observation and unfettered interpretation of facts4 ,the history of their controversies1 therefore1 does not belong to our design4 ,for like reasons we do not here speak of other authors1 who opposed the scholastic philosophy on general theoretical grounds of various kinds4 ,such examples of insurrection against the dogmatism which we have been reviewing1 are extremely interesting events in the history of the philosophy of science4 ,but1 in the present work1 we are to confine ourselves to the history of science itself2 in the hope that we may thus be able1 hereafter1 to throw a steadier light upon that philosophy by which the succession of stationary and progressive periods1 which we are here tracing1 may be in some measure explained4 ,we are now to close our account of the stationary period1 and to enter upon the great subject of the progress of physical science in modern times4 #e4 ,subjects omitted4 ,civil ,law1 ,medicine4--,my object has been to make my way1 as rapidly as possible1 to this period of progress2 and in doing this1 ,i have had to pass over a long and barren track1 where almost all traces of the right road disappear4 ,in exploring this region1 it is not without some difficulty that he who is travelling with objects such as mine1 continues a steady progress in the proper direction2 for many curious and attractive subjects of research come in his way3 he crosses the track of many a controversy1 which in its time divided the world of speculators1 and of which the results may be traced1 even now1 in the conduct of moral1 or political1 or metaphysical discussions2 or in the common associations of thought1 and forms of language4 ,the wars of the ,nominalists and ,realists2 the disputes concerning the foundations of morals1 and the motives of human actions2 the controversies concerning predestination1 free will1 grace1 and the many other points of metaphysical divinity2 the influence of theology and metaphysics upon each other1 and upon other subjects of human curiosity2 the effects of opinion upon politics1 and of political condition upon opinion2 the influence of literature and philosophy #bci upon each other1 and upon society2 and many other subjects2--might be well worth examination1 if our hope of success did not reside in pursuing1 steadily and directly1 those inquiries in which we can look for a definite and certain reply4 ,we must even neglect two of the leading studies of those times1 which occupied much of men's time and thoughts1 and had a very great influence on society2 the one dealing with ,notions1 the other with ,things2 the one employed about moral rules1 the other about material causes1 but both for practical ends2 ,i mean1 the study of the ,civil ,law1 and of ,medicine4 ,the second of these studies will hereafter come before us1 as one of the principal occasions which led to the cultivation of chemistry2 but1 in itself1 its progress is of too complex and indefinite a nature to be advantageously compared with that of the more exact sciences4 ,the ,roman ,law is held1 by its admirers1 to be a system of deductive science1 as exact as the mathematical sciences themselves2 and it may1 therefore1 be useful to consider it1 if we should1 in the sequel1 have to examine how far there can exist an analogy between moral and physical science4 ,but1 after a few more words on the middle ages1 we must return to our task of tracing the progress of the latter4 ,,chapter ,v4 ,,progress ,,of ,,the ,,arts ,,in ,,the ,,middle ,,ages4 ,,art ,,and ,,science4--,i shall1 before ,i resume the history of science1 say a few words on the subject described in the title of this chapter1 both because ,i might otherwise be accused of doing injustice to the period now treated of2 and also1 because we shall by this means bring under our notice some circumstances which were important as being the harbingers of the revival of progressive knowledge4 ,the accusation of injustice towards the state of science in the middle ages1 if we were to terminate our survey of them with what has hitherto been said1 might be urged from obvious topics4 ,how do we recognize1 it might be asked1 in a picture of mere confusion and mysticism of thought1 of servility and dogmatism of character1 the powers and acquirements to which we owe so many of the most important inventions which we now enjoy8 ,parchment and paper1 printing and engraving1 improved glass and steel1 gunpowder1 clocks1 telescopes1 #bdj the mariner's compass1 the reformed calendar1 the decimal notation1 algebra1 trigonometry1 chemistry1 counterpoint1 an invention equivalent to a new creation of music2--these are all possessions which we inherit from that which has been so disparagingly termed the ,stationary ,period4 ,above all1 let us look at the monuments of architecture of this period2--the admiration and the despair of modern architects1 not only for their beauty1 but for the skill disclosed in their construction4 ,with all these evidences before us1 how can we avoid allowing that the masters of the middle ages not only made some small progress in ,astronomy1 which has1 grudgingly as it would seem1 been admitted in a former ,book2 but also that they were no small proficients in other sciences1 in ,optics1 in ,harmonics1 in ,physics1 and1 above all1 in ,mechanics8 ,if1 it may be added1 we are allowed1 in the present day1 to refer to the perfection of our arts as evidence of the advanced state of our physical philosophy2--if our steam-engines1 our gas-illumination1 our buildings1 our navigation1 our manufactures1 are cited as triumphs of science2--shall not prior inventions1 made under far heavier disadvantages1--shall not greater works1 produced in an earlier state of knowledge1 also be admitted as witnesses that the middle ages had their share1 and that not a small or doubtful one1 of science8 ,to these questions ,i answer1 by distinguishing between ,art1 and ,science in that sense of general ,inductive ,systematic ,truth1 which it bears in this work4 ,to separate and compare1 with precision1 these two processes1 belongs to the ,philosophy of ,induction2 and the attempt must be reserved for another place3 but the leading differences are sufficiently obvious4 ,art is practical1 ,science is speculative3 the former is seen in doing2 the latter rests in the contemplation of what is known4 ,the ,art of the builder appears in his edifice1 though he may never have meditated on the abstract propositions on which its stability and strength depends4 ,the ,science of the mathematical mechanician consists in his seeing that1 under certain conditions1 bodies must sustain each other's pressure1 though he may never have applied his knowledge in a single case4 ,now the remark which ,i have to make is this3--in all cases the ,arts are prior to the related ,sciences4 ,art is the parent1 not the progeny1 of ,science2 the realization of principles in practice forms part of the prelude1 as well as of the sequel1 of theoretical discovery4 ,and thus the inventions of the middle ages1 which have been above enumerated1 though at the present day they may be portions of our sciences1 are no evidence that the sciences then existed2 but only that #bda those powers of practical observation and practical skill were at work1 which prepare the way for theoretical views and scientific discoveries4 ,it may be urged1 that the great works of art do virtually take for granted principles of science2 and that1 therefore1 it is unreasonable to deny science to great artists4 ,it may be said1 that the grand structures of ,cologne1 or ,amiens1 or ,canterbury1 could not have been erected without a profound knowledge of mechanical principles4 ,to this we reply1 that such knowledge is manifestly not of the nature of that which we call science4 ,if the beautiful and skilful structures of the middle ages prove that mechanics then existed as a science1 mechanics must have existed as a science also among the builders of the ,cyclopean walls of ,greece and ,italy1 or of our own ,stonehenge2 for the masses which are there piled on each other1 could not be raised without considerable mechanical skill4 ,but we may go much further4 ,the actions of every man who raises and balances weights1 or walks along a pole1 take for granted the laws of equilibrium2 and even animals constantly avail themselves of such principles4 ,are these1 then1 acquainted with mechanics as a science8 ,again1 if actions which are performed by taking advantage of mechanical properties prove a knowledge of the science of mechanics1 they must also be allowed to prove a knowledge of the science of geometry1 when they proceed on geometrical properties4 ,but the most familiar actions of men and animals proceed upon geometrical truths4 ,the ,epicureans held1 as ,proclus informs us1 that even asses knew that two sides of a triangle are greater than the third4 ,and animals may truly be said to have a practical knowledge of this truth2 but they have not1 therefore1 a science of geometry4 ,and in like manner among men1 if we consider the matter strictly1 a practical assumption of a principle does not imply a speculative knowledge of it4 ,we may1 in another way also1 show how inadmissible are the works of the ,master ,artists of the middle ages into the series of events which mark the advance of ,science4 ,the following maxim is applicable to a history1 such as we are here endeavoring to write4 ,we are employed in tracing the progress of such general principles as constitute each of the sciences which we are reviewing2 and no facts or subordinate truths belong to our scheme1 except so far as they tend to or are included in these higher principles2 nor are they important to us1 any further than as they prove such principles4 ,now with regard to processes of art like those which we have referred to1 namely1 the inventions of the middle ages1 let us ask1 what principle each of them #bdb illustrates8 ,what chemical doctrine rests for its support on the phenomena of gunpowder1 or glass1 or steel8 ,what new harmonical truth was illustrated in the ,gregorian chant8 ,what mechanical principle unknown to ,archimedes was displayed in the printing-press8 ,the practical value and use1 the ingenuity and skill of these inventions is not questioned2 but what is their place in the history of speculative knowledge8 ,even in those cases in which they enter into such a history1 how minute a figure do they make6 how great is the contrast between their practical and theoretical importance6 ,they may in their operation have changed the face of the world2 but in the history of the principles of the sciences to which they belong1 they may be omitted without being missed4 ,as to that part of the objection which was stated by asking1 why1 if the arts of our age prove its scientific eminence1 the arts of the middle ages should not be received as proof of theirs2 we must reply to it1 by giving up some of the pretensions which are often put forwards on behalf of the science of our times4 ,the perfection of the mechanical and other arts among us proves the advanced condition of our sciences1 only in so far as these arts have been perfected by the application of some great scientific truth1 with a clear insight into its nature4 ,the greatest improvement of the steam-engine was due to the steady apprehension of an atmological doctrine by ,watt2 but what distinct theoretical principle is illustrated by the beautiful manufactures of porcelain1 or steel1 or glass8 ,a chemical view of these compounds1 which would explain the conditions of success and failure in their manufacture1 would be of great value in art2 and it would also be a novelty in chemical theory2 so little is the present condition of those processes a triumph of science1 shedding intellectual glory on our age4 ,and the same might be said of many1 or of most1 of the processes of the arts as now practised4 #b4 ,arabian ,science4--,having1 ,i trust1 established the view ,i have stated1 respecting the relation of ,art and ,science1 we shall be able very rapidly to dispose of a number of subjects which otherwise might seem to require a detailed notice4 ,though this distinction has been recognized by others1 it has hardly been rigorously adhered to1 in consequence of the indistinct notion of science which has commonly prevailed4 ,thus ,gibbon1 in speaking of the knowledge of the period now under our notice1 says1#hhd ,much useful experience had been acquired in #bdc the practice of arts and manufactures2 but the science of chemistry owes its origin and improvement to the industry of the ,saracens4 ,they1 he adds1 first invented and named the alembic for the purposes of distillation1 analyzed the substances of the three kingdoms of nature1 tried the distinction and affinities of alkalies and acids1 and converted the poisonous minerals into soft and salutary medicines4 ,the formation and realization of the notions of analysis and of affinity1 were important steps in chemical science1 which1 as ,i shall hereafter endeavor to show1 it remained for the chemists of ,europe to make at a much later period4 ,if the ,arabians had done this1 they might with justice have been called the authors of the science of chemistry2 but no doctrines can be adduced from their works which give them any title to this eminent distinction4 ,their claims are dissipated at once by the application of the maxim above stated4 ,what analysis of theirs tended to establish any received principle of chemistry8 ,what true doctrine concerning the differences and affinities of acids and alkalies did they teach8 ,we need not wonder if ,gibbon1 whose views of the boundaries of scientific chemistry were probably very wide and indistinct1 could include the arts of the ,arabians within its domain2 but they cannot pass the frontier of science if philosophically defined1 and steadily guarded4 ,note #hhd3 ,decline and ,fall1 vol4 x4 p4 #dc4 ,the judgment which we are thus led to form respecting the chemical knowledge of the middle ages1 and of the ,arabians in particular1 may serve to measure the condition of science in other departments2 for chemistry has justly been considered one of their strongest points4 ,in botany1 anatomy1 zoology1 optics1 acoustics1 we have still the same observations to make1 that the steps in science which1 in the order of progress1 next followed what the ,greeks had done1 were left for the ,europeans of the sixteenth and seventeenth centuries4 ,the merits and advances of the ,arabian philosophers in astronomy and pure mathematics1 we have already described4 #c4 ,experimental ,philosophy of the ,arabians4--,the estimate to which we have thus been led1 of the scientific merits of the learned men of the middle ages1 is much less exalted than that which has been formed by many writers2 and1 among the rest1 by some of our own time4 ,but ,i am persuaded that any attempt to answer the questions just asked1 will expose the untenable nature of the higher claims which have been advanced in favor of the ,arabians4 ,we can deliver no just decision1 except we will consent to use the terms of science in a strict and precise sense3 and if we do this1 we shall find little1 either in the #bdd particular discoveries or general processes of the ,arabians1 which is important in the history of the ,inductive ,sciences4#hid ,note #hid3 ,if ,i might take the liberty of criticising an author who has given a very interesting view of the period in question 7,mahometanism ,unveiled1 by the ,rev4 ,charles ,forster1 #ahbi71 ,i would remark1 that in his work this caution is perhaps too little observed4 ,thus1 he says1 in speaking of ,alhazen 7vol4 ii4 p4 #bgj71 the theory of the telescope may be found in the work of this astronomer2 and of another1 the uses of magnifying glasses and telescopes1 and the principle of their construction1 are explained in the ,great ,work of 7,roger7 ,bacon1 with a truth and clearness which have commanded universal admiration4 ,such phrases would be much too strong1 even if used respecting the optical doctrines of ,kepler1 which were yet incomparably more true and clear than those of ,bacon4 ,to employ such language1 in such cases1 is to deprive such terms as theory and principle of all meaning4 ,the credit due to the ,arabians for improvements in the general methods of philosophizing1 is a more difficult question2 and cannot be discussed at length by us1 till we examine the history of such methods in the abstract1 which1 in the present work1 it is not our intention to do4 ,but we may observe1 that we cannot agree with those who rank their merits high in this respect4 ,we have already seen1 that their minds were completely devoured by the worst habits of the stationary period1--,mysticism and ,commentation4 ,they followed their ,greek leaders1 for the most part1 with abject servility1 and with only that kind of acuteness and independent speculation which the ,commentator's vocation implies4 ,and in their choice of the standard subjects of their studies1 they fixed upon those works1 the ,physical ,books of ,aristotle1 which have never promoted the progress of science1 except in so far as they incited men to refute them2 an effect which they never produced on the ,arabians4 ,that the ,arabian astronomers made some advances beyond the ,greeks1 we have already stated3 the two great instances are1 the discovery of the ,motion of the ,sun's ,apogee by ,albategnius1 and the discovery 7recently brought to light7 of the existence of the ,moon's ,second ,inequality1 by ,aboul ,wefa4 ,but we cannot but observe in how different a manner they treated these discoveries1 from that with which ,hipparchus or ,ptolemy would have done4 ,the ,variation of the ,moon1 in particular1 instead of being incorporated into the system by means of an ,epicycle1 as ,ptolemy had done with the ,evection1 was allowed1 almost immediately1 so far as we can judge1 to fall into neglect and oblivion3 so little were the learned ,arabians prepared to take their lessons from observation as well as from books4 ,that in many subjects they made experiments1 may easily be allowed3 there never was a period of the earth's history1 and least of all a period of commerce #bde and manufactures1 luxury and art1 medicine and engineering1 in which there were not going on innumerable processes1 which may be termed ,experiments2 and1 in addition to these1 the ,arabians adopted the pursuit of alchemy1 and the love of exotic plants and animals4 ,but so far from their being1 as has been maintained1#ijd a people whose experimental intellect fitted them to form sciences which the abstract intellect of the ,greeks failed in producing1 it rather appears1 that several of the sciences which the ,greeks had founded1 were never even comprehended by the ,arabians4 ,i do not know any evidence that these pupils ever attained to understand the real principles of ,mechanics1 ,hydrostatics1 and ,harmonics1 which their masters had established4 ,at any rate1 when these sciences again became progressive1 ,europe had to start where ,europe had stopped4 ,there is no ,arabian name which any one has thought of interposing between ,archimedes the ancient1 and ,stevinus and ,galileo the moderns4 ,note #ijd3 ,mahometanism ,unveiled1 ii4 #bga4 #d4 ,roger ,bacon4--,there is one writer of the middle ages1 on whom much stress has been laid1 and who was certainly a most remarkable person4 ,roger ,bacon's works are not only so far beyond his age in the knowledge which they contain1 but so different from the temper of the times1 in his assertion of the supremacy of experiment1 and in his contemplation of the future progress of knowledge1 that it is difficult to conceive how such a character could then exist4 ,that he received much of his knowledge from ,arabic writers1 there can be no doubt2 for they were in his time the repositories of all traditionary knowledge4 ,but that he derived from them his disposition to shake off the authority of ,aristotle1 to maintain the importance of experiment1 and to look upon knowledge as in its infancy1 ,i cannot believe1 because ,i have not myself hit upon1 nor seen quoted by others1 any passages in which ,arabian writers express such a disposition4 ,on the other hand1 we do find in ,european writers1 in the authors of ,greece and ,rome1 the solid sense1 the bold and hopeful spirit1 which suggest such tendencies4 ,we have already seen that ,aristotle asserts1 as distinctly as words can express1 that all knowledge must depend on observation1 and that science must be collected from facts by induction4 ,we have seen1 too1 that the ,roman writers1 and ,seneca in particular1 speak with an enthusiastic confidence of the progress which science must make in the course of ages4 ,when ,roger ,bacon holds similar language in the thirteenth century1 the resemblance is probably rather a sympathy of character1 than a matter of direct derivation2 but ,i know of nothing #bdf which proves even so much as this sympathy in the case of ,arabian philosophers4 ,a good deal has been said of late of the coincidences between his views1 and those of his great namesake in later times1 ,francis ,bacon4#iad ,the resemblances consist mainly in such points as ,i have just noticed2 and we cannot but acknowledge1 that many of the expressions of the ,franciscan ,friar remind us of the large thoughts and lofty phrases of the ,philosophical ,chancellor4 ,how far the one can be considered as having anticipated the method of the other1 we shall examine more advantageously1 when we come to consider what the character and effect of ,francis ,bacon's works really are4#ibd ,note #iad3 ,hallam's ,middle ,ages1 iii4 #edi4 ,forster's ,mahom4 ,u4 ii4 #cac4 ,note #ibd3 ,in the ,philosophy of the ,inductive ,sciences1 ,i have given an account at considerable length of ,roger ,bacon's mode of treating ,arts and ,sciences2 and have also compared more fully his philosophy with that of ,francis ,bacon2 and ,i have given a view of the bearing of this latter upon the progress of ,science in modern times4 ,see ,phil4 ,ind4 ,sc4 book xii4 chaps4 #g and #aa4 ,see also the ,appendix to this volume4 #e4 ,architecture of the ,middle ,ages4--,but though we are thus compelled to disallow several of the claims which have been put forwards in support of the scientific character of the middle ages1 there are two points in which we may1 ,i conceive1 really trace the progress of scientific ideas among them2 and which1 therefore1 may be considered as the prelude to the period of discovery4 ,i mean their practical architecture1 and their architectural treatises4 ,in a previous chapter of this book1 we have endeavored to explain how the indistinctness of ideas1 which attended the decline of the ,roman empire1 appears in the forms of their architecture2--in the disregard1 which the decorative construction exhibits1 of the necessary mechanical conditions of support4 ,the original scheme of ,greek ornamental architecture had been horizontal masses resting on vertical columns3 when the arch was introduced by the ,romans1 it was concealed1 or kept in a state of subordination3 and the lateral support which it required was supplied latently1 marked by some artifice4 ,but the struggle between the mechanical and the decorative construction#icd ended in the complete disorganization of the classical style4 ,the #bdg inconsistencies and extravagances of which we have noticed the occurrence1 were results and indications of the fall of good architecture4 ,the elements of the ancient system had lost all principle of connection and regard to rule4 ,building became not only a mere art1 but an art exercised by masters without skill1 and without feeling for real beauty4 ,note #icd3 ,see ,mr4 ,willis's admirable ,remarks on the ,architecture of the ,middle ,ages1 chap4 ii4 ,since the publication of my first edition1 ,mr4 ,willis has shown that much of the mason-craft of the middle ages consisted in the geometrical methods by which the artists wrought out of the blocks the complex forms of their decorative system4 ,to the general indistinctness of speculative notions on mechanical subjects prevalent in the middle ages1 there may have been some exceptions1 and especially so long as there were readers of ,archimedes4 ,bothius had translated the mechanical works of ,archimedes into ,latin1 as we learn from the enumeration of his works by his friend ,cassiodorus 7,variar4 lib i4 cap4 #de71 ,mechanicum etiam ,archimedem latialem siculis reddidisti4 ,but ,mechanicus was used in those times rather for one skilled in the art of constructing wonderful machines than in the speculative theory of them4 ,the letter from which the quotation is taken is sent by ,king ,theodoric to ,bothius1 to urge him to send the king a water-clock4 ,when1 after this deep decline1 architecture rose again1 as it did in the twelfth and succeeding centuries1 in the exquisitely beautiful and skilful forms of the ,gothic style1 what was the nature of the change which had taken place1 so far as it bears upon the progress of science8 ,it was this3--the idea of true mechanical relations in an edifice had been revived in men's minds1 as far as was requisite for the purposes of art and beauty3 and this1 though a very different thing from the possession of the idea as an element of speculative science1 was the proper preparation for that acquisition4 ,the notion of support and stability again became conspicuous in the decorative construction1 and universal in the forms of building4 ,the eye which1 looking for beauty in definite and significant relations of parts1 is never satisfied except the weights appear to be duly supported1#idd was again gratified4 ,architecture threw off its barbarous characters3 a new decorative construction was matured1 not thwarting and controlling1 but assisting and harmonizing with the mechanical construction4 ,all the ornamental parts were made to enter into the apparent construction4 ,every member1 almost every moulding1 became a sustainer of weight2 and by the multiplicity of props assisting each other1 and the consequent subdivision of weight1 the eye was satisfied of the stability of the structure1 notwithstanding the curiously-slender forms of the separate parts4 ,the arch and the vault1 no longer trammelled by an incompatible system of decoration1 but favoured by more tractable forms1 were only limited by the skill of the builders4 ,everything showed that1 practically at least1 men possessed and applied1 with steadiness and pleasure1 the idea of mechanical pressure and support4 ,note #idd3 ,willis1 pp4 #ae-ba4 ,i have throughout this description of the formation of the ,gothic style availed myself of ,mr4 ,willis's well-chosen expressions4 ,the possession of this idea1 as a principle of art1 led1 in the course of time1 to its speculative development as the foundation of a science2 #bdh and thus ,architecture prepared the way for ,mechanics4 ,but this advance required several centuries4 ,the interval between the admirable cathedrals of ,salisbury1 ,amiens1 ,cologne1 and the mechanical treatises of ,stevinus1 is not less than three hundred years4 ,during this time1 men were advancing towards science2 but in the mean time1 and perhaps from the very beginning of the time1 art had begun to decline4 ,the buildings of the fifteenth century1 erected when the principles of mechanical support were just on the verge of being enunciated in general terms1 exhibit those principles with a far less impressive simplicity and elegance than those of the thirteenth4 ,we may hereafter inquire whether we find any other examples to countenance the belief1 that the formation of ,science is commonly accompanied by the decline of ,art4 ,the leading principle of the style of the ,gothic edifices was1 not merely that the weights were supported1 but that they were seen to be so2 and that not only the mechanical relations of the larger masses1 but of the smaller members also1 were displayed4 ,hence we cannot admit1 as an origin or anticipation of the ,gothic1 a style in which this principle is not manifested4 ,i do not see1 in any of the representations of the early ,arabic buildings1 that distribution of weights to supports1 and that mechanical consistency of parts1 which would elevate them above the character of barbarous architecture4 ,their masses are broken into innumerable members1 without subordination or meaning1 in a manner suggested apparently by caprice and the love of the marvellous4 ,in the construction of their mosques1 it was a favorite artifice of the ,arabs to sustain immense and ponderous masses of stone by the support of pillars so slender1 that the incumbent weight seemed1 as it were1 suspended in the air by an invisible hand4#ied ,this pleasure in the contemplation of apparent impossibilities is a very general disposition among mankind2 but it appears to belong to the infancy1 rather than the maturity of intellect4 ,on the other hand1 the pleasure in the contemplation of what is clear1 the craving for a thorough insight into the reasons of things1 which marks the ,european mind1 is the temper which leads to science4 ,note #ied3 ,mahometanism ,unveiled1 ii4 #bee4 #f4 ,treatises on ,architecture4--,no one who has attended to the architecture which prevailed in ,england1 ,france1 and ,germany1 from the twelfth to the fifteenth century1 so far as to comprehend its beauty1 harmony1 consistency1 and uniformity1 even in the minutest parts and most obscure relations1 can look upon it otherwise than as a #bdi remarkably connected and definite artificial system4 ,nor can we doubt that it was exercised by a class of artists who formed themselves by laborious study and practice1 and by communication with each other4 ,there must have been bodies of masters and of scholars1 discipline1 traditions1 precepts of art4 ,how these associated artists diffused themselves over ,europe1 and whether history enables us to trace them in a distinct form1 ,i shall not here discuss4 ,but the existence of a course of instruction1 and of a body of rules of practice1 is proved beyond dispute by the great series of ,european cathedrals and churches1 so nearly identical in their general arrangements1 and in their particular details4 ,the question then occurs1 have these rules and this system of instruction anywhere been committed to writing8 ,can we1 by such evidence1 trace the progress of the scientific idea1 of which we see the working in these buildings8 ,we are not to be surprised1 if1 during the most flourishing and vigorous period of the art of the middle ages1 we find none of its precepts in books4 ,art has1 in all ages and countries1 been taught and transmitted by practice and verbal tradition1 not by writing4 ,it is only in our own times1 that the thought occurs as familiar1 of committing to books all that we wish to preserve and convey4 ,and1 even in our own times1 most of the ,arts are learned far more by practice1 and by intercourse with practitioners1 than by reading4 ,such is the case1 not only with ,manufactures and ,handicrafts1 but with the ,fine ,arts1 with ,engineering1 and even yet1 with that art1 ,building1 of which we are now speaking4 ,we are not1 therefore1 to wonder1 if we have no treatises on ,architecture belonging to the great period of the ,gothic masters2--or if it appears to have required some other incitement and some other help1 besides their own possession of their practical skill1 to lead them to shape into a literary form the precepts of the art which they knew so well how to exercise3--or if1 when they did write on such subjects1 they seem1 instead of delivering their own sound practical principles1 to satisfy themselves with pursuing some of the frivolous notions and speculations which were then current in the world of letters4 ,such appears to be the case4 ,the earliest treatises on ,architecture come before us under the form which the commentatorial spirit of the middle ages inspired4 ,they are ,translations of ,vitruvius1 with ,annotations4 ,in some of these1 particularly that of ,cesare ,cesariano1 published at ,como1 in #aeba1 we see1 in a very curious manner1 how the habit of assuming that1 in every department of literature1 the ancients #bej must needs be their masters1 led these writers to subordinate the members of their own architecture to the precepts of the ,roman author4 ,we have ,gothic shafts1 mouldings1 and arrangements1 given as parallelisms to others1 which profess to represent the ,roman style1 but which are1 in fact1 examples of that mixed manner which is called the style of the ,cinque cento by the ,italians1 of the ,renaissance by the ,french1 and which is commonly included in our ,elizabethan4 ,but in the early architectural works1 besides the superstitions and mistaken erudition which thus choked the growth of real architectural doctrines1 another of the peculiar elements of the middle ages comes into view2--its mysticism4 ,the dimensions and positions of the various parts of edifices and of their members1 are determined by drawing triangles1 squares1 circles1 and other figures1 in such a manner as to bound them2 and to these geometrical figures were assigned many abstruse significations4 ,the plan and the front of the ,cathedral at ,milan are thus represented in ,cesariano's work1 bounded and subdivided by various equilateral triangles2 and it is easy to see1 in the earnestness with which he points out these relations1 the evidence of a fanciful and mystical turn of thought4#ifd ,note #ifd3 ,the plan which he has given1 fol4 #ad1 he has entitled ,ichnographia ,fundamenti sacr dis baricephal1 ,germanico more1 ,trigono ac ,pariquadrato perstructa1 uti etiam ea qu nunc ,milani videtur4 ,the work of ,cesariano was translated into ,german by ,gualter ,rivius1 and published at ,nuremberg1 in #aedh1 under the title of ,vitruvius ,teutsch1 with copies of the ,italian diagrams4 ,a few years ago1 in an article in the ,wiener ,jahrbcher 7,oct4-,dec41 #ahba71 the reviewer maintained1 on the authority of the diagrams in ,rivius's book1 that ,gothic architecture had its origin in ,germany and not in ,england4 ,we thus find erudition and mysticism take the place of much of that development of the architectural principles of the middle ages which would be so interesting to us4 ,still1 however1 these works are by no means without their value4 ,indeed many of the arts appear to flourish not at all the worse1 for being treated in a manner somewhat mystical2 and it may easily be1 that the relations of geometrical figures1 for which fantastical reasons are given1 may really involve principles of beauty or stability4 ,but independently of this1 we find1 in the best works of the architects of all ages 7including engineers71 evidence that the true idea of mechanical pressure exists among them more distinctly than among men in general1 although it may not be developed in a scientific form4 ,this is true up to our own time1 and the arts which such persons cultivate could not be successfully #bea exercised if it were not so4 ,hence the writings of architects and engineers during the middle ages do really form a prelude to the works on scientific mechanics4 ,vitruvius1 in his ,architecture1 and ,julius ,frontinus1 who1 under ,vespasian1 wrote ,on ,aqueducts1 of which he was superintendent1 have transmitted to us the principal part of what we know respecting the practical mechanics and hydraulics of the ,romans4 ,in modern times the series is resumed4 ,the early writers on architecture are also writers on engineering1 and often on hydrostatics3 for example1 ,leonardo da ,vinci wrote on the equilibrium of water4 ,and thus we are led up to ,stevinus of ,bruges1 who was engineer to ,prince ,maurice of ,nassau1 and inspector of the dykes in ,holland2 and in whose work1 on the processes of his art1 is contained the first clear modern statement of the scientific principles of hydrostatics4 ,having thus explained both the obstacles and the prospects which the middle ages offered to the progress of science1 ,i now proceed to the history of the progress1 when that progress was once again resumed4 #bec ,,book ,v4 ,,history ,,of ,,formal ,,astronomy ,,after ,,the ,,stationary ,,period4 4 4 4 ,cyclopum educta caminis ,mnia conspicio1 atque adverso fornice portas4 4 4 4 4 4 ,his demum exactis1 perfecto munere ,div1 ,devenere locos ltos et amna vireta ,fortunatorum nemorum sedesque beatas4 ,largior hic campos ther et lumine vestit ,purpureo3 solemque suum1 sua sidera norunt4 ,,virgil1 n4 vi4 #fcj4 ,they leave at length the nether gloom1 and stand ,before the portals of a better land3 ,to happier plains they come1 and fairer groves1 ,the seats of those whom heaven1 benignant1 loves2 ,a brighter day1 a bluer ether1 spreads ,its lucid depths above their favored heads2 ,and1 purged from mists that veil our earthly skies1 ,shine suns and stars unseen by mortal eyes4 #bee ,,introduction4 ,of ,formal and ,physical ,astronomy4 ,,we have thus rapidly traced the causes of the almost complete blank which the history of physical science offers1 from the decline of the ,roman empire1 for a thousand years4 ,along with the breaking up of the ancient forms of society1 were broken up the ancient energy of thinking1 the clearness of idea1 and steadiness of intellectual action4 ,this mental declension produced a servile admiration for the genius of the better periods1 and thus1 the spirit of ,commentation3 ,christianity established the claim of truth to govern the world2 and this principle1 misinterpreted and combined with the ignorance and servility of the times1 gave rise to the ,dogmatic ,system3 and the love of speculation1 finding no secure and permitted path on solid ground1 went off into the regions of ,mysticism4 ,the causes which produced the inertness and blindness of the stationary period of human knowledge1 began at last to yield to the influence of the principles which tended to progression4 ,the indistinctness of thought1 which was the original feature in the decline of sound knowledge1 was in a measure remedied by the steady cultivation of ,pure ,mathematics and ,astronomy1 and by the progress of inventions in the ,arts1 which call out and fix the distinctness of our conceptions of the relations of natural phenomena4 ,as men's minds became clear1 they became less servile3 the perception of the nature of truth drew men away from controversies about mere opinion2 when they saw distinctly the relations of things1 they ceased to give their whole attention to what had been said concerning them2 and thus1 as science rose into view1 the spirit of commentation lost its way4 ,and when men came to feel what it was to think for themselves on subjects of science1 they soon rebelled against the right of others to impose opinions upon them4 ,when they threw off their blind admiration for the ancients1 they were disposed to cast away also their passive obedience to the ancient system of doctrines4 ,when they were no longer inspired by the spirit of commentation1 they were no longer submissive to the dogmatism of the schools4 ,when they began to feel that they could #bef discover truths1 they felt also a persuasion of a right and a growing will so to do4 ,thus the revived clearness of ideas1 which made its appearance at the revival of letters1 brought on a struggle with the authority1 intellectual and civil1 of the established schools of philosophy4 ,this clearness of idea showed itself1 in the first instance1 in ,astronomy1 and was embodied in the system of ,copernicus2 but the contest did not come to a crisis till a century later1 in the time of ,galileo and other disciples of the new doctrine4 ,it is our present business to trace the principles of this series of events in the history of philosophy4 ,i do not profess to write a history of ,astronomy1 any further than is necessary in order to exhibit the principles on which the progression of science proceeds2 and1 therefore1 ,i neglect subordinate persons and occurrences1 in order to bring into view the leading features of great changes4 ,now in the introduction of the ,copernican system into general acceptation1 two leading views operated upon men's minds2 the consideration of the system as exhibiting the apparent motions of the universe1 and the consideration of this system with reference to its causes2--the formal and the physical aspect of the ,theory2--the relations of ,space and ,time1 and the relations of ,force and ,matter4 ,these two divisions of the subject were at first not clearly separated2 the second was long mixed1 in a manner very dim and obscure1 with the first1 without appearing as a distinct subject of attention2 but at last it was extricated and treated in a manner suitable to its nature4 ,the views of ,copernicus rested mainly on the formal condition of the universe1 the relations of space and time2 but ,kepler1 ,galileo1 and others1 were led1 by controversies and other causes1 to give a gradually increasing attention to the physical relations of the heavenly bodies2 an impulse was given to the study of ,mechanics 7the ,doctrine of ,motion71 which became very soon an important and extensive science2 and in no long period1 the discoveries of ,kepler1 suggested by a vague but intense belief in the physical connection of the parts of the universe1 led to the decisive and sublime generalizations of ,newton4 ,the distinction of formal and physical ,astronomy thus becomes necessary1 in order to treat clearly of the discussions which the propounding of the ,copernican theory occasioned4 ,but it may be observed that1 besides this great change1 ,astronomy made very great advances in the same path which we have already been tracing1 namely1 the determination of the quantities and laws of the celestial motions1 in so far as they were exhibited by the ancient theories1 or #beg might be represented by obvious modifications of those theories4 ,i speak of new ,inequalities1 new ,phenomena1 such as ,copernicus1 ,galileo1 and ,tycho ,brahe discovered4 ,as1 however1 these were very soon referred to the ,copernican rather than the ,ptolemaic hypothesis1 they may be considered as developments rather of the new than of the old ,theory2 and ,i shall1 therefore1 treat of them1 agreeably to the plan of the former part1 as the sequel of the ,copernican ,induction4 ,,chapter ,i4 ,,prelude ,,to ,,the ,,inductive ,,epoch ,,of ,,copernicus4 ,,the ,doctrine of ,copernicus1 that the ,sun is the true centre of the celestial motions1 depends primarily upon the consideration that such a supposition explains very simply and completely all the obvious appearances of the heavens4 ,in order to see that it does this1 nothing more is requisite than a distinct conception of the nature of ,relative ,motion1 and a knowledge of the principal ,astronomical ,phenomena4 ,there was1 therefore1 no reason why such a doctrine might not be discovered1 that is1 suggested as a theory plausible at first sight1 long before the time of ,copernicus2 or rather1 it was impossible that this guess1 among others1 should not be propounded as a solution of the appearances of the heavens4 ,we are not1 therefore1 to be surprised if we find1 in the earliest times of ,astronomy1 and at various succeeding periods1 such a system spoken of by astronomers1 and maintained by some as true1 though rejected by the majority1 and by the principal writers4 ,when we look back at such a difference of opinion1 having in our minds1 as we unavoidably have1 the clear and irresistible considerations by which the ,copernican ,doctrine is established for us1 it is difficult for us not to attribute superior sagacity and candor to those who held that side of the question1 and to imagine those who clung to the ,ptolemaic ,hypothesis to have been blind and prejudiced2 incapable of seeing the beauty of simplicity and symmetry1 or indisposed to resign established errors1 and to accept novel and comprehensive truths4 ,yet in judging thus1 we are probably ourselves influenced by prejudices arising from the knowledge and received opinions of our own times4 ,for is it1 in reality1 clear that1 before the time of ,copernicus1 the #beh ,heliocentric ,theory 7that which places the centre of the celestial motions in the ,sun7 had a claim to assent so decidedly superior to the ,geocentric ,theory1 which places the ,earth in the centre8 ,what is the basis of the heliocentric theory8--,that the relative motions are the same1 on that and on the other supposition4 ,so far1 therefore1 the two hypotheses are exactly on the same footing4 ,but1 it is urged1 on the heliocentric side we have the advantage of simplicity3--true2 but we have1 on the other side1 the testimony of our senses2 that is1 the geocentric doctrine 7which asserts that the ,earth rests and the heavenly bodies move7 is the obvious and spontaneous interpretation of the appearances4 ,both these arguments1 simplicity on the one side1 and obviousness on the other1 are vague1 and we may venture to say1 both indecisive4 ,we cannot establish any strong preponderance of probability in favor of the former doctrine1 without going much further into the arguments of the question4 ,nor1 when we speak of the superior simplicity of the ,copernican theory1 must we forget1 that though this theory has undoubtedly1 in this respect1 a great advantage over the ,ptolemaic1 yet that the ,copernican system itself is very complex1 when it undertakes to account1 as the ,ptolemaic did1 for the ,inequalities of the ,motions of the sun1 moon1 and planets2 and1 that in the hands of ,copernicus1 it retained a large share of the eccentrics and epicycles of its predecessor1 and1 in some parts1 with increased machinery4 ,the heliocentric theory1 without these appendages1 would not approach the ,ptolemaic1 in the accurate explanation of facts2 and as those who had placed the sun in the centre had never1 till the time of ,copernicus1 shown how the inequalities were to be explained on that supposition1 we may assert that after the promulgation of the theory of eccentrics and epicycles on the geocentric hypothesis1 there was no published heliocentric theory which could bear a comparison with that hypothesis4 ,it is true1 that all the contrivances of epicycles1 and the like1 by which the geocentric hypothesis was made to represent the phenomena1 were susceptible of an easy adaptation to a heliocentric method1 when a good mathematician had once proposed to himself the problem3 and this was precisely what ,copernicus undertook and executed4 ,but1 till the appearance of his work1 the heliocentric system had never come before the world except as a hasty and imperfect hypothesis2 which bore a favorable comparison with the phenomena1 so long as their general features only were known2 but which had been completely thrown into the shade by the labor and intelligence bestowed upon #bei the ,hipparchian or ,ptolemaic theories by a long series of great astronomers of all civilized countries4 ,but1 though the astronomers who1 before ,copernicus1 held the heliocentric opinion1 cannot1 on any good grounds1 be considered as much more enlightened than their opponents1 it is curious to trace the early and repeated manifestations of this view of the universe4 ,the distinct assertion of the heliocentric theory among the ,greeks is an evidence of the clearness of their thoughts1 and the vigour of their minds2 and it is a proof of the feebleness and servility of intellect in the stationary period1 that1 till the period of ,copernicus1 no one was found to try the fortune of this hypothesis1 modified according to the improved astronomical knowledge of the time4 ,the most ancient of the ,greek philosophers to whom the ancients ascribe the heliocentric doctrine1 is ,pythagoras2 but ,diogenes ,laertius makes ,philolaus1 one of the followers of ,pythagoras1 the first author of this doctrine4 ,we learn from ,archimedes1 that it was held by his contemporary1 ,aristarchus4 ,aristarchus of ,samos1 says he1#ae makes this supposition1--that the fixed stars and the sun remain at rest1 and that the earth revolves round the sun in a circle4 ,plutarch#be asserts that this1 which was only a hypothesis in the hands of ,aristarchus1 was proved by ,seleucus2 but we may venture to say that1 at that time1 no such proof was possible4 ,aristotle had recognized the existence of this doctrine by arguing against it4 ,all things1 says he1#ce tend to the centre of the earth1 and rest there1 and therefore the whole mass of the earth cannot rest except there4 ,ptolemy had in like manner argued against the diurnal motion of the earth3 such a revolution would1 he urged1 disperse into surrounding space all the loose parts of the earth4 ,yet he allowed that such a supposition would facilitate the explanation of some phenomena4 ,cicero appears to make ,mercury and ,venus revolve about the sun1 as does ,martianus ,capella at a later period2 and ,seneca says#de it is a worthy subject of contemplation1 whether the earth be at rest or in motion3 but at this period1 as we may see from ,seneca himself1 that habit of intellect which was requisite for the solution of such a question1 had been succeeded by indistinct views1 and rhetorical forms of speech4 ,if there were any good mathematicians and good observers at this period1 they were employed in cultivating and verifying the ,hipparchian theory4 ,note #ae3 ,archim4 ,arenarius4 ,note #be3 ,quest4 ,plat4 ,delamb4 ,a4 ,a4 vi4 ,note #ce3 ,quoted by ,copernic4 i4 #g4 ,note #de3 ,quest4 ,nat4 vii4 #b4 ,next to the ,greeks1 the ,indians appear to have possessed that #bfj original vigor and clearness of thought1 from which true science springs4 ,it is remarkable that the ,indians1 also1 had their heliocentric theorists4 ,aryabatta#ee 7,a4 ,d4 #acbb71 and other astronomers of that country1 are said to have advocated the doctrine of the earth's revolution on its axis2 which opinion1 however1 was rejected by subsequent philosophers among the ,hindoos4 ,note #ee3 ,lib4 ,u4 ,k4 ,hist4 ,ast4 p4 #aa4 ,some writers have thought that the heliocentric doctrine was derived by ,pythagoras and other ,european philosophers1 from some of the oriental nations4 ,this opinion1 however1 will appear to have little weight1 if we consider that the heliocentric hypothesis1 in the only shape in which the ancients knew it1 was too obvious to require much teaching2 that it did not and could not1 so far as we know1 receive any additional strength from any thing which the oriental nations could teach2 and that each astronomer was induced to adopt or reject it1 not by any information which a master could give him1 but by his love of geometrical simplicity on the one hand1 or the prejudices of sense on the other4 ,real science1 depending on a clear view of the relation of phenomena to general theoretical ideas1 cannot be communicated in the way of secret and exclusive traditions1 like the mysteries of certain arts and crafts4 ,if the philosopher do not see that the theory is true1 he is little the better for having heard or read the words which assert its truth4 ,it is impossible1 therefore1 for us to assent to those views which would discover in the heliocentric doctrines of the ancients1 traces of a more profound astronomy than any which they have transmitted to us4 ,those doctrines were merely the plausible conjectures of men with sound geometrical notions2 but they were never extended so as to embrace the details of the existing astronomical knowledge2 and perhaps we may say1 that the analysis of the phenomena into the arrangements of the ,ptolemaic system1 was so much more obvious than any other1 that it must necessarily come first1 in order to form an introduction to the ,copernican4 ,the true foundation of the heliocentric theory for the ancients was1 as we have intimated1 its perfect geometrical consistency with the general features of the phenomena1 and its simplicity4 ,but it was unlikely that the human mind would be content to consider the subject under this strict and limited aspect alone4 ,in its eagerness for wide speculative views1 it naturally looked out for other and vaguer principles of connection and relation4 ,thus1 as it had been urged in #bfa favor of the geocentric doctrine1 that the heaviest body must be in the centre1 it was maintained1 as a leading recommendation of the opposite opinion1 that it placed the ,fire1 the noblest element1 in the ,centre of the ,universe4 ,the authority of mythological ideas was called in on both sides to support these views4 ,numa1 as ,plutarch#fe informs us1 built a circular temple over the ever-burning ,fire of ,vesta2 typifying1 not the earth1 but the ,universe1 which1 according to the ,pythagoreans1 has the ,fire seated at its ,centre4 ,the same writer1 in another of his works1 makes one of his interlocutors say1 ,only1 my friend1 do not bring me before a court of law on a charge of impiety2 as ,cleanthes said1 that ,aristarchus the ,samian ought to be tried for impiety1 because he removed the ,hearth of the ,universe4 ,this1 however1 seems to have been intended as a pleasantry4 ,note #fe3 ,de ,facie in ,orbe ,lun1 #f4 ,the prevalent physical views1 and the opinions concerning the causes of the motions of the parts of the universe1 were scarcely more definite than the ancient opinions concerning the relations of the four elements1 till ,galileo had founded the true ,doctrine of ,motion4 ,though1 therefore1 arguments on this part of the subject were the most important part of the controversy after ,copernicus1 the force of such arguments was at his time almost balanced4 ,even if more had been known on such subjects1 the arguments would not have been conclusive3 for instance1 the vast mass of the heavens1 which is commonly urged as a reason why the heavens do not move round the earth1 would not make such a motion impossible2 and1 on the other hand1 the motions of bodies at the earth's surface1 which were alleged as inconsistent with its motion1 did not really disprove such an opinion4 ,but according to the state of the science of motion before ,copernicus1 all reasonings from such principles were utterly vague and obscure4 ,we must not omit to mention a modern who preceded ,copernicus1 in the assertion at least of the heliocentric doctrine4 ,this was ,nicholas of ,cusa 7a village near ,treves71 a cardinal and bishop1 who1 in the first half of the fifteenth century1 was very eminent as a divine and mathematician2 and who in a work1 ,de ,doct ,ignoranti1 propounded the doctrine of the motion of the earth2 more1 however1 as a paradox than as a reality4 ,we cannot consider this as any distinct anticipation of a profound and consistent view of the truth4 ,we shall now examine further the promulgation of the ,heliocentric ,system by ,copernicus1 and its consequences4 #bfb ,,chapter ,,ii4 ,,induction ,,of ,,copernicus4--,,the ,,heliocentric ,,theory ,,asserted ,,on ,,formal ,,grounds4 ,,it will be recollected that the formal are opposed to the physical grounds of a theory2 the former term indicating that it gives a satisfactory account of the relations of the phenomena in ,space and ,time1 that is1 of the ,motions themselves2 while the latter expression implies further that we include in our explanation the ,causes of the motions1 the laws of ,force and ,matter4 ,the strongest of the considerations by which ,copernicus was led to invent and adopt his system of the universe were of the former kind4 ,he was dissatisfied1 he says1 in his ,preface addressed to the ,pope1 with the want of symmetry in the ,eccentric ,theory1 as it prevailed in his days2 and weary of the uncertainty of the mathematical traditions4 ,he then sought through all the works of philosophers1 whether any had held opinions concerning the motions of the world1 different from those received in the established mathematical schools4 ,he found1 in ancient authors1 accounts of ,philolaus and others1 who had asserted the motion of the earth4 ,then1 he adds1 ,i1 too1 began to meditate concerning the motion of the earth2 and though it appeared an absurd opinion1 yet since ,i knew that1 in previous times1 others had been allowed the privilege of feigning what circles they chose1 in order to explain the phenomena1 ,i conceived that ,i also might take the liberty of trying whether1 on the supposition of the earth's motion1 it was possible to find better explanations than the ancient ones1 of the revolutions of the celestial orbs4 ,having then assumed the motions of the earth1 which are hereafter explained1 by laborious and long observation ,i at length found1 that if the motions of the other planets be compared with the revolution of the earth1 not only their phenomena follow from the suppositions1 but also that the several orbs1 and the whole system1 are so connected in order and magnitude1 that no one part can be transposed without disturbing the rest1 and introducing confusion into the whole universe4 ,thus the satisfactory explanation of the apparent motions of the planets1 and the simplicity and symmetry of the system1 were the #bfc grounds on which ,copernicus adopted his theory2 as the craving for these qualities was the feeling which led him to seek for a new theory4 ,it is manifest that in this1 as in other cases of discovery1 a clear and steady possession of abstract ,ideas1 and an aptitude in comprehending real ,facts under these general conceptions1 must have been leading characters in the discoverer's mind4 ,he must have had a good geometrical head1 and great astronomical knowledge4 ,he must have seen1 with peculiar distinctness1 the consequences which flowed from his suppositions as to the relations of space and time1--the apparent motions which resulted from the assumed real ones2 and he must also have known well all the irregularities of the apparent motions for which he had to account4 ,we find indications of these qualities in his expressions4 ,a steady and calm contemplation of the theory is what he asks for1 as the main requisite to its reception4 ,if you suppose the earth to revolve and the heaven to be at rest1 you will find1 he says1 si serio animadvertas1 if you think steadily1 that the apparent diurnal motion will follow4 ,and after alleging his reasons for his system1 he says1#ge ,we are1 therefore1 not ashamed to confess1 that the whole of the space within the orbit of the moon1 along with the centre of the earth1 moves round the sun in a year among the other planets2 the magnitude of the world being so great1 that the distance of the earth from the sun has no apparent magnitude when compared with the sphere of the fixed stars4 ,all which things1 though they be difficult and almost inconceivable1 and against the opinion of the majority1 yet1 in the sequel1 by ,god's favor1 we will make clearer than the sun1 at least to those who are not ignorant of mathematics4 ,note #ge3 ,nicolai ,copernici ,torinensis de ,revolutionibus ,orbium ,clestium ,libri ,,vi4 ,norimberg1 ,m4,d4,,xliii4 p4 #i4 ,it will easily be understood1 that since the ancient geocentric hypothesis ascribed to the planets those motions which were apparent only1 and which really arose from the motion of the earth round the sun in the new hypothesis1 the latter scheme must much simplify the planetary theory4 ,kepler#he enumerates eleven motions of the ,ptolemaic system1 which are at once exterminated and rendered unnecessary by the new system4 ,still1 as the real motions1 both of the earth and the planets1 are unequable1 it was requisite to have some mode of representing their inequalities2 and1 accordingly1 the ancient theory of eccentrics and epicycles was retained1 so far as was requisite for this purpose4 ,the planets revolved round the sun by means of a ,deferent1 and a #bfd great and small ,epicycle2 or else by means of an ,eccentric and ,epicycle1 modified from ,ptolemy's1 for reasons which we shall shortly mention4 ,this mode of representing the motions of the planets continued in use1 until it was expelled by the discoveries of ,kepler4 ,note #he3 ,myst4 ,cosm4 cap4 #a4 ,besides the daily rotation of the earth on its axis1 and its annual circuit about the sun1 ,copernicus attributed to the axis a motion of declination1 by which1 during the whole annual revolution1 the pole was constantly directed towards the same part of the heavens4 ,this constancy in the absolute direction of the axis1 or its moving parallel to itself1 may be more correctly viewed as not indicating any separate motion4 ,the axis continues in the same direction1 because there is nothing to make it change its direction2 just as a straw1 lying on the surface of a cup of water1 continues to point nearly in the same direction when the cup is carried round a room4 ,and this was noticed by ,copernicus's adherent1 ,rothman1#ie a few years after the publication of the work ,de ,revolutionibus4 ,there is no occasion1 he says1 in a letter to ,tycho ,brahe1 for the triple motion of the earth3 the annual and diurnal motions suffice4 ,this error of ,copernicus1 if it be looked upon as an error1 arose from his referring the position of the axis to a limited space1 which he conceived to be carried round the sun along with the earth1 instead of referring it to fixed or absolute space4 ,when1 in a ,planetarium 7a machine in which the motions of the planets are imitated71 the earth is carried round the sun by being fastened to a material radius1 it is requisite to give a motion to the axis by additional machinery1 in order to enable it to preserve its parallelism4 ,a similar confusion of geometrical conception1 produced by a double reference to absolute space and to the centre of revolution1 often leads persons to dispute whether the moon1 which revolves about the earth1 always turning to it the same face1 revolves about her axis or not4 ,note #ie3 ,tycho4 ,epist4 i4 p4 #ahd1 ,a4 ,d4 #aeij4 ,it is also to be noticed that the precession of the equinoxes made it necessary to suppose the axis of the earth to be not exactly parallel to itself1 but to deviate from that position by a slight annual difference4 ,copernicus erroneously supposes the precession to be unequable2 and his method of explaining this change1 which is simpler than that of the ancients1 becomes more simple still1 when applied to the true state of the facts4 ,the tendencies of our speculative nature1 which carry us onwards in #bfe pursuit of symmetry and rule1 and which thus produced the theory of ,copernicus1 as they produce all theories1 perpetually show their vigor by overshooting their mark4 ,they obtain something by aiming at much more4 ,they detect the order and connection which exist1 by imagining relations of order and connection which have no existence4 ,real discoveries are thus mixed with baseless assumptions2 profound sagacity is combined with fanciful conjecture2 not rarely1 or in peculiar instances1 but commonly1 and in most cases2 probably in all1 if we could read the thoughts of the discoverers as we read the books of ,kepler4 ,to try wrong guesses is apparently the only way to hit upon right ones4 ,the character of the true philosopher is1 not that he never conjectures hazardously1 but that his conjectures are clearly conceived and brought into rigid contact with facts4 ,he sees and compares distinctly the ideas and the things1--the relations of his notions to each other and to phenomena4 ,under these conditions it is not only excusable1 but necessary for him1 to snatch at every semblance of general rule2--to try all promising forms of simplicity and symmetry4 ,copernicus is not exempt from giving us1 in his work1 an example of this character of the inventive spirit4 ,the axiom that the celestial motions must be circular and uniform1 appeared to him to have strong claims to acceptation2 and his theory of the inequalities of the planetary motions is fashioned upon it4 ,his great desire was to apply it more rigidly than ,ptolemy had done4 ,the time did not come for rejecting this axiom1 till the observations of ,tycho ,brahe and the calculations of ,kepler had been made4 ,i shall not attempt to explain1 in detail1 ,copernicus's system of the planetary inequalities4 ,he retained epicycles and eccentrics1 altering their centres of motion2 that is1 he retained what was true in the old system1 translating it into his own4 ,the peculiarities of his method consisted in making such a combination of epicycles as to supply the place of the equant1#aje and to make all the motions equable about the centres of motion4 ,this device was admired for a time1 till ,kepler's elliptic theory expelled it1 with all other forms of the theory of epicycles3 but we must observe that ,copernicus was aware of some of the discrepancies which belonged to that theory as it had1 up to that time1 been propounded4 ,in the case of ,mercury's orbit1 which is more eccentric than that of the other planets1 he makes suppositions which are complex indeed1 but which show his perception of the imperfection of #bff the common theory2 and he proposes a new theory of the moon1 for the very reason which did at last overturn the doctrine of epicycles1 namely1 that the ratio of their distances from the earth at different times was inconsistent with the circular hypothesis4#aae ,note #aje3 ,see ,b4 iii4 ,chap4 9999iv4 ,sect4 #g4 ,note #aae3 ,de ,rev4 iv4 c4 #b4 ,it is obvious1 that1 along with his mathematical clearness of view1 and his astronomical knowledge1 ,copernicus must have had great intellectual boldness and vigor1 to conceive and fully develop a theory so different as his was from all received doctrines4 ,his pupil and expositor1 ,rheticus1 says to ,schener1 ,i beg you to have this opinion concerning that learned man1 my ,preceptor2 that he was an ardent admirer and follower of ,ptolemy2 but when he was compelled by phenomena and demonstration1 he thought he did well to aim at the same mark at which ,ptolemy had aimed1 though with a bow and shafts of a very different material from his4 ,we must recollect what ,ptolemy says1 ' 4 ',he who is to follow philosophy must be a freeman in mind4' ,rheticus then goes on to defend his master from the charge of disrespect to the ancients3 ,that temper1 he says1 is alien from the disposition of every good man1 and most especially from the spirit of philosophy1 and from no one more utterly than from my ,preceptor4 ,he was very far from rashly rejecting the opinions of ancient philosophers1 except for weighty reasons and irresistible facts1 through any love of novelty4 ,his years1 his gravity of character1 his excellent learning1 his magnanimity and nobleness of spirit1 are very far from having any liability to such a temper1 which belongs either to youth1 or to ardent and light minds1 or to those 1 'who think much of themselves and know little1' as ,aristotle says4 ,undoubtedly this deference for the great men of the past1 joined with the talent of seizing the spirit of their methods when the letter of their theories is no longer tenable1 is the true mental constitution of discoverers4 ,besides the intellectual energy which was requisite in order to construct a system of doctrines so novel as those of ,copernicus1 some courage was necessary to the publication of such opinions2 certain1 as they were1 to be met1 to a great extent1 by rejection and dispute1 and perhaps by charges of heresy and mischievous tendency4 ,this last danger1 however1 must not be judged so great as we might infer from the angry controversies and acts of authority which occurred in #bfg ,galileo's time4 ,the ,dogmatism of the stationary period1 which identified the cause of philosophical and religious truth1 had not yet distinctly felt itself attacked by the advance of physical knowledge2 and therefore had not begun to look with alarm on such movements4 ,still1 the claims of ,scripture and of ecclesiastical authority were asserted as paramount on all subjects2 and it was obvious that many persons would be disquieted or offended with the new interpretation of many scriptural expressions1 which the true theory would make necessary4 ,this evil ,copernicus appears to have foreseen2 and this and other causes long withheld him from publication4 ,he was himself an ecclesiastic2 and1 by the patronage of his maternal uncle1 was prebendary of the church of ,st4 ,john at ,thorn1 and a canon of the church of ,frauenburg1 in the diocese of ,ermeland4#abe ,he had been a student at ,bologna1 and had taught mathematics at ,rome in the year #aejj2 and he afterwards pursued his studies and observations at his residence near the mouth of the ,vistula4#ace ,his discovery of his system must have occurred before #aejg1 for in #aedc he informs ,pope ,paulus the ,third1 in his dedication1 that he had kept his book by him for four times the nine years recommended by ,horace1 and then only published it at the earnest entreaty of his friend ,cardinal ,schomberg1 whose letter is prefixed to the work4 ,though ,i know1 he says1 that the thoughts of a philosopher do not depend on the judgment of the many1 his study being to seek out truth in all things as far as that is permitted by ,god to human reason3 yet when ,i considered1 he adds1 how absurd my doctrine would appear1 ,i long hesitated whether ,i should publish my book1 or whether it were not better to follow the example of the ,pythagoreans and others1 who delivered their doctrines only by tradition and to friends4 ,it will be observed that he speaks here of the opposition of the established school of ,astronomers1 not of ,divines4 ,the latter1 indeed1 he appears to consider as a less formidable danger4 ,if perchance1 he says at the end of his preface1 there be 1 vain babblers1 who knowing nothing of mathematics1 yet assume the right of judging on account of some place of ,scripture perversely wrested to their purpose1 and who blame and attack my undertaking2 ,i heed them not1 and look upon their judgments as rash and contemptible4 ,he then goes on to show that the globular figure of the earth 7which was1 of course1 at that time1 an undisputed point among astronomers71 had been opposed on similar grounds by ,lactantius1 who1 #bfh though a writer of credit in other respects1 had spoken very childishly in that matter4 ,in another epistle prefixed to the work 7by ,andreas ,osiander71 the reader is reminded that the hypotheses of astronomers are not necessarily asserted to be true1 by those who propose them1 but only to be a way of representing facts4 ,we may observe that1 in the time of ,copernicus1 when the motion of the earth had not been connected with the physical laws of matter and motion1 it could not be considered so distinctly real as it necessarily was held to be in after times4 ,note #abe3 ,rheticus1 ,nar4 p4 #id4 ,note #ace3 ,riccioli4 ,the delay of the publication of ,copernicus's work brought it to the end of his life2 he died in the year #aedc1 in which it was published4 ,it was entitled ,de ,revolutionibus ,orbium ,clestium ,libri ,,vi4 ,he received the only copy he ever saw on the day of his death1 and never opened it3 he had then1 says ,gassendi1 his biographer1 other cares4 ,his system was1 however1 to a certain extent1 promulgated1 and his fame diffused before that time4 ,cardinal ,schomberg1 in his letter of #aecf1 which has been already mentioned1 says1 ,some years ago1 when ,i heard tidings of your merit by the constant report of all persons1 my affection for you was augmented1 and ,i congratulated the men of our time1 among whom you flourish in so much honor4 ,for ,i had understood that you were not only acquainted with the discoveries of ancient mathematicians1 but also had formed a new system of the world1 in which you teach that the ,earth moves1 the ,sun occupies the lowest1 and consequently1 the middle place1 the sphere of the fixed stars remains immovable and fixed1 and the ,moon1 along with the elements included in her sphere1 placed between the orbits 7clum7 of ,mars and ,venus1 travels round the sun in a yearly revolution4#ade ,the writer goes on to say that he has heard that ,copernicus has written a book 7,commentarios71 in which this system is applied to the construction of ,tables of the ,planetary ,motions 7erraticarum stellarum74 ,he then proceeds to entreat him earnestly to publish his lucubrations4 #bfi ,note #ade3 ,this passage has so important a place in the history1 that ,i will give it in the original3--,intellexeram te non modo veterum mathematicorum inventa egregie callere sed etiam novam mundi rationem constituisse3 ,qua doceas terram moveri3 solem imum mundi1 atque medium locum obtinere3 clum octavum immotum atque fixum perpetuo manere3 ,lunam se una cum inclusis su spher elementis1 inter ,martis et ,veneris clum sitam1 anniversario cursu circum solem convertere4 ,atque de hac tota astronomi ratione commentarios a te confectos esse1 ac erraticarum stellarum motus calculis subductos tabulis te contulisse1 maxima omnium cum admiratione4 ,quamobrem vir doctissime1 nisi tibi molestus sum1 te etiam atque etiam oro vehementer ut hoc tuum inventum studiosis communices1 et tuas de mundi sphra lucubrationes1 una cum ,tabulis et si quid habes prterea quod ad eandem rem pertineat primo quoque tempore ad me mittas4 ,this letter is dated #aecf1 and implies that the work of ,copernicus was then written1 and known to persons who studied astronomy4 ,delambre says that ,achilles ,gassarus of ,lindau1 in a letter dated #aedj1 sends to his friend ,george ,vogelin of ,constance1 the book ,de ,revolutionibus4 ,but ,mr4 ,de ,morgan#aee has pointed out that the printed work which ,gassarus sent to ,vogelin was the ,narratio by ,rheticus of ,feldkirch1 a eulogium of ,copernicus and his system prefixed to the second edition of the ,de ,revolutionibus1 which appeared in #aeff4 ,in this ,narration1 ,rheticus speaks of the work of ,copernicus as a ,palingenesia1 or ,new ,birth of astronomy4 ,rheticus1 it appears1 had gone to ,copernicus for the purpose of getting knowledge about triangles and trigonometrical tables1 and had had his attention called to the heliocentric theory1 of which he became an ardent admirer4 ,he speaks of his ,preceptor with strong admiration1 as we have seen4 ,he appears to me1 says he1 more to resemble ,ptolemy than any other astronomers4 ,this1 it must be recollected1 was selecting the highest known subject of comparison4 ,note #aee3 ,ast4 ,mod4 i4 p4 #ach4 ,i owe this and many other corrections to the personal kindness of ,mr4 ,de ,morgan4 ,,chapter ,,iii4 ,,sequel ,,to ,,copernicus4--,,the ,,reception ,,and ,,development ,,of ,,the ,,copernican ,,theory4 ,sect4 #a4--;,first ,reception of the ,copernican ,theory4 ,,the theories of ,copernicus made their way among astronomers1 in the manner in which true astronomical theories always obtain the assent of competent judges4 ,they led to the construction of ,tables of the motion of the sun1 moon1 and planets1 as the theories of ,hipparchus and ,ptolemy had done2 and the verification of the doctrines was to be looked for1 from the agreement of these ,tables with observation1 through a sufficient course of time4 ,the work ,de ,revolutionibus contains such ,tables4 ,in #aeea ,reinhold improved and republished ,tables founded on the principles of ,copernicus4 ,we owe1 he says in his preface1 great obligations to ,copernicus1 both for his laborious #bgj observations1 and for restoring the doctrine of the ,motions4 ,but though his geometry is perfect1 the good old man appears to have been1 at times1 careless in his numerical calculations4 ,i have1 therefore1 recalculated the whole1 from a comparison of his observations with those of ,ptolemy and others1 following nothing but the general plan of ,copernicus's demonstrations4 ,these ,prutenic ,tables were republished in #aega and #aehe1 and continued in repute for some time2 till superseded by the ,rudolphine ,tables of ,kepler in #afbg4 ,the name ,prutenic1 or ,prussian1 was employed by the author as a mark of gratitude to his benefactor ,albert1 ,markgrave of ,brandenbourg4 ,the discoveries of ,copernicus had inspired neighboring nations with the ambition of claiming a place in the literary community of ,europe4 ,in something of the same spirit1 ,rheticus wrote an ,encomium ,borussi1 which was published along with his ,narratio4 ,the ,tables founded upon the ,copernican system were1 at first1 much more generally adopted than the heliocentric doctrine on which they were founded4 ,thus ,magini published at ,venice1 in #aehg1 ,new ,theories of the ,celestial ,orbits1 agreeing with the ,observations of ,nicholas ,copernicus4 ,but in the preface1 after praising ,copernicus1 he says1 ,since1 however1 he1 either for the sake of showing his talents1 or induced by his own reasons1 has revived the opinion of ,nicetas1 ,aristarchus1 and others1 concerning the motion of the earth1 and has disturbed the established constitution of the world1 which was a reason why many rejected1 or received with dislike1 his hypothesis1 ,i have thought it worth while1 that1 rejecting the suppositions of ,copernicus1 ,i should accommodate other causes to his observations1 and to the ,prutenic ,tables4 ,this doctrine1 however1 was1 as we have shown1 received with favor by many persons1 even before its general publication4 ,the doctrine of the motion of the earth was first publicly maintained at ,rome by ,widmanstadt1#afe who professed to have received it from ,copernicus1 and explained the ,system before the ,pope and the ,cardinals1 but did not teach it to the public4 ,note #afe3 ,see ,venturi1 ,essai sur les ,ouvrages ,physico-,mathmatiques de ,leonard da ,vinci1 avec des ,fragmens tirs de ses ,manuscrits apports d',italie4 ,paris1 #agig2 and1 as there quoted1 ,marini ,archiatri ,pontificii1 tom4 ii4 p4 #bea4 ,leonardo da ,vinci1 who was an eminent mathematician1 as well as painter1 about #aeaj1 explained how a body1 by describing a kind of spiral1 might descend towards a revolving globe1 so that its apparent motion relative to a point in the surface of the globe1 might be in a #bga straight line leading to the centre4 ,he thus showed that he had entertained in his thoughts the hypothesis of the earth's rotation1 and was employed in removing the difficulties which accompanied this supposition1 by means of the consideration of the composition of motions4 ,in like manner we find the question stirred by other eminent men4 ,thus ,john ,muller of ,konigsberg1 a celebrated astronomer who died in #adgf1 better known by the name of ,regiomontanus1 wrote a dissertation on the subject ,whether the earth be in motion or at rest1 in which he decides ex professo#age against the motion4 ,yet such discussions must have made generally known the arguments for the heliocentric theory4 ,note #age3 ,schoneri ,opera1 part ii4 p4 #abi4 ,we have already seen the enthusiasm with which ,rheticus1 who was ,copernicus's pupil in the latter years of his life1 speaks of him4 ,thus1 says he1 ,god has given to my excellent preceptor a reign without end2 which may ,he vouchsafe to guide1 govern1 and increase1 to the restoration of astronomical truth4 ,amen4 ,of the immediate converts of the ,copernican system1 who adopted it before the controversy on the subject had attracted attention1 ,i shall only add 9999,mstlin1 and his pupil1 ,kepler4 9999,mstlin published in #aehh an ,epitome ,astronomi1 in which the immobility of the earth is asserted2 but in #aeif he edited ,kepler's ,mysterium ,cosmographicum1 and the ,narratio of ,rheticus3 and in an epistle of his own1 which he inserts1 he defends the ,copernican system by those physical reasonings which we shall shortly have to mention1 as the usual arguments in this dispute4 ,kepler himself1 in the outset of the work just named1 says1 ,when ,i was at ,tbingen1 attending to ,michael ,mstlin1 being disturbed by the manifold inconveniences of the usual opinion concerning the world1 ,i was so delighted with ,copernicus1 of whom he made great mention in his lectures1 that ,i not only defended his opinions in our disputations of the candidates1 but wrote a thesis concerning the ,first ,motion which is produced by the revolution of the earth4 ,this must have been in #aeij4 ,the differences of opinion respecting the ,copernican system1 of which we thus see traces1 led to a controversy of some length and extent4 ,this controversy turned principally upon physical considerations1 which were much more distinctly dealt with by ,kepler1 and others of the followers of ,copernicus1 than they had been by the #bgb discoverer himself4 ,i shall1 therefore1 give a separate consideration to this part of the subject4 ,it may be proper1 however1 in the first place1 to make a few observations on the progress of the doctrine1 independently of these physical speculations4 ,sect4 #b4--;,diffusion of the ,copernican ,theory4 ,,the diffusion of the ,copernican opinions in the world did not take place rapidly at first4 ,indeed1 it was necessarily some time before the progress of observation and of theoretical mechanics gave the heliocentric doctrine that superiority in argument1 which now makes us wonder that men should have hesitated when it was presented to them4 ,yet there were some speculators of this kind1 who were attracted at once by the enlarged views of the universe which it opened to them4 ,among these was the unfortunate ,giordano ,bruno of ,nola1 who was burnt as a heretic at ,rome in #afjj4 ,the heresies which led to his unhappy fate were1 however1 not his astronomical opinions1 but a work which he published in ,england1 and dedicated to ,sir ,philip ,sydney1 under the title of ,spaccio della ,bestia ,trionfante1 and which is understood to contain a bitter satire of religion and the papal government4 ,montucla conceives that1 by his rashness in visiting ,italy after putting forth such a work1 he compelled the government to act against him4 ,bruno embraced the ,copernican opinions at an early period1 and connected with them the belief in innumerable worlds besides that which we inhabit2 as also certain metaphysical or theological doctrines which he called the ,nolan philosophy4 ,in #aeia he published ,de innumerabilibus1 immenso1 et infigurabili1 seu de ,universo et ,mundis1 in which he maintains that each star is a sun1 about which revolve planets like our earth2 but this opinion is mixed up with a large mass of baseless verbal speculations4 ,giordano ,bruno is a disciple of ,copernicus on whom we may look with peculiar interest1 since he probably had a considerable share in introducing the new opinions into ,england2#ahe although other persons1 as ,recorde1 ,field1 ,dee1 had adopted it nearly thirty years earlier2 and ,thomas ,digges ten years before1 much more expressly4 ,bruno visited this country in the reign of ,queen ,elizabeth1 and speaks of her and of her councillors in terms of praise1 which appear to show that #bgc his book was intended for ,english readers2 though he describes the mob which was usually to be met with in the streets of ,london with expressions of great disgust3 ,una plebe la quale in essere irrespettevole1 incivile1 rozza1 rustica1 selvatica1 et male allevata1 non cede ad altra che pascer possa la terra nel suo seno4#aie ,the work to which ,i refer is ,la ,cena de le ,cenere1 and narrates what took place at a supper held on the evening of ,ash ,wednesday 7about #aehc1 see p4 #ade of the book71 at the house of ,sir ,fulk ,greville1 in order to give ,il ,nolano an opportunity of defending his peculiar opinions4 ,his principal antagonists are two ,dottori d' ,oxonia1 whom ,bruno calls ,nundinio and ,torquato4 ,the subject is not treated in any very masterly manner on either side2 but the author makes himself have greatly the advantage not only in argument1 but in temper and courtesy3 and in support of his representations of pedantesca1 ostinatissima ignoranza et presunzione1 mista con una rustica incivilit1 che farebbe prevaricar la pazienza di ,giobbe1 in his opponents1 he refers to a public disputation which he had held at ,oxford with these doctors of theology1 in presence of ,prince ,alasco1 and many of the ,english nobility4#bje ,note #ahe3 ,see ,burton's ,anat4 ,mel4 ,pref4 ,some prodigious tenet or paradox of the earth's motion1 c4 ,bruno1 c4 ,note #aie3 ,opere di ,giordano ,bruno1 vol4 i4 p4 #adf4 ,note #bje3 ,ib4 vol4 i4 p4 #agi4 ,among the evidences of the difficulties which still lay in the way of the reception of the ,copernican system1 we may notice ,bacon1 who1 as is well known1 never gave a full assent to it4 ,it is to be observed1 however1 that he does not reject the opinion of the earth's motion in so peremptory and dogmatical a manner as he is sometimes accused of doing3 thus in the ,thema ,cli he says1 ,the earth1 then1 being supposed to be at rest 7for that now appears to us the more true opinion74 ,and in his tract ,on the ,cause of the ,tides1 he says1 ,if the tide of the sea be the extreme and diminished limit of the diurnal motion of the heavens1 it will follow that the earth is immovable2 or at least that it moves with a much slower motion than the water4 ,in the ,descriptio ,globi ,intellectualis he gives his reasons for not accepting the heliocentric theory4 ,in the system of ,copernicus there are many and grave difficulties3 for the threefold motion with which he encumbers the earth is a serious inconvenience2 and the separation of the sun from the planets1 with which he has so many affections in common1 is likewise a harsh step2 and the introduction of so many immovable bodies into nature1 as when he makes the sun and the stars immovable1 the bodies which are peculiarly lucid and radiant2 and his making the moon adhere to the earth in a sort of epicycle2 and some #bgd other things which he assumes1 are proceedings which mark a man who thinks nothing of introducing fictions of any kind into nature1 provided his calculations turn out well4 ,we have already explained that1 in attributing three motions to the earth1 ,copernicus had presented his system encumbered with a complexity not really belonging to it4 ,but it will be seen shortly1 that ,bacon's fundamental objection to this system was his wish for a system which could be supported by sound physical considerations2 and it must be allowed1 that at the period of which we are speaking1 this had not yet been done in favor of the ,copernican hypothesis4 ,we may add1 however1 that it is not quite clear that ,bacon was in full possession of the details of the astronomical systems which that of ,copernicus was intended to supersede2 and that thus he1 perhaps1 did not see how much less harsh were these fictions1 as he called them1 than those which were the inevitable alternatives4 ,perhaps he might even be liable to a little of that indistinctness1 with respect to strictly geometrical conceptions1 which we have remarked in ,aristotle4 ,we can hardly otherwise account for his not seeing any use in resolving the apparently irregular motion of a planet into separate regular motions4 ,yet he speaks slightingly of this important step4#bae ,the motion of planets1 which is constantly talked of as the motion of regression1 or renitency1 from west to east1 and which is ascribed to the planets as a proper motion1 is not true2 but only arises from appearance1 from the greater advance of the starry heavens towards the west1 by which the planets are left behind to the east4 ,undoubtedly those who spoke of such a motion of regression were aware of this2 but they saw how the motion was simplified by this way of conceiving it1 which ,bacon seems not to have seen4 ,though1 therefore1 we may admire ,bacon for the steadfastness with which he looked forward to physical astronomy as the great and proper object of philosophical interest1 we cannot give him credit for seeing the full value and meaning of what had been done1 up to his time1 in ,formal ,astronomy4 ,note #bae3 ,thema ,cli1 p4 #bdf4 ,bacon's contemporary1 ,gilbert1 whom he frequently praises as a philosopher1 was much more disposed to adopt the ,copernican opinions1 though even he does not appear to have made up his mind to assent to the whole of the system4 ,in his work4 ,de ,magnete 7printed #afjj71 he gives the principal arguments in favor of the ,copernican system1 and decides that the earth revolves on its axis4#bbe ,he connects #bge this opinion with his magnetic doctrines2 and especially endeavors by that means to account for the precession of the equinoxes4 ,but he does not seem to have been equally confident of its annual motion4 ,in a posthumous work1 published in #affa 7,de ,mundo ,nostra ,sublunari ,philosophia ,nova7 he appears to hesitate between the systems of ,tycho and ,copernicus4#bce ,indeed1 it is probable that at this period many persons were in a state of doubt on such subjects4 ,milton1 at a period somewhat later1 appears to have been still undecided4 ,in the opening of the eighth book of the ,paradise ,lost1 he makes ,adam state the difficulties of the ,ptolemaic hypothesis1 to which the archangel ,raphael opposes the usual answers2 but afterwards suggests to his pupil the newer system3 4 4 4 4 ,what if seventh to these ,the planet earth1 so steadfast though she seem1 ,insensibly three different motions move8 ,par4 ,lost1 b4 viii4 ,note #bbe3 ,lib4 vi4 cap4 #c1 #d4 ,note #bce3 ,lib4 ii4 cap4 #bj4 ,milton's leaning1 however1 seems to have been for the new system2 we can hardly believe that he would otherwise have conceived so distinctly1 and described with such obvious pleasure1 the motion of the earth3 ,or she from west her silent course advance ,with inoffensive pace1 that spinning sleeps ,on her soft axle1 while she paces even1 ,and bears thee soft with the smooth air along4 ,par4 ,lost1 b4 viii4 ,perhaps the works of the celebrated ,bishop ,wilkins tended more than any others to the diffusion of the ,copernican system in ,england1 since even their extravagances drew a stronger attention to them4 ,in #afch1 when he was only twenty-four years old1 he published a book entitled ,the ,discovery of a ,new ,world2 or a ,discourse tending to prove that it is probable there may be another habitable ,world in the ,moon2 with a ,discourse concerning the possibility of a passage thither4 ,the latter part of his subject was1 of course1 an obvious mark for the sneers and witticisms of critics4 ,two years afterwards1 in #afdj1 appeared his ,discourse concerning a new ,planet2 tending to prove that it is probable our ,earth is one of the ,planets3 in which he urged the reasons in favor of the heliocentric system2 and explained away the opposite arguments1 especially those drawn from the #bgf supposed declarations of ,scripture4 ,probably a good deal was done for the establishment of those opinions by ,thomas ,salusbury1 who was a warm admirer of ,galileo1 and published1 in #affa1 a translation of several of his works bearing upon this subject4 ,the mathematicians of this country1 in the seventeenth century1 as ,napier and ,briggs1 ,horrox and ,crabtree1 ,oughtred and ,seth ,ward1 ,wallis and ,wren1 were probably all decided ,copernicans4 ,kepler dedicates one of his works to ,napier1 and ,ward invented an approximate method of solving ,kepler's problem1 still known as the simple elliptical hypothesis4 ,horrox wrote1 and wrote well1 in defence of the ,copernican opinion1 in his ,keplerian ,astronomy defended and promoted1 composed 7in ,latin7 probably about #afce1 but not published till #afgc1 the author having died at the age of twenty-two1 and his papers having been lost4 ,but ,salusbury's work was calculated for another circle of readers4 ,the book1 he says in the introductory address1 being1 for subject and design1 intended chiefly for gentlemen1 ,i have been as careless of using a studied pedantry in my style1 as careful in contriving a pleasant and beautiful impression4 ,in order1 however1 to judge of the advantage under which the ,copernican system now came forward1 we must consider the additional evidence for it which was brought to light by ,galileo's astronomical discoveries4 ,sect4 #c4--,the ,heliocentric ,theory confirmed by ,facts4--,galileo's ,astronomical ,discoveries4 ,,the long interval which elapsed between the last great discoveries made by the ancients and the first made by the moderns1 had afforded ample time for the development of all the important consequences of the ancient doctrines4 ,but when the human mind had been thoroughly roused again into activity1 this was no longer the course of events4 ,discoveries crowded on each other2 one wide field of speculation was only just opened1 when a richer promise tempted the laborers away into another quarter4 ,hence the history of this period contains the beginnings of many sciences1 but exhibits none fully worked out into a complete or final form4 ,thus the science of ,statics1 soon after its revival1 was eclipsed and overlaid by that of ,dynamics2 and the ,copernican system1 considered merely with reference to the views of its author1 was absorbed in the commanding interest of ,physical ,astronomy4 ,still1 advances were made which had an important bearing on the #bgg heliocentric theory1 in other ways than by throwing light upon its physical principles4 ,i speak of the new views of the heavens which the ,telescope gave2 the visible inequalities of the moon's surface2 the moon-like phases of the planet ,venus2 the discovery of the ,satellites of ,jupiter1 and of the ,ring of ,saturn4 ,these discoveries excited at the time the strongest interest2 both from the novelty and beauty of the objects they presented to the sense2 from the way in which they seemed to gratify man's curiosity with regard to the remote parts of the universe2 and also from that of which we have here to speak1 their bearing upon the conflict of the old and the new philosophy1 the heliocentric and geocentric theories4 ,it may be true1 as ,lagrange and ,montucla say1 that the laws which ,galileo discovered in ,mechanics implied a profounder genius than the novelties he detected in the sky3 but the latter naturally attracted the greater share of the attention of the world1 and were matter of keener discussion4 ,it is not to our purpose to speak here of the details and of the occasion of the invention of the ,telescope2 it is well known that ,galileo constructed his about #afji1 and proceeded immediately to apply it to the heavens4 ,the discovery of the ,satellites of ,jupiter was almost immediately the reward of his activity2 and these were announced in his ,nuncius ,sidereus1 published at ,venice in #afaj4 ,the title of this work will best convey an idea of the claim it made to public notice3 ,the ,sidereal ,messenger1 announcing great and very wonderful spectacles1 and offering them to the consideration of every one1 but especially of philosophers and astronomers2 which have been observed by ,galileo ,galilei1 c4 c41 by the assistance of a perspective glass lately invented by him2 namely1 in the face of the moon1 in innumerable fixed stars in the milky-way1 in nebulous stars1 but especially in four planets which revolve round ,jupiter at different intervals and periods with a wonderful celerity2 which1 hitherto not known to any one1 the author has recently been the first to detect1 and has decreed to call the ,medicean stars4 ,the interest this discovery excited was intense3 and men were at this period so little habituated to accommodate their convictions on matters of science to newly observed facts1 that several of the paper-philosophers1 as ,galileo termed them1 appear to have thought they could get rid of these new objects by writing books against them4 ,the effect which the discovery had upon the reception of the ,copernican system was immediately very considerable4 ,it showed that the real universe was very different from that which ancient philosophers had imagined1 #bgh and suggested at once the thought that it contained mechanism more various and more vast than had yet been conjectured4 ,and when the system of the planet ,jupiter thus offered to the bodily eye a model or image of the solar system according to the views of ,copernicus1 it supported the belief of such an arrangement of the planets1 by an analogy all but irresistible4 ,it thus1 as a writer#bde of our own times has said1 gave the holding turn to the opinions of mankind respecting the ,copernican system4 ,we may trace this effect in ,bacon1 even though he does not assent to the motion of the earth4 ,we affirm1 he says1#bee the sun-following arrangement 7solisequium7 of ,venus and ,mercury2 since it has been found by ,galileo that ,jupiter also has attendants4 ,note #bde3 ,sir ,j4 ,herschel4 ,note #bee3 ,thema ,cli1 ix4 p4 #bec4 ,the ,nuncius ,sidereus contained other discoveries which had the same tendency in other ways4 ,the examination of the moon showed1 or at least seemed to show1 that she was a solid body1 with a surface extremely rugged and irregular4 ,this1 though perhaps not bearing directly upon the question of the heliocentric theory1 was yet a blow to the ,aristotelians1 who had1 in their philosophy1 made the moon a body of a kind altogether different from this1 and had given an abundant quantity of reasons for the visible marks on her surface1 all proceeding on these preconceived views4 ,others of his discoveries produced the same effect2 for instance1 the new stars invisible to the naked eye1 and those extraordinary appearances called ,nebul4 ,but before the end of the year1 ,galileo had new information to communicate1 bearing more decidedly on the ,copernican controversy4 ,this intelligence was indeed decisive with regard to the motion of ,venus about the sun2 for he found that that planet1 in the course of her revolution1 assumes the same succession of phases which the moon exhibits in the course of a month4 ,this he expressed by a ,latin verse3 ,cynthi figuras mulatur mater amorum3 ,the ,queen of ,love like ,cynthia shapes her forms3 transposing the letters of this line in the published account1 according to the practice of the age2 which thus showed the ancient love for combining verbal puzzles with scientific discoveries1 while it betrayed the newer feeling1 of jealousy respecting the priority of discovery of physical facts4 ,it had always been a formidable objection to the ,copernican theory that this appearance of the planets had not been observed4 ,the author #bgi of that theory had endeavored to account for this1 by supposing that the rays of the sun passed freely through the body of the planet2 and ,galileo takes occasion to praise him for not being deterred from adopting the system which1 on the whole1 appeared to agree best with the phenomena1 by meeting with some appearances which it did not enable him to explain4#bfe ,yet while the fate of the theory was yet undecided1 this could not but be looked upon as a weak point in its defences4 ,note #bfe3 ,drinkwater-,bethune1 ,life of ,galileo1 p4 #ce4 ,the objection1 in another form also1 was embarrassing alike to the ,ptolemaic and ,copernican systems4 ,why1 it was asked1 did not ,venus appear four times as large when nearest to the earth1 as when furthest from it8 ,the author of the ,epistle prefixed to ,copernicus's work had taken refuge in this argument from the danger of being supposed to believe in the reality of the system2 and ,bruno had attempted to answer it by saying1 that luminous bodies were not governed by the same laws of perspective as opake ones4 ,but a more satisfactory answer now readily offered itself4 ,venus does not appear four times as large when she is four times as near1 because her bright part is not four times as large1 though her visible diameter is2 and as she is too small for us to see her shape with the naked eye1 we judge of her size only by the quantity of light4 ,the other great discoveries made in the heavens by means of telescopes1 as that of ,saturn's ring and his satellites1 the spots in the sun1 and others1 belong to the further progress of astronomy4 ,but we may here observe1 that this doctrine of the motion of ,mercury and ,venus about the sun was further confirmed by ,kepler's observation of the transit of the former planet over the sun in #afca4 ,our countryman ,horrox was the first person who1 in #afci1 had the satisfaction of seeing a transit of ,venus4 ,these events are a remarkable instance of the way in which a discovery in art 7for at this period1 the making of telescopes must be mainly so considered7 may influence the progress of science4 ,we shall soon have to notice a still more remarkable example of the way in which two sciences 7,astronomy and ,mechanics7 may influence and promote the progress of each other4 #bhj ,sect4 #d4--,the ,copernican ,system opposed on ,theological ,grounds4 ,,the doctrine of the ,earth's motion round the ,sun1 when it was asserted and promulgated by ,copernicus1 soon after #aejj1 excited no visible alarm among the theologians of his own time4 ,indeed1 it was received with favor by the most intelligent ecclesiastics2 and lectures in support of the heliocentric doctrine were delivered in the ecclesiastical colleges4 ,but the assertion and confirmation of this doctrine by ,galileo1 about a century later1 excited a storm of controversy1 and was visited with severe condemnation4 ,galileo's own behavior appears to have provoked the interference of the ecclesiastical authorities2 but there must have been a great change in the temper of the times to make it possible for his adversaries to bring down the sentence of the ,inquisition upon opinions which had been so long current without giving any serious offence4 #b;d ,ed4 ,it appears to me that the different degree of toleration accorded to the heliocentric theory in the time of ,copernicus and of ,galileo1 must be ascribed in a great measure to the controversies and alarms which had in the mean time arisen out of the ,reformation in religion1 and which had rendered the ,romish ,church more jealous of innovations in received opinions than it had previously been4 ,it appears too that the discussion of such novel doctrines was1 at that time at least1 less freely tolerated in ,italy than in other countries4 ,in #aeig1 ,kepler writes to ,galileo thus3 ,confide ,galile et progredere4 ,si bene conjecto1 pauci de prcipuis ,europ ,mathematicis a nobis secedere volent2 tanta vis est veritatis4 ,si tibi ,italia minus est idonea ad publicationem et si aliqua habitures es impedimenta1 forsan ,germania nobis hanc libertatem concedet4--,venturi1 ,mem4 di ,galileo1 vol4 i4 p4 #ai4 ,i would not however be understood to assert the condemnation of new doctrines in science to be either a general or a characteristic practice of the ,romish ,church4 ,certainly the intelligent and cultivated minds of ,italy1 and many of the most eminent of her ecclesiastics among them1 have always been the foremost in promoting and welcoming the progress of science3 and1 as ,i have stated1 there were found among the ,italian ecclesiastics of ,galileo's time many of the earliest and most enlightened adherents of the ,copernican system4 ,the condemnation of the doctrine of the earth's motion1 is1 so far as ,i am aware1 the only instance in which the ,papal authority has pronounced a decree upon a point of science4 ,and the most candid of the #bha adherents of the ,romish ,church condemn the assumption of authority in such matters1 which in this one instance1 at least1 was made by the ecclesiastical tribunals4 ,the author of the ,ages of ,faith 7book viii4 p4 #bdh7 says1 ,a congregation1 it is to be lamented1 declared the new system to be opposed to ,scripture1 and therefore heretical4 ,in more recent times1 as ,i have elsewhere remarked1#bge the ,church of ,authority and the ,church of ,private ,judgment have each its peculiar temptations and dangers1 when there appears to be a discrepance between ,scripture and ,philosophy4 ,note #bge3 ,phil4 ,ind4 ,sci4 book x4 chap4 #d4 ,but though we may acquit the popes and cardinals in ,galileo's time of stupidity and perverseness in rejecting manifest scientific truths1 ,i do not see how we can acquit them of dissimulation and duplicity4 ,those persons appear to me to defend in a very strange manner the conduct of the ecclesiastical authorities of that period1 who boast of the liberality with which ,copernican professors were placed by them in important offices1 at the very time when the motion of the earth had been declared by the same authorities contrary to ,scripture4 ,such merits cannot make us approve of their conduct in demanding from ,galileo a public recantation of the system which they thus favored in other ways1 and which they had repeatedly told ,galileo he might hold as much as he pleased4 ,nor can any one1 reading the plain language of the ,sentence passed upon ,galileo1 and of the ,abjuration forced from him1 find any value in the plea which has been urged1 that the opinion was denominated a heresy only in a wide1 improper1 and technical sense4 ,but if we are thus unable to excuse the conduct of ,galileo's judges1 ,i do not see how we can give our unconditional admiration to the philosopher himself4 ,perhaps the conventional decorum which1 as we have seen1 was required in treating of the ,copernican system1 may excuse or explain the furtive mode of insinuating his doctrines which he often employs1 and which some of his historians admire as subtle irony1 while others blame it as insincerity4 ,but ,i do not see with what propriety ,galileo can be looked upon as a ,martyr of ,science4 ,undoubtedly he was very desirous of promoting what he conceived to be the cause of philosophical truth2 but it would seem that1 while he was restless and eager in urging his opinions1 he was always ready to make such submissions as the spiritual tribunals required4 ,he would really have acted as a martyr1 if he had uttered #bhb his ,e pur si muove1 in the place of his abjuration1 not after it4 ,but even in this case he would have been a martyr to a cause of which the merit was of a mingled scientific character2 for his own special and favorite share in the reasonings by which the ,copernican system was supported1 was the argument drawn from the flux and reflux of the sea1 which argument is altogether false4 ,he considered this as supplying a mechanical ground of belief1 without which the mere astronomical reasons were quite insufficient2 but in this case he was deserted by the mechanical sagacity which appeared in his other speculations4 ,the heliocentric doctrine had for a century been making its way into the minds of thoughtful men1 on the general ground of its simplicity and symmetry4 ,galileo appears to have thought that now1 when these original recommendations of the system had been reinforced by his own discoveries and reasonings1 it ought to be universally acknowledged as a truth and a reality4 ,and when arguments against the fixity of the sun and the motion of the earth were adduced from the expressions of ,scripture1 he could not be satisfied without maintaining his favorite opinion to be conformable to ,scripture as well as to ,philosophy2 and he was very eager in his attempts to obtain from authority a declaration to this effect4 ,the ecclesiastical authorities were naturally averse to express themselves in favor of a novel opinion1 startling to the common mind1 and contrary to the most obvious meaning of the words of the ,bible2 and when they were compelled to pronounce1 they decided against ,galileo and his doctrines4 ,he was accused before the ,inquisition in #afae2 but at that period the result was that he was merely recommended to confine himself to the mathematical reasonings upon the system1 and to abstain from meddling with the ,scripture4 ,galileo's zeal for his opinions soon led him again to bring the question under the notice of the ,pope1 and the result was a declaration of the ,inquisition that the doctrine of the earth's motion appeared to be contrary to the ,sacred ,scripture4 ,galileo was prohibited from defending and teaching this doctrine in any manner1 and promised obedience to this injunction4 ,but in #afcb he published his 9999,dialogo delli due ,massimi ,sistemi del ,mondo1 ,tolemaico e ,copernicano3 and in this he defended the heliocentric system by all the strongest arguments which its admirers used4 ,not only so1 but he introduced into this ,dialogue a character under the name of ,simplicius1 in whose mouth was put the defence of all the ancient dogmas1 and who was represented as defeated at all points in the discussion2 #bhc and he prefixed to the ,dialogue a ,notice1 ,to the ,discreet ,reader1 in which1 in a vein of transparent irony1 he assigned his reasons for the publication4 ,some years ago1 he says1 a wholesome edict was promulgated at ,rome1 which1 in order to check the perilous scandals of the present age1 imposed silence upon the ,pythagorean opinion of the motion of the earth4 ,there were not wanting1 he adds1 persons who rashly asserted that this decree was the result1 not of a judicious inquiry1 but of a passion ill-informed2 and complaints were heard that counsellors1 utterly unacquainted with astronomical observations1 ought not to be allowed1 with their undue prohibitions1 to clip the wings of speculative intellects4 ,at the hearing of rash lamentations like these1 my zeal could not keep silence4 ,and he then goes on to say that he wishes1 by the publication of his ,dialogue to show that the subject had been fully examined at ,rome4 ,the result of this was that ,galileo was condemned for his infraction of the injunction laid upon him in #afaf2 his ,dialogue was prohibited2 he himself was commanded to abjure on his knees the doctrine which he had taught2 and this abjuration he performed4 ,this celebrated event must be looked upon rather as a question of decorum than a struggle in which the interests of truth and free inquiry were deeply concerned4 ,the general acceptance of the ,copernican ,system was no longer a matter of doubt4 ,several persons in the highest positions1 including the ,pope himself1 looked upon the doctrine with favorable eyes2 and had shown their interest in ,galileo and his discoveries4 ,they had tried to prevent his involving himself in trouble by discussing the question on scriptural grounds4 ,it is probable that his knowledge of those favorable dispositions towards himself and his opinions led him to suppose that the slightest color of professed submission to the ,church in his belief1 would enable his arguments in favor of the system to pass unvisited3 the notice which ,i have quoted1 in which the irony is quite transparent and the sarcasm glaringly obvious1 was deemed too flimsy a veil for the purpose of decency1 and indeed must have aggravated the offence4 ,but it is not to be supposed that the inquisitors believed ,galileo's abjuration to be sincere1 or even that they wished it to be so4 ,it is stated that when ,galileo had made his renunciation of the earth's motion1 he rose from his knees1 and stamping on the earth with his foot1 said1 ,e pur si muove--,and yet it does move4 ,this is sometimes represented as the heroic soliloquy of a mind cherishing its conviction of the truth in spite of persecution2 ,i think we may more naturally conceive it uttered as a playful #bhd epigram in the ear of a cardinal's secretary1 with a full knowledge that it would be immediately repeated to his master4 #b;d ,ed4 ,throughout the course of the proceedings against him1 ,galileo was treated with great courtesy and indulgence4 ,he was condemned to a formal imprisonment and a very light discipline4 ,te damnamus ad formalem carcerem hujus ,s4 ,officii ad tempus arbitrio nostro limitandum2 et titulo pnitenti salutaris prcipimus ut tribus annis futuris recites 9999semel in hebdomad septem psalmos penitentiales4 ,but this confinement was reduced to his being placed under some slight restrictions1 first at the house of ,nicolini1 the ambassador of his own sovereign1 and afterwards at the country seat of ,archbishop ,piccolomini1 one of his own warmest friends4 ,it has sometimes been asserted or insinuated that ,galileo was subjected to bodily torture4 ,an argument has been drawn from the expressions used in his sentence3 ,cum vero nobis videretur non esse a te integram veritatem pronunciatam circa tuam intentionem2 judicavimus necesse esse venire ad rigorosum examen tui1 in quo respondisti catholic4 ,it has been argued by ,m4 ,libri 7,hist4 des ,sciences ,mathmatiques en ,italie1 vol4 ,,iv4 p4 #bei71 and ,m4 ,quinet 7,l',ultramontanisme1 ,,iv4 ,leon1 p4 #ajd71 that the rigorosum examen necessarily implies bodily torture1 notwithstanding that no such thing is mentioned by ,galileo and his contemporaries1 and notwithstanding the consideration with which he was treated in all other respects3 but ,m4 ,biot more justly remarks 7,biogr4 ,univ4 ,art4 ,galileo71 that such a procedure is incredible4 ,to the opinion of ,m4 ,biot1 we may add that of ,delambre1 who rejects the notion of ,galileo's having been put to the torture1 as inconsistent with the general conduct of the authorities towards him1 and as irreconcilable with the accounts of the trial given by ,galileo himself1 and by a servant of his1 who never quitted him for an instant4 ,he adds also1 that it is inconsistent with the words of his sentence1 ne tuus iste gravis et perniciosus error ac transgressio remaneat omnino impunitus2 for the error would have been already very far from impunity1 if ,galileo had been previously subjected to the rack4 ,he adds1 very reasonably1 il ne faut noircir personne sans preuve1 pas mme l',inquisition2--we must not calumniate even the ,inquisition4 ,the ecclesiastical authorities having once declared the doctrine of the earth's motion to be contrary to ,scripture and heretical1 long adhered in form to this declaration1 and did not allow the ,copernican system to be taught in any other way than as an hypothesis4 ,the #bhe ,padua edition of ,galileo's works1 published in #agdd1 contains the ,dialogue which now1 the editors say1 ,esce finalmente a pubblico libero uso colle debite licenze1 is now at last freely published with the requisite license2 but they add1 quanto alla ,quistione principale del moto della terra1 anche noi ci conformiamo alla ritrazione et protesta dell' ,autore1 dichiarando nella piu solenne forma1 che non pu1 n dee ammetersi se non come pura ,ipotesi ,mathematice1 che serve a spiegare piu agevolamento certi fenomeni2 neither can nor ought to be admitted except as a convenient hypothesis4 ,and in the edition of ,newton's ,principia1 published in #agfj1 by ,le ,sueur and ,jacquier1 of the ,order of ,minims1 the editors prefix to the ,third ,book their ,declaratio1 that though ,newton assumes the hypothesis of the motion of the earth1 and therefore they had used similar language1 they were1 in doing this1 assuming a character which did not belong to them4 ,hinc alienam coacti sumus gerere personam4 ,they add1 ,cterum latis a summis ,pontificibus contra telluris motum ,decretis1 nos obsequi profitemur4 ,by thus making decrees against a doctrine which in the course of time was established as an indisputable scientific truth1 the ,see of ,rome was guilty of an unwise and unfortunate stretch of ecclesiastical authority4 ,but though we do not hesitate to pronounce such a judgment on this case1 we may add that there is a question of no small real difficulty1 which the progress of science often brings into notice1 as it did then4 ,the ,revelation on which our religion is founded1 seems to declare1 or to take for granted1 opinions on points on which ,science also gives her decision2 and we then come to this dilemma1--that doctrines1 established by a scientific use of reason1 may seem to contradict the declarations of ,revelation1 according to our view of its meaning2--and yet1 that we cannot1 in consistency with our religious views1 make reason a judge of the truth of revealed doctrines4 ,in the case of ,astronomy1 on which ,galileo was called in question1 the general sense of cultivated and sober-minded men has long ago drawn that distinction between religious and physical tenets1 which is necessary to resolve this dilemma4 ,on this point1 it is reasonably held1 that the phrases which are employed in ,scripture respecting astronomical facts1 are not to be made use of to guide our scientific opinions2 they may be supposed to answer their end if they fall in with common notions1 and are thus effectually subservient to the moral and religions import of ,revelation4 ,but the establishment of this distinction was not accomplished without long and distressing controversies4 ,nor1 if we wish to #bhf include all cases in which the same dilemma may again come into play is it easy to lay down an adequate canon for the purpose4 ,for we can hardly foresee1 beforehand1 what part of the past history of the universe may eventually be found to come within the domain of science2 or what bearing the tenets1 which science establishes1 may have upon our view of the providential and revealed government of the world4 ,but without attempting here to generalize on this subject1 there are two reflections which may be worth our notice3 they are supported by what took place in reference to ,astronomy on the occasion of which we are speaking2 and may1 at other periods1 be applicable to other sciences4 ,in the first place1 the meaning which any generation puts upon the phrases of ,scripture1 depends1 more than is at first sight supposed upon the received philosophy of the time4 ,hence1 while men imagine that they are contending for ,revelation1 they are1 in fact1 contending for their own interpretation of ,revelation1 unconsciously adapted to what they believe to be rationally probable4 ,and the new interpretation1 which the new philosophy requires1 and which appears to the older school to be a fatal violence done to the authority of religion1 is accepted by their successors without the dangerous results which were apprehended4 ,when the language of ,scripture1 invested with its new meaning1 has become familiar to men1 it is found that the ideas which it calls up1 are quite as reconcilable as the former ones were with the soundest religious views4 ,and the world then looks back with surprise at the error of those who thought that the essence of ,revelation was involved in their own arbitrary version of some collateral circumstance4 ,at the present day we can hardly conceive how reasonable men should have imagined that religious reflections on the stability of the earth1 and the beauty and use of the luminaries which revolve round it1 would be interfered with by its being acknowledged that this rest and motion are apparent only4 ,in the next place1 we may observe that those who thus adhere tenaciously to the traditionary or arbitrary mode of understanding ,scriptural expressions of physical events1 are always strongly condemned by succeeding generations4 ,they are looked upon with contempt by the world at large1 who cannot enter into the obsolete difficulties with which they encumbered themselves2 and with pity by the more considerate and serious1 who know how much sagacity and rightmindedness are requisite for the conduct of philosophers and religious men on such occasions2 but who know also how weak and vain is the attempt #bhg to get rid of the difficulty by merely denouncing the new tenets as inconsistent with religious belief1 and by visiting the promulgators of them with severity such as the state of opinions and institutions may allow4 ,the prosecutors of ,galileo are still up to the scorn and aversion of mankind3 although1 as we have seen1 they did not act till it seemed that their position compelled them to do so1 and then proceeded with all the gentleness and moderation which were compatible with judicial forms4 ,sect4 #e4--,the ,heliocentric ,theory confirmed on ,physical considerations4--7,prelude to ,kepler's ,astronomical ,discoveries47 ,,by physical views1 ,i mean1 as ,i have already said1 those which depend on the causes of the motions of matter1 as1 for instance1 the consideration of the nature and laws of the force by which bodies fall downwards4 ,such considerations were necessarily and immediately brought under notice by the examination of the ,copernican theory2 but the loose and inaccurate notions which prevailed respecting the nature and laws of force1 prevented1 for some time1 all distinct reasoning on this subject1 and gave truth little advantage over error4 ,the formation of a new ,science1 the ,science of ,motion and its ,causes1 was requisite1 before the heliocentric system could have justice done it with regard to this part of the subject4 ,this discussion was at first carried on1 as was to be expected1 in terms of the received1 that is1 the ,aristotelian doctrines4 ,thus1 ,copernicus says that terrestrial things appear to be at rest when they have a motion according to nature1 that is1 a circular motion2 and ascend or descend when they have1 in addition to this1 a rectilinear motion by which they 9999endeavor to get into their own place4 ,but his disciples soon began to question the ,aristotelian dogmas1 and to seek for sounder views by the use of their own reason4 ,the great argument against this system1 says ,mstlin1 is that heavy bodies are said to move to the centre of the universe1 and light bodies from the centre4 ,but ,i would ask1 where do we get this experience of heavy and light bodies8 and how is our knowledge on these subjects extended so far that we can reason with certainty concerning the centre of the whole universe8 ,is not the only residence and home of all the things which are heavy and light to us1 the earth and the air which surrounds it8 and what is the earth and the ambient air1 with respect to the immensity of the universe8 ,it is a point1 a punctule1 or something1 if there be any thing1 still less4 ,as our light and heavy bodies tend to #bhh the centre of our earth1 it is credible that the sun1 the moon1 and the other lights1 have a similar affection1 by which they remain round as we see them2 but none of these centres is necessarily the centre of the universe4 ,the most obvious and important physical difficulty attendant upon the supposition of the motion of the earth was thus stated3 ,if the earth move1 how is it that a stone1 dropped from the top of a high tower1 falls exactly at the foot of the tower8 since the tower being carried from west to east by the diurnal revolution of the earth1 the stone must be left behind to the west of the place from which it was let fall4 ,the proper answer to this was1 that the motion which the falling body received from its tendency downwards was compounded with the motion which1 before it fell1 it had in virtue of the earth's rotation3 but this answer could not be clearly made or apprehended1 till ,galileo and his pupils had established the laws of such ,compositions of motion arising from different forces4 ,rothman1 ,kepler1 and other defenders of the ,copernican system1 gave their reply somewhat at a venture1 when they asserted that the motion of the earth was communicated to bodies at its surface4 ,still1 the facts which indicate and establish this truth are obvious1 when the subject is steadily considered2 and the ,copernicans soon found that they had the superiority of argument on this point as well as others4 ,the attacks upon the ,copernican system by ,durret1 ,morin1 ,riccioli1 and the defence of it by ,galileo1 ,lansberg1 ,gassendi1#bhe left on all candid reasoners a clear impression in favour of the system4 ,morin attempted to stop the motion of the earth1 which he called breaking its wings2 his ,al ,terr ,fract was published in #afdc1 and answered by ,gassendi4 ,and ,riccioli1 as late as #afec1 in his ,almagestum ,novum1 enumerated fifty-seven ,copernican arguments1 and pretended to refute them all3 but such reasonings now made no converts2 and by this time the mechanical objections to the motion of the earth were generally seen to be baseless1 as we shall relate when we come to speak of the progress of ,mechanics as a distinct science4 ,in the mean time1 the beauty and simplicity of the heliocentric theory were perpetually winning the admiration even of those who1 from one cause or other1 refused their assent to it4 ,thus ,riccioli1 the last of its considerable opponents1 allows its superiority in these respects2 and acknowledges 7in #afec7 that the ,copernican belief appears rather to increase than diminish under the condemnation of the decrees of the ,cardinals4 ,he applies to it the lines of ,horace3#bie #bhi ,per damna per cdes1 ab ipso ,sumit opes animumque ferro4 ,untamed its pride1 unchecked its course1 ,from foes and wounds it gathers force4 ,note #bhe3 ,del4 ,a4 ,m4 vol4 i4 p4 #eid4 ,note #bie3 ,almag4 ,nov4 p4 #ajb4 ,we have spoken of the influence of the motion of the earth on the motions of bodies at its surface2 but the notion of a physical connection among the parts of the universe was taken up by ,kepler in another point of view1 which would probably have been considered as highly fantastical1 if the result had not been1 that it led to by far the most magnificent and most certain train of truths which the whole expanse of human knowledge can show4 ,i speak of the persuasion of the existence of numerical and geometrical laws connecting the distances1 times1 and forces of the bodies which revolve about the central sun4 ,that steady and intense conviction of this governing principle1 which made its development and verification the leading employment of ,kepler's most active and busy life1 cannot be considered otherwise than as an example of profound sagacity4 ,that it was connected1 though dimly and obscurely1 with the notion of a central agency or influence of some sort1 emanating from the sun1 cannot be doubted4 ,kepler1 in his first essay of this kind1 the ,mysterium ,cosmographicum1 says1 ,the motion of the earth1 which ,copernicus had proved by mathematical reasons1 ,i wanted to prove by physical1 or1 if you prefer it1 metaphysical4 ,in the twentieth chapter of that work1 he endeavors to make out some relation between the distances of the ,planets from the ,sun and their velocities4 ,the inveterate yet vague notions of forces which preside in this attempt1 may be judged of by such passages as the following3--,we must suppose one of two things2 either that the moving spirits1 in proportion as they are more removed from the sun1 are more feeble2 or that there is one moving spirit in the centre of all the orbits1 namely1 in the sun1 which urges each body the more vehemently in proportion as it is nearer2 but in more distant spaces languishes in consequence of the remoteness and attenuation of its virtue4 ,we must not forget1 in reading such passages1 that they were written under a belief that force was requisite to keep up1 as well as to change the motion of each planet2 and that a body1 moving in a circle1 would stop when the force of the central point ceased1 instead of moving off in a tangent to the circle1 as we now know it would do4 ,the force which ,kepler supposes is a tangential force1 in the direction of the body's motion1 and nearly perpendicular to the radius2 the #bij force which modern philosophy has established1 is in the direction of the radius1 and nearly perpendicular to the body's path4 ,kepler was right no further than in his suspicion of a connection between the cause of motion and the distance from the centre2 not only was his knowledge imperfect in all particulars1 but his most general conception of the mode of action of a cause of motion was erroneous4 ,with these general convictions and these physical notions in his mind1 ,kepler endeavored to detect numerical and geometrical relations among the parts of the solar system4 ,after extraordinary labor1 perseverance1 and ingenuity1 he was eminently successful in discovering such relations2 but the glory and merit of interpreting them according to their physical meaning1 was reserved for his greater successor1 ,newton4 ,,chapter ,,iv4 ,,inductive ,,epoch ,,of ,,kepler4 ,sect4 #a4--;,intellectual ,character of ,kepler4 ,,several persons1#cje especially in recent times1 who have taken a view of the discoveries of ,kepler1 appear to have been surprised and somewhat discontented that conjectures1 apparently so fanciful and arbitrary as his1 should have led to important discoveries4 ,they seem to have been alarmed at the ,moral that their readers might draw1 from the tale of a ,quest of ,knowledge1 in which the ,hero1 though fantastical and self-willed1 and violating in his conduct1 as they conceived1 all right rule and sound philosophy1 is rewarded with the most signal triumphs4 ,perhaps one or two reflections may in some measure reconcile us to this result4 #bia ,note #cje3 ,laplace1 ,prcis de l',hist4 d',ast4 p4 #id4 ,il est affligeant pour l'esprit humain de voir ce grand homme1 mme dans ses derniers ouvrages1 se complaire avec dlices dans ses chimriques spculations1 et les regarder comme l'me et la vie de l'astronomie4 ,hist4 of ,ast41 ,l4 ,u4 ,k41 p4 #ec4 ,this success of ,kepler may well inspire with dismay those who are accustomed to consider experiment and rigorous induction as the only means to interrogate nature with success4 ,life of ,kepler1 ,l4 ,u4 ,k41 p4 #ad1 ,bad philosophy4 ,p4 #ae1 ,kepler's miraculous good fortune in seizing truths across the wildest and most absurd theories4 ,p4 #ed1 ,the danger of attempting to follow his method in the pursuit of truth4 ,in the first place1 we may observe that the leading thought which suggested and animated all ,kepler's attempts was true1 and we may add1 sagacious and philosophical2 namely1 that there must be some numerical or geometrical relations among the times1 distances1 and velocities of the revolving bodies of the solar system4 ,this settled and constant conviction of an important truth regulated all the conjectures1 apparently so capricious and fanciful1 which he made and examined1 respecting particular relations in the system4 ,in the next place1 we may venture to say1 that advances in knowledge are not commonly made without the previous exercise of some boldness and license in guessing4 ,the discovery of new truths requires1 undoubtedly1 minds careful and scrupulous in examining what is suggested2 but it requires1 no less1 such as are quick and fertile in suggesting4 ,what is ,invention1 except the talent of rapidly calling before us many possibilities1 and selecting the appropriate one8 ,it is true1 that when we have rejected all the inadmissible suppositions1 they are quickly forgotten by most persons2 and few think it necessary to dwell on these discarded hypotheses1 and on the process by which they were condemned1 as ,kepler has done4 ,but all who discover truths must have reasoned upon many errors1 to obtain each truth2 every accepted doctrine must have been one selected out of many candidates4 ,in making many conjectures1 which on trial proved erroneous1 ,kepler was no more fanciful or unphilosophical than other discoverers have been4 ,discovery is not a cautious or rigorous process1 in the sense of abstaining from such suppositions4 ,but there are great differences in different cases1 in the facility with which guesses are proved to be errors1 and in the degree of attention with which the error and the proof are afterwards dwelt on4 ,kepler certainly was remarkable for the labor which he gave to such self-refutations1 and for the candor and copiousness with which he narrated them2 his works are in this way extremely curious and amusing2 and are a very instructive exhibition of the mental process of discovery4 ,but in this respect1 ,i venture to believe1 they exhibit to us the usual process 7somewhat caricatured7 of inventive minds3 they rather exemplify the rule of genius than 7as has generally been hitherto taught7 the exception4 ,we may add1 that if many of ,kepler's guesses now appear fanciful and absurd1 because time and observation have refuted them1 others1 which were at the time equally gratuitous1 have been confirmed by succeeding discoveries in a manner which makes them appear marvellously sagacious2 as1 for instance1 his assertion of the rotation of #bib the sun on his axis1 before the invention of the telescope1 and his opinion that the obliquity of the ecliptic was decreasing1 but would1 after a long-continued diminution1 stop1 and then increase again4#cae ,nothing can be more just1 as well as more poetically happy1 than ,kepler's picture of the philosopher's pursuit of scientific truth1 conveyed by means of an allusion to ,virgil's shepherd and shepherdess3 ,malo me ,galatea petit1 lasciva puella ,et fugit ad salices et se cupit ante videri4 ,coy yet inviting1 ,galatea loves ,to sport in sight1 then plunge into the groves2 ,the challenge given1 she darts along the green1 ,will not be caught1 yet would not run unseen4 ,note #cae3 ,bailly1 ,a4 ,m4 iii4 #age4 ,we may notice as another peculiarity of ,kepler's reasonings1 the length and laboriousness of the processes by which he discovered the errors of his first guesses4 ,one of the most important talents requisite for a discoverer1 is the ingenuity and skill which devises means for rapidly testing false suppositions as they offer themselves4 ,this talent ,kepler did not possess3 he was not even a good arithmetical calculator1 often making mistakes1 some of which he detected and laments1 while others escaped him to the last4 ,but his defects in this respect were compensated by his courage and perseverance in undertaking and executing such tasks2 and1 what was still more admirable1 he never allowed the labor he had spent upon any conjecture to produce any reluctance in abandoning the hypothesis1 as soon as he had evidence of its inaccuracy4 ,the only way in which he rewarded himself for his trouble1 was by describing to the world1 in his lively manner1 his schemes1 exertions1 and feelings4 ,the mystical parts of ,kepler's opinions1 as his belief in astrology1 his persuasion that the earth was an animal1 and many of the loose moral and spiritual as well as sensible analyses by which he represented to himself the powers which he supposed to prevail in the universe1 do not appear to have interfered with his discovery1 but rather to have stimulated his invention1 and animated his exertions4 ,indeed1 where there are clear scientific ideas on one subject in the mind1 it does not appear that mysticism on others is at all unfavorable to the successful prosecution of research4 ,i conceive1 then1 that we may consider ,kepler's character as containing the general features of the character of a scientific discoverer1 #bic though some of the features are exaggerated1 and some too feebly marked4 ,his spirit of invention was undoubtedly very fertile and ready1 and this and his perseverance served to remedy his deficiency in mathematical artifice and method4 ,but the peculiar physiognomy is given to his intellectual aspect by his dwelling in a most prominent manner on those erroneous trains of thought which other persons conceal from the world1 and often themselves forget1 because they find means of stopping them at the outset4 ,in the beginning of his book 7,argumenta ,capitum7 he says1 if ,christopher ,columbus1 if ,magellan1 if the ,portuguese1 when they narrate their wanderings1 are not only excused1 but if we do not wish these passages omitted1 and should lose much pleasure if they were1 let no one blame me for doing the same4 ,kepler's talents were a kindly and fertile soil1 which he cultivated with abundant toil and vigor2 but with great scantiness of agricultural skill and implements4 ,weeds and the grain throve and flourished side by side almost undistinguished2 and he gave a peculiar appearance to his harvest1 by gathering and preserving the one class of plants with as much care and diligence as the other4 ,sect4 #b4--,kepler's ,discovery of his ,third ,law4 ,i ,,shall now give some account of ,kepler's speculations and discoveries4 ,the first discovery which he attempted1 the relation among the successive distances of the planets from the sun1 was a failure2 his doctrine being without any solid foundation1 although propounded by him with great triumph1 in a work which he called ,mysterium ,cosmographicum1 and which was published in #aeif4 ,the account which he gives of the train of his thoughts on this subject1 namely1 the various suppositions assumed1 examined1 and rejected1 is curious and instructive1 for the reasons just stated2 but we shall not dwell upon these essays1 since they led only to an opinion now entirely abandoned4 ,the doctrine which professed to give the true relation of the orbits of the different planets1 was thus delivered3#cbe ,the orbit of the earth is a circle3 round the sphere to which this circle belongs1 describe a dodecahedron2 the sphere including this will give the orbit of ,mars4 ,round ,mars describe a tetrahedron2 the circle including this will be the orbit of ,jupiter4 ,describe a cube round ,jupiter's orbit2 the circle including this will be the orbit of ,saturn4 ,now inscribe in the ,earth's orbit an icosahedron2 the circle inscribed in it will be the orbit of ,venus4 #bid ,inscribe an octahedron in the orbit of ,venus2 the circle inscribed in it will be ,mercury's orbit4 ,this is the reason of the number of the planets4 ,the five kinds of polyhedral bodies here mentioned are the only ,regular ,solids4 ,note #cbe3 ,l4 ,u4 ,k4 ,kepler1 #f4 ,but though this part of the ,mysterium ,cosmographicum was a failure1 the same researches continued to occupy ,kepler's mind2 and twenty-two years later led him to one of the important rules known to us as ,kepler's ,laws2 namely1 to the rule connecting the mean distances of the planets from the sun with the times of their revolutions4 ,this rule is expressed in mathematical terms1 by saying that the squares of the periodic times are in the same proportion as the cubes of the distances2 and was of great importance to ,newton in leading him to the law of the sun's attractive force4 ,we may properly consider this discovery as the sequel of the train of thought already noticed4 ,in the beginning of the ,mysterium1 ,kepler had said1 ,in the year #aeie1 ,i brooded with the whole energy of my mind on the subject of the ,copernican system4 ,there were three things in particular of which ,i pertinaciously sought the causes why they are not other than they are2 the number1 the size1 and the motion of the orbits4 ,we have seen the nature of his attempt to account for the two first of these points4 ,he had also made some essays to connect the motions of the planets with their distances1 but with his success in this respect he was not himself completely satisfied4 ,but in the fifth book of the ,harmonice ,mundi1 published in #afai1 he says1 ,what ,i prophesied two-and-twenty years ago as soon as ,i had discovered the ,five ,solids among the ,heavenly ,bodies2 what ,i firmly believed before ,i had seen the ,harmonics of ,ptolemy2 what ,i promised my friends in the title of this book 7,on the most perfect ,harmony of the ,celestial ,motions7 which ,i named before ,i was sure of my discovery2 what sixteen years ago ,i regarded as a thing to be sought2 that for which ,i joined ,tycho ,brahe1 for which ,i settled in ,prague1 for which ,i have devoted the best part of my life to astronomical contemplations2 at length ,i have brought to light1 and have recognized its truth beyond my most sanguine expectations4 ,the rule thus referred to is stated in the third ,chapter of this fifth ,book4 ,it is1 he says1 a most certain and exact thing that the proportion which exists between the periodic times of any two planets is precisely the sesquiplicate of the proportion of their mean distances2 that is1 of the radii of the orbits4 ,thus1 the period of the earth is one year1 that of ,saturn thirty years2 if any one trisect the proportion1 that #bie is1 take the cube root of it1 and double the proportion so found1 that is1 square it1 he will find the exact proportion of the distances of the ,earth and of ,saturn from the sun4 ,for the cube root of #a is #a1 and the square of this is #a2 and the cube root of #cj is greater than #c1 and therefore the square of it is greater than #i4 ,and ,saturn at his mean distance from the sun is at a little more than #i times the mean distance of the ,earth4 ,when we now look back at the time and exertions which the establishment of this law cost ,kepler1 we are tempted to imagine that he was strangely blind in not seeing it sooner4 ,his object1 we might reason1 was to discover a law connecting the distances and the periodic times4 ,what law of connection could be more simple and obvious1 we might say1 than that one of these quantities should vary as some power of the other1 or as some root2 or as some combination of the two1 which in a more general view1 may still be called a power8 ,and if the problem had been viewed in this way1 the question must have occurred1 to what power of the periodic times are the distances proportional8 ,and the answer must have been1 the trial being made1 that they are proportional to the square of the cube root4 ,this ex-post-facto obviousness of discoveries is a delusion to which we are liable with regard to many of the most important principles4 ,in the case of ,kepler1 we may observe1 that the process of connecting two classes of quantities by comparing their powers1 is obvious only to those who are familiar with general algebraical views2 and that in ,kepler's time1 algebra had not taken the place of geometry1 as the most usual vehicle of mathematical reasoning4 ,it may be added1 also1 that ,kepler always sought his formal laws by means of physical reasonings2 and these1 though vague or erroneous1 determined the nature of the mathematical connection which he assumed4 ,thus in the ,mysterium he had been led by his notions of moving virtue of the sun to this conjecture1 among others--that1 in the planets1 the increase of the periods will be double of the difference of the distances2 which supposition he found to give him an approach to the actual proportion of the distances1 but one not sufficiently close to satisfy him4 ,the greater part of the fifth ,book of the ,harmonics of the ,universe consists in attempts to explain various relations among the distances1 times1 and eccentricities of the planets1 by means of the ratios which belong to certain concords and discords4 ,this portion of the work is so complex and laborious1 that probably few modern readers have had courage to go through it4 ,delambre acknowledged that his patience #bif often failed him during the task2#cce and subscribes to the judgment of ,bailly3 ,after this sublime effort1 ,kepler replunges himself in the relations of music to the motions1 the distance1 and the eccentricities of the planets4 ,in all these harmonic ratios there is not one true relation2 in a crowd of ideas there is not one truth3 he becomes a man after being a spirit of light4 ,certainly these speculations are of no value1 but we may look on them with toleration1 when we recollect that ,newton has sought for analogies between the spaces occupied by the prismatic colors and the notes of the gamut4#cde ,the numerical relations of ,concords are so peculiar that we can easily suppose them to have other bearings than those which first offer themselves4 ,note #cce3 ,a4 ,m4 a4 #ceh4 ,note #cde3 ,optics1 b4 ii4 p4 iv4 ,obs4 #e4 ,it does not belong to my present purpose to speak at length of the speculations concerning the forces producing the celestial motions by which ,kepler was led to this celebrated law1 or of those which he deduced from it1 and which are found in the ,epitome ,astronomi ,copernican1 published in #afbb4 ,in that work also 7p4 #eed71 he extended this law1 though in a loose manner1 to the satellites of ,jupiter4 ,these physical speculations were only a vague and distant prelude to ,newton's discoveries2 and the law1 as a formal rule1 was complete in itself4 ,we must now attend to the history of the other two laws with which ,kepler's name is associated4 ,sect4 #c4--,kepler's ,discovery of his ,first and ,second ,laws4--,elliptical ,theory of the ,planets4 ,,the propositions designated as ,kepler's ,first and ,second ,laws are these3 ,that the orbits of the planets are elliptical2 and1 ,that the areas described1 or swept1 by lines drawn from the sun to the planet1 are proportional to the times employed in the motion4 ,the occasion of the discovery of these laws was the attempt to reconcile the theory of ,mars to the theory of eccentrics and epicycles2 the event of it was the complete overthrow of that theory1 and the establishment1 in its stead1 of the ,elliptical ,theory of the planets4 ,astronomy was now ripe for such a change4 ,as soon as ,copernicus had taught men that the orbits of the planets were to be referred to the sun1 it obviously became a question1 what was the true form of these orbits1 and the rule of motion of each planet in its own orbit4 ,copernicus represented the motions in longitude by means of #big eccentrics and epicycles1 as we have already said2 and the motions in latitude by certain librations1 or alternate elevations and depressions of epicycles4 ,if a mathematician had obtained a collection of true positions of a planet1 the form of the orbit and the motion of the star would have been determined with reference to the sun as well as to the earth2 but this was not possible1 for though the geocentric position1 or the direction in which the planet was seen1 could be observed1 its distance from the earth was not known4 ,hence1 when ,kepler attempted to determine the orbit of a planet1 he combined the observed geocentric places with successive modifications of the theory of epicycles1 till at last he was led1 by one step after another1 to change the epicyclical into the elliptical theory4 ,we may observe1 moreover1 that at every step he endeavored to support his new suppositions by what he called1 in his fanciful phraseology1 sending into the field a reserve of new physical reasonings on the rout and dispersion of the veterans2#cee that is1 by connecting his astronomical hypotheses with new imaginations1 when the old ones became untenable4 ,we find1 indeed1 that this is the spirit in which the pursuit of knowledge is generally carried on with success2 those men arrive at truth who eagerly endeavor to connect remote points of their knowledge1 not those who stop cautiously at each point till something compels them to go beyond it4 ,note #cee3 ,i will insert this passage1 as a specimen of ,kepler's fanciful mode of narrating the defeats which he received in the war which he carried on with ,mars4 ,dum in hunc modum de ,martis motibus triumpho1 eique ut plan devicto tabularum carceres et equationum compedes necto1 diversis nuntiatur locis1 futilem victoriam ut bellam tot mole recrudescere4 ,nam domi quidam hostis ut captivus contemptus1 rupit omnia equationum vincula1 carceresque tabularum effregit4 ,foris speculatores profligerunt meas causarum physicarum arcessitas copias earumque jugum excusserunt resumt libertate4 ,jamque parum abfuit quia hostis fugitivus sese cum rebellibus suis conjungeret meque in desperationem adigeret3 nisi raptim1 nova rationum physicarum subsidia1 fusis et palantibus veteribus1 submisissem1 et qua se captivus proripuisset1 omni diligentia1 edoctus vestigiis ipsius null mor interposit inhsisserem4 ,kepler joined ,tycho ,brahe at ,prague in #afjj1 and found him and ,longomontanus busily employed in correcting the theory of ,mars2 and he also then entered upon that train of researches which he published in #afji in his extraordinary work ,on the ,motions of ,mars4 ,in this work1 as in others1 he gives an account1 not only of his success1 but of his failures1 explaining1 at length1 the various suppositions which he had made1 the notions by which he had been led to invent or to entertain them1 the processes by which he had proved their #bih falsehood1 and the alternations of hope and sorrow1 of vexation and triumph1 through which he had gone4 ,it will not be necessary for us to cite many passages of these kinds1 curious and amusing as they are4 ,one of the most important truths contained in the motions of ,man is the discovery that the plane of the orbit of the planet should be considered with reference to the sun itself1 instead of referring it to any of the other centres of motion which the eccentric hypothesis introduced3 and that1 when so considered1 it had none of the librations which ,ptolemy and ,copernicus had attributed to it4 ,the fourteenth chapter of the second part asserts1 ,plana eccentricorum esse 2 that the planes are unlibrating2 retaining always the same inclination to the ecliptic1 and the same line of nodes4 ,with this step ,kepler appears to have been justly delighted4 ,copernicus1 he says1 not knowing the value of what he possessed 7his system71 undertook to represent ,ptolemy1 rather than nature1 to which1 however1 he had approached more nearly than any other person4 ,for being rejoiced that the quantity of the latitude of each planet was increased by the approach of the earth to the planet1 according to his theory1 he did not venture to reject the rest of ,ptolemy's increase of latitude1 but in order to express it1 devised librations of the planes of the eccentric1 depending not upon its own eccentric1 but 7most improbably7 upon the orbit of the earth1 which has nothing to do with it4 ,i always fought against this impertinent tying together of two orbits1 even before ,i saw the observations of ,tycho2 and ,i therefore rejoice much that in this1 as in others of my preconceived opinions1 the observations were found to be on my side4 ,kepler established his point by a fair and laborious calculation of the results of observations of ,mars made by himself and ,tycho ,brahe2 and had a right to exult when the result of these calculations confirmed his views of the symmetry and simplicity of nature4 ,we may judge of the difficulty of casting off the theory of eccentrics and epicycles1 by recollecting that ,copernicus did not do it at all1 and that ,kepler only did it after repeated struggles2 the history of which occupies thirty-nine ,chapters of his book4 ,at the end of them he says1 ,this prolix disputation was necessary1 in order to prepare the way to the natural form of the equations1 of which ,i am now to treat4#cfe ,my first error was1 that the path of a planet is a perfect circle2--an opinion which was a more mischievous thief of my time1 #bii in proportion as it was supported by the authority of all philosophers1 and apparently agreeable to metaphysics4 ,but before he attempts to correct this erroneous part of his hypothesis1 he sets about discovering the law according to which the different parts of the orbit are described in the case of the earth1 in which case the eccentricity is so small that the effect of the oval form is insensible4 ,the result of this inquiry was#cge the ,rule1 that the time of describing any arc of the orbit is proportional to the area intercepted between the curve and two lines drawn from the sun to the extremities of the arc4 ,it is to be observed that this rule1 at first1 though it had the recommendation of being selected after the unavoidable abandonment of many1 which were suggested by the notions of those times1 was far from being adopted upon any very rigid or cautious grounds4 ,a rule had been proved at the apsides of the orbit1 by calculation from observations1 and had then been extended by conjecture to other parts of the orbit2 and the rule of the areas was only an approximate and inaccurate mode of representing this rule1 employed for the purpose of brevity and convenience1 in consequence of the difficulty of applying1 geometrically1 that which ,kepler now conceived to be the true rule1 and which required him to find the sum of the lines drawn from the sun to every point of the orbit4 ,when he proceeded to apply this rule to ,mars1 in whose orbit the oval form is much more marked1 additional difficulties came in his way2 and here again the true supposition1 that the oval is of that special kind called ellipse1 was adopted at first only in order to simplify calculation1#che and the deviation from exactness in the result was attributed to the inaccuracy of those approximate processes4 ,the supposition of the oval had already been forced upon ,purbach in the case of ,mercury1 and upon ,reinhold in the case of the ,moon4 ,the centre of the epicycle was made to describe an egg-shaped figure in the former case1 and a lenticular figure in the latter4#cie ,note #cfe3 ,de ,stell ,martis1 iii4 #dj4 ,note #cge3 ,de ,stell ,martis1 p4 #aid4 ,note #che3 ,ib4 iv4 c4 #dg4 ,note #cie3 ,l4 ,u4 ,k4 ,kepler1 p4 #cj4 ,it may serve to show the kind of labor by which ,kepler was led to his result1 if we here enumerate1 as he does in his forty-seventh ,chapter1#dje six hypotheses1 on which he calculated the longitude of ,mars1 in order to see which best agreed with observation4 ,note #dje3 ,de ,stell ,martis1 p4 #bbh4 #a4 ,the simple eccentricity4 #b4 ,the bisection of the eccentricity1 and the duplication of the superior part of the equation4 #cjj #c4 ,the bisection of the eccentricity1 and a stationary point of equations1 after the manner of ,ptolemy4 #d4 ,the vicarious hypothesis by a free section of the eccentricity made to agree as nearly as possible with the truth4 #e4 ,the physical hypothesis on the supposition of a perfect circle4 #f4 ,the physical hypothesis on the supposition of a perfect ellipse4 ,by the physical hypothesis1 he meant the doctrine that the time of a planet's describing any part of its orbit is proportional to the distance of the planet from the sun1 for which supposition1 as we have said1 he conceived that he had assigned physical reasons4 ,the two last hypotheses came the nearest to the truth1 and differed from it only by about eight minutes1 the one in excess and the other in defect4 ,and1 after being much perplexed by this remaining error1 it at last occurred to him#dae that he might take another ellipsis1 exactly intermediate between the former one and the circle1 and that this must give the path and the motion of the planet4 ,making this assumption1 and taking the areas to represent the times1 he now saw#dbe that both the longitude and the distances of ,mars would agree with observation to the requisite degree of accuracy4 ,the rectification of the former hypothesis1 when thus stated1 may1 perhaps1 appear obvious4 ,and ,kepler informs us that he had nearly been anticipated in this step 7c4 #ee74 ,david ,fabricius1 to whom ,i had communicated my hypothesis of cap4 #de1 was able1 by his observations1 to show that it erred in making the distances too short at mean longitudes2 of which he informed me by letter while ,i was laboring1 by repeated efforts1 to discover the true hypothesis4 ,so nearly did he get the start of me in detecting the truth4 ,but this was less easy than it might seem4 ,when ,kepler's first hypothesis was enveloped in the complex construction requisite in order to apply it to each point of the orbit1 it was far more difficult to see where the error lay1 and ,kepler hit upon it only by noticing the coincidences of certain numbers1 which1 as he says1 raised him as if from sleep1 and gave him a new light4 ,we may observe1 also1 that he was perplexed to reconcile this new view1 according to which the planet described an exact ellipse1 with his former opinion1 which represented the motion by means of libration in an epicycle4 ,this1 he says1 was my greatest trouble1 that1 though ,i considered and reflected till ,i was almost mad1 ,i could not find why the planet to which1 with so much probability1 and with such an exact #cja accordance of the distances1 libration in the diameter of the epicycle was attributed1 should1 according to the indication of the equations1 go in an elliptical path4 ,what an absurdity on my part6 as if libration in the diameter might not be a way to the ellipse6 ,note #dae3 ,de ,stell ,martis1 c4 #eh4 ,note #dbe3 ,ibid4 p4 #bce4 ,another scruple respecting this theory arose from the impossibility of solving1 by any geometrical construction1 the problem to which ,kepler was thus led1 namely1 ,to divide the area of a semicircle in a given ratio1 by a line drawn from any point of the diameter4 ,this is still termed ,kepler's ,problem1 and is1 in fact1 incapable of exact geometrical solution4 ,as1 however1 the calculation can be performed1 and1 indeed1 was performed by ,kepler himself1 with a sufficient degree of accuracy to show that the elliptical hypothesis is true1 the insolubility of this problem is a mere mathematical difficulty in the deductive process1 to which ,kepler's induction gave rise4 ,of ,kepler's physical reasonings we shall speak more at length on another occasion4 ,his numerous and fanciful hypotheses had discharged their office1 when they had suggested to him his many lines of laborious calculation1 and encouraged him under the exertions and disappointments to which these led4 ,the result of this work was the formal laws of the motion of ,mars1 established by a clear induction1 since they represented1 with sufficient accuracy1 the best observations4 ,and we may allow that ,kepler was entitled to the praise which he claims in the motto on his first leaf4 ,ramus had said that if any one would construct an astronomy without hypothesis1 he would be ready to resign to him his professorship in the ,university of ,paris4 ,kepler quotes this passage1 and adds1 it is well1 ,ramus1 that you have run from this pledge1 by quitting life and your professorship2#dce if you held it still1 ,i should1 with justice1 claim it4 ,this was not saying too much1 since he had entirely overturned the hypothesis of eccentrics and epicycles1 and had obtained a theory which was a mere representation of the motions and distances as they were observed4 #cjb ,note #dce3 ,ramus perished in the ,massacre of ,st4 ,bartholomew4 ,,chapter ,v4 ,,sequel ,,to ,,the ,,epoch ,,of ,,kepler4 ,,reception1 ,,verification1 ,,and ,,extension ,,of ,,the ,,elliptical ,,theory4 ,sect4 #a4--;,application of the ,elliptical ,theory to the ,planets4 ,,the extension of ,kepler's discoveries concerning the orbit of ,mars to the other planets1 obviously offered itself as a strong probability1 and was confirmed by trial4 ,this was made in the first place upon the orbit of ,mercury2 which planet1 in consequence of the largeness of its eccentricity1 exhibits more clearly than the others the circumstances of the elliptical motion4 ,these and various other supplementary portions of the views to which ,kepler's discoveries had led1 appeared in the latter part of his ,epitome ,astronomi ,copernican1 published in #afbb4 ,the real verification of the new doctrine concerning the orbits and motions of the heavenly bodies was1 of course1 to be found in the construction of tables of those motions1 and in the continued comparison of such tables with observation4 ,kepler's discoveries had been founded1 as we have seen1 principally on ,tycho's observations4 ,longomontanus 7so called as being a native of ,langberg in ,denmark71 published in #afba1 in his ,astronomia ,danica1 tables founded upon the theories as well as the observations of his countryman4 ,kepler#dde in #afbg published his tables of the planets1 which he called ,rudolphine ,tables1 the result and application of his own theory4 ,in #afcc1 ,lansberg1 a ,belgian1 published also ,tabul ,perpetu1 a work which was ushered into the world with considerable pomp and pretension1 and in which the author cavils very keenly at ,kepler and ,brahe4 ,we may judge of the impression made upon the astronomical world in general by these rival works1 from the account which our countryman ,jeremy ,horrox has given of their effect on him4 ,he had been seduced by the magnificent promises of ,lansberg1 and the praises of his admirers1 which are prefixed to the work1 and was persuaded that the common opinion which preferred ,tycho and ,kepler to him was a prejudice4 ,in #afcf1 however1 he became acquainted with ,crabtree1 another young #cjc astronomer1 who lived in the same part of ,lancashire4 ,by him ,horrox was warned that ,lansberg was not to be depended on2 that his hypotheses were vicious1 and his observations falsified or forced into agreement with his theories4 ,he then read the works and adopted the opinions of ,kepler2 and after some hesitation which he felt at the thought of attacking the object of his former idolatry1 he wrote a dissertation on the points of difference between them4 ,it appears that1 at one time1 he intended to offer himself as the umpire who was to adjudge the prize of excellence among the three rival theories of ,longomontanus1 ,kepler1 and ,lansberg2 and1 in allusion to the story of ancient mythology1 his work was to have been called ,paris ,astronomicus2 we easily see that he would have given the golden apple to the ,keplerian goddess4 ,succeeding observations confirmed his judgment3 and the ,rudolphine ,tables1 thus published seventy-six years after the ,prutenic1 which were founded on the doctrines of ,copernicus1 were for a long time those universally used4 ,note #dde3 ,rheticus1 ,narratio1 p4 #ih4 ,sect4 #b4--;,application of the ,elliptical ,theory to the ,moon4 ,,the reduction of the ,moon's motions to rule was a harder task than the formation of planetary tables1 if accuracy was required2 for the ,moon's motion is affected by an incredible number of different and complex inequalities1 which1 till their law is detected1 appear to defy all theory4 ,still1 however1 progress was made in this work4 ,the most important advances were due to ,tycho ,brahe4 ,in addition to the first and second inequalities of the moon 7the ,equation of the ,centre1 known very early1 and the ,evection1 which ,ptolemy had discovered71 ,tycho proved that there was another inequality1 which he termed the ,variation1#dee which depended on the moon's position with respect to the sun1 and which at its maximum was forty minutes and a half1 about a quarter of the evection4 ,he also perceived1 though not very distinctly1 the necessity of another correction of the moon's place depending on the sun's longitude1 which has since been termed the ,annual ,equation4 ,note #dee3 ,we have seen 7chap4 iii471 that ,aboul-,wefa1 in the tenth century1 had already noticed this inequality2 but his discovery had been entirely forgotten long before the time of ,tycho1 and has only recently been brought again into notice4 ,these steps concerned the ,longitude of the ,moon2 ,tycho also made important advances in the knowledge of the ,latitude4 ,the ,inclination of the ,orbit had hitherto been assumed to be the same at all #cjd times2 and the motion of the ,node had been supposed uniform4 ,he found that the inclination increased and diminished by twenty minutes1 according to the position of the line of nodes2 and that the nodes1 though they regress upon the whole1 sometimes go forwards and sometimes go backwards4 ,tycho's discoveries concerning the moon are given in his ,progymnasmata1 which was published in #afjc1 two years after the author's death4 ,he represents the ,moon's motion in longitude by means of certain combinations of epicycles and eccentrics4 ,but after ,kepler had shown that such devices are to be banished from the planetary system1 it was impossible not to think of extending the elliptical theory to the moon4 ,horrox succeeded in doing this2 and in #afch sent this essay to his friend ,crabtree4 ,it was published in #afgc1 with the numerical elements requisite for its application added by ,flamsteed4 ,flamsteed had also 7in #afga-b7 compared this theory with observation1 and found that it agreed far more nearly than the ,philolaic ,tables of ,bullialdus1 or the ,carolinian ,tables of ,street 7,epilogus ad ,tabulas74 ,moreover ,horrox1 by making the centre of the ellipse revolve in an epicycle1 gave an explanation of the evection1 as well as of the equation of the centre4#dfe ,note #dfe3 ,horrox 7,horrockes as he himself spelt his name7 gave a first sketch of his theory in letters to his friend ,crabtree in #afch3 in which the variation of the eccentricity is not alluded to4 ,but in ,crabtree's letter to ,gascoigne in #afdb1 he gives ,horrox's rule concerning it2 and ,flamsteed in his ,epilogue to the ,tables1 published by ,wallis along with ,horrox's works in #afgc1 gave an explanation of the theory which made it amount very nearly to a revolution of the centre of the ellipse in an epicycle4 ,halley afterwards made a slight alteration2 but hardly1 ,i think1 enough to justify ,newton's assertion 7,princip4 ,lib4 iii4 ,prop4 #ce1 ,schol471 ,halleius centrum ellipseos in epicyclo locavit4 ,see ,baily's ,flamsteed1 p4 #fhc4 ,modern astronomers1 by calculating the effects of the perturbing forces of the solar system1 and comparing their calculations with observation1 have added many new corrections or equations to those known at the time of ,horrox2 and since the ,motions of the heavenly bodies were even then affected by these variations as yet undetected1 it is clear that the ,tables of that time must have shown some errors when compared with observation4 ,these errors much perplexed astronomers1 and naturally gave rise to the question whether the motions of the heavenly bodies really were exactly regular1 or whether they were not affected by accidents as little reducible to rule as wind and weather4 ,kepler had held the opinion of the casualty of such errors2 but ,horrox1 far more philosophically1 argues against this opinion1 though he #cje allows that he is much embarrassed by the deviations4 ,his arguments show a singularly clear and strong apprehension of the features of the case1 and their real import4 ,he says1#dge these errors of the tables are alternately in excess and defect2 how could this constant compensation happen if they were casual8 ,moreover1 the alternation from excess to defect is most rapid in the ,moon1 most slow in ,jupiter and ,saturn1 in which planets the error continues sometimes for years4 ,if the errors were casual1 why should they not last as long in the ,moon as in ,saturn8 ,but if we suppose the tables to be right in the mean motions1 but wrong in the equations1 these facts are just what must happen2 since ,saturn's inequalities are of long period1 while those of the ,moon are numerous1 and rapidly changing4 ,it would be impossible1 at the present moment1 to reason better on this subject2 and the doctrine1 that all the apparent irregularities of the celestial motions are really regular1 was one of great consequence to establish at this period of the science4 ,note #dge3 ,astron4 ,kepler4 ,proleg4 p4 #ag4 ,sect4 #c4--;,causes of the further ,progress of ,astronomy4 ,,we are now arrived at the time when theory and observation sprang forwards with emulous energy4 ,the physical theories of ,kepler1 and the reasonings of other defenders of the ,copernican theory1 led inevitably1 after some vagueness and perplexity1 to a sound science of ,mechanics2 and this science in time gave a new face to ,astronomy4 ,but in the mean time1 while mechanical mathematicians were generalizing from the astronomy already established1 astronomers were accumulating new facts1 which pointed the way to new theories and new generalizations4 ,copernicus1 while he had established the permanent length of the year1 had confirmed the motion of the sun's apogee1 and had shown that the eccentricity of the earth's orbit1 and the obliquity of the ecliptic1 were gradually1 though slowly1 diminishing4 ,tycho had accumulated a store of excellent observations4 ,these1 as well as the laws of the motions of the moon and planets already explained1 were materials on which the ,mechanics of the ,universe was afterwards to employ its most matured powers4 ,in the mean time1 the telescope had opened other new subjects of notice and speculation2 not only confirming the ,copernican doctrine by the phases of ,venus1 and the analogical examples of ,jupiter and ,saturn1 which with their ,satellites #cjf appeared like models of the ,solar ,system2 but disclosing unexpected objects1 as the ,ring of ,saturn1 and the ,spots of the ,sun4 ,the art of observing made rapid advances1 both by the use of the telescope1 and by the sounder notions of the construction of instruments which ,tycho introduced4 ,copernicus had laughed at ,rheticus1 when he was disturbed about single minutes2 and declared that if he could be sure to ten minutes of space1 he should be as much delighted as ,pythagoras was when he discovered the property of the right-angled triangle4 ,but ,kepler founded the revolution which he introduced on a quantity less than this4 ,since1 he says1#dhe the ,divine ,goodness has given us in ,tycho an observer so exact that this error of eight minutes is impossible1 we must be thankful to ,god for this1 and turn it to account4 ,and these eight minutes1 which we must not neglect1 will1 of themselves1 enable us to reconstruct the whole of astronomy4 ,in addition to other improvements1 the art of numerical calculation made an inestimable advance by means of ,napier's invention of ,logarithms2 and the progress of other parts of pure mathematics was proportional to the calls which astronomy and physics made upon them4 ,note #dhe3 ,de ,stell ,martis1 c4 #ai4 ,the exactness which observation had attained enabled astronomers both to verify and improve the existing theories1 and to study the yet unsystematized facts4 ,the science was1 therefore1 forced along by a strong impulse on all sides1 and its career assumed a new character4 ,up to this point1 the history of ,european ,astronomy was only the sequel of the history of ,greek ,astronomy2 for the heliocentric system1 as we have seen1 had had a place among the guesses1 at least1 of the inventive and acute intellects of the ,greek philosophers4 ,but the discovery of ,kepler's ,laws1 accompanied1 as from the first they were1 with a conviction that the relations thus brought to light were the effects and exponents of physical causes1 led rapidly and irresistibly to the ,mechanical ,science of the skies1 and collaterally1 to the ,mechanical ,science of the other parts of ,nature3 ,sound1 and ,light1 and ,heat2 and ,magnetism1 and ,electricity1 and ,chemistry4 ,the history of these ,sciences1 thus treated1 forms the sequel of the present work1 and will be the subject of the succeeding volumes4 ,and since1 as ,i have said1 our main object in this work is to deduce1 from the history of science1 the philosophy of scientific discovery1 it may be regarded as fortunate for our purpose that the history1 after this point1 so far changes its aspect as to offer new materials for such speculations4 ,the details of #cjg a history of astronomy1 such as the history of astronomy since ,newton has been1 though interesting to the special lovers of that science1 would be too technical1 and the features of the narrative too monotonous and unimpressive1 to interest the general reader1 or to suggest a comprehensive philosophy of science4 ,but when we pass from the ,ideas of ,space and ,time to the ,ideas of ,force and ,matter1 of ,mediums by which action and sensation are produced1 and of the ,intimate ,constitution of material bodies1 we have new fields of inquiry opened to us4 ,and when we find that in these fields1 as well as in astronomy1 there are large and striking trains of unquestioned discovery to be narrated1 we may gird ourselves afresh to the task of writing1 and ,i hope1 of reading1 the remaining part of the ,history of the ,inductive ,sciences1 in the trust that it will in some measure help us to answer the important questions1 ,what is ,truth8 and1 ,how is it to be discovered8 #cji ,,book ,,vi4 ,,the ,,mechanical ,,sciences4 ,,history ,,of ,,mechanics1 ,,including ,,fluid ,,mechanics4 ,i 1 1 ' ,,schylus4 ,prom4 ,vinct4 #ac4 ,you1 ,,force and ,,power1 have done your destined task3 ,and naught impedes the work of other hands4 #caa ,,introduction4 ,,we enter now upon a new region of the human mind4 ,in passing from ,astronomy to ,mechanics we make a transition from the formal to the physical sciences2--from time and space to force and matter2--from phenomena to causes4 ,hitherto we have been concerned only with the paths and orbits1 the periods and cycles1 the angles and distances1 of the objects to which our sciences applied1 namely1 the heavenly bodies4 ,how these motions are produced2--by what agencies1 impulses1 powers1 they are determined to be what they are2--of what nature are the objects themselves2--are speculations which we have hitherto not dwelt upon4 ,the history of such speculations now comes before us2 but1 in the first place1 we must consider the history of speculations concerning motion in general1 terrestrial as well as celestial4 ,we must first attend to ,mechanics1 and afterwards return to ,physical ,astronomy4 ,in the same way in which the development of ,pure ,mathematics1 which began with the ,greeks1 was a necessary condition of the progress of ,formal ,astronomy1 the creation of the science of ,mechanics now became necessary to the formation and progress of ,physical ,astronomy4 ,geometry and ,mechanics were studied for their own sakes2 but they also supplied ideas1 language1 and reasoning to other sciences4 ,if the ,greeks had not cultivated ,conic ,sections1 ,kepler could not have superseded ,ptolemy2 if the ,greeks had cultivated ,dynamics1#af ,kepler might have anticipated ,newton4 #cab ,note #af3 ,dynamics is the science which treats of the ,motions of ,bodies2 ,statics is the science which treats of the ,pressure of ,bodies which are in equilibrium1 and therefore at rest4 ,,chapter ,i4 ,,prelude ,,to ,,the ,,epoch ,,of ,,galileo4 ,sect4 #a4--,prelude to the ,science of ,statics4 ,,some steps in the science of ,motion1 or rather in the science of ,equilibrium1 had been made by the ancients1 as we have seen4 ,archimedes established satisfactorily the doctrine of the ,lever1 some important properties of the ,centre of ,gravity1 and the fundamental proposition of ,hydrostatics4 ,but this beginning led to no permanent progress4 ,whether the distinction between the principles of the doctrine of ,equilibrium and of ,motion was clearly seen by ,archimedes1 we do not know2 but it never was caught hold of by any of the other writers of antiquity1 or by those of the ,stationary ,period4 ,what was still worse1 the point which ,archimedes had won was not steadily maintained4 ,we have given some examples of the general ignorance of the ,greek philosophers on such subjects1 in noticing the strange manner in which ,aristotle refers to mathematical properties1 in order to account for the equilibrium of a lever1 and the attitude of a man rising from a chair4 ,and we have seen1 in speaking of the indistinct ideas of the ,stationary ,period1 that the attempts which were made to extend the statical doctrine of ,archimedes1 failed1 in such a manner as to show that his followers had not clearly apprehended the idea on which his reasoning altogether depended4 ,the clouds which he had1 for a moment1 cloven in his advance1 closed after him1 and the former dimness and confusion settled again on the land4 ,this dimness and confusion1 with respect to all subjects of mechanical reasoning1 prevailed still1 at the period we now have to consider2 namely1 the period of the first promulgation of the ,copernican opinions4 ,this is so important a point that ,i must illustrate it further4 ,certain general notions of the connection of cause and effect in motion1 exist in the human mind at all periods of its development1 and are implied in the formation of language and in the most familiar employments of men's thoughts4 ,but these do not constitute a science of #cac ,mechanics1 any more than the notions of square and round make a ,geometry1 or the notions of months and years make an ,astronomy4 ,the unfolding these ,notions into distinct ,ideas1 on which can be founded principles and reasonings1 is further requisite1 in order to produce a science2 and1 with respect to the doctrines of ,motion1 this was long in coming to pass2 men's thoughts remained long entangled in their primitive and unscientific confusion4 ,we may mention one or two features of this confusion1 such as we find in authors belonging to the period now under review4 ,we have already1 in speaking of the ,greek ,school ,philosophy1 noticed the attempt to explain some of the differences among ,motions1 by classifying them into ,natural ,motions and ,violent ,motions2 and we have spoken of the assertion that heavy bodies fall quicker in proportion to their greater weight4 ,these doctrines were still retained3 yet the views which they implied were essentially erroneous and unsound2 for they did not refer distinctly to a measurable ,force as the cause of all motion or change of motion2 and they confounded the causes which produce and those which preserve1 motion4 ,hence such principles did not lead immediately to any advance of knowledge1 though efforts were made to apply them1 in the cases both of terrestrial ,mechanics and of the motions of the heavenly bodies4 ,the effect of the ,inclined ,plane was one of the first1 as it was one of the most important1 propositions1 on which modern writers employed themselves4 ,it was found that a body1 when supported on a sloping surface1 might be sustained or raised by a force or exertion which would not have been able to sustain or raise it without such support4 ,and hence1 ,the ,inclined ,plane was placed in the list of ,mechanical ,powers1 or simple machines by which the efficacy of forces is increased3 the question was1 in what proportion this increase of efficiency takes place4 ,it is easily seen that the force requisite to sustain a body is smaller1 as the slope on which it rests is smaller2 ,cardan 7whose work1 ,de ,proportionibus ,numerorum1 ,motuum1 ,ponderum1 c41 was published in #aede7 asserts that the force is double when the angle of inclination is double1 and so on for other proportions2 this is probably a guess1 and is an erroneous one4 ,guido ,ubaldi1 of ,marchmont1 published at ,pesaro1 in #aegg1 a work which he called ,mechanicorum ,liber1 in which he endeavors to prove that an acute wedge will produce a greater mechanical effect than an obtuse one1 without determining in what proportion4 ,there is1 he observes1 a certain repugnance between the direction in which the side of the wedge tends to #cad move the obstacle1 and the direction in which it really does move4 ,thus the ,wedge and the ,inclined ,plane are connected in principle4 ,he also refers the ,screw to the ,inclined ,plane and the ,wedge1 in a manner which shows a just apprehension of the question4 ,benedetti 7#aehe7 treats the ,wedge in a different manner2 not exact1 but still showing some powers of thought on mechanical subjects4 ,michael ,varro1 whose ,tractatus de ,motu was published at ,geneva in #aehd1 deduces the wedge from the composition of hypothetical motions1 in a way which may appear to some persons an anticipation of the doctrine of the ,composition of ,forces4 ,there is another work on subjects of this kind1 of which several editions were published in the sixteenth century1 and which treats this matter in nearly the same way as ,varro1 and in favour of which a claim has been made#bf 7,i think an unfounded one71 as if it contained the true principle of this problem4 ,the work is ,jordanus ,nemorarius ,de ,ponderositate4 ,the date and history of this author were probably even then unknown2 for in #aeii1 ,benedetti1 correcting some of the errors of ,tartalea1 says they are taken a ,jordano quodam antiquo4 ,the book was probably a kind of school-book1 and much used2 for an edition printed at ,frankfort1 in #aecc1 is stated to be ,cum gratia et privilegio ,imperiali1 ,petro ,apiano mathematico ,ingolstadiano ad xxx annos concesso4 ,but this edition does not contain the ,inclined ,plane4 ,though those who compiled the work assert in words something like the inverse proportion of ,weights and their ,velocities1 they had not learnt at that time how to apply this maxim to the ,inclined ,plane2 nor were they ever able to render a sound reason for it4 ,in the edition of ,venice1 #aefe1 however1 such an application is attempted4 ,the reasonings are founded on the ,aristotelian assumption1 that bodies descend more quickly in proportion as they are heavier4 ,to this principle are added some others2 as1 that a body is heavier in proportion as it descends more directly to the centre1 and that1 in proportion as a body descends more obliquely1 the intercepted part of the direct descent is smaller4 ,by means of these principles1 the descending force of bodies1 on inclined planes1 was compared1 by a process1 which1 so far as it forms a line of proof at all1 is a somewhat curious example of confused and vicious reasoning4 ,when two bodies are supported on two inclined planes1 and are connected by a string passing over the junction of the planes1 so that when one descends the other ascends1 #cae they must move through equal spaces on the planes2 but on the plane which is more oblique 7that is1 more nearly horizontal71 the vertical descent will be smaller in the same proportion in which the plane is longer4 ,hence1 by the ,aristotelian principle1 the weight of the body on the longer plane is less2 and1 to produce an equality of effect1 the body must be greater in the same proportion4 ,we may observe that the ,aristotelian principle is not only false1 but is here misapplied2 for its genuine meaning is1 that when bodies fall freely by gravity1 they move quicker in proportion as they are heavier2 but the rule is here applied to the motions which bodies would have1 if they were moved by a force extraneous to their gravity4 ,the proposition was supposed by the ,aristotelians to be true of actual velocities2 it is applied by ,jordanus to virtual velocities1 without his being aware what he was doing4 ,this confusion being made1 the result is got at by taking for granted that bodies thus proved to be equally heavy1 have equal powers of descent on the inclined planes2 whereas1 in the previous part of the reasoning1 the weight was supposed to be proportional to the descent in the vertical direction4 ,it is obvious1 in all this1 that though the author had adopted the false ,aristotelian principle1 he had not settled in his own mind whether the motions of which it spoke were actual or virtual motions2--motions in the direction of the inclined plane1 or of the intercepted parts of the vertical1 corresponding to these2 nor whether the descending force of a body was something different from its weight4 ,we cannot doubt that1 if he had been required to point out1 with any exactness1 the cases to which his reasoning applied1 he would have been unable to do so2 not possessing any of those clear fundamental ,ideas of ,pressure and ,force1 on which alone any real knowledge on such subjects must depend4 ,the whole of ,jordanus's reasoning is an example of the confusion of thought of his period1 and of nothing more4 ,it no more supplied the want of some man of genius1 who should give the subject a real scientific foundation1 than ,aristotle's knowledge of the proportion of the weights on the lever superseded the necessity of ,archimedes's proof of it4 ,note #bf3 ,mr4 ,drinkwater's ,life of ,galileo1 in the ,lib4 ,usef4 ,kn4 p4 #hc4 ,we are not1 therefore1 to wonder that1 though this pretended theorem was copied by other writers1 as by ,tartalea1 in his ,quesiti et ,inventioni ,diversi1 published in #aeed1 no progress was made in the real solution of any one mechanical problem by means of it4 ,guido ,ubaldi1 who1 in #aegg1 writes in such a manner as to show that he had taken a good hold of his subject for his time1 refers to ,pappus's solution of the problem of the ,inclined ,plane1 but makes no mention of that of #caf ,jordanus and ,tartalea4#cf ,no progress was likely to occur1 till the mathematicians had distinctly recovered the genuine ,idea of ,pressure1 as a ,force producing equilibrium1 which ,archimedes had possessed1 and which was soon to reappear in ,stevinus4 ,note #cf3 ,ubaldi mentions and blames ,jordanus's way of treating the ,lever4 7,see his ,preface47 ,the properties of the ,lever had always continued known to mathematicians1 although1 in the dark period1 the superiority of the proof given by ,archimedes had not been recognized4 ,we are not to be surprised1 if reasonings like those of ,jordanus were applied to demonstrate the theories of the ,lever with apparent success4 ,writers on ,mechanics were1 as we have seen1 so vacillating in their mode of dealing with words and propositions1 that their maxims could be made to prove any thing which was already known to be true4 ,we proceed to speak of the beginning of the real progress of ,mechanics in modern times4 ,sect4 #b4--,revival of the ,scientific ,idea of ,pressure4--,stevinus4--,equilibrium of ,oblique ,forces4 ,,the doctrine of the ,centre of ,gravity was the part of the mechanical speculations of ,archimedes which was most diligently prosecuted after his time4 ,pappus and others1 among the ancients1 had solved some new problems on this subject1 and ,commandinus1 in #aefe1 published ,de ,centro ,gravitatis ,solidorum4 ,such treatises contained1 for the most part1 only mathematical consequences of the doctrines of ,archimedes2 but the mathematicians also retained a steady conviction of the mechanical property of the ,centre of ,gravity1 namely1 that all the weight of the body might be collected there1 without any change in the mechanical results2 a conviction which is closely connected with our fundamental conceptions of mechanical action4 ,such a principle1 also1 will enable us to determine the result of many simple mechanical arrangements2 for instance1 if a mathematician of those days had been asked whether a solid ball could be made of such a form1 that1 when placed on a horizontal plane1 it should go on rolling forwards without limit merely by the effect of its own weight1 he would probably have answered1 that it could not2 for that the centre of gravity of the ball would seek the lowest position it could find1 and that1 when it had found this1 the ball could have no tendency to roll any further4 ,and1 in making this assertion1 the supposed reasoner would not be #cag anticipating any wider proof of the impossibility of a perpetual motion drawn from principles subsequently discovered1 but would be referring the question to certain fundamental convictions1 which1 whether put into ,axioms or not1 inevitably accompany our mechanical conceptions4 ,in the same way1 ,stevinus of ,bruges1 in #aehf1 when he published his ,beghinselen der ,waaghconst 7,principles of ,equilibrium71 had been asked why a loop of chain1 hung over a triangular beam1 could not1 as he asserted it could not1 go on moving round and round perpetually1 by the action of its own weight1 he would probably have answered1 that the weight of the chain1 if it produced motion at all1 must have a tendency to bring it into some certain position1 and that when the chain had reached this position1 it would have no tendency to go any further2 and thus he would have reduced the impossibility of such a perpetual motion1 to the conception of gravity1 as a force tending to produce equilibrium2 a principle perfectly sound and correct4 ,upon this principle thus applied1 ,stevinus did establish the fundamental property of the ,inclined ,plane4 ,he supposed a loop of string1 loaded with fourteen equal balls at equal distances1 to hang over a triangular support which was composed of two inclined planes with a horizontal base1 and whose sides1 being unequal in the proportion of two to one1 supported four and two balls respectively4 ,he showed that this loop must hang at rest1 because any motion would only bring it into the same condition in which it was at first2 and that the festoon of eight balls which hung down below the triangle might be removed without disturbing the equilibrium2 so that four balls on the longer plane would balance two balls on the shorter plane2 or in other words1 the weights would be as the lengths of the planes intercepted by the horizontal line4 ,stevinus showed his firm possession of the truth contained in this principle1 by deducing from it the properties of forces acting in oblique directions under all kinds of conditions2 in short1 he showed his entire ability to found upon it a complete doctrine of equilibrium2 and upon his foundations1 and without any additional support1 the mathematical doctrines of ,statics might have been carried to the highest pitch of perfection they have yet reached4 ,the formation of the science was finished2 the mathematical development and exposition of it were alone open to extension and change4 #b;d ,ed4 ,simon ,stevin of ,bruges1 as he usually designates himself in the title-page of his work1 has lately become an object of general interest in his own country1 and it has been resolved to erect a #cah statue in honor of him in one of the public places of his native city4 ,he was born in #aedh1 as ,i learn from ,m4 ,quetelet's notice of him1 and died in #afbj4 ,montucla says that he died in #afcc2 misled apparently by the preface to ,albert ,girard's edition of ,stevin's works1 which was published in #afcd1 and which speaks of a death which took place in the preceding year2 but on examination it will be seen that this refers to ,girard1 not to ,stevin4 ,i ought to have mentioned1 in consideration of the importance of the proposition1 that ,stevin distinctly states the triangle of forces2 namely1 that three forces which act upon a point are in equilibrium when they are parallel and proportional to the three sides of any plane triangle4 ,this includes the principle of the ,composition of ,statical ,forces4 ,stevin also applies his principle of equilibrium to cordage1 pulleys1 funicular polygons1 and especially to the bits of bridles2 a branch of mechanics which he calls ,chalinothlipsis4 ,he has also the merit of having seen very clearly1 the distinction of statical and dynamical problems4 ,he remarks that the question1 ,what force will support a loaded wagon on an inclined plane8 is a statical question1 depending on simple conditions2 but that the question1 ,what force will move the wagon8 requires additional considerations to be introduced4 ,in ,chapter iv4 of this ,book1 ,i have noticed ,stevin's share in the rediscovery of the ,laws of the ,equilibrium of ,fluids4 ,he distinctly explains the hydrostatic paradox1 of which the discovery is generally ascribed to ,pascal4 ,earlier than ,stevinus1 ,leonardo da ,vinci must have a place among the discoverers of the ,conditions of ,equilibrium of ,oblique ,forces4 ,he published no work on this subject2 but extracts from his manuscripts have been published by ,venturi1 in his ,essai sur les ,ouvrages ,physico-,mathematiques de ,leonard da ,vinci1 avec des ,fragmens tirs de ses ,manuscrits apports d',italie1 ,paris1 #agig3 and by ,libri1 in his ,hist4 des ,sc4 ,math4 en ,italie1 #ahci4 ,i have also myself examined these manuscripts in the ,royal ,library at ,paris4 ,it appears that1 as early as #adii1 ,leonardo gave a perfectly correct statement of the proportion of the forces exerted by a cord which acts obliquely and supports a weight on a lever4 ,he distinguishes between the real lever1 and the potential levers1 that is1 the perpendiculars drawn from the centre upon the directions of the forces4 ,this is quite sound and satisfactory4 ,these views must in all probability have been sufficiently promulgated in ,italy to influence the speculations of ,galileo2 #cai whose reasonings respecting the lever much resemble those of ,leonardo4--,da ,vinci also anticipated ,galileo in asserting that the time of descent of a body down an inclined plane is to the time of descent down its vertical length in the proportion of the length of the plane to the height4 ,but this cannot1 ,i think1 have been more than a guess3 there is no vestige of a proof given4 ,the contemporaneous progress of the other branch of mechanics1 the ,doctrine of ,motion1 interfered with this independent advance of ,statics2 and to that we must now turn4 ,we may observe1 however1 that true propositions respecting the composition of forces appear to have rapidly diffused themselves4 ,the ,tractatus de ,motu of ,michael ,varro of ,geneva1 already noticed1 printed in #aehd1 had asserted1 that the forces which balance each other1 acting on the sides of a right-angled triangular wedge1 are in the proportion of the sides of the triangle2 and although this assertion does not appear to have been derived from a distinct idea of pressure1 the author had hence rightly deduced the properties of the wedge and the screw4 ,and shortly after this time1 ,galileo also established the same results on different principles4 ,in his ,treatise ,delle ,scienze ,mecaniche 7#aeib71 he refers the ,inclined ,plane to the ,lever1 in a sound and nearly satisfactory manner2 imagining a lever so placed1 that the motion of a body at the extremity of one of its arms should be in the same direction as it is upon the plane4 ,a slight modification makes this an unexceptionable proof4 ,sect4 #c4--,prelude to the ,science of ,dynamics4--,attempts at the ,first ,law of ,motion4 ,,we have already seen1 that ,aristotle divided ,motions into ,natural and ,violent4 ,cardan endeavored to improve this division by making three classes3 ,voluntary ,motion1 which is circular and uniform1 and which is intended to include the celestial motions2 ,natural ,motion1 which is stronger towards the end1 as the motion of a falling body1--this is in a straight line1 because it is motion to an end1 and nature seeks her ends by the shortest road2 and thirdly1 ,violent ,motion1 including in this term all kinds different from the former two4 ,cardan was aware that such ,violent ,motion might be produced by a very small force2 thus he asserts1 that a spherical body resting on a horizontal plane may be put in motion by any force which is sufficient to cleave the air2 for which1 however1 he erroneously assigns as a reason1 #cbj the smallness of the point of contact4#df ,but the most common mistake of this period was1 that of supposing that as force is requisite to move a body1 so a perpetual supply of force is requisite to keep it in motion4 ,the whole of what ,kepler called his physical reasoning1 depended upon this assumption4 ,he endeavored to discover the forces by which the motions of the planets about the sun might be produced2 but1 in all cases1 he considered the velocity of the planet as produced by1 and exhibiting the effect of1 a force which acted in the direction of the motion4 ,kepler's essays1 which are in this respect so feeble and unmeaning1 have sometimes been considered as disclosing some distant anticipation of ,newton's discovery of the existence and law of central forces4 ,there is1 however1 in reality1 no other connection between these speculations than that which arises from the use of the term force by the two writers in two utterly different meanings4 ,kepler's ,forces were certain imaginary qualities which appeared in the actual motion which the bodies had2 ,newton's ,forces were causes which appeared by the change of motion3 ,kepler's ,forces urged the bodies forwards2 ,newton's deflected the bodies from such a progress4 ,if ,kepler's ,forces were destroyed1 the body would instantly stop2 if ,newton's were annihilated1 the body would go on uniformly in a straight line4 ,kepler compares the action of his ,forces to the way in which a body might be driven round1 by being placed among the sails of a windmill2 ,newton's ,forces would be represented by a rope pulling the body to the centre4 ,newton's ,force is merely mutual attraction2 ,kepler's is something quite different from this2 for though he perpetually illustrates his views by the example of a magnet1 he warns us that the sun differs from the magnet in this respect1 that its force is not attractive1 but directive4#ef ,kepler's essays may with considerable reason be asserted to be an anticipation of the ,vortices of ,descartes2 but they can with no propriety whatever be said to anticipate ,newton's ,dynamical ,theory4 ,note #df3 ,in speaking of the force which would draw a body up an inclined plane he observes1 that per communem animi sententiam1 when the plane becomes horizontal1 the requisite force is nothing4 ,note #ef3 ,epitome ,astron4 ,copern4 p4 #agf4 ,the confusion of thought which prevented mathematicians from seeing the difference between producing and preserving motion1 was1 indeed1 fatal to all attempts at progress on this subject4 ,we have already noticed the perplexity in which ,aristotle involved himself1 by his endeavors to find a reason for the continued motion of a stone #cba after the moving power had ceased to act2 and that he had ascribed it to the effect of the air or other medium in which the stone moves4 ,tartalea1 whose ,nuova ,scienza is dated #aeej1 though a good pure mathematician1 is still quite in the dark on mechanical matters4 ,one of his propositions1 in the work just mentioned1 is 7,b4 i4 ,prop4 #c71 ,the more a heavy body recedes from the beginning1 or approaches the end of violent motion1 the slower and more inertly it goes2 which he applies to the horizontal motion of projectiles4 ,in like manner most other writers about this period conceived that a cannon-ball goes forwards till it loses all its projectile motion1 and then falls downwards4 ,benedetti1 who has already been mentioned1 must be considered as one of the first enlightened opponents of this and other ,aristotelian errors or puzzles4 ,in his ,speculationum ,liber 7,venice1 #aehe71 he opposes ,aristotle's mechanical opinions1 with great expressions of respect1 but in a very sweeping manner4 ,his chapter xxiv4 is headed1 ,whether this eminent man was right in his opinion concerning violent and natural motion4 ,and after stating the ,aristotelian opinion just mentioned1 that the body is impelled by the air1 he says that the air must impede rather than impel the body1 and that#ff the motion of the body1 separated from the mover1 arises by a certain natural impression from the impetuosity 7ex impetuositate7 received from the mover4 ,he adds1 that in natural motions this impetuosity continually increases by the continued action of the cause1--namely1 the propension of going to the place assigned it by nature2 and that thus the velocity increases as the body moves from the beginning of its path4 ,this statement shows a clearness of conception with regard to the cause of accelerated motion1 which ,galileo himself was long in acquiring4 ,note #ff3 ,p4 #ahd4 ,though ,benedetti was thus on the way to the ,first ,law of ,motion1--that all motion is uniform and rectilinear1 except so far as it is affected by extraneous forces2--this ,law was not likely to be either generally conceived1 or satisfactorily proved1 till the other ,laws of ,motion1 by which the action of ,forces is regulated1 had come into view4 ,hence1 though a partial apprehension of this principle had preceded the discovery of the ,laws of ,motion1 we must place the establishment of the principle in the period when those ,laws were detected and established1 the period of ,galileo and his followers4 #cbb ,,chapter ,,ii4 ,,inductive ,,epoch ,,of ,,galileo4--,,discovery ,,of ,,the ,,laws ,,of ,,motion ,,in ,,simple ,,cases4 ,sect4 #a4--;,establishment of the ,first ,law of ,motion4 ,,after mathematicians had begun to doubt or reject the authority of ,aristotle1 they were still some time in coming to the conclusion1 that the distinction of ,natural and ,violent ,motions was altogether untenable2--that the velocity of a body in motion increased or diminished in consequence of the action of extrinsic causes1 not of any property of the motion itself2--and that the apparently universal fact1 of bodies growing slower and slower1 as if by their own disposition1 till they finally stopped1 from which ,motions had been called ,violent1 arose from the action of external obstacles not immediately obvious1 as the friction and the resistance of the air when a ball runs on the ground1 and the action of gravity1 when it is thrown upwards4 ,but the truth to which they were at last led1 was1 that such causes would account for all the diminution of velocity which bodies experience when apparently left to themselves and that without such causes1 the motion of all bodies would go on forever1 in a straight line and with a uniform velocity4 ,who first announced this ,law in a general form1 it may be difficult to point out2 its exact or approximate truth was necessarily taken for granted in all complete investigations on the subject of the laws of motion of falling bodies1 and of bodies projected so as to describe curves4 ,in ,galileo's first attempt to solve the problem of falling bodies1 he did not carry his analysis back to the notion of force1 and therefore this law does not appear4 ,in #afjd he had an erroneous opinion on this subject and we do not know when he was led to the true doctrine which he published in his ,discorso1 in #afch4 ,in his third ,dialogue he gives the instance of water in a vessel1 for the purpose of showing that circular motion has a tendency to continue4 ,and in his first ,dialogue on the ,copernican ,system#gf 7published in #afcj71 he asserts #cbc ,circular ,motion alone to be naturally uniform1 and retains the distinction between ,natural and ,violent ,motion4 ,in the ,dialogues on ,mechanics1 however1 published in #afch1 but written apparently at an earlier period1 in treating of ,projectiles1#hf he asserts the true ,law4 ,mobile super planum horizontale projectum mente concipio omni secluso impedimento2 jam constat ex his qu fusius alibi dicta sunt1 illius motum equabilem et perpetuum super ipso plano futurum esse1 si planum in infinitum extendatur4 ,conceive a movable body upon a horizontal plane1 and suppose all obstacles to motion to be removed2 it is then manifest1 from what has been said more at large in another place1 that the body's motion will be uniform and perpetual upon the plane1 if the plane be indefinitely extended4 ,his pupil ,borelli1 in #affg 7in the treatise ,de ,vi ,percussionis71 states the proposition generally1 that ,velocity is1 by its nature1 uniform1 and perpetual2 and this opinion appears to have been1 at that time1 generally diffused1 as we find evidence in ,wallis and others4 ,it is commonly said that ,descartes was the first to state this generally4 ,his ,principia were published in #afdd2 but his proofs of this ,first ,law of ,motion are rather of a theological than of a mechanical kind4 ,his reason for this ,law is1#if the immutability and simplicity of the operation by which ,god preserves motion in matter4 ,for he only preserves it precisely as it is in that moment in which he preserves it1 taking no account of that which may have been previously4 ,reasoning of this abstract and priori kind1 though it may be urged in favor of true opinions after they have been inductively established1 is almost equally capable of being called in on the side of error1 as we have seen in the case of ,aristotle's philosophy4 ,we ought not1 however1 to forget that the reference to these abstract and priori principles is an indication of the absolute universality and necessity which we look for in complete ,sciences1 and a result of those faculties by which such ,science is rendered possible1 and suitable to man's intellectual nature4 ,note #gf3 ,dial4 9999i4 p4 #dj4 ,note #hf3 9999p4 #ada4 ,note #if3 ,princip4 p4 #cd4 ,the induction by which the ,first ,law of ,motion is established1 consists1 as induction consists in all cases1 in conceiving clearly the ,law1 and in perceiving the subordination of ,facts to it4 ,but the ,law speaks of bodies not acted upon by any external force1--a case which never occurs in fact2 and the difficulty of the step consisted in bringing all the common cases in which motion is gradually extinguished1 under the notion of the action of a retarding force4 ,in order to do this1 #cbd ,hooke and others showed that1 by diminishing the obvious resistances1 the retardation also became less2 and men were gradually led to a distinct appreciation of the ,resistance1 ,friction1 c41 which1 in all terrestrial motions1 prevent the ,law from being evident2 and thus they at last established by experiment a ,law which cannot be experimentally exemplified4 ,the natural uniformity of motion was proved by examining all kinds of cases in which motion was not uniform4 ,men culled the abstract ,rule out of the concrete ,experiment2 although the ,rule was1 in every case1 mixed with other ,rules1 and each ,rule could be collected from the ,experiment only by supposing the others known4 ,the perfect simplicity which we necessarily seek for in a law of nature1 enables us to disentangle the complexity which this combination appears at first sight to occasion4 ,the ,first ,law of ,motion asserts that the motion of a body1 when left to itself will not only be uniform1 but rectilinear also4 ,this latter part of the law is indeed obvious of itself as soon as we conceive a body detached from all special reference to external points and objects4 ,yet1 as we have seen1 ,galileo asserted that the naturally uniform motion of bodies was that which takes place in a circle4 ,benedetti1 however1 in #aehe1 had entertained sound notions on this subject4 ,in commenting on ,aristotle's question1 why we obtain an advantage in throwing by using a sling1 he says1#ajf that the body1 when whirled round1 tends to go on in a straight line4 ,in ,galileo's second ,dialogue1 he makes one of his interlocutors 7,simplicio71 when appealed to on this subject1 after thinking intently for a little while1 give the same opinion2 and the principle is1 from this time1 taken for granted by the authors who treat of the motion of projectiles4 ,descartes1 as might be supposed1 gives the same reason for this as for the other part of the law1 namely1 the immutability of the ,deity4 ,note #ajf3 ,corpus vellet recta iter peragere4 9999,speculationum ,liber1 p4 #afj4 ,sect4 #b4--;,formation and ,application of the ,notion of ,accelerating ,force4--,laws of ,falling ,bodies4 ,,we have seen how rude and vague were the attempts of ,aristotle and his followers to obtain a philosophy of bodies falling downwards or thrown in any direction4 ,if the ,first ,law of ,motion had been clearly known1 it would then1 perhaps1 have been seen that the way to understand and analyze the motion of any body1 is to consider the #cbe ,causes of change of motion which at each instant operate upon it2 and thus men would have been led to the notion of ,accelerating ,forces1 that is1 ,forces which act upon bodies already in motion1 and accelerate1 retard1 or deflect their motions4 ,it was1 however1 only after many attempts that they reached this point4 ,they began by considering the whole motion with reference to certain ill-defined abstract ,notions1 instead of considering1 with a clear apprehension of the conditions of ,causation1 the successive parts of which the motion consists4 ,thus1 they spoke of the tendency of bodies to the ,centre1 or to their ,own ,place2--of ,projecting ,force1 of ,impetus1 of ,retraction2--with little or no profit to knowledge4 ,the indistinctness of their notions may1 perhaps1 be judged of from their speculations concerning projectiles4 ,santbach1#aaf in #aefa1 imagined that a body thrown with great velocity1 as1 for instance1 a ball from a cannon1 went in a straight line till all its velocity was exhausted1 and then fell directly downwards4 ,he has written a treatise on gunnery1 founded on this absurd assumption4 ,to this succeeded another doctrine1 which1 though not much more philosophical than the former1 agreed much better with the phenomena4 ,nicolo ,tartalea 7,nuova ,scienza1 ,venice1 #aeej2 ,quesiti et ,inventioni ,diversi1 #aeed7 and 9999,gualter ,rivius 7,architectura1 c41 ,basil1 #aehb7 represented the path of a cannon-ball as consisting1 first of a straight line in the direction of the original projection1 then of an arc of a circle in which it went on till its motion became vertical downwards1 and then of a vertical line in which it continued to fall4 ,the latter of these writers1 however1 was aware that the path must1 from the first1 be a curve2 and treated it as a straight line1 only because the curvature is very slight4 ,even ,santbach's figure represents the path of the ball as partially descending before its final fall1 but then it descends by steps1 not in a curve4 ,santbach1 therefore1 did not conceive the ,composition of the effect of gravity with the existing motion1 but supposed them to act alternately2 ,rivius1 however1 understood this ,composition1 and saw that gravity must act as a deflecting force at every point of the path4 ,galileo1 in his second ,dialogue1#abf makes ,simplicius come to the same conclusion4 ,since1 he says1 there is nothing to support the body1 when it quits that which projects it1 it cannot be but that its proper gravity must operate1 and it must immediately begin to decline downwards4 #cbf ,note #aaf3 ,problematum ,astronomicorum et ,geometricorum ,sectiones vii4 c4 c4 ,auctore ,daniele ,santbach1 ,noviomago4 ,basile1 #aefa4 ,note #abf3 ,p4 #adg4 ,the ,force of ,gravity which thus produces deflection and curvature in the path of a body thrown obliquely1 constantly increases the velocity of a body when it falls vertically downwards4 ,the universality of this increase was obvious1 both from reasoning and in fact2 the law of it could only be discovered by closer consideration2 and the full analysis of the problem required a distinct measure of the quantity of ,accelerating ,force4 ,galileo1 who first solved this problem1 began by viewing it as a question of fact1 but conjectured the solution by taking for granted that the rule must be the simplest possible4 ,bodies1 he says1#acf will fall in the most simple way1 because ,natural ,motions are always the most simple4 ,when a stone falls1 if we consider the matter attentively1 we shall find that there is no addition1 no increase1 of the velocity more simple than that which is always added in the same manner1 that is1 when equal additions take place in equal times2 which we shall easily understand if we attend to the close connection of motion and time4 ,from this ,law1 thus assumed1 he deduced that the spaces described from the beginning of the motion must be as the squares of the times2 and1 again1 assuming that the laws of descent for balls rolling down inclined planes1 must be the same as for bodies falling freely1 he verified this conclusion by experiment4 ,note #acf3 ,dial4 ,sc4 iv4 p4 #ia4 ,it will1 perhaps1 occur to the reader that this argument1 from the simplicity of the assumed law1 is somewhat insecure4 ,it is not always easy for us to discern what that greatest simplicity is1 which nature adopts in her laws4 ,accordingly1 ,galileo was led wrong by this way of viewing the subject before he was led right4 ,he at first supposed1 that the ,velocity which the body had acquired at any point must be proportional to the ,space described from the point where the motion began4 ,this false law is as simple in its enunciation as the true law1 that the ,velocity is proportional to the ,time3 it had been asserted as the true law by ,m4 ,varro 7,de ,motu ,tractatus1 ,genev1 #aehd71 and by ,baliani1 a gentleman of ,genoa1 who published it in #afch4 ,it was1 however1 soon rejected by ,galileo1 though it was afterwards taken up and defended by ,casrus1 one of ,galileo's opponents4 ,it so happens1 indeed1 that the false law is not only at variance with fact1 but with itself3 it involves a mathematical self-contradiction4 ,this circumstance1 however1 was accidental3 it would be easy to state laws of the increase of velocity which should be simple1 and yet false in fact1 though quite possible in their own nature4 #cbg ,the ,law of ,velocity was hitherto1 as we have seen1 treated as a law of phenomena1 without reference to the ,causes of the law4 ,the cause of the acceleration of the motions of falling bodies is not1 ,galileo observes1 a necessary part of the investigation4 ,opinions are different4 ,some refer it to the approach to the centre2 others say that there is a certain extension of the centrical medium1 which1 closing behind the body1 pushes it forwards4 ,for the present1 it is enough for us to demonstrate certain properties of ,accelerated ,motion1 the acceleration being according to the very simple ,law1 that the ,velocity is proportional to the ,time4 ,and if we find that the properties of such motion are verified by the motions of bodies descending freely1 we may suppose that the assumption agrees with the laws of bodies falling freely by the action of gravity4#adf ,note #adf3 ,gal4 ,op4 iii4 #ia1 #ib4 ,it was1 however1 an easy step to conceive this acceleration as caused by the continual action of ,gravity4 ,this account had already been given by ,benedetti1 as we have seen4 ,when it was once adopted1 ,gravity was considered as a constant or uniform force2 on this point1 indeed1 the adherents of the law of ,galileo and of that of ,casrus were agreed2 but the question was1 what is a ,uniform ,force8 ,the answer which ,galileo was led to give was obviously this2--that is a ,uniform ,force which generates equal velocities in equal successive times2 and this principle leads at once to the doctrine1 that ,forces are to be compared by comparing the ,velocities generated by them in equal times4 ,though1 however1 this was a consequence of the rule by which ,gravity is represented as a ,uniform ,force1 the subject presents some difficulty at first sight4 ,it is not immediately obvious that we may thus measure forces by the ,velocity added in a given time1 without taking into account the velocity they have already4 ,if we communicate velocity to a body by the hand or by a spring1 the effect we produce in a second of time is lessened1 when the body has already a velocity which withdraws it from the pressure of the agent4 ,but it appears that this is not so in the case of gravity2 the velocity added in one second is the same1 whatever downward motion the body already possesses4 ,a body falling from rest acquires a velocity1 in one second1 of thirty-two feet2 and if a cannon-ball were shot downwards with a velocity of #ajjj feet a second1 it would equally1 at the end of one second1 have received an accession of #cb feet to its velocity4 ,this conception of ,gravity as a ,uniform ,force1--as constantly and #cbh equally increasing the velocity of a descending body1--will become clear by a little attention2 but it undoubtedly presents difficulty at first4 ,accordingly1 we find that ,descartes did not accept it4 ,it is certain1 he says1 that a stone is not equally disposed to receive a new motion or increase of velocity when it is already moving very quickly1 and when it is moving slowly4 ,descartes showed1 by other expressions1 that he had not caught hold of the true notion of accelerating force4 ,thus1 he says in a letter to ,mersenne1 ,i am astonished at what you tell me1 of having found1 by experiment1 that bodies thrown up in the air take neither more nor less time to rise than to fall again2 and you will excuse me if ,i say that ,i look upon the experiment as a very difficult one to make accurately4 ,yet it is clear from the ,notion of a ,constant ,force that 7omitting the resistance of the air7 this equality must take place2 for the ,force which will gradually destroy the whole velocity in a certain time in ascending1 will1 in the same time1 generate again the same velocity by the same gradations inverted2 and therefore the same space will be passed over in the same time in the descent and in the ascent4 ,another difficulty arose from a necessary consequence of the ,laws of ,falling ,bodies thus established2--the proposition1 namely1 that in acquiring its motion1 a body passes through every intermediate degree of velocity1 from the smallest conceivable1 up to that which it at last acquires4 ,when a body falls from rest1 it begins to fall with no velocity2 the velocity increases with the time2 and in one-thousandth part of a second1 the body has only acquired one-thousandth part of the velocity which it has at the end of one second4 ,this is certain1 and manifest on consideration2 yet there was at first much difficulty raised on the subject of this assertion2 and disputes took place concerning the velocity with which a body begins to fall4 ,on this subject also ,descartes did not form clear notions4 ,he writes to a correspondent1 ,i have been revising my notes on ,galileo1 in which ,i have not said expressly that falling bodies do not pass through every degree of slowness1 but ,i said that this cannot be known without knowing what ,weight is1 which comes to the same thing2 as to your example1 ,i grant that it proves that every degree of velocity is infinitely divisible1 but not that a falling body actually passes through all these divisions4 ,the ,principles of the ,motion of ,falling ,bodies being thus established by ,galileo1 the ,deduction of the principal mathematical consequences was1 as is usual1 effected with great rapidity1 and is to be found #cbi in his works1 and in those of his scholars and successors4 ,the motion of bodies falling freely was1 however1 in such treatises1 generally combined with the motion of bodies ,falling along ,inclined ,planes2 a part of the theory of which we have still to speak4 ,the ,notion of ,accelerating ,force and of its operation1 once formed1 was naturally applied in other cases than that of bodies falling freely4 ,the different velocities with which heavy and light bodies fall were explained by the different resistance of the air1 which diminishes the accelerating force2#aef and it was boldly asserted1 that in a vacuum a lock of wool and a piece of lead would fall equally quickly4 ,it was also maintained#aff that any falling body1 however large and heavy1 would always have its velocity in some degree diminished by the air in which it falls1 and would at last be reduced to a state of uniform motion1 as soon as the resistance upwards became equal to the accelerating force downwards4 ,though the law of progress of a body to this limiting velocity was not made out till the ,principia of ,newton appeared1 the views on which ,galileo made this assertion are perfectly sound1 and show that he had clearly conceived the nature and operation of accelerating and retarding force4 ,note #aef3 ,galileo1 iii4 #dc4 ,note #aff3 iii4 #ed4 ,when ,uniform ,accelerating ,forces had once been mastered1 there remained only mathematical difficulties in the treatment of ,variable ,forces4 ,a ,variable ,force was measured by the ,limit of the increment of the ,velocity1 compared with the increment of the ,time2 just as a ,variable ,velocity was measured by the ,limit of the increment of the ,space compared with that of the ,time4 ,with this introduction of the ,notion of ,limits1 we are1 of course1 led to the ,higher ,geometry1 either in its geometrical or its analytical form4 ,the general laws of bodies falling by the action of any ,variable ,forces were given by ,newton in the ,seventh ,section of the ,principia4 ,the subject is there1 according to ,newton's preference of geometrical methods1 treated by means of the ,quadrature of ,curves2 the ,doctrine of ,limits being exhibited in a peculiar manner in the ,first ,section of the work1 in order to prepare the way for such applications of it4 ,leibnitz1 the ,bernouillis1 ,euler1 and since their time1 many other mathematicians1 have treated such questions by means of the analytical method of limits1 the ,differential ,calculus4 ,the ,rectilinear ,motion of bodies acted upon by variable forces is1 of course1 a simpler problem than their ,curvilinear ,motion1 to which we have now to proceed4 ,but it #ccj may be remarked that ,newton1 having established the laws of ,curvilinear ,motion independently1 has1 in a great part of his ,seventh ,section1 deduced the simpler case of the ,rectilinear ,motion from the move complex problem1 by reasonings of great ingenuity and beauty4 ,sect4 #c4--;,establishment of the ,second ,law of ,motion4--,curvilinear ,motions4 ,a ,,slight degree of distinctness in men's mechanical notions enabled them to perceive1 as we have already explained1 that a body which traces a curved line must be urged by some force1 by which it is constantly made to deviate from that rectilinear path1 which it would pursue if acted upon by no force4 ,thus1 when a body is made to describe a circle1 as when a stone is whirled round in a sling1 we find that the string does exert such a force on the stone2 for the string is stretched by the effort1 and if it be too slender1 it may thus be broken4 ,this centrifugal force of bodies moving in circles was noticed even by the ancients4 ,the effect of force to produce curvilinear motion also appears in the paths described by projectiles4 ,we have already seen that though ,tartalea did not perceive this correctly1 ,rivius1 about the same time1 did4 ,to see that a transverse force would produce a curve1 was one step2 to determine what the curve is1 was another step1 which involved the discovery of the ,second ,law of ,motion4 ,this step was made by ,galileo4 ,in his ,dialogues on ,motion1 he asserts that a body projected horizontally will retain a uniform motion in the horizontal direction1 and will have1 compounded with this1 a uniformly accelerated motion downwards1 that is1 the motion of a body falling vertically from rest2 and will thus describe the curve called a parabola4 ,the ,second ,law of ,motion consists of this assertion in a general form2--namely1 that in all cases the motion which the force will produce is compounded with the motion which the body previously has4 ,this was not obvious2 for ,cardan had maintained1#agf that if a body is moved by two motions at once1 it will come to the place resulting from their composition slower than by either of them4 ,the proof of the truth of the law to ,galileo's mind was1 so far as we collect from the ,dialogue itself1 the simplicity of the supposition1 and his clear perception of the causes which1 in some cases1 produced an obvious deviation in practice #cca from this theoretical result4 ,for it may be observed1 that the curvilinear paths ascribed to military projectiles by ,rivius and ,tartalea1 and by other writers who followed them1 as ,digges and ,norton in our own country1 though utterly different from the theoretical form1 the parabola1 do1 in fact1 approach nearer the true paths of a cannon or musket ball than a parabola would do2 and this approximation more especially exists in that which at first sight appears most absurd in the old theory2 namely1 the assertion that the ball1 which ascends in a sloping direction1 finally descends vertically4 ,in consequence of the resistance of the air1 this is really the path of a projectile2 and when the velocity is very great1 as in military projectiles1 the deviation from the parabolic form is very manifest4 ,this cause of discrepancy between the theory1 which does not take resistance into the account1 and the fact1 ,galileo perceived2 and accordingly he says1#ahf that the velocities of the projectiles1 in such cases1 may be considered as excessive and supernatural4 ,with the due allowance to such causes1 he maintained that his theory was verified1 and might be applied in practice4 ,such practical applications of the doctrine of projectiles no doubt had a share in establishing the truth of ,galileo's views4 ,we must not forget1 however1 that the full establishment of this second law of motion was the result of the theoretical and experimental discussions concerning the motion of the earth3 its fortunes were involved in those of the ,copernican system2 and it shared the triumph of that doctrine4 ,this triumph was already decisive1 indeed1 in the time of ,galileo1 but not complete till the time of ,newton4 ,note #agf3 ,op4 vol4 iv4 p4 #dij4 ,note #ahf3 ,op4 vol4 iii4 p4 #adg4 ,sect4 #d4--;,generalization of the ,laws of ,equilibrium4--,principle of ,virtual ,velocities4 ,,it was known1 even as early as ,aristotle1 that the two weights which balance each other on the lever1 if they move at all1 move with velocities which are in the inverse proportions of the weights4 ,the peculiar resources of the ,greek language1 which could state this relation of inverse proportionality in a single word 771 fixed it in men's minds1 and prompted them to generalize from this property4 ,such attempts were at first made with indistinct ideas1 and on conjecture only1 and had1 therefore1 no scientific value4 ,this is the judgment which we must pass on the book of ,jordanus ,nemorarius1 which #ccb we have already mentioned4 ,its reasonings are professedly on ,aristotelian principles1 and exhibit the common ,aristotelian absence of all distinct mechanical ideas4 ,but in ,varro1 whose ,tractatus de ,motu appeared in #aehd1 we find the principle1 in a general form1 not satisfactorily proved1 indeed1 but much more distinctly conceived4 ,this is his first theorem3 ,duarum virium connexarum quarum 7si moveantur7 motus erunt ipsis proportionales1 neutra alteram movebit1 sed equilibrium facient4 ,the proof offered of this is1 that the resistance to a force is as the motion produced2 and1 as we have seen1 the theorem is rightly applied in the example of the wedge4 ,from this time it appears to have been usual to prove the properties of machines by means of this principle4 ,this is done1 for instance1 in ,les ,raisons des ,forces ,mouvantes1 the production of ,solomon de ,caus1 engineer to the ,elector ,palatine1 published at ,antwerp in #afaf2 in which the effect of ,toothed-,wheels and of the ,screw is determined in this manner1 but the ,inclined ,plane is not treated of4 ,the same is the case in ,bishop ,wilkins's ,mathematical ,magic1 in #afdh4 ,when the true doctrine of the ,inclined ,plane had been established1 the laws of equilibrium for all the simple machines or ,mechanical ,powers1 as they had usually been enumerated in books on ,mechanics1 were brought into view2 for it was easy to see that the ,wedge and the ,screw involved the same principle as the ,inclined ,plane1 and the ,pulley could obviously be reduced to the ,lever4 ,it was1 also1 not difficult for a person with clear mechanical ideas to perceive how any other combination of bodies1 on which pressure and traction are exerted1 may be reduced to these simple machines1 so as to disclose the relation of the forces4 ,hence by the discovery of ,stevinus1 all problems of equilibrium were essentially solved4 ,the conjectural generalization of the property of the lever1 which we have just mentioned1 enabled mathematicians to express the solution of all these problems by means of one proposition4 ,this was done by saying1 that in raising a weight by any machine1 we lose in ,time what we gain in ,force2 the weight raised moves as much slower than the power1 as it is larger than the power4 ,this was explained with great clearness by ,galileo1 in the preface to his ,treatise on ,mechanical ,science1 published in #aeib4 ,the motions1 however1 which we here suppose the parts of the machine to have1 are not motions which the forces produce2 for at present we are dealing with the case in which the forces balance each other1 and therefore produce no motion4 ,but we ascribe to the #ccc ,weights and ,powers hypothetical motions1 arising from some other cause2 and then1 by the construction of the machine1 the velocities of the ,weights and ,powers must have certain definite ratios4 ,these velocities1 being thus hypothetically supposed and not actually produced1 are called ,virtual ,velocities4 ,and the general law of equilibrium is1 that in any machine1 the ,weights which balance each other1 are reciprocally to each other as their ,virtual ,velocities4 ,this is called the ,principle of ,virtual ,velocities4 ,this ,principle 7which was afterwards still further generalized7 is1 by some of the admirers of ,galileo1 dwelt upon as one of his great services to ,mechanics4 ,but if we examine it more nearly1 we shall see that it has not much importance in our history4 ,it is a generalization1 but a generalization established rather by enumeration of cases1 than by any induction proceeding upon one distinct ,idea1 like those generalizations of ,facts by which ,laws are primarily established4 ,it rather serves verbally to conjoin ,laws previously known1 than to exhibit a connection in them3 it is rather a help for the memory than a proof for the reason4 ,the ,principle of ,virtual ,velocities is so far from implying any clear possession of mechanical ideas1 that any one who knows the property of the ,lever1 whether he is capable of seeing the reason for it or not1 can see that the greater weight moves slower in the exact proportion of its greater magnitude4 ,accordingly1 ,aristotle1 whose entire want of sound mechanical views we have shown1 has yet noticed this truth4 ,when ,galileo treats of it1 instead of offering any reasons which could independently establish this principle1 he gives his readers a number of analogies and illustrations1 many of them very loose ones4 ,thus the raising a great weight by a small force1 he illustrates by supposing the weight broken into many small parts1 and conceiving those parts raised one by one4 ,by other persons1 the analogy1 already intimated1 of gain and loss is referred to as an argument for the principle in question4 ,such images may please the fancy1 but they cannot be accepted as mechanical reasons4 ,since ,galileo neither first enunciated this rule1 nor ever proved it as an independent principle of ,mechanics1 we cannot consider the discovery of it as one of his mechanical achievements4 ,still less can we compare his reference to this principle with ,stevinus's proof of the ,inclined ,plane2 which1 as we have seen1 was rigorously inferred from the sound axiom1 that a body cannot put itself in motion4 ,if we were to assent to the really self-evident axioms of ,stevinus1 only in virtue #ccd of the unproved verbal generalization of ,galileo1 we should be in great danger of allowing ourselves to be referred successively from one truth to another1 without any reasonable hope of ever arriving at any thing ultimate and fundamental4 ,but though this ,principle of ,virtual ,velocity cannot be looked upon as a great discovery of ,galileo1 it is a highly useful rule2 and the various forms under which he and his successors urged it1 tended much to dissipate the vague wonder with which the effects of machines had been looked upon2 and thus to diffuse sounder and clearer notions on such subjects4 ,the ,principle of ,virtual ,velocities also affected the progress of mechanical science in another way3 it suggested some of the analogies by the aid of which the ,third ,law of ,motion was made out2 leading to the adoption of the notion of ,momentum as the arithmetical product of weight and velocity4 ,since on a machine on which a weight of two pounds at one part balances three pounds at another part1 the former weight would move through three inches while the latter would move through two inches2 we see 7since three multiplied into two is equal to two multiplied into three7 that the ,product of the weight and the velocity is the same for the two balancing weights2 and if we call this ,product ,momentum1 the ,law of ,equilibrium is1 that when two weights balance on a machine1 the ,momentum of the two would be the same1 if they were put in motion4 ,the ,notion of ,momentum was here employed in connection with ,virtual ,velocities2 but it also came under consideration in treating of ,actual ,velocities1 as we shall soon see4 ,sect4 #e4--;,attempts at the ,third ,law of ,motion4--,notion of ,momentum4 ,,in the questions we have hitherto had to consider respecting ,motion1 no regard is had to the ,size of the body moved1 but only to the ,velocity and ,direction of the motion4 ,we must now trace the progress of knowledge respecting the mode in which the ,mass of the body influences the effect of ,force4 ,this is a more difficult and complex branch of the subject2 but it is one which requires to be noticed1 as obviously as the former4 ,questions belonging to this department of ,mechanics1 as well as to the others1 occur in ,aristotle's ,mechanical ,problems4 ,why1 says he1 is it1 that neither very small nor very large bodies go far when we throw them2 but1 in order that this may #cce happen1 the thing thrown must have a certain proportion to the agent which throws it8 ,is it that what is thrown or pushed must react#aif against that which pushes it2 and that a body so large as not to yield at all1 or so small as to yield entirely1 and not to react1 produces no throw or push8 ,the same confusion of ideas prevailed after his time2 and mechanical questions were in vain discussed by means of general and abstract terms1 employed with no distinct and steady meaning2 such as impetus1 power1 momentum1 virtue1 energy1 and the like4 ,from some of these speculations we may judge how thorough the confusion in men's heads had become4 ,cardan perplexes himself with the difficulty1 already mentioned1 of the comparison of the forces of bodies at rest and in motion4 ,if the ,force of a body depends on its velocity1 as it appears to do1 how is it that a body at rest has any ,force at all1 and how can it resist the slightest effort1 or exert any pressure8 ,he flatters himself that he solves the question1 by asserting that bodies at rest have an occult motion4 ,corpus movetur occulto motu quiescendo4--,another puzzle1 with which he appears to distress himself rather more wantonly1 is this3 ,if one man can draw half of a certain weight1 and another man also one half2 when the two act together1 these proportions should be compounded2 so that they ought to be able to draw one half of one half1 or one quarter only4 ,the talent which ingenious men had for getting into such perplexities1 was certainly at one time very great4 ,arriaga1#bjf who wrote in #afci1 is troubled to discover how several flat weights1 lying one upon another on a board1 should produce a greater pressure than the lowest one alone produces1 since that alone touches the board4 ,among other solutions1 he suggests that the board affects the upper weight1 which it does not touch1 by determining its ubication1 or whereness4 ,note #aif3 4 ,note #bjf3 ,rod4 de ,arriaga1 ,cursus ,philosophicus4 ,paris1 #afci4 ,aristotle's doctrine1 that a body ten times as heavy as another1 will fall ten times as fast1 is another instance of the confusion of ,statical and ,dynamical ,forces3 the ,force of the greater body1 while at rest1 is ten times as great as that of the other2 but the ,force as measured by the velocity produced1 is equal in the two cases4 ,the two bodies would fall downwards with the same rapidity1 except so far as they are affected by accidental causes4 ,the merit of proving this by experiment1 and thus refuting the ,aristotelian dogma1 is usually ascribed to ,galileo1 who made his experiment from the famous leaning tower of ,pisa1 about #aeij4 ,but others about the same time had not #ccf overlooked so obvious a fact--,f4 ,piccolomini1 in his ,liber ,scienti de ,natura1 published at ,padua1 in #aeig1 says1 ,on the subject of the motion of heavy and light bodies1 ,aristotle has put forth various opinions1 which are contrary to sense and experience1 and has delivered rules concerning the proportion of quickness and slowness1 which are palpably false4 ,for a stone twice as great does not move twice as fast4 ,and ,stevinus1 in the ,appendix to his ,statics1 describes his having made the experiment1 and speaks with great correctness of the apparent deviations from the rule1 arising from the resistance of the air4 ,indeed1 the result followed by very obvious reasoning2 for ten bricks1 in contact with each other1 side by side1 would obviously fall in the same time as one2 and these might be conceived to form a body ten times as large as one of them4 ,accordingly1 ,benedetti1 in #aehe1 reasons in this manner with regard to bodies of different size1 though he retains ,aristotle's error as to the different velocity of bodies of different density4 ,the next step in this subject is more clearly due to ,galileo2 he discovered the true proportion which the ,accelerating ,force of a body falling down an inclined plane bears to the ,accelerating ,force of the same body falling freely4 ,this was at first a happy conjecture2 it was then confirmed by experiments1 and1 finally1 after some hesitation1 it was referred to its true principle1 the ,third ,law of ,motion1 with proper elementary simplicity4 ,the ,principle here spoken of is this3--that for the same body1 the ,dynamical effect of force is as the ,statical effect2 that is1 the ,velocity which any force generates in a given time when it puts the body in motion1 is proportional to the ,pressure which the same force produces in a body at rest4 ,the ,principle1 so stated1 appears very simple and obvious2 yet this was not the form in which it suggested itself either to ,galileo or to other persons who sought to prove it4 ,galileo1 in his ,dialogues on ,motion1 assumes1 as his fundamental proposition on this subject1 one much less evident than that we have quoted1 but one in which that is involved4 ,his ,postulate is1#baf that when the same body falls down different planes of the same height1 the velocities acquired are equal4 ,he confirms and illustrates this by a very ingenious experiment on a pendulum1 showing that the weight swings to the same height whatever path it be compelled to follow4 ,torricelli1 in his treatise published #afdd1 says that he had heard that ,galileo had1 towards the end of his life1 proved his #ccg assumption1 but that1 not having seen the proof1 he will give his own4 ,in this he refers us to the right principle1 but appears not distinctly to conceive the proof1 since he estimates momentum indiscriminately by the statical ,pressure of a body1 and by its ,velocity when in motion2 as if these two quantities were self-evidently equal4 ,huyghens1 in #afgc1 expresses himself dissatisfied with the proof by which ,galileo's assumption was supported in the later editions of his works4 ,his own proof rests on this principle2--that if a body fall down one inclined plane1 and proceed up another with the velocity thus acquired1 it cannot1 under any circumstances1 ascend to a higher position than that from which it fell4 ,this principle coincides very nearly with ,galileo's experimental illustration4 ,in truth1 however1 ,galileo's principle1 which ,huyghens thus slights1 may be looked upon as a satisfactory statement of the true law namely1 that1 in the same body1 the velocity produced is as the pressure which produces it4 ,we are agreed1 he says1#bbf that1 in a movable body1 the impetus1 energy1 momentum1 or propension to motion1 is as great as is the force or least resistance which suffices to support it4 ,the various terms here used1 both for dynamical and statical ,force1 show that ,galileo's ideas were not confused by the ambiguity of any one term1 as appears to have happened to some mathematicians4 ,the principle thus announced1 is1 as we shall see1 one of great extent and value2 and we read with interest the circumstances of its discovery1 which are thus narrated4#bcf ,when ,viviani was studying with ,galileo1 he expressed his dissatisfaction at the want of any clear reason for ,galileo's postulate respecting the equality of velocities acquired down inclined planes of the same heights2 the consequence of which was1 that ,galileo1 as he lay1 the same night1 sleepless through indisposition1 discovered the proof which he had long sought in vain1 and introduced it in the subsequent editions4 ,it is easy to see1 by looking at the proof1 that the discoverer had had to struggle1 not for intermediate steps of reasoning between remote notions1 as in a problem of geometry1 but for a clear possession of ideas which were near each other1 and which he had not yet been able to bring into contact1 because he had not yet a sufficiently firm grasp of them4 ,such terms as ,momentum and ,force had been sources of confusion from the time of ,aristotle2 and it required considerable steadiness of thought to compare the forces of bodies at rest and in motion under the obscurity and vacillation thus produced4 #cch ,note #baf3 ,opere1 iii4 #if4 ,note #bbf3 ,galileo1 ,op4 iii4 #ajd4 ,note #bcf3 ,drinkwater1 ,life of ,galileo1 p4 #ei4 ,the term ,momentum had been introduced to express the force of bodies in motion1 before it was known what that effect was4 ,galileo1 in his ,discorso intorno alle ,cose che stanno in su l' ,acqua1 says1 that ,momentum is the force1 efficacy1 or virtue1 with which the motion moves and the body moved resists1 depending not upon weight only1 but upon the velocity1 inclination1 and any other cause of such virtue4 ,when he arrived at more precision in his views1 he determined1 as we have seen1 that1 in the same body1 the ,momentum is proportional to the ,velocity2 and1 hence it was easily seen that in different bodies it was proportional to the ,velocity and ,mass jointly4 ,the principle thus enunciated is capable of very extensive application1 and1 among other consequences1 leads to a determination of the results of the mutual ,percussion of ,bodies4 ,but though ,galileo1 like others of his predecessors and contemporaries1 had speculated concerning the problem of ,percussion1 he did not arrive at any satisfactory conclusion2 and the problem remained for the mathematicians of the next generation to solve4 ,we may here notice ,descartes and his ,laws of ,motion1 the publication of which is sometimes spoken of as an important event in the history of ,mechanics4 ,this is saying far too much4 ,the ,principia of ,descartes did little for physical science4 ,his assertion of the ,laws of ,motion1 in their most general shape1 was perhaps an improvement in form2 but his ,third ,law is false in substance4 ,descartes claimed several of the discoveries of ,galileo and others of his contemporaries2 but we cannot assent to such claims1 when we find that1 as we shall see1 he did not understand1 or would not apply1 the ,laws of ,motion when he had them before him4 ,if we were to compare ,descartes with ,galileo1 we might say1 that of the mechanical truths which were easily attainable in the beginning of the seventeenth century1 ,galileo took hold of as many1 and ,descartes of as few1 as was well possible for a man of genius4 #b;d ,ed4 ,the following remarks of ,m4 ,libri appear to be just4 ,after giving an account of the doctrines put forth on the subject of ,astronomy1 ,mechanics1 and other branches of science1 by ,leonardo da ,vinci1 ,fracastoro1 ,maurolycus1 ,commandinus1 ,benedetti1 he adds 7,hist4 des ,sciences ,mathmatiques en ,italie1 t4 iii4 p4 #aca73 ,this short analysis is sufficient to show that1 at the period at which we are arrived1 ,aristotle no longer reigned unquestioned in the ,italian ,schools4 ,if we had to write the history of philosophy1 we should prove by a multitude of facts that it was the ,italians who overthrew the ancient idol of philosophers4 ,men go on incessantly repeating that the #cci struggle was begun by ,descartes1 and they proclaim him the legislator of modern philosophers4 ,but when we examine the philosophical writings of ,fracastoro1 of ,benedetti1 of ,cardan1 and above all1 those of ,galileo2 when we see on all sides energetic protests raised against the peripatetic doctrines2 we ask1 what there remained for the inventor of vortices to do1 in overturning the natural philosophy of ,aristotle8 ,in addition to this1 the memorable labors of the ,school of ,cosenza1 of ,telesius1 of ,giordano ,bruno1 of ,campanella2 the writings of ,patricius1 who was1 besides1 a good geometer2 of ,nizolius1 whom ,leibnitz esteemed so highly1 and of the other metaphysicians of the same epoch1--prove that the ancient philosophy had already lost its empire on that side the ,alps1 when ,descartes threw himself upon the enemy now put to the rout4 ,the yoke was cast off in ,italy1 and all ,europe had only to follow the example1 without its being necessary to give a new impulse to real science4 ,in ,england1 we are accustomed to hear ,francis ,bacon1 rather than ,descartes1 spoken of as the first great antagonist of the ,aristotelian schools1 and the legislator of modern philosophy4 ,but it is true1 both of one and the other1 that the overthrow of the ancient system had been effectively begun before their time by the practical discoverers here mentioned1 and others who1 by experiment and reasoning1 established truths inconsistent with the received ,aristotelian doctrines4 ,gilbert in ,england1 ,kepler in ,germany1 as well as ,benedetti and ,galileo in ,italy1 gave a powerful impulse to the cause of real knowledge1 before the influence of ,bacon and ,descartes had produced any general effect4 ,what ,bacon really did was this2--that by the august image which he presented of a future ,philosophy1 the rival of the ,aristotelian1 and far more powerful and extensive1 he drew to it the affections and hopes of all men of comprehensive and vigorous minds1 as well as of those who attended to special trains of discovery4 ,he announced a ,new ,method1 not merely a correction of special current errors2 he thus converted the ,insurrection into a ,revolution1 and established a new philosophical ,dynasty4 ,descartes had1 in some degree1 the same purpose2 and1 in addition to this1 he not only proclaimed himself the author of a ,new ,method1 but professed to give a complete system of the results of the ,method4 ,his physical philosophy was put forth as complete and demonstrative1 and thus involved the vices of the ancient dogmatism4 ,telesius and ,campanella had also grand notions of an entire reform in the method of philosophizing1 as ,i have noticed in the ,philosophy of the ,inductive ,sciences1 ,book xii4 #cdj ,,chapter ,,iii4 ,,sequel ,,to ,,the ,,epoch ,,of ,,galileo4--,,period ,,of ,,verification ,,and ,,deduction4 ,,the evidence on which ,galileo rested the truth of the ,laws of ,motion which he asserted1 was1 as we have seen1 the simplicity of the laws themselves1 and the agreement of their consequences with facts2 proper allowances being made for disturbing causes4 ,his successors took up and continued the task of making repeated comparisons of the theory with practice1 till no doubt remained of the exactness of the fundamental doctrines3 they also employed themselves in simplifying1 as much as possible1 the mode of stating these doctrines1 and in tracing their consequences in various problems by the aid of mathematical reasoning4 ,these employments led to the publication of various ,treatises on ,falling ,bodies1 ,inclined ,planes1 ,pendulums1 ,projectiles1 ,spouting ,fluids1 which occupied a great part of the seventeenth century4 ,the authors of these treatises may be considered as the ,school of ,galileo4 ,several of them were1 indeed1 his pupils or personal friends4 ,castelli was his disciple and astronomical assistant at ,florence1 and afterwards his correspondent4 ,torricelli was at first a pupil of ,castelli1 but became the inmate and amanuensis of ,galileo in #afda1 and succeeded him in his situation at the court of ,florence on his death1 which took place a few months afterwards4 ,viviani formed one of his family during the three last years of his life2 and surviving him and his contemporaries 7for ,viviani lived even into the eighteenth century71 has a manifest pleasure and pride in calling himself the last of the disciples of ,galileo4 ,gassendi1 an eminent ,french mathematician and professor1 visited him in #afbh2 and it shows us the extent of his reputation when we find ,milton referring thus to his travels in ,italy3#bdf ,there it was that ,i found and visited the famous ,galileo1 grown old1 a prisoner in the ,inquisition1 for thinking in astronomy otherwise than the ,franciscan and ,dominican licensers thought4 ,note #bdf3 ,speech for the ,liberty of ,unlicensed ,printing4 ,besides the above writers1 we may mention1 as persons who pursued and illustrated ,galileo's doctrines1 ,borelli1 who was professor at ,florence and ,pisa2 ,mersenne1 the correspondent of ,descartes1 who was #cda professor at ,paris2 ,wallis1 who was appointed ,savilian professor at ,oxford in #afdi1 his predecessor being ejected by the parliamentary commissioners4 ,it is not necessary for us to trace the progress of purely mathematical inventions1 which constitute a great part of the works of these authors2 but a few circumstances may be mentioned4 ,the question of the proof of the ,second ,law of ,motion was1 from the first1 identified with the controversy respecting the truth of the ,copernican ,system2 for this law supplied the true answer to the most formidable of the objections against the motion of the earth2 namely1 that if the earth were moving1 bodies which were dropt from an elevated object would be left behind by the place from which they fell4 ,this argument was reproduced in various forms by the opponents of the new doctrine2 and the answers to the argument1 though they belong to the history of ,astronomy1 and form part of the ,sequel to the ,epoch of ,copernicus1 belong more peculiarly to the history of ,mechanics1 and are events in the sequel to the ,discoveries of ,galileo4 ,so far1 indeed1 as the mechanical controversy was concerned1 the advocates of the ,second ,law of ,motion appealed1 very triumphantly1 to experiment4 ,gassendi made many experiments on this subject publicly1 of which an account is given in his ,epistol tres de ,motu ,impresso a ,motore ,translato#bef ,it appeared in these experiments1 that bodies let fall downwards1 or cast upwards1 forwards1 or backwards1 from a ship1 or chariot1 or man1 whether at rest1 or in any degree of motion1 had always the same motion relatively to the motor4 ,in the application of this principle to the system of the world1 indeed1 ,gassendi and other philosophers of his time were greatly hampered2 for the deference which religious scruples required1 did not allow them to say that the earth really moved1 but only that the physical reasons against its motion were invalid4 ,this restriction enabled ,riccioli and other writers on the geocentric side to involve the subject in metaphysical difficulties2 but the conviction of men was not permanently shaken by these1 and the ,second ,law of ,motion was soon assumed as unquestioned4 ,note #bef3 ,mont4 ii4 #aii4 ,the ,laws of the ,motion of ,falling ,bodies1 as assigned by ,galileo1 were confirmed by the reasonings of ,gassendi and ,fermat1 and the experiments of ,riccioli and ,grimaldi2 and the effect of resistance was pointed out by 9999,mersenne and ,dechales4 ,the parabolic motion of ,projectiles was more especially illustrated by experiments on the jet which spouts from an orifice in a vessel full of fluid4 ,this mode of experimenting #cdb is well adapted to attract notice1 since the curve described1 which is transient and invisible in the case of a single projectile1 becomes permanent and visible when we have a continuous stream4 ,the doctrine of the motions of fluids has always been zealously cultivated by the ,italians4 ,castelli's treatise1 ,della ,misura dell' ,acque ,corrente 7#afch71 is the first work on this subject1 and ,montucla with justice calls him the creator of a new branch of hydraulics2#bff although he mistakenly supposed the velocity of efflux to be as the depth of the orifice from the surface4 9999,mersenne and ,torricelli also pursued this subject1 and after them1 many others4 ,note #bff3 ,mont4 ii4 #bja4 ,galileo's belief in the near approximation of the curve described by a cannon-ball or musket-ball to the theoretical parabola1 was somewhat too obsequiously adopted by succeeding practical writers on artillery4 ,they underrated1 as he had done1 the effect of the resistance of the air1 which is in effect so great as entirely to change the form and properties of the curve4 ,notwithstanding this1 the parabolic theory was employed1 as in ,anderson's ,art of ,gunnery 7#afgd72 and ,blondel1 in his ,art de jeter les ,bombes 7#afhh71 not only calculated ,tables on this supposition1 but attempted to answer the objections which had been made respecting the form of the curve described4 ,it was not till a later period 7#agdj71 when ,robins made a series of careful and sagacious experiments on artillery1 and when some of the most eminent mathematicians calculated the curve1 taking into account the resistance1 that the ,theory of ,projectiles could be said to be verified in fact4 ,the ,third ,law of ,motion was still in some confusion when ,galileo died1 as we have seen4 ,the next great step made in the school of ,galileo was the determination of the ,laws of the motions of bodies in their ,direct ,impact1 so far as this impact affects the motion of translation4 ,the difficulties of the problem of ,percussion arose1 in part1 from the heterogeneous nature of ,pressure 7of a body at rest71 and ,momentum 7of a body in motion72 and1 in part1 from mixing together the effects of percussion on the parts of a body1 as1 for instance1 cutting1 bruising1 and breaking1 with its effect in moving the whole4 ,the former difficulty had been seen with some clearness by ,galileo himself4 ,in a posthumous addition to his ,mechanical ,dialogues1 he says1 ,there are two kinds of resistance in a movable body1 one internal1 as when we say it is more difficult to lift a weight of a thousand pounds than a weight of a hundred2 another respecting space1 as #cdc when we say that it requires more force to throw a stone one hundred paces than fifty4#bgf ,reasoning upon this difference1 he comes to the conclusion that the ,momentum of percussion is infinite1 since there is no resistance1 however great1 which is not overcome by a force of percussion1 however small4#bhf ,he further explains this by observing that the resistance to percussion must occupy some portion of time1 although this portion may be insensible4 ,this correct mode of removing the apparent incongruity of continuous and instantaneous force1 was a material step in the solution of the problem4 ,note #bgf3 ,op4 iii4 #baj4 ,note #bhf3 iii4 #baa4 ,the ,laws of the mutual ,impact of bodies were erroneously given by ,descartes in his ,principia2 and appear to have been first correctly stated by ,wren1 ,wallis1 and ,huyghens1 who about the same time 7#affi7 sent papers to the ,royal ,society of ,london on the subject4 ,in these solutions1 we perceive that men were gradually coming to apprehend the ,third ,law of ,motion in its most general sense2 namely1 that the ,momentum 7which is proportional to the ,mass of the body and its ,velocity jointly7 may be taken for the measure of the effect2 so that this ,momentum is as much diminished in the striking body by the resistance it experiences1 as it is increased in the body struck by the ,impact4 ,this was sometimes expressed by saying that the ,quantity of ,motion remains unaltered1 ,quantity of ,motion being used as synonymous with ,momentum4 ,newton expressed it by saying that ,action and ,reaction are equal and opposite1 which is still one of the most familiar modes of expressing the ,third ,law of ,motion4 ,in this mode of stating the ,law1 we see an example of a propensity which has prevailed very generally among mathematicians2 namely1 a disposition to present the fundamental laws of rest and of motion as if they were equally manifest1 and1 indeed1 identical4 ,the close analogy and connection which exists between the principles of equilibrium and of motion1 often led men to confound the evidence of the two2 and this confusion introduced an ambiguity in the use of words1 as we have seen in the case of ,momentum1 ,force1 and others4 ,the same may be said of ,action and ,reaction1 which have both a statical and a dynamical signification4 ,and by this means1 the most general statements of the laws of motion are made to coincide with the most general statical propositions4 ,for instance1 ,newton deduced from his principles the conclusion1 that by the mutual action of bodies1 the motion of their centre of gravity cannot be affected4 ,marriotte1 in his ,trait de la #cdd ,percussion 7#afhd71 had asserted this proposition for the case of direct impact4 ,but by the reasoners of ,newton's time1 the dynamical proposition1 that the motion of the centre of gravity is not altered by the actual free motion and impact of bodies1 was associated with the statical proposition1 that when bodies are in equilibrium1 the centre of gravity cannot be made to ascend or descend by the virtual motions of the bodies4 ,this latter is a proposition which was assumed as self-evident by ,torricelli2 but which may more philosophically be proved from elementary statical principles4 ,this disposition to identify the elementary laws of equilibrium and of motion1 led men to think too slightingly of the ancient solid and sufficient foundation of ,statics1 the doctrine of the lever4 ,when the progress of thought had opened men's minds to a more general view of the subject1 it was considered as a blemish in the science to found it on the properties of one particular machine4 ,descartes says in his ,letters1 that it is ridiculous to prove the pulley by means of the lever4 ,and ,varignon was led by similar reflections to the project of his ,nouvelle ,mcanique1 in which the whole of statics should be founded on the composition of forces4 ,this project was published in #afhg2 but the work did not appear till #agbe1 after the death of the author4 ,though the attempt to reduce the equilibrium of all machines to the composition of forces1 is philosophical and meritorious1 the attempt to reduce the composition of ,pressures to the composition of ,motions1 with which ,varignon's work is occupied1 was a retrograde step in the subject1 so far as the progress of distinct mechanical ideas was concerned4 ,thus1 at the period at which we have now arrived1 the ,principles of ,elementary ,mechanics were generally known and accepted2 and there was in the minds of mathematicians a prevalent tendency to reduce them to the most simple and comprehensive form of which they admitted4 ,the execution of this simplification and extension1 which we term the generalization of the laws1 is so important an event1 that though it forms part of the natural sequel of ,galileo1 we shall treat of it in a separate chapter4 ,but we must first bring up the history of the mechanics of fluids to the corresponding point4 #cde ,,chapter ,,iv4 ,,discovery ,,of ,,the ,,mechanical ,,principles ,,of ,,fluids4 ,sect4 #a4--,rediscovery of the ,laws of ,equilibrium of ,fluids4 ,,we have already said1 that the true laws of the equilibrium of fluids were discovered by ,archimedes1 and rediscovered by ,galileo and ,stevinus2 the intermediate time having been occupied by a vagueness and confusion of thought on physical subjects1 which made it impossible for men to retain such clear views as ,archimedes had disclosed4 ,stevinus must be considered as the earliest of the authors of this rediscovery2 for his work 7,principles of ,statik and ,hydrostatik7 was published in ,dutch about #aehe2 and in this1 his views are perfectly distinct and correct4 ,he restates the doctrines of ,archimedes1 and shows that1 as a consequence of them1 it follows that the pressure of a fluid on the bottom of a vessel may be much greater than the weight of the fluid itself3 this he proves1 by imagining some of the upper portions of the vessel to be filled with fixed solid bodies1 which take the place of the fluid1 and yet do not alter the pressure on the base4 ,he also shows what will be the pressure on any portion of a base in an oblique position2 and hence1 by certain mathematical artifices which make an approach to the ,infinitesimal ,calculus1 he finds the whole pressure on the base in such cases4 ,this mode of treating the subject would take in a large portion of our elementary ,hydrostatics as the science now stands4 ,galileo saw the properties of fluids no less clearly1 and explained them very distinctly1 in #afab1 in his ,discourse on ,floating ,bodies4 ,it had been maintained by the ,aristotelians1 that form was the cause of bodies floating2 and collaterally1 that ice was condensed water2 apparently from a confusion of thought between rigidity and density4 ,galileo asserted1 on the contrary1 that ice is rarefied water1 as appears by its floating3 and in support of this1 he proved1 by various experiments1 that the floating of bodies does not depend on their form4 ,the happy genius of ,galileo is the more remarkable in this case1 as the controversy was a good deal perplexed by the mixture of phenomena of another kind1 due to what is usually called capillary or molecular attraction4 ,thus it is a fact1 that a ball #cdf of ebony sinks in water1 while a flat slip of the same material lies on the surface2 and it required considerable sagacity to separate such cases from the general rule4 ,galileo's opinions were attacked by various writers1 as ,nozzolini1 ,vincenzio di ,grazia1 ,ludovico delle ,colombe2 and defended by his pupil ,castelli1 who published a reply in #afae4 ,these opinions were generally adopted and diffused2 but somewhat later1 ,pascal pursued the subject more systematically1 and wrote his ,treatise of the ,equilibrium of ,fluids in #afec2 in which he shows that a fluid1 inclosed in a vessel1 necessarily presses equally in all directions1 by imagining two pistons or sliding plugs1 applied at different parts1 the surface of one being centuple that of the other3 it is clear1 as he observes1 that the force of one man acting at the first piston1 will balance the force of one hundred men acting at the other4 ,and thus1 says he1 it appears that a vessel full of water is a new ,principle of ,mechanics1 and a new ,machine which will multiply force to any degree we choose4 ,pascal also referred the equilibrium of fluids to the principle of virtual velocities1 which regulates the equilibrium of other machines4 ,this1 indeed1 ,galileo had done before him4 ,it followed from this doctrine1 that the pressure which is exercised by the lower parts of a fluid arises from the weight of the upper parts4 ,in all this there was nothing which was not easily assented to2 but the extension of these doctrines to the air required an additional effort of mechanical conception4 ,the pressure of the air on all sides of us1 and its weight above us1 were two truths which had never yet been apprehended with any kind of clearness4 ,seneca1 indeed1#bif talks of the gravity of the air1 and of its power of diffusing itself when condensed1 as the causes of wind2 but we can hardly consider such propriety of phraseology in him as more than a chance2 for we see the value of his philosophy by what he immediately adds3 ,do you think that we have forces by which we move ourselves1 and that the air is left without any power of moving8 when even water has a motion of its own1 as we see in the growth of plants4 ,we can hardly attach much value to such a recognition of the gravity and elasticity of the air4 ,note #bif3 ,qust4 ,nat4 v4 #e4 ,yet the effects of these causes were so numerous and obvious1 that the ,aristotelians had been obliged to invent a principle to account for them2 namely1 ,nature's ,horror of a ,vacuum4 ,to this principle were referred many familiar phenomena1 as suction1 breathing1 the #cdg action of a pair of bellows1 its drawing water if immersed in water1 its refusing to open when the rent is stopped up4 ,the action of a cupping instrument1 in which the air is rarefied by fire2 the fact that water is supported when a full inverted bottle is placed in a basin2 or when a full tube1 open below and closed above1 is similarly placed2 the running out of the water1 in this instance1 when the top is opened2 the action of a siphon1 of a syringe1 of a pump2 the adhesion of two polished plates1 and other facts1 were all explained by the fuga vacui4 ,indeed1 we must contend that the principle was a very good one1 inasmuch as it brought together all these facts which are really of the same kind1 and referred them to a common cause4 ,but when urged as an ultimate principle1 it was not only unphilosophical1 but imperfect and wrong4 ,it was unphilosophical1 because it introduced the notion of an emotion1 ,horror1 as an account of physical facts2 it was imperfect1 because it was at best only a law of phenomena1 not pointing out any physical cause2 and it was wrong1 because it gave an unlimited extent to the effect4 ,accordingly1 it led to mistakes4 ,thus ,mersenne1 in #afdd1 speaks of a siphon which shall go over a mountain1 being ignorant then that the effect of such an instrument was limited to a height of thirty-four feet4 ,a few years later1 however1 he had detected this mistake2 and in his third volume1 published in #afdg1 he puts his siphon in his emendanda1 and speaks correctly of the weight of air as supporting the mercury in the tube of ,torricelli4 ,it was1 indeed1 by finding this horror of a vacuum to have a limit at the height of thirty-four feet1 that the true principle was suggested4 ,it was discovered that when attempts were made to raise water higher than this4 ,nature tolerated a vacuum above the water which rose4 ,in #afdc1 ,torricelli tried to produce this vacuum at a smaller height1 by using1 instead of water1 the heavier fluid1 quicksilver2 an attempt which shows that the true explanation1 the balance of the weight of the water by another pressure1 had already suggested itself4 ,indeed1 this appears from other evidence4 ,galileo had already taught that the air has weight2 and ,baliani1 writing to him in #afcj1 says1#cjf ,if we were in a vacuum1 the weight of the air above our heads would be felt4 ,descartes also appears to have some share in this discovery2 for1 in a letter of the date of #afca1 he explains the suspension of mercury in a tube1 closed at top1 by the pressure of the column of air reaching to the clouds4 #cdh ,note #cjf3 ,drinkwater's ,galileo1 p4 #ij4 ,still men's minds wanted confirmation in this view2 and they found such confirmation1 when1 in #afdg1 ,pascal showed practically1 that if we alter the length of the superincumbent column of air by going to a high place1 we alter the weight which it will support4 ,this celebrated experiment was made by ,pascal himself on a church-steeple in ,paris1 the column of mercury in the ,torricellian tube being used to compare the weights of the air2 but he wrote to his brother-in-law1 who lived near the high mountain of ,puy de ,dme in ,auvergne1 to request him to make the experiment there1 where the result would be more decisive4 ,you see1 he says1 that if it happens that the height of the mercury at the top of the hill be less than at the bottom 7which ,i have many reasons to believe1 though all those who have thought about it are of a different opinion71 it will follow that the weight and pressure of the air are the sole cause of this suspension1 and not the horror of a vacuum3 since it is very certain that there is more air to weigh on it at the bottom than at the top2 while we cannot say that nature abhors a vacuum at the foot of a mountain more than on its summit4--,m4 ,perrier1 ,pascal's correspondent1 made the observation as he had desired1 and found a difference of three inches of mercury1 which1 he says1 ravished us with admiration and astonishment4 ,when the least obvious case of the operation of the pressure and weight of fluids had thus been made out1 there were no further difficulties in the progress of the theory of ,hydrostatics4 ,when mathematicians began to consider more general cases than those of the action of gravity1 there arose differences in the way of stating the appropriate principles3 but none of these differences imply any different conception of the fundamental nature of fluid equilibrium4 ,sect4 #b4--;,discovery of the ,laws of ,motion of ,fluids4 ,,the art of conducting water in pipes1 and of directing its motion for various purposes1 is very old4 ,when treated systematically1 it has been termed ,hydraulics3 but ,hydrodynamics is the general name of the science of the laws of the motions of fluids1 under those or other circumstances4 ,the ,art is as old as the commencement of civilization3 the ,science does not ascend higher than the time of ,newton1 though attempts on such subjects were made by ,galileo and his scholars4 ,when a fluid spouts from an orifice in a vessel1 ,castelli saw that the velocity of efflux depends on the depth of the orifice below the #cdi surface3 but he erroneously judged the velocity to be exactly proportional to the depth4 ,torricelli found that the fluid1 under the inevitable causes of defect which occur in the experiment1 would spout nearly to the height of the surface3 he therefore inferred1 that the full velocity is that which a body would acquire in falling through the depth2 and that it is consequently proportional to the square root of the depth4--,this1 however1 he stated only as a result of experience1 or law of phenomena1 at the end of his treatise1 ,de ,motu ,naturaliter ,accelerato1 printed in #afdc4 ,newton treated the subject theoretically in the ,principia 7#afhg72 but we must allow1 as ,lagrange says1 that this is the least satisfactory passage of that great work4 ,newton1 having made his experiments in another manner than ,torricelli1 namely1 by measuring the quantity of the efflux instead of its velocity1 found a result inconsistent with that of ,torricelli4 ,the velocity inferred from the quantity discharged1 was only that due to half the depth of the fluid4 ,in the first edition of the ,principia1#caf ,newton gave a train of reasoning by which he theoretically demonstrated his own result1 going upon the principle1 that the momentum of the issuing fluid is equal to the momentum which the column vertically over the orifice would generate by its gravity4 ,but ,torricelli's experiments1 which had given the velocity due to the whole depth1 were confirmed on repetition3 how was this discrepancy to be explained8 ,note #caf3 ,b4 ii4 ,prop4 xxxvii4 ,newton explained the discrepancy by observing the contraction which the jet1 or vein of water1 undergoes1 just after it leaves the orifice1 and which he called the vena contracta4 ,at the orifice1 the velocity is that due to half the height2 at the vena contracta it is that due to the whole height4 ,the former velocity regulates the quantity of the discharge2 the latter1 the path of the jet4 ,this explanation was an important step in the subject2 but it made ,newton's original proof appear very defective1 to say the least4 ,in the second edition of the ,principia 7#agad71 ,newton attacked the problem in a manner altogether different from his former investigation4 ,he there assumed1 that when a round vessel1 containing fluid1 has a hole in its bottom1 the descending fluid may be conceived to be a conoidal mass1 which has its base at the surface of the fluid1 and its narrow end at the orifice4 ,this portion of the fluid he calls the cataract2 and supposes that while this part descends1 the surrounding #cej parts remain immovable1 as if they were frozen2 in this way he finds a result agreeing with ,torricelli's experiments on the velocity of the efflux4 ,we must allow that the assumptions by which this result is obtained are somewhat arbitrary2 and those which ,newton introduces in attempting to connect the problem of issuing fluids with that of the resistance to a body moving in a fluid1 are no less so4 ,but even up to the present time1 mathematicians have not been able to reduce problems concerning the motions of fluids to mathematical principles and calculations1 without introducing some steps of this arbitrary kind4 ,and one of the uses of experiments on this subject is1 to suggest those hypotheses which may enable us1 in the manner most consonant with the true state of things1 to reduce the motions of fluids to those general laws of mechanics1 to which we know they must be subject4 ,hence the science of the ,motion of ,fluids1 unlike all the other primary departments of ,mechanics1 is a subject on which we still need experiments1 to point out the fundamental principles4 ,many such experiments have been made1 with a view either to compare the results of deduction and observation1 or1 when this comparison failed1 to obtain purely empirical rules4 ,in this way the resistance of fluids1 and the motion of water in pipes1 canals1 and rivers1 has been treated4 ,italy has possessed1 from early times1 a large body of such writers4 ,the earlier works of this kind have been collected in sixteen quarto volumes4 ,lecchi and ,michelotti about #agfe1 ,bidone more recently1 have pursued these inquiries4 ,bossut1 ,buat1 ,hachette1 in ,france1 have labored at the same task1 as have ,coulomb and ,prony1 ,girard and ,poncelet4 ,eytelwein's ,german treatise 7,hydraulik7 contains an account of what others and himself have done4 ,many of these trains of experiments1 both in ,france and ,italy1 were made at the expense of governments1 and on a very magnificent scale4 ,in ,england less was done in this way during the last century1 than in most other countries4 ,the ,philosophical ,transactions1 for instance1 scarcely contain a single paper on this subject founded on experimental investigations4#cbf ,dr4 ,thomas ,young1 who was at the head of his countrymen in so many branches of science1 was one of the first to call back attention to this3 and ,mr4 ,rennie and others have recently made valuable experiments4 ,in many of the questions now spoken of1 the accordance which engineers are able to obtain1 between their calculated and observed results1 #cea is very great3 but these calculations are performed by means of empirical formul1 which do not connect the facts with their causes1 and still leave a wide space to be traversed1 in order to complete the science4 ,note #cbf3 ,rennie1 ,report to ,brit4 ,assoc4 ,in the mean time1 all the other portions of ,mechanics were reduced to general laws1 and analytical processes2 and means were found of including ,hydrodynamics1 notwithstanding the difficulties which attend its special problems1 in this common improvement of form4 ,this progress we must relate4 #b;d ,ed4 ,the hydrodynamical problems referred to above are1 the laws of a fluid issuing from a vessel1 the laws of the motion of water in pipes1 canals1 and rivers1 and the laws of the resistance of fluids4 ,to these may be added1 as an hydrodynamical problem important in theory1 in experiment1 and in the comparison of the two1 the laws of waves4 ,newton gave1 in the ,principia1 an explanation of the waves of water 7,lib4 ii4 ,prop4 #dd71 which appears to proceed upon an erroneous view of the nature of the motion of the fluid3 but in his solution of the problem of sound1 appeared1 for the first time1 a correct view of the propagation of an undulation in a fluid4 ,the history of this subject1 as bearing upon the theory of sound1 is given in ,book viii43 but ,i may here remark1 that the laws of the motion of waves have been pursued experimentally by various persons1 as ,bremontier 7,recherches sur le ,mouvement des ,ondes1 #ahji71 ,emy 7,du ,mouvement des ,ondes1 #ahca71 the ,webers 7,wellenlehre1 #ahbe72 and by ,mr4 ,scott ,russell 7,reports of the ,british ,association1 #ahdd74 ,the analytical theory has been carried on by ,poisson1 ,cauchy1 and1 among ourselves1 by ,prof4 ,kelland 7,edin4 ,trans47 and ,mr4 ,airy 7in the article ,tides1 in the ,encyclopdia ,metropolitana74 ,and though theory and experiment have not yet been brought into complete accordance1 great progress has been made in that work1 and the remaining chasm between the two is manifestly due only to the incompleteness of both4 ,perhaps the most remarkable case of fluid motion recently discussed1 is one which ,mr4 ,scott ,russell has presented experimentally2 and which1 though novel1 is easily seen to follow from known principles2 namely1 the ,great ,solitary ,wave4 ,a wave may be produced1 which shall move along a canal unaccompanied by any other wave3 and the simplicity of this case makes the mathematical conditions and consequences more simple than they are in most other problems of ,hydrodynamics4 #ceb ,,chapter ,v4 ,,generalization ,,of ,,the ,,principles ,,of ,,mechanics4 ,sect4 #a4--;,generalization of the ,second ,law of ,motion4--,central ,forces4 ,,the ,second ,law of ,motion being proved for constant ,forces which act in parallel lines1 and the ,third ,law for the ,direct ,action of bodies1 it still required great mathematical talent1 and some inductive power1 to see clearly the laws which govern the motion of any number of bodies1 acted upon by each other1 and by any forces1 anyhow varying in magnitude and direction4 ,this was the task of the generalization of the laws of motion4 ,galileo had convinced himself that the velocity of projection1 and that which gravity alone would produce1 are both maintained1 without being altered1 perturbed1 or impeded in their mixture4 ,it is to be observed1 however1 that the truth of this result depends upon a particular circumstance1 namely1 that gravity1 at all points1 acts in lines1 which1 as to sense1 are parallel4 ,when we have to consider cases in which this is not true1 as when the force tends to the centre of a circle1 the law of composition cannot be applied in the same way2 and1 in this case1 mathematicians were met by some peculiar difficulties4 ,one of these difficulties arises from the apparent inconsistency of the statical and dynamical measures of force4 ,when a body moves in a circle1 the force which urges the body to the centre is only a tendency to motion2 for the body does not1 in fact1 approach to the centre2 and this mere tendency to motion is combined with an actual motion1 which takes place in the circumference4 ,we appear to have to compare two things which are heterogeneous4 ,descartes had noticed this difficulty1 but without giving any satisfactory solution of it4#ccf ,if we combine the actual motion to or from the centre with the traverse motion about the centre1 we obtain a result which is false on mechanical principles4 ,galileo endeavored in this way to find the curve described by a body which falls towards the earth's centre1 and is1 at the same time1 carried #cec round by the motion of the earth2 and obtained an erroneous result4 ,kepler and ,fermat attempted the same problem1 and obtained solutions different from that of ,galileo1 but not more correct4 ,note #ccf3 ,princip4 ,p4 iii4 #ei4 ,even ,newton1 at an early period of his speculations1 had an erroneous opinion respecting this curve1 which he imagined to be a kind of spiral4 ,hooke animadverted upon this opinion when it was laid before the ,royal ,society of ,london in #afgi1 and stated1 more truly1 that1 supposing no resistance1 it would be an eccentric ellipsoid1 that is1 a figure resembling an ellipse4 ,but though he had made out the approximate form of the curve1 in some unexplained way1 we have no reason to believe that he possessed any means of determining the mathematical properties of the curve described in such a case4 ,the perpetual composition of a central force with the previous motion of the body1 could not be successfully treated without the consideration of the ,doctrine of ,limits1 or something equivalent to that doctrine4 ,the first example which we have of the right solution of such a problem occurs1 so far as ,i know1 in the ,theorems of ,huyghens concerning ,circular ,motion1 which were published1 without demonstration1 at the end of his ,horologium ,oscillatorium1 in #afgc4 ,it was there asserted that when equal bodies describe circles1 if the times are equal1 the centrifugal forces will be as the diameters of the circles2 if the velocities are equal1 the forces will be reciprocally as the diameters1 and so on4 ,in order to arrive at these propositions1 ,huyghens must1 virtually at least1 have applied the ,second ,law of ,motion to the limiting elements of the curve1 according to the way in which ,newton1 a few years later1 gave the demonstration of the theorems of ,huyghens in the ,principia4 ,the growing persuasion that the motions of the heavenly bodies about the sun might be explained by the action of central forces1 gave a peculiar interest to these mechanical speculations1 at the period now under review4 ,indeed1 it is not easy to state separately1 as our present object requires us to do1 the progress of ,mechanics1 and the progress of ,astronomy4 ,yet the distinction which we have to make is1 in its nature1 sufficiently marked4 ,it is1 in fact1 no less marked than the distinction between speaking logically and speaking truly4 ,the framers of the science of motion were employed in establishing those notions1 names1 and rules1 in conformity to which all mechanical truth must be expressed2 but what was the truth with regard to the mechanism of the universe remained to be determined by other means4 ,physical ,astronomy1 at the period of which we speak1 eclipsed and overlaid #ced theoretical ,mechanics1 as1 a little previously1 ,dynamics had eclipsed and superseded ,statics4 ,the laws of variable force and of curvilinear motion were not much pursued1 till the invention of ,fluxions and of the ,differential ,calculus again turned men's minds to these subjects1 as easy and interesting exercises of the powers of these new methods4 ,newton's ,principia1 of which the first two ,books are purely dynamical1 is the great exception to this assertion2 inasmuch as it contains correct solutions of a great variety of the most general problems of the science2 and indeed is1 even yet1 one of the most complete treatises which we possess upon the subject4 ,we have seen that ,kepler1 in his attempts to explain the curvilinear motions of the planets by means of a central force1 failed1 in consequence of his belief that a continued transverse action of the central body was requisite to keep up a continual motion4 ,galileo had founded his theory of projectiles on the principle that such an action was not necessary2 yet ,borelli1 a pupil of ,galileo1 when1 in #afff1 he published his theory of the ,medicean ,stars 7the satellites of ,jupiter71 did not keep quite clear of the same errors which had vitiated ,kepler's reasonings4 ,in the same way1 though ,descartes is sometimes spoken of as the first promulgator of the ,first ,law of ,motion1 yet his theory of ,vortices must have been mainly suggested by a want of an entire confidence in that law4 ,when he represented the planets and satellites as owing their motions to oceans of fluid diffused through the celestial spaces1 and constantly whirling round the central bodies1 he must have felt afraid of trusting the planets to the operation of the laws of motion in free space4 ,sounder physical philosophers1 however1 began to perceive the real nature of the question4 ,as early as #afff1 we read1 in the ,journals of the ,royal ,society1 that there was read a paper of ,mr4 ,hooke's explicating the inflexion of a direct motion into a curve by a supervening attractive principle2 and before the publication of the ,principia in #afhg1 ,huyghens1 as we have seen1 in ,holland1 and1 in our own country1 ,wren1 ,halley1 and ,hooke1 had made some progress in the true mechanics of circular motion1#cdf and had distinctly contemplated the problem of the motion of a body in an ellipse by a central force1 though they could not solve it4 ,halley went to ,cambridge in #afhd1cef for the express purpose of consulting ,newton upon the subject of the production of the elliptical motion of the planets by means of a central #cee force1 and1 on the #ajth of ,december1#cff announced to the ,royal ,society that he had seen ,mr4 ,newton's book1 ,de ,motu ,corporum4 ,the feeling that mathematicians were on the brink of discoveries such as are contained in this work was so strong1 that ,dr4 ,halley was requested to remind ,mr4 ,newton of his promise of entering them in the ,register of the ,society1 for securing the invention to himself till such time as he can be at leisure to publish it4 ,the manuscript1 with the title ,philosophi ,naturalis ,principia ,mathematica1 was presented to the society 7to which it was dedicated7 on the #bhth of ,april1 #afhf4 ,dr4 ,vincent1 who presented it1 spoke of the novelty and dignity of the subject2 and the president 7,sir ,j4 ,hoskins7 added1 with great truth1 that the method was so much the more to be prized as it was both invented and perfected at the same time4 ,note #cdf3 ,newt4 ,princip4 ,schol4 to ,prop4 iv4 ,note #cef3 ,sir ,d4 ,brewster's ,life of ,newton1 p4 #aed4 ,note #cff3 ,id4 p4 #ahd4 ,the reader will recollect that we are here speaking of the ,principia as a ,mechanical ,treatise only2 we shall afterwards have to consider it as containing the greatest discoveries of ,physical ,astronomy4 ,as a work on ,dynamics1 its merit is1 that it exhibits a wonderful store of refined and beautiful mathematical artifices1 applied to solve all the most general problems which the subject offered4 ,the ,principia can hardly be said to contain any new inductive discovery respecting the principles of mechanics2 for though ,newton's ,axioms or ,laws of ,motion which stand at the beginning of the book1 are a much clearer and more general statement of the grounds of ,mechanics than had yet appeared1 they do not involve any doctrines which had not been previously stated or taken for granted by other mathematicians4 ,the work1 however1 besides its unrivalled mathematical skill1 employed in tracing out1 deductively1 the consequences of the laws of motion1 and its great cosmical discoveries1 which we shall hereafter treat of1 had great philosophical value in the history of ,dynamics1 as exhibiting a clear conception of the new character and functions of that science4 ,in his ,preface1 ,newton says1 ,rational ,mechanics must be the science of the ,motions which result from any ,forces1 and of the ,forces which are required for any ,motions1 accurately propounded and demonstrated4 ,for many things induce me to suspect1 that all natural phenomena may depend upon some ,forces by which the particles of bodies are either drawn towards each other1 and cohere1 or repel and recede from each other3 and these ,forces being hitherto unknown1 philosophers have pursued their researches in vain4 ,and ,i hope #cef that the principles expounded in this work will afford some light1 either to this mode of philosophizing1 or to some mode which is more true4 ,before we pursue this subject further1 we must trace the remainder of the history of the ,third ,law4 ,sect4 #b4--;,generalization of the ,third ,law of ,motion4--,centre of ,oscillation4--,huyghens4 ,,the ,third ,law of ,motion1 whether expressed according to ,newton's formula 7by the equality of ,action and ,reaction71 or in any other of the ways employed about the same time1 easily gave the solution of mechanical problems in all cases of direct action2 that is1 when each body acted directly on others4 ,but there still remained the problems in which the action is indirect2--when bodies1 in motion1 act on each other by the intervention of levers1 or in any other way4 ,if a rigid rod1 passing through two weights1 be made to swing about its upper point1 so as to form a pendulum1 each weight will act and react on the other by means of the rod1 considered as a lever turning about the point of suspension4 ,what1 in this case1 will be the effect of this action and reaction8 ,in what time will the pendulum oscillate by the force of gravity8 ,where is the point at which a single weight must be placed to oscillate in the same time8 in other words1 where is the ,centre of ,oscillation8 ,such was the problem--an example only of the general problem of indirect action--which mathematicians had to solve4 ,that it was by no means easy to see in what manner the law of the communication of motion was to be extended from simpler cases to those where rotatory motion was produced1 is shown by this2--that ,newton1 in attempting to solve the mechanical problem of the ,precession of the ,equinoxes1 fell into a serious error on this very subject4 ,he assumed that1 when a part has to communicate rotatory movement to the whole 7as the protuberant portion of the terrestrial spheroid1 attracted by the sun and moon1 communicates a small movement to the whole mass of the earth71 the quantity of the motion1 motus1 will not be altered by being communicated4 ,this principle is true1 if1 by motion1 we understand what is called moment of inertia1 a quantity in which both the velocity of each particle and its distance from the axis of rotation are taken into account3 but ,newton1 in his calculations of its amount1 considered the velocity only2 thus making motion1 in this case1 identical with the momentum which he introduces in treating of the simpler case #ceg of the third law of motion1 when the action is direct4 ,this error was retained even in the later editions of the ,principia4#cgf ,note #cgf3 ,b4 iii4 ,lemma iii4 to ,prop1 xxxix4 ,the question of the centre of oscillation had been proposed by ,mersenne somewhat earlier1#chf in #afdf4 ,and though the problem was out of the reach of any principles at that time known and understood1 some of the mathematicians of the day had rightly solved some cases of it1 by proceeding as if the question had been to find the ,centre of ,percussion4 ,the ,centre of ,percussion is the point about which the momenta of all the parts of a body balance each other1 when it is in motion about any axis1 and is stopped by striking against an obstacle placed at that centre4 ,roberval found this point in some easy cases2 ,descartes also attempted the problem2 their rival labors led to an angry controversy3 and ,descartes was1 as in his physical speculations he often was1 very presumptuous1 though not more than half right4 ,note #chf3 ,mont4 ii4 #dbc4 ,huyghens was hardly advanced beyond boyhood when ,mersenne first proposed this problem2 and1 as he says1#cif could see no principle which even offered an opening to the solution1 and had thus been repelled at the threshold4 ,when1 however1 he published his ,horologium ,oscillatorium in #afgc1 the fourth part of that work was on the ,centre of ,oscillation or ,agitation2 and the principle which he then assumed1 though not so simple and self-evident as those to which such problems were afterwards referred1 was perfectly correct and general1 and led to exact solutions in all cases4 ,the reader has already seen repeatedly in the course of this history1 complex and derivative principles presenting themselves to men's minds1 before simple and elementary ones4 ,the hypothesis assumed by ,huyghens was this2 that if any weights are put in motion by the force of gravity1 they cannot move so that the centre of gravity of them all shall rise higher than the place from which it descended4 ,this being assumed1 it is easy to show that the centre of gravity will1 under all circumstances1 rise as high as its original position2 and this consideration leads to a determination of the oscillation of a compound pendulum4 ,we may observe1 in the principle thus selected1 a conviction that1 in all mechanical action1 the centre of gravity may be taken as the representative of the whole system4 ,this conviction1 as we have seen1 may be traced in the axioms of ,archimedes and ,stevinus2 and ,huyghens1 when he proceeds upon it1 undertakes to show1#djf that he assumes only this1 that a heavy body cannot1 of itself1 move upwards4 #ceh ,note #cif3 ,hor4 ,osc4 ,pref4 ,note #djf3 ,hor4 ,osc4 p4 #aba4 ,clear as ,huyghen's principle appeared to himself1 it was1 after some time1 attacked by the ,abb ,catelan1 a zealous ,cartesian4 ,catelan also put forth principles which he conceived were evident1 and deduced from them conclusions contradictory to those of ,huyghens4 ,his principles1 now that we know them to be false1 appear to us very gratuitous4 ,they are these2 that in a compound pendulum1 the sum of the velocities of the component weights is equal to the sum of the velocities which they would have acquired if they had been detached pendulums2 and that the time of the vibration of a compound pendulum is an arithmetic mean between the times of the vibrations of the weights1 moving as detached pendulums4 ,huyghens easily showed that these suppositions would make the centre of gravity ascend to a greater height than that from which it fell2 and after some time1 ,james ,bernoulli stept into the arena1 and ranged himself on the side of ,huyghens4 ,as the discussion thus proceeded1 it began to be seen that the question really was1 in what manner the ,third ,law of ,motion was to be extended to cases of indirect action2 whether by distributing the action and reaction according to statical principles1 or in some other way4 ,i propose it to the consideration of mathematicians1 says ,bernoulli in #afhf1 what law of the communication of velocity is observed by bodies in motion1 which are sustained at one extremity by a fixed fulcrum1 and at the other by a body also moving1 but more slowly4 ,is the excess of velocity which must be communicated from the one body to the other to be distributed in the same proportion in which a load supported on the lever would be distributed8 ,he adds1 that if this question be answered in the affirmative1 ,huyghens will be found to be in error2 but this is a mistake4 ,the principle1 that the action and reaction of bodies thus moving are to be distributed according to the rules of the lever1 is true2 but ,bernoulli mistook1 in estimating this action and reaction by the velocity acquired at any moment2 instead of taking1 as he should have done1 the increment of velocity which gravity tended to impress in the next instant4 ,this was shown by the ,marquis de l',hpital2 who adds1 with justice1 ,i conceive that ,i have thus fully answered the call of ,bernoulli1 when he says1 ,i propose it to the consideration of mathematicians1 c4 ,we may1 from this time1 consider as known1 but not as fully established1 the principle that ,when bodies in motion affect each other1 the action and reaction are distributed according to the laws of ,statics2 although there were still found occasional difficulties in the #cei generalization and application of the role4 ,james ,bernoulli1 in #agjc1 gave a ,general ,demonstration of the ,centre of ,oscillation1 drawn from the nature of the ,lever4 ,in this demonstration#daf he takes as a fundamental principle1 that bodies in motion1 connected by levers1 balance1 when the products of their momenta and the lengths of the levers are equal in opposite directions4 ,for the proof of this proposition1 he refers to ,marriotte1 who had asserted it of weights acting by percussion1#dbf and in order to prove it1 had balanced the effect of a weight on a lever by the effect of a jet of water1 and had confirmed it by other experiments4#dcf ,moreover1 says ,bernoulli1 there is no one who denies it4 ,still1 this kind of proof was hardly satisfactory or elementary enough4 ,john ,bernoulli took up the subject after the death of his brother ,james1 which happened in #agje4 ,the former published in #agad his ,meditatio de ,natur ,centri ,oscillationis4 ,in this memoir1 he assumes1 as his brother had done1 that the effects of forces on a lever in motion are distributed according to the common rules of the lever4#ddf ,the principal generalization which he introduced was1 that he considered gravity as a force soliciting to motion1 which might have different intensities in different bodies4 ,at the same time1 ,brook ,taylor in ,england solved the problem1 upon the same principles as ,bernoulli2 and the question of priority on this subject was one point in the angry intercourse which1 about this time1 became common between the ,english mathematicians and those of the ,continent4 ,hermann also1 in his ,phoronomia1 published in #agaf1 gave a proof which1 as he informs us1 he had devised before he saw ,john ,bernoulli's4 ,this proof is founded on the statical equivalence of the solicitations of gravity and the vicarious solicitations which correspond to the actual motion of each part2 or1 as it has been expressed by more modern writers1 the equilibrium of the impressed and effective forces4 ,note #daf3 ,op4 ii4 #icj4 ,note #dbf3 ,choq4 des ,corps1 p4 #bif4 ,note #dcf3 ,ib4 ,prop4 xi4 ,note #ddf3 ,p4 #agb4 ,it was shown by ,john ,bernoulli and ,hermann1 and was indeed easily proved1 that the proposition assumed by ,huyghens as the foundation of his solution1 was1 in fact1 a consequence of the elementary principles which belong to this branch of mechanics4 ,but this assumption of ,huyghens was an example of a more general proposition1 which by some mathematicians at this time had been put forward as an original and elementary law2 and as a principle which ought to supersede the usual measure of the forces of bodies in motion2 this principle they called the ,conservation of ,vis ,viva4 ,the attempt to #cfj make this change was the commencement of one of the most obstinate and curious of the controversies which form part of the history of mechanical science4 ,the celebrated ,leibnitz was the author of the new opinion4 ,in #afhf1 he published1 in the ,leipsic ,acts1 ,a short ,demonstration of a memorable ,error of ,descartes and others1 concerning the natural law by which they think that ,god always preserves the same quantity of motion2 in which they pervert mechanics4 ,the principle that the same quantity of motion1 and therefore of moving force1 is always preserved in the world1 follows from the equality of action and reaction2 though ,descartes had1 after his fashion1 given a theological reason for it2 ,leibnitz allowed that the quantity of moving force remains always the same1 but denied that this force is measured by the quantity of motion or momentum4 ,he maintained that the same force is requisite to raise a weight of one pound through four feet1 and a weight of four pounds through one foot1 though the momenta in this case are as one to two4 ,this was answered by the ,abb de ,conti2 who truly observed1 that allowing the effects in the two cases to be equal1 this did not prove the forces to be equal2 since the effect1 in the first case1 was produced in a double time1 and therefore it was quite consistent to suppose the force only half as great4 ,leibnitz1 however1 persisted in his innovation2 and in #afie laid down the distinction between vires mortu1 or pressures1 and vires viv1 the name he gave to his own measure of force4 ,he kept up a correspondence with ,john ,bernoulli1 whom he converted to his peculiar opinions on this subject2 or rather1 as ,bernoulli says1#def made him think for himself1 which ended in his proving directly that which ,leibnitz had defended by indirect reasons4 ,among other arguments1 he had pretended to show 7what is certainly not true71 that if the common measure of forces be adhered to1 a perpetual motion would be possible4 ,it is easy to collect many cases which admit of being very simply and conveniently reasoned upon by means of the vis viva1 that is1 by taking the force to be proportional to the square of the velocity1 and not to the velocity itself4 ,thus1 in order to give the arrow twice the velocity1 the bow must be four times as strong2 and in all cases in which no account is taken of the time of producing the effect1 we may conveniently use similar methods4 ,note #def3 ,op4 iii4 #dj4 ,but it was not till a later period that the question excited any general notice4 ,the ,academy of ,sciences of ,paris in #agbd proposed #cfa as a subject for their prize dissertation the laws of the impact of bodies4 ,bernoulli1 as a competitor1 wrote a treatise1 upon ,leibnitzian principles1 which1 though not honored with the prize1 was printed by the ,academy with commendation4#dff ,the opinions which he here defended and illustrated were adopted by several mathematicians2 the controversy extended from the mathematical to the literary world1 at that time more attentive than usual to mathematical disputes1 in consequence of the great struggle then going on between the ,cartesian and the ,newtonian system4 ,it was1 however1 obvious that by this time the interest of the question1 so far as the progress of ,dynamics was concerned1 was at an end2 for the combatants all agreed as to the results in each particular case4 ,the ,laws of ,motion were now established2 and the question was1 by means of what definitions and abstractions could they be best expressed2--a metaphysical1 not a physical discussion1 and therefore one in which the paper philosophers1 as ,galileo called them1 could bear a part4 ,in the first volume of the ,transactions of the ,academy of ,st4 ,petersburg1 published in #agbh1 there are three ,leibnitzian memoirs by ,hermann1 ,bullfinger1 and ,wolff4 ,in ,england1 ,clarke was an angry assailant of the ,german opinion1 which ,s',gravesande maintained4 ,in ,france1 ,mairan attacked the vis viva in #agbh2 with strong and victorious reasons1 as the ,marquise du ,chatelet declared1 in the first edition of her ,treatise on ,fire4#dgf ,but shortly after this praise was published1 the ,chateau de ,cirey1 where the ,marquise usually lived1 became a school of ,leibnitzian opinions1 and the resort of the principal partisans of the vis viva4 ,soon1 observes ,mairan1 their language was changed2 the vis viva was enthroned by the side of the monads4 ,the ,marquise tried to retract or explain away her praises2 she urged arguments on the other side4 ,still the question was not decided2 even her friend ,voltaire was not converted4 ,in #agda he read a memoir ,on the ,measure and ,nature of ,moving ,forces1 in which he maintained the old opinion4 ,finally1 ,d',alembert in #agdc declared it to be1 as it truly was1 a mere question of words2 and by the turn which ,dynamics then took1 it ceased to be of any possible interest or importance to mathematicians4 ,note #dff3 ,discours sur les ,loix de la ,communication du ,mouvement4 ,note #dgf3 ,mont4 iii4 #fdj4 ,the representation of the laws of motion and of the reasonings depending on them1 in the most general form1 by means of analytical language1 cannot be said to have been fully achieved till the time of ,d',alembert2 but as we have already seen1 the discovery of these laws #cfb had taken place somewhat earlier2 and that law which is more particularly expressed in ,d',alembert's ,principle 7the equality of the action gained and lost7 was1 it has been seen1 rather led to by the general current of the reasoning of mathematicians about the end of the seventeenth century than discovered by any one4 ,huyghens1 ,marriotte1 the two ,bernoulli's1 ,l',hpital1 ,taylor1 and ,hermann1 have each of them their name in the history of this advance2 but we cannot ascribe to any of them any great real inductive sagacity shown in what they thus contributed1 except to ,huyghens1 who first seized the principle in such a form as to find the centre of oscillation by means of it4 ,indeed1 in the steps taken by the others1 language itself had almost made the generalization for them at the time when they wrote2 and it required no small degree of acuteness and care to distinguish the old cases1 in which the law had already been applied1 from the new cases1 in which they had to apply it4 ,,chapter ,,vi4 ,,sequel ,,to ,,the ,,generalization ,,of ,,the ,,principles ,,of ,,mechanics4--,,period ,,of ,,mathematical ,,deduction4--,,analytical ,,mechanics4 ,,we have now finished the history of the discovery of ,mechanical ,principles1 strictly so called4 ,the three ,laws of ,motion1 generalized in the manner we have described1 contain the materials of the whole structure of ,mechanics2 and in the remaining progress of the science1 we are led to no new truth which was not implicitly involved in those previously known4 ,it may be thought1 therefore1 that the narrative of this progress is of comparatively small interest4 ,nor do we maintain that the application and development of principles is a matter of so much importance to the philosophy of science1 as the advance towards and to them4 ,still1 there are many circumstances in the latter stages of the progress of the science of ,mechanics1 which well deserve notice1 and make a rapid survey of that part of its history indispensable to our purpose4 ,the ,laws of ,motion are expressed in terms of ,space and ,number2 the development of the consequences of these laws must1 therefore1 be performed by means of the reasonings of mathematics2 and the science #cfc of ,mechanics may assume the various aspects which belong to the different modes of dealing with mathematical quantities4 ,mechanics1 like pure mathematics1 may be geometrical or may be analytical2 that is1 it may treat space either by a direct consideration of its properties1 or by a symbolical representation of them3 ,mechanics1 like pure mathematics1 may proceed from special cases1 to problems and methods of extreme generality2--may summon to its aid the curious and refined relations of symmetry1 by which general and complex conditions are simplified2--may become more powerful by the discovery of more powerful analytical artifices2--may even have the generality of its principles further expanded1 inasmuch as symbols are a more general language than words4 ,we shall very briefly notice a series of modifications of this kind4 #a4 ,geometrical ,mechanics4 ,newton1 c4--,the first great systematical ,treatise on ,mechanics1 in the most general sense1 is the two first ,books of the ,principia of ,newton4 ,in this work1 the method employed is predominantly geometrical3 not only space is not represented symbolically1 or by reference to number2 but numbers1 as1 for instance1 those which measure time and force1 are represented by spaces2 and the laws of their changes are indicated by the properties of curve lines4 ,it is well known that ,newton employed1 by preference1 methods of this kind in the exposition of his theorems1 even where he had made the discovery of them by analytical calculations4 ,the intuitions of space appeared to him1 as they have appeared to many of his followers1 to be a more clear and satisfactory road to knowledge1 than the operations of symbolical language4 ,hermann1 whose ,phoronomia was the next great work on this subject1 pursued a like course2 employing curves1 which he calls the scale of velocities1 of forces1 c4 ,methods nearly similar were employed by the two first ,bernoullis1 and other mathematicians of that period2 and were1 indeed1 so long familiar1 that the influence of them may still be traced in some of the terms which are used on such subjects2 as1 for instance1 when we talk of reducing a problem to quadratures1 that is1 to the finding the area of the curves employed in these methods4 #b4 ,analytical ,mechanics4 ,euler4--,as analysis was more cultivated1 it gained a predominancy over geometry2 being found to be a far more powerful instrument for obtaining results2 and possessing a beauty and an evidence1 which1 though different from those of geometry1 had great attractions for minds to which they became familiar4 ,the person who did most to give to analysis the generality and #cfd symmetry which are now its pride1 was also the person who made ,mechanics analytical2 ,i mean ,euler4 ,he began his execution of this task in various memoirs which appeared in the ,transactions of the ,academy of ,sciences at ,st4 ,petersburg1 commencing with its earliest volumes2 and in #agcf1 he published there his ,mechanics1 or the ,science of ,motion analytically expounded2 in the way of a ,supplement to the ,transactions of the ,imperial ,academy of ,sciences4 ,in the preface to this work1 he says1 that though the solutions of problems by ,newton and ,hermann were quite satisfactory1 yet he found that he had a difficulty in applying them to new problems1 differing little from theirs2 and that1 therefore1 he thought it would be useful to extract an analysis out of their synthesis4 #c4 ,mechanical ,problems4--,in reality1 however1 ,euler has done much more than merely give analytical methods1 which may be applied to mechanical problems3 he has himself applied such methods to an immense number of cases4 ,his transcendent mathematical powers1 his long and studious life1 and the interest with which he pursued the subject1 led him to solve an almost inconceivable number and variety of mechanical problems4 ,such problems suggested themselves to him on all occasions4 ,one of his memoirs begins1 by stating that1 happening to think of the line of ,virgil1 ,anchora de pror jacitur stant litore puppes2 ,the anchor drops1 the rushing keel is staid2 he could not help inquiring what would be the nature of the ship's motion under the circumstances here described4 ,and in the last few days of his life1 after his mortal illness had begun1 having seen in the newspapers some statements respecting balloons1 he proceeded to calculate their motions2 and performed a difficult integration1 in which this undertaking engaged him4 ,his ,memoirs occupy a very large portion of the ,petropolitan ,transactions during his life1 from #agbh to #aghc2 and he declared that he should leave papers which might enrich the publications of the ,academy of ,petersburg for twenty years after his death2--a promise which has been more than fulfilled2 for1 up to #ahah1 the volumes usually contain several ,memoirs of his4 ,he and his contemporaries may be said to have exhausted the subject2 for there are few mechanical problems which have been since treated1 which they have not in some manner touched upon4 ,i do not dwell upon the details of such problems2 for the next great step in ,analytical ,mechanics1 the publication of ,d',alembert's #cfe ,principle in #agdc1 in a great degree superseded their interest4 ,the ,transactions of the ,academies of ,paris and ,berlin1 as well as ,st4 ,petersburg1 are filled1 up to this time1 with various questions of this kind4 ,they require1 for the most part1 the determination of the motions of several bodies1 with or without weight1 which pull or push each other by means of threads1 or levers1 to which they are fastened1 or along which they can slide2 and which1 having a certain impulse given them at first1 are then left to themselves1 or are compelled to move in given lines and surfaces4 ,the postulate of ,huyghens1 respecting the motion of the centre of gravity1 was generally one of the principles of the solution2 but other principles were always needed in addition to this2 and it required the exercise of ingenuity and skill to detect the most suitable in each case4 ,such problems were1 for some time1 a sort of trial of strength among mathematicians3 the principle of ,d',alembert put an end to this kind of challenges1 by supplying a direct and general method of resolving1 or at least of throwing into equations1 any imaginable problem4 ,the mechanical difficulties were in this way reduced to difficulties of pure mathematics4 #d4 ,d',alembert's ,principle4--,d',alembert's ,principle is only the expression1 in the most general form1 of the principle upon which ,john ,bernoulli1 ,hermann1 and others1 had solved the problem of the centre of oscillation4 ,it was thus stated1 ,the motion impressed on each particle of any system by the forces which act upon it1 may be resolved into two1 the effective motion1 and the motion gained or lost3 the effective motions will be the real motions of the parts1 and the motions gained and lost will be such as would keep the system at rest4 ,the distinction of statics1 the doctrine of equilibrium1 and dynamics1 the doctrine of motion1 was1 as we have seen1 fundamental2 and the difference of difficulty and complexity in the two subjects was well understood1 and generally recognized by mathematicians4 ,d',alembert's principle reduces every dynamical question to a statical one2 and hence1 by means of the conditions which connect the possible motions of the system1 we can determine what the actual motions must be4 ,the difficulty of determining the laws of equilibrium1 in the application of this principle in complex cases is1 however1 often as great as if we apply more simple and direct considerations4 #e4 ,motion in ,resisting ,media4 ,ballistics4--,we shall notice more particularly the history of some of the problems of mechanics4 ,though ,john ,bernoulli always spoke with admiration of ,newton's ,principia1 and of its author1 he appears to have been well disposed to point out #cff real or imagined blemishes in the work4 ,against the validity of ,newton's determination of the path described by a body projected in any part of the solar system1 ,bernoulli urges a cavil which it is difficult to conceive that a mathematician1 such as he was1 could seriously believe to be well founded4 ,on ,newton's determination of the path of a body in a resisting medium1 his criticism is more just4 ,he pointed out a material error in this solution3 this correction came to ,newton's knowledge in ,london1 in ,october1 #agab1 when the impression of the second edition of the ,principia was just drawing to a close1 under the care of ,cotes at ,cambridge2 and ,newton immediately cancelled the leaf and corrected the error4#dhf ,note #dhf3 ,,ms4 ,correspondence in ,trin4 ,coll4 ,library4 ,this problem of the motion of a body in a resisting medium1 led to another collision between the ,english and the ,german mathematicians4 ,the proposition to which we have referred1 gave only an indirect view of the nature of the curve described by a projectile in the air2 and it is probable that ,newton1 when he wrote the ,principia1 did not see his way to any direct and complete solution of this problem4 ,at a later period1 in #agah1 when the quarrel had waxed hot between the admirers of ,newton and ,leibnitz1 ,keill1 who had come forward as a champion on the ,english side1 proposed this problem to the foreigners as a challenge4 ,keill probably imagined that what ,newton had not discovered1 no one of his time would be able to discover4 ,but the sedulous cultivation of analysis by the ,germans had given them mathematical powers beyond the expectations of the ,english2 who1 whatever might be their talents1 had made little advance in the effective use of general methods2 and for a long period seemed to be fascinated to the spot1 in their admiration of ,newton's excellence4 ,bernoulli speedily solved the problem2 and reasonably enough1 according to the law of honor of such challenges1 called upon the challenger to produce his solution4 ,keill was unable to do this2 and after some attempts at procrastination1 was driven to very paltry evasions4 ,bernoulli then published his solution1 with very just expressions of scorn towards his antagonist4 ,and this may1 perhaps1 be considered as the first material addition which was made to the ,principia by subsequent writers4 #f4 ,constellation of ,mathematicians4--,we pass with admiration along the great series of mathematicians1 by whom the science of theoretical mechanics has been cultivated1 from the time of ,newton to our own4 ,there is no group of men of science whose fame is #cfg higher or brighter4 ,the great discoveries of ,copernicus1 ,galileo1 ,newton1 had fixed all eyes on those portions of human knowledge on which their successors employed their labors4 ,the certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects2 and the beauty of mathematical relations1 and the subtlety of intellect which may be shown in dealing with them1 were fitted to win unbounded applause4 ,the successors of ,newton and the ,bernoullis1 as ,euler1 ,clairaut1 ,d',alembert1 ,lagrange1 ,laplace1 not to introduce living names1 have been some of the most remarkable men of talent which the world has seen4 ,that their talent is1 for the most part1 of a different kind from that by which the laws of nature were discovered1 ,i shall have occasion to explain elsewhere2 for the present1 ,i must endeavor to arrange the principal achievements of those whom ,i have mentioned4 ,the series of persons is connected by social relations4 ,euler was the pupil of the first generation of ,bernoullis1 and the intimate friend of the second generation2 and all these extraordinary men1 as well as ,hermann1 were of the city of ,basil1 in that age a spot fertile of great mathematicians to an unparalleled degree4 ,in #agdj1 ,clairaut and ,maupertuis visited ,john ,bernoulli1 at that time the ,nestor of mathematicians1 who died1 full of age and honors1 in #agdh4 ,euler1 several of the ,bernoullis1 ,maupertuis1 ,lagrange1 among other mathematicians of smaller note1 were called into the north by ,catharine of ,russia and ,frederic of ,prussia1 to inspire and instruct academies which the brilliant fame then attached to science1 had induced those monarchs to establish4 ,the prizes proposed by these societies1 and by the ,french ,academy of ,sciences1 gave occasion to many of the most valuable mathematical works of the century4 #g4 ,the ,problem of ,three ,bodies4--,in #agdg1 ,clairaut and ,d',alembert sent1 on the same day1 to this body1 their solutions of the celebrated ,problem of ,three ,bodies1 which1 from that time1 became the great object of attention of mathematicians2--the bow in which each tried his strength1 and endeavored to shoot further than his predecessors4 ,this problem was1 in fact1 the astronomical question of the effect produced by the attraction of the sun1 in disturbing the motions of the moon about the earth2 or by the attraction of one planet1 disturbing the motion of another planet about the sun2 but being expressed generally1 as referring to one body which disturbs any two others1 it became a mechanical problem1 and the history of it belongs to the present subject4 #cfh ,one consequence of the synthetical form adopted by ,newton in the ,principia1 was1 that his successors had the problem of the solar system to begin entirely anew4 ,those who would not do this1 made no progress1 as was long the case with the ,english4 ,clairaut says1 that he tried for a long time to make some use of ,newton's labors2 but that1 at last1 he resolved to take up the subject in an independent manner4 ,this1 accordingly1 he did1 using analysis throughout1 and following methods not much different from those still employed4 ,we do not now speak of the comparison of this theory with observation1 except to remark1 that both by the agreements and by the discrepancies of this comparison1 ,clairaut and other writers were perpetually driven on to carry forwards the calculation to a greater and greater degree of accuracy4 ,one of the most important of the cases in which this happened1 was that of the movement of the ,apogee of the ,moon2 and in this case1 a mode of approximating to the truth1 which had been depended on as nearly exact1 was1 after having caused great perplexity1 found by ,clairaut and ,euler to give only half the truth4 ,this same ,problem of ,three ,bodies was the occasion of a memoir of ,clairaut1 which gained the prize of the ,academy of ,st4 ,petersburg in #agea2 and1 finally1 of his ,thorie de la ,lune1 published in #agfe4 ,d',alembert labored at the same time on the same problem2 and the value of their methods1 and the merit of the inventors1 unhappily became a subject of controversy between those two great mathematicians4 ,euler also1 in #agec1 published a ,theory of the ,moon1 which was1 perhaps1 more useful than either of the others1 since it was afterwards the basis of ,mayer's method1 and of his ,tables4 ,it is difficult to give the general reader any distinct notion of these solutions4 ,we may observe1 that the quantities which determine the moon's position1 are to be determined by means of certain algebraical equations1 which express the mechanical conditions of the motion4 ,the operation1 by which the result is to be obtained1 involves the process of integration2 which1 in this instance1 cannot be performed in an immediate and definite manner2 since the quantities thus to be operated on depend upon the moon's position1 and thus require us to know the very thing which we have to determine by the operation4 ,the result must be got at1 therefore1 by successive approximations3 we must first find a quantity near the truth2 and then1 by the help of this1 one nearer still2 and so on2 and1 in this manner1 the moon's place will be given by a converging series of terms4 ,the form of these terms depends upon the relations of position between the sun #cfi and moon1 their apogees1 the moon's nodes1 and other quantities2 and by the variety of combinations of which these admit1 the terms become very numerous and complex4 ,the magnitude of the terms depends also upon various circumstances2 as the relative force of the sun and earth1 the relative times of the solar and lunar revolutions1 the eccentricities and inclinations of the two orbits4 ,these are combined so as to give terms of different orders of magnitudes2 and it depends upon the skill and perseverance of the mathematician how far he will continue this series of terms4 ,for there is no limit to their number3 and though the methods of which we have spoken do theoretically enable us to calculate as many terms as we please1 the labor and the complexity of the operations are so serious that common calculators are stopped by them4 ,none but very great mathematicians have been able to walk safely any considerable distance into this avenue1--so rapidly does it darken as we proceed4 ,and even the possibility of doing what has been done1 depends upon what we may call accidental circumstances2 the smallness of the inclinations and eccentricities of the system1 and the like4 ,if nature had not favored us in this way1 ,lagrange used to say1 there would have been an end of the geometers in this problem4 ,the expected return of the comet of #afhb in #agei1 gave a new interest to the problem1 and ,clairaut proceeded to calculate the case which was thus suggested4 ,when this was treated by the methods which had succeeded for the moon1 it offered no prospect of success1 in consequence of the absence of the favorable circumstances just referred to1 and1 accordingly1 ,clairaut1 after obtaining the six equations to which he reduces the solution1#dif adds1 ,integrate them who can 7,intgre maintenant qui pourra74 ,new methods of approximation were devised for this case4 ,note #dif3 ,journal des ,savans1 ,aug4 #agei4 ,the problem of three bodies was not prosecuted in consequence of its analytical beauty1 or its intrinsic attraction2 but its great difficulties were thus resolutely combated from necessity2 because in no other way could the theory of universal gravitation be known to be true or made to be useful4 ,the construction of ,tables of the ,moon1 an object which offered a large pecuniary reward1 as well as mathematical glory1 to the successful adventurer1 was the main purpose of these labors4 ,the ,theory of the ,planets presented the ,problem of ,three ,bodies in a new form1 and involved in peculiar difficulties2 for the #cgj approximations which succeed in the ,lunar theory fail here4 ,artifices somewhat modified are required to overcome the difficulties of this case4 ,euler had investigated1 in particular1 the motions of ,jupiter and ,saturn1 in which there was a secular acceleration and retardation1 known by observation1 but not easily explicable by theory4 ,euler's memoirs1 which gained the prize of the ,french ,academy1 in #agdh and #ageb1 contained much beautiful analysis2 and ,lagrange published also a theory of ,jupiter and ,saturn1 in which he obtained results different from those of ,euler4 ,laplace1 in #aghg1 showed that this inequality arose from the circumstance that two of ,saturn's years are very nearly equal to five of ,jupiter's4 ,the problems relating to ,jupiter's ,satellites1 were found to be even more complex than those which refer to the planets3 for it was necessary to consider each satellite as disturbed by the other three at once2 and thus there occurred the ,problem of ,five ,bodies4 ,this problem was resolved by ,lagrange4#ejf ,note #ejf3 ,bailly1 ,ast4 ,mod4 iii4 #agh4 ,again1 the newly-discovered small ,planets1 ,juno1 ,ceres1 ,vesta1 ,pallas1 whose orbits almost coincide with each other1 and are more inclined and more eccentric than those of the ancient planets1 give rise1 by their perturbations1 to new forms of the problem1 and require new artifices4 ,in the course of these researches respecting ,jupiter1 ,lagrange and ,laplace were led to consider particularly the secular ,inequalities of the solar system2 that is1 those inequalities in which the duration of the cycle of change embraces very many revolutions of the bodies themselves4 ,euler in #agdi and #agee1 and ,lagrange#eaf in #agff1 had introduced the method of the ,variation of the ,elements of the orbit2 which consists in tracing the effect of the perturbing forces1 not as directly altering the place of the planet1 but as producing a change from one instant to another1 in the dimensions and position of the ,elliptical orbit which the planet describes4#ebf ,taking this view1 he #cga determines the secular changes of each of the elements or determining quantities of the orbit4 ,in #aggc1 ,laplace also attacked this subject of secular changes1 and obtained expressions for them4 ,on this occasion1 he proved the celebrated proposition that1 the mean motions of the planets are invariable3 that is1 that there is1 in the revolutions of the system1 no progressive change which is not finally stopped and reversed2 no increase1 which is not1 after some period1 changed into decrease2 no retardation which is not at last succeeded by acceleration2 although1 in some cases1 millions of years may elapse before the system reaches the turning-point4 ,thomas ,simpson noticed the same consequence of the laws of universal attraction4 ,in #aggd and #aggf1 ,lagrange#ecf still labored at the secular equations2 extending his researches to the nodes and inclinations2 and showed that the invariability of the mean motions of the planets1 which ,laplace had proved1 neglecting the fourth powers of the eccentricities and inclinations of the orbits1#edf was true1 however far the approximation was carried1 so long as the squares of the disturbing masses were neglected4 ,he afterwards improved his methods2#eef and1 in #aghc1 he endeavored to extend the calculation of the changes of the elements to the periodical equations1 as well as the secular4 ,note #eaf3 ,gautier1 ,prob4 de ,trois ,corps1 p4 #aee4 ,note #ebf3 ,in the first edition of this ,history1 ,i had ascribed to ,lagrange the invention of the ,method of ,variation of ,elements in the theory of ,perturbations4 ,but justice to ,euler requires that we should assign this distinction to him2 at least1 next to ,newton1 whose mode of representing the paths of bodies by means of a ,revolving ,orbit1 in the ,ninth ,section of the ,principia1 may be considered as an anticipation of the method of variation of elements4 ,in the fifth volume of the ,mcanique ,cleste1 livre xv4 p4 #cje1 is an abstract of ,euler's paper of #agdi2 where ,laplace adds1 ,c'est le premier essai de la mthode de la variation des constantes arbitraires4 ,and in page #caj is an abstract of the paper of #agef3 and speaking of the method1 ,laplace says1 ,it consists in regarding the elements of the elliptical motion as variable in virtue of the perturbing forces4 ,those elements are1 #a1 the axis major2 #b1 the epoch of the body being at the apse2 #c1 the eccentricity2 #d1 the movement of the apse2 #e1 the inclination2 #f1 the longitude of the node2 and he then proceeds to show how ,euler did this4 ,it is possible that ,lagrange knew nothing of ,euler's paper4 ,see ,mc4 ,cl4 vol4 v4 p4 #cab4 ,but ,euler's conception and treatment of the method are complete1 so that he must be looked upon as the author of it4 ,note #ecf3 ,gautier1 p4 #ajd4 ,note #edf3 ,ib4 p4 #ahd4 ,note #eef3 ,ib4 p4 #aif4 #h4 ,mcanique ,cleste1 c4--,laplace also resumed the consideration of the secular changes2 and1 finally1 undertook his vast work1 the ,mcanique ,cleste1 which he intended to contain a complete view of the existing state of this splendid department of science4 ,we may see1 in the exultation which the author obviously feels at the thought of erecting this monument of his age1 the enthusiasm which had been excited by the splendid course of mathematical successes of which ,i have given a sketch4 ,the two first volumes of this great work appeared in #agii4 ,the third and fourth volumes were published in #ahjb and #ahje respectively4 ,since its publication1 little has been added to the solution of the great problems of which it treats4 ,in #ahjh1 ,laplace presented to the ,french ,bureau des ,longitudes1 a ,supplement to the ,mcanique ,cleste2 the object of which was to improve still further #cgb the mode of obtaining the secular variations of the elements4 ,poisson and ,lagrange proved the invariability of the major axes of the orbits1 as far as the second order of the perturbing forces4 ,various other authors have since labored at this subject4 ,burckhardt1 in #ahjh1 extended the perturbing function as far as the sixth order of the eccentricities4 ,gauss1 ,hansen1 and ,bessel1 ,ivory1 ,,mm4 ,lubbock1 ,plana1 ,pontcoulant1 and ,airy1 have1 at different periods up to the present time1 either extended or illustrated some particular part of the theory1 or applied it to special cases2 as in the instance of ,professor ,airy's calculation of an inequality of ,venus and the earth1 of which the period is #bdj years4 ,the approximation of the ,moon's motions has been pushed to an almost incredible extent by ,m4 ,damoiseau1 and1 finally1 ,plana has once more attempted to present1 in a single work 7three thick quarto volumes71 all that has hitherto been executed with regard to the theory of the ,moon4 ,i give only the leading points of the progress of analytical dynamics4 ,hence ,i have not spoken in detail of the theory of the ,satellites of ,jupiter1 a subject on which ,lagrange gained a prize for a ,memoir1 in #agff1 and in which ,laplace discovered some most curious properties in #aghd4 ,still less have ,i referred to the purely speculative question of ,tautochronous ,curves in a resisting medium1 though it was a subject of the labors of ,bernoulli1 ,euler1 ,fontaine1 ,d',alembert1 ,lagrange1 and ,laplace4 ,the reader will rightly suppose that many other curious investigations are passed over in utter silence4 #b;d ,ed4 ,although the analytical calculations of the great mathematicians of the last century had determined1 in a demonstrative manner1 a vast series of inequalities to which the motions of the sun1 moon1 and planets were subject in virtue of their mutual attraction1 there were still unsatisfactory points in the solutions thus given of the great mechanical problems suggested by the ,system of the ,universe4 ,one of these points was the want of any evident mechanical significance in the successive members of these series4 ,lindenau relates that ,lagrange1 near the end of his life1 expressed his sorrow that the methods of approximation employed in ,physical ,astronomy rested on arbitrary processes1 and not on any insight into the results of mechanical action4 ,but something was subsequently done to remove the ground of this complaint4 ,in #ahah1 ,gauss pointed out that secular equations may be conceived to result from the disturbing body being distributed along its orbit so as to form a ring1 and thus made the result conceivable more distinctly than as a mere result of calculation4 ,and it appears #cgc to me that ,professor ,airy's treatise entitled ,gravitation1 published at ,cambridge in #ahcd1 is of great value in supplying similar modes of conception with regard to the mechanical origin of many of the principal inequalities of the solar system4 ,bessel in #ahbd1 and ,hansen in #ahbh1 published works which are considered as belonging1 along with those of ,gauss1 to a new era in physical astronomy4#eff ,gauss's ,theoria ,motuum ,corporum ,celestium1 which had ,lalande's medal assigned to it by the ,french ,institute1 had already 7#ahaj7 resolved all problems concerning the determination of the place of a planet or comet in its orbit in function of the elements4 ,the value of ,hansen's labors respecting the ,perturbations of the ,planets was recognized by the ,astronomical ,society of ,london1 which awarded to them its gold medal4 ,note #eff3 ,abhand4 der ,akad4 d4 ,wissensch4 zu ,berlin4 #ahbd2 and ,disquisitiones circa ,theoriam ,perturbationum4 ,see ,jahn4 ,gesch4 der ,astron4 p4 #hd4 ,the investigations of ,m4 ,damoiseau1 and of ,,mm4 ,plana and ,carlini1 on the ,problem of the ,lunar ,theory1 followed nearly the same course as those of their predecessors4 ,in these1 as in the ,mcanique ,cleste and in preceding works on the same subject1 the ,moon's co-ordinates 7time1 radius vector1 and latitude7 were expressed in function of her true longitude4 ,the integrations were effected in series1 and then by reversion of the series1 the longitude was expressed in function of the time2 and then in the same manner the other two co-ordinates4 ,but ,sir ,john ,lubbock and ,m4 ,pontcoulant have made the mean longitude of the moon1 that is1 the time1 the independent variable1 and have expressed the moon's co-ordinates in terms of sines and cosines of angles increasing proportionally to the time4 ,and this method has been adopted by ,m4 ,poisson 7,mem4 ,inst4 xiii4 #ahce1 p4 #bab74 ,m4 ,damoiseau1 like ,laplace and ,clairaut1 had deduced the successive coefficients of the lunar inequalities by numerical equations4 ,but ,m4 ,plana expresses explicitly each coefficient in general terms of the letters expressing the constants of the problem1 arranging them according to the order of the quantities1 and substituting numbers at the end of the operation only4 ,by attending to this arrangement1 ,,mm4 ,lubbock and ,pontcoulant have verified or corrected a large portion of the terms contained in the investigations of ,,mm4 ,damoiseau and ,plana4 ,sir ,john ,lubbock has calculated the polar co-ordinates of the ,moon directly2 ,m4 ,poisson1 on the other hand1 has obtained the variable elliptical elements2 ,m4 ,pontcoulant conceives that the method of variation or arbitrary #cgd constants may most conveniently be reserved for secular inequalities and inequalities of long periods4 ,,mm4 ,lubbock and ,pontcoulant have made the mode of treating the ,lunar ,theory and the ,planetary ,theory agree with each other1 instead of following two different paths in the calculation of the two problems1 which had previously been done4 ,prof4 ,hansen1 also1 in his ,fundamenta ,nova ,investigationis ,orbit ver quam ,luna perlustrat 7,goth1 #ahch71 gives a general method1 including the ,lunar ,theory and the ,planetary ,theory as two special cases4 ,to this is annexed a solution of the ,problem of ,four ,bodies4 ,i am here speaking of the ,lunar and ,planetary ,theories as ,mechanical ,problems only4 ,connected with this subject1 ,i will not omit to notice a very general and beautiful method of solving problems respecting the motion of systems 9999of mutually attracting bodies1 given by ,sir ,w4 ,r4 ,hamilton1 in the ,philosophical ,transactions for #ahcd-e 7,on a ,general ,method in ,dynamics74 ,his method consists in investigating the ,principal ,function of the co-ordinates of the bodies3 this function being one1 by the differentiation of which1 the co-ordinates of the bodies of the system may be found4 ,moreover1 an approximate value of this function being obtained1 the same formul supply a means of successive approximation without limit4 #i4 ,precession4 ,motion of ,rigid ,bodies4--,the series of investigations of which ,i have spoken1 extensive and complex as it is1 treats the moving bodies as points only1 and takes no account of any peculiarity of their form or motion of their parts4 ,the investigation of the motion of a body of any magnitude and form1 is another branch of analytical mechanics1 which well deserves notice4 ,like the former branch1 it mainly owed its cultivation to the problems suggested by the solar system4 ,newton1 as we have seen1 endeavored to calculate the effect of the attraction of the sun and moon in producing the precession of the equinoxes2 but in doing this he made some mistakes4 ,in #agdg1 ,d',alembert solved this problem by the aid of his ,principle2 and it was not difficult for him to show1 as he did in his ,opuscules1 in #agfa1 that the same method enabled him to determine the motion of a body of any figure acted upon by any forces4 ,but1 as the reader will have observed in the course of this narrative1 the great mathematicians of this period were always nearly abreast of each other in their advances4--,euler1#egf in the mean time1 had published1 in #agea1 a solution of the #cge problem of the precession2 and in #ageb1 a memoir which he entitled ,discovery of a ,new ,principle of ,mechanics1 and which contains a solution of the general problem of the alteration of rotary motion by forces4 ,d',alembert noticed with disapprobation the assumption of priority which this title implied1 though allowing the merit of the memoir4 ,various improvements were made in these solutions2 but the final form was given them by ,euler2 and they were applied to a great variety of problems in his ,theory of the ,motion of ,solid and ,rigid ,bodies1 which was written#ehf about #agfj1 and published in #agfe4 ,the formul in this work were much simplified by the use of a discovery of ,segner1 that every body has three axes which were called ,principal ,axes1 about which alone 7in general7 it would permanently revolve4 ,the equations which ,euler and other writers had obtained1 were attacked as erroneous by ,landen in the ,philosophical ,transactions for #aghe2 but ,i think it is impossible to consider this criticism otherwise than as an example of the inability of the ,english mathematicians of that period to take a steady hold of the analytical generalizations to which the great ,continental authors had been led4 ,perhaps one of the most remarkable calculations of the motion of a rigid body is that which ,lagrange performed with regard to the ,moon's ,libration2 and by which he showed that the ,nodes of the ,moon's ,equator and those of her ,orbit must always coincide4 ,note #egf3 ,ac4 ,berl4 #agde1 #agej4 ,note #ehf3 ,see the preface to the book4 #aj4 ,vibrating ,strings4--,other mechanical questions1 unconnected with astronomy1 were also pursued with great zeal and success4 ,among these was the problem of a vibrating string1 stretched between two fixed points4 ,there is not much complexity in the mechanical conceptions which belong to this case1 but considerable difficulty in reducing them to analysis4 ,taylor1 in his ,method of ,increments1 published in #agaf1 had annexed to his work a solution of this problem2 obtained on suppositions1 limited indeed1 but apparently conformable to the most common circumstances of practice4 ,john ,bernoulli1 in #agbh1 had also treated the same problem4 ,but it assumed an interest altogether new1 when1 in #agdg1 ,d',alembert published his views on the subject2 in which he maintained that1 instead of one kind of curve only1 there were an infinite number of different curves1 which answered the conditions of the question4 ,the problem1 thus put forward by one great mathematician1 was1 as usual1 taken up by the others1 whose names the reader is now so familiar with in such an association4 ,in #cgf #agdh1 ,euler not only assented to the generalization of ,d',alembert1 but held that it was not necessary that the curves so introduced should be defined by any algebraical condition whatever4 ,from this extreme indeterminateness ,d',alembert dissented2 while ,daniel ,bernoulli1 trusting more to physical and less to analytical reasonings1 maintained that both these generalizations were inapplicable in fact1 and that the solution was really restricted1 as had at first been supposed1 to the form of the trochoid1 and to other forms derivable from that4 ,he introduced1 in such problems1 the ,law of ,coexistent ,vibrations1 which is of eminent use in enabling us to conceive the results of complex mechanical conditions1 and the real import of many analytical expressions4 ,in the mean time1 the wonderful analytical genius of ,lagrange had applied itself to this problem4 ,he had formed the ,academy of ,turin1 in conjunction with his friends ,saluces and ,cigna2 and the first memoir in their ,transactions was one by him on this subject3 in this and in subsequent writings he has established1 to the satisfaction of the mathematical world1 that the functions introduced in such cases are not necessarily continuous1 but are arbitrary to the same degree that the motion is so practically2 though capable of expression by a series of circular functions4 ,this controversy1 concerning the degree of lawlessness with which the conditions of the solution may be assumed1 is of consequence1 not only with respect to vibrating strings1 but also with respect to many problems1 belonging to a branch of ,mechanics which we now have to mention1 the ,doctrine of ,fluids4 #aa4 ,equilibrium of ,fluids4 ,figure of the ,earth4 ,tides4--,the application of the general doctrines of ,mechanics to fluids was a natural and inevitable step1 when the principles of the science had been generalized4 ,it was easily seen that a fluid is1 for this purpose1 nothing more than a body of which the parts are movable amongst each other with entire facility2 and that the mathematician must trace the consequences of this condition upon his equations4 ,this accordingly was done1 by the founders of mechanics1 both for the cases of the equilibrium and of motion4 ,newton's attempt to solve the problem of the figure of the earth1 supposing it fluid1 is the first example of such an investigation3 and this solution rested upon principles which we have already explained1 applied with the skill and sagacity which distinguished all that ,newton did4 ,we have already seen how the generality of the principle1 that fluids press equally in all directions1 was established4 ,in applying it to calculation1 ,newton took for his fundamental principle1 the equal #cgg weight of columns of the fluid reaching to the centre2 ,huyghens took1 as his basis1 the 9999perpendicularity of the resulting force at each point to the surface of the fluid2 ,bouguer conceived that both principles were necessary2 and ,clairaut showed that the equilibrium of all canals is requisite4 ,he also was the first mathematician who deduced from this principle the ,equations of ,partial ,differentials by which these laws are expressed2 a step which1 as ,lagrange says1#eif changed the face of ,hydrostatics1 and made it a new science4 ,euler simplified the mode of obtaining the ,equations of ,equilibrium for any forces whatever2 and put them in the form which is now generally adopted in our treatises4 ,note #eif3 ,mc4 ,analyt4 ii4 p4 #ahj4 ,the explanation of the ,tides1 in the way in which ,newton attempted it in the third book of the ,principia1 is another example of a hydrostatical investigation3 for he considered only the form that the ocean would have if it were at rest4 ,the memoirs of ,maclaurin1 ,daniel ,bernoulli1 and ,euler1 on the question of the ,tides1 which shared among them the prize of the ,academy of ,sciences in #agdj1 went upon the same views4 ,the ,treatise of the ,figure of the ,earth1 by ,clairaut1 in #agdc1 extended ,newton's solution of the same problem1 by supposing a solid nucleus covered with a fluid of different density4 ,no peculiar novelty has been introduced into this subject1 except a method employed by ,laplace for determining the attractions of spheroids of small eccentricity1 which is1 as ,professor ,airy has said1#fjf a calculus the most singular in its nature1 and the most powerful in its effects1 of any which has yet appeared4 ,note #fjf3 ,enc4 ,met4 ,fig4 of ,earth1 p4 #aib4 #ab4 ,capillary ,action4--,there is only one other problem of the statics of fluids on which it is necessary to say a word1--the doctrine of ,capillary ,attraction4 ,daniel ,bernoulli1#faf in #agch1 states that he passes over the subject1 because he could not reduce the facts to general laws3 but ,clairaut was more successful1 and ,laplace and ,poisson have since given great analytical completeness to his theory4 ,at present our business is1 not so much with the sufficiency of the theory to explain phenomena1 as with the mechanical problem of which this is an example1 which is one of a very remarkable and important character2 namely1 to determine the effect of attractions which are exercised by all the particles of bodies1 on the hypothesis that the #cgh attraction of each particle1 though sensible when it acts upon another particle at an extremely small distance from it1 becomes insensible and vanishes the moment this distance assumes a perceptible magnitude4 ,it may easily be imagined that the analysis by which results are obtained under conditions so general and so peculiar1 is curious and abstract2 the problem has been resolved in some very extensive cases4 ,note #faf3 ,hydrodyn4 ,pref4 p4 #e4 #ac4 ,motion of ,fluids4--,the only branch of mathematical mechanics which remains to be considered1 is that which is1 we may venture to say1 hitherto incomparably the most incomplete of all1--,hydrodynamics4 ,it may easily be imagined that the mere hypothesis of absolute relative mobility in the parts1 combined with the laws of motion and nothing more1 are conditions too vague and general to lead to definite conclusions4 ,yet such are the conditions of the problems which relate to the motion of fluids4 ,accordingly1 the mode of solving them has been1 to introduce certain other hypotheses1 often acknowledged to be false1 and almost always in some measure arbitrary1 which may assist in determining and obtaining the solution4 ,the ,velocity of a fluid issuing from an orifice in a vessel1 and the ,resistance which a solid body suffers in moving in a fluid1 have been the two main problems on which mathematicians have employed themselves4 ,we have already spoken of the manner in which ,newton attacked both these1 and endeavored to connect them4 ,the subject became a branch of ,analytical ,mechanics by the labors of ,d4 ,bernoulli1 whose ,hydrodynamica was published in #agch4 ,this work rests upon the ,huyghenian principle of which we have already spoken in the history of the centre of oscillation2 namely1 the equality of the actual descent of the particles and the potential ascent2 or1 in other words1 the conservation of vis viva4 ,this was the first analytical treatise2 and the analysis is declared by ,lagrange to be as elegant in its steps as it is simple in its results4 ,maclaurin also treated the subject2 but is accused of reasoning in such a way as to show that he had determined upon his result beforehand2 and the method of ,john ,bernoulli1 who likewise wrote upon it1 has been strongly objected to by ,d',alembert4 ,d',alembert himself applied the principle which bears his name to this subject2 publishing a ,treatise on the ,equilibrium and ,motion of ,fluids in #agdd1 and on the ,resistance of ,fluids in #agec4 ,his ,rflexions sur la ,cause ,gnrale des ,vents1 printed in #agdg1 are also a celebrated work1 belonging to this part of mathematics4 ,euler1 in this as in other cases1 was one of those who most contributed to give analytical elegance to the subject4 ,in addition to the questions which #cgi have been mentioned1 he and ,lagrange treated the problems of the small vibrations of fluids1 both inelastic and elastic2--a subject which leads1 like the question of vibrating strings1 to some subtle and abstruse considerations concerning the significations of the integrals of partial differential equations4 ,laplace also took up the subject of waves propagated along the surface of water2 and deduced a very celebrated theory of the tides1 in which he considered the ocean to be1 not in equilibrium1 as preceding writers had supposed1 but agitated by a constant series of undulations1 produced by the solar and lunar forces4 ,the difficulty of such an investigation may be judged of from this1 that ,laplace1 in order to carry it on1 is obliged to assume a mechanical proposition1 unproved1 and only conjectured to be true2 namely1#fbf that1 in a system of bodies acted upon by forces which are periodical1 the state of the system is periodical like the forces4 ,even with this assumption1 various other arbitrary processes are requisite2 and it appears still very doubtful whether ,laplace's theory is either a better mechanical solution of the problem1 or a nearer approximation to the laws of the phenomena1 than that obtained by ,d4 ,bernoulli1 following the views of ,newton4 ,note #fbf3 ,mc4 ,cl4 t4 ii4 p4 #bah4 ,in most cases1 the solutions of problems of hydrodynamics are not satisfactorily confirmed by the results of observation4 ,poisson and ,cauchy have prosecuted the subject of waves1 and have deduced very curious conclusions by a very recondite and profound analysis4 ,the assumptions of the mathematician here do not represent the conditions of nature2 the rules of theory1 therefore1 are not a good standard to which we may refer the aberrations of particular cases2 and the laws which we obtain from experiment are very imperfectly illustrated by priori calculation4 ,the case of this department of knowledge1 ,hydrodynamics1 is very peculiar2 we have reached the highest point of the science1--the laws of extreme simplicity and generality from which the phenomena flow2 we cannot doubt that the ultimate principles which we have obtained are the true ones1 and those which really apply to the facts2 and yet we are far from being able to apply the principles to explain or find out the facts4 ,in order to do this1 we want1 in addition to what we have1 true and useful principles1 intermediate between the highest and the lowest2--between the extreme and almost barren generality of the laws of motion1 and the endless varieties and inextricable complexity of fluid motions in special cases4 #chj ,the reason of this peculiarity in the science of ,hydrodynamics appears to be1 that its general principles were not discovered with reference to the science itself1 but by extension from the sister science of the ,mechanics of ,solids2 they were not obtained by ascending gradually from particulars1 to truths more and more general1 respecting the motions of fluids2 but were caught at once1 by a perception that the parts of fluids are included in that range of generality which we are entitled to give to the supreme laws of motions of solids4 ,thus1 ,solid ,dynamics and ,fluid ,dynamics resemble two edifices which have their highest apartment in common1 and though we can explore every part of the former building1 we have not yet succeeded in traversing the staircase of the latter1 either from the top or from the bottom4 ,if we had lived in a world in which there were no solid bodies1 we should probably not have yet discovered the laws of motion2 if we had lived in a world in which there were no fluids1 we should have no idea how insufficient a complete possession of the general laws of motion may be1 to give us a true knowledge of particular results4 #ad4 ,various ,general ,mechanical ,principles4--,the generalized laws of motion1 the points to which ,i have endeavored to conduct my history1 include in them all other laws by which the motions of bodies can be regulated2 and among such1 several laws which had been discovered before the highest point of generalization was reached1 and which thus served as stepping-stones to the ultimate principles4 ,such were1 as we have seen1 the ,principles of the ,conservation of vis viva1 the ,principle of the ,conservation of the ,motion of the ,centre of ,gravity1 and the like4 ,these principles may1 of course1 be deduced from our elementary laws1 and were finally established by mathematicians on that footing4 ,there are other principles which may be similarly demonstrated2 among the rest1 ,i may mention the ,principle of the ,conservation of areas1 which extends to any number of bodies a law analogous to that which ,kepler had observed1 and ,newton demonstrated1 respecting the areas described by each planet round the sun4 ,i may mention also1 the ,principle of the ,immobility of the plane of maximum areas1 a plane which is not disturbed by any mutual action of the parts of any system4 ,the former of these principles was published about the same time by ,euler1 ,d4 ,bernoulli1 and ,darcy1 under different forms1 in #agdf and #agdg2 the latter by ,laplace4 ,to these may be added a law1 very celebrated in its time1 and the occasion of an angry controversy1 the ,principle of least action4 #cha ,maupertuis conceived that he could establish priori1 by theological arguments1 that all mechanical changes must take place in the world so as to occasion the least possible quantity of action4 ,in asserting this1 it was proposed to measure the ,action by the product of ,velocity and ,space2 and this measure being adopted1 the mathematicians1 though they did not generally assent to ,maupertuis' reasonings1 found that his principle expressed a remarkable and useful truth1 which might be established on known mechanical grounds4 #ae4 ,analytical ,generality4 ,connection of ,statics and ,dynamics4--,before ,i quit this subject1 it is important to remark the peculiar character which the science of ,mechanics has now assumed1 in consequence of the extreme analytical generality which has been given it4 ,symbols1 and operations upon symbols1 include the whole of the reasoner's task2 and though the relations of space are the leading subjects in the science1 the great analytical treatises upon it do not contain a single diagram4 ,the ,mcanique ,analytique of ,lagrange1 of which the first edition appeared in #aghh1 is by far the most consummate example of this analytical generality4 ,the plan of this work1 says the author1 is entirely new4 ,i have proposed to myself to reduce the whole theory of this science1 and the art of resolving the problems which it includes1 to general formul1 of which the simple development gives all the equations necessary for the solution of the problem4--,the reader will find no figures in the work4 ,the methods which ,i deliver do not require either constructions1 or geometrical or mechanical reasonings2 but only algebraical operations1 subject to a regular and uniform rule of proceeding4 ,thus this writer makes ,mechanics a branch of ,analysis2 instead of making1 as had previously been done1 ,analysis an implement of ,mechanics4#fcf ,the transcendent generalizing genius of ,lagrange1 and his matchless analytical skill and elegance1 have made this undertaking as successful as it is striking4 ,note #fcf3 ,lagrange himself terms ,mechanics1 ,an ,analytical ,geometry of four dimensions4 ,besides the three co-ordinates which determine the place of a body in space1 the time enters as a fourth co-ordinate4 ,note by ,littrow4 ,the mathematical reader is aware that the language of mathematical symbols is1 in its nature1 more general than the language of words3 and that in this way truths1 translated into symbols1 often suggest their own generalizations4 ,something of this kind has happened in ,mechanics4 ,the same ,formula expresses the general condition of ,statics and that of ,dynamics4 ,the tendency to generalization which is thus introduced by analysis1 makes mathematicians unwilling to #chb acknowledge a plurality of ,mechanical principles2 and in the most recent analytical treatises on the subject1 all the doctrines are deduced from the single ,law of ,inertia4 ,indeed1 if we identify ,forces with the ,velocities which produce them1 and allow the ,composition of ,forces to be applicable to force so understood1 it is easy to see that we can reduce the ,laws of ,motion to the ,principles of ,statics2 and this conjunction1 though it may not be considered as philosophically just1 is verbally correct4 ,if we thus multiply or extend the meanings of the term ,force1 we make our elementary principles simpler and fewer than before2 and those persons1 therefore1 who are willing to assent to such a use of words1 can thus obtain an additional generalisation of dynamical principles2 and this1 as ,i have stated1 has been adopted in several recent treatises4 ,i shall not further discuss here how far this is a real advance in science4 ,having thus rapidly gone through the history of ,force and ,attraction in the abstract1 we return to the attempt to interpret the phenomena of the universe by the aid of these abstractions thus established4 ,but before we do so1 we may make one remark on the history of this part of science4 ,in consequence of the vast career into which the ,doctrine of ,motion has been drawn by the splendid problems proposed to it by ,astronomy1 the origin and starting-point of ,mechanics1 namely ,machines1 had almost been lost out of sight4 ,machines had become the smallest part of ,mechanics1 as ,land-measuring had become the smallest part of ,geometry4 ,yet the application of ,mathematics to the doctrine of ,machines has led1 at all periods of the ,science1 and especially in our own time1 to curious and valuable results4 ,some of these will be noticed in the ,additions to this volume4 #chc ,,book ,,vii4 ,,the ,,mechanical ,,sciences4 7,,continued47 ,,history ,,of ,,physical ,,astronomy4 ,,descend from heaven1 ,urania1 by that name ,if rightly thou art called1 whose voice divine ,following1 above the ,olympian hill ,i soar1 ,above the flight of ,pegasean wing4 ,the meaning1 not the name1 ,i call1 for thou ,nor of the muses nine1 nor on the top ,of old ,olympus dwell'st3 but heavenly-born1 ,before the hills appeared1 or fountain flowed1 ,thou with ,eternal ,wisdom didst converse1 ,wisdom1 thy sister4 ,paradise ,lost1 ,b4 vii4 #che ,,chapter ,i4 ,,prelude ,,to ,,the ,,inductive ,,epoch ,,of ,,newton4 ,,we have now to contemplate the last and most splendid period of the progress of ,astronomy2--the grand completion of the history of the most ancient and prosperous province of human knowledge2--the steps which elevated this science to an unrivalled eminence above other sciences2--the first great example of a wide and complex assemblage of phenomena indubitably traced to their single simple cause2--in short1 the first example of the formation of a perfect ,inductive ,science4 ,in this1 as in other considerable advances in real science1 the complete disclosure of the new truths by the principal discoverer1 was preceded by movements and glimpses1 by trials1 seekings1 and guesses on the part of others2 by indications1 in short1 that men's minds were already carried by their intellectual impulses in the direction in which the truth lay1 and were beginning to detect its nature4 ,in a case so important and interesting as this1 it is more peculiarly proper to give some view of this ,prelude to the ,epoch of the full discovery4 7,francis ,bacon47 ,that ,astronomy should become ,physical ,astronomy1--that the motions of the heavenly bodies should be traced to their causes1 as well as reduced to rule1--was felt by all persons of active and philosophical minds as a pressing and irresistible need1 at the time of which we speak4 ,we have already seen how much this feeling had to do in impelling ,kepler to the train of laborious research by which he made his discoveries4 ,perhaps it may be interesting to point out how strongly this persuasion of the necessity of giving a physical character to astronomy1 had taken possession of the mind of ,bacon1 who1 looking at the progress of knowledge with a more comprehensive spirit1 and from a higher point of view than ,kepler1 could have none of his astronomical prejudices1 since on that subject he was of a different school1 and of far inferior knowledge4 ,in his ,description of the ,intellectual ,globe1 ,bacon says that while ,astronomy had1 up to that time1 had it for her business to inquire into the rules of the heavenly motions1 and ,philosophy into their causes1 they had both so far worked without due appreciation of their respective tasks2 ,philosophy neglecting facts1 and ,astronomy claiming assent to her #chf mathematical hypotheses1 which ought to be considered as mere steps of calculation4 ,since1 therefore1 he continues1#ag each science has hitherto been a slight and ill-constructed thing1 we must assuredly take a firmer stand2 our ground being1 that these two subjects1 which on account of the narrowness of men's views and the traditions of professors have been so long dissevered1 are1 in fact1 one and the same thing1 and compose one body of science4 ,it must be allowed that1 however erroneous might be the points of ,bacon's positive astronomical creed1 these general views of the nature and position of the science are most sound and philosophical4 ,note #ag3 ,vol4 ix4 #bba4 7,kepler7 ,in his attempts to suggest a right physical view of the starry heavens and their relation to the earth1 ,bacon failed1 along with all the writers of his time4 ,it has already been stated that the main cause of this failure was the want of a knowledge of the true theory of motion2--the non-existence of the science of ,dynamics4 ,at the time of ,bacon and ,kepler1 it was only just beginning to be possible to reduce the heavenly motions to the laws of earthly motion1 because the latter were only just then divulged4 ,accordingly1 we have seen that the whole of ,kepler's physical speculations proceed upon an ignorance of the first law of motion1 and assume it to be the main problem of the physical astronomer to assign the cause which keeps up the motions of the planets4 ,kepler's doctrine is1 that a certain ,force or ,virtue resides in the sun1 by which all bodies within his influence are carried round him4 ,he illustrates#bg the nature of this ,virtue in various ways1 comparing it to ,light1 and to the ,magnetic ,power1 which it resembles in the circumstances of operating at a distance1 and also in exercising a feebler influence as the distance becomes greater4 ,but it was obvious that these comparisons were very imperfect2 for they do not explain how the sun produces in a body at a distance a motion athwart the line of emanation2 and though ,kepler introduced an assumed rotation of the sun on his axis as the cause of this effect1 that such a cause could produce the result could not be established by any analogy of terrestrial motions4 ,but another image to which he referred1 suggested a much more substantial and conceivable kind of mechanical action by which the celestial motions might be produced1 namely1 a current of fluid matter circulating round the sun1 and carrying the planet with it1 like a boat in a stream4 ,in the ,table of ,contents of the work on the planet ,mars1 the purport of the chapter to which ,i have alluded is #chg stated as follows3 ,a physical speculation1 in which it is demonstrated that the vehicle of that ,virtue which urges the planets1 circulates through the spaces of the universe after the manner of a river or whirlpool 7vortex71 moving quicker than the planets4 ,i think it will be found1 by any one who reads ,kepler's phrases concerning the moving force1--the magnetic nature1--the immaterial virtue of the sun1 that they convey no distinct conception1 except so far as they are interpreted by the expressions just quoted4 ,a vortex of fluid constantly whirling round the sun1 kept in this whirling motion by the rotation of the sun himself1 and carrying the planets round the sun by its revolution1 as a whirlpool carries straws1 could be readily understood2 and though it appears to have been held by ,kepler that this current and vortex was immaterial1 he ascribes to it the power of overcoming the inertia of bodies1 and of putting them and keeping them in motion1 the only material properties with which he had any thing to do4 ,kepler's physical reasonings1 therefore1 amount1 in fact1 to the doctrine of ,vortices round the central bodies1 and are occasionally so stated by himself2 though by asserting these vortices to be an immaterial species1 and by the fickleness and variety of his phraseology on the subject1 he leaves this theory in some confusion2--a proceeding1 indeed1 which both his want of sound mechanical conceptions1 and his busy and inventive fancy1 might have led us to expect4 ,nor1 we may venture to say1 was it easy for any one at ,kepler's time to devise a more plausible theory than the theory of vortices might have been made4 ,it was only with the formation and progress of the science of ,mechanics that this theory became untenable4 ,note #bg3 ,de ,stell ,martis1 ,p4 #c4 c4 xxxiv4 7,descartes7 ,but if ,kepler might be excused1 or indeed admired1 for propounding the theory of ,vortices at his time1 the case was different when the laws of motion had been fully developed1 and when those who knew the state of mechanical science ought to have learned to consider the motions of the stars as a mechanical problem1 subject to the same conditions as other mechanical problems1 and capable of the same exactness of solution4 ,and there was an especial inconsistency in the circumstance of the ,theory of ,vortices being put forwards by ,descartes1 who pretended1 or was asserted by his admirers1 to have been one of the discoverers of the true ,laws of ,motion4 ,it certainly shows both great conceit and great shallowness1 that he should have proclaimed with much pomp this crude invention of the ante-mechanical period1 at the time when the best mathematicians of ,europe1 as ,borelli in ,italy1 ,hooke and ,wallis in ,england1 ,huyghens in ,holland1 #chh were patiently laboring to bring the mechanical problem of the universe into its most distinct form1 in order that it might be solved at last and forever4 ,i do not mean to assert that ,descartes borrowed his doctrines from ,kepler1 or from any of his predecessors1 for the theory was sufficiently obvious2 and especially if we suppose the inventor to seek his suggestions rather in the casual examples offered to the sense than in the exact laws of motion4 ,nor would it be reasonable to rob this philosopher of that credit1 of the plausible deduction of a vast system from apparently simple principles1 which1 at the time1 was so much admired2 and which undoubtedly was the great cause of the many converts to his views4 ,at the same time we may venture to say that a system of doctrine thus deduced from assumed principles by a long chain of reasoning1 and not verified and confirmed at every step by detailed and exact facts1 has hardly a chance of containing any truth4 ,descartes said that he should think it little to show how the world is constructed1 if he could not also show that it must of necessity have been so constructed4 ,the more modest philosophy which has survived the boastings of his school is content to receive all its knowledge of facts from experience1 and never dreams of interposing its peremptory must be when nature is ready to tell us what is4 ,the priori philosopher has1 however1 always a strong feeling in his favor among men4 ,the deductive form of his speculations gives them something of the charm and the apparent certainty of pure mathematics2 and while he avoids that laborious recurrence to experiments1 and measures1 and multiplied observations1 which is irksome and distasteful to those who are impatient to grow wise at once1 every fact of which the theory appears to give an explanation1 seems to be an unasked and almost an infallible witness in its favor4 ,my business with ,descartes here is only with his physical ,theory of ,vortices2 which1 great as was its glory at one time1 is now utterly extinguished4 ,it was propounded in his ,principia ,philosophi1 in #afdd4 ,in order to arrive at this theory1 he begins1 as might be expected of him1 from reasonings sufficiently general4 ,he lays it down as a maxim1 in the first sentence of his book1 that a person who seeks for truth must1 once in his life1 doubt of all that he most believes4 ,conceiving himself thus to have stripped himself of all his belief on all subjects1 in order to resume that part of it which merits to be retained1 he begins with his celebrated assertion1 ,i think1 therefore ,i am2 which appears to him a certain and immovable principle1 by means of #chi which he may proceed to something more4 ,accordingly1 to this he soon adds the idea1 and hence the certain existence1 of ,god and his perfections4 ,he then asserts it to be also manifest1 that a vacuum in any part of the universe is impossible2 the whole must be filled with matter1 and the matter must be divided into equal angular parts1 this being the most simple1 and therefore the most natural supposition4#cg ,this matter being in motion1 the parts are necessarily ground into a spherical form2 and the corners thus rubbed off 7like filings or sawdust7 form a second and more subtle matter4#dg ,there is1 besides1 a third kind of matter1 of parts more coarse and less fitted for motion4 ,the first matter makes luminous bodies1 as the sun1 and the fixed stars2 the second is the transparent substance of the skies2 the third is the material of opake bodies1 as the earth1 planets1 and comets4 ,we may suppose1 also1#eg that the motions of these parts take the form of revolving circular currents1#fg or vortices4 ,by this means1 the first matter will be collected to the centre of each vortex1 while the second1 or subtle matter1 surrounds it1 and1 by its centrifugal effort1 constitutes light4 ,the planets are carried round the sun by the motion of his vortex1#gg each planet being at such a distance from the sun as to be in a part of the vortex suitable to its solidity and mobility4 ,the motions are prevented from being exactly circular and regular by various causes2 for instance1 a vortex may be pressed into an oval shape by contiguous vortices4 ,the satellites are1 in like manner1 carried round their primary planets by subordinate vortices2 while the comets have sometimes the liberty of gliding out of one vortex into the one next contiguous1 and thus travelling in a sinuous course1 from system to system1 through the universe4 ,it is not necessary for us to speak here of the entire deficiency of this system in mechanical consistency1 and in a correspondency to observation in details and measures4 ,its general reception and temporary sway1 in some instances even among intelligent men and good mathematicians1 are the most remarkable facts connected with it4 ,these may be ascribed1 in part1 to the circumstance that philosophers were now ready and eager for a physical astronomy commensurate with the existing state of knowledge2 they may have been owing also1 in some measure1 to the character and position of ,descartes4 ,he was a man of high claims in every department of speculation1 and1 in pure mathematics1 a genuine inventor of great eminence2--a man of family and a soldier2--an inoffensive philosopher1 attacked and persecuted #cij for his opinions with great bigotry and fury by a ,dutch divine1 ,voet2--the favorite and teacher of two distinguished princesses1 and1 it is said1 the lover of one of them4 ,this was ,elizabeth1 the daughter of the ,elector ,frederick1 and consequently grand-daughter of our ,james the ,first4 ,his other royal disciple1 the celebrated ,christiana of ,sweden1 showed her zeal for his instructions by appointing the hour of five in the morning for their interviews4 ,this1 in the climate of ,sweden1 and in the winter1 was too severe a trial for the constitution of the philosopher1 born in the sunny valley of the ,loire2 and1 after a short residence at ,stockholm1 he died of an inflammation of the chest in #afej4 ,he always kept up an active correspondence with his friend ,mersenne1 who was called1 by some of the ,parisians1 the ,resident of ,descartes at ,paris2 and who informed him of all that was done in the world of science4 ,it is said that he at first sent to ,mersenne an account of a system of the universe which he had devised1 which went on the assumption of a vacuum2 ,mersenne informed him that the vacuum was no longer the fashion at ,paris2 upon which he proceeded to remodel his system1 and to re-establish it on the principle of a plenum4 ,undoubtedly he tried to avoid promulgating opinions which might bring him into trouble4 ,he1 on all occasions1 endeavored to explain away the doctrine of the motion of the earth1 so as to evade the scruples to which the decrees of the pope had given rise2 and1 in stating the theory of vortices1 he says1#hg ,there is no doubt that the world was created at first with all its perfection2 nevertheless1 it is well to consider how it might have arisen from certain principles1 although we know that it did not4 ,indeed1 in the whole of his philosophy1 he appears to deserve the character of being both rash and cowardly1 pusillanimus simul et audax1 far more than ,aristotle1 to whose physical speculations ,bacon applies this description4#ig ,note #cg3 ,prin4 p4 #eh4 ,note #dg3 ,ib4 p4 #ei4 ,note #eg3 ,ib4 p4 #ef4 ,note #fg3 ,ib4 p4 #fa4 ,note #gg3 ,ib4 c4 #adj1 p4 #aad4 ,note #hg3 ,prin4 p4 #ef4 ,note #ig3 ,bacon1 ,descriptio ,globi ,intellectualis4 ,whatever the causes might be1 his system was well received and rapidly adopted4 ,gassendi1 indeed1 says that he found nobody who had the courage to read the ,principia through2#ajg but the system was soon embraced by the younger professors1 who were eager to dispute in its favor4 ,it is said#aag that the ,university of ,paris was on the point of publishing an edict against these new doctrines1 and was only prevented from doing so by a pasquinade which is worth mentioning4 ,it was composed by the poet ,boileau 7about #afhd71 and professed to be a ,request in favor of ,aristotle1 and an ,edict issued from ,mount #cia ,parnassus in consequence4 ,it is obvious that1 at this time1 the cause of ,cartesianism was looked upon as the cause of free inquiry and modern discovery1 in opposition to that of bigotry1 prejudice1 and ignorance4 ,probably the poet was far from being a very severe or profound critic of the truth of such claims4 ,this petition of the ,masters of ,arts1 ,professors and ,regents of the ,university of ,paris1 humbly showeth1 that it is of public notoriety that the sublime and incomparable ,aristotle was1 without contest1 the first founder of the four elements1 fire1 air1 earth1 and water2 that he did1 by special grace1 accord unto them a simplicity which belongeth not to them of natural right2 and so on4 ,nevertheless1 since1 a certain time past1 two individuals1 named ,reason and ,experience1 have leagued themselves together to dispute his claim to the rank which of justice pertains to him1 and have tried to erect themselves a throne on the ruins of his authority2 and1 in order the better to gain their ends1 have excited certain factious spirits1 who1 under the names of ,cartesians and ,gassendists1 have begun to shake off the yoke of their master1 ,aristotle2 and1 contemning his authority1 with unexampled temerity1 would dispute the right which he had acquired of making true pass for false and false for true2--,in fact1 this production does not exhibit any of the peculiar tenets of ,descartes1 although1 probably1 the positive points of his doctrines obtained a footing in the ,university of ,paris1 under the cover of this assault on his adversaries4 ,the ,physics of ,rohault1 a zealous disciple of ,descartes1 was published at ,paris about #afgj1abg and was1 for a time1 the standard book for students of this subject1 both in ,france and in ,england4 ,i do not here speak of the later defenders of the ,cartesian system1 for1 in their hands1 it was much modified by the struggle which it had to maintain against the ,newtonian system4 ,note #ajg3 ,del4 ,a4 ,m4 ii4 #aic4 ,note #aag3 ,enc4 ,brit4 art4 ,cartesianism4 ,note #abg3 ,and a second edition in #afgb4 ,we are concerned with ,descartes and his school only as they form part of the picture of the intellectual condition of ,europe just before the publication of ,newton's discoveries4 ,beyond this1 the ,cartesian speculations are without value4 ,when1 indeed1 ,descartes' countrymen could no longer refuse their assent and admiration to the ,newtonian theory1 it came to be the fashion among them to say that ,descartes had been the necessary precursor of ,newton2 and to adopt a favorite saying of ,leibnitz1 that the ,cartesian philosophy was the antechamber of ,truth4 ,yet this comparison is far from being happy3 it appeared rather as if these suitors had mistaken the door2 for those #cib who first came into the presence of ,truth herself1 were those who never entered this imagined antechamber1 and those who were in the antechamber first1 were the last in penetrating further4 ,in partly the same spirit1 ,playfair has noted it as a service which ,newton perhaps owed to ,descartes1 that he had exhausted one of the most tempting forms of error4 ,we shall see soon that this temptation had no attraction for those who looked at the problem in its true light1 as the ,italian and ,english philosophers already did4 ,voltaire has observed1 far more truly1 that ,newton's edifice rested on no stone of ,descartes' foundations4 ,he illustrates this by relating that ,newton only once read the work of ,descartes1 and1 in doing so1 wrote the word error1 repeatedly1 on the first seven or eight pages2 after which he read no more4 ,this volume1 ,voltaire adds1 was for some time in the possession of ,newton's nephew4#acg ,note #acg3 ,cartesianism1 ,enc4 ,phil4 7,gassendi47 ,even in his own country1 the system of ,descartes was by no means universally adopted4 ,we have seen that though ,gassendi was coupled with ,descartes as one of the leaders of the new philosophy1 he was far from admiring his work4 ,gassendi's own views of the causes of the motions of the heavenly bodies are not very clear1 nor even very clearly referrible to the laws of mechanics2 although he was one of those who had most share in showing that those laws apply to astronomical motions4 ,in a chapter1 headed#adg ,qu sit motrix siderum causa1 he reviews several opinions2 but the one which he seems to adopt1 is that which ascribes the motion of the celestial globes to certain fibres1 of which the action is similar to that of the muscles of animals4 ,it does not appear1 therefore1 that he had distinctly apprehended1 either the continuation of the movements of the planets by the ,first ,law of ,motion1 or their deflection by the ,second ,law2--the two main steps on the road to the discovery of the true forces by which they are made to describe their orbits4 ,note #adg3 ,gassendi1 ,opera1 vol4 i4 p4 #fci4 7,leibnitz1 c47 ,nor does it appear that in ,germany mathematicians had attained this point of view4 ,leibnitz1 as we have seen1 did not assent to the opinions of ,descartes1 as containing the complete truth2 and yet his own views of the physics of the universe do not seem to have any great advantage over these4 ,in #afga he published ,a new physical hypothesis1 by which the causes of most phenomena are deduced from a certain single universal motion supposed in our globe2--not to be despised either by the ,tychonians or the ,copernicans4 ,he supposes #cic the particles of the earth to have separate motions1 which produce collisions1 and thus propagate#aeg an agitation of the ether1 radiating in all directions2 and1#afg by the rotation of the sun on its axis1 concurring with its rectilinear action on the earth1 arises the motion of the earth about the sun4 ,the other motions of the solar system are1 as we might expect1 accounted for in a similar manner2 but it appears difficult to invest such an hypothesis with any mechanical consistency4 ,note #aeg3 ,art4 #e4 ,note #afg3 ,ib4 #h4 ,john ,bernoulli maintained to the last the ,cartesian hypothesis1 though with several modifications of his own1 and even pretended to apply mathematical calculation to his principles4 ,this1 however1 belongs to a later period of our history2 to the reception1 not to the prelude1 of the ,newtonian theory4 7,borelli47 ,in ,italy1 ,holland1 and ,england1 mathematicians appear to have looked much more steadily at the problem of the celestial motions1 by the light which the discovery of the real laws of motion threw upon it4 ,in ,borelli's ,theories of the ,medicean ,planets1 printed at ,florence in #afff1 we have already a conception of the nature of central action1 in which true notions begin to appear4 ,the attraction of a body upon another which revolves about it is spoken of and likened to magnetic action2 not converting the attracting force into a transverse force1 according to the erroneous views of ,kepler1 but taking it as a tendency of the bodies to meet4 ,it is manifest1 says he1#agg that every planet and satellite revolves round some principal globe of the universe as a fountain of virtue1 which so draws and holds them that they cannot by any means be separated from it1 but are compelled to follow it wherever it goes1 in constant and continuous revolutions4 ,and1 further on1 he describes#ahg the nature of the action1 as a matter of conjecture indeed1 but with remarkable correctness4#aig ,we shall account for these motions by supposing1 that which can hardly be denied1 that the planets have a certain natural appetite for uniting themselves with the globe round which they revolve1 and that they really tend1 with all their efforts1 to approach to such globe2 the planets1 for instance1 to the sun1 the ,medicean ,stars to ,jupiter4 ,it is certain1 also1 that circular motion gives a body a tendency to recede from the centre of such revolution1 as we find in a wheel1 or a stone whirled in a sling4 ,let us suppose1 then1 the planet to endeavor to approach the sun2 since1 in the mean time1 it requires1 by the circular motion1 a force to recede from the same central body1 it comes to pass1 that when #cid those two opposite forces are equal1 each compensates the other1 and the planet cannot go nearer to the sun nor further from him than a certain determinate space1 and thus appears balanced and floating about him4 ,note #agg3 ,cap4 #b4 ,note #ahg3 ,ib4 #aa4 ,note #aig3 ,p4 #dg4 ,this is a very remarkable passage2 but it will be observed1 at the same time1 that the author has no distinct conception of the manner in which the change of direction of the planet's motion is regulated from one instant to another2 still less do his views lead to any mode of calculating the distance from the central body at which the planet would be thus balanced1 or the space through which it might approach to the centre and recede from it4 ,there is a great interval from ,borelli's guesses1 even to ,huyghens' theorems and a much greater to the beginning of ,newton's discoveries4 7,england47 ,it is peculiarly interesting to us to trace the gradual approach towards these discoveries which took place in the minds of ,english mathematicians and this we can do with tolerable distinctness4 ,gilbert1 in his work1 ,de ,magnete1 printed in #afjj1 has only some vague notions that the magnetic virtue of the earth in some way determines the direction of the earth's axis1 the rate of its diurnal rotation1 and that of the revolution of the moon about it4#bjg ,he died in #afjc1 and1 in his posthumous work1 already mentioned 7,de ,mundo nostro ,sublunari ,philosophia nova1 #afea71 we have already a more distinct statement of the attraction of one body by another4#bag ,the force which emanates from the moon reaches to the earth1 and1 in like manner1 the magnetic virtue of the earth pervades the region of the moon3 both correspond and conspire by the joint action of both1 according to a proportion and conformity of motions2 but the earth has more effect1 in consequence of its superior mass2 the earth attracts and repels the moon1 and the moon1 within certain limits1 the earth2 not so as to make the bodies come together1 as magnetic bodies do1 but so that they may go on in a continuous course4 ,though this phraseology is capable of representing a good deal of the truth1 it does not appear to have been connected1 in the author's mind1 with any very definite notions of mechanical action in detail4 ,we may probably say the same of ,milton's language3 ,what if the sun ,be centre to the world2 and other stars1 ,by his attractive virtue and their own ,incited1 dance about him various rounds8 ,par4 ,lost1 ,b4 viii4 #cie ,note #bjg3 ,lib4 vi4 cap4 #f1 #g4 ,note #bag3 ,ib4 ii4 c4 #ai4 ,boyle1 about the same period1 seems to have inclined to the ,cartesian hypothesis4 ,thus1 in order to show the advantage of the natural theology which contemplates organic contrivances1 over that which refers to astronomy1 he remarks3 ,it may be said1 that in bodies inanimate1#bbg the contrivance is very rarely so exquisite but that the various motions and occurrences of their parts may1 without much improbability1 be suspected capable1 after many essays1 to cast one another into several of those circumvolutions called by ,epicurus and by ,descartes1 vortices2 which being once made1 may continue a long time after the manner explained by the latter4 ,neither ,milton nor ,boyle1 however1 can be supposed to have had an exact knowledge of the laws of mechanics2 and therefore they do not fully represent the views of their mathematical contemporaries4 ,but there arose about this time a group of philosophers1 who began to knock at the door where ,truth was to be found1 although it was left for ,newton to force it open4 ,these were the founders of the ,royal ,society1 ,wilkins1 ,wallis1 ,seth ,ward1 ,wren1 ,hooke1 and others4 ,the time of the beginning of the speculations and association of these men corresponds to the time of the civil wars between the king and parliament in ,england and it does not appear a fanciful account of their scientific zeal and activity1 to say1 that while they shared the common mental ferment of the times1 they sought in the calm and peaceful pursuit of knowledge a contrast to the vexatious and angry struggles which at that time disturbed the repose of society4 ,it was well if these dissensions produced any good to science to balance the obvious evils which flowed from them4 ,gascoigne1 the inventor of the micrometer1 a friend of ,horrox1 was killed in the battle of ,marston ,moor4 ,milburne1 another friend of ,horrox1 who like him detected the errors of ,lansberg's astronomical tables1 left papers on this subject1 which were lost by the coming of the ,scotch army into ,england in #afci2 in the civil war which ensued1 the anatomical collections of ,harvey were plundered and destroyed4 ,most of these persons of whom ,i have lately had to speak1 were involved in the changes of fortune of the ,commonwealth1 some on one side1 and some on the other4 ,wilkins was made ,warden of ,wadham by the committee of parliament appointed for reforming the ,university of ,oxford2 and was1 in #afei1 made ,master of ,trinity ,college1 ,cambridge1 by ,richard ,cromwell1 but ejected thence the year following1 upon the restoration of the #cif royal sway4 ,seth ,ward1 who was a ,fellow of ,sidney ,college1 ,cambridge1 was deprived of his ,fellowship by the parliamentary committee2 but at a later period 7#afdi7 he took the engagement to be faithful to the ,commonwealth1 and became ,savilian ,professor of ,astronomy at ,oxford4 ,wallis held a ,fellowship of ,queen's ,college1 ,cambridge1 but vacated it by marriage4 ,he was afterwards much employed by the royal party in deciphering secret writings1 in which art he had peculiar skill4 ,yet he was appointed by the parliamentary commissioners ,savilian ,professor of ,geometry at ,oxford1 in which situation he was continued by ,charles ,,ii4 after his restoration4 ,christopher ,wren was somewhat later1 and escaped these changes4 ,he was chosen ,fellow of ,all-,souls in #afeb1 and succeeded ,ward as ,savilian ,professor of ,astronomy4 ,these men1 along with ,boyle and several others1 formed themselves into a club1 which they called the ,philosophical1 or the ,invisible ,college2 and met1 from about the year #afde1 sometimes in ,london1 and sometimes in ,oxford1 according to the changes of fortune and residence of the members4 ,hooke went to ,christ ,church1 ,oxford1 in #affc1 where he was patronized by ,boyle1 ,ward1 and ,wallis2 and when the ,philosophical ,college resumed its meetings in ,london1 after the ,restoration1 as the ,royal ,society1 ,hooke was made curator of experiments4 ,halley was of the next generation1 and comes after ,newton2 he studied at ,queen's ,college1 ,oxford1 in #afgc2 but was at first a man of some fortune1 and not engaged in any official situation4 ,his talents and zeal1 however1 made him an active and effective ally in the promotion of science4 ,note #bbg3 ,shaw's ,boyle's ,works1 ii4 #afj4 ,the connection of the persons of whom we have been speaking has a bearing on our subject1 for it led1 historically speaking1 to the publication of ,newton's discoveries in physical astronomy4 ,rightly to propose a problem is no inconsiderable step to its solution2 and it was undoubtedly a great advance towards the true theory of the universe to consider the motion of the planets round the sun as a mechanical question1 to be solved by a reference to the laws of motion1 and by the use of mathematics4 ,so far the ,english philosophers appear to have gone1 before the time of ,newton4 ,hooke1 indeed1 when the doctrine of gravitation was published1 asserted that he had discovered it previously to ,newton2 and though this pretension could not be maintained1 he certainly had perceived that the thing to be done was1 to determine the effect of a central force in producing curvilinear motion2 which effect1 as we have already seen1 he illustrated by experiment as early as #afff4 ,hooke had also spoken more clearly on this subject #cig in ,an ,attempt to prove the ,motion of the ,earth from ,observations1 published in #afgd4 ,in this1 he distinctly states that the planets would move in straight lines1 if they were not deflected by central forces2 and that the central attractive power increases in approaching the centre in certain degrees1 dependent on the distance4 ,now what these degrees are1 he adds1 ,i have not yet experimentally verified2 but he ventures to promise to any one who succeeds in this undertaking1 a discovery of the cause of the heavenly motions4 ,he asserted1 in conversation1 to ,halley and ,wren1 that he had solved this problem1 but his solution was never produced4 ,the proposition that the attractive force of the sun varies inversely as the square of the distance from the centre1 had already been divined1 if not fully established4 ,if the orbits of the planets were circles1 this proportion of the forces might be deduced in the same manner as the propositions concerning circular motion1 which ,huyghens published in #afgc2 yet it does not appear that ,huyghens made this application of his principles4 ,newton1 however1 had already made this step some years before this time4 ,accordingly1 he says in a letter to ,halley1 on ,hooke's claim to this discovery1#bcg ,when ,huygenius put out his ,horologium ,oscillatorium1 a copy being presented to me1 in my letter of thanks ,i gave those rules in the end thereof a particular commendation for their usefulness in computing the forces of the moon from the earth1 and the earth from the sun4 ,he says1 moreover1 ,i am almost confident by circumstances1 that ,sir ,christopher ,wren knew the duplicate proportion when ,i gave him a visit2 and then ,mr4 ,hooke1 by his book ,cometa1 will prove the last of us three that knew it4 ,hooke's ,cometa was published in #afgh4 ,these inferences were all connected with ,kepler's law1 that the times are in the sesquiplicate ratio of the major axes of the orbits4 ,but ,halley had also been led to the duplicate proportion by another train of reasoning1 namely1 by considering the force of the sun as an emanation1 which must become more feeble in proportion to the increased spherical surface over which it is diffused1 and therefore in the inverse proportion of the square of the distances4#bdg ,in this view of the matter1 however1 the difficulty was to determine what would be the motion of a body acted on by such a force1 when the orbit is not circular but oblong4 ,the investigation of this case was a problem which1 we can #cih easily conceive1 must have appeared of very formidable complexity while it was unsolved1 and the first of its kind4 ,accordingly ,halley1 as his biographer says1 finding himself unable to make it out in any geometrical way1 first applied to ,mr4 ,hooke and ,sir ,christopher ,wren1 and meeting with no assistance from either of them1 he went to ,cambridge in ,august 7#afhd71 to ,mr4 ,newton1 who supplied him fully with what he had so ardently sought4 ,note #bcg3 ,biog4 ,brit41 art4 ,hooke4 ,note #bdg3 ,bullialdus1 in #afde1 had asserted that the force by which the sun prehendit et harpagat1 takes hold of and grapples the planets1 must be as the inverse square of the distance4 ,a paper of ,halley's in the ,philosophical ,transactions for ,january1 #afhf1 professedly inserted as a preparation for ,newton's work1 contains some arguments against the ,cartesian hypothesis of gravity1 which seem to imply that ,cartesian opinions had some footing among ,english philosophers2 and we are told by ,whiston1 ,newton's successor in his professorship at ,cambridge1 that ,cartesianism formed a part of the studies of that place4 ,indeed1 ,rohault's ,physics was used as a classbook at that ,university long after the time of which we are speaking2 but the peculiar ,cartesian doctrines which it contained were soon superseded by others4 ,with regard1 then1 to this part of the discovery1 that the force of the sun follows the inverse duplicate proportion of the distances1 we see that several other persons were on the verge of it at the same time with ,newton2 though he alone possessed that combination of distinctness of thought and power of mathematical invention1 which enabled him to force his way across the barrier4 ,but another1 and so far as we know1 an earlier train of thought1 led by a different path to the same result2 and it was the convergence of these two lines of reasoning that brought the conclusion to men's minds with irresistible force4 ,i speak now of the identification of the force which retains the moon in her orbit with the force of gravity by which bodies fall at the earth's surface4 ,in this comparison ,newton had1 so far as ,i am aware1 no forerunner4 ,we are now1 therefore1 arrived at the point at which the history of ,newton's great discovery properly begins4 #cii ,,chapter ,,ii4 ,,the ,,inductive ,,epoch ,,of ,,newton4--,,discovery ,,of ,,the ,,universal ,,gravitation ,,of ,,matter1 ,,according ,,to ,,the ,,law ,,of ,,the ,,inverse ,,square ,,of ,,the ,,distance4 ,,in order that we may the more clearly consider the bearing of this1 the greatest scientific discovery ever made1 we shall resolve it into the partial propositions of which it consists4 ,of these we may enumerate five4 ,the doctrine of universal gravitation asserts1 #a4 ,that the force by which the different planets are attracted to the sun is in the inverse proportion of the squares of their distances2 #b4 ,that the force by which the same planet is attracted to the sun1 in different parts of its orbit1 is also in the inverse proportion of the squares of the distances2 #c4 ,that the earth also exerts such a force on the moon1 and that this force is identical with the force of gravity2 #d4 ,that bodies thus act on other bodies1 besides those which revolve round them2 thus1 that the sun exerts such a force on the moon and satellites1 and that the planets exert such forces on one another2 #e4 ,that this force1 thus exerted by the general masses of the sun1 earth1 and planets1 arises from the attraction of each particle of these masses2 which attraction follows the above law1 and belongs to all matter alike4 ,the history of the establishment of these five truths will be given in order4 #a4 ,sun's ,force on ,different ,planets4--,with regard to the first of the above five propositions1 that the different planets are attracted to the sun by a force which is inversely as the square of the distance1 ,newton had so far been anticipated1 that several persons had discovered it to be true1 or nearly true2 that is1 they had discovered that if the orbits of the planets were circles1 the proportions of the central force to the inverse square of the distance would follow from ,kepler's third law1 of the sesquiplicate proportion of the periodic times4 ,as we have seen1 ,huyghens' theorems would have proved this1 if they had been so applied2 ,wren knew it2 ,hooke not only knew it1 but claimed a prior knowledge to ,newton2 and ,halley had satisfied himself that it was at #djj least nearly true1 before he visited ,newton4 ,hooke was reported to ,newton at ,cambridge1 as having applied to the ,royal ,society to do him justice with regard to his claims2 but when ,halley wrote and informed ,newton 7in a letter dated ,june #bi1 #afhf71 that ,hooke's conduct had been represented in worse colors than it ought1 ,newton inserted in his book a notice of these his predecessors1 in order1 as he said1 to compose the dispute4#beg ,this notice appears in a ,scholium to the fourth ,proposition of the ,principia1 which states the general law of revolutions in circles4 ,the case of the sixth corollary1 ,newton there says1 obtains in the celestial bodies1 as has been separately inferred by our countrymen1 ,wren1 ,hooke1 and ,halley2 he soon after names ,huyghens1 who1 in his excellent treatise ,de ,horologio ,oscillatorio1 compares the force of gravity with the centrifugal forces of revolving bodies4 ,note #beg3 ,biog4 ,brit4 folio1 art4 ,hooke4 ,the two steps requisite for this discovery were1 to propose the motions of the planets as simply a mechanical problem1 and to apply mathematical reasoning so as to solve this problem1 with reference to ,kepler's third law considered as a fact4 ,the former step was a consequence of the mechanical discoveries of ,galileo and his school2 the result of the firm and clear place which these gradually obtained in men's mind1 and of the utter abolition of all the notions of solid spheres by ,kepler4 ,the mathematical step required no small mathematical powers2 as appears1 when we consider that this was the first example of such a problem1 and that the method of limits1 under all its forms1 was at this time in its infancy1 or rather1 at its birth4 ,accordingly1 even this step1 though much the easiest in the path of deduction1 no one before ,newton completely executed4 #b4 ,force in different ,points of an ,orbit4--,the inference of the law of the force from ,kepler's two laws concerning the elliptical motion1 was a problem quite different from the preceding1 and much more difficult2 but the dispute with respect to priority in the two propositions was intermingled4 ,borelli1 in #afff1 had1 as we have seen1 endeavored to reconcile the general form of the orbit with the notion of a central attractive force1 by taking centrifugal force into the account2 and ,hooke1 in #afgi1 had asserted that the result of the law of the inverse square in the force of the earth would be an ellipse1#bfg or a curve like an ellipse4#bgg ,but it does not appear that this was any thing more than #dja a conjecture4 ,halley says#bhg that ,hooke1 in #afhc1 told him he had demonstrated all the laws of the celestial motions by the reciprocally duplicate proportion of the force of gravity2 but that1 being offered forty shillings by ,sir ,christopher ,wren to produce such a demonstration1 his answer was1 that he had it1 but would conceal it for some time1 that others1 trying and failing1 might know how to value it when he should make it public4 ,halley1 however1 truly observes1 that after the publication of the demonstration in the ,principia1 this reason no longer held2 and adds1 ,i have plainly told him1 that unless he produce another differing demonstration1 and let the world judge of it1 neither ,i nor any one else can believe it4 ,note #bfg3 ,newton's ,letter1 ,biog4 ,brit41 ,hooke1 p4 #bffj4 ,note #bgg3 ,birch's ,hist4 ,r4 ,s41 ,wallis's ,life4 ,note #bhg3 ,enc4 ,brit41 ,hooke1 p4 #bffj4 ,newton allows that ,hooke's assertions in #afgi gave occasion to his investigation on this point of the theory4 ,his demonstration is contained in the second and third ,sections of the ,principia4 ,he first treats of the general law of central forces in any curve2 and then1 on account1 as he states1 of the application to the motion of the heavenly bodies1 he treats of the case of force varying inversely as the square of the distance1 in a more diffuse manner4 ,in this1 as in the former portion of his discovery1 the two steps were1 the proposing the heavenly motions as a mechanical problem1 and the solving this problem4 ,borelli and ,hooke had certainly made the former step1 with considerable distinctness2 but the mathematical solution required no common inventive power4 ,newton seems to have been much ruffled by ,hooke's speaking slightly of the value of this second step2 and is moved in return to deny ,hooke's pretensions with some asperity1 and to assert his own4 ,he says1 in a letter to ,halley1 ,borelli did something in it1 and wrote modestly2 he 7,hooke7 has done nothing2 and yet written in such a way as if he knew1 and had sufficiently hinted all but what remained to be determined by the drudgery of calculations and observations2 excusing himself from that labor by reason of his other business2 whereas he should rather have excused himself by reason of his inability2 for it is very plain1 by his words1 he knew not how to go about it4 ,now is not this very fine8 ,mathematicians that find out1 settle1 and do all the business1 must content themselves with being nothing but dry calculators and drudges2 and another that does nothing but pretend and grasp at all things1 must carry away all the inventions1 as well of those that were to follow him as of those that #djb went before4 ,this was written1 however1 under the influence of some degree of mistake2 and in a subsequent letter1 ,newton says1 ,now ,i understand he was in some respects misrepresented to me1 ,i wish ,i had spared the postscript to my last1 in which is the passage just quoted4 ,we see1 by the melting away of rival claims1 the undivided honor which belongs to ,newton1 as the real discoverer of the proposition now under notice4 ,we may add1 that in the sequel of the third ,section of the ,principia1 he has traced its consequences1 and solved various problems flowing from it with his usual fertility and beauty of mathematical resource2 and has there shown the necessary connection of ,kepler's third law with his first and second4 #c4 ,moon's ,gravity to the ,earth4--,though others had considered cosmical forces as governed by the general laws of motion1 it does not appear that they had identified such forces with the force of terrestrial gravity4 ,this step in ,newton's discoveries has generally been the most spoken of by superficial thinkers2 and a false kind of interest has been attached to it1 from the story of its being suggested by the fall of an apple4 ,the popular mind is caught by the character of an eventful narrative which the anecdote gives to this occurrence2 and by the antithesis which makes a profound theory appear the result of a trivial accident4 ,how inappropriate is such a view of the matter we shall soon see4 ,the narrative of the progress of ,newton's thoughts1 is given by ,pemberton 7who had it from ,newton himself7 in his preface to his ,view of ,newton's ,philosophy1 and by ,voltaire1 who had it from ,mrs4 ,conduit1 ,newton's niece4#big ,the first thoughts1 we are told1 which gave rise to his ,principia1 he had when he retired from ,cambridge1 in #afff1 on account of the plague 7he was then twenty-four years of age74 ,as he sat alone in a garden1 he fell into a speculation on the power of gravity2 that as this power is not found sensibly diminished at the remotest distance from the centre of the earth to which we can rise1 neither at the tops of the loftiest buildings1 nor even on the summits of the highest mountains1 it appeared to him reasonable to conclude that this power must extend much further than was usually thought3 ,why not as high as the moon8 said he to himself2 and if so1 her motion must be influenced by it2 perhaps she is retained in her orbit thereby4 ,note #big3 ,elmens de ,phil4 de ,newton1 #cme partie1 chap4 iii4 ,the thought of cosmical gravitation was thus distinctly brought into being2 and ,newton's superiority here was1 that he conceived the #djc celestial motions as distinctly as the motions which took place close to him2--considered them as of the same kind1 and applied the same rules to each1 without hesitation or obscurity4 ,but so far1 this thought was merely a guess3 its occurrence showed the activity of the thinker2 but to give it any value1 it required much more than a why not8--a perhaps4 ,accordingly1 ,newton's why not8 was immediately succeeded by his if so1 what then8 ,his reasoning was1 that if gravity reach to the moon1 it is probably of the same kind as the central force of the sun1 and follows the same rule with respect to the distance4 ,what is this rule8 ,we have already seen that1 by calculating from ,kepler's laws1 and supposing the orbits to be circles1 the rule of the force appears to be the inverse duplicate proportion of the distance2 and this1 which had been current as a conjecture among the previous generation of mathematicians1 ,newton had already proved by indisputable reasonings1 and was thus prepared to proceed in his train of inquiry4 ,if1 then1 he went on1 pursuing his train of thought1 the earth's gravity extend to the moon1 diminishing according to the inverse square of the distance1 will it1 at the moon's orbit1 be of the proper magnitude for retaining her in her path8 ,here again came in calculation1 and a calculation of extreme interest2 for how important and how critical was the decision which depended on the resulting numbers8 ,according to ,newton's calculations1 made at this time1 the moon by her motion in her orbit1 was deflected from the tangent every minute through a space of thirteen feet4 ,but by noticing the space through which bodies would fall in one minute at the earth's surface1 and supposing this to be diminished in the ratio of the inverse square1 it appeared that gravity would1 at the moon's orbit1 draw a body through more than fifteen feet4 ,the difference seems small1 the approximation encouraging1 the theory plausible2 a man in love with his own fancies would readily have discovered or invented some probable cause of this difference4 ,but ,newton acquiesced in it as a disproof of his conjecture1 and laid aside at that time any further thoughts of this matter29999 thus resigning a favorite hypothesis1 with a candor and openness to conviction not inferior to ,kepler1 though his notion had been taken up on far stronger and sounder grounds than ,kepler dealt in2 and without even1 so far as we know1 ,kepler's regrets and struggles4 ,nor was this levity or indifference2 the idea1 though thus laid aside1 was not finally condemned and abandoned4 ,when ,hooke1 in #afgi1 contradicted ,newton on the subject of the curve described by a falling body1 and asserted it to be an ellipse1 ,newton #djd was led to investigate the subject1 and was then again conducted1 by another road1 to the same law of the inverse square of the distance4 ,this naturally turned his thoughts to his former speculations4 ,was there really no way of explaining the discrepancy which this law gave1 when he attempted to reduce the moon's motion to the action of gravity8 ,a scientific operation then recently completed1 gave the explanation at once4 ,he had been mistaken in the magnitude of the earth1 and consequently in the distance of the moon1 which is determined by measurements of which the earth's radius is the base4 ,he had taken the common estimate1 current among geographers and seamen1 that sixty ,english miles are contained in one degree of latitude4 ,but ,picard1 in #afgj1 had measured the length of a certain portion of the meridian in ,france1 with far greater accuracy than had yet been attained and this measure enabled ,newton to repeat his calculations with these amended data4 ,we may imagine the strong curiosity which he must have felt as to the result of these calculations4 ,his former conjecture was now found to agree with the phenomena to a remarkable degree of precision4 ,this conclusion1 thus coming after long doubts and delays1 and falling in with the other results of mechanical calculation for the solar system1 gave a stamp from that moment to his opinions1 and through him to those of the whole philosophical world4 #b;d ,ed4 ,dr4 ,robison 7,mechanical ,philosophy1 p4 #bhh7 says that ,newton having become a member of the ,royal ,society1 there learned the accurate measurement of the earth by ,picard1 differing very much from the estimation by which he had made his calculations in #afff4 ,and ,m4 ,biot1 in his ,life of ,newton1 published in the ,biographie ,universelle1 says1 ,according to conjecture1 about the month of ,june1 #afhb1 ,newton being in ,london at a meeting of the ,royal ,society1 mention was made of the new measure of a degree of the earth's surface1 recently executed in ,france by ,picard2 and great praise was given to the care which had been employed in making this measure exact4 ,i had adopted this conjecture as a fact in my first edition2 but it has been pointed out by ,prof4 ,rigaud 7,historical ,essay on the ,first ,publication of the ,principia1 #ahch71 that ,picard's measurement was probably well known to the ,fellows of the ,royal ,society as early as #afge1 there being an account of the results of it given in the ,philosophical ,transactions for that year4 ,newton appears to have discovered the method of determining that a body might describe an ellipse when acted upon by a force residing in the focus1 and varying #dje inversely as the square of the distance1 in #afgi1 upon occasion of his correspondence with ,hooke4 ,in #afhd1 at ,halley's request1 he returned to the subject1 and in ,february1 #afhe1 there was inserted in the ,register of the ,royal ,society a paper of ,newton's 7,isaaci ,newtoni ,propositiones de ,motu7 which contained some of the principal ,propositions of the first two ,books of the ,principia4 ,this paper1 however1 does not contain the ,proposition ,lunam gravitare in terram1 nor any of the other propositions of the third ,book4 ,the ,principia was printed in #afhf and #g1 apparently at the expense of ,halley4 ,on the #fth of ,april1 #afhg1 the third ,book was presented to the ,royal ,society4 ,it does not appear1 ,i think1 that before ,newton1 philosophers in general had supposed that terrestrial gravity was the very force by which the moon's motions are produced4 ,men had1 as we have seen1 taken up the conception of such forces1 and had probably called them gravity3 but this was done only to explain1 by analogy1 what kind of forces they were1 just as at other times they compared them with magnetism2 and it did not imply that terrestrial gravity was a force which acted in the celestial spaces4 ,after ,newton had discovered that this was so1 the application of the term gravity did undoubtedly convey such a suggestion2 but we should err if we inferred from this coincidence of expression that the notion was commonly entertained before him4 ,thus ,huyghens appears to use language which may be mistaken1 when he says1#cjg that ,borelli was of opinion that the primary planets were urged by gravity towards the sun1 and the satellites towards the primaries4 ,the notion of terrestrial gravity1 as being actually a cosmical force1 is foreign to all ,borelli's speculations4#cag ,but ,horrox1 as early as #afce1 appears to have entertained the true view on this subject1 although vitiated by ,keplerian errors concerning the connection between the rotation of the central body and its effect on the body which revolves about it4 ,thus he says1#cbg that the emanation of the earth carries a projected stone along with the motion of the earth1 just in the same way as it carries the moon in her orbit2 and that this force is greater on the stone than on the moon1 because the distance is less4 ,note #cjg3 9999,cosmotheoros1 l4 #b4 p4 #gbj4 ,note #cag3 ,i have found no instance in which the word is so used by him4 ,note #cbg3 ,astronomia ,kepleriana defensa et promota1 cap4 #b4 ,see further on this subject in the ,additions to this volume4 ,the ,proposition in which ,newton has stated the discovery of which we are now speaking1 is the fourth of his third ,book3 ,that the moon gravitates to the earth1 and by the force of gravity is perpetually #djf deflected from a rectilinear motion1 and retained in her orbit4 ,the proof consists in the numerical calculation1 of which he only gives the elements1 and points out the method2 but we may observe1 that no small degree of knowledge of the way in which astronomers had obtained these elements1 and judgment in selecting among them1 were necessary3 thus1 the mean distance of the moon had been made as little as fifty-six and a half semidiameters of the earth by ,tycho1 and as much as sixty-two and a half by ,kircher3 ,newton gives good reasons for adopting sixty-one4 ,the term gravity1 and the expression to gravitate1 which1 as we have just seen1 ,newton uses of the moon1 were to receive a still wider application in consequence of his discoveries2 but in order to make this extension clearer1 we consider it as a separate step4 #d4 ,mutual ,attraction of all the ,celestial ,bodies4--,if the preceding parts of the discovery of gravitation were comparatively easy to conjecture1 and difficult to prove1 this was much more the case with the part of which we have now to speak1 the attraction of other bodies1 besides the central ones1 upon the planets and satellites4 ,if the mathematical calculation of the unmixed effect of a central force required transcendent talents1 how much must the difficulty be increased1 when other influences prevented those first results from being accurately verified1 while the deviations from accuracy were far more complex than the original action6 ,if it had not been that these deviations1 though surprisingly numerous and complicated in their nature1 were very small in their quantity1 it would have been impossible for the intellect of man to deal with the subject2 as it was1 the struggle with its difficulties is even now a matter of wonder4 ,the conjecture that there is some mutual action of the planets1 had been put forth by ,hooke in his ,attempt to prove the ,motion of the ,earth 7#afgd74 ,it followed1 he said1 from his doctrine1 that not only the sun and moon act upon the course and motion of the earth1 but that ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn1 have also1 by their attractive power1 a considerable influence upon the motion of the earth1 and the earth in like manner powerfully affects the motions of those bodies4 ,and ,borelli1 in attempting to form theories of the satellites of ,jupiter1 had seen1 though dimly and confusedly1 the probability that the sun would disturb the motions of these bodies4 ,thus he says 7cap4 #ad71 ,how can we believe that the ,medicean globes are not1 like other planets1 impelled with a greater velocity when they approach the sun3 and thus they are acted upon by two moving forces1 one of #djg which produces their proper revolution about ,jupiter1 the other regulates their motion round the sun4 ,and in another place 7cap4 #bj71 he attempts to show an effect of this principle upon the inclination of the orbit2 though1 as might be expected1 without any real result4 ,the case which most obviously suggests the notion that the sun exerts a power to disturb the motions of secondary planets about primary ones1 might seem to be our own moon2 for the great inequalities which had hitherto been discovered1 had all1 except the first1 or elliptical anomaly1 a reference to the position of the sun4 ,nevertheless1 ,i do not know that any one had attempted thus to explain the curiously irregular course of the earth's attendant4 ,to calculate1 from the disturbing agency1 the amount of the irregularities1 was a problem which could not1 at any former period1 have been dreamt of as likely to be at any time within the verge of human power4 ,newton both made the step of inferring that there were such forces1 and1 to a very great extent1 calculated the effects of them4 ,the inference is made on mechanical principles1 in the sixth ,theorem of the third ,book of the ,principia2--that the moon is attracted by the sun1 as the earth is2--that the satellites of ,jupiter and ,saturn are attracted as the primaries are2 in the same manner1 and with the same forces4 ,if this were not so1 it is shown that these attendant bodies could not accompany the principal ones in the regular manner in which they do4 ,all those bodies at equal distances from the sun would be equally attracted4 ,but the complexity which must occur in tracing the results of this principle will easily be seen4 ,the satellite and the primary1 though nearly at the same distance1 and in the same direction1 from the sun1 are not exactly so4 ,moreover the difference of the distances and of the directions is perpetually changing2 and if the motion of the satellite be elliptical1 the cycle of change is long and intricate3 on this account alone the effects of the sun's action will inevitably follow cycles as long and as perplexed as those of the positions4 ,but on another account they will be still more complicated2 for in the continued action of a force1 the effect which takes place at first1 modifies and alters the effect afterwards4 ,the result at any moment is the sum of the results in preceding instants3 and since the terms1 in this series of instantaneous effects1 follow very complex rules1 the sums of such series will be1 it might be expected1 utterly incapable of being reduced to any manageable degree of simplicity4 ,it certainly does not appear that any one but ,newton could make #djh any impression on this problem1 or course of problems4 ,no one for sixty years after the publication of the ,principia1 and1 with ,newton's methods1 no one up to the present day1 had added any thing of any value to his deductions4 ,we know that he calculated all the principal lunar inequalities2 in many of the cases1 he has given us his processes2 in others1 only his results4 ,but who has presented1 in his beautiful geometry1 or deduced from his simple principles1 any of the inequalities which he left untouched8 ,the ponderous instrument of synthesis1 so effective in his hands1 has never since been grasped by one who could use it for such purposes2 and we gaze at it with admiring curiosity1 as on some gigantic implement of war1 which stands idle among the memorials of ancient days1 and makes us wonder what manner of man he was who could wield as a weapon what we can hardly lift as a burden4 ,it is not necessary to point out in detail the sagacity and skill which mark this part of the ,principia4 ,the mode in which the author obtains the effect of a disturbing force in producing a motion of the apse of an elliptical orbit 7the ninth ,section of the first ,book71 has always been admired for its ingenuity and elegance4 ,the general statement of the nature of the principal inequalities produced by the sun in the motion of a satellite1 given in the sixty-sixth ,proposition1 is1 even yet1 one of the best explanations of such action2 and the calculations of the quantity of the effects in the third ,book1 for instance1 the variation of the moon1 the motion of the nodes and its inequalities1 the change of inclination of the orbit1--are full of beautiful and efficacious artifices4 ,but ,newton's inventive faculty was exercised to an extent greater than these published investigations show4 ,in several cases he has suppressed the demonstration of his method1 and given us the result only2 either from haste or from mere weariness1 which might well overtake one who1 while he was struggling with facts and numbers1 with difficulties of conception and practice1 was aiming also at that geometrical elegance of exposition1 which he considered as alone fit for the public eye4 ,thus1 in stating the effect of the eccentricity of the moon's orbit upon the motion of the apogee1 he says1#ccg ,the computations1 as too intricate and embarrassed with approximations1 ,i do not choose to introduce4 ,note #ccg3 ,schol4 to ,prop4 #ce1 first edit4 ,the computations of the theoretical motion of the moon being thus difficult1 and its irregularities numerous and complex1 we may ask #dji whether ,newton's reasoning was sufficient to establish this part of his theory2 namely1 that her actual motions arise from her gravitation to the sun4 ,and to this we may reply1 that it was sufficient for that purpose1--since it showed that1 from ,newton's hypothesis1 inequalities must result1 following the laws which the moon's inequalities were known to follow2--since the amount of the inequalities given by the theory agreed nearly with the rules which astronomers had collected from observation2--and since1 by the very intricacy of the calculation1 it was rendered probable1 that the first results might be somewhat inaccurate1 and thus might give rise to the still remaining differences between the calculations and the facts4 ,a ,progression of the ,apogee2 a ,regression of the ,nodes2 and1 besides the ,elliptical1 or first ,inequality1 an inequality1 following the law of the ,evection1 or second inequality discovered by ,ptolemy2 another1 following the law of the ,variation discovered by ,tycho2--were pointed out in the first edition of the ,principia1 as the consequences of the theory4 ,moreover1 the quantities of these inequalities were calculated and compared with observation with the utmost confidence1 and the agreement in most instances was striking4 ,the ,variation agreed with ,halley's recent observations within a minute of a degree4#cdg ,the ,mean ,motion of the ,nodes in a year agreed within less than one-hundredth of the whole4#ceg ,the ,equation of the ,motion of the ,nodes also agreed well4#cfg ,the ,inclination of the ,plane of the ,orbit to the ecliptic1 and its changes1 according to the different situations of the nodes1 likewise agreed4#cgg ,the ,evection has been already noticed as encumbered with peculiar difficulties3 here the accordance was less close4 ,the ,difference of the daily progress of the ,apogee in syzygy1 and its daily ,regress in ,quadratures1 is1 ,newton says1 #d minutes by the ,tables1 #f by our calculation4 ,he boldly adds1 ,i suspect this difference to be due to the fault of the ,tables4 ,in the second edition 7#agaa7 he added the calculation of several other inequalities1 as the ,annual ,equation1 also discovered by ,tycho2 and he compared them with more recent observations made by ,flamsteed at ,greenwich2 but even in what has already been stated1 it must be allowed that there is a wonderful accordance of theory with phenomena1 both being very complex in the rules which they educe4 ,note #cdg3 ,b4 iii4 ,prop4 #bi4 ,note #ceg3 ,prop4 #cb4 ,note #cfg3 ,prop4 #cc4 ,note #cgg3 ,prop4 #ce4 ,the same theory which gave these ,inequalities in the motion of the ,moon produced by the disturbing force of the sun1 gave also #daj corresponding ,inequalities in the motions of the ,satellites of other planets1 arising from the same cause2 and likewise pointed out the necessary existence of irregularities in the motions of the ,planets arising from their mutual attraction4 ,newton gave propositions by which the ,irregularities of the motion of ,jupiter's moons might be deduced from those of our own2#chg and it was shown that the motions of their nodes would be slow by theory1 as ,flamsteed had found it to be by observation4#cig ,but ,newton did not attempt to calculate the effect of the mutual action of the planets1 though he observes1 that in the case of ,jupiter and ,saturn this effect is too considerable to be neglected2#djg and he notices in the second edition1#dag that it follows from the theory of gravity1 that the aphelia of ,mercury1 ,venus1 the ,earth1 and ,mars1 slightly progress4 ,note #chg3 ,b4 i4 ,prop4 #ff4 ,note #cig3 ,b4 iii4 ,prop4 #bc4 ,note #djg3 ,b4 iii4 ,prop4 #ac4 ,note #dag3 ,scholium to ,prop4 #ad4 ,b4 iii4 ,in one celebrated instance1 indeed1 the deviation of the theory of the ,principia from observation was wider1 and more difficult to explain2 and as this deviation for a time resisted the analysis of ,euler and ,clairaut1 as it had resisted the synthesis of ,newton1 it at one period staggered the faith of mathematicians in the exactness of the law of the inverse square of the distance4 ,i speak of the ,motion of the ,moon's ,apogee1 a problem which has already been referred to2 and in which ,newton's method1 and all the methods which could be devised for some time afterwards1 gave only half the observed motion2 a circumstance which arose1 as was discovered by ,clairaut in #agej1 from the insufficiency of the method of approximation4 ,newton does not attempt to conceal this discrepancy4 ,after calculating what the motion of apse would be1 upon the assumption of a disturbing force of the same amount as that which the sun exerts on the moon1 he simply says1#dbg the apse of the moon moves about twice as fast4 ,note #dbg3 ,b4 i4 ,prop4 #dd1 second edit4 ,there is reason to believe1 however1 that ,newton had1 in his unpublished calculations1 rectified this discrepancy4 ,the difficulty of doing what ,newton did in this branch of the subject1 and the powers it must have required1 may be judged of from what has already been stated2--that no one1 with his methods1 has yet been able to add any thing to his labors3 few have undertaken to illustrate what he has written1 and no great number have understood it throughout4 ,the extreme complication of the forces1 and of the conditions under which they act1 makes the subject by far the most thorny walk of mathematics4 ,it is necessary to resolve the action #daa into many elements1 such as can be separated2 to invent artifices for dealing with each of these2 and then to recompound the laws thus obtained into one common conception4 ,the moon's motion cannot be conceived without comprehending a scheme more complex than the ,ptolemaic epicycles and eccentrics in their worst form2 and the component parts of the system are not1 in this instance1 mere geometrical ideas1 requiring only a distinct apprehension of relations of space in order to hold them securely2 they are the foundations of mechanical notions1 and require to be grasped so that we can apply to them sound mechanical reasonings4 ,newton's successors1 in the next generation1 abandoned the hope of imitating him in this intense mental effort2 they gave the subject over to the operation of algebraical reasoning1 in which symbols think for us1 without our dwelling constantly upon their meaning1 and obtain for us the consequences which result from the relations of space and the laws of force1 however complicated be the conditions under which they are combined4 ,even ,newton's countrymen1 though they were long before they applied themselves to the method thus opposed to his1 did not produce any thing which showed that they had mastered1 or could retrace1 the ,newtonian investigations4 ,thus the ,problem of ,three ,bodies1#dcg treated geometrically1 belongs exclusively to ,newton2 and the proofs of the mutual action of the sun1 planets1 and satellites1 which depend upon such reasoning1 could not be discovered by any one but him4 ,note #dcg3 ,see the history of the ,problem of ,three ,bodies1 ante1 in ,book vi4 ,chap4 vi4 ,sect4 #g4 ,but we have not yet done with his achievements on this subject2 for some of the most remarkable and beautiful of the reasonings which he connected with this problem1 belong to the next step of his generalization4 #e4 ,mutual ,attraction of all ,particles of ,matter4--,that all the parts of the universe are drawn and held together by love1 or harmony1 or some affection to which1 among other names1 that of attraction may have been given1 is an assertion which may very possibly have been made at various times1 by speculators writing at random1 and taking their chance of meaning and truth4 ,the authors of such casual dogmas have generally nothing accurate or substantial1 either in their conception of the general proposition1 or in their reference to examples of it2 and1 therefore1 their doctrines are no concern of ours at present4 ,but among those who were really the first to think of the mutual #dab attraction of matter1 we cannot help noticing ,francis ,bacon2 for his notions were so far from being chargeable with the looseness and indistinctness to which we have alluded1 that he proposed an experiment#ddg which was to decide whether the facts were so or not2--whether the gravity of bodies to the earth arose from an attraction of the parts of matter towards each other1 or was a tendency towards the centre of the earth4 ,and this experiment is1 even to this day1 one of the best which can be devised1 in order to exhibit the universal gravitation of matter3 it consists in the comparison of the rate of going of a clock in a deep mine1 and on a high place4 ,huyghens1 in his book ,de ,caus ,gravitatis1 published in #afij1 showed that the earth would have an oblate form1 in consequence of the action of the centrifugal force2 but his reasoning does not suppose gravity to arise from the mutual attraction of the parts of the earth4 ,the apparent influence of the moon upon the tides had long been remarked2 but no one had made any progress in truly explaining the mechanism of this influence2 and all the analogies to which reference had been made1 on this and similar subjects1 as magnetic and other attractions1 were rather delusive than illustrative1 since they represented the attraction as something peculiar in particular bodies1 depending upon the nature of each body4 ,note #ddg3 ,nov4 ,org4 ,lib4 ii4 ,aph4 #cf4 ,that all such forces1 cosmical and terrestrial1 were the same single force1 and that this was nothing more than the insensible attraction which subsists between one stone and another1 was a conception equally bold and grand2 and would have been an incomprehensible thought1 if the views which we have already explained had not prepared the mind for it4 ,but the preceding steps having disclosed1 between all the bodies of the universe1 forces of the same kind as those which produce the weight of bodies at the earth1 and1 therefore1 such as exist in every particle of terrestrial matter2 it became an obvious question1 whether such forces did not also belong to all particles of planetary matter1 and whether this was not1 in fact1 the whole account of the forces of the solar system4 ,but1 supposing this conjecture to be thus suggested1 how formidable1 on first appearance at least1 was the undertaking of verifying it6 ,for if this be so1 every finite mass of matter exerts forces which are the result of the infinitely numerous forces of its particles1 these forces acting in different directions4 ,it does not appear1 at first sight1 that the law by which the force is related to the distance1 will be the same for the particles as it is for the masses2 and1 in reality1 it #dac is not so1 except in special cases4 ,and1 again1 in the instance of any effect produced by the force of a body1 how are we to know whether the force resides in the whole mass as a unit1 or in the separate particles8 ,we may reason1 as ,newton does1#deg that the rule which proves gravity to belong universally to the planets1 proves it also to belong to their parts2 but the mind will not be satisfied with this extension of the rule1 except we can find decisive instances1 and calculate the effects of both suppositions1 under the appropriate conditions4 ,accordingly1 ,newton had to solve a new series of problems suggested by this inquiry2 and this he did4 ,note #deg3 ,princip4 ,b4 iii4 ,prop4 #g4 ,these solutions are no less remarkable for the mathematical power which they exhibit1 than the other parts of the ,principia4 ,the propositions in which it is shown that the law of the inverse square for the particles gives the same law for spherical masses1 have that kind of beauty which might well have justified their being published for their mathematical elegance alone1 even if they had not applied to any real case4 ,great ingenuity is also employed in other instances1 as in the case of spheroids of small eccentricity4 ,and when the amount of the mechanical action of masses of various forms has thus been assigned1 the sagacity shown in tracing the results of such action in the solar system is truly admirable2 not only the general nature of the effect being pointed out1 but its quantity calculated4 ,i speak in particular of the reasonings concerning the ,figure of the ,earth1 the ,tides1 the ,precession of the ,equinoxes1 the ,regression of the ,nodes of a ring such as ,saturn's2 and of some effects which1 at that time1 had not been ascertained even as facts of observation2 for instance1 the difference of gravity in different latitudes1 and the ,nutation of the earth's axis4 ,it is true1 that in most of these cases1 ,newton's process could be considered only as a rude approximation4 ,in one 7the ,precession7 he committed an error1 and in all1 his means of calculation were insufficient4 ,indeed these are much more difficult investigations than the ,problem of ,three ,bodies1 in which three points act on each other by explicit laws4 ,up to this day1 the resources of modern analysis have been employed upon some of them with very partial success2 and the facts1 in all of them1 required to be accurately ascertained and measured1 a process which is not completed even now4 ,nevertheless the form and nature of the conclusions which ,newton did obtain1 were such as to inspire a strong confidence in the competency of his theory to explain #dad all such phenomena as have been spoken of4 ,we shall afterwards have to speak of the labors1 undertaken in order to examine the phenomena more exactly1 to which the theory gave occasion4 ,thus1 then1 the theory of the universal mutual gravitation of all the particles of matter1 according to the law of the inverse square of the distances1 was conceived1 its consequences calculated1 and its results shown to agree with phenomena4 ,it was found that this theory took up all the facts of astronomy as far as they had hitherto been ascertained2 while it pointed out an interminable vista of new facts1 too minute or too complex for observation alone to disentangle1 but capable of being detected when theory had pointed out their laws1 and of being used as criteria or confirmations of the truth of the doctrine4 ,for the same reasoning which explained the evection1 variation1 and annual equation of the moon1 showed that there must be many other inequalities besides these2 since these resulted from approximate methods of calculation1 in which small quantities were neglected4 ,and it was known that1 in fact1 the inequalities hitherto detected by astronomers did not give the place of the moon with satisfactory accuracy2 so that there was room1 among these hitherto untractable irregularities1 for the additional results of the theory4 ,to work out this comparison was the employment of the succeeding century2 but ,newton began it4 ,thus1 at the end of the proposition in which he asserts1#dfg that all the lunar motions and their irregularities follow from the principles here stated1 he makes the observation which we have just made2 and gives1 as examples1 the different motions of the apogee and nodes1 the difference of the change of the eccentricity1 and the difference of the moon's variation1 according to the different distances of the sun4 ,but this inequality1 he says1 in astronomical calculations1 is usually referred to the prosthaphresis of the moon1 and confounded with it4 ,note #dfg3 ,b4 iii4 ,prop4 #bb4 ,reflections on the ,discovery4--,such1 then1 is the great ,newtonian ,induction of ,universal ,gravitation1 and such its history4 ,it is indisputably and incomparably the greatest scientific discovery ever made1 whether we look at the advance which it involved1 the extent of the truth disclosed1 or the fundamental and satisfactory nature of this truth4 ,as to the first point1 we may observe that any one of the five steps into which we have separated the doctrine1 would1 of itself1 have been considered as an important advance2--would have conferred distinction on the persons who made it1 and the time to which it belonged4 ,all #dae the five steps made at once1 formed not a leap1 but a flight1--not an improvement merely1 but a metamorphosis1--not an epoch1 but a termination4 ,astronomy passed at once from its boyhood to mature manhood4 ,again1 with regard to the extent of the truth1 we obtain as wide a generalization as our physical knowledge admits1 when we learn that every particle of matter1 in all times1 places1 and circumstances1 attracts every other particle in the universe by one common law of action4 ,and by saying that the truth was of a fundamental and satisfactory nature1 ,i mean that it assigned1 not a rule merely1 but a cause1 for the heavenly motions2 and that kind of cause which most eminently and peculiarly we distinctly and thoroughly conceive1 namely1 mechanical force4 ,kepler's laws were merely formal rules1 governing the celestial motions according to the relations of space1 time1 and number2 ,newton's was a 9999causal law1 referring these motions to mechanical reasons4 ,it is no doubt conceivable that future discoveries may both extend and further explain ,newton's doctrines2--may make gravitation a case of some wider law1 and may disclose something of the mode in which it operates2 questions with which ,newton himself struggled4 ,but1 in the mean time1 few persons will dispute1 that both in generality and profundity1 both in width and depth1 ,newton's theory is altogether without a rival or neighbor4#dgg ,note #dgg3 ,the value and nature of this step have long been generally acknowledged wherever science is cultivated4 ,yet it would appear that there is1 in one part of ,europe1 a school of philosophers who contest the merit of this part of ,newton's discoveries4 ,kepler1 says a celebrated ,german metaphysician199 discovered the laws of free motion2 a discovery of immortal glory4 ,it has since been the fashion to say that ,newton first found out the proof of these rules4 ,it has seldom happened that the glory of the first discoverer has been more unjustly transferred to another person4 ,it may appear strange that any one in the present day should hold such language2 but if we examine the reasons which this author gives1 they will be found1 ,i think1 to amount to this3 that his mind is in the condition in which ,kepler's was2 and that the whole range of mechanical ideas and modes of conception which made the transition from ,kepler and ,newton possible1 are extraneous to the domain of his philosophy4 ,even this author1 however1 if ,i understand him rightly1 recognizes ,newton as the author of the doctrine of ,perturbations4 ,i have given a further account of these views1 in a ,memoir ,on ,hegel's ,criticism of ,newton's ,principia4 ,cambridge ,transactions1 #ahdi4 99 ,hegel1 ,encyclopdia1 #bgj4 ,the requisite conditions of such a discovery in the mind of its author were1 in this as in other cases1 the idea1 and its comparison with facts2--the conception of the law1 and the moulding this conception in such a form as to correspond with known realities4 ,the idea of mechanical #daf force as the cause of the celestial motions1 had1 as we have seen1 been for some time growing up in men's minds2 had gone on becoming more distinct and more general2 and had1 in some persons1 approached the form in which it was entertained by ,newton4 ,still1 in the mere conception of universal gravitation1 ,newton must have gone far beyond his predecessors and contemporaries1 both in generality and distinctness2 and in the inventiveness and sagacity with which he traced the consequences of this conception1 he was1 as we have shown1 without a rival1 and almost without a second4 ,as to the facts which he had to include in his law1 they had been accumulating from the very birth of astronomy2 but those which he had more peculiarly to take hold of were the facts of the planetary motions as given by ,kepler1 and those of the moon's motions as given by ,tycho ,brahe and ,jeremy ,horrox4 ,we find here occasion to make a remark which is important in its bearing on the nature of progressive science4 ,what ,newton thus used and referred to as facts1 were the laws which his predecessors had established4 ,what ,kepler and ,horrox had put forth as theories1 were now established truths1 fit to be used in the construction of other theories4 ,it is in this manner that one theory is built upon another2--that we rise from particulars to generals1 and from one generalization to another2--that we have1 in short1 successive steps of induction4 ,as ,newton's laws assumed ,kepler's1 ,kepler's laws assumed as facts the results of the planetary theory of ,ptolemy2 and thus the theories of each generation in the scientific world are 7when thoroughly verified and established199997 the facts of the next generation4 ,newton's theory is the circle of generalization which includes all the others2--the highest point of the inductive ascent2--the catastrophe of the philosophic drama to which ,plato had prologized2--the point to which men's minds had been journeying for two thousand years4 ,character of ,newton4--,it is not easy to anatomize the constitution and the operations of the mind which makes such an advance in knowledge4 ,yet we may observe that there must exist in it1 in an eminent degree1 the elements which compose the mathematical talent4 ,it must possess distinctness of intuition1 tenacity and facility in tracing logical connection1 fertility of invention1 and a strong tendency to generalization4 ,it is easy to discover indications of these characteristics in ,newton4 ,the distinctness of his intuitions of space1 and we may add of force also1 was seen in the amusements of his youth2 in his constructing clocks and mills1 carts and dials1 as well as the facility with which he #dag mastered geometry4 ,this fondness for handicraft employments1 and for making models and machines1 appears to be a common prelude of excellence in physical science2#dhg probably on this very account1 that it arises from the distinctness of intuitive power with which the child conceives the shapes and the working of such material combinations4 ,newton's inventive power appears in the number and variety of the mathematical artifices and combinations which he devised1 and of which his books are full4 ,if we conceive the operation of the inventive faculty in the only way in which it appears possible to conceive it2--that while some hidden source supplies a rapid stream of possible suggestions1 the mind is on the watch to seize and detain any one of these which will suit the case in hand1 allowing the rest to pass by and be forgotten2--we shall see what extraordinary fertility of mind is implied by so many successful efforts2 what an innumerable host of thoughts must have been produced1 to supply so many that deserved to be selected4 ,and since the selection is performed by tracing the consequences of each suggestion1 so as to compare them with the requisite conditions1 we see also what rapidity and certainty in drawing conclusions the mind must possess as a talent1 and what watchfulness and patience as a habit4 ,note #dhg3 ,as in ,galileo1 ,hooke1 ,huyghens1 and others4 ,the hidden fountain of our unbidden thoughts is for us a mystery2 and we have1 in our consciousness1 no standard by which we can measure our own talents2 but our acts and habits are something of which we are conscious2 and we can understand1 therefore1 how it was that ,newton could not admit that there was any difference between himself and other men1 except in his possession of such habits as we have mentioned1 perseverance and vigilance4 ,when he was asked how he made his discoveries1 he answered1 by always thinking about them2 and at another time he declared that if he had done any thing1 it was due to nothing but industry and patient thought3 ,i keep the subject of my inquiry constantly before me1 and wait till the first dawning opens gradually1 by little and little1 into a full and clear light4 ,no better account can be given of the nature of the mental effort which gives to the philosopher the full benefit of his powers2 but the natural powers of men's minds are not on that account the less different4 ,there are many who might wait through ages of darkness without being visited by any dawn4 ,the habit to which ,newton thus1 in some sense1 owed his #dah discoveries1 this constant attention to the rising thought1 and development of its results in every direction1 necessarily engaged and absorbed his spirit1 and made him inattentive and almost insensible to external impressions and common impulses4 ,the stories which are told of his extreme absence of mind1 probably refer to the two years during which he was composing his ,principia1 and thus following out a train of reasoning the most fertile1 the most complex1 and the most important1 which any philosopher had ever had to deal with4 ,the magnificent and striking questions which1 during this period1 he must have had daily rising before him2 the perpetual succession of difficult problems of which the solution was necessary to his great object2 may well have entirely occupied and possessed him4 ,he existed only to calculate and to think4#dig ,often1 lost in meditation1 he knew not what he did1 and his mind appeared to have quite forgotten its connection with the body4 ,his servant reported that1 on rising in a morning1 he frequently sat a large portion of the day1 half-dressed1 on the side of his bed and that his meals waited on the table for hours before he came to take them4 ,even with his transcendent powers1 to do what he did was almost irreconcilable with the common conditions of human life2 and required the utmost devotion of thought1 energy of effort1 and steadiness of will--the strongest character1 as well as the highest endowments1 which belong to man4 ,note #dig3 ,biot4 ,newton has been so universally considered as the greatest example of a natural philosopher1 that his moral qualities1 as well as his intellect1 have been referred to as models of the philosophical character2 and those who love to think that great talents are naturally associated with virtue1 have always dwelt with pleasure upon the views given of ,newton by his contemporaries2 for they have uniformly represented him as candid and humble1 mild and good4 ,we may take as an example of the impressions prevalent about him in his own time1 the expressions of ,thomson1 in the ,poem on his ,death4#ejg #dai ,say ye who best can tell1 ye happy few1 ,who saw him in the softest lights of life1 ,all unwithheld1 indulging to his friends ,the vast unborrowed treasures of his mind1 ,oh1 speak the wondrous man6 how mild1 how calm ,how greatly humble1 how divinely good1 ,how firm established on eternal truth6 ,fervent in doing well1 with every nerve ,still pressing on1 forgetful of the past1 ,and panting for perfection2 far above ,those little cares and visionary joys ,that so perplex the fond impassioned heart ,of ever-cheated1 ever-trusting man4 ,note #ejg3 ,in the same strain we find the general voice of the time4 ,for instance1 one of ,loggan's ,views of ,cambridge is dedicated ,isaaco ,newtono 4 4 ,mathematico1 ,physico1 ,chymico consummatissimo2 nec minus suavitate morum et candore animi 4 4 4 spectabili4 ,in opposition to the general current of such testimony1 we have the complaints of ,flamsteed1 who ascribes to ,newton angry language and harsh conduct in the matter of the publication of the ,greenwich ,observations1 and of ,whiston4 ,yet even ,flamsteed speaks well of his general disposition4 ,whiston was himself so weak and prejudiced that his testimony is worth very little4 #b;d ,ed4 ,in the first edition of the ,principia1 published in #afhg1 ,newton showed that the nature of all the then known inequalities of the moon1 and in some cases1 their quantities1 might be deduced from the principles which he laid down but the determination of the amount and law of most of the inequalities was deferred to a more favorable opportunity1 when he might be furnished with better astronomical observations4 ,such observations as he needed for this purpose had been made by ,flamsteed1 and for these he applied1 representing how much value their use would add to the observations4 ,if1 he says1 in #afid1 you publish them without such a theory to recommend them1 they will only be thrown into the heap of the observations of former astronomers1 till somebody shall arise that by perfecting the theory of the moon shall discover your observations to be exacter than the rest2 but when that shall be1 ,god knows3 ,i fear1 not in your lifetime1 if ,i should die before it is done4 ,for ,i find this theory so very intricate1 and the theory of gravity so necessary to it1 that ,i am satisfied it will never be perfected but by somebody who understands the theory of gravity as well1 or better than ,i do4 ,he obtained from ,flamsteed the lunar observations for which he applied1 and by using these he framed the ,theory of the ,moon which is given as his in ,david ,gregory's ,astronomi ,elementa4#eag ,he also obtained from ,flamsteed the diameters of the planets as observed at various times1 and the greatest elongation of ,jupiter's ,satellites1 both of which1 ,flamsteed says1 he made use of in his ,principia4 ,note #eag3 ,in the ,preface to a ,treatise on ,dynamics1 ,part i41 published in #ahcf1 ,i have endeavored to show that ,newton's modes of determining several of the lunar inequalities admitted of an accuracy not very inferior to the modern analytical methods4 ,newton1 in his letters to ,flamsteed in #afid and #e1 acknowledges this service4#ebg9999 #dbj ,note #ebg3 ,the quarrel on the subject of the publication of ,flamsteed's ,observations took place at a later period4 ,flamsteed wished to have his ,observations printed complete and entire4 ,halley1 who1 under the authority of ,newton and others1 had the management of the printing1 made many alterations and omissions1 which ,flamsteed considered as deforming and spoiling the work4 ,the advantages of publishing a complete series of observations1 now generally understood1 were not then known to astronomers in general1 though well known to ,flamsteed1 and earnestly insisted upon in his remonstrances4 ,the result was that ,flamsteed published his ,observations at his own expense1 and finally obtained permission to destroy the copies printed by ,halley1 which he did4 ,in #agbf1 after ,flamsteed's death1 his widow applied to the ,vice-,chancellor of ,oxford1 requesting that the volume printed by ,halley might be removed out of the ,bodleian ,library1 where it exists1 as being nothing more than an erroneous abridgment of ,mr4 ,flamsteed's works1 and unfit to see the light4 ,,chapter ,,iii4 ,,sequel ,,to ,,the ,,epoch ,,of ,,newton4--,,reception ,,of ,,the ,,newtonian ,,theory4 ,sect4 #a4--;,general ,remarks4 ,,the doctrine of universal gravitation1 like other great steps in science1 required a certain time to make its way into men's minds2 and had to be confirmed1 illustrated1 and completed1 by the labors of succeeding philosophers4 ,as the discovery itself was great beyond former example1 the features of the natural sequel to the discovery were also on a gigantic scale2 and many vast and laborious trains of research1 each of which might1 in itself1 be considered as forming a wide science1 and several of which have occupied many profound and zealous inquirers from that time to our own day1 come before us as parts only of the verification of ,newton's ,theory4 ,almost every thing that has been done1 and is doing1 in astronomy1 falls inevitably under this description2 and it is only when the astronomer travels to the very limits of his vast field of labor1 that he falls in with phenomena which do not acknowledge the jurisdiction of the ,newtonian legislation4 ,we must give some account of the events of this part of the history of astronomy2 but our narrative must necessarily be extremely brief and imperfect2 for the subject is most large and copious1 and our limits are fixed and narrow4 ,we have here to do with the history of discoveries1 only so far as it illustrates their philosophy4 ,and though the #dba astronomical discoveries of the last century are by no means poor1 even in interest of this kind1 the generalizations which they involve are far less important for our object1 in consequence of being included in a previous generalization4 ,newton shines out so brightly1 that all who follow seem faint and dim4 ,it is not precisely the case which the poet describes-- ,as in a theatre the eyes of men1 ,after some well-graced actor leaves the stage1 ,are idly bent on him that enters next1 ,thinking his prattle to be tedious3 but our eyes are at least less intently bent on the astronomers who succeeded1 and we attend to their communications with less curiosity1 because we know the end1 if not the course of their story2 we know that their speeches have all closed with ,newton's sublime declaration1 asserted in some new form4 ,still1 however1 the account of the verification and extension of any great discovery is a highly important part of its history4 ,in this instance it is most important2 both from the weight and dignity of the theory concerned1 and the ingenuity and extent of the methods employed3 and1 of course1 so long as the ,newtonian theory still required verification1 the question of the truth or falsehood of such a grand system of doctrines could not but excite the most intense curiosity4 ,in what ,i have said1 ,i am very far from wishing to depreciate the value of the achievements of modern astronomers1 but it is essential to my purpose to mark the subordination of narrower to wider truths--the different character and import of the labors of those who come before and after the promulgation of a master-truth4 ,with this warning ,i now proceed to my narrative4 ,sect4 #b4--,reception of the ,newtonian ,theory in ,england4 ,,there appears to be a popular persuasion that great discoveries are usually received with a prejudiced and contentious opposition1 and the authors of them neglected or persecuted4 ,the reverse of this was certainly the case in ,england with regard to the discoveries of ,newton4 ,as we have already seen1 even before they were published1 they were proclaimed by ,halley to be something of transcendent value2 and from the moment of their appearance1 they rapidly made their way from one class of thinkers to another1 nearly as fast as the nature of men's intellectual capacity allows4 ,halley1 ,wren1 and all the leading #dbb members of the ,royal ,society1 appear to have embraced the system immediately and zealously4 ,men whose pursuits had lain rather in literature than in science1 and who had not the knowledge and habits of mind which the strict study of the system required1 adopted1 on the credit of their mathematical friends1 the highest estimation of the ,principia1 and a strong regard for its author1 as ,evelyn1 ,locke1 and ,pepys4 ,only five years after the publication1 the principles of the work were referred to from the pulpit1 as so incontestably proved that they might be made the basis of a theological argument4 ,this was done by ,dr4 ,bentley1 when he preached the ,boyle's ,lectures in ,london1 in #afib4 ,newton himself1 from the time when his work appeared1 is never mentioned except in terms of profound admiration2 as1 for instance1 when he is called by ,dr4 ,bentley1 in his sermon1#ecg ,that very excellent and divine theorist1 ,mr4 ,isaac ,newton4 ,it appears to have been soon suggested1 that the ,government ought to provide in some way for a person who was so great an honor to the nation4 ,some delay took place with regard to this2 but1 in #afie1 his friend ,mr4 ,montague1 afterwards ,earl of ,halifax1 at that time ,chancellor of the ,exchequer1 made him ,warden of the ,mint2 and in #afii1 he succeeded to the higher office of ,master of the ,mint1 a situation worth #abjj or #aejj a year1 which he filled to the end of his life4 ,in #agjc1 he became ,president of the ,royal ,society1 and was annually re-elected to this office during the remaining twenty-five years of his life4 ,in #agje1 he was knighted in the ,master's ,lodge1 at ,trinity ,college1 by ,queen ,anne1 then on a visit to the ,university of ,cambridge4 ,after the accession of ,george the ,first1 ,newton's conversation was frequently sought by the ,princess1 afterwards ,queen ,caroline1 who had a taste for speculative studies1 and was often heard to declare in public1 that she thought herself fortunate in living at a time which enabled her to enjoy the society of so great a genius4 ,his fame1 and the respect paid him1 went on increasing to the end of his life2 and when1 in #agbg1 full of years and glory1 his earthly career was ended1 his death was mourned as a national calamity1 with the forms usually confined to royalty4 ,his body lay in state in the ,jerusalem chamber2 his pall was borne by the first nobles of the land and his earthly remains were deposited in the centre of ,westminster ,abbey1 in the midst of the memorials of the greatest and wisest men whom ,england has produced4 ,note #ecg3 ,serm4 vii4 #bba4 ,it cannot be superfluous to say a word or two on the reception of #dbc his philosophy in the universities of ,england4 ,these are often represented as places where bigotry and ignorance resist1 as long as it is possible to resist1 the invasion of new truths4 ,we cannot doubt that such opinions have prevailed extensively1 when we find an intelligent and generally temperate writer1 like the late ,professor ,playfair of ,edinburgh1 so far possessed by them1 as to be incapable of seeing1 or interpreting1 in any other way1 any facts respecting ,oxford and ,cambridge4 ,yet1 notwithstanding these opinions1 it will be found that1 in the ,english universities1 new views1 whether in science or in other subjects1 have been introduced as soon as they were clearly established2--that they have been diffused from the few to the many more rapidly there than elsewhere occurs2--and that from these points1 the light of newly-discovered truths has most usually spread over the land4 ,in most instances undoubtedly there has been something of a struggle1 on such occasions1 between the old and the new opinions4 ,few men's minds can at once shake off a familiar and consistent system of doctrines1 and adopt a novel and strange set of principles as soon as presented2 but all can see that one change produces many1 and that change1 in itself1 is a source of inconvenience and danger4 ,in the case of the admission of the ,newtonian opinions into ,cambridge and ,oxford1 however1 there are no traces even of a struggle4 ,cartesianism had never struck its roots deep in this country2 that is1 the peculiar hypotheses of ,descartes4 ,the ,cartesian books1 such1 for instance1 as that of ,rohault1 were indeed in use2 and with good reason1 for they contained by far the best treatises on most of the physical sciences1 such as ,mechanics1 ,hydrostatics1 ,optics1 and ,formal ,astronomy1 which could then be found4 ,but ,i do not conceive that the ,vortices were ever dwelt upon as a matter of importance in our academic teaching4 ,at any rate1 if they were brought among us1 they were soon dissipated4 ,newton's ,college1 and his ,university1 exulted in his fame1 and did their utmost to honor and aid him4 ,he was exempted by the king from the obligation of taking orders1 under which the fellows of ,trinity ,college in general are2 by his college he was relieved from all offices which might interfere1 however slightly1 with his studious employments1 though he resided within the walls of the society thirty-five years1 almost without the interruption of a month4#edg ,by the ,university he was elected their representative in parliament in #afhh1 #dbd and again in #agja2 and though he was rejected in the dissolution of #agje1 those who opposed him acknowledged him#eeg to be the glory of the ,university and nation1 but considered the question as a political one1 and ,newton as sent to tempt them from their duty1 by the great and just veneration they had for him4 ,instruments and other memorials1 valued because they belonged to him1 are still preserved in his college1 along with the tradition of the chambers which he occupied4 ,note #edg3 ,his name is nowhere found on the college-books1 as appointed to any of the offices which usually pass down the list of resident fellows in rotation4 ,this might be owing in part1 however1 to his being ,lucasian ,professor4 ,the constancy of his residence in college appears from the exit and redit book of that time1 which is still preserved4 ,note #eeg3 ,a pamphlet by ,styan ,thurlby4 ,the most active and powerful minds at ,cambridge became at once disciples and followers of ,newton4 ,samuel ,clarke1 afterwards his friend1 defended in the public schools a thesis taken from his philosophy1 as early as #afid2 and in #afig published an edition of ,rohault's ,physics1 with notes1 in which ,newton is frequently referred to with expressions of profound respect1 though the leading doctrines of the ,principia are not introduced till a later edition1 in #agjc4 ,in #afii1 ,bentley1 whom we have already mentioned as a ,newtonian1 became ,master of ,trinity ,college2 and in the same year1 ,whiston1 another of ,newton's disciples1 was appointed his deputy as professor of mathematics4 ,whiston delivered the ,newtonian doctrines1 both from the professor's chair1 and in works written for the use of the ,university2 yet it is remarkable that a taunt respecting the late introduction of the ,newtonian system into the ,cambridge course of education1 has been founded on some peevish expressions which he uses in his ,memoirs1 written at a period when1 having incurred expulsion from his professorship and the ,university1 he was naturally querulous and jaundiced in his views4 ,in #agji-aj1 ,dr4 ,laughton1 who was tutor in ,clare ,hall1 procured himself to be appointed moderator of the ,university disputations1 in order to promote the diffusion of the new mathematical doctrines4 ,by this time the first edition of the ,principia was become rare1 and fetched a great price4 ,bentley urged ,newton to publish a new one2 and ,cotes1 by far the first1 at that time1 of the mathematicians of ,cambridge1 undertook to superintend the printing1 and the edition was accordingly published in #agac4 #b;d ,ed4 ,i perceive that my accomplished ,german translator1 ,littrow1 has incautiously copied the insinuations of some modern writers to the effect that ,clarke's reference to ,newton1 in his ,edition of ,rohault's ,physics1 was a mode of introducing ,newtonian doctrines covertly1 when it was not allowed him to introduce such novelties #dbe openly4 ,i am quite sure that any one who looks into this matter will see that this supposition of any unwillingness at ,cambridge to receive ,newton's doctrine is quite absurd1 and can prove nothing but the intense prejudices of those who maintain such an opinion4 ,newton received and held his professorship amid the unexampled admiration of all contemporary members of the ,university4 ,whiston1 who is sometimes brought as an evidence against ,cambridge on this point1 says1 ,i with immense pains set myself with the utmost zeal to the study of ,sir ,isaac ,newton's wonderful discoveries in his ,philosophi ,naturalis ,principia ,mathematica1 one or two of which lectures ,i had heard him read in the public schools1 though ,i understood them not at the time4 ,as to ,rohault's ,physics1 it really did contain the best mechanical philosophy of the time2--the doctrines which were held by ,descartes in common with ,galileo1 and with all the sound mathematicians who succeeded them4 ,nor does it look like any great antipathy to novelty in the ,university of ,cambridge1 that this book1 which was quite as novel in its doctrines as ,newton's ,principia1 and which had only been published at ,paris in #afga1 had obtained a firm hold on the ,university in less than twenty years4 ,nor is there any attempt made in ,clarke's notes to conceal the novelty of ,newton's discoveries1 but on the contrary1 admiration is claimed for them as new4 ,the promptitude with which the ,mathematicians of the ,university of ,cambridge adopted the best parts of the mechanical philosophy of ,descartes1 and the greater philosophy of ,newton1 in the seventeenth century1 has been paralleled in our own times1 in the promptitude with which they have adopted and followed into their consequences the ,mathematical ,theory of ,heat of ,fourier and ,laplace1 and the ,undulatory ,theory of ,light of ,young and ,fresnel4 ,in ,newton's ,college1 we possess1 besides the memorials of him mentioned above 7which include two locks of his silver-white hair71 a paper in his own handwriting1 describing the preparatory reading which was necessary in order that our ,college students might be able to read the ,principia4 ,i have printed this paper in the ,preface to my ,edition of the ,first ,three ,sections of the ,principia in the original ,latin 7#ahdf74 ,bentley1 who had expressed his admiration for ,newton in his ,boyle's ,lectures in #afib1 was made ,master of the ,college in #afii1 as ,i have stated2 and partly1 no doubt1 in consequence of the ,newtonian sermons which he had preached4 ,in his administration of the ,college1 he zealously stimulated and assisted the exertions of ,cotes1 ,whiston1 and other disciples of ,newton4 ,smith1 ,bentley's successor as ,master of #dbf the ,college1 erected a statue of ,newton in the ,college ,chapel 7a noble work of ,roubiliac71 with the inscription1 ,qui genus humanum ingenio superavit4 ,at ,oxford1 ,david ,gregory and ,halley1 both zealous and distinguished disciples of ,newton1 obtained the ,savilian professorships of astronomy and geometry in #afia and #agjc4 ,david ,gregory's ,astronomi ,physic et ,geometric ,elementa issued from the ,oxford ,press in #agjb4 ,the author1 in the first sentence of the ,preface1 states his object to be to explain the mechanics of the universe 7,physica ,clestis71 which ,isaac ,newton1 the ,prince of ,geometers1 has carried to a point of elevation which all look up to with admiration4 ,and this design is executed by a full exposition of the ,newtonian doctrines and their results4 ,keill1 a pupil of ,gregory1 followed his tutor to ,oxford1 and taught the ,newtonian philosophy there in #agjj1 being then ,deputy ,sedleian ,professor4 ,he illustrated his lectures by experiments1 and published an ,introduction to the ,principia which is not out of use even yet4 ,in ,scotland1 the ,newtonian philosophy was accepted with great alacrity1 as appears by the instances of ,david ,gregory and ,keill4 ,david ,gregory was professor at ,edinburgh before he removed to ,oxford1 and was succeeded there by his brother ,james4 ,the latter had1 as early as #afij1 printed a thesis1 containing in twenty-two propositions1 a compend of ,newton's ,principia4#efg ,probably these were intended as theses for academical disputations2 as ,laughton at ,cambridge introduced the ,newtonian philosophy into these exercises4 ,the formula at ,cambridge1 in use till very recently in these disputations1 was ,rect statuit ,newtonus de ,motu ,lun2 or the like4 ,note #efg3 ,see ,hutton's ,math4 ,dict41 art4 ,james ,gregory4 ,if it fell in with my plan to notice derivative works1 ,i might speak of ,maclaurin's admirable ,account of ,sir ,isaac ,newton's ,discoveries1 published in #agdh4 ,this is still one of the best books on the subject4 ,the late ,professor ,rigaud's ,historical ,essay on the ,first ,publication of ,sir ,isaac ,newton's ,principia 7,oxf4 #ahch7 contains a careful and candid view of the circumstances of that event4 ,the general diffusion of these opinions in ,england took place1 not only by means of books1 but through the labors of various experimental lecturers1 like ,desaguliers1 who removed from ,oxford to ,london in #agac2 when he informs us1#egg that he found the ,newtonian philosophy generally received among persons of all ranks and professions1 and even among the ladies by the help of experiments4 #dbg ,note #egg3 ,desag4 ,pref4 ,we might easily trace in our literature indications of the gradual progress of the ,newtonian doctrines4 ,for instance1 in the earlier editions of ,pope's ,dunciad1 this couplet occurred1 in the description of the effects of the reign of ,dulness3 ,philosophy1 that reached the heavens before1 ,shrinks to her hidden cause1 and is no more4 ,and this1 says his editor1 ,warburton1 was intended as a censure on the ,newtonian philosophy4 ,for the poet had been misled by the prejudices of foreigners1 as if that philosophy had recurred to the occult qualities of ,aristotle4 ,this was the idea he received of it from a man educated much abroad1 who had read every thing1 but every thing superficially4#ehg ,when ,i hinted to him how he had been imposed upon1 he changed the lines with great pleasure into a compliment 7as they now stand7 on that divine genius1 and a satire on that very folly by which he himself had been misled4 ,in #agdc it was printed1 ,philosophy1 that leaned on heaven before1 ,shrinks to her second cause1 and is no more4 ,the ,newtonians repelled the charge of dealing in occult causes2#eig and1 referring gravity to the will of the ,deity1 as the ,first ,cause1 assumed a superiority over those whose philosophy rested in second causes4 ,note #ehg3 ,i presume ,bolingbroke is here meant4 ,note #eig3 ,see ,cotes's ,pref4 to the ,principia4 ,to the cordial reception of the ,newtonian theory by the ,english astronomers1 there is only one conspicuous exception2 which is1 however1 one of some note1 being no other than ,flamsteed1 the ,astronomer ,royal1 a most laborious and exact observer4 ,flamsteed at first listened with complacency to the promises of improvements in the ,lunar ,tables1 which the new doctrines held forth1 and was willing to assist ,newton1 and to receive assistance from him4 ,but after a time1 he lost his respect for ,newton's theory1 and ceased to take any interest in it4 ,he then declared to one of his correspondents1#fjg ,i have determined to lay these crotchets of ,sir ,isaac ,newton's wholly aside4 ,we need not1 however1 find any difficulty in this1 if we recollect that ,flamsteed1 though a good observer1 was no philosopher2--never understood by a ,theory any thing more than a ,formula which should predict results2--and was incapable of comprehending the object of ,newton's theory1 which was to assign causes as well as rules1 and to satisfy the conditions of ,mechanics as well as of ,geometry4 #dbh ,note #fjg3 ,baily's ,account of ,flamsteed1 c41 p4 #cji4 #b;d ,ed4 ,i do not see any reason to retract what was thus said2 but it ought perhaps to be distinctly said that on these very accounts ,flamsteed's rejection of ,newton's rules did not imply a denial of the doctrine of gravitation4 ,in the letter above quoted1 ,flamsteed says that he has been employed upon the ,moon1 and that the heavens reject that equation of ,sir ,i4 ,newton which ,gregory and ,newton called his sixth3 ,i had then when he wrote before compared but #gb of my observations with the tables1 now ,i have examined above #ajj more4 ,i find them all firm in the same1 and the seventh equation too4 ,and thereupon he comes to the determination above stated4 ,at an earlier period ,flamsteed1 as ,i have said1 had received ,newton's suggestions with great deference1 and had regulated his own observations and theories with reference to them4 ,the calculation of the lunar inequalities upon the theory of gravitation was found by ,newton and his successors to be a more difficult and laborious task than he had anticipated1 and was not performed without several trials and errors4 ,one of the equations was at first published 7in ,gregory's ,astronomi ,elementa7 with a wrong sign4 ,and when ,newton had done all1 ,flamsteed found that the rules were far from coming up to the degree of accuracy which had been claimed for them1 that they could give the moon's place true to #b or #c minutes4 ,it was not till considerably later that this amount of exactness was attained4 ,the late ,mr4 ,baily1 to whom astronomy and astronomical literature are so deeply indebted1 in his ,supplement to the ,account of ,flamsteed1 has examined with great care and great candor the assertion that ,flamsteed did not understand ,newton's ,theory4 ,he remarks1 very justly1 that what ,newton himself at first presented as his ,theory1 might more properly be called ,rules for computing lunar tables1 than a physical ,theory in the modern acceptation of the term4 ,he shows1 too1 that ,flamsteed had read the ,principia with attention4#fag ,nor do ,i doubt that many considerable mathematicians gave the same imperfect assent to ,newton's doctrine which ,flamsteed did4 ,but when we find that others1 as ,halley1 ,david ,gregory1 and ,cotes1 at once not only saw in the doctrine a source of true formul1 but also a magnificent physical discovery1 we are obliged1 ,i think1 to make ,flamsteed1 in this respect1 an exception to the first class of astronomers of his own time4 ,note #fag3 ,supp4 p4 #fia4 ,mr4 ,baily's suggestion that the annual equations for the corrections of the lunar apogee and node were collected from ,flamsteed's tables #dbi and observations independently of their suggestion by ,newton as the results of ,theory 7,supp4 p4 #fib1 ,note1 and p4 #fih71 appears to me not to be adequately supported by the evidence given4 ,sect4 #c4--,reception of the ,newtonian ,theory abroad4 ,,the reception of the ,newtonian theory on the ,continent1 was much more tardy and unwilling than in its native island4 ,even those whose mathematical attainments most fitted them to appreciate its proofs1 were prevented by some peculiarity of view from adopting it as a system2 as ,leibnitz1 ,bernoulli1 ,huyghens2 who all clung to one modification or other of the system of vortices4 ,in ,france1 the ,cartesian system had obtained a wide and popular reception1 having been recommended by ,fontenelle with the graces of his style2 and its empire was so firm and well established in that country1 that it resisted for a long time the pressure of ,newtonian arguments4 ,indeed1 the ,newtonian opinions had scarcely any disciples in ,france1 till ,voltaire asserted their claims1 on his return from ,england in #agbh3 until then1 as he himself says1 there were not twenty ,newtonians out of ,england4 ,the hold which the ,philosophy of ,descartes had upon the minds of his countrymen is1 perhaps1 not surprising4 ,he really had the merit1 a great one in the history of science1 of having completely overturned the ,aristotelian system1 and introduced the philosophy of matter and motion4 ,in all branches of mixed mathematics1 as we have already said1 his followers were the best guides who had yet appeared4 ,his hypothesis of vortices1 as an explanation of the celestial motions1 had an apparent advantage over the ,newtonian doctrine1 in this respect2--that it referred effects to the most intelligible1 or at least most familiar kinds of mechanical causation1 namely1 pressure and impulse4 ,and above all1 the system was acceptable to most minds1 in consequence of being1 as was pretended1 deduced from a few simple principles by necessary consequences2 and of being also directly connected with metaphysical and theological speculations4 ,we may add1 that it was modified by its mathematical adherents in such a way as to remove most of the objections to it4 ,a vortex revolving about a centre could be constructed1 or at least it was supposed that it could be constructed1 so as to produce a tendency of bodies to the centre4 ,in all cases1 therefore1 where a central force acted1 a vortex was supposed2 but in reasoning to the results of this hypothesis1 it was #dcj easy to leave out of sight all other effects of the vortex1 and to consider only the central force2 and when this was done1 the ,cartesian mathematician could apply to his problems a mechanical principle of some degree of consistency4 ,this reflection will1 in some degree1 account for what at first seems so strange2--the fact that the language of the ,french mathematicians is ,cartesian1 for almost half a century after the publication of the ,principia of ,newton4 ,there was1 however1 a controversy between the two opinions going on all this time1 and every day showed the insurmountable difficulties under which the ,cartesians labored4 ,newton1 in the ,principia1 had inserted a series of propositions1 the object of which was to prove1 that the machinery of vortices could not be accommodated to one part of the celestial phenomena1 without contradicting another part4 ,a more obvious difficulty was the case of gravity of the earth2 if this force arose1 as ,descartes asserted1 from the rotation of the earth's vortex about its axis1 it ought to tend directly to the axis1 and not to the centre4 ,the asserters of vortices often tried their skill in remedying this vice in the hypothesis1 but never with much success4 ,huyghens supposed the ethereal matter of the vortices to revolve about the centre in all directions2 ,perrault made the strata of the vortex increase in velocity of rotation as they recede from the centre2 ,saurin maintained that the circumambient resistance which comprises the vortex will produce a pressure passing through the centre4 ,the elliptic form of the orbits of the planets was another difficulty4 ,descartes had supposed the vortices themselves to be oval but others1 as ,john ,bernoulli1 contrived ways of having elliptical motion in a circular vortex4 ,the mathematical prize-questions proposed by the ,french ,academy1 naturally brought the two sets of opinions into conflict4 ,the ,cartesian memoir of ,john ,bernoulli1 to which we have just referred1 was the one which gained the prize in #agcj4 ,it not unfrequently happened that the ,academy1 as if desirous to show its impartiality1 divided the prize between the ,cartesians and ,newtonians4 ,thus in #agcd1 the question being1 the cause of the inclination of the orbits of the planets1 the prize was shared between ,john ,bernoulli1 whose ,memoir was founded on the system of vortices1 and his son ,daniel1 who was a ,newtonian4 ,the last act of homage of this kind to the ,cartesian system was performed in #agdj1 when the prize on the question of the ,tides was distributed between ,daniel ,bernoulli1 ,euler1 ,maclaurin1 and ,cavallieri2 the last of whom had tried to patch up and amend the ,cartesian hypothesis on this subject4 #dca ,thus the ,newtonian system was not adopted in ,france till the ,cartesian generation had died off2 ,fontenelle1 who was secretary to the ,academy of ,sciences1 and who lived till #agef1 died a ,cartesian4 ,there were exceptions2 for instance1 ,delisle1 an astronomer who was selected by ,peter the ,great of ,russia1 to found the ,academy of ,st ,petersburg2 who visited ,england in #agbd1 and to whom ,newton then gave his picture1 and ,halley his ,tables4 ,but in general1 during the interval1 that country and this had a national difference of creed on physical subjects4 ,voltaire1 who visited ,england in #agbg1 notices this difference in his lively manner4 ,a ,frenchman who arrives in ,london1 finds a great alteration in philosophy1 as in other things4 ,he left the world full 9999a plenum1 he finds it empty4 ,at ,paris you see the universe composed of vortices of subtle matter1 in ,london we see nothing of the kind4 ,with you it is the pressure of the moon which causes the tides of the sea1 in ,england it is the sea which gravitates towards the moon2 so that when you think the moon ought to give us high water1 these gentlemen believe that you ought to have low water2 which unfortunately we cannot test by experience2 for in order to do that1 we should have examined the ,moon and the ,tides at the moment of the creation4 ,you will observe also that the sun1 which in ,france has nothing to do with the business1 here comes in for a quarter of it4 ,among you ,cartesians1 all is done by an impulsion which one does not well understand2 with the ,newtonians1 it is done by an attraction of which we know the cause no better4 ,at ,paris you fancy the earth shaped like a melon1 at ,london it is flattened on the two sides4 ,it was ,voltaire himself as we have said1 who was mainly instrumental in giving the ,newtonian doctrines currency in ,france4 ,he was at first refused permission to print his ,elements of the ,newtonian ,philosophy1 by the ,chancellor1 ,d',aguesseaux1 who was a ,cartesian2 but after the appearance of this work in #agch1 and of other writings by him on the same subject1 the ,cartesian edifice1 already without real support or consistency1 crumbled to pieces and disappeared4 ,the first ,memoir in the ,transactions of the ,french ,academy in which the doctrine of central force is applied to the solar system1 is one by the ,chevalier de ,louville in #agbj1 ,on the ,construction and ,theory of ,tables of the ,sun4 ,in this1 however1 the mode of explaining the motions of the planets by means of an original impulse and an attractive force is attributed to ,kepler1 not to ,newton4 ,the first ,memoir which refers to the universal gravitation of matter is by ,maupertuis1 in #dcb #agcf4 ,but ,newton was not unknown or despised in ,france till this time4 ,in #afii he was admitted one of the very small number of foreign associates of the ,french ,academy of ,sciences4 ,even ,fontenelle1 who1 as we have said1 never adopted his opinions1 spoke of him in a worthy manner1 in the ,eloge which he composed on the occasion of his death4 ,at a much earlier period too1 ,fontenelle did homage to his fame4 ,the following passage refers1 ,i presume1 to ,newton4 ,in the ,history of the ,academy for #agjh1 which is written by the secretary1 he says1#fbg in referring to the difficulty which the comets occasion in the ,cartesian hypothesis3 ,we might relieve ourselves at once from all the embarrassment which arises from the directions of these motions1 by suppressing1 as has been done by one of the greatest geniuses of the age1 all this immense fluid matter1 which we commonly suppose between the planets1 and conceiving them suspended in a perfect void4 ,note #fbg3 ,hist4 ,ac4 ,sc4 #agjh4 p4 #ajc4 ,comets1 as the above passage implies1 were a kind of artillery which the ,cartesian plenum could not resist4 ,when it appeared that the paths of such wanderers traversed the vortices in all directions1 it was impossible to maintain that these imaginary currents governed the movements of bodies immersed in them and the mechanism ceased to have any real efficacy4 ,both these phenomena of comets1 and many others1 became objects of a stronger and more general interest1 in consequence of the controversy between the rival parties2 and thus the prevalence of the ,cartesian system did not seriously impede the progress of sound knowledge4 ,in some cases1 no doubt1 it made men unwilling to receive the truth1 as in the instance of the deviation of the comets from the zodiacal motion2 and again1 when ,rmer discovered that light was not instantaneously propagated4 ,but it encouraged observation and calculation1 and thus forwarded the verification and extension of the ,newtonian system2 of which process we must now consider some of the incidents4 #dcc ,,chapter ,,iv4 ,,sequel ,,to ,,the ,,epoch ,,of ,,newton1 ,,continued4--,,verification ,,and ,,completion ,,of ,,the ,,newtonian ,,theory4 ,sect4 #a4--;,division of the ,subject4 ,,the verification of the ,law of ,universal ,gravitation as the governing principle of all cosmical phenomena1 led1 as we have already stated1 to a number of different lines of research1 all long and difficult4 ,of these we may treat successively1 the motions of the ,moon1 of the ,sun1 of the ,planets1 of the ,satellites1 of ,comets2 we may also consider separately the ,secular ,inequalities1 which at first sight appear to follow a different law from the other changes2 we may then speak of the results of the principle as they affect this ,earth1 in its ,figure1 in the amount of ,gravity at different places1 and in the phenomena of the ,tides4 ,each of these subjects has lent its aid to confirm the general law3 but in each the confirmation has had its peculiar difficulties1 and has its separate history4 ,our sketch of this history must be very rapid1 for our aim is only to show what is the kind and course of the confirmation which such a theory demands and receives4 ,for the same reason we pass over many events of this period which are highly important in the history of astronomy4 ,they have lost much of their interest for us1 and even for common readers1 because they are of a class with which we are already familiar1 truths included in more general truths to which our eyes now most readily turn4 ,thus1 the discovery of new satellites and planets is but a repetition of what was done by ,galileo3 the determination of their nodes and apses1 the reduction of their motions to the law of the ellipse1 is but a fresh exemplification of the discoveries of ,kepler4 ,otherwise1 the formation of ,tables of the satellites of ,jupiter and ,saturn1 the discovery of the eccentricities of the orbits1 and of the motions of the nodes and apses1 by ,cassini1 ,halley1 and others1 would rank with the great achievements in astronomy4 ,newton's peculiar advance in the ,tables of the celestial motions is the introduction of ,perturbations4 ,to these motions1 so affected1 we now proceed4 #dcd ,sect4 #b4--;,application of the ,newtonian ,theory to the ,moon4 ,,the ,motions of the ,moon may be first spoken of1 as the most obvious and the most important of the applications of the ,newtonian ,theory4 ,the verification of such a theory consists1 as we have seen in previous cases1 in the construction of ,tables derived from the theory1 and the comparison of these with observation4 ,the advancement of astronomy would alone have been a sufficient motive for this labor2 but there were other reasons which urged it on with a stronger impulse4 ,a perfect ,lunar ,theory1 if the theory could be perfected1 promised to supply a method of finding the ,longitude of any place on the earth's surface2 and thus the verification of a theory which professed to be complete in its foundations1 was identified with an object of immediate practical use to navigators and geographers1 and of vast acknowledged value4 ,a good method for the near discovery of the longitude had been estimated by nations and princes at large sums of money4 ,the ,dutch were willing to tempt ,galileo to this task by the offer of a chain of gold3 ,philip the ,third of ,spain had promised a reward for this object still earlier2#fcg the parliament of ,england1 in #agad1 proposed a recompense of #bj1jjjl4 sterling2 the ,regent ,duke of ,orlans1 two years afterwards1 offered #ajj1jjj francs for the same purpose4 ,these prizes1 added to the love of truth and of fame1 kept this object constantly before the eyes of mathematicians1 during the first half of the last century4 ,note #fcg3 ,del4 ,a4 ,m4 i4 #ci1 #ff4 ,if the ,tables could be so constructed as to represent the moon's real place in the heavens with extreme precision1 as it would be seen from a standard observatory1 the observation of her apparent place1 as seen from any other point of the earth's surface1 would enable the observer to find his longitude from the standard point4 ,the motions of the moon had hitherto so ill agreed with the best ,tables1 that this method failed altogether4 ,newton had discovered the ground of this want of agreement4 ,he had shown that the same force which produces the ,evection1 ,variation1 and ,annual ,equation1 must produce also a long series of other ,inequalities1 of various magnitudes and cycles1 which perpetually drag the moon before or behind the place where she would be sought by an astronomer who knew only of those principal and notorious inequalities4 ,but to calculate and apply the new inequalities1 was no slight undertaking4 #dce ,in the first edition of the ,principia in #afhg1 ,newton had not given any calculations of new inequalities affecting the longitude of the moon4 ,but in ,david ,gregory's ,elements of ,physical and ,geometrical ,astronomy1 published in #agjb1 is inserted#fdg ,newton's ,lunar ,theory as applied by him to ,practice2 in which the great discoverer has given the results of his calculations of eight of the lunar ,equations1 their quantities1 epochs1 and periods4 ,these calculations were for a long period the basis of new ,tables of the ,moon1 which were published by various persons2#feg as by ,delisle in #agae or #agaf1 ,grammatici at ,ingoldstadt in #agbf1 ,wright in #agcb1 ,angelo ,capelli at ,venice in #agcc1 ,dunthorne at ,cambridge in #agci4 ,note #fdg3 ,p4 #ccb4 ,note #feg3 ,lalande1 #adeg4 ,flamsteed had given ,tables of the ,moon upon ,horrox's theory in #afha1 and wished to improve them2 and though1 as we have seen1 he would not1 or could not1 accept ,newton's doctrines in their whole extent1 ,newton communicated his theory to the observer in the shape in which he could understand it and use it3#ffg and ,flamsteed employed these directions in constructing new ,lunar ,tables1 which he called his ,theory4#fgg ,these ,tables were not published till long after his death1 by ,le ,monnier at ,paris in #agdf4 ,they are said1 by ,lalande1#fhg not to differ much from ,halley's4 ,halley's ,tables of the ,moon were printed in #agai or #agbj1 but not published till after his death in #agdi4 ,they had been founded on ,flamsteed's observations and his own2 and when1 in #agbj1 ,halley succeeded ,flamsteed in the post of ,astronomer ,royal at ,greenwich1 and conceived that he had the means of much improving what he had done before1 he began by printing what he had already executed4#fig ,note #ffg3 ,baily4 ,account of ,flamsteed1 p4 #gb4 ,note #fgg3 ,p4 #baa4 ,note #fhg3 ,lal4 #adei4 ,note #fig3 ,mr4 ,baily99 says that ,mayer's ,nouvelles ,tables de la ,lune in 9999#agec1 published upwards of fifty years after ,gregory's ,astronomy1 may be considered as the first lunar tables formed solely on ,newton's principles4 ,though ,wright in #agcb published ,new and ,correct ,tables of the ,lunar ,motions according to the ,newtonian ,theory1 ,newton's rules were in them only partially adopted4 ,in #agce ,leadbetter published his ,uranoscopia1 in which those rules were more fully followed4 ,but these ,newtonian ,tables did not supersede ,flamsteed's ,horroxian ,tables1 till both were supplanted by those of ,mayer4 99 ,supp4 p4 #gjb4 ,but ,halley had long proposed a method1 different from that of ,newton1 but marked by great ingenuity1 for amending the ,lunar ,tables4 ,he proposed to do this by the use of a cycle1 which we have mentioned as one of the earliest discoveries in astronomy2--the ,period of #bbc lunations1 or eighteen years and eleven days1 the ,chaldean #dcf ,saros4 ,this period was anciently used for predicting the eclipses of the sun and moon2 for those eclipses which happen during this period1 are repeated again in the same order1 and with nearly the same circumstances1 after the expiration of one such period and the commencement of a second4 ,the reason of this is1 that at the end of such a cycle1 the moon is in nearly the same position with respect to the sun1 her nodes1 and her apogee1 as she was at first2 and is only a few degrees distant from the same part of the heavens4 ,but on the strength of this consideration1 ,halley conjectured that all the irregularities of the moon's motion1 however complex they may be1 would recur after such an interval2 and that1 therefore1 if the requisite corrections were determined by observation for one such period1 we might by means of them give accuracy to the ,tables for all succeeding periods4 ,this idea occurred to him before he was acquainted with ,newton's views4#gjg ,after the lunar theory of the ,principia had appeared1 he could not help seeing that the idea was confirmed2 for the inequalities of the moon's motion1 which arise from the attraction of the sun1 will depend on her positions with regard to the sun1 the apogee1 and the node2 and therefore1 however numerous1 will recur when these positions recur4 ,note #gjg3 ,phil4 ,trans4 #agca1 p4 #ahh4 ,halley announced1 in #afia1gag his intention of following this idea into practice2 in a paper in which he corrected the text of three passages in ,pliny1 in which this period is mentioned1 and from which it is sometimes called the ,plinian period4 ,in #agaj1 in the preface to a new edition to ,street's ,caroline ,tables1 he stated that he had already confirmed it to a considerable extent4#gbg ,and even after ,newton's theory had been applied1 he still resolved to use his cycle as a means of obtaining further accuracy4 ,on succeeding to the ,observatory at ,greenwich in #agbj1 he was further delayed by finding that the instruments had belonged to ,flamsteed1 and were removed by his executors4 ,and this1 he says1#gcg was the more grievous to me1 on account of my advanced age1 being then in my sixty-fourth year3 which put me past all hopes of ever living to see a complete period of eighteen years' observation4 ,but1 thanks to ,god1 he has been pleased hitherto 7in #agca7 to afford me sufficient health and strength to execute my office1 in all its parts1 with my own hands and eyes1 without any assistance or interruption1 during one whole period of the moon's #dcg apogee1 which period is performed in somewhat less than nine years4 ,he found the agreement very remarkable1 and conceived hopes of attaining the great object1 of finding the ,longitude with the requisite degree of exactness2 nor did he give up his labors on this subject till he had completed his ,plinian period in #agci4 ,note #gag3 ,ib4 p4 #ecf4 ,note #gbg3 ,ib4 #agca1 p4 #ahg4 ,note #gcg3 ,ib4 p4 #aic4 ,the accuracy with which ,halley conceived himself able to predict the moon's place#gdg was within two minutes of space1 or one fifteenth of the breadth of the moon herself4 ,the accuracy required for obtaining the national reward was considerably greater4 ,le ,monnier pursued the idea of ,halley4#geg ,but before ,halley's method had been completed1 it was superseded by the more direct prosecution of ,newton's views4 ,note #gdg3 ,phil4 ,trans4 #agca1 p4 #aie4 ,note #geg3 ,bailly1 ,a4 ,m4 c4 #aca4 ,we have already remarked1 in the history of analytical mechanics1 that in the ,lunar ,theory1 considered as one of the cases of the ,problem of ,three ,bodies1 no advance was made beyond what ,newton had done1 till mathematicians threw aside the ,newtonian artifices1 and applied the newly developed generalizations of the analytical method4 ,the first great apparent deficiency in the agreement of the law of universal gravitation with astronomical observation1 was removed by ,clairaut's improved approximation to the theoretical ,motion of the ,moon's ,apogee1 in #agej2 yet not till it had caused so much disquietude1 that ,clairaut himself had suggested a modification of the law of attraction2 and it was only in tracing the consequences of this suggestion1 that he found the ,newtonian law of the inverse square to be that which1 when rightly developed1 agreed with the facts4 ,euler solved the problem by the aid of his analysis in #agde1gfg and published ,tables of the ,moon in #agdf4 ,his tables were not very accurate at first2#ggg but he1 ,d',alembert1 and ,clairaut1 continued to labor at this object1 and the two latter published ,tables of the ,moon in #aged4ghg ,finally1 ,tobias ,mayer1 an astronomer of ,gttingen1 having compared ,euler's tables with observations1 corrected them so successfully1 that in #agec he published ,tables of the ,moon1 which really did possess the accuracy which ,halley only flattered himself that he had attained4 ,mayer's success in his first ,tables encouraged him to make them still more perfect4 ,he applied himself to the mechanical theory of the moon's orbit2 corrected all the coefficients of the series by a great number of observations2 and in #agee1 sent his new ,tables to ,london as worthy to claim the prize offered for the discovery of longitude4 ,he died soon after #dch 7in #agfb71 at the early age of thirty-nine1 worn out by his incessant labors2 and his widow sent to ,london a copy of his ,tables with additional corrections4 ,these ,tables were committed to ,bradley1 then ,astronomer ,royal1 in order to be compared with observation4 ,bradley labored at this task with unremitting zeal and industry1 having himself long entertained hopes that the ,lunar ,method of finding the ,longitude might be brought into general use4 ,he and his assistant1 ,gael ,morris1 introduced corrections into ,mayer's ,tables of #agee4 ,in his report of #agef1 he says1#gig that he did not find any difference so great as a minute and a quarter2 and in #agfj1 he adds1 that this deviation had been further diminished by his corrections4 ,it is not foreign to our purpose to observe the great labor which this verification required4 ,not less than #abbj observations1 and long calculations founded upon each1 were employed4 ,the accuracy which ,mayer's ,tables possessed was considered to entitle them to a part of the parliamentary reward2 they were printed in #aggj1 and his widow received #cjjjl4 from the ,english nation4 ,at the same time1 ,euler1 whose ,tables had been the origin and foundation of ,mayer's1 also had a recompense of the same amount4 ,note #gfg3 ,lal4 #adfj4 ,note #ggg3 ,bradley's ,correspondence4 ,note #ghg3 ,lal4 #adfj4 ,note #gig3 ,bradley's ,mem4 p4 xcviii4 ,this public national acknowledgment of the practical accuracy of these ,tables is1 it will be observed1 also a solemn recognition of the truth of the ,newtonian theory1 as far as truth can be judged of by men acting under the highest official responsibility1 and aided by the most complete command of the resources of the skill and talents of others4 ,the finding the ,longitude is thus the seal of the moon's gravitation to the sun and earth2 and with this occurrence1 therefore1 our main concern with the history of the ,lunar ,theory ends4 ,various improvements have been since introduced into this research2 but on these we1 with so many other subjects before us1 must forbear to enter4 ,sect4 #c4--;,application of the ,newtonian ,theory to the ,planets1 ,satellites1 and ,earth4 ,,the theories of the ,planets and ,satellites1 as affected by the law of universal gravitation1 and therefore by perturbations1 were naturally subjects of interest1 after the promulgation of that law4 ,some of the effects of the mutual attraction of the planets had1 indeed1 already attracted notice4 ,the inequality produced by the mutual attraction of ,jupiter and ,saturn cannot be overlooked by a good observer4 ,in the #dci preface to the second edition of the ,principia1 ,cotes remarks1#hjg that the perturbation of ,jupiter and ,saturn is not unknown to astronomers4 ,in ,halley's ,tables it was noticed#hag that there are very great deviations from regularity in these two planets1 and these deviations are ascribed to the perturbing force of the planets on each other2 but the correction of these by a suitable equation is left to succeeding astronomers4 ,note #hjg3 ,preface to ,principia1 p4 xxi4 ,note #hag3 ,end of ,planetary ,tables4 ,the motion of the planes and apsides of the planetary orbits was one of the first results of their mutual perturbation which was observed4 ,in #agjf1 ,la ,hire and ,maraldi compared ,jupiter with the ,rudolphine ,tables1 and those of ,bullialdus3 it appeared that his aphelion had advanced1 and that his nodes had regressed4 ,in #agbh1 ,j4 ,cassini found that ,saturn's aphelion had in like manner travelled forwards4 ,in #agbj1 when ,louville refused to allow in his solar tables the motion of the aphelion of the earth1 ,fontenelle observed that this was a misplaced scrupulousness1 since the aphelion of ,mercury certainly advances4 ,yet this reluctance to admit change and irregularity was not yet overcome4 ,when astronomers had found an approximate and apparent constancy and regularity1 they were willing to believe it absolute and exact4 ,in the satellites of ,jupiter1 for instance1 they were unwilling to admit even the eccentricity of the orbits2 and still more1 the variation of the nodes1 inclinations1 and apsides4 ,but all the fixedness of these was successively disproved4 ,fontenelle in #agcb1 on the occasion of ,maraldi's discovery of the change of inclination of the fourth satellite1 expresses a suspicion that all the elements might prove liable to change4 ,we see1 says he1 the constancy of the inclination already shaken in the three first satellites1 and the eccentricity in the fourth4 ,the immobility of the nodes holds out so far1 but there are strong indications that it will share the same fate4 ,the motions of the nodes and apsides of the satellites are a necessary part of the ,newtonian theory2 and even the ,cartesian astronomers now required only data1 in order to introduce these changes into their ,tables4 ,the complete reformation of the ,tables of the ,sun1 ,planets1 and ,satellites1 which followed as a natural consequence from the revolution which ,newton had introduced1 was rendered possible by the labors of the great constellation of mathematicians of whom we have spoken in the last book1 ,clairaut1 ,euler1 ,d',alembert1 and their successors2 and #ddj it was carried into effect in the course of the last century4 ,thus ,lalande applied ,clairaut's theory to ,mars1 as did ,mayer2 and the inequalities in this case1 says ,bailly#hbg in #aghe1 may amount to two minutes1 and therefore must not be neglected4 ,lalande determined the inequalities of ,venus1 as did ,father ,walmesley1 an ,english mathematician2 these were found to reach only to thirty seconds4 ,note #hbg3 ,ast4 ,mod4 iii4 #agj4 ,the ,planetary ,tables#hcg which were in highest repute1 up to the end of the last century1 were those of ,lalande4 ,in these1 the perturbations of ,jupiter and ,saturn were introduced1 their magnitude being such that they cannot be dispensed with2 but the ,tables of ,mercury1 ,venus1 and ,mars1 had no perturbations4 ,hence these latter ,tables might be considered as accurate enough to enable the observer to find the object1 but not to test the theory of perturbations4 ,but when the calculation of the mutual disturbances of the planets was applied1 it was always found that it enabled mathematicians to bring the theoretical places to coincide more exactly with those observed4 ,in improving1 as much as possible1 this coincidence1 it is necessary to determine the mass of each planet2 for upon that1 according to the law of universal gravitation1 its disturbing power depends4 ,thus1 in #ahac1 ,lindenau published ,tables of ,mercury1 and concluded1 from them1 that a considerable increase of the supposed mass of ,venus was necessary to reconcile theory with observation4#hdg ,he had published ,tables of ,venus in #ahaj1 and of ,mars in #ahaa4 ,and1 in proving ,bouvard's ,tables of ,jupiter and ,saturn1 values were obtained of the masses of those planets4 ,the form in which the question of the truth of the doctrine of universal gravitation now offers itself to the minds of astronomers1 is this3--that it is taken for granted that it will account for the motions of the heavenly bodies1 and the question is1 with what supposed masses it will give the best account4#heg ,the continually increasing accuracy of the table shows the truth of the fundamental assumption4 ,note #hcg3 ,airy1 ,report on ,ast4 to ,brit4 ,ass4 #ahcb4 ,note #hdg3 ,airy1 ,report on ,ast4 to ,brit4 9999,ass4 #ahcb4 ,note #heg3 ,among the most important corrections of the supposed masses of the planets1 we may notice that of ,jupiter1 by ,professor ,airy4 ,this determination of ,jupiter's mass was founded1 not on the effect as seen in perturbations1 but on a much more direct datum1 the time of revolution of his fourth satellite4 ,it appeared1 from this calculation1 that ,jupiter's mass required to be increased by about #ahjth4 ,this result agrees with that which has been derived by ,german astronomers from the perturbations which the attractions of ,jupiter produce in the four new planets1 and has been generally adopted as an improvement of the elements of our system4 ,the question of perturbation is exemplified in the satellites also4 #dda ,thus the satellites of ,jupiter are not only disturbed by the sun1 as the moon is1 but also by each other1 as the planets are4 ,this mutual action gives rise to some very curious relations among their motions2 which1 like most of the other leading inequalities1 were forced upon the notice of astronomers by observation before they were obtained by mathematical calculation4 ,in ,bradley's remarks upon his own ,tables of ,jupiter's ,satellites1 published among ,halley's ,tables1 he observes that the places of the three interior satellites are affected by errors which recur in a cycle of #dcg days1 answering to the time in which they return to the same relative position with regard to each other1 and to the axis of ,jupiter's shadow4 ,wargentin1 who had noticed the same circumstance without knowledge of what ,bradley had done1 applied it1 with all diligence1 to the purpose of improving the tables of the satellites in #agdf4 ,but1 at a later period1 ,laplace established1 by mathematical reasoning1 the very curious theorem on which this cycle depends1 which he calls the libration of ,jupiter's satellites2 and ,delambre was then able to publish ,tables of ,jupiter's ,satellites more accurate than those of ,wargentin1 which he did in #aghi4hfg ,note #hfg3 ,voiron1 ,hist4 ,ast4 p4 #cbb4 ,the progress of physical astronomy from the time of ,euler and ,clairaut1 has consisted of a series of calculations and comparisons of the most abstruse and recondite kind4 ,the formation of ,tables of the ,planets and ,satellites from the theory1 required the solution of problems much more complex than the original case of the ,problem of ,three ,bodies4 ,the real motions of the planets and their orbits are rendered still further intricate by this1 that all the lines and points to which we can refer them1 are themselves in motion4 ,the task of carrying order and law into this mass of apparent confusion1 has required a long series of men of transcendent intellectual powers2 and a perseverance and delicacy of observation1 such as we have not the smallest example of in any other subject4 ,it is impossible here to give any detailed account of these labors2 but we may mention one instance of the complex considerations which enter into them4 ,the nodes of ,jupiter's fourth satellite do not go backwards1#hgg as the ,newtonian theory seems to require2 they advance upon ,jupiter's orbit4 ,but then1 it is to be recollected that the theory requires the nodes to retrograde upon the orbit of the perturbing body1 which is here the third satellite2 and ,lalande showed that1 by the necessary relations of space1 the latter motion may be retrograde though the former is direct4 #ddb ,note #hgg3 ,bailly1 iii4 #age4 ,attempts have been made1 from the time of the solution of the ,problem of three bodies to the present1 to give the greatest possible accuracy to the ,tables of the ,sun1 by considering the effect of the various perturbations to which the earth is subject4 ,thus1 in #agef1 ,euler calculated the effect of the attractions of the planets on the earth 7the prize-question of the ,french ,academy of ,sciences71 and ,clairaut soon after4 ,lacaille1 making use of these results1 and of his own numerous observations1 published ,tables of the ,sun4 ,in #aghf1 ,delambre#hhg undertook to verify and improve these tables1 by comparing them with #cad observations made by ,maskelyne1 at ,greenwich1 in #agge and #aghd1 and in some of the intermediate years4 ,he corrected most of the elements2 but he could not remove the uncertainty which occurred respecting the amount of the inequality produced by the reaction of the moon4 ,he admitted also1 in pursuance of ,clairaut's theory1 a second term of this inequality depending on the moon's latitude2 but irresolutely1 and half disposed to reject it on the authority of the observations4 ,succeeding researches of mathematicians have shown1 that this term is not admissible as a result of mechanical principles4 ,delambre's ,tables1 thus improved1 were exact to seven or eight seconds2#hig which was thought1 and truly1 a very close coincidence for the time4 ,but astronomers were far from resting content with this4 ,in #ahjf1 the ,french ,board of ,longitude published ,delambre's improved ,solar ,tables2 and in the ,connaissance des ,tems for #ahaf1 ,burckhardt gave the results of a comparison of ,delambre's ,tables with a great number of ,maskelyne's observations2--far greater than the number on which they were founded4#ijg ,it appeared that the epoch1 the perigee1 and the eccentricity1 required sensible alterations1 and that the mass of ,venus ought to be reduced about one-ninth1 and that of the ,moon to be sensibly diminished4 ,in #ahbg1 ,professor ,airy#iag compared ,delambre's tables with #bjjj ,greenwich observations1 made with the new transit-instrument at ,cambridge1 and deduced from this comparison the correction of the elements4 ,these in general agreed closely with ,burckhardt's1 excepting that a diminution of ,mars appeared necessary4 ,some discordances1 however1 led ,professor ,airy to suspect the existence of an inequality which had escaped the sagacity of ,laplace and ,burckhardt4 ,and1 a few weeks after this suspicion had been expressed1 the same mathematician announced to the ,royal ,society that he had #ddc detected1 in the planetary theory such an inequality1 hitherto unnoticed1 arising from the mutual attraction of ,venus and the ,earth4 ,its whole effect on the earth's longitude1 would be to increase or diminish it by nearly three seconds of space1 and its period is about #bdj years4 ,this term1 he adds1 accounts completely for the difference of the secular motions given by the comparison of the epochs of #aghc and #ahba1 and by that of the epochs of #ahja and #ahba4 ,note #hhg3 ,voiron1 ,hist4 p4 #cae4 ,note #hig3 ,montucla1 iv4 #db4 ,note #ijg3 ,airy1 ,report1 p4 #aej4 ,note #iag3 ,phil4 ,trans4 #ahbh4 ,many excellent ,tables of the motions of the sun1 moon1 and planets1 were published in the latter part of the last century2 but the ,bureau des ,longitudes which was established in ,france in #agie1 endeavored to give new or improved tables of most of these motions4 ,thus were produced ,delambre's ,tables of the ,sun1 ,burg's ,tables of the ,moon1 ,bouvard's ,tables of ,jupiter1 ,saturn1 and ,uranus4 ,the agreement between these and observation is1 in general1 truly marvellous4 ,we may notice here a difference in the mode of referring to observation when a theory is first established1 and when it is afterwards to be confirmed and corrected4 ,it was remarked as a merit in the method of ,hipparchus1 and an evidence of the mathematical coherence of his theory1 that in order to determine the place of the sun's apogee1 and the eccentricity of his orbit1 he required to know nothing besides the lengths of winter and spring4 ,but if the fewness of the requisite data is a beauty in the first fixation of a theory1 the multitude of observations to which it applies is its excellence when it is established2 and in correcting ,tables1 mathematicians take far more data than would be requisite to determine the elements4 ,for the theory ought to account for all the facts3 and since it will not do this with mathematical rigor 7for observation is not perfect71 the elements are determined1 not so as to satisfy any selected observations1 but so as to make the whole mass of error as small as possible4 ,and thus1 in the adaptation of theory to observation1 even in its most advanced state1 there is room for sagacity and skill1 prudence and judgment4 ,in this manner1 by selecting the best mean elements of the motions of the heavenly bodies1 the observed motions deviate from this mean in the way the theory points out1 and constantly return to it4 ,to this general rule1 of the constant return to a mean1 there are1 however1 some apparent exceptions1 of which we shall now speak4 #ddd ,sect4 #d4--;,application of the ,newtonian ,theory to ,secular ,inequalities4 ,,secular ,inequalities in the motions of the heavenly bodies occur in consequence of changes in the elements of the solar system1 which go on progressively from age to age4 ,the example of such changes which was first studied by astronomers1 was the ,acceleration of the ,moon's ,mean ,motion1 discovered by ,halley4 ,the observed fact was1 that the moon now moves in a very small degree quicker than she did in the earlier ages of the world4 ,when this was ascertained1 the various hypotheses which appeared likely to account for the fact were reduced to calculation4 ,the resistance of the medium in which the heavenly bodies move was the most obvious of these hypotheses4 ,another1 which was for some time dwelt upon by ,laplace1 was the successive transmission of gravity1 that is1 the hypothesis that the gravity of the earth takes a certain finite time to reach the moon4 ,but none of these suppositions gave satisfactory conclusions2 and the strength of ,euler1 ,d',alembert1 ,lagrange1 and ,laplace1 was for a time foiled by this difficulty4 ,at length1 in #aghg1 ,laplace announced to the ,academy that he had discovered the true cause of this acceleration1 and that it arose from the action of the sun upon the moon1 combined with the secular variation of the eccentricity of the earth's orbit4 ,it was found that the effects of this combination would exactly account for the changes which had hitherto so perplexed mathematicians4 ,a very remarkable result of this investigation was1 that this ,secular ,inequality of the motion of the moon is periodical1 but it requires millions of years to re-establish itself2 so that after an almost inconceivable time1 the acceleration will become a retardation4 ,laplace some time after 7in #agig71 announced other discoveries1 relative to the secular motions of the apogee and the nodes of the moon's orbit4 ,laplace collected these researches in his ,theory of the ,moon1 which he published in the third volume of the ,mcanique ,cleste in #ahjb4 ,a similar case occurred with regard to an acceleration of ,jupiter's mean motion1 and a retardation of ,saturn's1 which had been observed by ,cassini1 ,maraldi1 and ,horrox4 ,after several imperfect attempts by other mathematicians1 ,laplace1 in #aghg1 found that there resulted from the mutual attraction of these two planets a great ,inequality1 of which the period is #ibi years and a half1 and which has accelerated ,jupiter and retarded ,saturn ever since the restoration of astronomy4 #dde ,thus the secular inequalities of the celestial motions1 like all the others1 confirm the law of universal gravitation4 ,they are called secular1 because ages are requisite to unfold their existence1 and because they are not obviously periodical4 ,they might1 in some measure1 be considered as extensions of the ,newtonian theory1 for though ,newton's law accounts for such facts1 he did not1 so far as we know1 foresee such a result of it4 ,but on the other hand1 they are exactly of the same nature as those which he did foresee and calculate4 ,and when we call them secular in opposition to periodical1 it is not that there is any real difference1 for they1 too1 have their cycle2 but it is that we have assumed our mean motion without allowing for these long inequalities4 ,and thus1 as ,laplace observes on this very occasion1#ibg the lot of this great discovery of gravitation is no less than this1 that every apparent exception becomes a proof1 every difficulty a new occasion of a triumph4 ,and such1 as he truly adds1 is the character of a true theory1--of a real representation of nature4 ,note #ibg3 ,syst4 du ,monde1 #hvo1 ii4 #cg4 ,it is impossible for us here to enumerate even the principal objects which have thus filled the triumphal march of the ,newtonian theory from its outset up to the present time4 ,but among these secular changes1 we may mention the ,diminution of the ,obliquity of the ,ecliptic1 which has been going on from the earliest times to the present4 ,this change has been explained by theory1 and shown to have1 like all the other changes of the system1 a limit1 after which the diminution will be converted into an increase4 ,we may mention here some subjects of a kind somewhat different from those just spoken of4 ,the true theoretical quantity of the ,precession of the ,equinoxes1 which had been erroneously calculated by ,newton1 was shown by ,d',alembert to agree with observation4 ,the constant coincidence of the ,nodes of the ,moon's ,equator with those of her ,orbit1 was proved to result from mechanical principles by ,lagrange4 ,the curious circumstance that the ,time of the ,moon's rotation on her axis is equal to the ,time of her revolution about the earth1 was shown to be consistent with the results of the laws of motion by ,laplace4 ,laplace also1 as we have seen1 explained certain remarkable relations which constantly connect the longitudes of the three first satellites of ,jupiter2 ,bailly and ,lagrange analyzed and explained the curious librations of the nodes and inclinations of their orbits2 and ,laplace traced the effect of ,jupiter's oblate figure on their motions1 #ddf which masks the other causes of inequality1 by determining the direction of the motions of the perijove and node of each satellite4 ,sect4 #e4--;,application of the ,newtonian ,theory to the ,new ,planets4 ,,we are now so accustomed to consider the ,newtonian theory as true1 that we can hardly imagine to ourselves the possibility that those planets which were not discovered when the theory was founded1 should contradict its doctrines4 ,we can scarcely conceive it possible that ,uranus or ,ceres should have been found to violate ,kepler's laws1 or to move without suffering perturbations from ,jupiter and ,saturn4 ,yet if we can suppose men to have had any doubt of the exact and universal truth of the doctrine of universal gravitation1 at the period of these discoveries1 they must have scrutinized the motions of these new bodies with an interest far more lively than that with which we now look for the predicted return of a comet4 ,the solid establishment of the ,newtonian theory is thus shown by the manner in which we take it for granted not only in our reasonings1 but in our feelings4 ,but though this is so1 a short notice of the process by which the new planets were brought within the domain of the theory may properly find a place here4 ,william ,herschel1 a man of great energy and ingenuity1 who had made material improvements in reflecting telescopes1 observing at ,bath on the #acth of ,march1 #agha1 discovered1 in the constellation ,gemini1 a star larger and less luminous than the fixed stars4 ,on the application of a more powerful telescope1 it was seen magnified1 and two days afterwards he perceived that it had changed its place4 ,the attention of the astronomical world was directed to this new object1 and the best astronomers in every part of ,europe employed themselves in following it along the sky4#icg ,note #icg3 ,voiron1 ,hist4 ,ast4 p4 #ab4 ,the admission of an eighth planet into the long-established list1 was a notion so foreign to men's thoughts at that time1 that other suppositions were first tried4 ,the orbit of the new body was at first calculated as if it had been a comet running in a parabolic path4 ,but in a few days the star deviated from the course thus assigned it3 and it was in vain that in order to represent the observations1 the perihelion distance of the parabola was increased from fourteen to eighteen times the earth's distance from the sun4 ,saron1 of the ,academy of ,sciences of ,paris1 is said#idg to have been the first person who perceived that the #ddg places were better represented by a circle than by a parabola3 and ,lexell1 a celebrated mathematician of ,petersburg1 found that a motion in a circular orbit1 with a radius double of that of ,saturn1 would satisfy all the observations4 ,this made its period about eighty-two years4 ,note #idg3 ,ibid4 ,lalande soon discovered that the circular motion was subject to a sensible inequality3 the orbit was1 in fact1 an ellipse1 like those of the other planets4 ,to determine the equation of the centre of a body which revolves so slowly1 would1 according to the ancient methods1 have required many years2 but ,laplace contrived methods by which the elliptical elements were determined from four observations1 within little more than a year from its first discovery by ,herschel4 ,these calculations were soon followed by tables of the new planet1 published by ,nouet4 ,in order to obtain additional accuracy1 it now became necessary to take account of the perturbations4 ,the ,french ,academy of ,sciences proposed1 in #aghi1 the construction of new ,tables of this ,planet as its prize-question4 ,it is a curious illustration of the constantly accumulating evidence of the theory1 that the calculation of the perturbations of the planet enabled astronomers to discover that it had been observed as a star in three different positions in former times2 namely1 by ,flamsteed in #afij1 by ,mayer in #agef1 and by ,le ,monnier in #agfi4 ,delambre1 aided by this discovery and by the theory of ,laplace1 calculated ,tables of the planet1 which1 being compared with observation for three years1 never deviated from it more than seven seconds4 ,the ,academy awarded its prize to these ,tables1 they were adopted by the astronomers of ,europe1 and the planet of ,herschel now conforms to the laws of attraction1 along with those ancient members of the known system from which the theory was inferred4 ,the history of the discovery of the other new planets1 ,ceres1 ,pallas1 ,juno1 and ,vesta1 is nearly similar to that just related1 except that their planetary character was more readily believed4 ,the first of these was discovered on the first day of this century by ,piazzi1 the astronomer at ,palermo2 but he had only begun to suspect its nature1 and had not completed his third observation1 when his labors were suspended by a dangerous illness2 and on his recovery the star was invisible1 being lost in the rays of the sun4 ,he declared it to be a planet with an elliptical orbit2 but the path which it followed1 on emerging from the neighborhood of the sun1 was not that which ,piazzi had traced out for it4 ,its extreme smallness made it difficult to rediscover2 and the whole of the year #ahja was #ddh employed in searching the sky for it in vain4 ,at last1 after many trials1 ,von ,zach and ,olbers again found it1 the one on the last day of #ahja1 the other on the first day of #ahjb4 ,gauss and ,burckhardt immediately used the new observations in determining the elements of the orbit2 and the former invented a new method for the purpose4 ,ceres now moves in a path of which the course and inequalities are known1 and can no more escape the scrutiny of astronomers4 ,the second year of the nineteenth century also produced its planet4 ,this was discovered by ,dr4 ,olbers1 a physician of ,bremen1 while he was searching for ,ceres among the stars of the constellation ,virgo4 ,he found a star which had a perceptible motion even in the space of two hours4 ,it was soon announced as a new planet1 and received from its discoverer the name of ,pallas4 ,as in the case of ,ceres1 ,burckhardt and ,gauss employed themselves in calculating its orbit4 ,but some peculiar difficulties here occurred4 ,its eccentricity is greater than that of any of the old planets1 and the inclination of its orbit to the ecliptic is not less than thirty-five degrees4 ,these circumstances both made its perturbations large1 and rendered them difficult to calculate4 ,burckhardt employed the known processes of analysis1 but they were found insufficient3 and the ,imperial ,institute 7as the ,french ,academy was termed during the reign of ,napoleon7 proposed the ,perturbations of ,pallas as a prize-question4 ,to these discoveries succeeded others of the same kind4 ,the ,german astronomers agreed to examine the whole of the zone in which ,ceres and ,pallas move2 in the hope of finding other planets1 fragments1 as ,olbers conceived they might possibly be1 of one original mass4 ,in the course of this research1 ,mr4 ,harding of ,lilienthal1 on the first of ,september1 #ahjd1 found a new star1 which he soon was led to consider as a planet4 ,gauss and ,burckhardt also calculated the elements of this orbit1 and the planet was named ,juno4 ,after this discovery1 ,olbers sought the sky for additional fragments of his planet with extraordinary perseverance4 ,he conceived that one of two opposite constellations1 the ,virgin or the ,whale1 was the place where its separation must have taken place2 and where1 therefore1 all the orbits of all the portions must pass4 ,he resolved to survey1 three times a year1 all the small stars in these two regions4 ,this undertaking1 so curious in its nature1 was successful4 ,the #bith of ,march1 #ahjg1 he discovered ,vesta1 which was soon found to be a planet4 ,and to show the manner in which ,olbers pursued his labors1 we may state that he afterwards published a notification that he had examined the #ddi same parts of the heavens with such regularity1 that he was certain no new planet had passed that way between #ahjh and #ahaf4 ,gauss and ,burckhardt computed the orbit of ,vesta2 and when ,gauss compared one of his orbits with twenty-two observations of ,m4 ,bouvard1 he found the errors below seventeen seconds of space in right ascension1 and still less in declination4 ,the elements of all these orbits have been successively improved1 and this has been done entirely by the ,german mathematicians4#ieg ,these perturbations are calculated1 and the places for some time before and after opposition are now given in the ,berlin ,ephemeris4 ,i have lately observed1 says ,professor ,airy1 and compared with the ,berlin ,ephemeris1 the right ascensions of ,juno and ,vesta1 and ,i find that they are rather more accurate than those of ,venus3 so complete is the confirmation of the theory by these new bodies2 so exact are the methods of tracing the theory to its consequences4 ,note #ieg3 ,airy1 ,rep4 #aeg4 ,we may observe that all these new-discovered bodies have received names taken from the ancient mythology4 ,in the case of the first of these1 astronomers were originally divided2 the discoverer himself named it the ,georgium ,sidus1 in honor of his patron1 ,george the ,third2 ,lalande and others called it ,herschel4 ,nothing can be more just than this mode of perpetuating the fame of the author of a discovery2 but it was felt to be ungraceful to violate the homogeneity of the ancient system of names4 ,astronomers tried to find for the hitherto neglected denizen of the skies1 an appropriate place among the deities to whose assembly he was at last admitted2 and ,uranus1 the father of ,saturn1 was fixed upon as best suiting the order of the course4 ,the mythological nomenclature of planets appeared1 from this time1 to be generally agreed to4 ,piazzi termed his ,ceres ,ferdinandea4 ,the first term1 which contains a happy allusion to ,sicily1 the country of the discovery in modern1 and of the goddess in ancient1 times1 has been accepted2 the attempt to pay a compliment to royalty out of the products of science1 in this as in most other cases1 has been set aside4 ,pallas1 ,juno1 and ,vesta1 were named1 without any peculiar propriety of selection1 according to the choice of their discoverers4 ,sect4 #f4--;,application of the ,newtonian ,theory to ,comets4 ,a ,,few words must be said upon another class of bodies1 which at first seemed as lawless as the clouds and winds2 and which astronomy #dej has reduced to a regularity as complete as that of the sun2--upon ,comets4 ,no part of the ,newtonian discoveries excited a more intense interest than this4 ,these anomalous visitants were anciently gazed at with wonder and alarm2 and might still1 as in former times1 be accused of perplexing nations1 though with very different fears and questionings4 ,the conjecture that they1 too1 obeyed the law of universal gravitation1 was to be verified by showing that they described a curve such as that force would produce4 ,hevelius1 who was a most diligent observer of these objects1 had1 without reference to gravitation1 satisfied himself that they moved in parabolas4#ifg ,to determine the elements of the parabola from observations1 even ,newton called#igg problema longe difficillimum4 ,newton determined the orbit of the comet of #afhj by certain graphical methods4 ,his methods supposed the orbit to be a parabola1 and satisfactorily represented the motion in the visible part of the comet's path4 ,but this method did not apply to the possible return of the wandering star4 ,halley has the glory of having first detected a periodical comet1 in the case of that which has since borne his name4 ,but this great discovery was not made without labor4 ,in #agje1 ,halley#ihg explained how the parabolic orbit of a planet may be determined from three observations2 and1 joining example to precept1 himself calculated the positions and orbits of twenty-four comets4 ,he found1 as the reward of this industry1 that the comets of #afjg and of #aeca had the same orbit as that of #afhb4 ,and here the intervals are also nearly the same1 namely1 about seventy-five years4 ,are the three comets then identical8 ,in looking back into the history of such appearances1 he found comets recorded in #adef1 in #achj1 and in #acje2 the intervals are still the same1 seventy-five or seventy-six years4 ,it was impossible now to doubt that they were the periods of a revolving body2 that the comet was a planet2 its orbit a long ellipse1 not a parabola4#iig ,note #ifg3 ,bailly1 ii4 #bdf4 ,note #igg3 ,principia1 ed4 #a4 p4 #did4 ,note #ihg3 ,bailly1 ii4 #fdf4 ,note #iig3 ,the importance of ,halley's labors on ,comets has always been acknowledged4 ,in speaking of ,halley's ,synopsis ,astronomic ,cometic1 ,delambre says 7,ast4 xviii4 ,sicle1 p4 #acj71 ,voil bien1 depuis ,kepler1 ce qu'on a fait de plus grand1 de plus beau1 de plus neuf en astronomie4 ,halley1 in predicting the comet of #ageh1 says1 if it returns1 ,hoc primum ab homine ,anglo iuventum fuisse non inficiabitur qua posteritas4 ,but if this were so1 the ,comet must reappear in #ageh or #agei4 ,halley predicted that it would do so2 and the fulfilment of this prediction was naturally looked forwards to1 as an additional stamp of the truths of the theory of gravitation4 #dea ,but in all this1 the ,comet had been supposed to be affected only by the attraction of the sun4 ,the planets must disturb its motion as they disturb each other4 ,how would this disturbance affect the time and circumstances of its reappearance8 ,halley had proposed1 but not attempted to solve1 this question4 ,the effect of perturbations upon a comet defeats all known methods of approximation1 and requires immense labor4 ,clairaut1 says ,bailly1#ajjg undertook this3 with courage enough to dare the adventure1 he had talent enough to obtain a memorable victory2 the difficulties1 the labors1 grew upon him as he advanced1 but he fought his way through them1 assisted by ,lalande1 and by a female calculator1 ,madame ,lepaute4 ,he predicted that the comet would reach its perihelion ,april #ac1 #agei1 but claimed the license of a month for the inevitable inaccuracy of a calculation which1 in addition to all other sources of error1 was made in haste1 that it might appear as a prediction4 ,the comet justified his calculations and his caution together2 for it arrived at its perihelion on the #acth of ,march4 ,note #ajjg3 ,bailly1 ,a4 ,m4 iii4 #aij4 ,two other ,comets1 of much shorter period1 have been detected of late years2 ,encke's1 which revolves round the sun in three years and one-third1 and ,biela's which describes an ellipse1 not extremely eccentric1 in six years and three-quarters4 ,these bodies1 apparently thin and vaporous masses1 like other comets1 have1 since their orbits were calculated1 punctually conformed to the law of gravitation4 ,if it were still doubtful whether the more conspicuous comets do so1 these bodies would tend to prove the fact1 by showing it to be true in an intermediate case4 #b;d ,ed4 ,a third ,comet of short period was discovered by ,faye1 at the ,observatory of ,paris1 ,nov4 #bb1 #ahdc4 ,it is included between the orbits of ,mars and ,saturn1 and its period is seven years and three-tenths4 ,this is commonly called ,faye's ,comet1 as the two mentioned in the text are called ,encke's and ,biela's4 ,in the former edition ,i had expressed my assent to the rule proposed by ,m4 ,arago1 that the latter ought to be called ,gambart's ,comet1 in honor of the astronomer who first proved it to revolve round the ,sun4 ,but astronomers in general have used the former name1 considering that the discovery and observation of the object are more distinct and conspicuous merits than a calculation founded upon the observations of others4 ,and in reality #deb ,biela had great merit in the discovery of his ,comet's periodicity1 having set about his search of it from an anticipation of its return founded upon former observations4 ,also a ,comet was discovered by ,de ,vico at ,rome on ,aug4 #bb1 #ahdd1 which was found to describe an elliptical orbit having its aphelion near the orbit of ,jupiter1 which is consequently one of those of short period4 ,and on ,feb4 #bf1 #ahdf1 ,m4 ,brorsen of ,kiel discovered a telescopic ,comet whose orbit is found to be elliptical4 ,we may add to the history of ,comets1 that of ,lexell's1 which1 in #aggj1 appeared to be revolving in a period of about five years1 and whose motion was predicted accordingly4 ,the prediction was disappointed2 but the failure was sufficiently explained by the comet's having passed close to ,jupiter1 by which occurrence its orbit was utterly deranged4 ,it results from the theory of universal gravitation1 that ,comets are collections of extremely attenuated matter4 ,lexell's is supposed to have passed twice 7in #agfg and #aggi7 through the system of ,jupiter's ,satellites1 without disturbing their motions1 though suffering itself so great a disturbance as to have its orbit entirely altered4 ,the same result is still more decidedly proved by the last appearance of ,biela's ,comet4 ,it appeared double1 but the two bodies did not perceptibly affect each other's motions1 as ,i am informed by ,professor ,challis of ,cambridge1 who observed both of them from ,jan4 #bc to ,mar4 #be1 #ahdf4 ,this proves the quantity of matter in each body to have been exceedingly small4 ,thus1 no verification of the ,newtonian theory1 which was possible in the motions of the stars1 has yet been wanting4 ,the return of ,halley's ,comet again in #ahce1 and the extreme exactitude with which it conformed to its predicted course1 is a testimony of truth1 which must appear striking even to the most incurious respecting such matters4#ajag ,note #ajag3 ,m4 de ,humboldt 7,kosmos1 p4 #aaf7 speaks of nine returns of ,halley's ,comet1 the comet observed in ,china in #acgh being identified with this4 ,but whether we take #acgh or #achj for the appearance in that century1 if we begin with that1 we have only seven appearances1 namely1 in #acgh or #achj1 in #adef1 in #aeca1 in #afjg1 in #afhb1 in #agei1 and in #ahce4 ,sect4 #g4--;,application of the ,newtonian ,theory to the ,figure of the ,earth4 ,,the ,heavens had thus been consulted respecting the ,newtonian doctrine1 and the answer given1 over and over again1 in a thousand #dec different forms1 had been1 that it was true2 nor had the most persevering cross-examination been able to establish any thing of contradiction or prevarication4 ,the same question was also to be put to the ,earth and the ,ocean1 and we must briefly notice the result4 ,according to the ,newtonian principles1 the form of the earth must be a globe somewhat flattened at the poles4 ,this conclusion1 or at least the amount of the flattening1 depends not only upon the existence and law of attraction1 but upon its belonging to each particle of the mass separately2 and thus the experimental confirmation of the form asserted from calculation1 would be a verification of the theory in its widest sense4 ,the application of such a test was the more necessary to the interests of science1 inasmuch as the ,french astronomers had collected from their measures1 and had connected with their ,cartesian system1 the opinion that the earth was not oblate but oblong4 ,dominic ,cassini had measured seven degrees of latitude from ,amiens to ,perpignan1 in #agja1 and found them to decrease in going from south to north4 ,the prolongation of this measure to ,dunkirk confirmed the same result4 ,but if the ,newtonian doctrine was true1 the contrary ought to be the case1 and the degrees ought to increase in proceeding towards the pole4 ,the only answer which the ,newtonians could at this time make to the difficulty thus presented1 was1 that an arc so short as that thus measured1 was not to be depended upon for the determination of such a question2 inasmuch as the inevitable errors of observation might exceed the differences which were the object of research4 ,it would1 undoubtedly1 have become the ,english to have given a more complete answer1 by executing measurements under circumstances not liable to this uncertainty4 ,the glory of doing this1 however1 they for a long time abandoned to other nations4 ,the ,french undertook the task with great spirit4#ajbg ,in #agcc1 in one of the meetings of the ,french ,academy1 when this question was discussed1 ,de la ,condamine1 an ardent and eager man1 proposed to settle this question by sending members of the ,academy to measure a degree of the meridian near the equator1 in order to compare it with the ,french degrees1 and offered himself for the expedition4 ,maupertuis1 in like manner1 urged the necessity of another expedition to measure a degree in the neighborhood of the pole4 ,the government received the applications favorably1 and these remarkable scientific missions were sent out at the national expense4 #ded ,note #ajbg3 ,bailly1 iii4 #aa4 ,as soon as the result of these measurements was known1 there was no longer any doubt as to the fact of the earth's oblateness1 and the question only turned upon its quantity4 ,even before the return of the academicians1 the ,cassinis and ,lacaille had measured the ,french arc1 and found errors which subverted the former result1 making the earth oblate to the amount of #aafhth of its diameter4 ,the expeditions to ,peru and to ,lapland had to struggle with difficulties in the execution of their design1 which make their narratives resemble some romantic history of irregular warfare1 rather than the monotonous records of mere measurements4 ,the equatorial degree employed the observers not less than eight years4 ,when they did return1 and the results were compared1 their discrepancy1 as to quantity1 was considerable4 ,the comparison of the ,peruvian and ,french arcs gave an ellipticity of nearly #acadth1 that of the ,peruvian and ,swedish arcs gave #abacth for its value4 ,newton had deduced from his theory1 by reasonings of singular ingenuity1 an ellipticity of #abcjth2 but this result had been obtained by supposing the earth homogeneous4 ,if the earth be1 as we should most readily conjecture it to be1 more dense in its interior than at its exterior1 its ellipticity will be less than that of a homogeneous spheroid revolving in the same time4 ,it does not appear that ,newton was aware of this2 but ,clairaut1 in #agdc1 in his ,figure of the ,earth1 proved this and many other important results of the attraction of the particles4 ,especially he established that1 in proportion as the fraction expressing the ,ellipticity becomes smaller1 that expressing the ,excess of the polar over the equatorial gravity becomes larger2 and he thus connected the measures of the ellipticity obtained by means of ,degrees1 with those obtained by means of ,pendulums in different latitudes4 ,the altered rate of a ,pendulum when carried towards the equator1 had been long ago observed by ,richer and ,halley1 and had been quoted by ,newton as confirmatory of his theory4 ,pendulums were swung by the academicians who measured the degrees1 and confirmed the general character of the results4 ,but having reached this point of the verification of the ,newtonian theory1 any additional step becomes more difficult4 ,many excellent measures1 both of ,degrees and of ,pendulums1 have been made since those just mentioned4 ,the results of the ,arcs#ajcg is an ,ellipticity of #abihth2--of the ,pendulums1 an ,ellipticity of about #abheth4 ,this difference #dee is considerable1 if compared with the quantities themselves2 but does not throw a shadow of doubt on the truth of the theory4 ,indeed1 the observations of each kind exhibit irregularities which we may easily account for1 by ascribing them to the unknown distribution of the denser portions of the earth2 but which preclude the extreme of accuracy and certainty in our result4 ,note #ajcg3 ,airy1 ,fig4 ,earth1 p4 #bcj4 ,but the near agreement of the determination1 from ,degrees and from ,pendulums1 is not the only coincidence by which the doctrine is confirmed4 ,we can trace the effect of the earth's ,oblateness in certain minute apparent motions of the stars2 for the attraction of the sun and moon on the protuberant matter of the spheroid produces the ,precession of the equinoxes1 and a ,nutation of the earth's axis4 ,the ,precession had been known from the time of ,hipparchus1 and the existence of ,nutation was foreseen by ,newton2 but the quantity is so small1 that it required consummate skill and great labor in ,bradley to detect it by astronomical observation4 ,being1 however1 so detected1 its amount1 as well as that of the ,precession1 gives us the means of determining the amount of ,terrestrial ,ellipticity1 by which the effect is produced4 ,but it is found1 upon calculation1 that we cannot obtain this determination without assuming some law of density in the homogeneous strata of which we suppose the earth to consist#ajdg ,the density will certainly increase in proceeding towards the centre1 and there is a simple and probable law of this increase1 which will give #acjjth for the ,ellipticity1 from the amount of two lunar ,inequalities 7one in latitude and one in longitude71 which are produced by the earth's oblateness4 ,nearly the same result follows from the quantity of ,nutation4 ,thus every thing tends to convince us that the ellipticity cannot deviate much from this fraction4 ,note #ajdg3 ,airy1 ,fig4 ,earth1 p4 #bce4 #b;d ,ed4 ,i ought not to omit another class of phenomena in which the effects of the ,earth's ,oblateness1 acting according to the law of universal gravitation1 have manifested themselves2--,i speak of the ,moon's ,motion1 as affected by the ,earth's ,ellipticity4 ,in this case1 as in most others1 observation anticipated theory4 ,mason had inferred from lunar observations a certain ,inequality in ,longitude1 depending upon the distance of the ,moon's ,node from the ,equinox4 ,doubts were entertained by astronomers whether this inequality really existed2 but ,laplace showed that such an inequality would arise from the oblate form of the earth2 and that its magnitude might serve to #def determine the amount of the oblateness4 ,laplace showed1 at the same time1 that along with this ,inequality in ,longitude there must be an ,inequality in ,latitude2 and this assertion ,burg confirmed by the discussion of observations4 ,the two ,inequalities1 as shown in the observations1 agree in assigning to the earth's form an ,ellipticity of #acjeth4 ,sect4 #h4--;,confirmation of the ,newtonian ,theory by ,experiments on ,attraction4 ,,the attraction of all the parts of the earth to one another was thus proved by experiments1 in which the whole mass of the earth is concerned4 ,but attempts have also been made to measure the attraction of smaller portions2 as mountains1 or artificial masses4 ,this is an experiment of great difficulty2 for the attraction of such masses must be compared with that of the earth1 of which it is a scarcely perceptible fraction2 and1 moreover1 in the case of mountains1 the effect of the mountain will be modified or disguised by unknown or unappreciable circumstances4 ,in many of the measurements of degrees1 indications of the attraction of mountains had been perceived2 but at the suggestion of ,maskelyne1 the experiment was carefully made1 in #aggd1 upon the mountain ,schehallien1 in ,scotland1 the mountain being mineralogically surveyed by ,playfair4 ,the result obtained was1 that the attraction of the mountain drew the plumb-line about six seconds from the vertical2 and it was deduced from this1 by ,hutton's calculations1 that the density of the earth was about once and four-fifths that of ,schehallien1 or four and a half times that of water4 ,cavendish1 who had suggested many of the artifices in this calculation1 himself made the experiment in the other form1 by using leaden balls1 about nine inches diameter4 ,this observation was conducted with an extreme degree of ingenuity and delicacy1 which could alone make it valuable2 and the result agreed very nearly with that of the ,schehallien experiment1 giving for the density of the earth about five and one-third times that of water4 ,nearly the same result was obtained by ,carlini1 in #ahbd1 from observations of the pendulum1 made at a point of the ,alps 7the ,hospice1 on ,mount ,cenis7 at a considerable elevation above the average surface of the earth4 #deg ,sect4 #i4--;,application of the ,newtonian ,theory to the ,tides4 ,,we come1 finally1 to that result1 in which most remains to be done for the verification of the general law of attraction--the subject of the ,tides4 ,yet1 even here1 the verification is striking1 as far as observations have been carried4 ,newton's theory explained1 with singular felicity1 all the prominent circumstances of the tides then known2--the difference of spring and neap tides2 the effect of the moon's and sun's declination and parallax2 even the difference of morning and evening tides1 and the anomalous tides of particular places4 ,about1 and after1 this time1 attempts were made both by the ,royal ,society of ,england1 and by the ,french ,academy1 to collect numerous observations but these were not followed up with sufficient perseverance4 ,perhaps1 indeed1 the theory had not been at that time sufficiently developed but the admirable prize-essays of ,euler1 ,bernoulli1 and ,d',alembert1 in #agdj1 removed1 in a great measure1 this deficiency4 ,these dissertations supplied the means of bringing this subject to the same test to which all the other consequences of gravitation had been subjected2--namely1 the calculation of tables1 and the continued and orderly comparison of these with observation4 ,laplace has attempted this verification in another way1 by calculating the results of the theory 7which he has done with an extraordinary command of analysis71 and then by comparing these1 in supposed critical cases1 with the ,brest observations4 ,this method has confirmed the theory as far as it could do so2 but such a process cannot supersede the necessity of applying the proper criterion of truth in such cases1 the construction and verification of ,tables4 ,bernoulli's theory1 on the other hand1 has been used for the construction of ,tide-tables2 but these have not been properly compared with experiment2 and when the comparison has been made1 having been executed for purposes of gain rather than of science1 it has not been published1 and cannot be quoted as a verification of the theory4 ,thus we have1 as yet1 no sufficient comparison of fact with theory1 for ,laplace's is far from a complete comparison4 ,in this1 as in other parts of physical astronomy1 our theory ought not only to agree with observations selected and grouped in a particular manner1 but with the whole course of observation1 and with every part of the phenomena4 ,in this1 as in other cases1 the true theory should be verified by its giving us the best ,tables2 but ,tide-tables were never1 ,i believe1 #deh calculated upon ,laplace's theory1 and thus it was never fairly brought to the test4 ,it is1 perhaps1 remarkable1 considering all the experience which astronomy had furnished1 that men should have expected to reach the completion of this branch of science by improving the mathematical theory1 without1 at the same time1 ascertaining the laws of the facts4 ,in all other departments of astronomy1 as1 for instance1 in the cases of the moon and the planets1 the leading features of the phenomena had been made out empirically1 before the theory explained them4 ,the course which analogy would have recommended for the cultivation of our knowledge of the tides1 would have been1 to ascertain1 by an analysis of long series of observations1 the effect of changes in the time of transit1 parallax1 and declination of the moon1 and thus to obtain the laws of phenomena and then proceed to investigate the laws of causation4 ,though this was not the course followed by mathematical theorists1 it was really pursued by those who practically calculated ,tide-tables2 and the application of knowledge to the useful purposes of life being thus separated from the promotion of the theory1 was naturally treated as a gainful property1 and preserved by secrecy4 ,art1 in this instance1 having cast off her legitimate subordination to ,science1 or rather1 being deprived of the guidance which it was the duty of ,science to afford1 resumed her ancient practices of exclusiveness and mystery4 ,liverpool1 ,london1 and other places1 had their ,tide-tables1 constructed by undivulged methods1 which methods1 in some instances at least1 were handed down from father to son for several generations as a family possession2 and the publication of new ,tables1 accompanied by a statement of the mode of calculation1 was resented as an infringement of the rights of property4 ,the mode in which these secret methods were invented1 was that which we have pointed out2--the analysis of a considerable series of observations4 ,probably the best example of this was afforded by the ,liverpool ,tide-tables4 ,these were deduced by a clergyman named ,holden1 from observations made at that port by a harbor-master of the name of ,hutchinson2 who was led1 by a love of such pursuits1 to observe the tides carefully for above twenty years1 day and night4 ,holden's ,tables1 founded on four years of these observations1 were remarkably accurate4 ,at length men of science began to perceive that such calculations were part of their business2 and that they were called upon1 as the #dei guardians of the established theory of the universe1 to compare it in the greatest possible detail with the facts4 ,mr4 ,lubbock was the first mathematician who undertook the extensive labors which such a conviction suggested4 ,finding that regular tide-observations had been made at the ,london ,docks from #agie1 he took nineteen years of these 7purposely selecting the length of a cycle of the motions of the lunar orbit71 and caused them 7in #ahca7 to be analyzed by ,mr4 ,dessiou1 an expert calculator4 ,he thus obtained#ajeg ,tables for the effect of the ,moon's ,declination1 ,parallax1 and hour of ,transit1 on the tides2 and was enabled to produce ,tide-tables founded upon the data thus obtained4 ,some mistakes in these as first published 7mistakes unimportant as to the theoretical value of the work71 served to show the jealousy of the practical tide-table calculators1 by the acrimony with which the oversights were dwelt upon2 but in a very few years1 the tables thus produced by an open and scientific process were more exact than those which resulted from any of the secrets2 and thus practice was brought into its proper subordination to theory4 ,note #ajeg3 ,phil4 ,trans4 #ahca4 ,british ,almanac1 #ahcb4 ,the theory with which ,mr4 ,lubbock was led to compare his results1 was the ,equilibrium-theory of ,daniel ,bernoulli2 and it was found that this theory1 with certain modifications of its elements1 represented the facts to a remarkable degree of precision4 ,mr4 ,lubbock pointed out this agreement especially in the semi-mensual inequality of the times of high water4 ,the like agreement was afterwards 7in #ahcc7 shown by ,mr4 ,whewell#ajfg to obtain still more accurately at ,liverpool1 both for the ,times and ,heights2 for by this time1 nineteen years of ,hutchinson's ,liverpool ,observations had also been discussed by ,mr4 ,lubbock4 ,the other inequalities of the ,times and ,heights 7depending upon the ,declination and ,parallax of the ,moon and ,sun17 were variously compared with the ,equilibrium-theory by ,mr4 ,lubbock and ,mr4 ,whewell2 and the general result was1 that the facts agreed with the condition of equilibrium at a certain anterior time1 but that this anterior time was different for different phenomena4 ,in like manner it appeared to follow from these researches1 that in order to explain the facts1 the mass of the moon must be supposed different in the calculation at different places4 ,a result in effect the same was obtained by ,m4 ,daussy1#ajgg an active ,french ,hydrographer2 for he found that observations at various stations could not be reconciled with the formul of ,laplace's ,mcanique #dfj ,cleste 7in which the ratio of the heights of spring-tides and neap-tides was computed on an assumed mass of the moon7 without an alteration of level which was1 in fact1 equivalent to an alteration of the moon's mass4 ,thus all things appeared to tend to show that the ,equilibrium-theory would give the formul for the inequalities of the tides1 but that the magnitudes which enter into these formul must be sought from observation4 ,note #ajfg3 ,phil4 ,trans4 #ahcd4 ,note #ajgg3 ,connaissance des ,tems1 #ahch4 ,whether this result is consistent with theory1 is a question not so much of ,physical ,astronomy as of ,hydrodynamics1 and has not yet been solved4 ,a ,theory of the ,tides which should include in its conditions the phenomena of ,derivative ,tides1 and of their combinations1 will probably require all the resources of the mathematical mechanician4 ,as a contribution of empirical materials to the treatment of this hydrodynamical problem1 it may be allowable to mention here ,mr4 ,whewell's attempts to trace the progress of the tide into all the seas of the globe1 by drawing on maps of the ocean what he calls ,cotidal ,lines2--lines marking the contemporaneous position of the various points of the great wave which carries high water from shore to shore4#ajhg ,this is necessarily a task of labor and difficulty1 since it requires us to know the time of high water on the same day in every part of the world2 but in proportion as it is completed1 it supplies steps between our general view of the movements of the ocean and the phenomena of particular ports4 ,note #ajhg3 ,essay towards a ,first ,approximation to a ,map of ,cotidal ,lines4 ,phil4 ,trans4 #ahcc1 #ahcf4 ,looking at this subject by the light which the example of the history of astronomy affords1 we may venture to repeat1 that it will never have justice done it till it is treated as other parts of astronomy are treated2 that is1 till ,tables of all the phenomena which can be observed1 are calculated by means of the best knowledge which we at present possess1 and till these tables are constantly improved by a comparison of the predicted with the observed fact4 ,a set of ,tide-observations and ,tide-ephemerides of this kind1 would soon give to this subject that precision which marks the other parts of astronomy2 and would leave an assemblage of unexplained residual phenomena1 in which a careful research might find the materials of other truths as yet unsuspected4 #b;d ,ed4 ,that there would be1 in the tidal movements of the ocean1 inequalities of the heights and times of high and low water #dfa corresponding to those which the equilibrium theory gives1 could be considered only as a conjecture1 till the comparison with observation was made4 ,it was1 however1 a natural conjecture2 since the waters of the ocean are at every moment tending to acquire the form assumed in the equilibrium theory3 and it may be considered likely that the causes which prevent their assuming this form produce an effect nearly constant for each place4 ,whatever be thought of this reasoning1 the conjecture is confirmed by observation with curious exactness4 ,the laws of a great number of the tidal phenomena--namely1 of the ,semi-mensual ,inequality of the ,heights1 of the ,semi-mensual ,inequality of the ,times1 of the ,diurnal ,inequality1 of the effect of the ,moon's ,declination1 of the effect of the ,moon's ,parallax--are represented very closely by formul derived from the equilibrium theory4 ,the hydrodynamical mode of treating the subject has not added any thing to the knowledge of the laws of the phenomena to which the other view had conducted us4 ,we may add1 that ,laplace's assumption1 that in the moving fluid the motions must have a periodicity corresponding to that of the forces1 is also a conjecture4 ,and though this conjecture may1 in some cases of the problem1 be verified1 by substituting the resulting expressions in the equations of motion1 this cannot be done in the actual case1 where the revolving motion of the ocean is prevented by the intrusion of tracts of land running nearly from pole to pole4 ,yet in ,mr4 ,airy's ,treatise ,on ,tides and ,waves 7in the ,encyclopdia ,metropolitana7 much has been done to bring the hydrodynamical theory of oceanic tides into agreement with observation4 ,in this admirable work1 ,mr4 ,airy has1 by peculiar artifices1 solved problems which come so near the actual cases that they may represent them4 ,he has1 in this way1 deduced the laws of the semi-diurnal and the diurnal tide1 and the other features of the tides which the equilibrium theory in some degree imitates2 but he has also1 taking into account the effect of friction1 shown that the actual tide may be represented as the tide of an earlier epoch2--that the relative mass of the moon and sun1 as inferred from the tides1 would depend upon the depth of the ocean 7,art4 #dee72--with many other results remarkably explaining the observed phenomena4 ,he has also shown that the relation of the cotidal lines to the tide waves really propagated is1 in complex cases1 very obscure1 because different waves of different magnitudes1 travelling in different directions1 may coexist1 and the cotidal line is the compound result of all these4 #dfb ,with reference to the ,maps of ,cotidal ,lines1 mentioned in the text1 ,i may add1 that we are as yet destitute of observations which should supply the means of drawing such lines on a large scale in the ,pacific ,ocean4 ,admiral ,ltke has however supplied us with some valuable materials and remarks on this subject in his ,notice sur les ,mares ,priodiques dans le grand ,ocan ,boral et dans la ,mer ,glaciale2 and has drawn them1 apparently on sufficient data1 in the ,white ,sea4 ,,chapter ,v4 ,,discoveries ,,added ,,to ,,the ,,newtonian ,,theory4 ,sect4 #a4--,tables of ,astronomical ,refraction4 ,,we have travelled over an immense field of astronomical and mathematical labor in the last few pages1 and have yet1 at the end of every step1 still found ourselves under the jurisdiction of the ,newtonian laws4 ,we are reminded of the universal monarchies1 where a man could not escape from the empire without quitting the world4 ,we have now to notice some other discoveries1 in which this reference to the law of universal gravitation is less immediate and obvious2 ,i mean the astronomical discoveries respecting ,light4 ,the general truths to which the establishment of the true laws of ,atmospheric ,refraction led astronomers1 were the law of ,deflection of the rays of light1 which applies to all refractions1 and the real structure and size of the ,atmosphere1 so far as it became known4 ,the great discoveries of ,rmer and ,bradley1 namely1 the ,velocity of ,light1 the ,aberration of ,light1 and the ,nutation of the earth's axis1 gave a new distinctness to the conceptions of the propagation of light in the minds of philosophers1 and confirmed the doctrines of ,copernicus1 ,kepler1 and ,newton1 respecting the motions which belong to the earth4 ,the true laws of ,atmospheric ,refraction were slowly discovered4 ,tycho attributed the apparent displacement of the heavenly bodies to the low and gross part of the atmosphere only1 and hence made it cease at a point half-way to the zenith2 but ,kepler rightly extended it to the zenith itself4 ,dominic ,cassini endeavored to discover the law of this correction by observation1 and gave his result in the form #dfc which1 as we have said1 sound science prescribes1 a ,table to be habitually used for all observations4 ,but great difficulties at this time embarrassed this investigation1 for the parallaxes of the sun and of the planets were unknown1 and very diverse values had been assigned them by different astronomers4 ,to remove some of these difficulties1 ,richer1 in #agfb1 went to observe at the equator2 and on his return1 ,cassini was able to confirm and amend his former estimations of parallax and refraction4 ,but there were still difficulties4 ,according to ,la ,hire1 though the phenomena of twilight give an altitude of #cd1jjj toises to the atmosphere1#ajig those of refraction make it only #bjjj4 ,john ,cassini undertook to support and improve the calculations of his father ,dominic1 and took the true supposition1 that the light follows a curvilinear path through the air4 ,the ,royal ,society of ,london had already ascertained experimentally the refractive power of air4#aajg ,newton calculated a ,table of ,refractions1 which was published under ,halley's name in the 9999,philosophical ,transactions for #agba1 without any indication of the method by which it was constructed4 ,but ,m4 ,biot has recently shown1#aaag by means of the published correspondence of ,flamsteed1 that ,newton had solved the problem in a manner nearly corresponding to the most improved methods of modern analysis4 ,note #ajig3 ,bailly1 ii4 #fab4 ,note #aajg3 ,ibid4 ii4 #fjg4 ,note #aaag3 ,biot1 ,acad4 ,sc4 ,compte ,rendu1 ,sept4 #e1 #ahcf4 ,dominic ,cassini and ,picard proved1#aabg ,le ,monnier in #agch confirmed more fully1 the fact that the variations of the ,thermometer affect the ,refraction4 ,mayer1 taking into account both these changes1 and the changes indicated by the ,barometer1 formed a theory1 which ,lacaille1 with immense labor1 applied to the construction of a ,table of ,refractions from observation4 ,but ,bradley's ,table 7published in #agfc by ,maskelyne7 was more commonly adopted in ,england2 and his formula1 originally obtained empirically1 has been shown by ,young to result from the most probable suppositions we can make respecting the atmosphere4 ,bessel's ,refraction ,tables are now considered the best of those which have appeared4 ,note #aabg3 ,bailly1 iii4 #ib4 ,sect4 #b4--;,discovery of the ,velocity of ,light4--,rmer4 ,,the astronomical history of ,refraction is not marked by any great discoveries1 and was1 for the most part1 a work of labor only4 ,the progress of the other portions of our knowledge respecting light is #dfd more striking4 ,in #afgf1 a great number of observations of eclipses of ,jupiter's satellites were accumulated1 and could be compared with ,cassini's ,tables4 ,rmer1 a ,danish astronomer1 whom ,picard had brought to ,paris1 perceived that these eclipses happened constantly later than the calculated time at one season of the year1 and earlier at another season2--a difference for which astronomy could offer no account4 ,the error was the same for all the satellites2 if it had depended on a defect in the ,tables of ,jupiter1 it might have affected all1 but the effect would have had a reference to the velocities of the satellites4 ,the cause1 then1 was something extraneous to ,jupiter4 ,rmer had the happy thought of comparing the error with the earth's distance from ,jupiter1 and it was found that the eclipses happened later in proportion as ,jupiter was further off4#aacg ,thus we see the eclipse later1 as it is more remote2 and thus light1 the messenger which brings us intelligence of the occurrence1 travels over its course in a measurable time4 ,by this evidence1 light appeared to take about eleven minutes in describing the diameter of the earth's orbit4 ,note #aacg3 ,bailly1 ii4 #ag4 ,this discovery1 like so many others1 once made1 appears easy and inevitable2 yet ,dominic ,cassini had entertained the idea for a moment1#aadg and had rejected it2 and ,fontenelle had congratulated himself publicly on having narrowly escaped this seductive error4 ,the objections to the admission of the truth arose principally from the inaccuracy of observation1 and from the persuasion that the motions of the satellites were circular and uniform4 ,their irregularities disguised the fact in question4 ,as these irregularities became clearly known1 ,rmer's discovery was finally established1 and the ,equation of ,light took its place in the ,tables4 ,note #aadg3 ,ib4 ii4 #dai4 ,sect4 #c4--;,discovery of ,aberration4--,bradley4 ,,improvements in instruments1 and in the art of observing1 were requisite for making the next great step in tracing the effect of the laws of light4 ,it appears clear1 on consideration1 that since light and the spectator on the earth are both in motion1 the apparent direction of an object will be determined by the composition of these motions4 ,but yet the effect of this composition of motions was 7as is usual in such cases7 traced as a fact in observation1 before it was clearly seen as a consequence of reasoning4 ,this fact1 the ,aberration of ,light1 the greatest astronomical discovery of the eighteenth century1 belongs to ,bradley1 #dfe who was then ,professor of ,astronomy at ,oxford1 and afterwards ,astronomer ,royal at ,greenwich4 ,molyneux and ,bradley1 in #agbe1 began a series of observations for the purpose of ascertaining1 by observations near the zenith1 the existence of an annual parallax of the fixed stars1 which ,hooke had hoped to detect1 and ,flamsteed thought he had discovered4 ,bradley#aaeg soon found that the star observed by him had a minute apparent motion different from that which the annual parallax would produce4 ,he thought of a nutation of the earth's axis as a mode of accounting for this2 but found1 by comparison of a star on the other side of the pole1 that this explanation would not apply4 ,bradley and ,molyneux then considered for a moment an annual alteration of figure in the earth's atmosphere1 such as might affect the refractions1 but this hypothesis was soon rejected4#aafg ,in #agbg1 ,bradley resumed his observations1 with a new instrument1 at ,wanstead1 and obtained empirical rules for the changes of declination of different stars4 ,at last1 accident turned his thoughts to the direction in which he was to find the cause of the variations which he had discovered4 ,being in a boat on the ,thames1 he observed that the vane on the top of the mast gave a different apparent direction to the wind1 as the boat sailed one way or the other4 ,here was an image of his case3 the boat represented the earth moving in different directions at different seasons1 and the wind represented the light of a star4 ,he had now to trace the consequences of this idea2 he found that it led to the empirical rules1 which he had already discovered1 and1 in #agbi1 he gave his discovery to the ,royal ,society4 ,his paper is a very happy narrative of his labors and his thoughts4 ,his theory was so sound that no astronomer ever contested it2 and his observations were so accurate1 that the quantity which he assigned as the greatest amount of the change 7one nineteenth of a degree7 has hardly been corrected by more recent astronomers4 ,it must be noticed1 however1 that he considered the effects in declination only2 the effects in right ascension required a different mode of observation1 and a consummate goodness in the machinery of clocks1 which at that time was hardly attained4 ,note #aaeg3 ,rigaud's ,bradley4 ,note #aafg3 ,rigaud1 p4 xxiii4 ,sect4 #d4--;,discovery of ,nutation4 ,,when ,bradley went to ,greenwich as ,astronomer ,royal1 he continued with perseverance observations of the same kind as those by which he had detected ,aberration4 ,the result of these was another #dff discovery2 namely1 that very ,nutation which he had formerly rejected4 ,this may appear strange1 but it is easily explained4 ,the aberration is an annual change1 and is detected by observing a star at different seasons of the year3 the ,nutation is a change of which the cycle is eighteen years2 and which1 therefore1 though it does not much change the place of a star in one year1 is discoverable in the alterations of several successive years4 ,a very few years' observations showed ,bradley the effect of this change2#aagg and long before the half cycle of nine years had elapsed1 he had connected it in his mind with the true cause1 the motion of the moon's nodes4 ,machin was then ,secretary to the ,royal ,society1#aahg and was employed in considering the theory of gravity1 and its consequences with regard to the celestial motions3 to him ,bradley communicated his conjectures2 from him he soon received a ,table containing the results of his calculations2 and the law was found to be the same in the ,table and in observation1 though the quantities were somewhat different4 ,it appeared by both1 that the earth's pole1 besides the motion which the precession of the equinoxes gives it1 moves1 in eighteen years1 through a small circle2--or rather1 as was afterwards found by ,bradley1 an ellipse1 of which the axes are nineteen and fourteen seconds4#aaig ,note #aagg3 ,rigaud1 lxiv4 ,note #aahg3 ,ib4 #be4 ,note #aaig3 ,ib4 lxvi4 ,for the rigorous establishment of the mechanical theory of that effect of the moon's attraction from which the phenomena of ,nutation flow1 ,bradley rightly and prudently invited the assistance of the great mathematicians of his time4 ,d',alembert1 ,thomas ,simpson1 ,euler1 and others1 answered this call1 and the result was1 as we have already said in the last chapter 7,sect4 #g71 that this investigation added another to the recondite and profound evidences of the doctrine of universal gravitation4 ,it has been said#abjg that ,bradley's discoveries assure him the most distinguished place among astronomers after ,hipparchus and ,kepler4 ,if his discoveries had been made before ,newton's1 there could have been no hesitation as to placing him on a level with those great men4 ,the existence of such suggestions as the ,newtonian theory offered on all astronomical subjects1 may perhaps dim1 in our eyes1 the brilliance of ,bradley's achievements2 but this circumstance cannot place any other person above the author of such discoveries1 and therefore we may consider ,delambre's adjudication of precedence as well warranted1 and deserving to be permanent4 #dfg ,note #abjg3 ,delambre1 ,ast4 du #ah ,sic4 p4 #dbj4 ,rigaud1 xxxvii4 ,sect4 #e4--;,discovery of the ,laws of ,double ,stars4--,the two ,herschels4 ,,no truth1 then1 can be more certainly established1 than that the law of gravitation prevails to the very boundaries of the solar system4 ,but does it hold good further8 ,do the fixed stars also obey this universal sway8 ,the idea1 the question1 is an obvious one--but where are we to find the means of submitting it to the test of observation8 ,if the ,stars were each insulated from the rest1 as our ,sun appears to be from them1 we should have been quite unable to answer this inquiry4 ,but among the stars1 there are some which are called ,double ,stars1 and which consist of two stars1 so near to each other that the telescope alone can separate them4 ,the elder ,herschel diligently observed and measured the relative positions of the two stars in such pairs2 and as has so often happened in astronomical history1 pursuing one object he fell in with another4 ,supposing such pairs to be really unconnected1 he wished to learn1 from their phenomena1 something respecting the annual parallax of the earth's orbit4 ,but in the course of twenty years' observations he made the discovery 7in #ahjc7 that some of these couples were turning round each other with various angular velocities4 ,these revolutions were for the most part so slow that he was obliged to leave their complete determination as an inheritance to the next generation4 ,his son was not careless of the bequest1 and after having added an enormous mass of observations to those of his father1 he applied himself to determine the laws of these revolutions4 ,a problem so obvious and so tempting was attacked also by others1 as ,savary and ,encke1 in #ahcj and #ahcb1 with the resources of analysis4 ,but a problem in which the data are so minute and inevitably imperfect1 required the mathematician to employ much judgment1 as well as skill in using and combining these data2 and ,sir ,john ,herschel1 by employing positions only of the line joining the pair of stars 7which can be observed with comparative exactness71 to the exclusion of their distances 7which cannot be measured with much correctness71 and by inventing a method which depended upon the whole body of observations1 and not upon selected ones only1 for the determination of the motion1 has made his investigations by far the most satisfactory of those which have appeared4 ,the result is1 that it has been rendered very probable1 that in several of the double stars the two stars describe ellipses about each other2 and therefore that here also1 at an #dfh immeasurable distance from our system1 the law of attraction according to the inverse square of the distance1 prevails4 ,and1 according to the practice of astronomers when a law has been established1 ,tables have been calculated for the future motions2 and we have ,ephemerides of the revolutions of suns round each other1 in a region so remote1 that the whole circle of our earth's orbit1 if placed there1 would be imperceptible by our strongest telescopes4 ,the permanent comparison of the observed with the predicted motions1 continued for more than one revolution1 is the severe and decisive test of the truth of the theory2 and the result of this test astronomers are now awaiting4 #b;d ,ed4 ,in calculating the orbits of revolving systems of double stars1 there is a peculiar difficulty1 arising from the plane of the orbit being in a position unknown1 but probably oblique1 to the visual ray4 ,hence it comes to pass that even if the orbit be an ellipse described about the focus by the laws of planetary motion1 it will appear otherwise2 and the true orbit will have to be deduced from the apparent one4 ,with regard to a difficulty which has been mentioned1 that the two stars1 if they are governed by gravity1 will not revolve the one about the other1 but both about their common centre of gravity2--this circumstance adds little difficulty to the problem4 ,newton has shown 7,princip4 lib4 i4 ,prop4 #fa7 in the problem of two bodies1 the relation between the relative orbits and the orbit about the common centre of gravity4 ,how many of the apparently double stars have orbitual motions8 ,sir ,john ,herschel in #ahcc gave1 in his ,astronomy 7,art4 #fjf71 a list of nine stars1 with periods extending from #dc years 7 ,coron7 to #abjj years 7 ,leonis71 which he presented as the chief results then obtained in this department4 ,in his work on ,double ,stars1 the fruit of his labors in both hemispheres1 which the astronomical world are looking for with eager expectation1 he will1 ,i believe1 have a few more to add to these4 ,is it well established that such double stars attract each other according to the law of the inverse square of the distance8 ,the answer to this question must be determined by ascertaining whether the above cases are regulated by the laws of elliptical motion4 ,this is a matter which it must require a long course of careful observation to determine in such a number of cases as to prove the universality of the rule4 ,perhaps the minds of astronomers are still in suspense upon the subject4 ,when ,sir ,john ,herschel's work shall appear1 it will probably #dfi be found that with regard to some of these stars1 and ,virginis in particular1 the conformity of the observations with the laws of elliptical motion amounts to a degree of exactness which must give astronomers a strong conviction of the truth of the law4 ,for since ,sir ,w4 ,herschel's first measures in #agha1 the arc described by one star about the other is above #cje degrees2 and during this period the angular annual motion has been very various1 passing through all gradations from about #bj minutes to #hj degrees4 ,yet in the whole of this change1 the two curves constructed1 the one from the observations1 the other from the elliptical elements1 for the purpose of comparison1 having a total ordinate of #cje parts1 do not1 in any part of their course1 deviate from each other so much as two such parts4 ,the verification of ,newton's discoveries was sufficient employment for the last century2 the first step in the extension of them belongs to this century4 ,we cannot at present foresee the magnitude of this task1 but every one must feel that the law of gravitation1 before verified in all the particles of our own system1 and now probably extended to the all but infinite distance of the fixed stars1 presses upon our minds with a strong claim to be accepted as a universal law of the whole material creation4 ,thus1 in this and the preceding chapter1 ,i have given a brief sketch of the history of the verification and extension of ,newton's great discovery4 ,by the mass of labor and of skill which this head of our subject includes1 we may judge of the magnitude of the advance in our knowledge which that discovery made4 ,a wonderful amount of talent and industry have been requisite for this purpose2 but with these1 external means have co-operated4 ,wealth1 authority1 mechanical skill1 the division of labor1 the power of associations and of governments1 have been largely and worthily applied in bringing astronomy to its present high and flourishing condition4 ,we must consider briefly what has thus been done4 #dgj ,,chapter ,,vi4 ,,the ,,instruments ,,and ,,aids ,,of ,,astronomy ,,during ,,the ,,newtonian ,,period4 ,sect4 #a4--;,instruments4 ,,some instruments or other were employed at all periods of astronomical observation4 ,but it was only when observation had attained a considerable degree of delicacy1 that the exact construction of instruments became an object of serious care4 ,gradually1 as the possibility and the value of increased exactness became manifest1 it was seen that every thing which could improve the astronomer's instruments was of high importance to him4 ,and hence in some cases a vast increase of size and of expense was introduced2 in other cases new combinations1 or the result of improvements in other sciences1 were brought into play4 ,extensive knowledge1 intense thought1 and great ingenuity1 were requisite in the astronomical instrument maker4 ,instead of ranking with artisans1 he became a man of science1 sharing the honor and dignity of the astronomer himself4 #a4 ,measure of ,angles4--,tycho ,brahe was the first astronomer who acted upon a due appreciation of the importance of good instruments4 ,the collection of such at ,uraniburg was by far the finest which had ever existed4 ,he endeavored to give steadiness to the frame1 and accuracy to the divisions of his instruments4 ,his ,mural ,quadrant was well adapted for this purpose2 its radius was five cubits3 it is clear1 that as we enlarge the instrument we are enabled to measure smaller arcs4 ,on this principle many large gnomons were erected4 ,cassini's celebrated one in the church of ,st4 ,petronius at ,bologna1 was eighty-three feet 7,french7 high4 ,but this mode of obtaining accuracy was soon abandoned for better methods4 ,three great improvements were introduced about the same time4 ,the application of the ,micrometer to the telescope1 by ,huyghens1 ,malvasia1 and ,auzout2 the application of the ,telescope to the astronomical quadrant2 and the fixation of the centre of its field by a ,cross of fine wires placed in the focus by ,gascoigne1 and afterwards by ,picard4 ,we may judge how great was the improvement which these contrivances introduced into the art of #dga observing1 by finding that ,hevelius refused to adopt them because they would make all the old observations of no value4 ,he had spent a laborious and active life in the exercise of the old methods1 and could not bear to think that all the treasures which he had accumulated had lost their worth by the discovery of a new mine of richer ore4 #b;d ,ed4 ,littrow1 in his ,die ,wunder des ,himmels1 ,ed4 #b1 pp4 #fhd1 #fhe1 says that ,gascoigne invented and used the telescope with wires in the common focus of the lenses in #afdj4 ,he refers to ,phil4 ,trans4 xxx4 #fjc4 ,picard reinvented this arrangement in #affg4 ,i have already spoken of ,gascoigne as the inventor of the micrometer4 ,rmer 7already mentioned1 p4 #dfd7 brought into use the ,transit ,instrument1 and the employment of complete ,circles1 instead of the ,quadrants used till then2 and by these means gave to practical astronomy a new form1 of which the full value was not discovered till long afterwards49999 ,the apparent place of the object in the instrument being so precisely determined by the new methods1 the exact ,division of the arc into degrees and their subdivisions became a matter of great consequence4 ,a series of artists1 principally ,english1 have acquired distinguished places in the lists of scientific fame by their performances in this way2 and from that period1 particular instruments have possessed historical interest and individual reputation4 ,graham was one of the first of these artists4 ,he executed a great ,mural ,arc for ,halley at ,greenwich2 for ,bradley he constructed the ,sector which detected aberration4 ,he also made the ,sector which the ,french academicians carried to ,lapland2 and probably the goodness of this instrument1 compared with the imperfection of those which were sent to ,peru1 was one main cause of the great difference of duration in the two series of observations4 ,bird1 somewhat later#abag 7about #agej71 divided several ,quadrants for public observatories4 ,his method of dividing was considered so perfect1 that the knowledge of it was purchased by the ,english government1 and published in #agfg4 ,ramsden was equally celebrated4 ,the error of one of his best ,quadrants 7that at ,padua7 is said to be never greater than two seconds4 ,but at a later period1 ,ramsden constructed ,mural ,circles only1 holding this to be a kind of instrument far superior to the quadrant4 ,he made one of five feet diameter1 in #aghh1 for ,m4 ,piazzi at ,palermo2 and one of eight feet for the observatory of ,dublin4 ,troughton1 a worthy successor of the #dgb artists we have mentioned1 has invented a method of dividing the circle still superior to the former ones2 indeed1 one which is theoretically perfect1 and practically capable of consummate accuracy4 ,in this way1 circles have been constructed for ,greenwich1 ,armagh1 ,cambridge1 and many other places2 and probably this method1 carefully applied1 offers to the astronomer as much exactness as his other implements allow him to receive2 but the slightest casualty happening to such an instrument1 after it has been constructed1 or any doubt whether the method of graduation has been rightly applied1 makes it unfit for the jealous scrupulosity of modern astronomy4 ,note #abag3 ,mont4 iv4 #ccg4 ,the ,english artists sought to attain accurate measurements by continued bisection and other aliquot subdivision of the limb of their circle2 but ,mayer proposed to obtain this end otherwise1 by repeating the measure on different parts of the circumference till the error of the division becomes unimportant1 instead of attempting to divide an instrument without error4 ,this invention of the ,repeating ,circle was zealously adopted by the ,french1 and the relative superiority of the rival methods is still a matter of difference of opinion4 #b;d ,ed4 ,in the series of these great astronomical mechanists1 we must also reckon ,george ,reichenbach4 ,he was born ,aug4 #bd1 #aggb1 at ,durlach2 became ,lieutenant of ,artillery in the ,bavarian service in #agid2 7,salinenrath7 ,commissioner of ,salt-works in #ahaa2 and in #ahbj1 ,first ,commissioner of ,water-works and ,roads4 ,he became1 with ,fraunhofer1 the ornament of the mechanical and optical ,institute erected in #ahje at ,benedictbeuern by ,utzschneider2 and his astronomical instruments1 meridian circles1 transit instruments1 equatorials1 heliometers1 make an epoch in ,observing ,astronomy4 ,his contrivances in the ,salt-works at ,berchtesgaden and ,reichenhall1 in the ,arms ,manufactory at ,amberg1 and in the works for boring cannon at ,vienna1 are enduring monuments of his rare mechanical talent4 ,he died ,may #ba1 #ahbf1 at ,munich4 #b4 ,clocks4--,the improvements in the measures of space require corresponding improvements in the measure of time4 ,the beginning of any thing which we can call accuracy1 in this subject1 was the application of the ,pendulum to clocks1 by ,huyghens1 in #afef4 ,that the successive oscillations of a pendulum occupy equal times1 had been noticed by ,galileo2 but in order to take advantage of this property1 the pendulum must be connected with machinery by which its motion is kept from languishing1 and by which the number of its swings is recorded4 ,by inventing such machinery1 ,huyghens at once obtained #dgc a measure of time more accurate than the sun itself4 ,hence astronomers were soon led to obtain the right ascension of a star1 not directly1 by measuring a ,distance in the heavens1 but indirectly1 by observing the ,moment of its ,transit4 ,this observation is now made with a degree of accuracy which might1 at first sight1 appear beyond the limits of human sense1 being noted to a tenth of a second of time3 but we may explain this1 by remarking that though the number of the second at which the transit happens is given by the clock1 and is reckoned according to the course of time1 the subdivision of the second of time into smaller fractions is performed by the eye1--by seeing the space described by the heavenly body in a whole second1 and hence estimating a smaller time1 according to the space which its description occupies4 ,but in order to make clocks so accurate as to justify this degree of precision1 their construction was improved by various persons in succession4 ,picard soon found that ,huyghens' clocks were affected in their going by temperature1 for heat caused expansion of the metallic pendulum4 ,this cause of error was remedied by combining different metals1 as iron and copper1 which expand in a different degree1 in such a way that their effects compensate each other4 ,graham afterwards used quicksilver for the same purpose4 ,the ,escapement too 7which connects the force which impels the clock with the pendulum which regulates it71 and other parts of the machinery1 had the most refined mechanical skill and ingenuity of the best artists constantly bestowed upon then4 ,the astronomer of the present day1 constantly testing the going of such a clock by the motions of the fixed stars1 has a scale of time as stable and as minutely exact as the scales on which he measures distance4 ,the construction of good ,watches1 that is1 portable or marine clocks1 was important on another account1 namely1 because they might be used in determining the longitude of places4 ,hence the improvement of this little machine became an object of national interest1 and was included in the reward of #bj1jjjl41 which we have already noticed as offered by the ,english parliament for the discovery of the longitude4 ,harrison1#abbg originally a carpenter1 turned his mind to this subject with success4 ,after thirty years of labor1 in which he was encouraged by many eminent persons1 he produced1 in #ageh1 a time-keeper1 which was sent on a voyage to ,jamaica for trial4 ,after #afa days1 the error #dgd of the watch was only one minute five seconds1 and the artist received from the nation #ejjjl4 ,at a later period1#abcg at the age of seventy-five years1 after a life devoted to this object1 having still further satisfied the commissioners1 he received1 in #agfe1 #aj1jjjl41 at the same time that ,euler and the heirs of ,mayer received each #cjjjl4 for the lunar tables which they had constructed4 ,note #abbg3 ,mont4 iv4 #eed4 ,note #abcg3 ,mont4 iv4 #efj4 ,the two methods of finding the longitude1 by ,chronometers and by ,lunar ,observations1 have solved the problem for all practical purposes2 but the latter could not have been employed at sea without the aid of that invaluable instrument1 the ,sextant1 in which the distance of two objects is observed1 by bringing one to coincide apparently with the reflected image of the other4 ,this instrument was invented by ,hadley1 in #agca4 ,though the problem of finding the longitude be1 in fact1 one of geography rather than astronomy1 it is an application of astronomical science which has so materially affected the progress of our knowledge1 that it deserves the notice we have bestowed upon it4 #c4 ,telescopes4--,we have spoken of the application of the telescope to astronomical measurements1 but not of the improvement of the telescope itself4 ,if we endeavor to augment the optical power of this instrument1 we run1 according to the path we take1 into various inconveniences2--distortion1 confusion1 want of light1 or colored images4 ,distortion and confusion are produced1 if we increase the magnifying power1 retaining the length and the aperture of the object-glass4 ,if we diminish the aperture we suffer from loss of light4 ,what remains then is to increase the focal length4 ,this was done to an extraordinary extent1 in telescopes constructed in the beginning of the last century4 ,huyghens1 in his first attempts1 made them #bb feet long2#abdg afterwards1 ,campani1 by order of ,louis the ,fourteenth1 made them of #hf1 #ajj1 and #acf feet4 ,huyghens1 by new exertions1 made a telescope #baj feet long4 ,auzout and ,hartsoecker are said to have gone much further1 and to have succeeded in making an object-glass of #fjj feet focus4 ,but even such telescopes as those of ,campani are almost unmanageable3 in that of ,huyghens1 the object-glass was placed on a pole1 and the observer was placed at the focus with an eye-glass4 ,note #abdg3 ,bailly1 ii4 #bec4 ,the most serious objection to the increase of the aperture of object-glasses1 was the coloration of the image produced1 in consequence of the unequal refrangibility of differently colored rays4 ,newton1 who discovered the principle of this defect in lenses1 had maintained that #dge the evil was irremediable1 and that a compound lens could no more refract without producing color1 than a single lens could4 ,euler and ,klingenstierna doubted the exactness of ,newton's proposition2 and1 in #agee1 ,dollond disproved it by experiment4 ,this discovery pointed out a method of making object-glasses which should give no color2--which should be achromatic4 ,for this purpose ,dollond fabricated various kinds of glass 7flint and crown glass72 and ,clairaut and ,d',alembert calculated formul4 ,dollond and his son#abeg succeeded in constructing telescopes of three feet long 7with a triple object-glass7 which produced an effect as great as those of forty-five feet on the ancient principles4 ,at first it was conceived that these discoveries opened the way to a vast extension of the astronomer's power of vision2 but it was found that the most material improvement was the compendious size of the new instruments2 for1 in increasing the dimensions1 the optician was stopped by the impossibility of obtaining lenses of flint-glass of very large dimensions4 ,and this branch of art remained long stationary2 but1 after a time1 its epoch of advance again arrived4 ,in the present century1 ,fraunhofer1 at ,munich1 with the help of ,guinand and the pecuniary support of ,utzschneider1 succeeded in forming lenses of flint-glass of a magnitude till then unheard of4 ,achromatic object-glasses1 of a foot in diameter1 and twenty feet focal length1 are now no longer impossible2 although in such attempts the artist cannot reckon on certain success4 ,note #abeg3 ,bailly1 iii4 #aah4 #b;d ,ed4 ,joseph ,fraunhofer was born ,march #f1 #aghg1 at ,straubing in ,bavaria1 the son of a poor glazier4 ,he was in his earlier years employed in his father's trade1 so that he was not able to attend school1 and remained ignorant of writing and arithmetic till his fourteenth year4 ,at a later period he was assisted by ,utzschneider1 and tried rapidly to recover his lost ground4 ,in the year #ahjf he entered the establishment of ,utzschneider as an optician4 ,in this establishment 7transferred from ,benedictbeuern to ,munich in #ahai7 he soon came to be the greatest ,optician of ,germany4 ,his excellent telescopes and microscopes are known throughout ,europe4 ,his greatest telescope1 that in the ,observatory at ,dorpat1 has an object-glass of #i inches diameter1 and a focal length of #ac feet4 ,his written productions are to be found in the ,memoirs of the ,bavarian ,academy1 in ,gilbert's ,annalen der ,physik1 and in ,schumacher's ,astronomische ,nachrichten4 ,he died the #gth of ,june1 #ahbf4 #dgf ,such telescopes might be expected to add something to our knowledge of the heavens1 if they had not been anticipated by reflectors of an equal or greater scale4 ,james ,gregory had invented1 and ,newton had more efficaciously introduced1 reflecting telescopes4 ,but these were not used with any peculiar effect1 till the elder ,herschel made them his especial study4 ,his skill and perseverance in grinding specula1 and in contriving the best apparatus for their use1 were rewarded by a number of curious and striking discoveries1 among which1 as we have already related1 was the discovery of a new planet beyond ,saturn4 ,in #aghi1 ,herschel surpassed all his former attempts1 by bringing into action a reflecting telescope of forty feet length1 with a speculum of four feet in diameter4 ,the first application of this magnificent instrument showed a new satellite 7the sixth7 of ,saturn4 ,he and his son have1 with reflectors of twenty feet1 made a complete survey of the heavens1 so far as they are visible in this country2 and the latter is now in a distant region completing this survey1 by adding to it the other hemisphere4 ,in speaking of the improvements of telescopes we ought to notice1 that they have been pursued in the eye-glasses as well as in the object-glasses4 ,instead of the single lens1 ,huyghens substituted an eye-piece of two lenses1 which1 though introduced for another purpose1 attained the object of destroying color4#abfg ,ramsden's eye-piece is one fit to be used with a micrometer1 and others of more complex construction have been used for various purposes4 ,note #abfg3 ,coddington's ,optics1 ii4 #ba4 ,sect4 #b4--,observatories4 ,,astronomy1 which is thus benefited by the erection of large and stable instruments1 requires also the establishment of permanent ,observatories1 supplied with funds for their support1 and for that of the observers4 ,such observatories have existed at all periods of the history of the science2 but from the commencement of the period which we are now reviewing1 they multiplied to such an extent that we cannot even enumerate them4 ,yet we must undoubtedly look upon such establishments1 and the labors of which they have been the scene1 as important and essential parts of the history of the progress of astronomy4 ,some of the most distinguished of the observatories of modern times we may mention4 ,the first of these were that of ,tycho ,brahe #dgg at ,uraniburg1 and that of the ,landgrave of ,hesse ,cassel1 at ,cassel1 where ,rothman and ,byrgius observed4 ,but by far the most important observations1 at least since those of ,tycho1 which were the basis of the discoveries of ,kepler and ,newton1 have been made at ,paris and ,greenwich4 ,the ,observatory of ,paris was built in #affg4 ,it was there that the first ,cassini made many of his discoveries2 three of his descendants have since labored in the same place1 and two others of his family1 the ,maraldis2#abgg besides many other eminent astronomers1 as ,picard1 ,la ,hire1 ,lefvre1 ,fouchy1 ,legentil1 ,chappe1 ,mchain1 ,bouvard4 ,greenwich ,observatory was built a few years later 7#afge72 and ever since its erection1 the observations there made have been the foundation of the greatest improvements which astronomy1 for the time1 received4 ,flamsteed1 ,halley1 ,bradley1 ,bliss1 ,maskelyne1 ,pond1 have occupied the place in succession3 on the retirement of the last-named astronomer in #ahce1 ,professor ,airy was removed thither from the ,cambridge ,observatory4 ,in every state1 and in almost every principality in ,europe1 ,observatories have been established2 but these have often fallen speedily into inaction1 or have contributed little to the progress of astronomy1 because their observations have not been published4 ,from the same causes1 the numerous private observatories which exist throughout ,europe have added little to our knowledge1 except where the attention of the astronomer has been directed to some definite points2 as1 for instance1 the magnificent labors of the ,herschels1 or the skilful observations made by ,mr4 ,pond with the ,westbury circle1 which first pointed out the error of graduation of the ,greenwich quadrants4 ,the ,observations1 now regularly published1#abhg are those of ,greenwich1 begun by ,maskelyne1 and continued quarterly by ,mr4 ,pond2 those of ,knigsberg1 published by ,bessel since #ahad2 of ,vienna1 by ,littrow since #ahbj2 of ,speier1 by ,schwerd since #ahbf2 those of ,cambridge1 commenced by ,airy in #ahbh2 of ,armagh1 by ,robinson in #ahbi4 ,besides these1 a number of useful observations have been published in journals and occasional forms2 as1 for instance1 those of ,zach1 made by ,seeberg1 near ,gotha1 since #aghh2 and others have been employed in forming catalogues1 of which we shall speak shortly4 ,note #abgg3 ,mont4 iv4 #cdf4 ,note #abhg3 ,airy1 ,rep4 p4 #abh4 #b;d ,ed4 ,i have left the statement of published ,observations in the text as it stood originally4 ,i believe that at present 7#ahdg7 the twelve places contained in the following list publish their ,observations quite regularly1 or nearly so2--,greenwich1 ,oxford1 ,cambridge1 ,vienna1 #dgh ,berlin1 ,dorpat1 ,munich1 ,geneva1 ,paris1 ,knigsberg1 ,madras1 the ,cape of ,good ,hope4 ,littrow1 in his translation1 adds to the publications noticed in the text as containing astronomical ,observations1 ,zach's ,monatliche ,correspondenz1 ,lindenau and ,bohnenberger's ,zeitschrift fr ,astronomie1 ,bode's ,astronomisches ,jahrbuch1 ,schumacher's ,astronomische ,nachrichten4 ,nor has the establishment of observatories been confined to ,europe4 ,in #aghf1 ,m4 de ,beauchamp1 at the expense of ,louis the ,sixteenth1 erected an observatory at ,bagdad1 built to restore the ,chaldean and ,arabian observations1 as the inscription stated2 but1 probably1 the restoration once effected1 the main intention had been fulfilled1 and little perseverance in observing was thought necessary4 ,in #ahbh1 the ,british government completed the building of an observatory at the ,cape of ,good ,hope1 which ,lacaille had already made an astronomical station by his observations there at an earlier period 7#agej72 and an observatory formed in ,new ,south ,wales by ,sir ,t4 ,m4 ,brisbane in #ahbb1 and presented by him to the government1 is also in activity4 ,the ,east ,india ,company has founded observatories at ,madras1 ,bombay1 and ,st4 ,helena2 and observations made at the former of these places1 and at ,st4 ,helena1 have been published4 ,the bearing of the work done at such observatories upon the past progress of astronomy1 has already been seen in the preceding narrative4 ,their bearing upon the present condition of the science will be the subject of a few remarks hereafter4 ,sect4 #c4--,scientific ,societies4 ,,the influence of ,scientific ,societies1 or ,academical ,bodies1 has also been very powerful in the subject before us4 ,in all branches of knowledge1 the use of such associations of studious and inquiring men is great2 the clearness and coherence of a speculator's ideas1 and their agreement with facts 7the two main conditions of scientific truth71 are severally but beneficially tested by collision with other minds4 ,in astronomy1 moreover1 the vast extent of the subject makes requisite the division of labor and the support of sympathy4 ,the ,royal ,societies of ,london and of ,paris were founded nearly at the same time as the metropolitan ,observatories of the two countries4 ,we have seen what constellations of philosophers1 and what activity of research1 existed at those periods2 these philosophers appear in the lists1 their discoveries #dgi in the publications1 of the above-mentioned eminent ,societies4 ,as the progress of physical science1 and principally of astronomy1 attracted more and more admiration1 ,academies were created in other countries4 ,that of ,berlin was founded by ,leibnitz in #agaj2 that of ,st ,petersburg was established by ,peter the ,great in #agbe2 and both these have produced highly valuable ,memoirs4 ,in more modern times these associations have multiplied almost beyond the power of estimation4 ,they have been formed according to divisions1 both of locality and of subject1 conformable to the present extent of science1 and the vast population of its cultivators4 ,it would be useless to attempt to give a view either of their number or of the enormous mass of scientific literature which their ,transactions present4 ,but we may notice1 as especially connected with our present subject1 the ,astronomical ,society of ,london1 founded in #ahbj1 which gave a strong impulse to the pursuit of the science in ,england4 ,sect4 #d4--,patrons of ,astronomy4 ,the advantages which letters and philosophy derive from the patronage of the great have sometimes been questioned2 that love of knowledge1 it has been thought1 cannot be genuine which requires such stimulation1 nor those speculations free and true which are thus forced into being4 ,in the sciences of observation and calculation1 however1 in which disputed questions can be experimentally decided1 and in which opinions are not disturbed by men's practical principles and interests1 there is nothing necessarily operating to poison or neutralize the resources which wealth and power supply to the investigation of truth4 ,astronomy has1 in all ages1 flourished under the favor of the rich and powerful2 in the period of which we speak1 this was eminently the case4 ,louis the ,fourteenth gave to the astronomy of ,france a distinction which1 without him1 it could not have attained4 ,no step perhaps tended more to this than his bringing the celebrated ,dominic ,cassini to ,paris4 ,this ,italian astronomer 7for he was born at ,permaldo1 in the county of ,nice1 and was professor at ,bologna71 was already in possession of a brilliant reputation1 when the ,french ambassador1 in the name of his sovereign1 applied to ,pope ,clement the ,ninth1 and to the senate of ,bologna1 that he should be allowed to remove to ,paris4 ,the request was granted only so far as an absence of six years2 but at the end of that time1 the benefits and honors which #dhj the king had conferred upon him1 fixed him in ,france4 ,the impulse which his arrival 7in #affi7 and his residence gave to astronomy1 showed the wisdom of the measure4 ,in the same spirit1 the ,french government drew to ,paris ,rmer from ,denmark1 ,huyghens from ,holland1 and gave a pension to ,hevelius1 and a large sum when his observatory at ,dantzic had been destroyed by fire in #afgi4 ,when the sovereigns of ,prussia and ,russia were exerting themselves to encourage the sciences in their countries1 they followed the same course which had been so successful in ,france4 ,thus1 as we have said1 the ,czar ,peter took ,delisle to ,petersburg in #agbe2 the celebrated ,frederick the ,great drew to ,berlin1 ,voltaire and ,maupertuis1 ,euler and ,lagrange2 and the ,empress ,catharine obtained in the same way ,euler1 two of the ,bernoulli's1 and other mathematicians4 ,in none of these instances1 however1 did it happen that the generous plant did still its stock renew1 as we have seen was the case at ,paris1 with the ,cassinis1 and their kinsmen the ,maraldis4 #b;d ,ed4 ,i may notice among instances of the patronage of ,astronomy1 the reward at present offered by the ,king of ,denmark for the discovery of a ,comet4 ,it is not necessary to mention here the more recent cases in which sovereigns or statesmen have attempted to patronize individual astronomers4 ,sect4 #e4--;,astronomical ,expeditions4 ,,besides the pensions thus bestowed upon resident mathematicians and astronomers1 the governments of ,europe have wisely and usefully employed considerable sums upon expeditions and travels undertaken by men of science for some appropriate object4 ,thus ,picard1 in #afga1 was sent to ,uraniburg1 the scene of ,tycho's observations1 to determine its latitude and its longitude4 ,he found that the ,city of the ,skies had utterly disappeared from the earth2 and even its foundations were retraced with difficulty4 ,with the same object1 that of accurately connecting the labors of the places which had been at different periods the metropolis of astronomy1 ,chazelles was sent1 in #afic1 to ,alexandria4 ,we have already mentioned ,richer's astronomical expedition to ,cayenne in #afgb4 ,varin and ,deshayes#abig were sent a few years later into the same regions for similar purposes4 ,halley's expedition to ,st4 #dha ,helena in #afgg1 with the view of observing the southern stars1 was at his own expense2 but at a later period 7in #afih71 he was appointed to the command of a small vessel by ,king ,william the ,third1 in order that he might make his magnetical observations in all parts of the world4 ,lacaille was maintained by the ,french government four years at the ,cape of ,good ,hope 7#agej-d71 for the purpose of observing the stars of the southern hemisphere4 ,the two transits of ,venus in #agfa and #agfi1 occasioned expeditions to be sent to ,kamtschatka and ,tobolsk by the ,russians2 to the ,isle of ,france1 and to ,coromandel1 by the ,french2#acjg to the isles of ,st4 ,helena and ,otaheite by the ,english2 to ,lapland and to ,drontheim1 by the ,swedes and ,danes4 ,i shall not here refer to the measures of degrees executed by various nations1 still less the innumerable surveys by land and sea2 but ,i may just notice the successive ,english expeditions of ,captains ,basil ,hall1 ,sabine1 and ,foster1 for the purpose of determining the length of the seconds' pendulum in different latitudes2 and the voyages of ,m4 ,biot and others1 sent by the ,french government for the same purpose4 ,much has been done in this way1 but not more than the progress of astronomy absolutely required2 and only a small portion of that which the completion of the subject calls for4 ,note #abig3 ,bailly1 ii4 #cgd4 ,note #acjg3 ,bailly1 iii4 #ajg4 ,sect4 #f4--,present ,state of ,astronomy4 ,,astronomy1 in its present condition1 is not only much the most advanced of the sciences1 but is also in far more favorable circumstances than any other science for making any future advance1 as soon as this is possible4 ,the general methods and conditions by which such an advantage is to be obtained for the various sciences1 we shall endeavor hereafter to throw some light upon2 but in the mean time1 we may notice here some of the circumstances in which this peculiar felicity of the present state of astronomy may be traced4 ,the science is cultivated by a number of votaries1 with an assiduity and labor1 and with an expenditure of private and public resources1 to which no other subject approaches2 and the mode of its cultivation in all public and most private observatories1 has this character--that it forms1 at the same time1 a constant process of verification of existing discoveries1 and a strict search for any new discoverable laws4 ,the observations made are immediately referred to the best tables1 and #dhb corrected by the best formul which are known2 and if the result of such a reduction leaves any thing unaccounted for1 the astronomer is forthwith curious and anxious to trace this deviation from the expected numbers to its rule and its origin2 and till the first1 at least1 of these things is performed1 he is dissatisfied and unquiet4 ,the reference of observations to the state of the heavens as known by previous researches1 implies a great amount of calculation4 ,the exact places of the stars at some standard period are recorded in ,catalogues2 their movements1 according to the laws hitherto detected1 are arranged in ,tables2 and if these tables are applied to predict the numbers which observation on each day ought to give1 they form ,ephemerides4 ,thus the catalogues of fixed stars of ,flamsteed1 of ,piazzi1 of ,maskelyne1 of the ,astronomical ,society1 are the basis of all observation4 ,to these are applied the ,corrections for ,refraction of ,bradley or ,bessel1 and those for ,aberration1 for ,nutation1 for ,precession1 of the best modern astronomers4 ,the observations so corrected enable the observer to satisfy himself of the delicacy and fidelity of his measures of time and space2 his ,clocks and his ,arcs4 ,but this being done1 different stars so observed can be compared with each other1 and the astronomer can then endeavor further to correct his fundamental ,elements2--his ,catalogue1 or his ,tables of ,corrections4 ,in these ,tables1 though previous discovery has ascertained the law1 yet the exact quantity1 the constant or coefficient of the formula1 can be exactly fixed only by numerous observations and comparisons4 ,this is a labor which is still going on1 and in which there are differences of opinion on almost every point2 but the amount of these differences is the strongest evidence of the certainty and exactness of those doctrines in which all agree4 ,thus ,lindenau makes the coefficient of ,nutation rather less than nine seconds1 which other astronomers give as about nine seconds and three-tenths4 ,the ,tables of ,refraction are still the subject of much discussion1 and of many attempts at improvement4 ,and after or amid these discussions1 arise questions whether there be not other corrections of which the law has not yet been assigned4 ,the most remarkable example of such questions is the controversy concerning the existence of an ,annual ,parallax of the fixed stars1 which ,brinkley asserted1 and which ,pond denied4 ,such a dispute between two of the best modern observers1 only proves that the quantity in question1 if it really exist1 is of the same order as the hitherto unsurmounted errors of instruments and corrections4 #b;d ,ed4 ,the belief in an appreciable parallax of some of the fixed #dhc stars appears to gain ground among astronomers4 ,the parallax of #fa ,cygni1 as determined by ,bessel1 is #jcd2 about one-third of a second1 or #aajjjj of a degree4 ,that of ,centauri1 as determined by ,maclear1 is #ji1 or #adjjj of a degree4 ,but besides the fixed stars and their corrections1 the astronomer has the motions of the planets for his field of action4 ,the established theories have given us tables of these1 from which their daily places are calculated and given in our ,ephemerides1 as the ,berliner ,jahrbuch of ,encke1 or the ,nautical ,almanac1 published by the government of this country1 the ,connaissance des ,tems which appears at ,paris1 or the ,effemeridi di ,milano4 ,the comparison of the observed with the tabular place1 gives us the means of correcting the coefficients of the tables2 and thus of obtaining greater exactness in the constants of the solar system4 ,but these constants depend upon the mass and form of the bodies of which the system is composed2 and in this province1 as well as in sidereal astronomy1 different determinations1 obtained by different paths1 may be compared2 and doubts may be raised and may be solved4 ,in this way1 the perturbations produced by ,jupiter on different planets gave rise to a doubt whether his attraction be really proportional to his mass1 as the law of universal gravitation asserts4 ,the doubt has been solved by ,nicolai and ,encke in ,germany1 and by ,airy in ,england4 ,the mass of ,jupiter1 as shown by the perturbations of ,juno1 of ,vesta1 and of ,encke's ,comet1 and by the motion of his outermost ,satellite1 is found to agree1 though different from the mass previously received on the authority of ,laplace4 ,thus also ,burckhardt1 ,littrow1 and ,airy1 have corrected the elements of the ,solar ,tables4 ,in other cases1 the astronomer finds that no change of the coefficients will bring the ,tables and the observations to a coincidence2--that a new term in the formula is wanting4 ,he obtains1 as far as he can1 the law of this unknown term2 if possible1 he traces it to some known or probable cause4 ,thus ,mr4 ,airy1 in his examination of the ,solar ,tables1 not only found that a diminution of the received mass of ,mars was necessary1 but perceived discordances which led him to suspect the existence of a new inequality4 ,such an inequality was at length found to result theoretically from the attraction of ,venus4 ,encke1 in his examination of his comet1 found a diminution of the periodic time in the successive revolutions2 from which he inferred the existence of a resisting medium4 ,uranus still deviates from his tabular place1 and the cause remains yet to be discovered4 7,but see the ,additions to this volume47 #dhd ,thus it is impossible that an assertion1 false to any amount which the existing state of observation can easily detect1 should have any abiding prevalence in astronomy4 ,such errors may long keep their ground in any science which is contained mainly in didactic works1 and studied in the closet1 but not acted upon elsewhere2--which is reasoned upon much1 but brought to the test of experiment rarely or never4 ,here1 on the contrary1 an error1 if it arise1 makes its way into the ,tables1 into the ,ephemeris1 into the observer's nightly ,list1 or his sheet of ,reductions2 the evidence of sense flies in its face in a thousand observatories2 the discrepancy is traced to its source1 and soon disappears forever4 ,in this favored branch of knowledge1 the most recondite and delicate discoveries can no more suffer doubt or contradiction1 than the most palpable facts of sense which the face of nature offers to our notice4 ,the last great discovery in astronomy--the motion of the stars arising from ,aberration--is as obvious to the vast population of astronomical observers in all parts of the world1 as the motion of the stars about the pole is to the casual night wanderer4 ,and this immunity from the danger of any large error in the received doctrines1 is a firm platform on which the astronomer can stand and exert himself to reach perpetually further and further into the region of the unknown4 ,the same scrupulous care and diligence in recording all that has hitherto been ascertained1 has been extended to those departments of astronomy in which we have as yet no general principles which serve to bind together our acquired treasures4 ,these records may be considered as constituting a ,descriptive ,astronomy2 such are1 for instance1 ,catalogues of ,stars1 and ,maps of the ,heavens1 ,maps of the ,moon1 representations of the appearance of the ,sun and ,planets as seen through powerful telescopes1 pictures of ,nebul1 of ,comets1 and the like4 ,thus1 besides the ,catalogue of ,fundamental ,stars which may be considered as standard points of reference for all observations of the ,sun1 ,moon1 and ,planets1 there exist many large catalogues of smaller stars4 ,flamsteed's ,historia ,celestis1 which much surpassed any previous catalogue1 contained above #cjjj stars4 ,but in #ahja1 the ,french ,histoire ,cleste appeared1 comprising observations of #ej1jjj stars4 ,catalogues or charts of other special portions of the sky have been published more recently2 and in #ahbe1 the ,berlin ,academy proposed to the astronomers of ,europe to carry on this work by portioning out the heavens among them4 #b;d ,ed4 ,before ,flamsteed1 the best ,catalogue of the ,stars was #dhe ,tycho ,brahe's1 containing the places of about #ajjj stars1 determined very roughly with the naked eye4 ,on the occasion of a project of finding the longitude1 which was offered to ,charles ,,ii41 in #afgd1 ,flamsteed represented that the method was quite useless1 in consequence1 among other things1 of the inaccuracy of ,tycho's places of the stars4 ,flamsteed's letters being shown ,king ,charles1 he was startled at the assertion of the fixed stars' places being false in the ,catalogue1 and said1 with some vehemence1 ,he must have them anew observed1 examined1 and corrected for the use of his seamen4 ,this was the immediate occasion of building ,greenwich ,observatory1 and placing ,flamsteed there as an observer4 ,flamsteed's ,historia ,celestis contained above #cjjj stars1 observed with telescopic sights4 ,it has recently been republished with important improvements by ,mr4 ,baily4 ,see ,baily's ,flamsteed1 p4 #ch4 ,the ,french ,histoire ,cleste was published in #ahja by ,lalande1 containing #ej1jjj stars1 simply as observed by himself and other ,french astronomers4 ,the reduction of the observations contained in this ,catalogue to the mean places at the beginning of the year #ahjj may be effected by means of ,tables published by ,schumacher for that purpose in #ahbe4 ,in #ahjg1 ,piazzi's ,catalogue of #fgdh stars1 founded on ,maskelyne's ,catalogue of #agjj1 was published2 afterwards extended to #gfdf stars in #ahad4 ,this is considered as the greatest work undertaken by any modern astronomer2 the observations being well made1 reduced1 and compared with those of former astronomers4 ,piazzi's ,catalogue is the standard and accurate ,catalogue1 as the ,histoire ,cleste is the standard approximate ,catalogue for small stars4 ,but the new planets were discovered mostly by a comparison of the heavens with ,bode's 7,berlin7 ,catalogue4 ,i may mention other ,catalogues of ,stars which have recently been published4 ,pond's ,catalogue contains #aaab ,northern stars2 ,johnson's1 #fjf2 ,wrottesley's1 #acah 7in ,right ,ascension only72 ,airy's ,first ,cambridge ,catalogue1 #gbf2 his ,greenwich ,catalogue1 #adci4 ,pearson's has #ebj zodiacal stars2 ,groombridge's1 #dbdc circumpolar stars as far as #ej degrees of ,north ,polar distance2 ,santini's1 a zone #ah degrees ,north of the equator4 ,besides these1 ,mr4 ,taylor has published1 by order of the ,madras government1 a ,catalogue of #aa1jjj stars observed by him at ,madras2 and ,rumker1 who observed in the ,observatory established by ,sir ,thomas ,brisbane at ,paramatta 7in ,australia71 has commenced a ,catalogue which is to contain #ab1jjj4 ,mr4 ,baily #dhf published two ,standard ,catalogues2 that of the ,royal ,astronomical ,society1 containing #bhha stars2 and that of the ,british ,association1 containing #hcgg stars4 ,i omit other ,catalogues1 as those of ,argelander1 c41 and ,catalogues of ,southern ,stars4 ,of the ,berlin ,maps1 fourteen hours in ,right ,ascension have been published2 and their value may be judged of by this circumstance1 that it was in a great measure by comparing the heavens with these ,maps that the new planet ,astra was discovered4 ,the ,zone observations made at ,knigsberg1 by the late illustrious astronomer ,bessel1 deserve to be mentioned1 as embracing a vast number of stars4 ,the common mode of designating the ,stars is founded upon the ancient constellations as given by ,ptolemy2 to which ,bayer1 of ,augsburg1 in his ,uranometria1 added the artifice of designating the brightest stars in each constellation by the ,greek letters1 1 1 1 c41 applied in order of brightness1 and when these were exhausted1 the ,latin letters4 ,flamsteed used numbers4 ,as the number of observed stars increased1 various methods were employed for designating them2 and the confusion which has been thus introduced1 both with regard to the boundaries of the constellations and the nomenclature of the stars in each1 has been much complained of lately4 ,some attempts have been made to remedy this variety and disorder4 ,mr4 ,argelander has recently recorded stars1 according to their magnitudes as seen by the naked eye1 in a ,neue ,uranometrie4 ,among representations of the ,moon ,i may mention ,hevelius's ,selenographia1 a work of former times1 and ,beer and ,madler's ,map of the ,moon1 recently published4 ,i have already said something of the observations of the two ,herschels on ,double ,stars1 which have led to a knowledge of the law of the revolution of such systems4 ,but besides these1 the same illustrious astronomers have accumulated enormous treasures of observations of ,nebul2 the materials1 it may be1 hereafter1 of some vast new generalization with respect to the history of the system of the universe4 #b;d ,ed4 ,a few measures of ,double ,stars are to be found in previous astronomical records4 ,but the epoch of the creation of this part of the science of astronomy must be placed at the beginning of the present century1 when ,sir ,william ,herschel 7in #ahjb7 published in the ,phil4 ,trans4 a ,catalogue of #ejj new ,nebul of various classes1 and in the ,phil4 ,trans4 #ahjc1 a paper ,on the changes in the relative situation of the ,double ,stars in #be years4 ,in succeeding papers he pursued the subject4 ,in one in #ahad he noticed the breaking up of the #dhg ,milky ,way in different places1 apparently from some principle of ,attraction2 and in this1 and in one in #ahag1 he published those remarkable views on the distribution of the stars in our own cluster as forming a large stratum1 and on the connection of stars and nebul 7the stars appearing sometimes to be accompanied by nebul1 sometimes to have absorbed a part of the nebula1 and sometimes to have been formed from nebul71 which have been accepted and propounded by others as the ,nebular ,theory4 ,sir ,william ,herschel's last paper was a ,catalogue of #ade new ,double ,stars communicated to the ,astronomical ,society in #ahbb4 ,in #ahbg ,m4 ,struve1 of ,dorpat 7in ,russia71 published his ,catalogus ,novus1 containing the places of #caab double stars4 ,while this was going on1 ,sir ,john ,herschel and ,sir ,james ,south published 7in the ,phil4 ,trans4 #ahbd7 accurate measures of #chj ,double and ,triple ,stars1 to which ,sir ,j4 ,south afterwards added #deh4 ,mr4 ,dunlop published measures of #bec ,southern ,double ,stars4 ,other ,observations have been published by ,capt4 ,smyth1 ,mr4 ,dawes1 c4 ,the great work of ,struve1 ,mensur ,micrometric1 c41 contains #cacd such objects1 including most of ,sir ,w4 ,herschel's ,double ,stars4 ,sir ,j4 ,herschel in #ahbf1 #g1 and #h presented to the ,astronomical ,society about #ajjj measures of ,double ,stars2 and in #ahcj1 good measures of #abcf1 made with his #bj-;feet reflector4 ,his paper in vol4 v4 of the ,ast4 ,soc4 ,mem41 besides measures of #cfd such stars1 exhibits all the most striking results1 as to the motion of ,double ,stars1 which have yet been obtained4 ,in #ahce he carried his #bj-;feet reflector to the ,cape of ,good ,hope for the purpose of completing the survey of ,double ,stars and ,nebul in the southern hemisphere with the same instruments which had explored the northern skies4 ,he returned from the ,cape in #ahch1 and is now 7#ahdf7 about to give the world the results of his labors4 ,besides the stars just mentioned1 his work will contain from #aejj to #bjjj additional double stars2 making a gross number of above #hjjj2 in which of course are included a number of objects of no great scientific interest1 but in which also are contained the materials of the most important discoveries which remain to be made by astronomers4 ,the publication of ,sir ,john ,herschel's great work upon ,double ,stars and ,nebul is looked for with eager interest by astronomers4 ,of the observations of ,nebul we may say what has just been said of the observations of ,double ,stars2--that they probably contain the materials of important future discoveries4 ,it is impossible not to regard these phenomena with reference to the ,nebular ,hypothesis1 which has been propounded by ,laplace1 and much more strongly #dhh insisted upon by other persons2--namely1 the hypothesis that systems of revolving planets1 of which the ,solar ,system is an example1 arise from the gradual contraction and separation of vast masses of nebulous matter4 ,yet it does not appear that any changes have been observed in nebul which tend to confirm this hypothesis2 and the most powerful telescope in the world1 recently erected by the ,earl of ,rosse1 has given results which militate against the hypothesis2 inasmuch as it has shown that what appeared a diffused nebulous mass is1 by a greater power of vision1 resolved1 in all cases yet examined1 into separate stars4 ,when astronomical phenomena are viewed with reference to the ,nebular ,hypothesis1 they do not belong so properly to ,astronomy1 in the view here taken of it1 as to ,cosmogony4 ,if such speculations should acquire any scientific value1 we shall have to arrange them among those which ,i have called ,paltiological ,sciences2 namely1 those ,sciences which contemplate the universe1 the earth1 and its inhabitants1 with reference to their historical changes and the causes of those changes4 #dhi ,,additions ,,to ,,the ,,third ,,edition4 ,,introduction4 ,,there is a difficulty in writing for popular readers a ,history of the ,inductive ,sciences1 arising from this2--that the sympathy of such readers goes most readily and naturally along the course which leads to false science and to failure4 ,men1 in the outset of their attempts at knowledge1 are prone to rush from a few hasty observations of facts to some wide and comprehensive principles2 and then1 to frame a system on these principles4 ,this is the opposite of the method by which the ,sciences have really and historically been conducted2 namely1 the method of a gradual and cautious ascent from observation to principles of limited generality1 and from them to others more general4 ,this latter1 the true ,scientific ,method1 is ,induction1 and has led to the ,inductive ,sciences4 ,the other1 the spontaneous and delusive course1 has been termed by ,francis ,bacon1 who first clearly pointed out the distinction1 and warned men of the error1 ,anticipation4 ,the hopelessness of this course is the great lesson of his philosophy2 but by this course proceeded all the earlier attempts of the ,greek philosophers to obtain a knowledge of the ,universe4 ,laborious observation1 narrow and modest inference1 caution1 slow and gradual advance1 limited knowledge1 are all unwelcome efforts and restraints to the mind of man1 when his speculative spirit is once roused3 yet these are the necessary conditions of all advance in the ,inductive ,sciences4 ,hence1 as ,i have said1 it is difficult to win the sympathy of popular readers to the true history of these sciences4 ,the career of bold systems and fanciful pretences of knowledge is more entertaining and striking4 ,not only so1 but the bold guesses and fanciful reasonings of men unchecked by doubt or fear of failure are often presented as the dictates of ,common ,sense2--as the plain1 unsophisticated1 unforced reason of man1 acting according to no artificial rules1 but following its own natural course4 ,such ,common ,sense1 while it #dij complacently plumes itself on its clear-sightedness in rejecting arbitrary systems of others1 is no less arbitrary in its own arguments1 and often no less fanciful in its inventions1 than those whom it condemns4 ,we cannot take a better representative of the ,common ,sense of the ancient ,greeks than ,socrates3 and we find that his ,common ,sense1 judging with such admirable sagacity and acuteness respecting moral and practical matters1 offered1 when he applied it to physical questions1 examples of the unconscious assumptions and fanciful reasonings which1 as we have said1 ,common ,sense on such subjects commonly involves4 ,socrates1 ,xenophon tells us 7,memorabilia1 iv4 #g71 recommended his friends not to study astronomy1 so as to pursue it into scientific details4 ,this was practical advice3 but he proceeded further to speak of the palpable mistakes made by those who had carried such studies farthest4 ,anaxagoras1 for instance1 he said1 held that the ,sun was a ,fire3--he did not consider that men can look at a fire1 but they cannot look at the ,sun2 they become dark by the ,sun shining upon them1 but not so by the fire4 ,he did not consider that no plants can grow well except they have sunshine1 but if they are exposed to the fire they are spoiled4 ,again1 when he said that the ,sun was a stone red-hot1 he did not consider that a stone heated by the fire is not luminous1 and soon cools1 but the ,sun is always luminous and always hot4 ,we may easily conceive how a disciple of ,anaxagoras would reply to these arguments4 ,he would say1 for example1 as we should probably say at present1 that if there were a mass of matter so large and so hot as ,anaxagoras supposed the ,sun to be1 its light might be as great and its heat as permanent as the heat and light of the ,sun are1 as yet1 known to be4 ,in this case the arguments of ,socrates are at any rate no better than the doctrine of ,anaxagoras4 #dia ,,book ,i4 ,,the ,,greek ,,school ,,philosophy4 ,,chapter ,,ii4 ,,the ,,greek ,,schools4 ,the ,platonic ,doctrine of ,ideas4 ,,in speaking of the ,foundation of the ,greek ,school ,philosophy1 ,i have referred to the dialogue entitled ,parmenides1 commonly ascribed to ,plato4 ,and the doctrines ascribed to ,parmenides1 in that and in other works of ancient authors1 are certainly remarkable examples of the tendency which prevailed among the ,greeks to rush at once to the highest generalizations of which the human mind is capable4 ,the distinctive dogma of the ,eleatic ,school1 of which ,parmenides was one of the most illustrious teachers1 was that ,all ,things are ,one4 ,this indeed was rather a doctrine of metaphysical theology than of physical science4 ,it tended to1 or agreed with1 the doctrine that ,all things are ,god3--the doctrine commonly called ,pantheism4 ,but the tenet of the ,platonists which was commonly put in opposition to this1 that we must seek ,the ,one in the ,many1 had a bearing upon physical science2 at least1 if we interpret it1 as it is generally interpreted1 that we must seek the one ,law which pervades a multiplicity of ,phenomena4 ,we may however take the liberty of remarking1 that to speak of a ,rule which is exemplified in many cases1 as being the ,one in the ,many 7a way of speaking by which we put out of sight the consideration what very different kinds of things the ,one and the ,many are71 is a mode of expression which makes a very simple matter look very mysterious2 and is another example of the tendency which urges speculative men to aim at metaphysical generality rather than scientific truth4 ,the ,dialogue ,parmenides is1 as ,i have said1 commonly referred to ,plato4 ,yet it is entirely different in substance1 manner1 and tendency #dib from the most characteristic of the ,platonic ,dialogues4 ,in these1 ,socrates is represented as finally successful in refuting or routing his adversaries1 however confident their tone and however popular their assertions4 ,they are angered or humbled2 he retains his good temper and his air of superiority1 and when they are exhausted1 he sums up in his own way4 ,in the ,parmenides1 on the contrary1 everything is the reverse of this4 ,parmenides and ,zeno exchange good-humoured smiles at ,socrates's criticism1 when the bystanders expect them to grow angry4 ,they listen to ,socrates while he propounds ,plato's doctrine of ,ideas2 and reply to him with solid arguments which he does not answer1 and which have never yet been answered4 ,parmenides1 in a patronising way1 lets him off2 and having done this1 being much entreated1 he pronounces a discourse concerning the ,one and the ,many2 which1 obscure as it may seem to us1 was obviously intended to be irrefutable3 and during the whole of this part of the ,dialogue1 the friend of ,socrates appears only as a passive respondent1 saying ,yes or ,no as the assertions of ,parmenides require him to do2 just in the same way in which the opponents of ,socrates are represented in other ,dialogues4 ,these circumstances1 to which other historical difficulties might be added1 seem to show plainly that the ,parmenides must be regarded as an ,eleatic1 not as a ,platonic ,dialogue2--as composed to confute1 not to assert1 the ,platonic doctrine of ,ideas4 ,the ,platonic doctrine of ,ideas has an important bearing upon the philosophy of ,science1 and was suggested in a great measure by the progress which the ,greeks had really made in ,geometry1 ,astronomy1 and other ,sciences1 as ,i shall elsewhere endeavor to show4 ,this doctrine has been recommended in our own time1#a;,a as containing a mighty substance of imperishable truth4 ,it cannot fail to be interesting to see in what manner the doctrine is presented by those who thus judge of it4 ,the following is the statement of its leading features which they give us4 ,note #a;,a3 ,a4 ,butler's ,lectures1 ,second ,series1 ,lect4 viii4 p4 #acb4 ,man's soul is made to contain not merely a consistent scheme of its own notions1 but a direct apprehension of real and eternal laws beyond it4 ,these real and eternal laws are things intelligible1 and not things sensible4 ,the laws1 impressed upon creation by its ,creator1 and apprehended by man1 are something equally distinct from the ,creator #dic and from man2 and the whole mass of them may be termed the ,world of ,things purely ,intelligible4 ,further2 there are qualities in the ,supreme and ,ultimate ,cause of all1 which are manifested in his creation2 and not merely manifested1 but in a manner--after being brought out of his super-essential nature into the stage of being which is below him1 but next to him--are then1 by the causative act of creation1 deposited in things1 differencing them one from the other1 so that the things participate of them 771 communicate with them 774 ,the ,intelligence of man1 excited to reflection by the impressions of these objects1 thus 7though themselves transitory7 participant of a divine quality1 may rise to higher conceptions of the perfections thus faintly exhibited2 and inasmuch as the perfections are unquestionably real existences1 and known to be such in the very act of contemplation1 this may be regarded as a distinct intellectual apprehension of them2--a union of the ,reason with the ,ideas in that sphere of being which is common to both4 ,finally1 the ,reason1 in proportion as it learns to contemplate the ,perfect and ,eternal1 desires the enjoyment of such contemplations in a more consummate degree1 and cannot be fully satisfied except in the actual fruition of the ,perfect itself4 ,these propositions taken together constitute the ,,theory ,,of ,,ideas4 ,when we have to treat of the ,philosophy of ,science1 it may be worth our while to resume the consideration of this subject4 ,in this part of the ,history1 the ,timus of ,plato is referred to as an example of the loose notions of the ,greek philosophers in their physical reasonings4 ,and undoubtedly this ,dialogue does remarkably exemplify the boldness of the early ,greek attempts at generalization on such subjects4 ,yet in this and in other parts the writings of ,plato contain speculations which may be regarded as containing germs of true physical science2 inasmuch as they assume that the phenomena of the world are governed by mathematical laws2--by relations of space and number2--and endeavor1 too boldly1 no doubt1 but not vaguely or loosely1 to assign those laws4 ,the ,platonic writings offer1 in this way1 so much that forms a ,prelude to the ,astronomy and other ,physical ,sciences of the ,greeks1 that they will deserve our notice1 as supplying materials for the next two ,books of the ,history1 in which these subjects are treated of4 #did ,,chapter ,,iii4 ,,failure ,,of ,,the ,,greek ,,physical ,,philosophy4 ,francis ,bacon's ,remarks4 ,,though we do not accept1 as authority1 even the judgments of ,francis ,bacon1 and shall have to estimate the strong and the weak parts of his1 no less than of other philosophies1 we shall find his remarks on the ,greek philosophers very instructive4 ,thus he says of ,aristotle1 7,nov4 ,org4 #a4 ,aph4 lxiii473 ,he is an example of the kind of philosophy in which much is made out of little2 so that the basis of experience is too narrow4 ,he corrupted ,natural ,philosophy by his ,logic1 and made the world out of his ,categories4 ,he disposed of the distinction of dense and rare1 by which bodies occupy more or less dimensions or space1 by the frigid distinction of act and power4 ,he assigned to each kind of body a single proper motion1 so that if they have any other motion they must receive it from some extraneous source2 and imposed many other arbitrary rules upon ,nature2 being everywhere more careful how one may give a ready answer1 and make a positive assertion1 than how he may apprehend the variety of nature4 ,and this appears most evidently by the comparison of his philosophy with the other philosophies which had any vogue in ,greece4 ,for the ,homoiomeria#b;,a of ,anaxagoras1 the ,atoms of ,leucippus and ,democritus1 the ,heaven and ,earth of ,parmenides1 the ,love and ,hate of ,empedocles1 the ,fire of ,heraclitus1 had some trace of the thoughts of a natural philosopher2 some savor of experience1 and nature1 and bodily things2 while the ,physics of ,aristotle1 in general1 sound only of ,logical ,terms4 ,note #b;,a3 ,for these technical forms of the ,greeks1 see ,sec4 #c of this chapter4 ,nor let any one be moved by this--that in his books ,of ,animals1 and in his ,problems1 and in others of his tracts1 there is often a quoting of experiments4 ,for he had made up his mind beforehand2 and did not consult experience in order to make right propositions and axioms1 but when he had settled his system to his will1 he twisted experience #die round1 and made her bend to his system3 so that in this way he is even more wrong than his modern followers1 the ,schoolmen1 who have deserted experience altogether4 ,we may note also what ,bacon says of the term ,sophist4 7,aph4 lxxi47 ,the wisdom of the ,greeks was professorial1 and prone to run into disputations3 which kind is very adverse to the discovery of ,truth4 ,and the name of ,sophists1 which was cast in the way of contempt1 by those who wished to be reckoned philosophers1 upon the old professors of rhetoric1 ,gorgias1 ,protagoras1 ,hippias1 ,polus1 does1 in fact1 fit the whole race of them1 ,plato1#c;,a ,aristotle1 ,zeno1 ,epicurus1 ,theophrastus2 and their successors1 ,chrysippus1 ,carneades1 and the rest4 ,note #c;,a3 ,it is curious that the attempt to show that ,plato's opponents were not commonly illusive and immoral reasoners1 has been represented as an attempt to obliterate the distinction of ,sophist and ,philosopher4--,see ,a4 ,butler's ,lectures1 i4 #ceg4 ,note4 ,that these two classes of teachers1 as moralists1 were not different in their kind1 has been urged by ,mr4 ,grote in a very striking and amusing manner4 ,but ,bacon speaks of them here as physical philosophers2 in which character he holds that all of them were sophists1 that is1 illusory reasoners4 ,aristotle's ,account of the ,rainbow4 ,to exemplify the state of physical knowledge among the ,greeks1 we may notice briefly ,aristotle's account of the ,rainbow2 a phenomenon so striking and definite1 and so completely explained by the optical science of later times4 ,we shall see that not only the explanations there offered were of no value1 but that even the observation of facts1 so common and so palpable1 was inexact4 ,in his ,meteorologica 7lib4 iii4 c4 #b7 he says1 ,the ,rainbow is never more than a semicircle4 ,and at sunset and sunrise1 the circle is least1 but the arch is greatest2 when the sun is high1 the circle is larger1 but the arch is less4 ,this is erroneous1 for the diameter of the circle of which the arch of the rainbow forms a part1 is always the same1 namely #hb4 ,after the autumnal equinox1 he adds1 it appears at every hour of the day2 but in the summer season1 it does not appear about noon4 ,it is curious that he did not see the reason of this4 ,the centre of the circle of which the rainbow is part1 is always opposite to the sun4 ,and therefore if the sun be more than #da above the horizon1 the centre of the rainbow will be so much below the horizon1 that the place of the rainbow will #dif be entirely below the horizon4 ,in the latitude of ,athens1 which is #ch1 the equator is #eb above the horizon1 and the rainbow can be visible only when the sun is #aa lower than it is at the equinoctial noon4 ,these remarks1 however1 show a certain amount of careful observation2 and so do those which ,aristotle makes respecting the colors4 ,two rainbows at most appear3 and of these1 each has three colors2 but those in the outer bow are duller2 and their order opposite to those in the inner4 ,for in the inner bow the first and largest arch is red2 but in the outer bow the smallest arch is red1 the nearest to the inner2 and the others in order4 ,the colors are red1 green1 and purple1 such as painters cannot imitate4 ,it is curious to observe how often modern painters disregard even the order of the colors1 which they could imitate1 if they attended to it4 ,it may serve to show the loose speculation which we oppose to science1 if we give ,aristotle's attempt to explain the phenomenon of the ,rainbow4 ,it is produced1 he says 7c4 iv471 by ,reflexion 77 from a cloud opposite to the sun1 when the cloud forms into drops4 ,and as a reason for the red color1 he says that a bright object seen through darkness appears red1 as the flame through the smoke of a fire of green wood4 ,this notion hardly deserves notice2 and yet it was taken up again by ,gthe in our own time1 in his speculations concerning colors4 #dig ,,book ,,ii4 ,,the ,,physical ,,sciences ,,in ,,ancient ,,greece4 ,plato's ,timus and ,republic4 ,,although a great portion of the physical speculations of the ,greek philosophers was fanciful1 and consisted of doctrines which were rejected in the subsequent progress of the ,inductive ,sciences2 still many of these speculations must be considered as forming a ,prelude to more exact knowledge afterwards attained2 and thus1 as really belonging to the ,progress of knowledge4 ,these speculations express1 as we have already said1 the conviction that the phenomena of nature are governed by laws of space and number2 and commonly1 the mathematical laws which are thus asserted have some foundation in the facts of nature4 ,this is more especially the case in the speculations of ,plato4 ,it has been justly stated by ,professor ,thompson 7,a4 ,butler's ,lectures1 ,third ,series1 ,lect4 i4 ,note #aa71 that it is ,plato's merit to have discovered that the laws of the physical universe are resolvable into numerical relations1 and therefore capable of being represented by mathematical formul4 ,of this truth1 it is there said1 ,aristotle does not betray the slightest consciousness4 ,the ,timus of ,plato contains a scheme of mathematical and physical doctrines concerning the universe1 which make it far more analogous than any work of ,aristotle to ,treatises which1 in modern times1 have borne the titles of ,principia1 ,system of the ,world1 and the like4 ,and fortunately the work has recently been well and carefully studied1 with attention1 not only to the language1 but to the doctrines and their bearing upon our real knowledge4 ,stallbaum has published an edition of the ,dialogue1 and has compared the opinions of ,plato with those of ,aristotle on the like subjects4 ,professor ,archer ,butler of ,dublin has devoted to it several of his striking and eloquent ,lectures2 and these have been furnished with valuable annotations by ,professor ,thompson of ,cambridge2 and ,m4 ,the4 ,henri ,martin1 then ,professor at ,rennes1 published in #ahda two volumes of ,etudes sur le ,time de ,platon1 in #dih which the bearings of the work on ,science are very fully discussed4 ,the ,dialogue treats not only concerning the numerical laws of harmonical sounds1 of visual appearances1 and of the motions of planets and stars1 but also concerning heat1 as well as light2 and concerning water1 ice1 gold1 gems1 iron1 rust1 and other natural objects2--concerning odors1 tastes1 hearing1 sight1 light1 colors1 and the powers of sense in general3--concerning the parts and organs of the body1 as the bones1 the marrow1 the brain1 the flesh1 muscles1 tendons1 ligaments1 nerves2 the skin1 the hair1 the nails2 the veins and arteries2 respiration2 generation2 and in short every obvious point of physiology4 ,but the opinions delivered in the ,timus upon these latter subjects have little to do with the progress of real knowledge4 ,the doctrines1 on the other hand1 which depend upon geometrical and arithmetical relations1 are portions or preludes of the sciences which1 in the fulness of time1 assumed a mathematical form for the expression of truth4 ,among these may be mentioned the arithmetical relations of harmonical sounds1 to which ,i have referred in the ,history4 ,these occur in various parts of ,plato's writings4 ,in the ,timus1 in which the numbers are most fully given1 the meaning of the numbers is1 at first sight1 least obvious4 ,the numbers are given as representing the proportion of the parts of the ,soul 7,tim4 pp4 #ce1 #cf71 which does not immediately refer us to the relations of ,sounds4 ,but in a subsequent part of the ,dialogue 7#dg1 ,d71 we are told that music is a privilege of the hearing given on account of ,harmony2 and that ,harmony has ,cycles corresponding to the movements of the ,soul2 7referring plainly to those already asserted47 ,and the numbers which are thus given by ,plato as elements of harmony1 are in a great measure the same as those which express the musical relations of the tones of the musical scale at this day in use1 as ,m4 ,henri ,martin shows 7,et4 sur le ,time1 note xxiii47 ,the intervals ,c to ,d1 ,c to ,f1 ,c to ,g1 ,c to ,c1 are expressed by the fractions #i_/h1 #d_/c1 #c_/b1 #b_/a1 and are now called a ,tone1 a ,fourth1 a ,fifth1 an ,octave4 ,they were expressed by the same fractions among the ,greeks1 and were called ,tone1 ,diatessaron1 ,diapente1 ,diapason4 ,the ,major and ,minor ,third1 and the ,major and ,minor ,sixth1 were however wanting1 it is conceived1 in the musical scale of ,plato4 ,the ,timus contains also a kind of theory of vision by reflexion from a plane1 and in a concave mirror2 although the theory is in this case less mathematical and less precise than that of ,euclid1 referred to in chap4 ii4 of this ,book4 ,one of the most remarkable speculations in the ,timus is that in #dii which the ,regular ,solids are assigned as the forms of the ,elements of which the ,universe is composed4 ,this curious branch of mathematics1 ,solid ,geometry1 had been pursued with great zeal by ,plato and his friends1 and with remarkable success4 ,the five ,regular ,solids1 the ,tetrahedron or regular ,triangular ,pyramid1 the ,cube1 the ,octahedron1 the ,dodecahedron1 and the ,icosahedron1 had been discovered2 and the remarkable theorem1 that of regular solids there can be just so many1 these and no others1 was known4 ,and in the ,timus it is asserted that the particles of the various elements have the forms of these solids4 ,fire has the ,pyramid2 ,earth has the ,cube2 ,water the ,octahedron2 ,air the ,icosahedron2 and the ,dodecahedron is the plan of the ,universe itself4 ,it was natural that when ,plato had learnt that other mathematical properties had a bearing upon the constitution of the ,universe1 he should suppose that the singular property of space1 which the existence of this limited and varied class of solids implied1 should have some corresponding property in the ,universe1 which exists in space4 ,we find afterwards1 in ,kepler and others1 a recurrence to this assumption2 and we may say perhaps that ,crystallography shows us that there are properties of bodies1 of the most intimate kind1 which involve such spatial relations as are exhibited in the ,regular ,solids4 ,if the distinctions of ,crystalline ,system in bodies were hereafter to be found to depend upon the chemical elements which predominate in their composition1 the admirers of ,plato might point to his doctrine1 of the different form of the particles of the different elements of the ,universe1 as a remote ,prelude to such a discovery4 ,but the mathematical doctrines concerning the parts and elements of the ,universe are put forwards by ,plato1 not so much as assertions concerning physical facts1 of which the truth or falsehood is to be determined by a reference to nature herself4 ,they are rather propounded as examples of a truth of a higher kind than any reference to observation can give or can test1 and as revelations of principles such as must have prevailed in the mind of the ,creator of the ,universe2 or else as contemplations by which the mind of man is to be raised above the region of sense1 and brought nearer to the ,divine ,mind4 ,in the ,timus these doctrines appear rather in the former of the two lights2 as an exposition of the necessary scheme of creation1 so far as its leading features are concerned4 ,in the seventh ,book of the ,polity1 the same doctrines are regarded more as a mental discipline2 as the necessary study of the true philosopher4 ,but in both places these mathematical #ejj propositions are represented as ,realities more real than the ,phenomena2--as a ,natural ,philosophy of a higher kind than the study of ,nature itself can teach4 ,this is no doubt an erroneous assumption3 yet even in this there is a germ of truth2 namely1 that the mathematical laws1 which prevail in the universe1 involve mathematical truths which being demonstrative1 are of a higher and more cogent kind than mere experimental truths4 ,notions1 such as these of ,plato1 respecting a truth at which science is to aim1 which is of an exact and demonstrative kind1 and is imperfectly manifested in the phenomena of nature1 may help or may mislead inquirers2 they may be the impulse and the occasion to great discoveries2 or they may lead to the assertion of false and the loss of true doctrines4 ,plato considers the phenomena which nature offers to the senses as mere suggestions and rude sketches of the objects which the philosophic mind is to contemplate4 ,the heavenly bodies and all the splendors of the sky1 though the most beautiful of visible objects1 being only visible objects1 are far inferior to the true objects of which they are the representatives4 ,they are merely diagrams which may assist in the study of the higher truth as we might study geometry by the aid of diagrams constructed by some consummate artist4 ,even then1 the true object about which we reason is the conception which we have in the mind4 ,we have1 ,i conceive1 an instance of the error as well as of the truth1 to which such views may lead1 in the speculations of ,plato concerning ,harmony1 contained in that part of his writings 7the seventh ,book of the ,republic71 in which these views are especially urged4 ,he there1 by way of illustrating the superiority of philosophical truth over such exactness as the senses can attest1 speaks slightingly of those who take immense pains in measuring musical notes and intervals by the ear1 as the astronomers measure the heavenly motions by the eye4 ,they screw their pegs and pinch their strings1 and dispute whether two notes are the same or not4 ,now1 in truth1 the ear is the final and supreme judge whether two notes are the same or not4 ,but there is a case in which notes which are nominally the same1 are different really and to the ear2 and it is probably to disputes on this subject1 which we know did prevail among the ,greek musicians1 that ,plato here refers4 ,we may ascend from a note ,a#a to a note ,c#c by two octaves and a third4 ,we may also ascend from the same note ,a#a to ,c#c by fifths four times repeated4 ,but the two notes ,c#c thus arrived at are not the same3 they differ by a small interval1 which the ,greeks called a #eja ,comma1 of which the notes are in the ratio of #hj to #ha4 ,that the ear really detects this defect of the musical coincidence of the two notes under the proper conditions1 is a proof of the coincidence of our musical perceptions with the mathematical relations of the notes2 and is therefore an experimental confirmation of the mathematical principles of harmony4 ,but it seems to be represented by ,plato1 that to look out for such confirmation of mathematical principles1 implies a disposition to lean on the senses1 which he regards as very unphilosophical4 ,hero of ,alexandria4 ,,the other branches of mathematical science which ,i have spoken of in the ,history as cultivated by the ,greeks1 namely ,mechanics and ,hydrostatics1 are not treated expressly by ,plato2 though we know from ,aristotle and others that some of the propositions of those sciences were known about his time4 ,machines moved not only by weights and springs1 but by water and air1 were constructed at an early period4 ,ctesibius1 who lived probably about ,b4 ,c4 #bej1 under the ,ptolemies1 is said to have invented a clepsydra or water-clock1 and an hydraulic organ2 and to have been the first to discover the elastic power of air1 and to apply it as a moving power4 ,of his pupil ,hero1 the name is to this day familiar1 through the little pneumatic instrument called ,hero's ,fountain4 ,he also described pumps and hydraulic machines of various kinds2 and an instrument which has been spoken of by some modern writers as a steam-engine1 but which was merely a toy made to whirl round by the steam emitted from holes in its arms4 ,concerning mechanism1 besides descriptions of ,automatons1 ,hero composed two works3 the one entitled ,mechanics1 or ,mechanical ,introductions2 the other ,barulcos1 the ,weight-lifter4 ,in these works the elementary contrivances by which weights may be lifted or drawn were spoken of as the ,five ,mechanical ,powers1 the same enumeration of such machines as prevails to this day2 namely1 the ,lever1 the ,wheel and ,axle1 the ,pulley1 the ,wedge1 and the ,screw4 ,in his ,mechanics1 it appears that ,hero reduced all these machines to one single machine1 namely to the lever4 ,in the ,barulcos1 ,hero proposed and solved the problem which it was the glory of ,archimedes to have solved3 ,to move any object 7however large7 by any power 7however small74 ,this1 as may easily be conceived by any one acquainted with the elements of ,mechanics1 is done by means of a combination of the mechanical powers1 and especially by means of a train of toothed-wheels and axles4 #ejb ,the remaining writings of ,hero of ,alexandria have been the subject of a special1 careful1 and learned examination by ,m4 ,th4 ,h4 ,martin 7,paris1 #ahed71 in which the works of this writer1 ,hero the ,ancient1 as he is sometimes called1 are distinguished from those of another writer of the same name of later date4 ,hero of ,alexandria wrote also1 as it appears1 a treatise on ,pneumatics1 in which he described machines1 either useful or amusing1 moved by the force of air and vapor4 ,he also wrote a work called ,catoptrics1 which contained proofs of properties of the rays of reflected light4 ,and a treatise ,on the ,dioptra2 which subject however must be carefully distinguished from the subject entitled ,dioptrics by the moderns4 ,this latter subject treats of the properties of refracted light2 a subject on which the ancients had little exact knowledge till a later period2 as ,i have shown in the ,history4 ,the ,dioptra1 as understood by ,hero1 was an instrument for taking angles so as to measure the position and hence to determine the distance of inaccessible objects2 as is done by the ,theodolite in our times4 ,m4 ,martin is of opinion that ,hero of ,alexandria lived at a later period than is generally supposed2 namely1 after ,b4 ,c4 #ha4 #ejc ,,book ,,iii4 ,,the ,,greek ,,astronomy4 ,,introduction4 ,,the mathematical opinions of ,plato respecting the philosophy of nature1 and especially respecting what we commonly call the heavenly bodies1 the ,sun1 ,moon1 and ,planets1 were founded upon the view which ,i have already described3 namely1 that it is the business of philosophy to aim at a truth higher than observation can teach2 and to solve problems which the phenomena of the universe only suggest4 ,and though the students of nature in more recent times have learnt that this is too presumptuous a notion of human knowledge1 yet the very boldness and hopefulness which it involved impelled men in the pursuit of truth1 with more vigor than a more timorous temper could have done2 and the belief that there must be1 in nature1 mathematical laws more exact than experience could discover1 stimulated men often to discover true laws1 though often also to invent false laws4 ,plato's writings1 supplying examples of both these processes1 belong to the ,prelude of true ,astronomy1 as well as to the errors of false philosophy4 ,we may find specimens of both kinds in those parts of his ,dialogues to which we have referred in the preceding ,book of our ,history4 ,to ,plato's merits in preparing the way for the ,theory of ,epicycles1 ,i have already referred in ,chapter ii4 of this ,book4 ,i conceive that he had a great share in that which is an important step in every discovery1 the proposing distinctly the problem to be solved2 which was1 in this case1 as he states it1 ,to account for the apparent movements of the planets by a combination of two circular motions for each3--the motion of identity1 and the motion of difference4 7,tim4 #ci1 ,a47 ,in the tenth ,book of the ,republic1 quoted in our text1 the spindle which ,destiny or ,necessity holds between her knees1 and on which are rings1 by means of which the planets revolve round it as an axis1 is a step towards the conception of the problem1 as the construction of a machine4 ,it will not be thought surprising that ,plato expected that #ejd ,astronomy1 when further advanced1 would be able to render an account of many things for which she has not accounted even to this day4 ,thus1 in the passage in the seventh ,book of the ,republic1 he says that the philosopher requires a reason for the proportion of the day to the month1 and the month to the year1 deeper and more substantial than mere observation can give4 ,yet ,astronomy has not yet shown us any reason why the proportion of the times of the earth's rotation on its axis1 the moon's revolution round the earth1 and the earth's revolution round the sun1 might not have been made by the ,creator quite different from what they are4 ,but in thus asking ,mathematical ,astronomy for reasons which she cannot give1 ,plato was only doing what a great astronomical discoverer1 ,kepler1 did at a later period4 ,one of the questions which ,kepler especially wished to have answered was1 why there are five planets1 and why at such particular distances from the sun8 ,and it is still more curious that he thought he had found the reason of these things1 in the relations of those ,five ,regular ,solids which1 as we have seen1 ,plato was desirous of introducing into the philosophy of the universe4 ,we have ,kepler's account of this1 his imaginary discovery1 in the ,mysterium ,cosmographicum1 published in #aeif1 as stated in our ,history1 ,book v4 ,chap4 iv4 ,sect4 #b4 ,kepler regards the law which thus determines the number and magnitude of the planetary orbits by means of the five regular solids as a discovery no less remarkable and certain than the ,three ,laws which give his name its imperishable place in the history of astronomy4 ,we are not on this account to think that there is no steady criterion of the difference between imaginary and real discoveries in science4 ,as discovery becomes possible by the liberty of guessing1 it becomes real by allowing observation constantly and authoritatively to determine the value of guesses4 ,kepler added to ,plato's boldness of fancy his own patient and candid habit of testing his fancies by a rigorous and laborious comparison with the phenomena2 and thus his discoveries led to those of ,newton4 #eje ,,chapter ,i4 ,,earliest ,,stages ,,of ,,astronomy4 ,the ,globular ,form of the ,earth4 ,,there are parts of ,plato's writings which have been adduced as bearing upon the subsequent progress of science2 and especially upon the globular form of the earth1 and the other views which led to the discovery of ,america4 ,in the ,timus we read of a great continent lying in the ,ocean west of the ,pillars of ,hercules1 which ,plato calls ,atlantis4 ,he makes the personage in his ,dialogue who speaks of this put it forward as an ,egyptian tradition4 ,m4 ,h4 ,martin1 who has discussed what has been written respecting the ,atlantis of ,plato1 and has given therein a dissertation rich in erudition and of the most lively interest1 conceives that ,plato's notions on this subject arose from his combining his conviction of the spherical form of the earth1 with interpretations of ,homer1 and perhaps with traditions which were current in ,egypt 7,etudes sur le ,time1 ,note xiii4 ix474 ,he does not consider that the belief in ,plato's ,atlantis had any share in the discoveries of ,columbus4 ,it may perhaps surprise modern readers who have a difficulty in getting rid of the persuasion that there is a natural direction upwards and a natural direction downwards1 to learn that both ,plato and ,aristotle1 and of course other philosophers also1 had completely overcome this difficulty4 ,they were quite ready to allow and to conceive that down meant nothing but towards some centre1 and up1 the opposite direction4 7,aristotle has1 besides1 an ingenious notion that while heavy bodies1 as earth and water1 tend to the centre1 and light bodies1 as fire1 tend from the centre1 the fifth element1 of which the heavenly bodies are composed1 tends to move round the centre47 ,plato explains this in the most decided manner in the ,timus 7#fb1 ,c74 ,it is quite erroneous to suppose that there are two opposite regions in the universe1 one above and the other below2 and that heavy things naturally tend to the latter place4 ,the heavens are spherical1 and every thing tends to the centre2 and thus above and below have no real meaning4 ,if there be a solid globe in the middle1 #ejf and if a person walk round it1 he will become the antipodes to himself1 and the direction which is up at one time will be down at another4 ,the notion of antipodes1 the inhabitants of the part of the globe of the earth opposite to ourselves1 was very familiar4 ,thus in ,cicero's ,academic ,questions 7ii4 #ci7 one of the speakers says1 ,etiam dicitis esse e regione nobis1 e contraria parte terr1 qui adversis vestigiis stant contra nostra vestigia1 quos ,antipodas vocatis4 ,see also ,tusc4 ,disp4 i4 #bh and v4 #bd4 ,the ,heliocentric ,system among the ,ancients4 ,as the more clear-sighted of the ancients had overcome the natural prejudice of believing that there is an absolute up and down1 so had they also overcome the natural prejudice of believing that the earth is at rest4 ,cicero says 7,acad4 ,quest4 ii4 #ci71 ,hicetas of ,syracuse1 as ,theophrastus tells us1 thinks that the heavens1 the sun1 the moon1 the stars1 do not move2 and that nothing does move but the earth4 ,the earth revolves about her axis with immense velocity2 and thus the same effect is produced as if the earth were at rest and the heavens moved2 and this1 he says1 ,plato teaches in the ,timus1 though somewhat obscurely4 ,of course the assertion that the moon and planets do not move1 was meant of the diurnal motion only4 ,the passage referred to in the ,timus seems to be this 7#dj1 ,c7--,as to the ,earth1 which is our nurse1 and which clings to the axis which stretches through the universe1 ,god made her the producer and preserver of day and night4 ,the word 1 which ,i have translated clings to1 some translate revolves2 and an extensive controversy has prevailed1 both in ancient and modern times 7beginning with ,aristotle71 whether ,plato did or did not believe in the rotation of the earth on her axis4 7,see ,m4 ,cousin's ,note on the ,timus1 and ,m4 ,henri ,martin's ,dissertation1 ,note xxxvii41 in his ,etudes sur le ,time47 ,the result of this discussion seems to be that1 in the ,timus1 the ,earth is supposed to be at rest4 ,it is however related by ,plutarch 7,platonic ,questions1 viii4 #a71 that ,plato in his old age repented of having given to the ,earth the place in the centre of the universe which did not belong to it4 ,in describing the ,prelude to the ,epoch of ,copernicus 7,book v4 ,chap4 i471 ,i have spoken of ,philolaus1 one of the followers of ,pythagoras1 who lived at the time of ,socrates1 as having held the doctrine that the earth revolves about the sun4 ,this has been a current #ejg opinion2--so current1 indeed1 that the ,abb ,bouillaud1 or ,bullialdus1 as we more commonly call him1 gave the title of ,philolaus to the defence of ,copernicus which he published in #afci2 and ,chiaramonti1 an ,aristotelian1 published his answer under the title of ,antiphilolaus4 ,in #afde ,bullialdus published his ,astronomia ,philolaica1 which was another exposition of the heliocentric doctrine4 ,yet notwithstanding this general belief1 it appears to be tolerably certain that ,philolaus did not hold the doctrine of the earth's motion round the sun4 7,m4 ,h4 ,martin1 ,etudes sur le ,time1 #ahda1 ,note xxxvii4 ,sect4 i42 and ,bckh1 ,de vera ,indole ,astronomi ,philolaic1 #ahaj47 ,in the system of ,philolaus1 the earth revolved about the central fire2 but this central fire was not the sun4 ,the ,sun1 along with the moon and planets1 revolved in circles external to the earth4 ,the ,earth had the ,antichthon or ,counter-,earth between it and the centre2 and revolving round this centre in one day1 the ,antichthon1 being always between it and the centre1 was1 during a portion of the revolution1 interposed between the ,earth and the ,sun1 and thus made night2 while the ,sun1 by his proper motion1 produced the changes of the year4 ,when men were willing to suppose the earth to be in motion1 in order to account for the recurrence of day and night1 it is curious that they did not see that the revolution of a spherical earth about an axis passing through its centre was a scheme both simple and quite satisfactory4 ,yet the illumination of a globular earth by a distant sun1 and the circumstances and phenomena thence resulting1 appear to have been conceived in a very confused manner by many persons4 ,thus ,tacitus 7,agric4 xii471 after stating that he has heard that in the northern part of the island of ,britain1 the night disappears in the height of summer1 says1 as his account of this phenomenon1 that the extreme parts of the earth are low and level1 and do not throw their shadow upwards2 so that the shade of night falls below the sky and the stars4 ,but1 as a little consideration will show1 it is the globular form of the earth1 and not the level character of the country1 which produces this effect4 ,it is not in any degree probable that ,pythagoras taught that the ,earth revolves round the ,sun1 or that it rotates on its own axis4 ,nor did ,plato hold either of these motions of the ,earth4 ,they got so far as to believe in the ,spherical ,form of the ,earth2 and this was apparently such an effort that the human mind made a pause before going any further4 ,it required1 says ,m4 ,h4 ,martin1 a great struggle for #ejh men to free themselves from the prejudices of the senses1 and to interpret their testimony in such a manner as to conceive the sphericity of the earth4 ,it is natural that they should have stopped at this point1 before putting the earth in motion in space4 ,some of the expressions which have been understood1 as describing a system in which the ,sun is the centre of motion1 do really imply merely the ,sun is the middle term of the series of heavenly bodies which revolve round the earth3 the series being ,moon1 ,mercury1 ,venus1 ,sun1 ,mars1 ,jupiter1 ,saturn4 ,this is the case1 for instance1 in a passage of ,cicero's ,vision of ,scipio1 which has been supposed to imply1 7as ,i have stated in the ,history17 that ,mercury and ,venus revolve about the ,sun4 ,but though the doctrine of the diurnal rotation and annual revolution of the earth is not the doctrine of ,pythagoras1 or of ,philolaus1 or of ,plato1 it was nevertheless held by some of the philosophers of antiquity4 ,the testimony of ,archimedes that this doctrine was held by his contemporary ,aristarchus of ,samos1 is unquestionable and there is no reason to doubt ,plutarch's assertion that ,seleucus further enforced it4 ,it is curious that ,copernicus appears not to have known anything of the opinions of ,aristarchus and ,seleucus1 which were really anticipations of his doctrine2 and to have derived his notion from passages which1 as ,i have been showing1 contain no such doctrine4 ,he says1 in his ,dedication to ,pope ,paul ,,iii41 ,i found in ,cicero that ,nicetas or ,hicetas held that the earth was in motion3 and in ,plutarch ,i found that some others had been of that opinion3 and his words ,i will transcribe that any one may read them3 ',philosophers in general hold that the earth is at rest4 ,but ,philolaus the ,pythagorean teaches that it moves round the central fire in an oblique circle1 in the same direction as the ,sun and the ,moon4 ,heraclides of ,pontus and ,ecphantus the ,pythagorean give the earth a motion1 but not a motion of translation2 they make it revolve like a wheel about its own centre from west to east4' ,this last opinion was a correct assertion of the diurnal motion4 ,the ,eclipse of ,thales4 ,,the ,eclipse of ,thales is so remarkable a point in the history of astronomy1 and has been the subject of so much discussion among astronomers1 that it ought to be more especially noticed4 ,the original #eji record is in the first ,book of ,herodotus's ,history 7chap4 lxxiv47 ,he says that there was a war between the ,lydians and the ,medes2 and after various turns of fortune1 in the sixth year a conflict took place2 and on the battle being joined1 it happened that the day suddenly became night4 ,and this change1 ,thales of ,miletus had predicted to them1 definitely naming this year1 in which the event really took place4 ,the ,lydians and the ,medes1 when they saw day turned into night1 ceased from fighting2 and both sides were desirous of peace4 ,probably this prediction was founded upon the ,chaldean period of eighteen years1 of which ,i have spoken in ,section #aa4 ,it is probable1 as ,i have already said1 that this period was discovered by noticing the recurrence of eclipses4 ,it is to be observed that ,thales predicted only the year of the eclipse1 not the day or the month4 ,in fact1 the exact prediction of the circumstances of an eclipse of the sun is a very difficult problem2 much more difficult1 it may be remarked1 than the prediction of the circumstance of an eclipse of the moon4 ,now that the ,theory of the ,moon is brought so far towards completeness1 astronomers are able to calculate backwards the eclipses of the sun which have taken place in former times2 and the question has been much discussed in what year this ,eclipse of ,thales really occurred4 ,the ,memoir of ,mr4 ,airy1 the ,astronomer ,royal1 on this subject1 in the ,phil4 ,trans4 for #ahec1 gives an account of the modern examinations of this subject4 ,mr4 ,airy starts from the assumption that the eclipse must have been one decidedly total2 the difference between such a one and an eclipse only nearly total being very marked4 ,a total eclipse alone was likely to produce so strong an effect on the minds of the combatants4 ,mr4 ,airy concludes from his calculations that the eclipse predicted by ,thales took place ,b4 ,c4 #ehe4 ,ancient eclipses of the ,moon and ,sun1 if they can be identified1 are of great value for modern astronomy2 for in the long interval of between two and three thousand years which separates them from our time1 those of the inequalities1 that is1 accelerations or retardations of the ,moon's motion1 which go on increasing constantly1#d;,a accumulate to a large amount2 so that the actual time and circumstances of the eclipse give astronomers the means of determining what the rate of these accelerations or retardations has been4 ,accordingly ,mr4 ,airy has discussed1 as even more important than the eclipse of ,thales1 an eclipse which ,diodorus relates to have happened during an expedition of #eaj ,agathocles1 the ruler of ,sicily1 and which is hence known as the ,eclipse of ,agathocles4 ,he determines it to have occurred ,b4 ,c4 #caj4 ,note #d;,a3 ,or at least for very long periods4 ,m4 ,h4 ,martin1 in ,note xxxvii4 to his ,etudes sur le ,time1 discusses among other astronomical matters1 the ,eclipse of ,thales4 ,he does not appear to render a very cordial belief to the historical fact of ,thales having delivered the prediction before the event4 ,he says that even if ,thales did make such a prediction of an eclipse of the sun1 as he might do1 by means of the ,chaldean period of #ah years1 or #bbc lunations1 he would have to take the chance of its being visible in ,greece1 about which he could only guess3--that no author asserts that ,thales1 or his successors ,anaximander and ,anaxagoras1 ever tried their luck in the same way again3--that en revanche we are told that ,anaximander predicted an earthquake1 and ,anaxagoras the fall of arolites1 which are plainly fabulous stories1 though as well attested as the ,eclipse of ,thales4 ,he adds that according to ,aristotle1 ,thales and ,anaximenes were so far from having sound notions of cosmography1 that they did not even believe in the roundness of the earth4 #eaa ,,book ,,iv4 ,,physical ,,science ,,in ,,the ,,middle ,,ages4 ,,general ,,remarks4 ,,in the twelfth ,book of the ,philosophy1 in which ,i have given a ,review of ,opinions on the ,nature of ,knowledge and the method of seeking it1 ,i have given some account of several of the most important persons belonging to the ages now under consideration4 ,i have there 7vol4 ii4 b4 xii4 p4 #adf7 spoken of the manner in which remarks made by ,aristotle came to be accepted as fundamental maxims in the schools of the middle ages1 and of the manner in which they were discussed by the greatest of the schoolmen1 as ,thomas ,aquinas1 ,albertus ,magnus1 and the like4 ,i have spoken also 7p4 #adi7 of a certain kind of recognition of the derivation of our knowledge from experience2 as shown in ,richard of ,st4 ,victor1 in the twelfth century4 ,i have considered 7p4 #aeb7 the plea of the admirers of those ages1 that religious authority was not claimed for physical science4 ,i have noticed that the rise of ,experimental ,philosophy exhibited two features 7chap4 vii4 p4 #aee71 the ,insurrection against ,authority1 and the ,appeal to ,experience3 and as exemplifying these features1 ,i have spoken of ,raymond ,lully and of ,roger ,bacon4 ,i have further noticed the opposition to the prevailing ,aristotelian dogmatism manifested 7chap4 viii47 by ,nicolas of ,cus1 ,marsilius ,ficinus1 ,francis ,patricius1 ,picus of ,mirandula1 ,cornelius ,agrippa1 ,theophrastus ,paracelsus1 ,robert ,fludd4 ,i have gone on to notice the ,theoretical ,reformers of ,science 7chap4 ix471 ,bernardinus ,telesius1 ,thomas ,campanella1 ,andreas ,csalpinus1 ,peter ,ramus2 and the ,protestant ,reformers1 as ,melancthon4 ,after these come the ,practical ,reformers of ,science1 who have their place in the subsequent history of ,inductive ,philosophy2 ,leonardo da ,vinci1 and the ,heralds of the dawning light of real science1 whom ,francis ,bacon welcomes1 as ,heralds are accosted in ,homer3 4 ,hail1 ,heralds1 messengers of ,gods and men6 #eab ,i have1 in the part of the ,philosophy referred to1 discussed the merits and defects of ,francis ,bacon's ,method1 and ,i shall have occasion1 in the next ,book1 to speak of his mode of dealing with the positive science of his time4 ,there is room for much more reflexion on these subjects1 but the references now made may suffice at present4 ,,chapter ,v4 ,,progress ,,in ,,the ,,middle ,,ages4 ,thomas ,aquinas4 ,,aquinas wrote 7besides the ,summa mentioned in the text7 a ,commentary on the ,physics of ,aristotle3 ,commentaria in ,aristotelis ,libros ,physicorum1 ,venice1 #adib4 ,this work is of course of no scientific value2 and the commentary consists of empty permutations of abstract terms1 similar to those which constitute the main substance of the text in ,aristotle's physical speculations4 ,there is1 however1 an attempt to give a more technical form to the propositions and their demonstrations4 ,as specimens of these1 ,i may mention that in ,book vi4 c4 #b1 we have a demonstration that when bodies move1 the time and the magnitude 7that is1 the space described71 are divided similarly2 with many like propositions4 ,and in ,book viii4 we have such propositions as this 7c4 #aj73 ,demonstration that a finite mover 7movens7 cannot move anything in an infinite time4 ,this is illustrated by a diagram in which two hands are represented as engaged in moving a whole sphere1 and one hand in moving a hemisphere4 ,this mode of representing force1 in diagrams illustrative of mechanical reasonings1 by human hands pushing1 pulling1 and the like1 is still employed in elementary books4 ,probably this is the first example of such a mode of representation4 ,roger ,bacon4 ,,this writer1 a contemporary of ,thomas ,aquinas1 exhibits to us a kind of knowledge1 speculation1 and opinion1 so different from that of any known person near his time1 that he deserves especial notice here2 #eac and ,i shall transfer to this place the account which ,i have given of him in the ,philosophy4 ,i do this the more willingly because ,i regard the existence of such a work as the ,opus ,majus at that period as a problem which has never yet been solved4 ,also ,i may add1 that the scheme of the ,contents of this work which ,i have given1 deserves1 as ,i conceive1 more notice than it has yet received4 ,roger ,bacon was born in #abad1 near ,ilchester1 in ,somersetshire1 of an old family4 ,in his youth he was a student at ,oxford1 and made extraordinary progress in all branches of learning4 ,he then went to the ,university of ,paris1 as was at that time the custom of learned ,englishmen1 and there received the degree of ,doctor of ,theology4 ,at the persuasion of ,robert ,grostte1 bishop of ,lincoln1 he entered the brotherhood of ,franciscans in ,oxford1 and gave himself up to study with extraordinary fervor4 ,he was termed by his brother monks ,doctor ,mirabilis4 ,we know from his own works1 as well as from the traditions concerning him1 that he possessed an intimate acquaintance with all the science of his time which could be acquired from books2 and that he had made many remarkable advances by means of his own experimental labors4 ,he was acquainted with ,arabic1 as well as with the other languages common in his time4 ,in the title of his works1 we find the whole range of science and philosophy1 ,mathematics and ,mechanics1 ,optics1 ,astronomy1 ,geography1 ,chronology1 ,chemistry1 ,magic1 ,music1 ,medicine1 ,grammar1 ,logics1 ,metaphysics1 ,ethics1 and ,theology2 and judging from those which are published1 these works are full of sound and exact knowledge4 ,he is1 with good reason1 supposed to have discovered1 or to have had some knowledge of1 several of the most remarkable inventions which were made generally known soon afterwards2 as gunpowder1 lenses1 burning specula1 telescopes1 clocks1 the correction of the calendar1 and the explanation of the rainbow4 ,thus possessing1 in the acquirements and habits of his own mind1 abundant examples of the nature of knowledge and of the process of invention1 ,roger ,bacon felt also a deep interest in the growth and progress of science1 a spirit of inquiry respecting the causes which produced or prevented its advance1 and a fervent hope and trust in its future destinies2 and these feelings impelled him to speculate worthily and wisely respecting a ,reform of the ,method of ,philosophizing4 ,the manuscripts of his works have existed for nearly six hundred years in many of the libraries of ,europe1 and especially in those of ,england2 and for a long period the very imperfect portions of them which were #ead generally known1 left the character and attainments of the author shrouded in a kind of mysterious obscurity4 ,about a century ago1 however1 his ,opus ,majus was published#e;,a by ,dr4 ,s4 ,jebb1 principally from a manuscript in the library of ,trinity ,college1 ,dublin2 and this contained most or all of the separate works which were previously known to the public1 along with others still more peculiar and characteristic4 ,we are thus able to judge of ,roger ,bacon's knowledge and of his views1 and they are in every way well worthy our attention4 ,note #e;,a3 ,fratris ,rogeri ,bacon ,ordinis ,minorum ,opus ,majus ad ,clementem ,quartum1 ,pontificem ,romanum1 ex ,,ms4 ,codice ,dubliniensi cum aliis quibusdam collato nunc primum edidit ,s4 ,jebb1 ,m4,d4 ,londini1 #agcc4 ,the ,opus ,majus is addressed to ,pope ,clement the ,fourth1 whom ,bacon had known when he was legate in ,england as ,cardinal-bishop of ,sabina1 and who admired the talents of the monk1 and pitied him for the persecutions to which he was exposed4 ,on his elevation to the papal chair1 this account of ,bacon's labours and views was sent1 at the earnest request of the pontiff4 ,besides the ,opus ,majus1 he wrote two others1 the ,opus ,minus and ,opus ,tertium2 which were also sent to the pope1 as the author says1#f;,a 'on account of the danger of roads1 and the possible loss of the work4' ,these works still exist unpublished1 in the ,cottonian and other libraries4 ,note #f;,a3 ,opus ,majus1 ,prf4 ,the ,opus ,majus is a work equally wonderful with regard to its general scheme1 and to the special treatises with which the outlines of the plan are filled up4 ,the professed object of the work is to urge the necessity of a reform in the mode of philosophizing1 to set forth the reasons why knowledge had not made a greater progress1 to draw back attention to the sources of knowledge which had been unwisely neglected1 to discover other sources which were yet almost untouched1 and to animate men in the undertaking1 by a prospect of the vast advantages which it offered4 ,in the developement of this plan1 all the leading portions of science are expounded in the most complete shape which they had at that time assumed2 and improvements of a very wide and striking kind are proposed in some of the principal of these departments4 ,even if the work had had no leading purpose1 it would have been highly valuable as a treasure of the most solid knowledge and soundest speculations of the time2 even if it had contained no such details1 it would have been a work most remarkable for its general views and scope4 ,it may be considered as1 at the same time1 the ,encyclopedia and the ,novum ,organon of the thirteenth century4 #eae ,since this work is thus so important in the history of ,inductive ,philosophy ,i shall give1 in a ,note1 a view#g;,a of its divisions and contents4 ,but ,i must now endeavor to point out more especially the way in which the various principles1 which the reform of scientific method involved1 are here brought into view4 ,note #g;,a3 ,contents of ,roger ,bacon's ,opus ,majus3 ,part ,i4 ,on the four causes of human ignorance3--,authority1 ,custom1 ,popular ,opinion1 and the ,pride of supposed ,knowledge4 ,part ,,ii4 ,on the source of perfect wisdom in the ,sacred ,scripture4 ,part ,,iii4 ,on the ,usefulness of ,grammar4 ,part ,,iv4 ,on the ,usefulness of ,mathematics4 7#a47 ,the ,necessity of ,mathematics in ,human ,things 7published separately as the ,specula ,mathematica74 7#b47 ,the ,necessity of ,mathematics in ,divine ,things4--#a4 ,this study has occupied holy men3 #b4 ,geography3 #c4 ,chronology3 #d4 ,cycles2 the ,golden ,number1 c43 #e4 ,natural ,phenomena1 as the ,rainbow3 #f4 ,arithmetic3 #g4 ,music4 7#c47 ,the ,necessity of ,mathematics in ,ecclesiastical ,things4 #a4 ,the ,certification of ,faith3 #b4 ,the ,correction of the ,calendar4 7#d47 ,the ,necessity of ,mathematics in the ,state4--#a4 ,of ,climates3 #b4 ,hydrography3 #c4 ,geography3 #d4 ,astrology4 ,part ,v4 ,on ,perspective 7published separately as ,perspectiva74 7#a47 ,the organs of vision4 7#b47 ,vision in straight lines4 7#c47 ,vision reflected and refracted4 7#d47 ,de multiplicatione specierum 7on the propagation of the impressions of light1 heat1 c47 ,part ,,vi4 ,on ,experimental ,science4 ,one of the first points to be noticed for this purpose1 is the resistance to authority2 and at the stage of philosophical history with which we here have to do1 this means resistance to the authority of ,aristotle1 as adopted and interpreted by the ,doctors of the ,schools4 ,bacon's work#h;,a is divided into ,six ,parts2 and of these ,parts1 the ,first is1 ,of the four universal ,causes of all ,human ,ignorance4 ,the causes thus enumerated#i;,a are3--the force of unworthy authority2--traditionary habit2--the imperfection of the undisciplined senses2--and the disposition to conceal our ignorance and to make an ostentatious show of our knowledge4 ,these influences involve every man1 occupy every condition4 ,they prevent our obtaining the most useful and large and fair doctrines of wisdom1 the secrets of all sciences and arts4 ,he then proceeds to argue1 from the testimony of philosophers themselves1 that the authority of antiquity1 and especially of ,aristotle1 is not infallible4 ',we find#aj;,a their books full of doubts1 obscurities1 and perplexities4 ,they #eaf scarce agree with each other in one empty question or one worthless sophism1 or one operation of science1 as one man agrees with another in the practical operations of medicine1 surgery1 and the like arts of secular men4 ,indeed1' he adds1#aa;,a 'not only the philosophers1 but the saints have fallen into errors which they have afterwards retracted1' and this he instances in ,augustin1 ,jerome1 and others4 ,he gives an admirable sketch of the progress of philosophy from the ,ionic ,school to ,aristotle2 of whom he speaks with great applause4 ',yet1' he adds1 'those who came after him corrected him in some things1 and added many things to his works1 and shall go on adding to the end of the world4' ,aristotle1 he adds1 is now called peculiarly#ab;,a the ,philosopher1 'yet there was a time when his philosophy was silent and unregarded1 either on account of the rarity of copies of his works1 or their difficulty1 or from envy2 till after the time of ,mahomet1 when ,avicenna and ,averroes1 and others1 recalled this philosophy into the full light of exposition4 ,and although the ,logic and some other works were translated by ,boethius from the ,greek1 yet the philosophy of ,aristotle first received a quick increase among the ,latins at the time of ,michael ,scot2 who1 in the year of our ,lord #abcj1 appeared1 bringing with him portions of the books of ,aristotle on ,natural ,philosophy and ,mathematics4 ,and yet a small part only of the works of this author is translated1 and a still smaller part is in the hands of common students4' ,he adds further#ac;,a 7in the ,third ,part of the ,opus ,majus1 which is a ,dissertation on ,language7 that the translations which are current of these writings1 are very bad and imperfect4 ,with these views1 he is moved to express himself somewhat impatiently#ad;,a respecting these works3 ',if ,i had1' he says1 'power over the works of ,aristotle1 ,i would have them all burnt2 for it is only a loss of time to study in them1 and a course of error1 and a multiplication of ignorance beyond expression4' ',the common herd of students1' he says1 'with their heads1 have no principle by which they can be excited to any worthy employment2 and hence they mope and make asses of themselves over their bad translations1 and lose their time1 and trouble1 and money4' #eag ,note #h;,a3 ,op4 ,maj4 p4 #a4 ,note #i;,a3 ,ib4 p4 #b4 ,note #aj;,a3 ,ib4 p4 #aj4 ,note #aa;,a3 ,op4 ,maj4 p4 #cf4 ,note #ab;,a3 ,autonomatic4 ,note #ac;,a3 ,op4 ,maj4 p4 #df4 ,note #ad;,a3 ,see ,pref4 to ,jebb's edition4 ,the passages there quoted1 however1 are not extracts from the ,opus ,majus1 but 7apparently7 from the ,opus ,minus 7,,ms4 ,cott4 ,tib4 c 4 #e74 ,si haberem potestatem supra libros ,aristotelis1 ego facerem omnes cremari2 quia non est nisi temporis amissio studere in illis1 et causa erroris1 et multiplicatio ignoranti ultra id quod valeat explicari4 4 4 4 ,vulgus studentum cum capitibus suis non habet unde excitetur ad aliquid dignum1 et ideo languet et asininat circa male translata1 et tempus et studium amittit in omnibus et expensas4 ,the remedies which he recommends for these evils1 are1 in the first place1 the study of that only perfect wisdom which is to be found in the ,sacred ,scripture2#ae;,a in the next place1 the study of mathematics and the use of experiment4#af;,a ,by the aid of these methods1 ,bacon anticipates the most splendid progress for human knowledge4 ,he takes up the strain of hope and confidence which we have noticed as so peculiar in the ,roman writers2 and quotes some of the passages of ,seneca which we adduced in illustration of this3--that the attempts in science were at first rude and imperfect1 and were afterwards improved2--that the day will come1 when what is still unknown shall be brought to light by the progress of time and the labors of a longer period2--that one age does not suffice for inquiries so wide and various2--that the people of future times shall know many things unknown to us2--and that the time shall arrive when posterity will wonder that we overlooked what was so obvious4 ,bacon himself adds anticipations more peculiarly in the spirit of his own time4 ',we have seen1' he says1 at the end of the work1 'how ,aristotle1 by the ways which wisdom teaches1 could give to ,alexander the empire of the world4 ,and this the ,church ought to take into consideration against the infidels and rebels1 that there may be a sparing of ,christian blood1 and especially on account of the troubles that shall come to pass in the days of ,antichrist2 which by the grace of ,god it would be easy to obviate1 if prelates and princes would encourage study1 and join in searching out the secrets of nature and art4' ,note #ae;,a3 ,part ii4 ,note #af;,a3 ,parts iv4 v4 and vi4 ,it may not be improper to observe here that this belief in the appointed progress of knowledge1 is not combined with any overweening belief in the unbounded and independent power of the human intellect4 ,on the contrary1 one of the lessons which ,bacon draws from the state and prospects of knowledge1 is the duty of faith and humility4 ',to him1' he says1#ag;,a 'who denies the truth of the faith because he is unable to understand it1 ,i will propose in reply the course of nature1 and as we have seen it in examples4' ,and after giving some instances1 he adds1 ',these1 and the like1 ought to move men and to excite them to the reception of divine truths4 ,for if1 in the vilest objects of creation1 truths are found1 before which the inward pride of man must bow1 and believe though it cannot understand1 how much more should man humble his mind before the glorious truths of ,god6' ,he had before said3#ah;,a ',man is incapable of perfect wisdom in this life2 it is hard for #eah him to ascend towards perfection1 easy to glide downwards to falsehoods and vanities3 let him then not boast of his wisdom1 or extol his knowledge4 ,what he knows is little and worthless1 in respect of that which he believes without knowing2 and still less1 in respect of that which he is ignorant of4 ,he is mad who thinks highly of his wisdom2 he most mad1 who exhibits it as something to be wondered at4' ,he adds1 as another reason for humility1 that he has proved by trial1 he could teach in one year1 to a poor boy1 the marrow of all that the most diligent person could acquire in forty years' laborious and expensive study4 ,note #ag;,a3 ,op4 ,maj4 p4 #dgf4 ,note #ah;,a3 ,ib4 p4 #ae4 ,to proceed somewhat more in detail with regard to ,roger ,bacon's views of a ,reform in ,scientific ,inquiry1 we may observe that by making ,mathematics and ,experiment the two great points of his recommendation1 he directed his improvement to the two essential parts of all knowledge1 ,ideas and ,facts1 and thus took the course which the most enlightened philosophy would have suggested4 ,he did not urge the prosecution of experiment1 to the comparative neglect of the existing mathematical sciences and conceptions2 a fault which there is some ground for ascribing to his great namesake and successor ,francis ,bacon3 still less did he content himself with a mere protest against the authority of the schools1 and a vague demand for change1 which was almost all that was done by those who put themselves forward as reformers in the intermediate time4 ,roger ,bacon holds his way steadily between the two poles of human knowledge2 which1 as we have seen1 it is far from easy to do4 ',there are two modes of knowing1' says he2#ai;,a 'by argument1 and by experiment4 ,argument concludes a question2 but it does not make us feel certain1 or acquiesce in the contemplation of truth1 except the truth be also found to be so by experience4' ,it is not easy to express more decidedly the clearly-seen union of exact conceptions with certain facts1 which1 as we have explained1 constitutes real knowledge4 ,note #ai;,a3 ,op4 ,maj4 p4 #dde2 see also p4 #ddh4 ,scienti ali sciunt sua principia invenire per experimenta1 sed conclusiones per argumenta facta ex principiis inventis4 ,si vero debeant habere experientiam conclusionum suarum particularem et completam1 tunc oportet quod habeant per adjutorium istius scienti nobilis 7experimentalis74 ,one large division of the ,opus ,majus is ',on the ,usefulness of ,mathematics1' which is shown by a copious enumeration of existing branches of knowledge1 as ,chronology1 ,geography1 the ,calendar and 7in a separate ,part7 ,optics4 ,there is a chapter1#bj;,a in which it is proved #eai by reason1 that all science requires mathematics4 ,and the arguments which are used to establish this doctrine1 show a most just appreciation of the office of mathematics in science4 ,they are such as follows3--,that other sciences use examples taken from mathematics as the most evident3--,that mathematical knowledge is1 as it were1 innate to us1 on which point he refers to the well-known dialogue of ,plato1 as quoted by ,cicero3--,that this science1 being the easiest1 offers the best introduction to the more difficult3--,that in mathematics1 things as known to us are identical with things as known to nature3--,that we can here entirely avoid doubt and error1 and obtain certainty and truth3--,that mathematics is prior to other sciences in nature1 because it takes cognizance of quantity1 which is apprehended by intuition 7intuitu intellectus74 ',moreover1' he adds1#ba;,a 'there have been found famous men1 as ,robert1 bishop of ,lincoln1 and ,brother ,adam ,marshman 7de ,marisco71 and many others1 who by the power of mathematics have been able to explain the causes of things2 as may be seen in the writings of these men1 for instance1 concerning the ,rainbow and ,comets1 and the generation of heat1 and climates1 and the celestial bodies4' ,note #bj;,a3 ,ib4 p4 #fj4 ,note #ba;,a3 ,op4 ,maj4 p4 #fd4 ,but undoubtedly the most remarkable portion of the ,opus ,majus is the ,sixth and last ,part1 which is entitled ',de ,scientia experimentali4' ,it is indeed an extraordinary circumstance to find a writer of the thirteenth century1 not only recognizing experiment as one source of knowledge1 but urging its claims as something far more important than men had yet been aware of1 exemplifying its value by striking and just examples1 and speaking of its authority with a dignity of diction which sounds like a foremurmur of the ,baconian sentences uttered nearly four hundred years later4 ,yet this is the character of what we here find4#bb;,a ',experimental science1 the sole mistress of speculative sciences1 has three great ,prerogatives among other parts of knowledge3 ,first she tests by experiment the noblest conclusions of all other sciences3 ,next she discovers respecting the notions which other sciences deal with1 magnificent truths to which these sciences of themselves can by no means attain3 her ,third dignity is1 that she by her own power and without respect of other sciences1 investigates the secrets of nature4' #ebj ,note #bb;,a3 ,veritates magnificas in terminis aliarum scientiarum in quas per nullam viam possunt ill scienti1 hc sola scientiarum domina speculativarum1 potest dare4--,op4 ,maj4 p4 #dfe4 ,the examples which ,bacon gives of these ',prerogatives' are very curious1 exhibiting1 among some error and credulity1 sound and clear views4 ,his leading example of the ,first ,prerogative is the ,rainbow1 of which the cause1 as given by ,aristotle1 is tested by reference to experiment with a skill which is1 even to us now1 truly admirable4 ,the examples of the ,second ,prerogative are three--first1 the art of making an artificial sphere which shall move with the heavens by natural influences1 which ,bacon trusts may be done1 though astronomy herself cannot do it--'et tunc1' he says1 'thesaurum unius regis valeret hoc instrumentum2'--secondly1 the art of prolonging life1 which experiment may teach1 though medicine has no means of securing it except by regimen2#bc;,a--thirdly1 the art of making gold finer than fine gold1 which goes beyond the power of alchemy4 ,the ,third ,prerogative of experimental science1 arts independent of the received sciences1 is exemplified in many curious examples1 many of them whimsical traditions4 ,thus it is said that the character of a people may be altered by altering the air4#bd;,a ,alexander1 it seems1 applied to ,aristotle to know whether he should exterminate certain nations which he had discovered1 as being irreclaimably barbarous2 to which the philosopher replied1 ',if you can alter their air1 permit them to live2 if not1 put them to death4' ,in this part1 we find the suggestion that the fire-works made by children1 of saltpetre1 might lead to the invention of a formidable military weapon4 ,note #bc;,a3 ,one of the ingredients of a preparation here mentioned1 is the flesh of a dragon1 which1 it appears1 is used as food by the ,ethiopians4 ,the mode of preparing this food cannot fail to amuse the reader4 ,where there are good flying dragons1 by the art which they possess1 they draw them out of their dens1 and have bridles and saddles in readiness1 and they ride upon them1 and make them bound about in the air in a violent manner1 that the hardness and toughness of the flesh may be reduced1 as boars are hunted and bulls are baited before they are killed for eating4--,op4 ,maj4 p4 #dgj4 ,note #bd;,a3 ,op4 ,maj4 p4 #dgb4 ,it could not be expected that ,roger ,bacon1 at a time when experimental science hardly existed1 could give any precepts for the discovery of truth by experiment4 ,but nothing can be a better example of the method of such investigation1 than his inquiry concerning the cause of the ,rainbow4 ,neither ,aristotle1 nor ,avicenna1 nor ,seneca1 he says1 have given us any clear knowledge of this matter1 but experimental science can do so4 ,let the experimenter 7experimentator7 consider the cases in which he finds the same colors1 as the hexagonal crystals from ,ireland and ,india2 by looking into these he will see colors like those of the rainbow4 ,many think that this arises from some #eba special virtue of these stones and their hexagonal figure2 let therefore the experimenter go on1 and he will find the same in other transparent stones1 in dark ones as well as in light-colored4 ,he will find the same effect also in other forms than the hexagon1 if they be furrowed in the surface1 as the ,irish crystals are4 ,let him consider too1 that he sees the same colors in the drops which are dashed from oars in the sunshine2--and in the spray thrown by a mill wheel2--and in the dew drops which lie on the grass in a meadow on a summer morning2--and if a man takes water in his mouth and projects it on one side into a sunbeam2--and if in an oil lamp hanging in the air1 the rays fall in certain positions upon the surface of the oil2--and in many other ways1 are colors produced4 ,we have here a collection of instances1 which are almost all examples of the same kind as the phenomenon under consideration2 and by the help of a principle collected by induction from these facts1 the colors of the rainbow were afterwards really explained4 ,with regard to the form and other circumstances of the bow he is still more precise4 ,he bids us measure the height of the bow and of the sun1 to show that the centre of the bow is exactly opposite to the sun4 ,he explains the circular form of the bow1--its being independent of the form of the cloud1 its moving when we move1 its flying when we follow1--by its consisting of the reflections from a vast number of minute drops4 ,he does not1 indeed1 trace the course of the rays through the drop1 or account for the precise magnitude which the bow assumes2 but he approaches to the verge of this part of the explanation2 and must be considered as having given a most happy example of experimental inquiry into nature1 at a time when such examples were exceedingly scanty4 ,in this respect1 he was more fortunate than ,francis ,bacon1 as we shall hereafter see4 ,we know but little of the biography of ,roger ,bacon1 but we have every reason to believe that his influence upon his age was not great4 ,he was suspected of magic1 and is said to have been put into close confinement in consequence of this charge4 ,in his work he speaks of ,astrology1 as a science well worth cultivating4 ',but1' says he1 ',theologians and ,decretists1 not being learned in such matters1 and seeing that evil as well as good may be done1 neglect and abhor such things1 and reckon them among ,magic ,arts4' ,we have already seen1 that at the very time when ,bacon was thus raising his voice against the habit of blindly following authority1 and seeking for all science in ,aristotle1 ,thomas ,aquinas was employed in fashioning ,aristotle's tenets into that fixed form in which they became the great impediment to the #ebb progress of knowledge4 ,it would seem1 indeed1 that something of a struggle between the progressive and stationary powers of the human mind was going on at this time4 ,bacon himself says1#be;,a ',never was there so great an appearance of wisdom1 nor so much exercise of study in so many ,faculties1 in so many regions1 as for this last forty years4 ,doctors are dispersed everywhere1 in every castle1 in every burgh1 and especially by the students of two ,orders1 7he means the ,franciscans and ,dominicans1 who were almost the only religious orders that distinguished themselves by an application to study1#bf;,a7 which has not happened except for about forty years4 ,and yet there was never so much ignorance1 so much error4' ,and in the part of his work which refers to ,mathematics1 he says of that study1#bg;,a that it is the door and the key of the sciences2 and that the neglect of it for thirty or forty years has entirely ruined the studies of the ,latins4 ,according to these statements1 some change1 disastrous to the fortunes of science1 must have taken place about #abcj1 soon after the foundation of the ,dominican and ,franciscan ,orders4#bh;,a ,nor can we doubt that the adoption of the ,aristotelian philosophy by these two ,orders1 in the form in which the ,angelical ,doctor had systematized it1 was one of the events which most tended to defer1 for three centuries1 the reform which ,roger ,bacon urged as a matter of crying necessity in his own time4 ,note #be;,a3 ,quoted by ,jebb1 ,pref4 to ,op4 ,maj4 ,note #bf;,a3 ,mosheim1 ,hist4 iii4 #afa4 ,note #bg;,a3 ,op4 ,maj4 p4 #eg4 ,note #bh;,a3 ,mosheim1 iii4 #afa4 ,it is worthy of remark that in the ,opus ,majus of ,roger ,bacon1 as afterwards in the ,novum ,organon of ,francis ,bacon1 we have certain features of experimental research pointed out conspicuously as ,prrogativ3 although in the former1 this term is employed to designate the superiority of experimental science in general to the science of the schools2 in the latter work1 the term is applied to certain classes of experiments as superior to others4 #ebc ,,book ,v4 ,,formal ,,astronomy4 ,,chapter ,i4 ,,prelude ,,to ,,copernicus4 ,nicolas of ,cus4 ,i ,,will quote the passage1 in the writings of this author1 which bears upon the subject in question4 ,i translate it from the edition of his book ,de ,docta ,ignorantia1 from his works published at ,basil in #aefe4 ,he praises ,learned ,ignorance--that is1 ,acknowledged ,ignorance--as the source of knowledge4 ,his ground for asserting the motions of the earth is1 that there is no such thing as perfect rest1 or an exact centre1 or a perfect circle1 nor perfect uniformity of motion4 ,neque verus circulus dabilis est1 quinetiam verior dari possit1 neque unquam uno tempore sicut alio qualiter prcis1 aut movetur1 aut circulum veri similem1 qualem describit1 etiamsi nobis hoc non appareat4 ,et ubicumque quis fuerit1 se in centro esse credit4 7,lib4 i4 cap4 xi4 p4 #ci47 ,he adds1 ,the ,ancients did not attain to this knowledge1 because they were wanting in ,learned ,ignorance4 ,now it is manifest to us that the ,earth is truly in motion1 although this do not appear to us2 since we do not apprehend motion except by comparison with something fixed4 ,for if any one were in a boat in the middle of a river1 ignorant that the water was flowing1 and not seeing the banks1 how could he apprehend that the boat was moving8 ,and thus since every one1 whether he be in the ,earth1 or in the ,sun1 or in any other star1 thinks that he is in an immovable centre1 and that everything else is moving2 he would assign different poles for himself1 others as being in the ,sun1 others in the ,earth1 and others in the ,moon1 and so of the rest4 ,whence the machine of the world is as if it had its centre everywhere and its circumference nowhere4 ,this train of thought #ebd might be a preparation for the reception of the ,copernican system2 but it is very different from the doctrine that the ,sun is the centre of the ,planetary ,motions4 ,,chapter ,,ii4 ,,the ,,copernican ,,theory4 ,the ,moon's ,rotation4 ,i ,,have said1 in page #bfd1 that a confusion of mind produced by the double reference of motion to absolute space1 and to a centre of revolution1 often leads persons to dispute whether the ,moon1 while she revolves about the ,earth1 always turning to it the same face1 revolves about her axis or not4 ,this dispute has been revived very lately1 and has been conducted in a manner which shows that popular readers and writers have made little progress in the clearness of their notions during the last two or three centuries2 and that they have accepted the ,newtonian doctrines in words with a very dim apprehension of their real import4 ,if the ,moon were carried round the ,earth by a rigid arm revolving about the ,earth as a centre1 being rigidly fastened to this arm1 as a mimic ,moon might be1 in a machine constructed to represent her motions1 this contrivance1 while it made her revolve round the ,earth would make her also turn the same face to the ,earth3 and if we were to make such a machine the standard example of rotation1 the ,moon might be said not to rotate on her axis4 ,but we are speedily led to endless confusion by taking this case as the standard of rotation4 ,for the selection of the centre of rotation in a system which includes several bodies is arbitrary4 ,the ,moon turns all her faces successively to the ,sun1 and therefore with regard to the ,sun1 she does rotate on her axis2 and yet she revolves round the ,sun as truly as she revolves round the ,earth4 ,and the only really simple and consistent mode of speaking of rotation1 is to refer the motion not to any relative centre1 but to absolute space4 ,this is the argument merely on the ground of simplicity and consistency4 ,but we find physical reasons1 as well as mathematical1 for referring the motion to absolute space4 ,if a cup of water be carried round a centre so as to describe a circle1 a straw floating on the surface #ebe of the water1 if it point to the centre of the circle at first1 does not continue to do so1 but remains parallel to itself during the whole revolution4 ,now there is no cause to make the water 7and therefore the straw7 rotate on its axis2 and therefore it is not a clear or convenient way of speaking1 to say that the water in this case does revolve on its axis4 ,but if the water in this case do not revolve on its axis1 a body in the case of the ,moon does revolve on its axis4 ,the difficulty1 as ,i have said in the text1 is of the same nature as that which the ,copernicans at first found in the parallel motion of the ,earth's axis4 ,in order to make the axis of the ,earth's rotation remain parallel to itself while the ,earth revolves about the ,sun1 in a mechanical representation1 some machinery is needed in addition to the machinery which produces the revolution round the centre 7the ,sun73 but the simplest way of regarding the parallel motion is1 to conceive that the axis has no motion except that which carries it round the central ,sun4 ,and it was seen1 when the science of ,mechanics was established1 that no force was needed in nature to produce this parallelism of the ,earth's axis4 ,it was therefore the only scientific course1 to conceive this parallelism as not being a rotation3 and in like manner we are to conceive the parallelism of a revolving body as not being a rotation4 ,m4 ,foucault's ,proofs of the ,earth's ,motion4 ,,it was hardly to be expected that we should discover1 in our own day1 a new physical proof of the earth's motion1 yet so it has been4 ,the experiments of ,m4 ,foucault have enabled us to see the ,rotation of the ,earth on its axis1 as taking place1 we may say1 before our eyes4 ,these experiments are1 in fact1 a result of what has been said in speaking of the ,moon's rotation3 namely1 ,that the mechanical causes of motion operate with reference to absolute1 not relative1 space2 so that where there is no cause operating to change a motion1 it will retain its direction in absolute space2 and may on that account seem to change1 if regarded relatively in a limited space4 ,in ,m4 ,foucault's first experiment1 the motion employed was that of a pendulum4 ,if a pendulum oscillate quite freely1 there is no cause acting to change the vertical plane of oscillation absolutely2 for the forces which produce the oscillation are in the vertical plane4 ,but if the vertical plane remain the same absolutely1 at a spot on the surface of the revolving ,earth1 it will change relatively to the spectator4 ,he will see the pendulum oscillate in a vertical plane which gradually #ebf turns away from its first position4 ,now this is what really happens2 and thus the revolution of the ,earth in absolute space is experimentally proved4 ,in subsequent experiments1 ,m4 ,foucault has used the rotation of a body to prove the same thing4 ,for when a body rotates freely1 acted upon by no power1 there is nothing to change the position of the axis of rotation in absolute space4 ,but if the position of the axis remain the same in absolute space1 it will1 in virtue of its relative motion1 change as seen by a spectator at any spot on the rotating ,earth4 ,by taking a heavy disk or globe and making it rotate on its axis rapidly1 the force of absolute permanence 7as compared with the inevitable casual disturbances arising from the machinery which supports the revolving disk7 becomes considerable and hence the relative motion can1 in this way also1 be made visible4 ,mr4 ,de ,morgan has said 7,comp4 to ,brit4 ,alm4 #ahcf1 p4 #ah7 that astronomy does not supply any argument for the earth's motion which is absolutely and demonstrably conclusive1 till we come to the ,aberration of ,light4 ,but we may now venture to say that the experiments of ,m4 ,foucault prove the diurnal motion of the ,earth in the most conclusive manner1 by palpable and broad effects1 if we accept the doctrines of the ,science of ,mechanics3 while ,aberration proves the annual motion1 if we suppose that we can observe the places of the fixed stars to the accuracy of a few seconds2 and if we accept1 in addition to the doctrines of ,mechanics1 the doctrine of the motion of light with a certain great velocity4 ,,chapter ,,iii4 ,,sequel ,,to ,,copernicus4 ,english ,copernicans4 ,,professor ,,de ,,morgan has made numerous and interesting contributions to the history of the progress and reception of the ,copernican ,system4 ,these are given mainly in the ,companion to the ,british ,almanac2 especially in his papers entitled ,old ,arguments against the ,motion of the ,earth 7#ahcf72 ,english ,mathematical and ,astronomical ,writers 7#ahcg72 ,on the ,difficulty of ,correct #ebg ,description of ,books 7#ahec72 ,the ,progress of the ,doctrine of the ,earth's ,motion between the ,times of ,copernicus and ,galileo 7#ahee74 ,in these papers he insists very rightly upon the distinction between the mathematical and the physical aspect of the doctrines of ,copernicus3 a distinction corresponding very nearly with the distinction which we have drawn between ,formal and ,physical ,astronomy2 and in accordance with which we have given the history of the ,heliocentric ,doctrine as a ,formal ,theory in ,book v41 and as a ,physical ,theory in ,book vii4 ,another interesting part of ,mr4 ,de ,morgan's researches are the notices which he has given of the early assertors of the heliocentric doctrine in ,england4 ,these make their appearance as soon as it was well possible they should exist4 ,the work of ,copernicus was published1 as we have said1 in #aedc4 ,in ,september #aeef1 ,john ,field published an ,ephemeris for #aeeg1 juxta ,copernici et ,reinholdi ,canones1 in the preface to which he avows his conviction of the truth of the ,copernican hypothesis4 ,robert ,recorde1 the author of various works on ,arithmetic1 published among others1 ,the ,pathway to ,knowledge in #aeea4 ,in this book1 the author discusses the question of the quietnes of the earth1 and professes to leave it undecided3 but ,mr4 ,de ,morgan 7,comp4 ,a4 #ahcg1 p4 #cc7 conceives that it appears from what is said1 that he was really a ,copernican1 but did not think the world ripe for any such doctrine4 ,mr4 ,joseph ,hunter also has brought to notice#bi;,a the claims of ,field1 whom he designates as the ,proto-,copernican of ,england4 ,he quotes the ,address to the ,reader prefixed to his first ,ephemeris1 and dated ,may #ca1 #aeef1 in which he says that1 since abler men decline the task1 ,i have therefore published this ,ephemeris of the year #aeeg1 following in it as my authorities1 ,n4 ,copernicus and ,erasmus ,reinhold1 whose writings are established and founded on true1 certain1 and authentic demonstrations4 ,i conceive that this passage1 however1 only shows that ,field had adopted the ,copernican scheme as a basis for the calculation of ,ephemerides2 which1 as ,mr4 ,de ,morgan has remarked1 is a very different thing from accepting it as a physical truth4 ,field1 in this same address1 makes mention of the errors illius turb qu ,alphonsi utitur hypothesi2 but the word hypothesis is still indecisive4 ,note #bi;,a3 ,ast4 ,soc4 ,notices1 vol4 iii4 p4 #c 7#ahcc74 ,as evidence that ,field was regarded in his own day as a man who #ebh had rendered good service to science1 ,mr4 ,hunter notices that1 in #aeeh1 the ,heralds granted to him the right of using1 with his arms1 the crest or additional device of a red right arm issuing from the clouds1 and presenting a golden armillary sphere4 ,recorde's claims depend upon a passage in a ,dialogue between ,master and ,scholar1 in which the ,master expounds the doctrine of ,copernicus1 and the authorities against it2 to which the ,scholar answers1 taking the common view3 ,nay1 sir1 in good faith ,i desire not to hear such vaine phantasies1 so far against common reason1 and repugnant to all the learned multitude of wryters1 and therefore let it passe for ever and a day longer4 ,the ,master1 more sagely1 warns him against a hasty judgment1 and says1 ,another time ,i will so declare his supposition1 that you shall not only wonder to hear it1 but also peradventure be as earnest then to credit it1 as you now are now to condemne it4 ,i conceive that this passage proves ,mr4 ,de ,morgan's assertion1 that ,recorde was a ,copernican1 and very likely the first in ,england4 ,in #aeee1 also1 ,leonard ,digges published his ,prognostication ,everlasting2 but this is1 as ,mr4 ,de ,morgan says 7,comp4 ,a4 #ahcg1 p4 #dj7 a meteorological work4 ,it was republished in #aeib by his son ,thomas ,digges with additions2 and as these have been the occasion of some confusion among those who have written on the history of astronomy1 ,i am glad to be able1 through the kindness of ,professor ,walker of ,oxford1 to give a distinct account of the editions of the work4 ,in the ,bodleian ,library1 besides the editions of #aeee and #aeib of the ,prognostication ,everlasting1 there is an edition of #aefd4 ,it is still decidedly ,ptolemaic1 and contains a ,diagram representing a number of concentric circles1 which are marked1 in order1 as-- ,the ,earth1 ,moone1 ,venus1 ,mercury1 ,sunne1 ,mars1 ,jupiter1 ,saturne1 ,the ,starrie ,firmament1 ,the ,crystalline ,heavens1 ,the ,first ,mover1 ,the ,abode of ,god and the ,elect4 ,here the ,learned do approve4 #ebi ,the third edition1 of #aeib1 contains an ,addition1 by the son1 of twenty pages4 ,he there speaks of having found1 apparently among his father's papers1 ,a description or modile of the world and situation of ,spheres ,clestiall and elementare according to the doctrine of ,ptolemie1 whereunto all universities 7led thereunto chiefly by the authoritie of ,aristotle7 do consent4 ,he adds3 ,but in this our age1 one rare witte 7seeing the continuall errors that from time to time more and more continually have been discovered1 besides the infinite absurdities in their ,theoricks1 which they have been forced to admit that would not confesse any ,mobilitie in the ball of the ,earth7 hath by long studye1 paynfull practise1 and rare invention1 delivered a new ,theorick or ,model of the world1 shewing that the ,earth resteth not in the ,center of the whole world or globe of elements1 which encircled and enclosed in the ,moone's orbe1 and together with the whole globe of mortalitye is carried yearely round about the ,sunne1 which like a king in the middest of all1 raygneth and giveth lawes of motion to all the rest1 sphrically dispersing his glorious beames of light through all this sacred clestiall ,temple4 ,and the ,earth itselfe to be one of the ,planets1 having his peculiar and strange courses1 turning every #bd hours rounde upon his owne centre1 whereby the ,sunne and great globe of fixed ,starres seem to sway about and turne1 albeit indeed they remaine fixed--,so many ways is the sense of mortal man abused4 ,this ,addition is headed3 ,a ,perfit ,description of the ,clestiall ,orbes1 according to the most ancient doctrine of the ,pythagoreans3 lately revived by ,copernicus1 and by ,geometrical ,demonstrations approved4 ,mr4 ,de ,morgan1 not having seen this edition1 and knowing the title-page only as far as the word ,pythagoreans1 says their astrological doctrines we presume1 not their reputed ,copernican ones4 ,but it now appears that in this1 as in other cases1 the authority of the ,pythagoreans was claimed for the ,copernican system4 ,antony a ,wood quotes the latter part of the title thus3 ,cui subnectitur orbium ,copernicarum accurata descriptio2 which is inaccurate4 ,weidler1 still more inaccurately1 cites it1 ,cui subnectitur operum ,copernici accurata descriptio4 ,lalande goes still further1 attempting1 it would seem1 to recover the ,english title-page from the ,latin3 we find in the ,bibl4 ,astron4 the following3 #aeib 4 4 ,leonard ,digges1 ,accurate ,description of the ,copernican ,system to the ,astronomical perpetual ,prognostication4 ,thomas ,digges appears1 by others also of his writings1 to have been #ecj a clear and decided ,copernican4 ,in his ,al sive ,scal ,mathematic1 #aegc1 he bestows high praise upon ,copernicus and upon his system3 and appears to have been a believer in the real motion of the ,earth1 and not merely an admirer of the system of ,copernicus as an explanatory hypothesis4 ,giordano ,bruno4 ,the complete title of the work referred to is3 ,jordani ,bruni ,nolani ,de ,monade ,numero et ,figura liber consequens ,quinque ,de ,minimo ,magno et ,mensura1 item ,de ,innumerabilibus1 ,immenso et ,infigurabili2 seu ,de ,universo et ,mundis libri octo4 7,francofurti1 #aeia47 ,that the ,reader may judge of the value of ,bruno's speculations1 ,i give the following quotations3 ,lib4 iv4 c4 #aa 7,index74 ,tellurem totam habitabilem esse intus et extra1 et innumerabilia animantium complecti tum nobis sensibilium tum occultorum genera4 ,c4 #ac4 ,ut ,mundorum ,synodi in ,universo et particulares ,mundi in ,synodis ordinentur1' c4 ,he says 7,lib4 v4 c4 #a1 p4 #dfa73 ,besides the stars and the great worlds there are smaller living creatures carried through the etherial space1 in the form of a small sphere which has the aspect of a bright fire1 and is by the vulgar regarded as a fiery beam4 ,they are below the clouds1 and ,i saw one which seemed to touch the roofs of the houses4 ,now this sphere1 or beam as they call it1 was really a living creature 7animal71 which ,i once saw moving in a straight path1 and grazing as it were the roofs of the city of ,nola1 as if it were going to impinge on ,mount ,cicada2 which however it went over4 ,there are two recent editions of the works of ,giordano ,bruno2 by ,adolf ,wagner1 ,leipsick1 #ahcj1 in two volumes2 and by ,gfrrer1 ,berlin1 #ahcc4 ,of the latter ,i do not know that more than one volume 7vol4 ii47 has appeared4 ,did ,francis ,bacon reject the ,copernican ,system8 ,,mr4 ,,de ,,morgan has very properly remarked 7,comp4 ,b4 ,a4 #ahee1 p4 #aa7 that the notice of the heliocentric question in the ,novum ,organon must be considered one of the most important passages in his works upon this point1 as being probably the latest written and best #eca matured4 ,it occurs in ,lib4 ii4 ,aphorism xxxvi41 in which he is speaking of ,prerogative ,instances1 of which he gives twenty-seven species4 ,in the passage now referred to1 he is speaking of a kind of ,prerogative ,instances1 better known to ordinary readers than most of the kinds by name1 the ,instantia ,crucis3 though probably the metaphor from which this name is derived is commonly wrongly apprehended4 ,bacon's meaning is ,guide-,post ,instances3 and the ,crux which he alludes to is not a ,cross1 but a ,guide-,post at ,cross-roads4 ,and among the cases to which such ,instances may be applied1 he mentions the diurnal motion of the heavens from east to west1 and the special motion of the particular heavenly bodies from west to east4 ,and he suggests what he conceives may be an ,instantia ,crucis in each case4 ,if1 he says1 we find any motion from east to west in the bodies which surround the earth1 slow in the ocean1 quicker in the air1 quicker still in comets1 gradually quicker in planets according to their greater distance from the earth3 then we may suppose that there is a cosmical diurnal motion1 and the motion of the earth must be denied4 ,with regard to the special motions of the heavenly bodies1 he first remarks that each body not coming quite so far westwards as before1 after one revolution of the heavens1 and going to the north or the south1 does not imply any special motion2 since it may be accounted for by a modification of the diurnal motion in each1 which produces a defect of the return1 and a spiral path2 and he says that if we look at the matter as common people#cj;,a and disregard the devices of astronomers1 the motion is really so to the senses2 and that he has made an imitation of it by means of wires4 ,the instantia crucis which he here suggests is1 to see if we can find in any credible history an account of any comet which did not share in the diurnal revolution of the skies4 ,note #cj;,a3 ,et certissimum est si paulisper pro plebeiis nos geramus 7missis astronomorum et schol commentis1 quibus illud in more est1 ut sensui in multis immerito vim faciant et obscuriora malint7 talem esse motum istum ad sensum qualem diximus4 ,on his assertion that the motion of each separate planet is1 to sense1 a spiral1 we may remark that it is certainly true2 but that the business of science1 here1 as elsewhere1 consists in resolving the complex phenomenon into simple phenomena2 the complex spiral motion into simple circular motions4 ,with regard to the diurnal motion of the earth1 it would seem as if ,bacon himself had a leaning to believe it when he wrote this passage2 for neither is he himself1 nor are any of the ,anticopernicans1 #ecb accustomed to assert that the immensely rapid motion of the sphere of the ,fixed ,stars graduates by a slower and slower motion of ,planets1 ,comets1 ,air1 and ,ocean1 into the immobility of the ,earth4 ,so that the conditions are not satisfied on which he hypothetically says1 tum abnegandus est motus terr4 ,with regard to the proper motions of the planets1 this passage seems to me to confirm what ,i have already said of him2 that he does not appear to have seen the full value and meaning of what had been done1 up to his time1 in ,formal ,astronomy4 ,we may however fully agree with ,mr4 ,de ,morgan2 that the whole of what he has said on this subject1 when put together1 does not justify ,hume's assertion that he rejected the ,copernican system with the most positive disdain4 ,mr4 ,de ,morgan1 in order to balance the ,copernican argument derived from the immense velocity of the stars in their diurnal velocity on the other supposition1 has reminded us that those who reject this great velocity as improbable1 accept without scruple the greater velocity of light4 ,it is curious that ,bacon also has made this comparison1 though using it for a different purpose2 namely1 to show that the transmission of the visual impression may be instantaneous4 ,in ,aphorism xlvi4 of ,book ii4 of the ,novum ,organon he is speaking of what he calls ,instanti curriculi1 or ,instanti ad aquam1 which we may call ,instances by the clock3 and he says that the great velocity of the diurnal sphere makes the marvellous velocity of the rays of light more credible4 ,immensa illa velocitas in ipso corpore1 qu cernitur in motu diurno 7qu etiam viros graves ita obstupefecit ut mallent credere motum terr71 facit motum illum ejaculationis ab ipsis stellis 7licet celeritate ut diximus admirabilem7 magis credibilem4 ,this passage shows an inclination towards the opinion of the earth's being at rest1 but not a very strong conviction4 ,kepler persecuted4 ,,we have seen 7p4 #bhj7 that ,kepler writes to ,galileo in #aeig--;,be trustful and go forwards4 ,if ,italy is not a convenient place for the publication of your views1 and if you are likely to meet with any obstacles1 perhaps ,germany will grant us the necessary liberty4 ,kepler however had soon afterwards occasion to learn that in ,germany also1 the cultivators of science were exposed to persecution4 ,it is true that #ecc in his case the persecution went mainly on the broad ground of his being a ,protestant1 and extended to great numbers of persons at that time4 ,the circumstances of this and other portions of ,kepler's life have been brought to light only recently through an examination of public documents in the ,archives of ,wrtemberg and unpublished letters of ,kepler4 7,johann ,keppler's ,leben und ,wirken1 nach neuerlich aufgefundenen ,manuscripten bearbeitet von ,j4 ,l4 ,c4 ,freiherrn v4 ,breitschwart1 ,k4 ,wrtemberg4 ,staats-,rath4 ,stuttgart1 #ahca47 ,schiller1 in his ,history of the ,thirty ,years' ,war1 says that when ,ferdinand of ,austria succeeded to the ,archduchy of ,stiria1 and found a great number of ,protestants among his subjects1 he suppressed their public worship without cruelty and almost without noise4 ,but it appears now that the ,protestants were treated with great severity4 ,kepler held a professorship in ,stiria1 and had married1 in #aejg1 ,barbara ,mller1 who had landed property in that province4 ,on the #aath of ,june1 #aeih1 he writes to his friend ,mstlin that the arrival of the ,prince out of ,italy is looked forwards to with terror4 ,in ,december he writes that the ,protestants had irritated the ,catholics by attacks from the pulpit and by caricatures2 that hereupon the ,prince1 at the prayer of the ,estates1 had declared the ,letter of ,license granted by his father to be forfeited1 and had ordered all the ,evangelical ,teachers to leave the country on pain of death4 ,they went to the frontiers of ,hungary and ,croatia2 but after a month1 ,kepler was allowed to return1 on condition of keeping quiet4 ,his discoveries appear to have operated in his favor4 ,but the next year he found his situation in ,stiria intolerable1 and longed to return to his native country of ,wrtemberg1 and to find some position there4 ,this he did not obtain4 ,he wrote a circular letter to his ,brother ,protestants1 to give them consolation and courage2 and this was held to be a violation of the conditions on which his residence was tolerated4 ,fortunately1 at this time he was invited to join ,tycho ,brahe1 who had also been driven from his native country1 and was living at ,prague4 ,the two astronomers worked together under the patronage of the ,emperor ,rudolph ,,ii42 and when ,tycho died in #afja1 ,kepler became the ,imperial ,mathematicus4 ,we are not to imagine that even among ,protestants1 astronomical notions were out of the sphere of religious considerations4 ,when ,kepler was established in ,stiria1 his first official business was the calculation of the ,calendar for the ,evangelical ,community4 ,they protested against the new ,calendar1 as manifestly calculated for the furtherance of an impious papistry3 and1 say they1 ,we hold the ,pope for a #ecd horrible roaring ,lion4 ,if we take his ,calendar1 we must needs go into the church when he rings us in4 ,kepler however did not fail to see1 and to say1 that the ,papal ,reformation of the ,calendar was a vast improvement4 ,kepler1 as court-astronomer1 was of course required to provide such observations of the heavens as were requisite for the calculations of the ,astrologers4 ,that he considered ,astrology to be valuable only as the nurse of ,astronomy1 he did not hesitate to reveal4 ,he wrote a work with a title of which the following is the best translation which ,i can give3 ,tertius interveniens1 or3 ,a ,warning to certain ,theologi1 ,medici1 ,philosophi1 that while they reasonably reject star-gazing superstition1 they do not throw away the kernel with the shell4#ca;,a #afaj4 ,in this he says1 ,you over-clever ,philosophers blame this ,daughter of ,astronomy more than is reasonable4 ,do you not know that she must maintain her mother with her charms8 ,how many men would be able to make ,astronomy their business1 if men did not cherish the hope to read the ,future in the skies8 ,note #ca;,a3 ,the ,german passage involves a curious image1 borrowed1 ,i suppose1 from some odd story3 dass sie mit billiger ,verwerfung des sternguckerischen ,aberglaubens das ,kind nicht mit dem ,bade ausschtten4 ,that they do not throw away the child along with the dirty water of his bath4 ,were the ,papal ,edicts against the ,copernican ,system repealed8 ,,admiral ,,smyth1 in his ,cycle of ,celestial ,objects1 vol4 i4 p4 #fe1 says--,at length1 in #ahah1 the voice of truth was so prevailing that ,pius ,,vii4 repealed the edicts against the ,copernican system1 and thus1 in the emphatic words of ,cardinal ,toriozzi1 'wiped off this scandal from the ,church4' ,a like story is referred to by ,sir ,francis ,palgrave1 in his entertaining and instructive fiction1 ,the ,merchant and the ,friar4 ,having made inquiry of persons most likely to be well informed on this subject1 ,i have not been able to learn that there is any further foundation for these statements than this3 ,in #ahah1 on the revisal of the ,index ,expurgatorius1 ,galileo's writings were1 after some opposition1 expunged from that ,catalogue4 ,monsignor ,marino ,marini1 an eminent ,roman ,prelate1 had addressed to the ,romana ,accademia di ,archeologia1 certain historico-critical ,memoirs1 which he published in #ahej1 with the title ,galileo e l',inquisizione4 ,in these1 he confirms the conclusion which1 ,i think1 almost #ece all persons who have studied the facts have arrived at2#cb;,a that ,galileo trifled with authority to which he professed to submit1 and was punished for obstinate contumacy1 not for heresy4 ,m4 ,marini renders full justice to ,galileo's ability1 and does not at all hesitate to regard his scientific attainments as among the glories of ,italy4 ,he quotes1 what ,galileo himself quoted1 an expression of ,cardinal ,baronius1 that the intention of the ,holy ,spirit was to teach how to go to heaven1 not how heaven goes4#cc;,a ,he shows that ,galileo pleaded 7p4 #fb7 that he had not held the ,copernican opinion after it had been intimated to him 7by ,bellarmine in #afaf71 that he was not to hold it2 and that his breach of promise in this respect was the cause of the proceedings against him4 ,note #cb;,a3 ,m4 ,marini 7p4 #bi7 mentions ,leibnitz1 ,guizot1 ,spittler1 ,eichhorn1 ,raumer1 ,ranke1 among the storici eterodossi who have at last done justice to the ,roman ,church4 ,note #cc;,a3 ,come si vada al ,cielo1 e non come vada il ,cielo4 ,those who admire ,galileo and regard him as a martyr because1 after escaping punishment by saying ,it does not move1 he forthwith said ,and yet it does move1 will perhaps be interested to know that the former answer was suggested to him by friends anxious for his safety4 ,niccolini writes to ,bali ,cioli 7,april #i1 #afcc7 that ,galileo continued to be so persuaded of the truth of his opinions that he was resolved 7some moments before his sentence7 to defend them stoutly2 but ,i 7continues ,niccolini7 exhorted him to make an end of this2 not to mind defending them2 and to submit himself to that which he sees that they may desire him to believe or to hold about this matter of the motion of the earth4 ,he was extremely afflicted4 ,but the ,inquisition was satisfied with his answers1 and required no more4#cd;,a ,note #cd;,a3 ,marini1 p4 #fa4 #ecf ,,book ,,vi4 ,,mechanics4 ,,chapter ,,iii4 ,,principles ,,and ,,problems4 ,significance of ,analytical ,mechanics4 ,,in the text1 page #cgb1 ,i have stated that ,lagrange1 near the end of his life1 expressed his sorrow that the methods of approximation employed in ,physical ,astronomy rested on arbitrary processes1 and not on any insight into the results of mechanical action4 ,from the recent biography of ,gauss1 the greatest physical mathematician of modern times1 we learn that he congratulated himself on having escaped this error4 ,he remarked#ce;,a that many of the most celebrated mathematicians1 ,euler very often1 ,lagrange sometimes1 had trusted too much to the symbolical calculation of their problems1 and would not have been able to give an account of the meaning of each successive step of their investigation4 ,he said that he himself1 on the other hand1 could assert that at every step which he took1 he always had the aim and purpose of his operations before his eyes without ever turning aside from the way4 ,the same1 he remarked1 might be said of ,newton4 ,note #ce;,a3 ,gauss1 ,zum ,gedchtniss1 von ,w4 ,sartorius v4 ,waltershausen1 p4 #hj4 ,engineering ,mechanics4 ,the principles of the science of ,mechanics were discovered by observations made upon bodies within the reach of men2 as we have seen in speaking of the discoveries of ,stevinus1 ,galileo1 and others1 up to the time of ,newton4 ,and when there arose the controversy about vis viva 7,chap4 v4 ,sect4 #b of this ,book72--namely1 whether the living force of a body is measured by the product of the weight into the #ecg velocity1 or of the weight into the square of the velocity2--still the examples taken were cases of action in machines and the like terrestrial objects4 ,but ,newton's discoveries identified celestial with terrestrial mechanics2 and from that time the mechanical problems of the heavens became more important and attractive to mathematicians than the problems about earthly machines4 ,and thus the generalizations of the problems1 principles1 and methods of the mathematical science of ,mechanics from this period are principally those which have reference to the motions of the heavenly bodies3 such as the ,problem of ,three ,bodies1 the ,principles of the ,conservation of ,areas1 and of the ,immovable ,plane1 the ,method of ,variation of ,parameters1 and the like 7,chap4 vi4 ,sect4 #g and #ad74 ,and the same is the case in the more recent progress of that subject1 in the hands of ,gauss1 ,bessel1 ,hansen1 and others4 ,but yet the science of ,mechanics as applied to terrestrial machines--,industrial ,mechanics1 as it has been termed--has made some steps which it may be worth while to notice1 even in a general history of science4 ,for the most part1 all the most general laws of mechanical action being already finally established1 in the way which we have had to narrate1 the determination of the results and conditions of any combination of materials and movements becomes really a mathematical deduction from known principles4 ,but such deductions may be made much more easy and much more luminous by the establishment of general terms and general propositions suited to their special conditions4 ,among these ,i may mention a new abstract term1 introduced because a general mechanical principle can be expressed by means of it1 which has lately been much employed by the mathematical engineers of ,france1 ,,mm4 ,poncelet1 ,navier1 ,morin1 c4 ,the abstract term is ,travail1 which has been translated ,laboring ,force2 and the principle which gives it its value1 and makes it useful in the solution of problems1 is this2--that the work done 7in overcoming resistance or producing any other effect7 is equal to the ,laboring ,force1 by whatever contrivances the force be applied4 ,this is not a new principle1 being in fact mathematically equivalent to the conservation of ,vis ,viva2 but it has been employed by the mathematicians of whom ,i have spoken with a fertility and simplicity which make it the mark of a new school of ,the ,mechanics of ,engineering4 ,the ,laboring ,force expended and the work done have been described by various terms1 as ,theoretical ,effect and ,practical ,effect1 and the like4 ,the usual term among ,english engineers for the work #ech which an ,engine usually does1 is ,duty2 but as this word naturally signifies what the engine ought to do1 rather than what it does1 we should at least distinguish between the ,theoretical and the ,actual ,duty4 ,the difference between the ,theoretical and ,actual ,duty of a ,machine arises from this3 that a portion of the ,laboring ,force is absorbed in producing effects1 that is1 in doing work which is not reckoned as ,duty3 for instance1 overcoming the resistance and waste of the machine itself4 ,and so long as this resistance and waste are not rightly estimated1 no correspondence can be established between the theoretical and the practical ,duty4 ,though much had been written previously upon the theory of the steam-engine1 the correspondence between the ,force expended and the ,work done was not clearly made out till ,comte ,de ,pambour published his ,treatise on ,locomotive ,engines in #ahce1 and his ,theory of the ,steam-,engine in #ahci4 ,strength of ,materials4 ,among the subjects which have specially engaged the attention of those who have applied the science of ,mechanics to practical matters1 is the strength of materials3 for example1 the strength of a horizontal beam to resist being broken by a weight pressing upon it4 ,this was one of the problems which ,galileo took up4 ,he was led to his study of it by a visit which he made to the arsenal and dockyards of ,venice1 and the conclusions which he drew were published in his ,dialogues1 in #afcc4 ,in his mode of regarding the problem1 he considers the section at which the beam breaks as the short arm of a bent lever which resists fracture1 and the part of the beam which is broken off as the longer arm of the lever1 the lever turning about the fracture as a hinge4 ,so far this is true2 and from this principle he obtained results which are also true as1 that the strength of a rectangular beam is proportional to the breadth multiplied into the square of the depth3--that a hollow beam is stronger than a solid beam of the same mass2 and the like4 ,but he erred in this1 that he supposed the hinge about which the breaking beam turns1 to be exactly at the unrent surface1 that surface resisting all change1 and the beam being rent all the way across4 ,whereas the fact is1 that the unrent surface yields to compression1 while the opposite surface is rent2 and the hinge about which the breaking beam turns is at an intermediate point1 where the extension #eci and rupture end1 and the compression and crushing begin3 a point which has been called the neutral axis4 ,this was pointed out by ,mariotte2 and the notion1 once suggested1 was so manifestly true that it was adopted by mathematicians in general4 ,james ,bernoulli1#cf;,a in #agje1 investigated the strength of beams on this view2 and several eminent mathematicians pursued the subject2 as ,varignon1 ,parent1 and ,bulfinger2 and at a later period1 ,dr4 ,robison in our own country4 ,note #cf;,a3 ,opera1 ii4 p4 #igf4 ,but along with the fracture of beams1 the mathematicians considered also another subject1 the flexure of beams1 which they undergo before they break1 in virtue of their elasticity4 ,what is the elastic curve8--the curve into which an elastic line forms itself under the pressure of a weight--is a problem which had been proposed by ,galileo1 and was fully solved1 as a mathematical problem1 by ,euler and others4 ,but beams in practice are not mere lines3 they are solids4 ,and their resistance to flexure1 and the amount of it1 depends upon the resistance of their internal parts to extension and compression1 and is different for different substances4 ,to measure these differences1 ,dr4 ,thomas ,young introduced the notion of the ,modulus of ,elasticity3#cg;,a meaning thereby a column of the substance of the same diameter1 such as would by its weight produce a compression equal to the whole length of the beam1 the rate of compression being supposed to continue the same throughout4 ,thus if a rod of any kind1 #ajj inches long1 were compressed #a inch by a weight #ajjj pounds1 the weight of its modulus of elasticity would be #ajj1jjj pounds4 ,this notion assumes ,hooke's law that the extension of a substance is as its tension2 and extends this law to compression also4 ,note #cg;,a3 ,lecture xiii4 ,the height of the modulus is the same for the same substance1 whatever its breadth and thickness may be2 for atmospheric air it is about five miles1 and for steel nearly #aejj miles4 ,there is this great advantage in introducing the definition of the ,modulus of ,elasticity1--that it applies equally to the flexure of a substance and to the minute vibrations which propagate sound1 and the like4 ,and the notion was applied so as to lead to curious and important results with regard to the power of beams to resist flexure1 not only when loaded transversely1 but when pressed in the direction of their length1 and in any oblique direction4 ,but in the fracture of beams1 the resistance to extension and to compression are not practically equal2 and it was necessary to determine #edj the difference of these two forces by experiments4 ,several persons pursued researches on this subject2 especially ,mr4 ,barlow1 of the ,royal ,military ,academy1#ch;,a who investigated the subject with great labor and skill1 so far as wood is concerned4 ,but the difference between the resistance to tension and to compression requires more special study in the case of iron2 and has been especially attended to in recent times1 in consequence of the vast increase in the number of iron structures1 and in particular1 railways4 ,it appears that wrought iron yields to compressive somewhat more easily than to tensile force1 while cast iron yields far more easily to tensile than to compressive strains4 ,in all cases the power of a beam to resist fracture resides mainly in the upper and the under side1 for there the tenacity of the material acts at the greatest leverage round the hinge of fracture4 ,hence the practice was introduced of making iron beams with a broad flange at the upper and another flange at the under side1 connected by a vertical plate or web1 of which the office was to keep the two flanges asunder4 ,mr4 ,hodgkinson made many valuable experiments1 on a large scale1 to determine the forms and properties of such beams4 ,note #ch;,a3 ,an ,essay on the ,strength and ,shape of ,timber4 #c;d edition1 #ahbf4 ,but though engineers were1 by such experiments and reasonings1 enabled to calculate the strength of a given iron beam1 and the dimensions of a beam which should bear a given load1 it would hardly have occurred to the boldest speculator1 a few years ago1 to predict that there might be constructed beams nearly #ejj feet long1 resting merely on their two extremities1 of which it could be known beforehand1 that they would sustain1 without bending or yielding in any perceptible degree1 the weight of a railroad train1 and the jar of its unchecked motion4 ,yet of such beams1 constructed beforehand with the most perfect confidence1 crowned with the most complete success1 is composed the great tubular bridge which that consummate engineer1 ,mr4 ,robert ,stephenson1 has thrown across the ,menai ,strait1 joining ,wales with the island of ,anglesey4 ,the upper and under surfaces of this quadrangular tube are the flanges of the beam1 and the two sides are the webs which connect them4 ,in planning this wonderful structure1 the point which required especial care was to make the upper surface strong enough to resist the compressive force which it has to sustain2 and this was done by constructing the upper part of the beam of a series of cells1 made of iron plate4 ,the application of the arch1 of the dome1 and of groined vaulting1 to the widest space over which they have ever been thrown1 #eda are achievements which have1 in the ages in which they occurred1 been received with great admiration and applause2 but in those cases the principle of the structure had been tried and verified for ages upon a smaller scale4 ,here not only was the space thus spanned wider than any ever spanned before1 but the principle of such a beam with a cellular structure of its parts1 was invented for this very purpose1 experimentally verified with care1 and applied with the most exact calculation of its results4 ,roofs--,arches--,vaults4 ,the calculations of the mechanical conditions of structures consisting of several beams1 as for instance1 the frames of roofs1 depends upon elementary principles of mechanics2 and was a subject of investigation at an early period of the science4 ,such frames may be regarded as assemblages of levers4 ,the parts of which they consist are rigid beams which sustain and convey force1 and ,ties which resist such force by their tension4 ,the former parts must be made rigid in the way just spoken of with regard to iron beams2 but ties may be rods merely4 ,the wide structures of many of the roofs of railway stations1 compared with the massive wooden roofs of ancient buildings1 may show us how boldly and how successfully this distinction has been carried out in modern times4 ,the investigation of the conditions and strength of structures consisting of wooden beams has been cultivated by ,mathematicians and ,engineers1 and is often entitled ,carpentry in our ,mechanical ,treatises4 ,in our own time1 ,dr4 ,robison and ,dr4 ,thomas ,young have been two of the most eminent mathematicians who have written upon this subject4 ,the properties of the simple machines have been known1 as we have narrated1 from the time of the ,ancient ,greeks4 ,but it is plain that such machines are prevented from producing their full effect by various causes4 ,among the rest1 the rubbing of one part of the machine upon another produces an obstacle to the effectiveness of a machine3 for instance1 the rubbing of the axle of a wheel in the hole in which it rests1 the rubbing of a screw against the sides of its hollow screw2 the rubbing of a wedge against the sides of its notch2 the rubbing of a cord against its pulley4 ,in all these cases1 the effect of the machine to produce motion is diminished by the friction4 ,and this ,friction may be measured and its effects calculated2 and thus we have a new branch of mechanics1 which has been much cultivated4 #edb ,among the effects of friction1 we may notice the standing of a stone arch4 ,for each of the vaulting stones of an arch is a truncated wedge2 and though a collection of such stones might be so proportioned in their weights as to balance exactly1 yet this balance would be a tottering equilibrium1 which the slightest shock would throw down1 and which would not practically subsist4 ,but the friction of the vaulting stones against one another prevents this instability from being a practical inconvenience2 and makes an equilibrated arch to be an arch strong for practical purposes4 ,the ,theory of ,arches is a portion of ,mechanics which has been much cultivated1 and which has led to conclusions of practical use1 as well as of theoretical beauty4 ,i have already spoken of the invention of the ,arch1 the ,dome1 and ,groined ,vaulting1 as marked steps in building4 ,in all these cases the invention was devised by practical builders2 and mechanical theory1 though it can afterwards justify these structures1 did not originally suggest them4 ,they are not part of the result1 nor even of the application of theory1 but only of its exemplification4 ,the authors of all these inventions are unknown2 and the inventions themselves may be regarded as a part of the ,prelude of the science of mechanics1 because they indicate that the ideas of mechanical pressure and support1 in various forms1 are acquiring clearness and fixity4 ,in this point of view1 ,i spoke 7,book iv4 chap4 v4 sect4 #e7 of the ,architecture of the ,middle ,ages as indicating a progress of thought which led men towards the formation of ,statics as a science4 ,as particular instances of the operation of such ideas1 we have the ,flying ,buttresses which support stone vaults2 and especially1 as already noted1 the various contrivances by which stone vaults are made to intersect one another1 so as to cover a complex pillared space below with ,groined ,vaulting4 ,this invention1 executed as it was by the builders of the twelfth and succeeding centuries1 is the most remarkable advance in the mechanics of building1 after the invention of the ,arch itself4 ,it is curious that it has been the fortune of our times1 among its many inventions1 to have produced one in this department1 of which we may say that it is the most remarkable step in the mechanics of arches which has been made since the introduction of pointed groined vaults4 ,i speak of what are called ,skew ,arches1 in which the courses of stone or brick of which the bridge is built run obliquely to the walls of the bridge4 ,such bridges have become very common in the works of railroads2 for they save space and material1 and the #edc invention once made1 the cost of the ingenuity is nothing4 ,of course1 the mechanical principles involved in such structures are obvious to the mathematician1 when the problem has been practically solved4 ,and in this case1 as in the previous cardinal inventions in structure1 though the event has taken place within a few years1 no single person1 so far as ,i am aware1 can be named as the inventor4#ci;,a ,note #ci;,a3 ,since this was written1 ,i have been referred to ,rees's ,cyclopdia1 ,article ,oblique ,arches1 where this invention is correctly explained1 and is claimed for an engineer named ,chapman4 ,it is there said1 that the first arch of this kind was erected in #aghg at ,naas1 near ,kildare in ,ireland4 #edd ,,book ,,vii4 ,,physical ,,astronomy4 ,,chapter ,i4 ,,prelude ,,to ,,newton4 ,the ,ancients4 ,,expressions in ancient writers which may be interpreted as indicating a notion of gravitation in the ,newtonian sense1 no doubt occur4 ,but such a notion1 we may be sure1 must have been in the highest degree obscure1 wavering1 and partial4 ,i have mentioned 7,book i4 ,chap4 #c7 an author who has fancied that he traces in the works of the ancients the origin of most of the vaunted discoveries of the moderns4 ,but to ascribe much importance to such expressions would be to give a false representation of the real progress of science4 ,yet some of ,newton's followers put forward these passages as well deserving notice2 and ,newton himself appears to have had some pleasure in citing such expressions2 probably with the feeling that they relieved him of some of the odium which1 he seems to have apprehended1 hung over new discoveries4 ,the ,preface to the ,principia1 begins by quoting#dj;,a the authority of the ancients1 as well as the moderns1 in favor of applying the science of ,mechanics to ,natural ,philosophy4 ,in the ,preface to ,david ,gregory's ,astronomi ,physic et ,geometric ,elementa1 published in #agjb1 is a large array of names of ancient authors1 and of quotations1 to prove the early and wide diffusion of the doctrine of the gravity of the ,heavenly ,bodies4 ,and it appears to be now made out1 that this collection of ancient authorities #ede was supplied to ,gregory by ,newton himself4 ,the late ,professor ,rigaud1 in his ,historical ,essay on the ,first ,publication of ,sir ,isaac ,newton's ,principia1 says 7pp4 #hj and #aja7 that having been allowed to examine ,gregory's papers1 he found that the quotations given by him in his ,preface are copied or abridged from notes which ,newton had supplied to him in his own handwriting4 ,some of the most noticeable of the quotations are those taken from ,plutarch's ,dialogue on the ,face which appears in the ,moon's ,disk3 it is there said1 for example1 by one of the speakers1 that the ,moon is perhaps prevented from falling to the earth by the rapidity of her revolution round it2 as a stone whirled in a sling keeps it stretched4 ,lucretius also is quoted1 as teaching that all bodies would descend with an equal celerity in a vacuum3 ,omnia quapropter debent per inane quietum que ponderibus non quis concita ferri4 ,lib4 ii4 v4 #bch4 ,note #dj;,a3 ,cum veteres ,mechanicam 7uti author est ,pappus71 in rerum ,naturalium investigatione maximi fecerint1 et recentiores1 missis formis substantialibus et qualitatibus occultis1 ,phenonmena ,natur ad leges mathematicas revocare aggressa sunt2 visum est in hoc ,tractatu ,mathesin excolere quatenus ea ad ,philosophiam spectat4 ,it is asserted in ,gregory's ,preface that ,pythagoras was not unacquainted with the important law of gravity1 the inverse squares of the distances from the centre4 ,for1 it is argued1 the seven strings of ,apollo's lyre mean the seven planets2 and the proportions of the notes of strings are reciprocally as the inverse squares of the weights which stretch them4 ,i have attempted1 throughout this work1 to trace the progress of the discovery of the great truths which constitute real science1 in a more precise manner than that which these interpretations of ancient authors exemplify4 ,jeremiah ,horrox4 ,in describing the ,prelude to the ,epoch of ,newton1 ,i have spoken 7p4 #cie7 of a group of philosophers in ,england who began1 in the first half of the seventeenth century1 to knock at the door where ,truth was to be found1 although it was left for ,newton to force it open2 and ,i have there noticed the influence of the civil wars on the progress of philosophical studies4 ,to the persons thus tending towards the true physical theory of the solar system1 ,i ought to have added ,jeremy ,horrox1 whom ,i have mentioned in a former part 7,book v4 chap4 #e7 as one of the earliest admirers of ,kepler's discoveries4 ,he died at the early age of twenty-two1 having been the first person who ever saw ,venus pass across the disk of the ,sun according to astronomical prediction1 which took place in #afci4 ,his ,venus in sole visa1 #edf in which this is described1 did not appear till #affa1 when it was published by ,hevelius of ,dantzic4 ,some of his papers were destroyed by the soldiers in the ,english civil wars2 and his remaining works were finally published by ,wallis1 in #afgc4 ,the passage to which ,i here specially wish to refer is contained in a letter to his astronomical ally1 ,william ,crabtree1 dated #afch4 ,he appears to have been asked by his friend to suggest some cause for the motion of the aphelion of a planet2 and in reply1 he uses an experimental illustration which was afterwards employed by ,hooke in #afff4 ,a ball at the end of a string is made to swing so that it describes an oval4 ,this contrivance ,hooke employed to show the way in which an orbit results from the combination of a projectile motion with a central force4 ,but the oval does not keep its axis constantly in the same position4 ,the apsides1 as ,horrox remarked1 move in the same direction as the pendulum1 though much slower4 ,and it is true1 that this experiment does illustrate1 in a general way1 the cause of the motion of the aphelia of the ,planetary ,orbits2 although the form of the orbit is different in the experiment and in the solar system2 being an ellipse with the centre of force in the centre of the ellipse1 in the former case1 and an ellipse with the centre of force in the focus1 in the latter case4 ,these two forms of orbits correspond to a central force varying directly as the distance1 and a central force varying inversely as the square of the distance2 as ,newton proved in the ,principia4 ,but the illustration appears to show that ,horrox pretty clearly saw how an orbit arose from a central force4 ,so far1 and no further1 ,newton's contemporaries could get2 and then he had to help them onwards by showing what was the law of the force1 and what larger truths were now attainable4 ,newton's ,discovery of ,gravitation4 ,page #djb4 ,as ,i have already remarked1 men have a willingness to believe that great discoveries are governed by casual coincidences1 and accompanied by sudden revolutions of feeling4 ,newton had entertained the thought of the moon being retained in her orbit by gravitation as early as #affe or #afff4 ,he resumed the subject and worked the thought out into a system in #afhd and #e4 ,what induced him to return to the question8 ,what led to his success on this last occasion8 ,with what feelings was the success attended8 ,it is easy to make an imaginary connection of facts4 ,his optical discoveries had recommended him to the ,royal ,society1 and he was now a member4 ,he #edg there learned the accurate measurement of the ,earth by ,picard1 differing very much from the estimation by which he had made his calculation in #afff2 and he thought his conjecture now more likely to be just4#da;,a ,m4 ,biot gives his assent to this guess4#db;,a ,the ,english translation of ,m4 ,biot's biography#dc;,a converts the guess into an assertion4 ,but1 says ,professor ,rigaud1#dd;,a ,picard's measurement of the ,earth was well known to the ,fellows of the ,royal ,society as early as #afge1 there being an account of the results of it given in the ,philosophical ,transactions for that year4 ,moreover1 ,norwood1 in his ,seaman's ,practice1 dated #afcf1 had given a much more exact measure than ,newton employed in #afff4 ,but ,norwood1 says ,voltaire1 had been buried in oblivion by the civil wars4 ,no1 again says the exact and truth-loving ,professor ,rigaud1 ,norwood was in communication with the ,royal ,society in #affg and #affh4 ,so these guesses at the accident which made the apple of #affe germinate in #afhd1 are to be carefully distinguished from history4 ,note #da;,a3 ,robison's ,mechanical ,philosophy1 vol4 iii4 p4 #id4 7,art4 #aie47 ,note #db;,a3 ,biographie ,universelle4 ,note #dc;,a3 ,library of ,useful ,knowledge4 ,note #dd;,a3 ,historical ,essay on the ,first ,publication of the ,principia 7#ahch74 ,but with what feelings did ,newton attain to his success8 ,here again we have1 ,i fear1 nothing better than conjecture4 ,he went home1 took out his old papers1 and resumed his calculations4 ,as they drew near to a close1 he was so much agitated that he was obliged to desire a friend to finish them4 ,his former conjecture was now found to agree with the phnomena with the utmost precision4#de;,a ,this conjectural story has been called a tradition2 but he who relates it does not call it so4 ,every one must decide1 says ,professor ,rigaud1 from his view of ,newton's character1 how far he thinks it consistent with this statement4 ,is it likely that ,newton1 so calm and so indifferent to fame as he generally showed himself1 should be thus agitated on such an occasion8 ,no1 says ,sir ,david ,brewster2 it is not supported by what we know of ,newton's character4#df;,a ,to this we may assent2 and this conjectural incident we must therefore1 ,i conceive1 separate from history4 ,i had incautiously admitted it into the text of the first ,edition4 ,note #de;,a3 ,robison1 ibid4 ,note #df;,a3 ,life of ,newton1 vol4 i4 p4 #bib4 ,newton appears to have discovered the method of demonstrating that a body might describe an ellipse when acted upon by a force residing in the focus1 and varying inversely as the square of the distance1 in #affi1 upon occasion of his correspondence with ,hooke4 ,in #afhd1 #edh at ,halley's request1 he returned to the subject2 and in ,february1 #afhe there was inserted in the ,register of the ,royal ,society a paper of ,newton's 7,isaaci ,newtoni ,propositiones de ,motu71 which contained some of the principal propositions of the first two ,books of the ,principia4 ,this paper1 however1 does not contain the proposition ,lunam gravitare in ,terram1 nor any of the propositions of the ,third ,book4 ,,chapter ,,iii4 ,,the ,,principia4 ,sect4 #b4--,reception of the ,principia4 ,,lord ,,brougham has very recently 7,analytical ,view of ,sir ,isaac ,newton's ,principia1 #ahee7 shown a strong disposition still to maintain1 what he says has frequently been alleged1 that the reception of the work was not1 even in this country1 such as might have been expected4 ,he says1 in explanation of the facts which ,i have adduced1 showing the high estimation in which ,newton was held immediately after the publication of the ,principia1 that ,newton's previous fame was great by former discoveries4 ,this is true2 but the effect of this was precisely what was most honorable to ,newton's countrymen1 that they received with immediate acclamations this new and greater discovery4 ,lord ,brougham adds1 after its appearance the ,principia was more admired than studied2 which is probably true of the ,principia still1 and of all great works of like novelty and difficulty at all times4 ,but1 says ,lord ,brougham1 there is no getting over the inference on this head which arises from the dates of the two first editions4 ,there elapsed an interval of no less than twenty-seven years between them2 and although ,cotes in his ,preface speaks of the copies having become scarce and in very great demand when the second edition appeared in #agac1 yet had this urgent demand been of many years' continuance1 the reprinting could never have been so long delayed4 ,but ,lord ,brougham might have learnt from ,sir ,david ,brewster's ,life of ,newton 7vol4 i4 p4 #cab71 which he extols so emphatically1 that already in #afia 7only four years after the publication71 a copy of the ,principia could hardly be procured1 and that even at that #edi time an improved edition was in contemplation2 that ,newton had been pressed by his friends to undertake it1 and had refused4 ,when ,bentley had induced ,newton to consent that a new edition should be printed1 he announces his success with obvious exultation to ,cotes1 who was to superintend the work4 ,and in the mean time the ,astronomy of ,david ,gregory1 published in #agjb1 showed in every page how familiar the ,newtonian doctrines were to ,english philosophers1 and tended to make them more so1 as the sermons of ,bentley himself had done in #afib4 ,newton's ,cambridge contemporaries were among those who took a part in bringing the ,principia before the world4 ,the manuscript draft of it was conveyed to the ,royal ,society 7,april #bh1 #afhf7 by ,dr4 ,vincent1 ,fellow of ,clare ,hall1 who was the tutor of ,whiston1 ,newton's deputy in his professorship2 and he1 in presenting the work1 spoke of the novelty and dignity of the subject4 ,there exists in the library of the ,university of ,cambridge a manuscript containing the early ,propositions of the ,principia as far as ,prop4 xxxiii4 7which is a part of ,section vii41 about ,falling ,bodies74 ,this appears to have been a transcript of ,newton's ,lectures1 delivered as ,lucasian ,professor3 it is dated ,october1 #afhd4 ,is ,gravitation proportional to ,quantity of ,matter8 ,it was a portion of ,newton's assertion in his great discovery1 that all the bodies of the universe attract each other with forces which are as the quantity of matter in each3 that is1 for instance1 the sun attracts the satellites of any planet just as much as he attracts the planet itself1 in proportion to the quantity of matter in each2 and the planets attract one another just as much as they attract the sun1 according to the quantity of matter4 ,to prove this part of the law exactly is a matter which requires careful experiments2 and though proved experimentally by ,newton1 has been considered in our time worthy of re-examination by the great astronomer ,bessel4 ,there was some ground for doubt2 for the mass of ,jupiter1 as deduced from the perturbations of ,saturn1 was only #a_/ajgj of the mass of the sun2 the mass of the same planet as deduced from the perturbations of ,juno and ,pallas was #a_/ajde of that of the ,sun4 ,if this difference were to be confirmed by accurate observations and calculations1 it would follow that the attractive power exercised by ,jupiter upon the minor planets was greater than that exercised upon #eej ,saturn4 ,and in the same way1 if the attraction of the ,earth had any specific relation to different kinds of matter1 the time of oscillation of a pendulum of equal length composed wholly or in part of the two substances would be different4 ,if1 for instance1 it were more intense for magnetized iron than for stone1 the iron pendulum would oscillate more quickly4 ,bessel showed#dg;,a that it was possible to assume hypothetically a constitution of the sun1 planets1 and their appendages1 such that the attraction of the ,sun on the ,planets and ,satellites should be proportional to the quantity of matter in each2 but that the attraction of the ,planets on one another would not be on the same scale4 ,note #dg;,a3 ,berlin ,mem4 #ahbd4 ,newton had made experiments 7described in the ,principia1 ,book iii41 ,prop4 vi47 by which it was shown that there could be no considerable or palpable amount of such specific difference among terrestrial bodies1 but his experiments could not be regarded as exact enough for the requirements of modern science4 ,bessel instituted a laborious series of experiments 7presented to the ,berlin ,academy in #ahcb7 which completely disproved the conjecture of such a difference2 every substance examined having given exactly the same coefficient of gravitating intensity as compared with inertia4 ,among the substances examined were metallic and stony masses of meteoric origin1 which might be supposed1 if any bodies could1 to come from other parts of the solar system4 ,,chapter ,,iv4 ,,verification ,,and ,,completion ,,of ,,the ,,newtonian ,,theory4 ,tables of the ,moon and ,planets4 ,,the ,newtonian discovery of ,universal ,gravitation1 so remarkable in other respects1 is also remarkable as exemplifying the immense extent to which the verification of a great truth may be carried1 the amount of human labor which may be requisite to do it justice1 and the striking extension of human knowledge to which it may lead4 ,i have said that it is remarked as a beauty in the first fixation of a theory that its measures or elements are established by means of a few #eea data2 but that its excellence when established is in the number of observations which it explains4 ,the multiplicity of observations which are explained by astronomy1 and which are made because astronomy explains them1 is immense1 as ,i have noted in the text4 ,and the multitude of observations thus made is employed for the purpose of correcting the first adopted elements of the theory4 ,i have mentioned some of the examples of this process3 ,i might mention many others in order to continue the history of this part of ,astronomy up to the present time4 ,but ,i will notice only those which seem to me the most remarkable4 ,in #ahab1 ,burckhardt's ,tables de la ,lune were published by the ,french ,bureau des ,longitudes4 ,a comparison of these and ,burg's with a considerable number of observations1 gave #i-ajjths of a second as the mean error of the former in the ,moon's longitude1 while the mean error of ,burg's was #ah-ajjths4 ,the preference was therefore accorded to ,burckhardt's4 ,yet the ,lunar ,tables were still as much as thirty seconds wrong in single observations4 ,this circumstance1 and ,laplace's expressed wish1 induced the ,french ,academy to offer a prize for a complete and purely theoretical determination of the ,lunar path1 instead of determinations resting1 as hitherto1 partly upon theory and partly upon observations4 ,in #ahbj1 two prize essays appeared1 the one by ,damoiseau1 the other by ,plana and ,carlini4 ,and some years afterwards 7in #ahbd1 and again in #ahbh71 ,damoiseau published ,tables de la ,lune formes sur la seule ,thorie d',attraction4 ,these agree very closely with observation4 ,that we may form some notion of the complexity of the problem1 ,i may state that the longitude of the ,moon is in these ,tables affected by no fewer than forty-seven equations2 and the other quantities which determine her place are subject to inequalities not much less in number4 ,still ,i had to state in the second ,edition1 published in #ahdg1 that there remained an unexplained discordance between theory and observation in the motions of the ,moon2 an inequality of long period as it seemed1 which the theory did not give4 ,a careful examination of a long series of the best observations of the ,moon1 compared throughout with the theory in its most perfect form1 would afford the means both of correcting the numerical elements of the theory1 and of detecting the nature1 and perhaps the law1 of any still remaining discrepancies4 ,such a work1 however1 required vast labor1 as well as great skill and profound mathematical knowledge4 #eeb ,mr4 ,airy undertook the task2 employing for that purpose1 the ,observations of the ,moon made at ,greenwich from #agej to #ahcj4 ,above #hjjj observed places of the ,moon were compared with theory by the computation of the same number of places1 each separately and independently calculated from ,plana's ,formul4 ,a body of calculators 7sometimes sixteen71 at the expense of the ,british ,government1 was employed for about eight years in this work4 ,when we take this in conjunction with the labor which the observations themselves imply1 it may serve to show on what a scale the verification of the ,newtonian theory has been conducted4 ,the first results of this labor were published in two quarto volumes2 the final deductions as to correction of elements1 c41 were given in the ,memoirs of the ,astronomical ,society in #ahdh4dh;,a ,note #dh;,a3 ,the total expense of computers1 to the end of reading the proof-sheets1 was #dcjjl4 ,mr4 ,airy's estimate of days' works made before beginning1 for the heavy part of calculations only1 was thirty-six years of one computer4 ,this was somewhat exceeded1 but not very greatly1 in that part4 ,even while the calculations were going on1 it became apparent that there were some differences between the observed places of the ,moon1 and the theory so far as it had then been developed4 ,m4 ,hansen1 an eminent ,german mathematician who had devised new and powerful methods for the mathematical determination of the results of the law of gravitation1 was thus led to explore still further the motions of the ,moon in pursuance of this law4 ,the result was that he found there must exist two lunar inequalities1 hitherto not known2 the one of #bgc1 and the other of #bci years1 the coefficients of which are respectively #bg and #bc seconds4 ,both these originate in the attraction of ,venus2 one of them being connected with the long inequality in the ,solar ,tables1 of which ,mr4 ,airy had already proved the existence1 as stated in ,chap4 vi4 ,sect4 #f of this ,book4 ,these inequalities fell in with the discrepancies between the actual observations and the previously calculated ,tables1 which ,mr4 ,airy had discovered4 ,and again1 shortly afterwards1 ,m4 ,hansen found that there resulted from the theory two other new equations of the ,moon2 one in latitude and one in longitude1 agreeing with two which were found by ,mr4 ,airy in deducing from the observations the correction of the elements of the ,lunar ,tables4 ,and again1 a little later1 there was detected by these mathematicians a theoretical correction for the #eec motion of the ,node of the ,moon's orbit1 coinciding exactly with one which had been found to appear in the observations4 ,nothing can more strikingly exhibit the confirmation which increased scrutiny brings to light between the ,newtonian theory on the one hand1 and the celestial motions on the other4 ,we have here a very large mass of the best observations which have ever been made1 systematically examined1 with immense labor1 and with the set purpose of correcting at once all the elements of the ,lunar ,tables4 ,the corrections of the elements thus deduced imply of course some error in the theory as previously developed4 ,but at the same time1 and with the like determination thoroughly to explore the subject1 the theory is again pressed to yield its most complete results1 by the invention of new and powerful mathematical methods2 and the event is1 that residual errors of the old ,tables1 several in number1 following the most diverse laws1 occurring in several detached parts1 agree with the residual results of the ,theory thus newly extracted from it4 ,and thus every additional exactness of scrutiny into the celestial motions on the one hand and the ,newtonian theory on the other1 has ended1 sooner or later1 in showing the exactness of their coincidence4 ,the comparison of the theory with observation in the case of the motions of the ,planets1 the motion of each being disturbed by the attraction of all the others1 is a subject in some respects still more complicated and laborious4 ,this work also was undertaken by the same indefatigable astronomer2 and here also his materials belonged to the same period as before2 being the admirable observations made at ,greenwich from #agej to #ahcj1 during the time that ,bradley1 ,maskelyne1 and ,pond were the ,astronomers ,royal4#di;,a ,these ,planetary observations were deduced1 and the observed places were compared with the tabular places3 with ,lindenau's ,tables of ,mercury1 ,venus1 and ,mars2 and with ,bouvard's ,tables of ,jupiter1 ,saturn1 and ,uranus2 and thus1 while the received theory and its elements were confirmed1 the means of testing any improvement which may hereafter be proposed1 either in the form of the theoretical results or in the constant elements which they involved1 was placed within the reach of the #eed astronomers of all future time4 ,the work appeared in #ahde2 the expense of the compilations and the publication being defrayed by the ,british ,government4 ,note #di;,a3 ,the observations of stars made by ,bradley1 who preceded ,maskelyne at ,greenwich1 had already been discussed by ,bessel1 a great ,german astronomer2 and the results published in #ahah1 with a title that well showed the estimation in which he held those materials3 ,fundamenta ,astronomi pro anno #agge1 deducta ex ,ohservationibus viri incomparabilis ,james ,bradley in specula ,astronomica ,grenovicensi per annos #agej-agfb institutis4 ,the ,discovery of ,neptune4 ,the theory of gravitation was destined to receive a confirmation more striking than any which could arise from any explanation1 however perfect1 given by the motions of a known planet2 namely1 in revealing the existence of an unknown planet1 disclosed to astronomers by the attraction which it exerted upon a known one4 ,the story of the discovery of ,neptune by the calculations of ,mr4 ,adams and ,m4 ,le ,verrier was partly told in the former edition of this ,history4 ,i had there stated 7vol4 ii4 p4 #cjf7 that a deviation of observation from the theory occurs at the very extremity of the solar system1 and that its existence appears to be beyond doubt4 ,uranus does not conform to the ,tables calculated for him on the theory of gravitation4 ,in #ahba1 ,bouvard said in the ,preface to the ,tables of this ,planet1 the formation of these ,tables offers to us this alternative1 that we cannot satisfy modern observations to the requisite degree of precision without making our ,tables deviate from the ancient observations4 ,but when we have done this1 there is still a discordance between the ,tables and the more modern observations1 and this discordance goes on increasing4 ,at present the ,tables make the ,planet come upon the meridian about eight seconds later than he really does4 ,this discrepancy has turned the thoughts of astronomers to the effects which would result from a planet external to ,uranus4 ,it appears that the observed motion would be explained by applying a planet at twice the distance of ,uranus from the ,sun to exercise a disturbing force1 and it is found that the present longitude of this disturbing body must be about #cbe degrees4 ,i added1 ,m4 ,le ,verrier 7,comptes ,rendus1 ,jan4 #a1 #ahdf7 and1 as ,i am informed by the ,astronomer ,royal1 ,mr4 ,adams1 of ,st4 ,john's ,college1 ,cambridge1 have both arrived independently at this result4 ,to this ,edition ,i added a ,postscript1 dated1 ,nov4 #g1 #ahdf1 in which ,i said3 ,the planet exterior to ,uranus1 of which the existence was inferred by ,m4 ,le ,verrier and ,mr4 ,adams from the motions of ,uranus 7vol4 ii4 ,note 7,l4771 has since been discovered4 ,this confirmation of calculations founded upon the doctrine of universal gravitation1 may be looked upon as the most remarkable event of the kind since the return of ,halley's comet in #ageg and in some respects1 as a more striking event #eee even than that2 inasmuch as the new planet had never been seen at all1 and was discovered by mathematicians entirely by their feeling of its influence1 which they perceived through the organ of mathematical calculation4 ,there can be no doubt that to ,m4 ,le ,verrier belongs the glory of having first published a prediction of the place and appearance of the new planet1 and of having thus occasioned its discovery by astronomical observers4 ,m4 ,le ,verrier's first prediction was published in the ,comptes ,rendus de l',acad4 des ,sciences1 for ,june #a1 #ahdf 7not ,jan4 #a1 as erroneously printed in my ,note74 ,a subsequent paper on the subject was read ,aug4 #ca4 ,the planet was seen by ,m4 ,galle1 at the ,observatory of ,berlin1 on ,september #bc1 on which day he had received an express application from ,m4 ,le ,verrier1 recommending him to endeavor to recognize the stranger by its having a visible disk4 ,professor ,challis1 at the ,observatory of ,cambridge1 was looking out for the new planet from ,july #bi1 and saw it on ,august #d1 and again on ,august #ab1 but without recognizing it1 in consequence of his plan of not comparing his observations till he had accumulated a greater number of them4 ,on ,sept4 #bi1 having read for the first time ,m4 ,le ,verrier's second paper1 he altered his plan1 and paid attention to the physical appearance rather than the position of the star4 ,on that very evening1 not having then heard of ,m4 ,galle's discovery1 he singled out the star by its seeming to have a disk4 ,m4 ,le ,verrier's mode of discussing the circumstances of ,uranus's motion1 and inferring the new planet from these circumstances1 is in the highest degree sagacious and masterly4 ,justice to him cannot require that the contemporaneous1 though unpublished1 labors of ,mr4 ,adams1 of ,st ,john's ,college1 ,cambridge1 should not also be recorded4 ,mr4 ,adams made his first calculations to account for the anomalies in the motion of ,uranus1 on the hypothesis of a more distant planet1 in #ahdc4 ,at first he had not taken into account the earlier ,greenwich observations2 but these were supplied to him by the ,astronomer ,royal1 in #ahdd4 ,in ,september1 #ahde1 ,mr4 ,adams communicated to ,professor ,challis values of the elements of the supposed disturbing body2 namely1 its mean distance1 mean longitude at a given epoch1 longitude of perihelion1 eccentricity of orbit1 and mass4 ,in the next month1 he communicated to the ,astronomer ,royal values of the same elements1 somewhat corrected4 ,the note 7,l471 vol4 ii41 of the present work 7#b;d ,ed471 in which the names of ,,mm4 ,le ,verrier and ,adams are mentioned in conjunction1 was in the press in ,august1 #ahdf1 a #eef month before the planet was seen4 ,as ,i have stated in the text1 ,mr4 ,adams and ,m4 ,le ,verrier assigned to the unseen planet nearly the same position2 they also assigned to it nearly the same mass2 namely1 #b times the mass of ,uranus4 ,and hence1 supposing the density to be not greater than that of ,uranus1 it followed that the visible diameter would be about #c1 an apparent magnitude not much smaller than ,uranus himself4 ,m4 ,le ,verrier has mentioned for the new planet the name ,neptunus2 and probably1 deference to his authority as its discoverer1 will obtain general currency for this name4 ,mr4 ,airy has given a very complete history of the circumstances attending the discovery of ,neptune1 in the ,memoirs of the ,astronomical ,society 7read ,november #ac1 #ahdf74 ,in this he shows that the probability of some disturbing body beyond ,uranus had suggested itself to ,m4 ,a4 ,bouvard and ,mr4 ,hussey as early as #ahcd4 ,mr4 ,airy himself then thought that the time was not ripe for making out the nature of any external action on the planets4 ,but ,mr4 ,adams soon afterwards proceeded to work at the problem4 ,as early as #ahda 7as he himself informs me7 he conjectured the existence of a planet exterior to ,uranus1 and recorded in a memorandum his design of examining its effect2 but deferred the calculations till he had completed his preparations for the ,university examination which he was to undergo in ,january1 #ahdc1 in order to receive the ,degree of ,bachelor of ,arts4 ,he was the ,senior ,wrangler of that occasion1 and soon afterwards proceeded to carry his design into effect2 applying to the ,astronomer ,royal for recorded observations which might aid him in his task4 ,on one of the last days of ,october1 #ahde1 ,mr4 ,adams went to the ,observatory at ,greenwich2 and finding the ,astronomer ,royal abroad1 he left there a paper containing the elements of the extra-,uranian ,planet3 the longitude was in this paper stated as #cbc degrees4 ,it was1 as we have seen1 in ,june1 #ahdf1 that ,m4 ,le ,verrier's ,memoir appeared1 in which he assigned to the disturbing body a longitude of #cbe degrees4 ,the coincidence was striking4 ,i cannot sufficiently express1 says ,mr4 ,airy1 the feeling of delight and satisfaction which ,i received from the ,memoir of ,m4 ,le ,verrier4 ,this feeling communicated itself to others4 ,sir ,john ,herschel said in ,september1 #ahdf1 at a meeting of the ,british ,association at ,southampton1 ,we see it 7the probable new planet7 as ,columbus saw ,america from the shores of ,spain4 ,its movements have been felt1 trembling along the far-reaching line of our analysis1 with a certainty hardly inferior to that of ocular demonstration4 #eeg ,in truth1 at the moment when this was uttered1 the new ,planet had already been seen by ,professor ,challis2 for1 as we have said1 he had seen it in the early part of ,august4 ,he had included it in the net which he had cast among the stars for this very purpose2 but employing a slow and cautious process1 he had deferred for a time that examination of his capture which would have enabled him to detect the object sought4 ,as soon as he received ,m4 ,le ,verrier's paper of ,august #ca on ,september #bi1 he was so much impressed with the sagacity and clearness of the limitations of the field of observation there laid down1 that he instantly changed his plan of observation1 and noted the planet1 as an object having a visible disk1 on the evening of the same day4 ,in this manner the theory of gravitation predicted and produced the discovery4 ,thus to predict unknown facts found afterwards to be true1 is1 as ,i have said1 a confirmation of a theory which in impressiveness and value goes beyond any explanation of known facts4 ,it is a confirmation which has only occurred a few times in the history of science2 and in the case only of the most refined and complete theories1 such as those of ,astronomy and ,optics4 ,the mathematical skill which was requisite in order to arrive at such a discovery1 may in some measure be judged of by the account which we have had to give of the previous mathematical progress of the theory of gravitation4 ,it there appeared that the lives of many of the most acute1 clear-sighted1 and laborious of mankind1 had been employed for generations in solving the problem4 ,given the planetary bodies1 to find their mutual perturbations3 but here we have the inverse problem--,given the perturbations1 to find the planets4#ej;,a ,note #ej;,a3 ,this may be called the inverse problem with reference to the older and more familiar problem2 but we may remark that the usual phraseology of the ,problem of ,central ,forces differs from this analogy4 ,in ,newton's ,principia1 the earlier ,sections1 in which the motion is given to find the force1 are spoken of as containing the ,direct ,problem of ,central ,forces3 the ,eighth ,section of the ,first ,book1 where the ,force is given to find the orbit1 is spoken of as containing the ,inverse ,problem of ,central ,forces4 ,the ,minor ,planets4 ,the discovery of the ,minor ,planets which revolve between the orbits of ,mars and ,jupiter was not a consequence or confirmation of the ,newtonian theory4 ,that theory gives no reason for the distance of #eeh the ,planets from the ,sun2 nor does any theory yet devised give such reason4 ,but an empirical formula proposed by the ,astronomer ,bode of ,berlin1 gives a law of these distances 7,bode's ,law71 which1 to make it coherent1 requires a planet between ,mars and ,jupiter4 ,with such an addition1 the distance of ,mercury1 ,venus1 ,earth1 ,mars1 the ,missing ,planet1 ,jupiter1 ,saturn1 and ,uranus1 are nearly as the numbers #d1 #g1 #aj1 #af1 #bh1 #eb1 #ajj1 #aif1 in which the excesses of each number above the preceding are the series #c1 #c1 #f1 #ab1 #bd1 #dh1 #if4 ,on the strength of this law the ,germans wrote on the long-expected ,planet1 and formed themselves into associations for the discovery of it4 ,not only did this law stimulate the inquiries for the ,missing ,planet1 and thus lead to the discovery of the ,minor ,planets1 but it had also a share in the discovery of ,neptune4 ,according to the law1 a planet beyond ,uranus may be expected to be at the distance represented by #chh4 ,mr4 ,adams and ,m4 ,le ,verrier both of them began by assuming a distance of nearly this magnitude for the ,planet which they sought2 that is1 a distance more than #ch times the earth's distance4 ,it was found afterwards that the distance of ,neptune is only #cj times that of the earth2 yet the assumption was of essential use in obtaining the result and ,mr4 ,airy remarks that the history of the discovery shows the importance of using any received theory as far as it will go1 even if the theory can claim no higher merit than that of being plausible4#ea;,a ,note #ea;,a3 ,account of the ,discovery of ,neptune1 c41 ,mem4 ,ast4 ,soc41 vol4 xvi4 p4 #dad4 ,the discovery of ,minor ,planets in a certain region of the interval between ,mars and ,jupiter has gone on to such an extent1 that their number makes them assume in a peculiar manner the character of representatives of a ,missing ,planet4 ,at first1 as ,i have said in the text1 it was supposed that all these portions must pass through or near a common node2 this opinion being founded on the very bold doctrine1 that the portions must at one time have been united in one ,planet1 and must then have separated4 ,at this node1 as ,i have stated1 ,olbers lay in wait for them1 as for a hostile army at a defile4 ,ceres1 ,pallas1 and ,juno had been discovered in this way in the period from #ahja to #ahjd2 and ,vesta was caught in #ahjg4 ,for a time the chase for new planets in this region seemed to have exhausted the stock4 ,but after thirty-eight years1 to the astonishment of astronomers1 they began to be again detected in extraordinary numbers4 ,in #ahde1 ,m4 ,hencke of #eei ,driessen discovered a fifth of these planets1 which was termed ,astra4 ,in various quarters the chase was resumed with great ardor4 ,in #ahdg were found ,hebe1 ,iris1 and ,flora2 in #ahdh1 ,metis2 in #ahdi1 ,hyga2 in #ahej1 ,parthenope1 ,victoria1 and ,egeria2 in #ahfa1 ,irene and ,eunomia2 in #aheb1 ,psyche1 ,thetis1 ,melpomene1 ,fortuna1 ,massilia1 ,lutetia1 ,calliope4 ,to these we have now 7at the close of #ahef7 to add nineteen others2 making up the whole number of these ,minor ,planets at present known to forty-two4 ,as their enumeration will show1 the ancient practice has been continued of giving to the ,planets mythological names4 ,and for a time1 till the numbers became too great1 each of the ,minor ,planets was designated in astronomical books by some symbol appropriate to the character of the mythological person2 as from ancient times ,mars has been denoted by a mark indicating a spear1 and ,venus by one representing a looking-glass4 ,thus1 when a ,minor ,planet was discovered at ,london in #ahea1 the year in which the peace of the world was1 in a manner1 celebrated by the ,great ,exhibition of the ,products of ,all ,nations1 held at that metropolis1 the name ,irene was given to the new star1 as a memorial of the auspicious time of its discovery4 ,and it was agreed1 for awhile1 that its symbol should be a dove with an olive-branch4 ,but the vast multitude of the ,minor ,planets1 as discovery went on1 made any mode of designation1 except a numerical one1 practically inconvenient4 ,they are now denoted by a small circle inclosing a figure in the order of their discovery4 ,thus1 ,ceres is 7#a71 ,irene is 7#ad71 and ,isis is 7#db74 ,the rapidity with which these discoveries were made was owing in part to the formation of star-maps1 in which all known fixed stars being represented1 the existence of a new and movable star might be recognized by comparison of the sky with the map4 ,these maps were first constructed by astronomers of different countries at the suggestion of the ,academy of ,berlin2 but they have since been greatly extended1 and now include much smaller stars than were originally laid down4 ,i will mention the number of planets discovered in each year4 ,after the start was once made1 by ,hencke's discovery of ,astra in #ahde1 the same astronomer discovered ,hebe in #ahdg2 and in the same year ,mr4 ,hind1 of ,london1 discovered two others1 ,iris and ,flora4 ,the years #ahdh and #ahdi each supplied one2 the year #ahej1 three2 #ahea1 two2 #aheb was marked by the extraordinary discovery of eight new members of the planetary system4 ,the year #ahec supplied four2 #ahed1 six2 #ahee1 four2 and #ahef has already given us five4 #efj ,these discoveries have been distributed among the observatories of ,europe4 ,the bright sky of ,naples has revealed seven new planets to the telescope of ,signer ,gasparis4 ,marseilles has given us one2 ,germany1 four1 discovered by ,m4 ,luther at ,bilk2 ,paris has furnished seven2 and ,mr4 ,hind1 in ,mr4 ,bishop's private observatory in ,london1 notwithstanding our turbid skies1 has discovered no less than ten planets2 and there also ,mr4 ,marth discovered 7#bi7 ,amphitrite4 ,mr4 ,graham1 at the private observatory of ,mr4 ,cooper1 in ,ireland1 discovered 7#i7 ,metis4 ,america has supplied its planet1 namely 7#ca7 ,euphrosyne1 discovered by ,mr4 ,ferguson at ,washington and the most recent of these discoveries is that by ,mr4 ,pogson1 of ,oxford1 who has found the forty-second of these ,minor ,planets1 which has been named ,isis4#eb;,a ,note #eb;,a3 ,i take this list from a ,memoir of ,m4 ,bruhns1 ,berlin1 #ahef4 ,i may add that it appears to follow from the best calculations that the total mass of all these bodies is very small4 ,herschel reckoned the diameters of ,ceres at #ce1 and of ,pallas at #bf miles4 ,it has since been calculated#ec;,a that some of them are smaller still2 ,victoria having a diameter of #i miles1 ,lutetia of #h1 and ,atalanta of little more than #d4 ,it follows from this that the whole mass would probably be less than the sixth part of our moon4 ,hence their perturbing effects on each other or on other planets are null2 but they are not the less disturbed by the action of the other planets1 and especially of ,jupiter4 ,note #ec;,a3 ,bruhns1 as above4 ,anomalies in the ,action of ,gravitation4 ,the complete and exact manner in which the doctrine of gravitation explains the motions of the ,comets as well as of the ,planets1 has made astronomers very bold in proposing hypotheses to account for any deviations from the motion which the theory requires4 ,thus ,encke's ,comet is found to have its motion accelerated by about one-eighth of a day in every revolution4 ,this result was conceived to be established by former observations1 and is confirmed by the facts of the appearance of #aheb4ed;,a ,the hypothesis which is proposed in order to explain this result is1 that the ,comet moves in a resisting medium1 which makes it fall inwards from its path1 towards the ,sun1 and thus1 by narrowing its orbit1 diminishes its periodic time4 ,on the other hand1 ,m4 ,le ,verrier has found that ,mercury's mean motion has gone on diminishing2 #efa as if the planet were1 in the progress of his revolutions1 receding further from the ,sun4 ,this is explained1 if we suppose that there is1 in the region of ,mercury1 a resisting medium which moves round the ,sun in the same direction as the ,planets move4 ,evidence of a kind of nebulous disk surrounding the ,sun1 and extending beyond the orbits of ,mercury and ,venus1 appears to be afforded us by the phenomenon called the ,zodiacal ,light2 and as the ,sun itself rotates on its axis1 it is most probable that this kind of atmosphere rotates also4#ee;,a ,on the other hand1 ,m4 ,le ,verrier conceives that the ,comets which now revolve within the ordinary planetary limits have not always done so1 but have been caught and detained by the ,planets among which they move4 ,in this way the action of ,jupiter has brought the ,comets of ,faye and ,vico into their present limited orbits1 as it drew the ,comet of ,lexell out of its known orbit1 when the ,comet passed over the ,planet in #aggi1 since which time it has not been seen4 ,note #ed;,a3 ,berlin ,memoirs1 #ahed4 ,note #ee;,a3 ,m4 ,le ,verrier1 ,annales de l',obs4 de ,paris1 vol4 i4 p4 #hi4 ,among the examples of the boldness with which astronomers assume the doctrine of gravitation even beyond the limits of the solar system to be so entirely established1 that hypotheses may and must be assumed to explain any apparent irregularity of motion1 we may reckon the mode of accounting for certain supposed irregularities in the proper motion of ,sirius1 which has been proposed by ,bessel1 and which ,m4 ,peters thinks is proved to be true by his recent researches 7,astr4 ,nach4 xxxi4 p4 #bai1 and xxxii4 p4 #a74 ,the hypothesis is1 that ,sirius has a companion star1 dark1 and therefore invisible to us2 and that the two1 revolving round their common centre as the system moves on1 the motion of ,sirius is seen to be sometimes quicker and sometimes slower4 ,the ,earth's ,density4 ,cavendish's experiment1 as it is commonly called--the measure of the attractions of manageable masses by the torsion balance1 in order to determine the density of the ,earth--has been repeated recently by ,professor ,reich at ,freiberg1 and by ,mr4 ,baily in ,england1 with great attention to the means of attaining accuracy4 ,professor ,reich's result for the density of the ,earth is #edd2 ,mr4 ,baily's is #eib4 ,cavendish's result was #edh2 according to recent revisions#ef;,a it is #eeb4 #efb ,note #ef;,a3 ,the calculation has been revised by ,m4 ,edward ,schmidt4 ,humboldt's ,kosmos1 ii4 p4 #dbe4 ,but the statical effect of the attraction of manageable masses1 or even of mountains1 is very small4 ,the effect of a small change in gravity may be accumulated by being constantly repeated in the oscillations of a pendulum1 and thus may become perceptible4 ,mr4 ,airy attempted to determine the density of the ,earth by a method depending on this view4 ,a pendulum oscillating at the surface was to be compared with an equal pendulum at a great depth below the surface4 ,the difference of their rates would disclose the different force of gravity at the two positions2 and hence1 the density of the ,earth4 ,in #ahbf and #ahbh1 ,mr4 ,airy attempted this experiment at the copper mine of ,dolcoath in ,cornwall1 but failed from various causes4 ,but in #ahed1 he resumed it at the ,harton coal mine in ,durham1 the depth of which is #abfj feet2 having in this new trial1 the advantage of transmitting the time from one station to the other by the instantaneous effect of galvanism1 instead of by portable watches4 ,the result was a density of #fef2 which is much larger than the preceding results1 but1 as ,mr4 ,airy holds1 is entitled to compete with the others on at least equal terms4 ,tides4 ,i should be wanting in the expression of gratitude to those who have practically assisted me in ,researches on the ,tides1 if ,i did not mention the grand series of ,tide ,observations made on the coast of ,europe and ,america in ,june1 #ahce1 through the authority of the ,board of ,admiralty1 and the interposition of the late ,duke of ,wellington1 at that time ,foreign ,secretary4 ,tide observations were made for a fortnight at all the ,coast-guard stations of ,great ,britain and ,ireland in ,june1 #ahcd2 and these were repeated in ,june1 #ahce1 with corresponding observations on all the coasts of ,europe1 from the ,north ,cape of ,norway to the ,straits of ,gibraltar2 and from the mouth of the ,st4 ,lawrence to the mouth of the ,mississippi4 ,the results of these observations1 which were very complete so far as the coast tides were concerned1 were given in the ,philosophical ,transactions for #ahcf4 ,additional accuracy respecting the ,tides of the ,north ,american coast may be expected from the survey now going on under the direction of ,superintendent ,a4 ,bache4 ,the ,tides of the ,english ,channel have been further investigated1 and the phenomena presented under a new point of view by ,admiral ,beechey4 #efc ,the ,tides of the ,coast of ,ireland have been examined with great care by ,mr4 ,airy4 ,numerous and careful observations were made with a view1 in the first instance1 of determining what was to be regarded as the ,level of the ,sea2 but the results were discussed so as to bring into view the laws and progress1 on the ,irish coast1 of the various inequalities of the ,tides mentioned in ,chap4 iv4 ,sect4 #i of this ,book4 ,i may notice as one of the curious results of the ,tide ,observations of #ahcf1 that it appeared to me1 from a comparison of the ,observations1 that there must be a point in the ,german ,ocean1 about midway between ,lowestoft on the ,english coast1 and the ,brill on the ,dutch coast1 where the tide would vanish3 and this was ascertained to be the case by observation2 the observations being made by ,captain ,hewett1 then employed in a survey of that sea4 ,cotidal ,lines supply1 as ,i conceive1 a good and simple method of representing the progress and connection of littoral tides4 ,but to draw cotidal lines across oceans1 is a very precarious mode of representing the facts1 except we had much more knowledge on the subject than we at present possess4 ,in the ,phil4 ,trans4 for #ahdh1 ,i have resumed the subject of the ,tides of the ,pacific2 and ,i have there expressed my opinion1 that while the littoral tides are produced by progressive waves1 the oceanic tides are more of the nature of stationary undulations4 ,but many points of this kind might be decided1 and our knowledge on this subject might be brought to a condition of completeness1 if a ship or ships were sent expressly to follow the phenomena of the ,tides from point to point1 as the observations themselves might suggest a course4 ,till this is done1 our knowledge cannot be completed4 ,detached and casual observations1 made aliud agendo1 can never carry us much beyond the point where we at present are4 ,double ,stars4 ,sir ,john ,herschel's work1 referred to in the ,history 7#b;d ,ed47 as then about to appear1 was published in #ahdg4eg;,a ,in this work1 besides a vast amount of valuable observations and reasonings on other subjects #efd 7as ,nebul1 the ,magnitude of ,stars1 and the like71 the orbits of several double stars are computed by the aid of the new observations4 ,but ,sir ,john ,herschel's conviction on the point in question1 the operation of the ,newtonian law of gravitation in the region of the stars1 is expressed perhaps more clearly in another work which he published in #ahdi4eh;,a ,he there speaks of ,double ,stars1 and especially of gamma ,virginis1 the one which has been most assiduously watched1 and has offered phenomena of the greatest interest4#ei;,a ,he then finds that the two components of this star revolve round each other in a period of #ahb years2 and says that the elements of the calculated orbit represent the whole series of recorded observations1 comprising an angular movement of nearly nine-tenths of a complete circuit1 both in angle and distance1 with a degree of exactness fully equal to that of observation itself4 ,no doubt can therefore1 he adds1 remain as to the 9999prevalence in this remote system of the ,newtonian ,law of ,gravitation4 ,note #eg;,a3 ,results of ,astronomical ,observations made during the years #ahcd1 #e1 #f1 #g1 #h1 at the ,cape of ,good ,hope1 being the completion of a ,telescopic ,survey of the whole ,surface of the visible ,heavens commenced in #ahbe4 ,note #eh;,a3 ,outlines of ,astronomy4 ,note #ei;,a3 ,out4 #hdd4 ,yet ,m4 ,yvon de ,villarceau has endeavored to show#fj;,a that this conclusion1 however probable1 is not yet proved4 ,he holds1 even for the ,double ,stars1 which have been most observed1 the observations are only equivalent to seven or eight really distinct data1 and that seven data are not sufficient to determine that an ellipse is described according to the ,newtonian law4 ,without going into the details of this reasoning1 ,i may remark1 that the more rapid relative angular motion of the components of a ,double ,star when they are more near each other1 proves1 as is allowed on all hands1 that they revolve under the influence of a mutual attractive force1 obeying the ,keplerian ,law of ,areas4 ,but that1 whether this force follows the law of the inverse square or some other law1 can hardly have been rigorously proved as yet1 we may easily conceive1 when we recollect the manner in which that law was proved for the ,solar ,system4 ,it was by means of an error of eight minutes1 observed by ,tycho1 that ,kepler was enabled1 as he justly boasted1 to reform the scheme of the ,solar ,system1--to show1 that is1 that the planetary orbits are ellipses with the sun in the focus4 ,now1 the observations of ,double ,stars cannot pretend to such accuracy as this2 and therefore the ,keplerian theorem cannot1 as yet1 have been fully demonstrated from those observations4 ,but when we know #efe that ,double ,stars are held together by a central force1 to prove that this force follows a different law from the only law which has hitherto been found to obtain in the universe1 and which obtains between all the known masses of the universe1 would require very clear and distinct evidence1 of which astronomers have as yet seen no trace4 ,note #fj;,a3 ,connaissance des ,temps1 for #aheb2 published in #ahdi4 ,,chapter ,,vi4 ,sect4 #a4 ,instruments4--#b4 ,clocks4 ,,in page #dgc1 ,i have described the manner in which astronomers are able to observe the transit of a star1 and other astronomical phenomena1 to the exactness of a tenth of a second of time4 ,the mode of observation there described implies that the observer at the moment of observation compares the impressions of the eye and of the ear4 ,now it is found that the habit which the observer must form of doing this operates differently in different observers1 so that one observer notes the same fact as happening a fraction of a second earlier or later than another observer does2 and this in every case4 ,thus1 using the term equation1 as we use it in ,astronomy1 to express a correction by which we get regularity from irregularity1 there is a personal equation belonging to this mode of observation1 showing that it is liable to error4 ,can this error be got rid of8 ,it is at any rate much diminished by a method of observation recently introduced into observatories1 and first practised in ,america4 ,the essential feature of this mode of observation consists in combining the impression of sight with that of touch1 instead of with that of hearing4 ,the observer at the moment of observation presses with his finger so as to make a mark on a machine which by its motion measures time with great accuracy and on a large scale2 and thus small intervals of time are made visible4 ,a universal1 though not a necessary1 part of this machinery1 as hitherto adopted1 is1 that a galvanic circuit has been employed in conveying the impression from the finger to the part where time is measured and marked4 ,the facility with which galvanic wires can #eff thus lead the impression by any path to any distance1 and increase its force in any degree1 has led to this combination1 and almost identification1 of observation by touch with its record by galvanism4 ,the method having been first used by ,mr4 ,bond at ,cambridge1 in ,north ,america1 has been adopted elsewhere1 and especially at ,greenwich1 where it is used for all the instruments2 and consequently a collection of galvanic batteries is thus as necessary a part of the apparatus of the establishment as its graduated circles and arcs4 ,,end ,,of ,,vol4 ,i4 ,,history ,,of ,,the ,,inductive ,,sciences4 ,,volume ,,ii4 ,,history ,,of ,,the ,,inductive ,,sciences1 ,,from ,,the ,,earliest ,,to ,,the ,,present ,,time4 ,,by ,,william ,,whewell1 ,d4 ,d41 ,,master ,,of ,,trinity ,,college1 ,,cambridge4 ,,the ,,third ,,edition1 ,,with ,,additions4 ,,in ,,two ,,volumes4 ,,volume ,,ii4 ,,new ,,york3 ,d4 ,,appleton ,,and ,,company1 #edi #eea ,,broadway4 #ahge4 ,,contents ,,of ,,the ,,second ,,volume4 ,,the ,,secondary ,,mechanical ,,sciences4 ,,book ,,viii4 ,,history ,,of ,,acoustics4 ,,page ,introduction4 #bc ,,chapter ,i4--,,prelude ,,to ,,the ,,solution ,,of ,,problems ,,in ,,acoustics4 #bd ,,chapter ,,ii4--,,problem ,,of ,,the ,,vibrations ,,of ,,strings4 #bh ,,chapter ,,iii4--,,problem ,,of ,,the ,,propagation ,,of ,,sound4 #cb ,,chapter ,,iv4--,,problem ,,of ,,different ,,sounds ,,of ,,the ,,same ,,string4 #cf ,,chapter ,v4--,,problem ,,of ,,the ,,sounds ,,of ,,pipes4 #ch ,,chapter ,,vi4--,,problem ,,of ,,different ,,modes ,,of ,,vibration ,,of ,,bodies ,,in ,,general4 #da ,,book ,,ix4 ,,history ,,of ,,optics1 ,,formal ,,and ,,physical4 ,introduction4 #ea #h ,,formal ,,optics4 ,,chapter ,i4--,,primary ,,induction ,,of ,,optics4--,,rays ,,of ,,light ,,and ,,laws ,,of ,,reflection4 #ec ,,chapter ,,ii4--,,discovery ,,of ,,the ,,law ,,of ,,refraction4 #ed ,,chapter ,,iii4--,,discovery ,,of ,,the ,,law ,,of ,,dispersion ,,by ,,refraction4 #eh ,,chapter ,,iv4--,,discovery ,,of ,,achromatism4 #ff ,,chapter ,v4--,,discovery ,,of ,,the ,,laws ,,of ,,double ,,refraction4 #fi ,,chapter ,,vi4--,,discovery ,,of ,,the ,,laws ,,of ,,polarization4 #gb ,,chapter ,,vii4--,,discovery ,,of ,,the ,,laws ,,of ,,the ,,colors ,,of ,,thin ,,plates4 #gf ,,chapter ,,viii4--,,attempts ,,to ,,discover ,,the ,,laws ,,of ,,other ,,phenomena4 #gh ,,chapter ,,ix4--,,discovery ,,of ,,the ,,laws ,,of ,,phenomena ,,of ,,dipolarized ,,light4 #hj ,,physical ,,optics4 ,,chapter ,x4--,,prelude ,,to ,,the ,,epoch ,,of ,,young ,,and ,,fresnel4 #he ,,chapter ,,xi4--,,epoch ,,of ,,young ,,and ,,fresnel4 ,sect4 #a4 ,introduction4 #ib ,sect4 #b4 ,explanation of the ,periodical ,colors of ,thin ,plates and ,shadows by the ,undulatory ,theory4 #ic ,sect4 #c4 ,explanation of ,double ,refraction by the ,undulatory ,theory4 #ih ,sect4 #d4 ,explanation of ,polarization by the ,undulatory ,theory4 #ajj ,sect4 #e4 ,explanation of ,dipolarization by the ,undulatory ,theory4 #aje #i ,,chapter ,,xii4--,,sequel ,,to ,,the ,,epoch ,,of ,,young ,,and ,,fresnel4--,,reception ,,of ,,the ,,undulatory ,,theory4 #aaa ,,chapter ,,xiii4--,,confirmation ,,and ,,extension ,,of ,,the ,,undulatory ,,theory4 #aah #a4 ,double ,refraction of ,compressed ,glass4 #aai #b4 ,circular ,polarization4 #aai #c4 ,elliptical ,polarization in ,quartz4 #abb #d4 ,differential ,equations of ,elliptical ,polarization4 #abb #e4 ,elliptical ,polarization of ,metals4 #abc #f4 ,newton's ,rings by ,polarized ,light4 #abd #g4 ,conical ,refraction4 #abd #h4 ,fringes of ,shadows4 #abf #i4 ,objections to the ,theory4 #abf #aj4 ,dispersion1 on the ,undulatory ,theory4 #abh #aa4 ,conclusion4 #abh ,,book ,x4 ,,history ,,of ,,thermotics ,,and ,,atmology4 ,introduction4 #acg ,,thermotics ,,proper4 ,,chapter ,i4--,,the ,,doctrines ,,of ,,conduction ,,and ,,radiation4 ,sect4 #a4 ,introduction of the ,doctrine of ,conduction4 #aci ,sect4 #b4 ,radiation4 #adb ,sect4 #c4 ,verification of the ,doctrines of ,conduction and ,radiation4 #adc ,sect4 #d4 ,the ,geological and ,cosmological ,application of ,thermotics4 #add #a4 ,effect of ,solar ,heat on the ,earth4 #ade #b4 ,climate4 #adf #c4 ,temperature of the ,interior of the ,earth4 #adg #d4 ,heat of the ,planetary ,spaces4 #adh ,sect4 #e4 ,correction of ,newton's ,law of ,cooling4 #adi ,sect4 #f4 ,other ,laws of ,phenomena with respect to ,radiation4 #aea ,sect4 #g4 ,fourier's ,theory of ,radiant ,heat4 #aeb ,sect4 #h4 ,discovery of the ,polarization of ,heat4 #aec #aj ,,chapter ,,ii4--,,the ,,laws ,,of ,,changes ,,occasioned ,,by ,,heat4 ,sect4 #a4 ,expansion by ,heat4--,the ,law of ,dalton and ,gay-,lussac for ,gases4 #aeg ,sect4 #b4 ,specific ,heat4--,change of ,consistence4 #aei ,sect4 #c4 ,the ,doctrine of ,latent ,heat4 #afj ,,atmology4 ,,chapter ,,iii4--,,the ,,relation ,,of ,,vapor ,,and ,,air4 ,sect4 #a4 ,the ,boylean ,law of the ,air's ,elasticity4 #afc ,sect4 #b4 ,prelude to ,dalton's ,doctrine of ,evaporation4 #afe ,sect4 #c4 ,dalton's ,doctrine of ,evaporation4 #agj ,sect4 #d4 ,determination of the ,laws of the ,elastic ,force of ,steam4 #agb ,sect4 #e4 ,consequences of the ,doctrine of ,evaporation4--,explanation of ,rain1 ,dew1 and ,clouds4 #agf ,,chapter ,,iv4--,,physical ,,theories ,,of ,,heat4 ,thermotical ,theories4 #aha ,atmological ,theories4 #ahd ,conclusion4 #ahg ,,the ,,mechanico-,,chemical ,,sciences4 ,,book ,,xi4 ,,history ,,of ,,electricity4 ,introduction4 #aia ,,chapter ,i4--,,discovery ,,of ,,laws ,,of ,,electric ,,phenomena4 #aic ,,chapter ,,ii4--,,the ,,progress ,,of ,,electrical ,,theory4 #bja ,question of ,one or ,two ,fluids4 #baj ,question of the ,material ,reality of the ,electric ,fluid4 #bab #aa ,,book ,,xii4 ,,history ,,of ,,magnetism4 ,,chapter ,i4--,,discovery ,,of ,,laws ,,of ,,magnetic ,,phenomena4 #bag ,,chapter ,,ii4--,,progress ,,of ,,magnetic ,,theory4 ,theory of ,magnetic ,action4 #bbj ,theory of ,terrestrial ,magnetism4 #bbd ,conclusion4 #bcb ,,book ,,xiii4 ,,history ,,of ,,galvanism1 ,,or ,,voltaic ,,electricity4 ,,chapter ,i4--,,discovery ,,of ,,voltaic ,,electricity4 #bcg ,,chapter ,,ii4--,,reception ,,and ,,confirmation ,,of ,,the ,,discovery ,,of ,,voltaic ,,electricity4 #bdj ,,chapter ,,iii4--,,discovery ,,of ,,the ,,laws ,,of ,,the ,,mutual ,,attraction ,,and ,,repulsion ,,of ,,voltaic ,,currents4--,,amp,,re4 #bdb ,,chapter ,,iv4--,,discovery ,,of ,,electro-,,magnetic ,,action4--,,oersted4 #bdc ,,chapter ,v4--,,discovery ,,of ,,the ,,laws ,,of ,,electro-,,magnetic ,,action4 #bde ,,chapter ,,vi4--,,theory ,,of ,,electrodynamical ,,action4 ,ampre's ,theory4 #bdf ,reception of ,ampre's ,theory4 #bdi ,,chapter ,,vii4--,,consequences ,,of ,,the ,,electrodynamic ,,theory4 #bej ,discovery of ,diamagnetism4 #beb #ab ,,chapter ,,viii4--,,discovery ,,of ,,the ,,laws ,,of ,,magneto-,,electric ,,induction4--,,faraday4 #bec ,,chapter ,,ix4--,,transition ,,to ,,chemical ,,science4 #bef ,,the ,,analytical ,,science4 ,,book ,,xiv4 ,,history ,,of ,,chemistry4 ,,chapter ,i4--,,improvement ,,of ,,the ,,notion ,,of ,,chemical ,,analysis1 ,,and ,,recognition ,,of ,,it ,,as ,,the ,,spagiric ,,art4 #bfa ,,chapter ,,ii4--,,doctrine ,,of ,,acid ,,and ,,alkali4--,,sylvius4 #bfb ,,chapter ,,iii4--,,doctrine ,,of ,,elective ,,attractions4--,,geoffroy4 ,,bergman4 #bfe ,,chapter ,,iv4--,,doctrine ,,of ,,acidification ,,and ,,combustion4--,,phlogistic ,,theory4 ,publication of the ,theory by ,beccher and ,stahl4 #bfg ,reception and ,application of the ,theory4 #bga ,,chapter ,v4--,,chemistry ,,of ,,gases4--,,black4 ,,cavendish4 #bgb ,,chapter ,,vi4--,,epoch ,,of ,,the ,,theory ,,of ,,oxygen4--,,lavoisier4 ,sect4 #a4 ,prelude to the ,theory4--,its ,publication4 #bge ,sect4 #b4 ,reception and ,confirmation of the ,theory of ,oxygen4 #bgh ,sect4 #c4 ,nomenclature of the ,oxygen ,theory4 #bha ,,chapter ,,vii4--,,application ,,and ,,correction ,,of ,,the ,,oxygen ,,theory4 #bhb #ac ,,chapter ,,viii4--,,theory ,,of ,,definite1 ,,reciprocal1 ,,and ,,multiple ,,proportions4 ,sect4 #a4 ,prelude to the ,atomic ,theory1 and its ,publication by ,dalton4 #bhe ,sect4 #b4 ,reception and ,confirmation of the ,atomic ,theory4 #bhh ,sect4 #c4 ,the ,theory of ,volumes4--,gay-,lussac4 #bij ,,chapter ,,ix4--,,epoch ,,of ,,davy ,,and ,,faraday4 ,sect4 #a4 ,promulgation of the ,electro-chemical ,theory by ,davy4 #bia ,sect4 #b4 ,establishment of the ,electro-chemical ,theory by ,faraday4 #bif ,sect4 #c4 ,consequences of ,faraday's ,discoveries4 #cjb ,sect4 #d4 ,reception of the ,electro-chemical ,theory4 #cjc ,,chapter ,x4--,,transition ,,from ,,the ,,chemical ,,to ,,the ,,classificatory ,,sciences4 #cje ,,the ,,analytico-,,classificatory ,,science4 ,,book ,,xv4 ,,history ,,of ,,mineralogy4 ,,introduction ,sect4 #a4 ,of the ,classificatory ,sciences4 #cac ,sect4 #b4 ,of ,mineralogy as the ,analytico-classificatory ,science4 #cad ,,crystallography4 ,,chapter ,i4--,,prelude ,,to ,,the ,,epoch ,,of ,,de ,,lisle ,,and ,,ha,y4 #caf ,,chapter ,,ii4--,,epoch ,,of ,,rom ,,de ,,lisle ,,and ,,ha,y4--,,establishment ,,of ,,the ,,fixity ,,of ,,crystalline ,,angles1 ,,and ,,the ,,simplicity ,,of ,,the ,,laws ,,of ,,derivation4 #cbj ,,chapter ,,iii4--,,reception ,,and ,,corrections ,,of ,,the ,,hau,,an ,,crystallography4 #cbd #ad ,,chapter ,,iv4--,,establishment ,,of ,,the ,,distinction ,,of ,,systems ,,of ,,crystallization4--,,weiss ,,and ,,mohs4 #cbf ,,chapter ,v4--,,reception ,,and ,,confirmation ,,of ,,the ,,distinction ,,of ,,systems ,,of ,,crystallization4 ,diffusion of the ,distinction of ,systems4 #ccj ,confirmation of the ,distinction of ,systems by the ,optical ,properties of ,minerals4--,brewster4 #cca ,,chapter ,,vi4--,,correction ,,of ,,the ,,law ,,of ,,the ,,same ,,angle ,,for ,,the ,,same ,,substance4 ,discovery of ,isomorphism4--,mitscherlich4 #ccd ,dimorphism4 #ccf ,,chapter ,,vii4--,,attempts ,,to ,,establish ,,the ,,fixity ,,of ,,other ,,physical ,,properties4--,,werner4 #ccf ,,systematic ,,mineralogy4 ,,chapter ,,viii4--,,attempts ,,at ,,the ,,classification ,,of ,,minerals4 ,sect4 #a4 ,proper ,object of ,classification4 #cci ,sect4 #b4 ,mixed ,systems of ,classification4 #cdj ,,chapter ,,ix4--,,attempts ,,at ,,the ,,reform ,,of ,,mineralogical ,,systems4--,,separation ,,of ,,the ,,chemical ,,and ,,natural ,,history ,,methods4 ,sect4 #a4 ,natural ,history ,system of ,mohs4 #cdd ,sect4 #b4 ,chemical ,system of ,berzelius and others4 #cdg ,sect4 #c4 ,failure of the ,attempts at ,systematic ,reform4 #cdi ,sect4 #d4 ,return to ,mixed ,systems with ,improvements4 #cea ,,classificatory ,,sciences4 ,,book ,,xvi4 ,,history ,,of ,,systematic ,,botany ,,and ,,zoology4 ,introduction4 #ceg #ae ,,chapter ,i4--,,imaginary ,,knowledge ,,of ,,plants4 #ceh ,,chapter ,,ii4--,,unsystematic ,,knowledge ,,of ,,plants4 #cfa ,,chapter ,,iii4--,,formation ,,of ,a ,,system ,,of ,,arrangement ,,of ,,plants4 ,sect4 #a4 ,prelude to the ,epoch of ,csalpinus4 #cfi ,sect4 #b4 ,epoch of ,csalpinus4--,formation of a ,system of ,arrangement4 #cgc ,sect4 #c4 ,stationary ,interval4 #cgh ,sect4 #d4 ,sequel to the ,epoch of ,csalpinus4--,further ,formation and ,adoption of ,systematic ,arrangement4 #chb ,,chapter ,,iv4--,,the ,,reform ,,of ,,linn,,us4 ,sect4 #a4 ,introduction of the ,reform4 #chg ,sect4 #b4 ,linnan ,reform of ,botanical ,terminology4 #chi ,sect4 #c4 ,nomenclature4 #cia ,sect4 #d4 ,linnus's ,artificial ,system1 #cie ,sect4 #e4 ,linnus's ,views on a ,natural ,method4 #cif ,sect4 #f4 ,reception and ,diffusion of the ,linnan ,reform4 #djj ,,chapter ,v4--,,progress ,,towards ,a ,,natural ,,system ,,of ,,botany4 #djd ,,chapter ,,vi4--,,the ,,progress ,,of ,,systematic ,,zoology4 #dab ,,chapter ,,vii4--,,the ,,progress ,,of ,,ichthyology4 #dai ,period of ,unsystematic ,knowledge4 #dbj ,period of ,erudition4 #dba ,period of ,accumulation of ,materials4--,exotic ,collections4 #dbb ,epoch of the ,fixation of ,characters4--,ray and ,willoughby4 #dbb ,improvement of the ,system4--,artedi4 #dbc ,separation of the ,artificial and ,natural ,methods in ,ichthyology4 #dbf ,,organical ,,sciences4 ,,book ,,xvii4 ,,history ,,of ,,physiology ,,and ,,comparative ,,anatomy4 ,introduction4 #dce #af ,,chapter ,i4--,,discovery ,,of ,,the ,,organs ,,of ,,voluntary ,,motion4 ,sect4 #a4 ,knowledge of ,galen and his ,predecessors4 #dch ,sect4 #b4 ,recognition of ,final ,causes in ,physiology4--,galen4 #ddb ,,chapter ,,ii4--,,discovery ,,of ,,the ,,circulation ,,of ,,the ,,blood4 ,sect4 #a4 ,prelude to the ,discovery4 #ddd ,sect4 #b4 ,the ,discovery of the ,circulation made by ,harvey4 #ddg ,sect4 #c4 ,reception of the ,discovery4 #ddh ,sect4 #d4 ,bearing of the ,discovery on the ,progress of ,physiology4 #ddi ,,chapter ,,iii4--,,discovery ,,of ,,the ,,motion ,,of ,,the ,,chyle1 ,,and ,,consequent ,,speculations4 ,sect4 #a4 ,the ,discovery of the ,motion of the ,chyle4 #deb ,sect4 #b4 ,the ,consequent ,speculations4 ,hypotheses of ,digestion4 #dec ,,chapter ,,iv4--,,examination ,,of ,,the ,,process ,,of ,,reproduction ,,in ,,animals ,,and ,,plants1 ,,and ,,consequent ,,speculations4 ,sect4 #a4 ,the ,examination of the ,process of ,reproduction in ,animals4 #dee ,sect4 #b4 in ,vegetables4 #deg ,sect4 #c4 ,the ,consequent ,speculations4--,hypotheses of ,generation4 #dei ,,chapter ,v4--,,examination ,,of ,,the ,,nervous ,,system1 ,,and ,,consequent ,,speculations4 ,sect4 #a4 ,the ,examination of the ,nervous ,system4 #dfa ,sect4 #b4 ,the ,consequent ,speculations4 ,hypotheses respecting ,life1 ,sensation1 and ,volition4 #dfd ,,chapter ,,vi4--,,introduction ,,of ,,the ,,principle ,,of ,,developed ,,and ,,metamorphosed ,,symmetry4 ,sect4 #a4 ,vegetable ,morphology4--,gthe4 ,de ,candolle4 #dfh ,sect4 #b4 ,application of ,vegetable ,morphology4 #dgd ,,chapter ,,vii4--,,progress ,,of ,,animal ,,morphology4 ,sect4 #a4 ,rise of ,comparative ,anatomy4 #dge ,sect4 #b4 ,distinction of the ,general ,types of the ,forms of ,animals4--,cuvier4 #dgh ,sect4 #c4 ,attempts to establish the ,identity of the ,types of ,animal ,forms4 #dhj #ag ,,chapter ,,viii4--,,the ,,doctrine ,,of ,,final ,,causes ,,in ,,physiology4 ,sect4 #a4 ,assertion of the ,principle of ,unity of ,plan4 #dhb ,sect4 #b4 ,estimate of the ,doctrine of ,unity of ,plan4 #dhg ,sect4 #c4 ,establishment and ,application of the ,principle of the ,conditions of ,existence of ,animals4--,cuvier4 #dib ,,the ,,pal,,tiological ,,sciences4 ,,book ,,xviii4 ,,history ,,of ,,geology4 ,introduction4 #dii ,,descriptive ,,geology4 ,,chapter ,i4--,,prelude ,,to ,,systematic ,,descriptive ,,geology4 ,sect4 #a4 ,ancient ,notices of ,geological ,facts4 #eje ,sect4 #b4 ,early ,descriptions and ,collections of ,fossils4 #ejf ,sect4 #c4 ,first ,construction of ,geological ,maps4 #eji ,,chapter ,,ii4--,,formation ,,of ,,systematic ,,descriptive ,,geology4 ,sect4 #a4 ,discovery of the ,order and ,stratification of the ,materials of the ,earth4 #eaa ,sect4 #b4 ,systematic ,form given to ,descriptive ,geology4--,werner4 #eac ,sect4 #c4 ,application of ,organic ,remains as a ,geological ,character4--,smith4 #eae ,sect4 #d4 ,advances in ,palontology4--,cuvier4 #eag ,sect4 #e4 ,intellectual ,characters of the ,founders of ,systematic ,descriptive ,geology4 #ebj ,,chapter ,,iii4--,,sequel ,,to ,,the ,,formation ,,of ,,systematic ,,descriptive ,,geology4 ,sect4 #a4 ,reception and ,diffusion of ,systematic ,geology4 #ebc ,sect4 #b4 ,application of ,systematic ,geology4--,geological ,surveys and ,maps4 #ebf ,sect4 #c4 ,geological ,nomenclature4 #ebg ,sect4 #d4 ,geological ,synonymy1 or ,determination of ,geological ,equivalents4 #eca #ah ,,chapter ,,iv4--,,attempts ,,to ,,discover ,,general ,,laws ,,in ,,geology4 ,sect4 #a4 ,general ,geological ,phenomena4 #ecg ,sect4 #b4 ,transition to ,geological ,dynamics4 #eda ,,geological ,,dynamics4 ,,chapter ,v4--,,inorganic ,,geological ,,dynamics4 ,sect4 #a4 ,necessity and ,object of a ,science of ,geological ,dynamics4 #edb ,sect4 #b4 ,aqueous ,causes of ,change4 #ede ,sect4 #c4 ,igneous ,causes of ,change4--,motions of the ,earth's ,surface4 #edi ,sect4 #d4 ,the ,doctrine of ,central ,heat4 #eed ,sect4 #e4 ,problems respecting ,elevations and ,crystalline ,forces4 #eef ,sect4 #f4 ,theories of ,changes of ,climate4 #eei ,,chapter ,,vi4--,,progress ,,of ,,the ,,geological ,,dynamics ,,of ,,organized ,,beings4 ,sect4 #a4 ,objects of this ,science4 #efa ,sect4 #b4 ,geography of ,plants and ,animals4 #efb ,sect4 #c4 ,questions of the ,transmutation of ,species4 #efc ,sect4 #d4 ,hypothesis of ,progressive ,tendencies4 #efe ,sect4 #e4 ,question of ,creation as related to ,science4 #efh ,sect4 #f4 ,the ,hypothesis of the ,regular ,creation and ,extinction of ,species4 #egc #a4 ,creation of ,species4 #egc #b4 ,extinction of ,species4 #egf ,sect4 #g4 ,the ,imbedding of ,organic ,remains4 #egg ,,physical ,,geology4 ,,chapter ,,vii4--,,progress ,,of ,,physical ,,geology4 ,sect4 #a4 ,object and ,distinctions of ,physical ,geology4 #egi ,sect4 #b4 ,of ,fanciful ,geological ,opinions4 #ehj ,sect4 #c4 ,of ,premature ,geological ,theories4 #ehd ,,chapter ,,viii4--,,the ,,two ,,antagonist ,,doctrines ,,of ,,geology4 ,sect4 #a4 ,of the ,doctrine of ,geological ,catastrophes4 #ehf ,sect4 #b4 ,uniformity4 #ehh #ai ,,additions ,,to ,,the ,,third ,,edition4 ,,book ,,viii4--,,acoustics4 ,,sound4 ,the ,velocity of ,sound in ,water4 #eii ,,book ,,ix4--,,optics4 ,photography4 #fja ,fluorescence4 #fja ,,undulatory ,,theory4 ,direction of the ,transverse ,vibrations in ,polarization4 #fjc ,final ,disproof of the ,emission ,theory4 #fjd ,,book ,x4--,,thermotics4--,,atmology4 ,,the ,,relation ,,of ,,vapor ,,and ,,air4 ,force of ,steam4 #fjf ,temperature of the ,atmosphere4 #fjg ,,theories ,,of ,,heat4 ,the ,dynamical ,theory of ,heat4 #fjh ,,book ,,xi4--,,electricity4 ,general ,remarks4 #faj ,dr4 ,faraday's ,views of ,statical ,electrical ,induction4 #faa ,,book ,,xii4--,,magnetism4 ,recent ,progress of ,terrestrial ,magnetism4 #fac ,correction of ,ships' ,compasses4 #faf #bj ,,book ,,xiii4--,,voltaic ,,electricity4 ,,magneto-,,electric ,,induction4 ,diamagnetlc ,polarity4 #fbj ,magneto-optic ,effects and ,magnecrystallic ,polarity4 #fba ,magneto-electric ,machines4 #fbc ,applications of ,electrodynamic ,discoveries4 #fbc ,,book ,,xiv4--,,chemistry4 ,,the ,,electro-,,chemical ,,theory4 ,the ,number of ,elementary ,substances4 #fbe ,,book ,,xv4--,,mineralogy4 ,crystallography4 #fbg ,optical ,properties of ,minerals4 #fbi ,classification of ,minerals4 #fcj ,,book ,,xvi4--,,classificatory ,,sciences4 ,recent ,views of ,botany4 #fca ,zoology4 #fcd ,,book ,,xvii4--,,physiological ,,and ,,comparative ,,anatomy4 ,,vegetable ,,morphology4 #fcf ,,animal ,,morphology4 #fch ,final ,causes4 #fdb ,,book ,,xviii4 ,,geology4 #fdf #ba ,,book ,,viii4 ,,the ,,secondary ,,mechanical ,,sciences4 ,,history ,,of ,,acoustics4 4 4 4 4 4 4 ,go1 demand ,of mighty ,nature1 if 'twas ever meant ,that we should pry far off and be unraised1 ,that we should pore1 and dwindle as we pore1 ,viewing all objects unremittingly ,in disconnexion dead and spiritless2 ,and still dividing1 and dividing still1 ,break down all grandeur1 still unsatisfied ,with the perverse attempt1 while littleness ,may yet become more little2 waging thus ,an impious warfare 'gainst the very life ,of our own souls4 ,,wordsworth1 ,excursion4 4 4 4 4 4 4 ,i 1 ,,nonnus4 ,dionysiac4 xli4 #bge4 ,along the skiey arch the goddess trode1 ,and sought ,harmonia's august abode2 ,the universal plan1 the mystic ,four1 ,defines the figure of the palace-floor4 ,solid and square the ancient fabric stands1 ,raised by the labors of unnumbered hands4 #bc ,,book ,,viii4 ,,introduction4 ,the ,secondary ,mechanical ,sciences4 ,,in the sciences of ,mechanics and ,physical ,astronomy1 ,motion and ,force are the direct and primary objects of our attention4 ,but there is another class of sciences in which we endeavor to reduce phenomena1 not evidently mechanical1 to a known dependence upon mechanical properties and laws4 ,in the cases to which ,i refer1 the facts do not present themselves to the senses as modifications of position and motion1 but as secondary qualities1 which are found to be in some way derived from those primary attributes4 ,also1 in these cases the phenomena are reduced to their mechanical laws and causes in a secondary manner2 namely1 by treating them as the operation of a medium interposed between the object and the organ of sense4 ,these1 then1 we may call ,secondary ,mechanical ,sciences4 ,the sciences of this kind which require our notice are those which treat of the sensible qualities1 ,sound1 ,light1 and ,heat2 that is4 ,acoustics1 ,optics1 and ,thermotics4 ,it will be recollected that our object is not by any means to give a full statement of all the additions which have been successively made to our knowledge on the subjects under review1 or a complete list of the persons by whom such additions have been made2 but to present a view of the progress of each of those branches of knowledge as a theoretical science2--to point out the ,epochs of the discovery of those general principles which reduce many facts to one theory2 and to note all that is most characteristic and instructive in the circumstances and persons which bear upon such ,epochs4 ,a history of any science1 written with such objects1 will not need to be long2 but it will fail in its purpose altogether1 if it do not distinctly exhibit some well-marked and prominent features4 #bd ,we begin our account of the ,secondary ,mechanical ,sciences with ,acoustics1 because the progress towards right theoretical views1 was1 in fact1 made much earlier in the science of ,sound1 than in those of ,light and of ,heat2 and also1 because a clear comprehension of the theory to which we are led in this case1 is the best preparation for the difficulties 7by no means inconsiderable7 of the reasonings of theorists on the other subjects4 ,,chapter ,i4 ,,prelude ,,to ,,the ,,solution ,,of ,,problems ,,in ,,acoustics4 ,,in some measure the true theory of sound was guessed by very early speculators on the subject2 though undoubtedly conceived in a very vague and wavering manner4 ,that sound is caused by some motion of the sounding body1 and conveyed by some motion of the air to the ear1 is an opinion which we trace to the earliest times of physical philosophy4 ,we may take ,aristotle as the best expounder of this stage of opinion4 ,in his ,treatise ,on ,sound and ,hearing1 he says1 ,sound takes place when bodies strike the air1 not by the air having a form impressed upon it 771 as some think1 but by its being moved in a corresponding manner2 7probably he means in a manner corresponding to the impulse27 the air being contracted1 and expanded1 and overtaken1 and again struck by the impulses of the breath and of the strings4 ,for when the breath falls upon and strikes the air which is next it1 the air is carried forwards with an impetus1 and that which is contiguous to the first is carried onwards2 so that the same voice spreads every way as far as the motion of the air takes place4 ,as is the case with all such specimens of ancient physics1 different persons would find in such a statement very different measures of truth and distinctness4 ,the admirers of antiquity might easily1 by pressing the language closely1 and using the light of modern discovery1 detect in this passage an exact account of the production and propagation of sound3 while others might maintain that in ,aristotle's own mind1 there were only vague notions1 and verbal generalizations4 ,this #be latter opinion is very emphatically expressed by ,bacon4#ah ,the collision or thrusting of air1 which they will have to be the cause of sound1 neither denotes the form nor the latent process of sound2 but is a term of ignorance and of superficial contemplation4 ,nor can it be justly denied1 that an exact and distinct apprehension of the kind of motion of the air by which sound is diffused1 was beyond the reach of the ancient philosophers1 and made its way into the world long afterwards4 ,it was by no means easy to reconcile the nature of such motion with obvious phenomena4 ,for the process is not evident as motion2 since1 as ,bacon also observes1#bh it does not visibly agitate the flame of a candle1 or a feather1 or any light floating substance1 by which the slightest motions of the air are betrayed4 ,still1 the persuasion that sound is some motion of the air1 continued to keep hold of men's minds1 and acquired additional distinctness4 ,the illustration employed by ,vitruvius1 in the following passage1 is even now one of the best we can offer4#ch ,voice is breath1 flowing1 and made sensible to the hearing by striking the air4 ,it moves in infinite circumferences of circles1 as when1 by throwing a stone into still water1 you produce innumerable circles of waves1 increasing from the centre and spreading outwards1 till the boundary of the space1 or some obstacle1 prevents their outlines from going further4 ,in the same manner the voice makes its motion in circles4 ,but in water the circle moves breadthways upon a level plain2 the voice proceeds in breadth1 and also successively ascends in height4 ,note #ah3 ,hist4 ,son4 et ,aud4 vol4 ix4 p4 #fh4 ,note #bh3 ,ibid4 ,note #ch3 ,de ,arch4 v4 #c4 ,both the comparison1 and the notice of the difference of the two cases1 prove the architect to have had very clear notions on the subject2 which he further shows by comparing the resonance of the walls of a building to the disturbance of the outline of the waves of water when they meet with a boundary1 and are thrown back4 ,therefore1 as in the outlines of waves in water1 so in the voice1 if no obstacle interrupt the foremost1 it does not disturb the second and the following ones1 so that all come to the ears of persons1 whether high up or low down1 without resonance4 ,but when they strike against obstacles1 the foremost1 being thrown back1 disturb the lines of those which follow4 ,similar analogies were employed by the ancients in order to explain the occurrence of ,echoes4 ,aristotle says1#dh ,an ,echo takes place1 when the air1 being as one body in consequence of the vessel which bounds it1 and being prevented from being thrust forwards1 is reflected #bf back like a ball4 ,nothing material was added to such views till modern times4 ,note #dh3 ,de ,anim1 ii4 #h4 ,thus the first conjectures of those who philosophized concerning sound1 led them to an opinion concerning its causes and laws1 which only required to be distinctly understood1 and traced to mechanical principles1 in order to form a genuine science of ,acoustics4 ,it was1 no doubt1 a work which required a long time and sagacious reasoners1 to supply what was thus wanting2 but still1 in consequence of this peculiar circumstance in the early condition of the prevalent doctrine concerning sound1 the history of ,acoustics assumes a peculiar form4 ,instead of containing1 like the history of ,astronomy or of ,optics1 a series of generalizations1 each including and rising above preceding generalizations2 in this case1 the highest generalization is in view from the first2 and the object of the philosopher is to determine its precise meaning and circumstances in each example4 ,instead of having a series of inductive ,truths1 successively dawning on men's minds1 we have a series of ,explanations1 in which certain experimental facts and laws are reconciled1 as to their mechanical principles and their measures1 with the general doctrine already in our possession4 ,instead of having to travel gradually towards a great discovery1 like ,universal ,gravitation1 or ,luminiferous ,undulations1 we take our stand upon acknowledged truths1 the production and propagation of sound by the motion of bodies and of air2 and we connect these with other truths1 the laws of motion and the known properties of bodies1 as1 for instance1 their elasticity4 ,instead of ,epochs of ,discovery1 we have ,solutions of ,problems2 and to these we must now proceed4 ,we must1 however1 in the first place1 notice that these ,problems include other subjects than the mere production and propagation of sound generally4 ,for such questions as these obviously occur3--what are the laws and cause of the differences of sounds2--of acute and grave1 loud and low1 continued and instantaneous2--and1 again1 of the differences of articulate sounds1 and of the quality of different voices and different instruments8 ,the first of these questions1 in particular1 the real nature of the difference of acute and grave sounds1 could not help attracting attention2 since the difference of notes in this respect was the foundation of one of the most remarkable mathematical sciences of antiquity4 ,accordingly1 we find attempts to explain this difference in the ancient writers on music4 ,in ,ptolemy's ,harmonics1 the third ,chapter of the first ,book is entitled1 ,how the #bg acuteness and graveness of notes is produced2 and in this1 after noting generally the difference of sounds1 and the causes of difference 7which he states to be the force of the striking body1 the physical constitution of the body struck1 and other causes71 he comes to the conclusion1 that the things which produce acuteness in sounds1 are a greater density and a smaller size2 the things which produce graveness1 are a greater rarity and a bulkier form4 ,he afterwards explains this so as to include a considerable portion of truth4 ,thus he says1 ,that in strings1 and in pipes1 other things remaining the same1 those which are stopped at the smaller distance from the bridge give the most acute note2 and in pipes1 those notes which come through holes nearest to the mouth-hole are most acute4 ,he even attempts a further generalization1 and says that the greater acuteness arises1 in fact1 from the body being more tense2 and that thus hardness may counteract the effect of greater density1 as we see that brass produces a more acute sound than lead4 ,but this author's notions of tension1 since they were applied so generally as to include both the tension of a string1 and the tension of a piece of solid brass1 must necessarily have been very vague4 ,and he seems to have been destitute of any knowledge of the precise nature of the motion or impulse by which sound is produced2 and1 of course1 still more ignorant of the mechanical principles by which these motions are explained4 ,the notion of vibrations of the parts of sounding bodies1 does not appear to have been dwelt upon as an essential circumstance2 though in some cases1 as in sounding strings1 the fact is very obvious4 ,and the notion of vibrations of the air does not at all appear in ancient writers1 except so far as it may be conceived to be implied in the comparison of arial and watery waves1 which we have quoted from ,vitruvius4 ,it is however1 very unlikely that1 even in the case of water1 the motions of the particles were distinctly conceived1 for such conception is far from obvious4 ,the attempts to apprehend distinctly1 and to explain mechanically1 the phenomena of sound1 gave rise to a series of ,problems1 of which we most now give a brief history4 ,the questions which more peculiarly constitute the ,science of ,acoustics1 are the questions concerning those motions or affections of the air by which it is the medium of hearing4 ,but the motions of sounding bodies have both so much connexion with those of the medium1 and so much resemblance to them1 that we shall include in our survey researches on that subject also4 #bh ,,chapter ,,ii4 ,,problem ,,of ,,the ,,vibrations ,,of ,,strings4 ,,that the continuation of sound depends on a continued minute and rapid motion1 a shaking or trembling1 of the parts of the sounding body1 was soon seen4 ,thus ,bacon says1#eh ,the duration of the sound of a bell or a string when struck1 which appears to be prolonged and gradually extinguished1 does not proceed from the first percussion2 but the trepidation of the body struck perpetually generates a new sound4 ,for if that trepidation be prevented1 and the bell or string be stopped1 the sound soon dies3 as in spinets1 as soon as the spine is let fall so as to touch the string1 the sound ceases4 ,in the case of a stretched string1 it is not difficult to perceive that the motion is a motion back and forwards across the straight line which the string occupies when at rest4 ,the further examination of the quantitative circumstances of this oscillatory motion was an obvious problem2 and especially after oscillations1 though of another kind 7those of a pendulous body71 had attracted attention1 as they had done in the school of ,galileo4 ,mersenne1 one of the promulgators of ,galileo's philosophy in ,france1 is the first author in whom ,i find an examination of the details of this case 7,harmonicorum ,liber1 ,paris1 #afcf74 ,he asserts1#fh that the differences and concords of acute and grave sounds depend on the rapidity of vibrations1 and their ratio2 and he proves this doctrine by a series of experimental comparisons4 ,thus he finds#gh that the note of a string is as its length1 by taking a string first twice1 and then four times as long as the original string1 other things remaining the same4 ,this1 indeed1 was known to the ancients1 and was the basis of that numerical indication of the notes which the proposition expresses4 ,mersenne further proceeds to show the effect of thickness and tension4 ,he finds 7,prop4 #g7 that a string must be four times as thick as another1 to give the octave below2 he finds1 also 7,prop4 #h71 that the tension must be about four times as great in order to produce the octave above4 ,from these proportions various others are deduced1 and the law of the #bi phenomena of this kind may be considered as determined4 ,mersenne also undertook to measure the phenomena numerically1 that is to determine the number of vibrations of the string in each of such cases2 which at first might appear difficult1 since it is obviously impossible to count with the eye the passages of a sounding string backwards and forwards4 ,but ,mersenne rightly assumed1 that the number of vibrations is the same so long as the tone is the same1 and that the ratios of the numbers of vibrations of different strings may be determined from the numerical relations of their notes4 ,he had1 therefore1 only to determine the number of vibrations of one certain string1 or one known note1 to know those of all others4 ,he took a musical string of three-quarters of a foot long1 stretched with a weight of six pounds and five eighths1 which he found gave him by its vibrations a certain standard note in his organ3 he found that a string of the same material and tension1 fifteen feet1 that is1 twenty times as long1 made ten recurrences in a second2 and he inferred that the number of vibrations of the shorter string must also be twenty times as great2 and thus such a string must make in one second of time two hundred vibrations4 ,note #eh3 ,hist4 ,son4 et ,aud4 vol4 ix4 p4 #ga4 ,note #fh3 ,l4 i4 ,prop4 #ae4 ,note #gh3 ,l4 ii4 ,prop4 #f4 ,this determination of ,mersenne does not appear to have attracted due notice2 but some time afterwards attempts were made to ascertain the connexion between the sound and its elementary pulsations in a more direct manner4 ,hooke1 in #afha1 produced sounds by the striking of the teeth of brass wheels1#hh and ,stancari1 in #agjf1 by whirling round a large wheel in air1 showed1 before the ,academy of ,bologna1 how the number of vibrations in a given note might be known4 ,sauveur1 who1 though deaf for the first seven years of his life1 was one of the greatest promoters of the science of sound1 and gave it its name of ,acoustics1 endeavored also1 about the same time1 to determine the number of vibrations of a standard note1 or1 as he called it1 ,fixed ,sound4 ,he employed two methods1 both ingenious and both indirect4 ,the first was the method of beats4 ,two organ-pipes1 which form a discord1 are often heard to produce a kind of howl1 or wavy noise1 the sound swelling and declining at small intervals of time4 ,this was readily and rightly ascribed to the coincidences of the pulsations of sound of the two notes after certain cycles4 ,thus1 if the number of vibrations of the notes were as fifteen to sixteen in the same time1 every fifteenth vibration of the one would coincide with every #cj sixteenth vibration of the other1 while all the intermediate vibrations of the two tones would1 in various degrees1 disagree with each other2 and thus every such cycle1 of fifteen and sixteen vibrations1 might be heard as a separate beat of sound4 ,now1 ,sauveur wished to take a case in which these beats were so slow as to be counted1#ih and in which the ratio of the vibrations of the notes was known from a knowledge of their musical relations4 ,thus if the two notes form an interval of a semitone1 their ratio will be that above supposed1 fifteen to sixteen2 and if the beats be found to be six in a second1 we know that1 in that time1 the graver note makes ninety and the acuter ninety-six vibrations4 ,in this manner ,sauveur found that an open organ-pipe1 five feet long1 gave one hundred vibrations in a second4 ,note #hh3 ,life1 p4 xxiii4 ,note #ih3 ,ac4 ,sc4 ,hist4 #agjj1 p4 #aca4 ,sauveur's other method is more recondite1 and approaches to a mechanical view of the question4#ajh ,he proceeded on this basis2 a string1 horizontally stretched1 cannot be drawn into a mathematical straight line1 but always hangs in a very flat curve1 or festoon4 ,hence ,sauveur assumed that its transverse vibrations may be conceived to be identical with the lateral swingings of such a festoon4 ,observing that the string ,c1 in the middle of a harpsichord1 hangs in such a festoon to the amount of #acbcrd of an inch1 he calculates1 by the laws of pendulums1 the time of oscillation1 and finds it #aabbnd of a second4 ,thus this ,c1 his fixed note1 makes one hundred and twenty-two vibrations in a second4 ,it is curious that this process1 seemingly so arbitrary1 is capable of being justified on mechanical principles2 though we can hardly give the author credit for the views which this justification implies4 ,it is1 therefore1 easy to understand that it agreed with other experiments1 in the laws which it gave for the dependence of the tone on the length and tension4 ,note #ajh3 ,ac4 ,sc4 ,hist4 #agac4 ,the problem of satisfactorily explaining this dependence1 on mechanical principles1 naturally pressed upon the attention of mathematicians when the law of the phenomena was thus completely determined by ,mersenne and ,sauveur4 ,it was desirable to show that both the circumstances and the measure of the phenomena were such as known mechanical causes and laws would explain4 ,but this problem1 as might be expected1 was not attacked till mechanical principles1 and the modes of applying them1 had become tolerably familiar4 ,as the vibrations of a string are produced by its tension1 it appeared to be necessary1 in the first place1 to determine the law of the tension #ca which is called into action by the motion of the string2 for it is manifest that1 when the string is drawn aside from the straight line into which it is stretched1 there arises an additional tension1 which aids in drawing it back to the straight line as soon as it is let go4 ,hooke 7,on ,spring1 #afgh7 determined the law of this additional tension1 which he expressed in his noted formula1 ,ut tensio sic vis1 the ,force is as the ,tension2 or rather1 to express his meaning more clearly1 the ,force of tension is as the ,extension1 or1 in a string1 as the increase of length4 ,but1 in reality1 this principle1 which is important in many acoustical problems1 is1 in the one now before us1 unimportant2 the force which urges the string towards the straight line1 depends1 with such small extensions as we have now to consider1 not on the extension1 but on the curvature2 and the power of treating the mathematical difficulty of curvature1 and its mechanical consequences1 was what was requisite for the solution of this problem4 ,the problem1 in its proper aspect1 was first attacked and mastered by ,brook ,taylor1 an ,english mathematician of the school of ,newton1 by whom the solution was published in #agae1 in his ,methodus ,incrementorum4 ,taylor's solution was indeed imperfect1 for it only pointed out a form and a mode of vibration1 with which the string might move consistently with the laws of mechanics2 not the mode in which it must move1 supposing its form to be any whatever4 ,it showed that the curve might be of the nature of that which is called the companion to the cycloid2 and1 on the supposition of the curve of the string being of this form1 the calculation confirmed the previously established laws by which the tone1 or the time of vibration1 had been discovered to depend on the length1 tension1 and bulk of the string4 ,the mathematical incompleteness of ,taylor's reasoning must not prevent us from looking upon his solution of the problem as the most important step in the progress of this part of the subject3 for the difficulty of applying mechanical principles to the question being once overcome1 the extension and correction of the application was sure to be undertaken by succeeding mathematicians2 and1 accordingly1 this soon happened4 ,we may add1 moreover1 that the subsequent and more general solutions require to be considered with reference to ,taylor's1 in order to apprehend distinctly their import2 and further1 that it was almost evident to a mathematician1 even before the general solution had appeared1 that the dependence of the time of vibration on the length and tension1 would be the same in the general case as in the #cb ,taylorian curve2 so that1 for the ends of physical philosophy1 the solution was not very incomplete4 ,john ,bernoulli1 a few years afterwards1#aah solved the problem of vibrating chords on nearly the same principles and suppositions as ,taylor2 but a little later 7in #agdg71 the next generation of great mathematicians1 ,d',alembert1 ,euler1 and ,daniel ,bernoulli1 applied the increased powers of analysis to give generality to the mode of treating this question2 and especially the calculus of partial differentials1 invented for this purpose4 ,but at this epoch1 the discussion1 so far as it bore on physics1 belonged rather to the history of another problem1 which comes under our notice hereafter1 that of the composition of vibrations2 we shall1 therefore1 defer the further history of the problem of vibrating strings1 till we have to consider it in connexion with new experimental facts4 ,note #aah3 ,op4 iii4 p4 #bjg4 ,,chapter ,,iii4 ,,problem ,,of ,,the ,,propagation ,,of ,,sound4 ,,we have seen that the ancient philosophers1 for the most part1 held that sound was transmitted1 as well as produced1 by some motion of the air1 without defining what kind of motion this was2 that some writers1 however1 applied to it a very happy similitude1 the expansive motion of the circular waves produced by throwing a stone into still water2 but that notwithstanding1 some rejected this mode of conception1 as1 for instance1 ,bacon1 who ascribed the transmission of sound to certain spiritual species4 ,though it was an obvious thought to ascribe the motion of sound to some motion of air2 to conceive what kind of motion could and did produce this effect1 must have been a matter of grave perplexity at the time of which we are speaking2 and is far from easy to most persons even now4 ,we may judge of the difficulty of forming this conception1 when we recollect that ,john ,bernoulli the younger#abh declared1 that he could not understand ,newton's proposition on this subject4 ,the difficulty consists in this2 that the movement of the parts of air1 in which sound consists1 travels along1 but that the parts #cc of air themselves do not so travel4 ,accordingly ,otto ,guericke1#ach the inventor of the air-pump1 asks1 ,how can sound be conveyed by the motion of the air8 when we find that it is better conveyed through air that is still1 than when there is a wind4 ,we may observe1 however1 that he was partly misled by finding1 as he thought1 that a bell could be heard in the vacuum of his air-pump2 a result which arose1 probably1 from some imperfection in his apparatus4 ,note #abh3 ,prize ,dis4 on ,light1 #agcf4 ,note #ach3 ,de ,vac4 ,spat4 p4 #ach4 ,attempts were made to determine1 by experiment1 the circumstances of the motion of sound2 and especially its velocity4 ,gassendi#adh was one of the first who did this4 ,he employed fire-arms for the purpose1 and thus found the velocity to be #adgc ,paris feet in a second4 ,roberval found a velocity so small 7#efj feet7 that it threw uncertainty upon the rest1 and affected ,newton's reasonings subsequently4#aeh ,cassini1 ,huyghens1 ,picard1 ,rmer1 found a velocity of #aagb ,paris feet1 which is more accurate than the former4 ,gassendi had been surprised to find that the velocity with which sounds travel1 is the same whether they are loud or gentle4 ,note #adh3 ,fischer1 ,gesch4 d4 ,physik4 vol4 i4 #aga4 ,note #aeh3 ,newt4 ,prin4 ,b4 ii4 ,p4 #ej1 ,schol4 ,the explanation of this constant velocity of sound1 and of its amount1 was one of the problems of which a solution was given in the ,great ,charter of modern science1 ,newton's ,principia 7#afhg74 ,there1 for the first time1 were explained the real nature of the motions and mutual action of the parts of the air through which sound is transmitted4 ,it was shown#afh that a body vibrating in an elastic medium1 will propagate pulses through the medium2 that is1 the parts of the medium will move forwards and backwards1 and this motion will affect successively those parts which are at a greater and greater distance from the origin of motion4 ,the parts1 in going forwards1 produce condensation2 in returning to their first places1 they allow extension2 and the play of the elasticities developed by these expansions and contractions1 supplies the forces which continue to propagate the motion4 ,note #afh3 ,newt4 ,prin4 ,b4 ii4 ,p4 #dc4 ,the idea of such a motion as this1 is1 as we have said1 far from easy to apprehend distinctly3 but a distinct apprehension of it is a step essential to the physical part of the sciences now under notice2 for it is by means of such pulses1 or undulations1 that not only sound1 but light1 and probably heat1 are propagated4 ,we constantly meet with evidence of the difficulty which men have in conceiving this undulatory motion1 and in separating it from a local motion of the medium as a #cd mass4 ,for instance1 it is not easy at first to conceive the waters of a great river flowing constantly down towards the sea1 while waves are rolling up the very same part of the stream2 and while the great elevation1 which makes the tide1 is travelling from the sea perhaps with a velocity of fifty miles an hour4 ,the motion of such a wave1 or elevation1 is distinct from any stream1 and is of the nature of undulations in general4 ,the parts of the fluid stir for a short time and for a small distance1 so as to accumulate themselves on a neighboring part1 and then retire to their former place2 and this movement affects the parts in the order of their places4 ,perhaps if the reader looks at a field of standing corn when gusts of wind are sweeping over it in visible waves1 he will have his conception of this matter aided2 for he will see that here1 where each ear of grain is anchored by its stalk1 there can be no permanent local motion of the substance1 but only a successive stooping and rising of the separate straws1 producing hollows and waves1 closer and laxer strips of the crowded ears4 ,newton had1 moreover1 to consider the mechanical consequences which such condensations and rarefactions of the elastic medium1 air1 would produce in the parts of the fluid itself4 ,employing known laws of the elasticity of air1 he showed1 in a very remarkable proposition1#agh the law according to which the particles of air might vibrate4 ,we may observe1 that in this solution1 as in that of the vibrating string already mentioned1 a rule was exhibited according to which the particles might oscillate1 but not the law to which they must conform4 ,it was proved that1 by taking the motion of each particle to be perfectly similar to that of a pendulum1 the forces1 developed by contraction and expansion1 were precisely such as the motion required2 but it was not shown that no other type of oscillation would give rise to the same accordance of force and motion4 ,newton's reasoning also gave a determination of the speed of propagation of the pulses3 it appeared that sound ought to travel with the velocity which a body would acquire by falling freely through half the height of a homogeneous atmosphere2 the height of a homogeneous atmosphere being the height which the air must have1 in order to produce1 at the earth's surface1 the actual atmospheric pressure1 supposing no diminution of density to take place in ascending4 ,this height is about #bi1jjj feet2 and hence it followed that the velocity was #ifh feet4 ,this velocity is really considerably less than that of sound2 but at the time of which #ce we speak1 no accurate measure had been established2 and ,newton persuaded himself1 by experiments made in the cloister of ,trinity ,college1 his residence1 that his calculation was not far from the fact4 ,when1 afterwards1 more exact experiments showed the velocity to be #aadb ,english feet1 ,newton attempted to explain the difference by various considerations1 none of which were adequate to the purpose2--as1 the dimensions of the solid particles of which the fluid air consists2--or the vapors which are mixed with it4 ,other writers offered other suggestions2 but the true solution of the difficulty was reserved for a period considerably subsequent4 ,note #agh3 ,princ4 ,b4 ii4 ,p4 #dh4 ,newton's calculation of the motion of sound1 though logically incomplete1 was the great step in the solution of the problem2 for mathematicians could not but presume that his result was not restricted to the hypothesis on which he had obtained it2 and the extension of the solution required only mere ordinary talents4 ,the logical defect of his solution was assailed1 as might have been expected4 ,cranmer 7professor at ,geneva71 in #agda1 conceived that he was destroying the conclusiveness of ,newton's reasoning1 by showing that it applied equally to other modes of oscillation4 ,this1 indeed1 contradicted the enunciation of the #dhth ,prop4 of the ,second ,book of the ,principia2 but it confirmed and extended all the general results of the demonstration2 for it left even the velocity of sound unaltered1 and thus showed that the velocity did not depend mechanically on the type of the oscillation4 ,but the satisfactory establishment of this physical generalization was to be supplied from the vast generalizations of analysis1 which mathematicians were now becoming able to deal with4 ,accordingly this task was performed by the great master of analytical generalization1 ,lagrange1 in #agei1 when1 at the age of twenty-three1 he and two friends published the first volume of the ,turin ,memoirs4 ,euler1 as his manner was1 at once perceived the merit of the new solution1 and pursued the subject on the views thus suggested4 ,various analytical improvements and extensions were introduced into the solution by the two great mathematicians2 but none of these at all altered the formula by which the velocity of sound was expressed2 and the discrepancy between calculation and observation1 about one-sixth of the whole1 which had perplexed ,newton1 remained still unaccounted for4 ,the merit of satisfactorily explaining this discrepancy belongs to ,laplace4 ,he was the first to remark#ahh that the common law of the #cf changes of elasticity in the air1 as dependent on its compression1 cannot be applied to those rapid vibrations in which sound consists1 since the sudden compression produces a degree of heat which additionally increases the elasticity4 ,the ratio of this increase depended on the experiments by which the relation of heat and air is established4 ,laplace1 in #ahaf1 published#aih the theorem on which the correction depends4 ,on applying it1 the calculated velocity of sound agreed very closely with the best antecedent experiments1 and was confirmed by more exact ones instituted for that purpose4 ,note #ahh3 ,mc4 ,cl4 t4 v4 l4 xii4 p4 #if4 ,note #aih3 ,ann4 ,phys4 et ,chim4 t4 iii4 p4 #bhh4 ,this step completes the solution of the problem of the propagation of sound1 as a mathematical induction1 obtained from1 and verified by1 facts4 ,most of the discussions concerning points of analysis to which the investigations on this subject gave rise1 as1 for instance1 the admissibility of discontinuous functions into the solutions of partial differential equations1 belong to the history of pure mathematics4 ,those which really concern the physical theory of sound may be referred to the problem of the motion of air in tubes1 to which we shall soon have to proceed2 but we must first speak of another form which the problem of vibrating strings assumed4 ,it deserves to be noticed that the ultimate result of the study of the undulations of fluids seems to show that the comparison of the motion of air in the diffusion of sound with the motion of circular waves from a centre in water1 which is mentioned at the beginning of this chapter1 though pertinent in a certain way1 is not exact4 ,it appears by ,mr4 ,scott's recent investigations concerning waves1#bjh that the circular waves are oscillating waves of the ,second order1 and are gregarious4 ,the sound-wave seems rather to resemble the great solitary ,wave of ,translation of the ,first order1 of which we have already spoken in ,book vi4 chapter vi4 ,note #bjh3 ,brit4 ,ass4 ,reports for #ahdd1 p4 #cfa4 ,,chapter ,,iv4 ,,problem ,,of ,,different ,,sounds ,,of ,,the ,,same ,,string4 ,,it had been observed at an early period of acoustical knowledge1 that one string might give several sounds4 ,mersenne and others #cg had noticed#bah that when a string vibrates1 one which is in unison with it vibrates without being touched4 ,he was also aware that this was true if the second string was an octave or a twelfth below the first4 ,this was observed as a new fact in ,england in #afgd1 and communicated to the ,royal ,society by ,wallis4#bbh ,but the later observers ascertained further1 that the longer string divides itself into two1 or into three equal parts1 separated by nodes1 or points of rest2 this they proved by hanging bits of paper on different parts of the string4 ,the discovery so modified was again made by ,sauveur#bch about #agjj4 ,the sounds thus produced in one string by the vibration of another1 have been termed ,sympathetic ,sounds4 ,similar sounds are often produced by performers on stringed instruments1 by touching the string at one of its aliquot divisions1 and are then called the ,acute harmonics4 ,such facts were not difficult to explain on ,taylor's view of the mechanical condition of the string2 but the difficulty was increased when it was noticed that a sounding body could produce these different notes at the same time4 ,mersenne had remarked this1 and the fact was more distinctly observed and pursued by ,sauveur4 ,the notes thus produced in addition to the genuine note of the string1 have been called ,secondary ,notes2 those usually heard are1 the ,octave1 the ,twelfth1 and the ,seventeenth above the note itself4 ,to supply a mode of conceiving distinctly1 and explaining mechanically1 vibrations which should allow of such an effect1 was therefore a requisite step in acoustics4 ,note #bah3 ,harm4 lib4 iv4 ,prop4 #bh 7#afcf74 ,note #bbh3 ,ph4 ,tr4 #afgg1 ,april4 ,note #bch3 ,a4 ,p4 #agja4 ,this task was performed by ,daniel ,bernoulli in a memoir published in #agee4bdh ,he there stated and proved the ,principle of the coexistence of small vibrations4 ,it was already established1 that a string might vibrate either in a single swelling 7if we use this word to express the curve between two nodes which ,bernoulli calls a ventre71 or in two or three or any number of equal swellings with immoveable nodes between4 ,daniel ,bernoulli showed further1 that these nodes might be combined1 each taking place as if it were the only one4 ,this appears sufficient to explain the coexistence of the harmonic sounds just noticed4 ,d',alembert1 indeed1 in the article ,fundamental in the ,french ,encyclopdie1 and ,lagrange in his ,dissertation on ,sound in the ,turin ,memoirs1#beh offer several objections to this explanation2 and it cannot be denied that the subject has its difficulties2 but #ch still these do not deprive ,bernoulli of the merit of having pointed out the principle of ,coexistent ,vibrations1 or divest that principle of its value in physical science4 ,note #bdh3 ,berlin ,mem4 #agec1 p4 #adg4 ,note #beh3 ,t4 i4 pp4 #fd1 #ajc4 ,daniel ,bernoulli's ,memoir1 of which we speak1 was published at a period when the clouds which involve the general analytical treatment of the problem of vibrating strings1 were thickening about ,euler and ,d',alembert1 and darkening into a controversial hue2 and as ,bernoulli ventured to interpose his view1 as a solution of these difficulties1 which1 in a mathematical sense1 it is not1 we can hardly be surprised that he met with a rebuff4 ,the further prosecution of the different modes of vibration of the same body need not be here considered4 ,the sounds which are called ,grave ,harmonics1 have no analogy with the ,acute ,harmonics above-mentioned2 nor do they belong to this section2 for in the case of ,grave ,harmonics1 we have one sound from the co-operation of two strings1 instead of several sounds from one string4 ,these harmonics are1 in fact1 connected with beats1 of which we have already spoken2 the beats becoming so close as to produce a note of definite musical quality4 ,the discovery of the ,grave ,harmonics is usually ascribed to ,tartini1 who mentions them in #aged2 but they are first noticed#bfh in the work of ,sorge ,on tuning ,organs1 #agdd4 ,he there expresses this discovery in a query4 ,whence comes it1 that if we tune a fifth 7#b 3 #c71 a third sound is faintly heard1 the octave below the lower of the two notes8 ,nature shows that with #b 3 #c1 she still requires the unity1 to perfect the order #a1 #b1 #c4 ,the truth is1 that these numbers express the frequency of the vibrations1 and thus there will be coincidences of the notes #b and #c1 which are of the frequency #a1 and consequently give the octave below the sound #b4 ,this is the explanation given by ,lagrange1#bgh and is indeed obvious4 ,note #bfh3 ,chladni4 ,acoust4 p4 #bed4 ,note #bgh3 ,mem4 ,tur4 i4 p4 #ajd4 ,,chapter ,v4 ,,problem ,,of ,,the ,,sounds ,,of ,,pipes4 ,,it was taken for granted by those who reasoned on sounds1 that the sounds of flutes1 organ-pipes1 and wind-instruments in general1 #ci consisted in vibrations of some kind2 but to determine the nature and laws of these vibrations1 and to reconcile them with mechanical principles1 was far from easy4 ,the leading facts which had been noticed were1 that the note of a pipe was proportional to its length1 and that a flute and similar instruments might be made to produce some of the acute harmonics1 as well as the genuine note4 ,it had further been noticed1#bhh that pipes closed at the end1 instead of giving the series of harmonics #a1 1 1 1 c41 would give only those notes which answer to the odd numbers #a1 1 1 c4 ,in this problem also1 ,newton#bih made the first step to the solution4 ,at the end of the propositions respecting the velocity of sound1 of which we have spoken1 he noticed that it appeared by taking ,mersenne's or ,sauveur's determination of the number of vibrations corresponding to a given note1 that the pulse of air runs over twice the length of the pipe in the time of each vibration4 ,he does not follow out this observation1 but it obviously points to the theory1 that the sound of a pipe consists of pulses which travel back and forwards along its length1 and are kept in motion by the breath of the player4 ,this supposition would account for the observed dependence of the note on the length of the pipe4 ,the subject does not appear to have been again taken up in a theoretical way till about #agfj2 when ,lagrange in the second volume of the ,turin ,memoirs1 and ,d4 ,bernoulli in the ,memoirs of the ,french ,academy for #agfb1 published important essays1 in which some of the leading facts were satisfactorily explained1 and which may therefore be considered as the principal solutions of the problem4 ,note #bhh3 ,d4 ,bernoulli1 ,berlin4 ,mem4 #agec1 p4 #aej4 ,note #bih3 ,princip4 ,schol4 ,prop4 #ej4 ,in these solutions there was necessarily something hypothetical4 ,in the case of vibrating strings1 as we have seen1 the ,form of the vibrating curve was guessed at only1 but the existence and position of the ,nodes could be rendered visible to the eye4 ,in the vibrations of air1 we cannot see either the places of nodes1 or the mode of vibration2 but several of the results are independent of these circumstances4 ,thus both of the solutions explain the fact1 that a tube closed at one end is in unison with an open tube of double the length2 and1 by supposing nodes to occur1 they account for the existence of the odd series of harmonics alone1 #a1 #c1 #e1 in closed tubes1 while the whole series1 #a1 #b1 #c1 #d1 #e1 c41 occurs in open ones4 ,both views of the nature of the vibration appear to be nearly the same2 though ,lagrange's is expressed with an analytical generality which renders it obscure1 and ,bernoulli has perhaps #dj laid down an hypothesis more special than was necessary4 ,lagrange#cjh considers the vibration of open flutes as the oscillations of a fibre of air1 under the condition that its elasticity at the two ends is1 during the whole oscillation1 the same as that of the surrounding atmosphere4 ,bernoulli supposes#cah the whole inertia of the air in the flute to be collected into one particle1 and this to be moved by the whole elasticity arising from this displacement4 ,it may be observed that both these modes of treating the matter come very near to what we have stated as ,newton's theory2 for though ,bernoulli supposes all the air in the flute to be moved at once1 and not successively1 as by ,newton's pulse1 in either case the whole elasticity moves the whole air in the tube1 and requires more time to do this according to its quantity4 ,since that time1 the subject has received further mathematical developement from ,euler1#cbh ,lambert1#cch and ,poisson2#cdh but no new explanation of facts has arisen4 ,attempts have however been made to ascertain experimentally the places of the nodes4 ,bernoulli himself had shown that this place was affected by the amount of the opening1 and ,lambert#ceh had examined other cases with the same view4 ,savart traced the node in various musical pipes under different conditions2 and very recently ,mr4 ,hopkins1 of ,cambridge1 has pursued the same experimental inquiry4#cfh ,it appears from these researches1 that the early assumptions of mathematicians with regard to the position of the nodes1 are not exactly verified by the facts4 ,when the air in a pipe is made to vibrate so as to have several nodes which divide it into equal parts1 it had been supposed by acoustical writers that the part adjacent to the open end was half of the other parts2 the outermost node1 however1 is found experimentally to be displaced from the position thus assigned to it1 by a quantity depending on several collateral circumstances4 ,note #cjh3 ,mm4 ,turin1 vol4 ii4 p4 #aed4 ,note #cah3 ,mm4 ,berlin1 #agec1 p4 #ddf4 ,note #cbh3 ,nov4 ,act4 ,petrop4 tom4 xvi4 ,note #cch3 ,acad4 ,berlin1 #agge4 ,note #cde3 ,journ4 ,ec4 ,polyt4 cap4 #ad4 ,note #ceh3 ,acad4 ,berlin1 #agge4 ,note #cfh3 ,camb4 ,trans4 vol4 v4 p4 #bcd4 ,since our purpose was to consider this problem only so far as it has tended towards its mathematical solution1 we have avoided saying anything of the dependence of the mode of vibration on the cause by which the sound is produced2 and consequently1 the researches on the effects of reeds1 embouchures1 and the like1 by ,chladni1 ,savart1 ,willis1 and others1 do not belong to our subject4 ,it is easily seen that the complex effect of the elasticity and other properties of the reed and of the air together1 is a problem of which we can hardly #da hope to give a complete solution till our knowledge has advanced much beyond its present condition4 ,indeed1 in the science of ,acoustics there is a vast body of facts to which we might apply what has just been said2 but for the sake of pointing out some of them1 we shall consider them as the subjects of one extensive and yet unsolved problem4 ,,chapter ,,vi4 ,,problem ,,of ,,different ,,modes ,,of ,,vibration ,,of ,,bodies ,,in ,,general4 ,,not only the objects of which we have spoken hitherto1 strings and pipes1 but almost all bodies are capable of vibration4 ,bells1 gongs1 tuning-forks1 are examples of solid bodies2 drums and tambourines1 of membranes2 if we run a wet finger along the edge of a glass goblet1 we throw the fluid which it contains into a regular vibration2 and the various character which sounds possess according to the room in which they are uttered1 shows that large masses of air have peculiar modes of vibration4 ,vibrations are generally accompanied by sound1 and they may1 therefore1 be considered as acoustical phenomena1 especially as the sound is one of the most decisive facts in indicating the mode of vibration4 ,moreover1 every body of this kind can vibrate in many different ways1 the vibrating segments being divided by ,nodal ,lines and ,surfaces of various form and number4 ,the mode of vibration1 selected by the body in each case1 is determined by the way in which it is held1 the way in which it is set in vibration1 and the like circumstances4 ,the general problem of such vibrations includes the discovery and classification of the phenomena2 the detection of their formal laws2 and1 finally1 the explanation of these on mechanical principles4 ,we must speak very briefly of what has been done in these ways4 ,the facts which indicate ,nodal ,lines had been remarked by ,galileo1 on the sounding board of a musical instrument2 and ,hooke had proposed to observe the vibrations of a bell by strewing flour upon it4 ,but it was ,chladni1 a ,german philosopher1 who enriched acoustics with the discovery of the vast variety of symmetrical figures of ,nodal ,lines1 which are exhibited on plates of regular forms1 when #db made to sound4 ,his first investigations on this subject1 ,entdeckungen ber die ,theorie des ,klangs1 were published #aghg2 and in #ahjb and #ahag he added other discoveries4 ,in these works he not only related a vast number of new and curious facts1 but in some measure reduced some of them to order and law4 ,for instance1 he has traced all the vibrations of square plates to a resemblance with those forms of vibration in which ,nodal ,lines are parallel to one side of the square1 and those in which they are parallel to another side2 and he has established a notation for the modes of vibration founded on this classification4 ,thus1 #e-b denotes a form in which there are five nodal lines parallel to one side1 and two to another2 or a form which can be traced to a disfigurement of such a standard type4 ,savart pursued this subject still further2 and traced1 by actual observation1 the forms of the ,nodal ,surfaces which divide solid bodies1 and masses of air1 when in a state of vibration4 ,the dependence of such vibrations upon their physical cause1 namely1 the elasticity of the substance1 we can conceive in a general way2 but the mathematical theory of such cases is1 as might be supposed1 very difficult1 even if we confine ourselves to the obvious question of the mechanical possibility of these different modes of vibration1 and leave out of consideration their dependence upon the mode of excitation4 ,the transverse vibrations of elastic rods1 plates1 and rings1 had been considered by ,euler in #aggi2 but his calculation concerning plates had foretold only a small part of the curious phenomena observed by ,chladni2#cgh and the several notes which1 according to his calculation1 the same ring ought to give1 were not in agreement with experiment4#chh ,indeed1 researches of this kind1 as conducted by ,euler1 and other authors1#cih rather were1 and were intended for1 examples of analytical skill1 than explanations of physical facts4 ,james ,bernoulli1 after the publication of ,chladni's experiments in #aghg1 attempted to solve the problem for plates1 by treating a plate as a collection of fibres2 but1 as ,chladni observes1 the justice of this mode of conception is disproved1 by the disagreement of the results with experiment4 ,note #cgh3 ,fischer1 vi4 #ehg4 ,note #chh3 ,ib4 vi4 #eif4 ,note #cih3 ,see ,chladni1 p4 #dgd4 ,the ,institute of ,france1 which had approved of ,chladni's labours1 proposed1 in #ahji1 the problem now before us as a prize-question3#djh--,to give the mathematical theory of the vibrations of elastic #dc surfaces1 and to compare it with experiment4 ,only one memoir was sent in as a candidate for the prize2 and this was not crowned1 though honorable mention was made of it4#dah ,the formul of ,james ,bernoulli were1 according to ,m4 ,poisson's statement1 defective1 in consequence of his not taking into account the normal force which acts at the exterior boundary of the plate4#dbh ,the author of the anonymous memoir corrected this error1 and calculated the note corresponding to various figures of the nodal lines2 and he found an agreement with experiment sufficient to justify his theory4 ,he had not1 however1 proved his fundamental equation1 which ,m4 ,poisson demonstrated in a ,memoir1 read in #ahad4dch ,at a more recent period also1 ,,mm4 ,poisson and ,cauchy 7as well as a lady1 ,mlle4 ,sophie ,germain7 have applied to this problem the artifices of the most improved analysis4 ,m4 ,poisson#ddh determined the relation of the notes given by the longitudinal and the transverse vibrations of a rod2 and solved the problem of vibrating circular plates when the nodal lines are concentric circles4 ,in both these cases1 the numerical agreement of his results with experience1 seemed to confirm the justice of his fundamental views4#deh ,he proceeds upon the hypothesis1 that elastic bodies are composed of separate particles held together by the attractive forces which they exert upon each other1 and distended by the repulsive force of heat4 ,m4 ,cauchy#dfh has also calculated the transverse1 longitudinal1 and rotatory vibrations of elastic rods1 and has obtained results agreeing closely with experiment through a considerable list of comparisons4 ,the combined authority of two profound analysts1 as ,,mm4 ,poisson and ,cauchy are1 leads us to believe that1 for the simpler cases of the vibrations of elastic bodies1 ,mathematics has executed her task2 but most of the more complex cases remain as yet unsubdued4 ,note #djh3 ,see ,chladni1 p4 #ceg4 ,note #dah3 ,poisson's ,mm4 in ,ac4 ,sc4 #ahab1 p4 #afi4 ,note #dbh3 ,ib4 p4 #bbj4 ,note #dch3 ,ib4 #ahab1 p4 #b4 ,note #ddh3 ,ib4 t4 viii4 #ahbi4 ,note #deh3 ,an4 ,chim4 tom4 xxxvi4 #ahbg1 p4 #ij4 ,note #dfh3 ,exercices de ,mathmatique1 iii4 and iv4 ,the two brothers1 ,ernest and ,william ,weber1 made many curious observations on undulations1 which are contained in their ,wellenlehre1 7,doctrine of ,waves17 published at ,leipsig in #ahbe4 ,they were led to suppose1 7as ,young had suggested at an earlier period17 that ,chladni's figures of nodal lines in plates were to be accounted for by the superposition of undulations4#dgh ,mr4 ,wheatstone#dhh has undertaken to account for ,chladni's figures of vibrating square plates by this #dd superposition of two or more simple and obviously allowable modes of nodal division1 which have the same time of vibration4 ,he assumes1 for this purpose1 certain primary figures1 containing only parallel nodal lines2 and by combining these1 first in twos1 and then in fours1 he obtains most of ,chladni's observed figures1 and accounts for their transitions and deviations from regularity4 ,note #dgh3 ,wellenlehre1 p4 #dgd4 ,note #dhh3 ,phil4 ,trans4 #ahcc1 p4 #eic4 ,the principle of the superposition of vibrations is so solidly established as a mechanical truth1 that we may consider an acoustical problem as satisfactorily disposed of when it is reduced to that principle1 as well as when it is solved by analytical mechanics3 but at the same time we may recollect1 that the right application and limitation of this law involves no small difficulty2 and in this case1 as in all advances in physical science1 we cannot but wish to have the new ground which has been gained1 gone over by some other person in some other manner2 and thus secured to us as a permanent possession4 ,savart's ,laws4--,in what has preceded1 the vibrations of bodies have been referred to certain general classes1 the separation of which was suggested by observation2 for example1 the transverse1 longitudinal1 and rotatory1#dih vibrations of rods4 ,the transverse vibrations1 in which the rod goes backwards and forwards across the line of its length1 were the only ones noticed by the earlier acousticians3 the others were principally brought into notice by ,chladni4 ,as we have already seen in the preceding pages1 this classification serves to express important laws2 as1 for instance1 a law obtained by ,m4 ,poisson which gives the relation of the notes produced by the transverse and longitudinal vibrations of a rod4 ,but this distinction was employed by ,m4 ,felix ,savart to express laws of a more general kind2 and then1 as often happens in the progress of science1 by pursuing these laws to a higher point of generality1 the distinction again seemed to vanish4 ,a very few words will explain these steps4 ,note #dih3 ,vibrations tournantes4 ,it was long ago known that vibrations may be communicated by contact4 ,the distinction of transverse and longitudinal vibrations being established1 ,savart found that if one rod touched another perpendicularly1 the longitudinal vibrations of the first occasion transverse vibrations in the second1 and vice vers4 ,this is the more remarkable1 since the two sets of vibrations are not equal in rapidity1 and therefore cannot sympathize in any obvious manner4#ejh ,savart found himself #de able to generalize this proposition1 and to assert that in any combination of rods1 strings1 and lamin1 at right angles to each other1 the longitudinal and transverse vibrations affect respectively the rods in the one and other direction1#eah so that when the horizontal rods1 for example1 vibrate in the one way1 the vertical rods vibrate in the other4 ,note #ejh3 ,an4 ,chim4 #ahai1 tom4 xiv4 p4 #ach4 ,note #eah3 ,an4 ,chim4 p4 #aeb4 ,this law was thus expressed in terms of that classification of vibrations of which we have spoken4 ,yet we easily see that we may express it in a more general manner1 without referring to that classification1 by saying1 that vibrations are communicated so as always to be parallel to their original direction4 ,and by following it out in this shape by means of experiment1 ,m4 ,savart was led1 a short time afterwards1 to deny that there is any essential distinction in these different kinds of vibration4 ,we are thus led1 he says#ebh in #ahbb1 to consider normal transverse vibrations as only one circumstance in a more general motion common to all bodies1 analogous to tangential longitudinal and rotatory vibrations2 that is1 as produced by small molecular oscillations1 and differently modified according to the direction which it affects1 relatively to the dimensions of the vibrating body4 ,note #ebh3 ,ib4 t4 xxv4 p4 #cc4 ,these inductions1 as he properly calls them1 are supported by a great mass of ingenious experiments2 and may be considered as well established1 when they are limited to molecular oscillations1 employing this phrase in the sense in which it is understood in the above statement2 and also when they are confined to bodies in which the play of elasticity is not interrupted by parts more rigid than the rest1 as the sound-post of a violin4#ech ,and before ,i quit the subject1 ,i may notice a consequence which ,m4 ,savart has deduced from his views1 and which1 at first sight1 appears to overturn most of the earlier doctrines respecting vibrating bodies4 ,it was formerly held that tense strings and elastic rods could vibrate only in a determinate series of modes of division1 with no intermediate steps4 ,but ,m4 ,savart maintains1#edh on the contrary1 that they produce sounds which are gradually transformed into one another1 by indefinite intermediate degrees4 ,the reader may naturally ask1 what is the solution of this apparent #df contradiction between the earliest and the latest discoveries in acoustics4 ,and the answer must be1 that these intermediate modes of vibration are complex in their nature1 and difficult to produce2 and that those which were formerly believed to be the only possible vibrating conditions1 are so eminent above all the rest by their features1 their simplicity1 and their facility1 that we may still1 for common purposes1 consider them as a class apart2 although for the sake of reaching a general theorem1 we may associate them with the general mass of cases of molecular vibrations4 ,and thus we have no exception here1 as we can have none in any case1 to our maxim1 that what formed part of the early discoveries of science1 forms part of its latest systems4 ,note #ech3 ,for the suggestion of the necessity of this limitation ,i am indebted to ,mr4 ,willis4 ,note #edh3 ,an4 ,chim4 #ahbf1 t4 xxxii4 p4 #chd4 ,we have thus surveyed the progress of the science of sound up to recent times1 with respect both to the discovery of laws of phenomena1 and the reduction of these to their mechanical causes4 ,the former branch of the science has necessarily been inductively pursued2 and therefore has been more peculiarly the subject of our attention4 ,and this consideration will explain why we have not dwelt more upon the deductive labors of the great analysts who have treated of this problem4 ,to those who are acquainted with the high and deserved fame which the labors of ,d',alembert1 ,euler1 ,lagrange1 and others1 upon this subject1 enjoy among mathematicians1 it may seem as if we had not given them their due prominence in our sketch4 ,but it is to be recollected here1 as we have already observed in the case of hydrodynamics1 that even when the general principles are uncontested1 mere mathematical deductions from them do not belong to the history of physical science1 except when they point out laws which are intermediate between the general principle and the individual facts1 and which observation may confirm4 ,the business of constructing any science may be figured as the task of forming a road on which our reason can travel through a certain province of the external world4 ,we have to throw a bridge which may lead from the chambers of our own thoughts1 from our speculative principles1 to the distant shore of material facts4 ,but in all cases the abyss is too wide to be crossed1 except we can find some intermediate points on which the piers of our structure may rest4 ,mere facts1 without connexion or law1 are only the rude stones hewn from the opposite bank1 of which our arches may1 at some time1 be built4 ,but mere hypothetical mathematical calculations are only plans of projected structures2 and those plans which exhibit only one vast #dg and single arch1 or which suppose no support but that which our own position supplies1 will assuredly never become realities4 ,we must have a firm basis of intermediate generalizations in order to frame a continuous and stable edifice4 ,in the subject before us1 we have no want of such points of intermediate support1 although they are in many instances irregularly distributed and obscurely seen4 ,the number of observed laws and relations of the phenomena of sound1 is already very great2 and though the time may be distant1 there seems to be no reason to despair of one day uniting them by clear ideas of mechanical causation1 and thus of making acoustics a perfect secondary mechanical science4 ,the historical sketch just given includes only such parts of acoustics as have been in some degree reduced to general laws and physical causes2 and thus excludes much that is usually treated of under that head4 ,moreover1 many of the numerical calculations connected with sound belong to its agreeable effect upon the ear2 as the properties of the various systems of ,temperament4 ,these are parts of ,theoretical ,music1 not of ,acoustics2 of the ,philosophy of the ,fine ,arts1 not of ,physical ,science2 and may be referred to in a future portion of this work1 so far as they bear upon our object4 ,the science of ,acoustics may1 however1 properly consider other differences of sound than those of acute and grave1--for instance1 the articulate differences1 or those by which the various letters are formed4 ,some progress has been made in reducing this part of the subject to general rules2 for though ,kempelen's talking machine was only a work of art1 ,mr4 ,willis's machine1#eeh which exhibits the relation among the vowels1 gives us a law such as forms a step in science4 ,we may1 however1 consider this instrument as a phthongometer1 or measure of vowel quality2 and in that point of view we shall have to refer to it again when we come to speak of such measures4 ,note #eeh3 ,on the ,vowel ,sounds1 and on ,reed ,organ-pipes4 ,camb4 ,trans4 iii4 #bcg4 #di ,,book ,,ix4 ,,secondary ,,mechanical ,,sciences4 7,,continued7 ,,history ,,of ,,optics1 ,,formal ,,and ,,physical4 1 1 1 1 9999 ,i1 1 9999 1 1 1 9999 4 ,,orpheus4 ,,hymn4 ,o thou who fillest the palaces of ,jove2 ,who flowest round moon1 and sun1 and stars above2 ,pervading1 bright1 life-giving element1 ,supernal ,,ether1 fair and excellent2 ,fountain of hope and joy1 of light and day1 ,we own at length thy tranquil1 steady sway4 #ea ,,introduction4 ,formal and ,physical ,optics4 ,,the history of the science of ,optics1 written at length1 would be very voluminous2 but we shall not need to make our history so2 since our main object is to illustrate the nature of science and the conditions of its progress4 ,in this way ,optics is peculiarly instructive2 the more so1 as its history has followed a course in some respects different from both the sciences previously reviewed4 ,astronomy1 as we have seen1 advanced with a steady and continuous movement from one generation to another1 from the earliest time1 till her career was crowned by the great unforeseen discovery of ,newton2 ,acoustics had her extreme generalization in view from the first1 and her history consists in the correct application of it to successive problems2 ,optics advanced through a scale of generalizations as remarkable as those of ,astronomy2 but for a long period she was almost stationary2 and1 at last1 was rapidly impelled through all those stages by the energy of two or three discoverers4 ,the highest point of generality which ,optics has reached is little different from that which ,acoustics occupied at once2 but in the older and earlier science we still want that palpable and pointed confirmation of the general principle1 which the undulatory theory receives from optical phenomena4 ,astronomy has amassed her vast fortune by long-continued industry and labor2 ,optics has obtained hers in a few years by sagacious and happy speculations2 ,acoustics1 having early acquired a competence1 has since been employed rather in improving and adorning than in extending her estate4 ,the successive inductions by which ,optics made her advances1 might1 of course1 be treated in the same manner as those of ,astronomy1 each having its prelude and its sequel4 ,but most of the discoveries in ,optics are of a smaller character1 and have less employed the minds of men1 than those of ,astronomy2 and it will not be necessary to exhibit them in this detailed manner1 till we come to the great generalization by which the theory was established4 ,i shall1 therefore1 now pass rapidly in review the earlier optical discoveries1 without any such division of the series4 #eb ,optics1 like ,astronomy1 has for its object of inquiry1 first1 the laws of phenomena1 and next1 their causes2 and we may hence divide this science1 like the other1 into ,formal ,optics and ,physical ,optics4 ,the distinction is clear and substantive1 but it is not easy to adhere to it in our narrative2 for1 after the theory had begun to make its rapid advance1 many of the laws of phenomena were studied and discovered in immediate reference to the theoretical cause1 and do not occupy a separate place in the history of science1 as in ,astronomy they do4 ,we may add1 that the reason why ,formal ,astronomy was almost complete before ,physical ,astronomy began to exist1 was1 that it was necessary to construct the science of ,mechanics in the mean time1 in order to be able to go on2 whereas1 in ,optics1 mathematicians were able to calculate the results of the undulatory theory as soon as it had suggested itself from the earlier facts1 and while the great mass of facts were only becoming known4 ,we shall1 then1 in the first nine chapters of the ,history of ,optics treat of the ,formal ,science1 that is1 the discovery of the laws of phenomena4 ,the classes of phenomena which will thus pass under oar notice are numerous2 namely1 reflection1 refraction1 chromatic dispersion1 achromatization1 double refraction1 polarization1 dipolarization1 the colors of thin plates1 the colors of thick plates1 and the fringes and bands which accompany shadows4 ,all these cases had been studied1 and1 in most of them1 the laws had been in a great measure discovered1 before the physical theory of the subject gave to our knowledge a simpler and more solid form4 #ec ,,formal ,,optics4 ,,chapter ,i4 ,,primary ,,induction ,,of ,,optics4--,,rays ,,of ,,light ,,and ,,laws ,,of ,,reflection4 ,,in speaking of the ,ancient ,history of ,physics1 we have already noticed that the optical philosophers of antiquity had satisfied themselves that vision is performed in straight lines2--that they had fixed their attention upon those straight lines1 or rays1 as the proper object of the science2--they had ascertained that rays reflected from a bright surface make the angle of reflection equal to the angle of incidence2--and they had drawn several consequences from these principles4 ,we may add to the consequences already mentioned1 the art of perspective1 which is merely a corollary from the doctrine of rectilinear visual rays2 for if we suppose objects to be referred by such rays to a plane interposed between them and the eye1 all the rules of perspective follow directly4 ,the ancients practised this art1 as we see in the pictures which remain to us and we learn from ,vitruvius1#ai that they also wrote upon it4 ,agatharchus1 who had been instructed by ,eschylus in the art of making decorations for the theatre1 was the first author on this subject1 and ,anaxagoras1 who was a pupil of ,agatharchus1 also wrote an ,actinographia1 or doctrine of drawing by rays3 but none of these treatises are come down to us4 ,the moderns re-invented the art in the flourishing times of the art of painting1 that is1 about the end of the fifteenth century2 and1 belonging to that period also1 we have treatises#bi upon it4 ,note #ai3 ,de ,arch4 ix4 ,mont4 i4 #gjg4 ,note #bi3 ,gauricus1 #aejd4 ,but these are only deductive applications of the most elementary optical doctrines2 we must proceed to the inductions by which further discoveries were made4 #ed ,,chapter ,,ii4 ,,discovery ,,of ,,the ,,law ,,of ,,refraction4 ,,we have seen in the former part of this history that the ,greeks had formed a tolerably clear conception of the refraction as well as the reflection of the rays of light2 and that ,ptolemy had measured the amount of refraction of glass and water at various angles4 ,if we give the names of the angle of incidence and the angle of refraction respectively to the angles which a ray of light makes with the line perpendicular to surface of glass or water 7or any other medium7 within and without the medium1 ,ptolemy had observed that the angle of refraction is always less than the angle of incidence4 ,he had supposed it to be less in a given proportion1 but this opinion is false2 and was afterwards rightly denied by the ,arabian mathematician ,alhazen4 ,the optical views which occur in the work of ,alhazen are far sounder than those of his predecessors2 and the book may be regarded as the most considerable monument which we have of the scientific genius of the ,arabians2 for it appears1 for the most part1 not to be borrowed from ,greek authorities4 ,the author not only asserts 7lib4 vii471 that refraction takes place towards the perpendicular1 and refers to experiment for the truth of this3 and that the quantities of the refraction differ according to the magnitudes of the angles which the directions of the incidental rays 7prim line7 make with the perpendiculars to the surface2 but he also says distinctly and decidedly that the angles of refraction do not follow the proportion of the angles of incidence4 #bnd ,ed4 ,there appears to be good ground to assent to the assertion of ,alhazen's originality1 made by his editor ,risner1 who says1 ,euclideum hic vel ,ptolemaicum nihil fere est4 ,besides the doctrine of reflection and refraction of light1 the ,arabian author gives a description of the eye4 ,he distinguishes three fluids1 humor aqueus1 crystallinus1 vitreus1 and four coats of the eye1 tunica adherens1 cornea1 uvea1 tunica reti similis4 ,he distinguishes also three kinds of vision3 ,visibile percipitur aut solo visu1 aut visu et syllogismo1 aut visu et anticipat notione4 ,he has several propositions relating to what we sometimes call the ,philosophy of ,vision3 for instance this3 ,e visibili spius viso remanet in anima generalis notio1 c4 #ee ,the assertion1 that the angles of refraction are not proportional to the angles of incidence1 was an important remark2 and if it had been steadily kept in mind1 the next thing to be done with regard to refraction was to go on experimenting and conjecturing till the true law of refraction was discovered2 and in the mean time to apply the principle as far as it was known4 ,alhazen1 though he gives directions for making experimental measures of refraction1 does not give any ,table of the results of such experiments1 as ,ptolemy had done4 ,vitello1 a ,pole1 who in the #acth century published an extensive work upon ,optics1 does give such a table2 and asserts it to be deduced from experiment1 as ,i have already said 7vol4 i474 ,but this assertion is still liable to doubt in consequence of the table containing impossible observations4 #bnd ,ed4 ,as ,i have already stated1 ,vitello asserts that his ,tables were derived from his own observations4 ,their near agreement with those of ,ptolemy does not make this improbable3 for where the observations were only made to half a degree1 there was not much room for observers to differ4 ,it is not unlikely that the observations of refraction out of air into water and glass1 and out of water into glass1 were actually made2 while the impossible values which accompany them1 of the refraction out of water and glass into air1 and out of glass into water1 were calculated1 and calculated from an erroneous rule4 ,the principle that a ray refracted in glass or water is turned towards the perpendicular1 without knowing the exact law of refraction1 enabled mathematicians to trace the effects of transparent bodies in various cases4 ,thus in ,roger ,bacon's works we find a tolerably distinct explanation of the effect of a convex glass2 and in the work of ,vitello the effect of refraction at the two surfaces of a glass globe is clearly traceable4 ,notwithstanding ,alhazen's assertion of the contrary1 the opinion was still current among mathematicians that the angle of refraction was proportional to the angle of incidence4 ,but when ,kepler's attention was drawn to the subject1 he saw that this was plainly inconsistent with the observations of ,vitello for large angles2 and he convinced himself by his own experiments that the true law was something different from the one commonly supposed4 ,the discovery of this true law excited in him an eager curiosity2 and this point had the more interest for him in consequence of the introduction of a correction for atmospheric refraction into astronomical calculations1 which had been made by ,tycho1 and of the invention of the telescope4 ,in #ef his ,supplement to ,vitello1 published in #afjd1 ,kepler attempts to reduce to a rule the measured quantities of refraction4 ,the reader who recollects what we have already narrated1 the manner in which ,kepler attempted to reduce to law the astronomical observations of ,tycho1--devising an almost endless variety of possible formul1 tracing their consequences with undaunted industry1 and relating1 with a vivacious garrulity1 his disappointments and his hopes1--will not be surprised to find that he proceeded in the same manner with regard to the ,tables of ,observed ,refractions4 ,he tried a variety of constructions by triangles1 conic sections1 c41 without being able to satisfy himself2 and he at last#ci is obliged to content himself with an approximate rule1 which makes the refraction partly proportional to the angle of incidence1 and partly1 to the secant of that angle4 ,in this way he satisfies the observed refractions within a difference of less than half a degree each way4 ,when we consider how simple the law of refraction is1 7that the ratio of the sines of the angles of incidence and refraction is constant for the same medium17 it appears strange that a person attempting to discover it1 and drawing triangles for the purpose1 should fail2 but this lot of missing what afterwards seems to have been obvious1 is a common one in the pursuit of truth4 ,note #ci3 ,l4 ,u4 ,k4 ,life of ,kepler1 p4 #aae4 ,the person who did discover the ,law of the ,sines1 was ,willebrord ,snell1 about #afba2 but the law was first published by ,descartes1 who had seen ,snell's papers4#di ,descartes does not acknowledge this law to have been first detected by another2 and after his manner1 instead of establishing its reality by reference to experiment1 he pretends to prove priori that it must be true1#ei comparing1 for this purpose1 the particles of light to balls striking a substance which accelerates them4 ,note #di3 ,huyghens1 ,dioptrica1 p4 #b4 ,note #ei3 ,diopt4 p4 #ec4 #bnd ,ed4 ,huyghens says of ,snell's papers1 ,qu et nos vidimus aliquando1 et ,cartesium quoque vidisse accepimus1 et hinc fortasse mensuram illam qu in sinibus consistit elicuerit4 ,isaac ,vossius1 ,de ,lucis ,natur et ,proprietate1 says that he also had seen this law in ,snell's unpublished optical ,treatise4 ,the same writer says1 ,quod itaque 7,cartesius7 habet1 refractionum momenta non exigenda esse ad angulos sed ad lineas1 id tuo ,snellio1 acceptum ferre debuisset1 cujus nomen more solito dissimulavit4 ,cartesius got his law from ,snell1 and in his usual way1 concealed it4 #eg ,huyghens' assertion1 that ,snell did not attend to the proportion of the sines1 is very captious2 and becomes absurdly so1 when it is made to mean that ,snell did not know the law of the sines4 ,it is not denied that ,snell knew the true law1 or that the true law is the law of the sines4 ,snell does not use the trigonometrical term sine1 but he expresses the law in a geometrical form more simply4 ,even if he had attended to the law of the sines1 he might reasonably have preferred his own way of stating it4 ,james ,gregory also independently discovered the true law of refraction2 and1 in publishing it1 states that he had learnt that it had already been published by ,descartes4 ,but though ,descartes does not1 in this instance1 produce any good claims to the character of an inductive philosopher1 he showed considerable skill in tracing the consequences of the principle when once adopted4 ,in particular we must consider him as the genuine author of the explanation of the rainbow4 ,it is true that ,fleischer#fi and ,kepler had previously ascribed this phenomenon to the rays of sunlight which1 falling on drops of rain1 are refracted into each drop1 reflected at its inner surface1 and refracted out again3 ,antonio de ,dominis had found that a glass globe of water1 when placed in a particular position with respect to the eye1 exhibited bright colors2 and had hence explained the circular form of the bow1 which1 indeed1 ,aristotle had done before4#gi ,but none of these writers had shown why there was a narrow bright circle of a definite diameter2 for the drops which send rays to the eye after two refractions and a reflection1 occupy a much wider space in the heavens4 ,descartes assigned the reason for this in the most satisfactory manner1#hi by showing that the rays which1 after two refractions and a reflection1 come to the eye at an angle of about forty-one degrees with their original direction1 are far more dense than those in any other position4 ,he showed1 in the same manner1 that the existence and position of the secondary bow resulted from the same laws4 ,this is the complete and adequate account of the state of things1 so far as the brightness of the bows only is concerned2 the explanation of the colors belongs to the next article of our survey4 ,note #fi3 ,mont4 i4 #gja4 ,note #gi3 ,meteorol4 iii4 #c4 ,note #hi3 ,meteorum1 cap4 viii4 p4 #aif4 ,the explanation of the rainbow and of its magnitude1 afforded by ,snell's law of sines1 was perhaps one of the leading points in the verification of the law4 ,the principle1 being once established1 was applied1 by the aid of mathematical reasoning1 to atmospheric refractions1 #eh optical instruments1 diacaustic curves1 7that is1 the curves of intense light produced by refraction17 and to various other cases2 and was1 of course1 tested and confirmed by such applications4 ,it was1 however1 impossible to pursue these applications far1 without a due knowledge of the laws by which1 in such cases1 colors are produced4 ,to these we now proceed4 #bnd ,ed4 ,i have omitted many interesting parts of the history of ,optics about this period1 because ,i was concerned with the inductive discovery of laws1 rather than with mathematical deductions from such laws when established1 or applications of them in the form of instruments4 ,i might otherwise have noticed the discovery of ,spectacle ,glasses1 of the ,telescope1 of the ,microscope1 of the ,camera ,obscura1 and the mathematical explanation of these and other phenomena1 as given by ,kepler and others4 ,i might also have noticed the progress of knowledge respecting the ,eye and ,vision4 ,we have seen that ,alhazen described the structure of the eye4 ,the operation of the parts was gradually made out4 ,baptista ,porta compares the eye to his ,camera ,obscura 7,magia ,naturalis1 #aegi74 ,scheiner1 in his ,oculus1 published #afeb1 completed the ,theory of the ,eye4 ,and ,kepler discussed some of the questions even now often agitated2 as the causes and conditions of our seeing objects single with two eyes1 and erect with inverted images4 ,,chapter ,,iii4 ,,discovery ,,of ,,the ,,law ,,of ,,dispersion ,,by ,,refraction4 ,,early attempts were made to account for the colors of the rainbow1 and various other phenomena in which colors are seen to arise from transient and unsubstantial combinations of media4 ,thus ,aristotle explains the colors of the rainbow by supposing#ii that it is light seen through a dark medium3 ,now1 says he1 the bright seen through the dark appears red1 as1 for instance1 the fire of green wood seen through the smoke1 and the sun through mist4 ,also#aji the weaker is the light1 or the visual power1 and the nearer the color approaches to the black2 becoming first red1 then green1 then purple4 ,but#aai the #ei vision is strongest in the outer circle1 because the periphery is greater2--thus we shall have a gradation from red1 through green1 to purple1 in passing from the outer to the inner circle4 ,this account would hardly have deserved much notice1 if it had not been for a strange attempt to revive it1 or something very like it1 in modern times4 ,the same doctrine is found in the work of ,de ,dominis4#abi ,according to him1 light is white3 but if we mix with the light something dark1 the colors arise1--first red1 then green1 then blue or violet4 ,he applies this to explain the colors of the rainbow1#aci by means of the consideration that1 of the rays which come to the eye from the globes of water1 some go through a larger thickness of the globe than others1 whence he obtains the gradation of colors just described4 ,note #ii3 ,meteor4 iii4 #c1 p4 #cgc4 ,note #aji3 ,ib4 p4 #cgd4 ,note #aai3 ,ib4 p4 #cge4 ,note #abi3 ,cap4 iii4 p4 #i4 ,see also ,gthe1 ,farbenl4 vol4 ii4 p4 #bea4 ,note #aci3 ,gthe1 p4 #bfc4 ,descartes came far nearer the true philosophy of the iridal colors4 ,he found that a similar series of colors was produced by refraction of light bounded by shade1 through a prism2#adi and he rightly inferred that neither the curvature of the surface of the drops of water1 nor the reflection1 nor the repetition of refraction1 were necessary to the generation of such colors4 ,in further examining the course of the rays1 he approaches very near to the true conception of the case2 and we are led to believe that he might have anticipated ,newton in his discovery of the unequal refrangibility of different colors1 if it had been possible for him to reason any otherwise than in the terms and notions of his preconceived hypotheses4 ,the conclusion which he draws is1#aei that the particles of the subtile matter which transmit the action of light1 endeavor to rotate with so great a force and impetus1 that they cannot move in a straight line 7whence comes refraction73 and that those particles which endeavor to revolve much more strongly produce a red color1 those which endeavor to move only a little more strongly produce yellow4 ,here we have a clear perception that colors and unequal refraction are connected1 though the cause of refraction is expressed by a gratuitous hypothesis4 ,and we may add1 that he applies this notion rightly1 so far as he explains himself1#afi to account for the colors of the rainbow4 ,note #adi3 ,meteor4 ,sect4 viii4 p4 #aij4 ,note #aei3 ,sect4 vii4 p4 #aib4 ,note #afi3 ,meteor4 ,sect4 ix4 ,it appears to me that ,newton and others have done ,descartes injustice1 in ascribing to ,de ,dominis the true theory of the rainbow4 ,there are two main points of this theory1 namely1 the showing that a bright circular band1 of a certain definite diameter1 arises from the #fj great intensity of the light returned at a certain angle2 and the referring the different colors to the different quantity of the refraction2 and both these steps appear indubitably to be the discoveries of ,descartes4 ,and he informs us that these discoveries were not made without some exertion of thought4 ,at first1 he says1#agi ,i doubted whether the iridal colors were produced in the same way as those in the prism2 but1 at last1 taking my pen1 and carefully calculating the course of the rays which fell on each part of the drop1 ,i found that many more come at an angle of forty-one degrees1 than either at a greater or a less angle4 ,so that there is a bright bow terminated by a shade2 and hence the colors are the same as those produced through a prism4 ,note #agi3 ,sect4 ix4 p4 #aic4 ,the subject was left nearly in the same state1 in the work of ,grimaldi1 ,physico-,mathesis1 de ,lumine1 ,coloribus et ,iride1 published at ,bologna in #affe4 ,there is in this work a constant reference to numerous experiments1 and a systematic exposition of the science in an improved state4 ,the author's calculations concerning the rainbow are put in the same form as those of ,descartes2 but he is further from seizing the true principle on which its coloration depends4 ,he rightly groups together a number of experiments in which colors arise from refraction2#ahi and explains them by saying that the color is brighter where the light is denser3 and the light is denser on the side from which the refraction turns the ray1 because the increments of refraction are greater in the rays that are more inclined4#aii ,this way of treating the question might be made to give a sort of explanation of most of the facts1 but is much more erroneous than a developement of ,descartes's view would have been4 ,note #ahi3 ,prop4 #ce1 p4 #bed4 ,note #aii3 ,ib4 p4 #bef4 ,at length1 in #afgb1 ,newton gave#bji the true explanation of the facts2 namely1 that light consists of rays of different colors and different refrangibility4 ,this now appears to us so obvious a mode of interpreting the phenomena1 that we can hardly understand how they can be conceived in any other manner2 but yet the impression which this discovery made1 both upon ,newton and upon his contemporaries1 shows how remote it was from the then accepted opinions4 ,there appears to have been a general persuasion that the coloration was produced1 not by any peculiarity in the law of refraction itself but by some collateral circumstance1--some dispersion or variation of density of the light1 in addition to the refraction4 ,newton's discovery consisted in #fa teaching distinctly that the law of refraction was to be applied1 not to the beam of light in general1 but to the colors in particular4 ,note #bji3 ,phil4 ,trans4 t4 vii4 p4 #cjge4 ,when ,newton produced a bright spot on the wall of his chamber1 by admitting the sun's light through a small hole in his window-shutter1 and making it pass through a prism1 he expected the image to be round2 which1 of course1 it would have been1 if the colors had been produced by an equal dispersion in all directions2 but to his surprise he saw the image1 or spectrum1 five times as long as it was broad4 ,he found that no consideration of the different thickness of the glass1 the possible unevenness of its surface1 or the different angles of rays proceeding from the two sides of the sun1 could be the cause of this shape4 ,he found1 also1 that the rays did not go from the prism to the image in curves2 he was then convinced that the different colors were refracted separately1 and at different angles2 and he confirmed this opinion by transmitting and refracting the rays of each color separately4 ,the experiments are so easy and common1 and ,newton's interpretation of them so simple and evident1 that we might have expected it to receive general assent2 indeed1 as we have shown1 ,descartes had already been led very near the same point4 ,in fact1 ,newton's opinions were not long in obtaining general acceptance2 but they met with enough of cavil and misapprehension to annoy extremely the discoverer1 whose clear views and quiet temper made him impatient alike of stupidity and of contentiousness4 ,we need not dwell long on the early objections which were made to ,newton's doctrine4 ,a ,jesuit1 of the name of ,ignatius ,pardies1 professor at ,clermont1 at first attempted to account for the elongation of the image by the difference of the angles made by the rays from the two edges of the sun1 which would produce a difference in the amount of refraction of the two borders2 but when ,newton pointed out the calculations which showed the insufficiency of this explanation1 he withdrew his opposition4 ,another more pertinacious opponent appeared in ,francis ,linus1 a physician of ,liege2 who maintained1 that having tried the experiment1 he found the sun's image1 when the sky was clear1 to be round and not oblong2 and he ascribed the elongation noticed by ,newton1 to the effect of clouds4 ,newton for some time refused to reply to this contradiction of his assertions1 though obstinately persisted in2 and his answer was at last sent1 just about the time of ,linus's death1 in #afge4 ,but ,gascoigne1 a friend of ,linus1 still maintained that he and others had seen what the ,dutch physician had described2 and ,newton1 who was pleased with the candor of #fb ,gascoigne's letter1 suggested that the ,dutch experimenters might have taken one of the images reflected from the surfaces of the prism1 of which there are several1 instead of the proper refracted one4 ,by the aid of this hint1 ,lucas of ,liege repeated ,newton's experiments1 and obtained ,newton's result1 except that he never could obtain a spectrum whose length was more than three and a half times its breadth4 ,newton1 on his side1 persisted in asserting that the image would be five times as long as it was broad1 if the experiment were properly made4 ,it is curious that he should have been so confident of this1 as to conceive himself certain that such would be the result in all cases4 ,we now know that the dispersion1 and consequently the length1 of the spectrum1 is very different for different kinds of glass1 and it is very probable that the ,dutch prism was really less dispersive than the ,english one4#bai ,the erroneous assumption which ,newton made in this instance1 he held by to the last2 and was thus prevented from making the discovery of which we have next to speak4 ,note #bai3 ,brewster's ,newton1 p4 #ej4 ,newton was attacked by persons of more importance than those we have yet mentioned2 namely1 ,hooke and ,huyghens4 ,these philosophers1 however1 did not object so much to the laws of refraction of different colors1 as to some expressions used by ,newton1 which1 they conceived1 conveyed false notions respecting the composition and nature of light4 ,newton had asserted that all the different colors are of distinct kinds1 and that1 by their composition1 they form white light4 ,this is true of colors as far as their analysis and composition by refraction are concerned2 but ,hooke maintained that all natural colors are produced by various combinations of two primary ones1 red and violet2#bbi and ,huyghens held a similar doctrine1 taking1 however1 yellow and blue for his basis4 ,newton answers1 that such compositions as they speak of are not compositions of simple colors in his sense of the expressions4 ,these writers also had both of them adopted an opinion that light consisted in vibrations2 and objected to ,newton that his language was erroneous1 as involving the hypothesis that light was a body4 ,newton appears to have had a horror of the word hypothesis1 and protests against its being supposed that his theory rests on such a foundation4 ,note #bbi3 ,brewster's ,newton1 p4 #ed4 ,phil4 ,trans4 viii4 #ejhd1 #fjhf4 ,the doctrine of the unequal refrangibility of different rays is clearly exemplified in the effects of lenses1 which produce images more or #fc less bordered with color1 in consequence of this property4 ,the improvement of telescopes was1 in ,newton's time1 the great practical motive for aiming at the improvement of theoretical optics4 ,newton's theory showed why telescopes were imperfect1 namely1 in consequence of the different refraction of different colors1 which produces a chromatic aberration3 and the theory was confirmed by the circumstances of such imperfections4 ,the false opinion of which we have already spoken1 that the dispersion must be the same when the refraction is the same1 led him to believe that the imperfection was insurmountable1--that achromatic refraction could not be obtained3 and this view made him turn his attention to the construction of reflecting instead of refracting telescopes4 ,but the rectification of ,newton's error was a further confirmation of the general truth of his principles in other respects2 and since that time1 the soundness of the ,newtonian law of refraction has hardly been questioned among physical philosophers4 ,it has1 however1 in modern times1 been very vehemently controverted in a quarter from which we might not readily have expected a detailed discussion on such a subject4 ,the celebrated ,gthe has written a work on ,the ,doctrine of ,colors1 7,farbenlehre2 ,tbingen1 #ahaj17 one main purpose of which is1 to represent ,newton's opinions1 and the work in which they are formally published1 7his ,opticks17 as utterly false and mistaken1 and capable of being assented to only by the most blind and obstinate prejudice4 ,those who are acquainted with the extent to which such an opinion1 promulgated by ,gthe1 was likely to be widely adopted in ,germany1 will not be surprised that similar language is used by other writers of that nation4 ,thus ,schelling#bci says3 ,newton's ,opticks is the greatest proof of the possibility of a whole structure of fallacies1 which1 in all its parts1 is founded upon observation and experiment4 ,gthe1 however1 does not concede even so much to ,newton's work4 ,he goes over a large portion of it1 page by page1 quarrelling with the experiments1 diagrams1 reasoning1 and language1 without intermission2 and holds that it is not reconcileable with the most simple facts4 ,he declares1#bdi that the first time he looked through a prism1 he saw the white walls of the room still look white1 and though alone1 ,i pronounced1 as by an instinct1 that the ,newtonian doctrine is false4 ,we need not here point out how inconsistent with the ,newtonian doctrine it was1 to expect1 as ,gthe expected1 that the wall should be all over colored various colors4 #fd ,note #bci3 ,vorlesungen1 p4 #bgj4 ,note #bdi3 ,farbenlehre1 vol4 ii4 p4 #fgh4 ,gthe not only adopted and strenuously maintained the opinion that the ,newtonian theory was false1 but he framed a system of his own to explain the phenomena of color4 ,as a matter of curiosity1 it may be worth our while to state the nature of this system2 although undoubtedly it forms no part of the progress of physical science4 ,gthe's views are1 in fact1 little different from those of ,aristotle and ,antonio de ,dominis1 though more completely and systematically developed4 ,according to him1 colors arise when we see through a dim medium 7ein trbes mittel74 ,light in itself is colorless2 but if it be seen through a somewhat dim medium1 it appears yellow2 if the dimness of the medium increases1 or if its depth be augmented1 we see the light gradually assume a yellow-red color1 which finally is heightened to a ruby-red4 ,on the other hand1 if darkness is seen through a dim medium which is illuminated by a light falling on it1 a blue color is seen1 which becomes clearer and paler1 the more the dimness of the medium increases1 and darker and fuller1 as the medium becomes more transparent2 and when we come to the smallest degree of the purest dimness1 we see the most perfect violet4#bei ,in addition to this doctrine of the dim medium1 we have a second principle asserted concerning refraction4 ,in a vast variety of cases1 images are accompanied by accessory images1 as when we see bright objects in a looking-glass4#bfi ,now1 when an image is displaced by refraction1 the displacement is not complete1 clear and sharp1 but incomplete1 so that there is an accessory image along with the principal one4#bgi ,from these principles1 the colors produced by refraction in the image of a bright object on a dark ground1 are at once derivable4 ,the accessory image is semitransparent2#bhi and hence that border of it which is pushed forwards1 is drawn from the dark over the bright1 and there the yellow appears2 on the other hand1 where the clear border laps over the dark ground1 the blue is seen2#bii and hence we easily see that the image must appear red and yellow at one end1 and blue and violet at the other4 ,note #bei3 ,farbenlehre1 #aej1 p4 #aea4 ,note #bfi3 ,ib4 #bbc4 ,note #bgi3 ,ib4 #bbg4 ,note #bhi3 ,ib4 #bch4 ,note #bii3 ,ib4 #bci4 ,we need not explain this system further1 or attempt to show how vague and loose1 as well as baseless1 are the notions and modes of conception which it introduces4 ,perhaps it is not difficult to point out the peculiarities in ,gthe's intellectual character which led to his singularly unphilosophical views on this subject4 ,one important #fe circumstance is1 that he appears1 like many persons in whom the poetical imagination is very active1 to have been destitute of the talent and the habit of geometrical thought4 ,in all probability1 he never apprehended clearly and steadily those relations of position on which the ,newtonian doctrine depends4 ,another cause of his inability to accept the doctrine probably was1 that he had conceived the composition of colors in some way altogether different from that which ,newton understands by composition4 ,what ,gthe expected to see1 we cannot clearly collect2 but we know1 from his own statement1 that his intention of experimenting with a prism arose from his speculations on the roles of coloring in pictures2 and we can easily see that any notion of the composition of colors which such researches would suggest1 would require to be laid aside1 before he could understand ,newton's theory of the composition of light4 ,other objections to ,newton's theory1 of a kind very different1 have been recently made by that eminent master of optical science1 ,sir ,david ,brewster4 ,he contests ,newton's opinion1 that the colored rays into which light is separated by refraction are altogether simple and homogeneous1 and incapable of being further analysed and modified4 ,for he finds that by passing such rays through colored media 7as blue glass for instance71 they are not only absorbed and transmitted in very various degrees1 but that some of them have their color altered2 which effect he conceives as a further analysis of the rays1 one component color being absorbed and the other transmitted4#cji ,and on this subject we can only say1 as we have before said1 that ,newton has incontestably and completely established his doctrine1 so far as analysis and decomposition by refraction are concerned2 but that with regard to any other analysis1 which absorbing media or other agents may produce1 we have no right from his experiments to assert1 that the colors of the spectrum are incapable of such decomposition4 ,the whole subject of the colors of objects1 both opake and transparent1 is still in obscurity4 ,newton's conjectures concerning the causes of the colors of natural bodies1 appear to help us little2 and his opinions on that subject are to be separated altogether from the important step which he made in optical science1 by the establishment of the true doctrine of refractive dispersion4 ,note #cji3 ,this latter fact has1 however1 been denied by other experimenters4 #bnd ,ed4 ,after a careful re-consideration of ,sir ,d4 ,brewster's asserted analysis of the solar light into three colors by means of #ff absorbing media1 ,i cannot consider that he has established his point as an exception to ,newton's doctrine4 ,in the first place1 the analysis of light into three colors appears to be quite arbitrary1 granting all his experimental facts4 ,i do not see why1 using other media1 he might not just as well have obtained other elementary colors4 ,in the next place1 this cannot be called an analysis in the same sense as ,newton's analysis1 except the relation between the two is shown4 ,is it meant that ,newton's experiments prove nothing8 ,or is ,newton's conclusion allowed to be true of light which has not been analysed by absorption8 ,and where are we to find such light1 since the atmosphere absorbs8 ,but1 ,i must add1 in the third place1 that with a very sincere admiration of ,sir ,d4 ,brewster's skill as an experimenter1 ,i think his experiment requires1 not only limitation1 but confirmation by other experimenters4 ,mr4 ,airy repeated the experiments with about thirty different absorbing substances1 and could not satisfy himself that in any case they changed the color of a ray of given refractive power4 ,these experiments were described by him at a meeting of the ,cambridge ,philosophical ,society4 ,we now proceed to the corrections which the next generation introduced into the details of this doctrine4 ,,chapter ,,iv4 ,,discovery ,,of ,,achromatism4 ,,the discovery that the laws of refractive dispersion of different substances were such as to allow of combinations which neutralised the dispersion without neutralizing the refraction1 is one which has hitherto been of more value to art than to science4 ,the property has no definite bearing1 which has yet been satisfactorily explained1 upon the theory of light2 but it is of the greatest importance in its application to the construction of telescopes2 and it excited the more notice1 in consequence of the prejudices and difficulties which for a time retarded the discovery4 ,newton conceived that he had proved by experiment1#cai that light #fg is white after refraction1 when the emergent rays are parallel to the incident1 and in no other case4 ,if this were so1 the production of colorless images by refracting media would be impossible2 and such1 in deference to ,newton's great authority1 was for some time the general persuasion4 ,euler#cbi observed1 that a combination of lenses which does not color the image must be possible1 since we have an example of such a combination in the human eye2 and he investigated mathematically the conditions requisite for such a result4 ,klingenstierna1#cci a ,swedish mathematician1 also showed that ,newton's rule could not be universally true4 ,finally1 ,john ,dollond1#cdi in #ageg1 repeated ,newton's experiment1 and obtained an opposite result4 ,he found that when an object was seen through two prisms1 one of glass and one of water1 of such angles that it did not appear displaced by refraction1 it was colored4 ,hence it followed that1 without being colored1 the rays might be made to undergo refraction2 and that thus1 substituting lenses for prisms1 a combination might be formed1 which should produce an image without coloring it1 and make the construction of an achromatic telescope possible4 ,note #cai3 ,opticks1 ,b4 i4 p4 ii4 ,prop4 #c4 ,note #cbi3 ,ac4 ,berlin4 #agdg4 ,note #cci3 ,swedish ,trans4 #aged4 ,note #cdi3 ,phil4 ,trans4 #ageh4 ,euler at first hesitated to confide in ,dollond's experiments2 but he was assured of their correctness by ,clairaut1 who had throughout paid great attention to the subject2 and those two great mathematicians1 as well as ,d',alembert1 proceeded to investigate mathematical formul which might be useful in the application of the discovery4 ,the remainder of the deductions1 which were founded upon the laws of dispersion of various refractive substances1 belongs rather to the history of art than of science4 ,dollond used at first1 for his achromatic object-glass1 a lens of crown-glass1 and one of flint-glass4 ,he afterwards employed two lenses of the former substance1 including between them one of the latter1 adjusting the curvatures of his lenses in such a way as to correct the imperfections arising from the spherical form of the glasses1 as well as the fault of color4 ,afterwards1 ,blair used fluid media along with glass lenses1 in order to produce improved object-glasses4 ,this has more recently been done in another form by ,mr4 ,barlow4 ,the inductive laws of refraction being established1 their results have been deduced by various mathematicians1 as ,sir ,j4 ,herschel and ,professor ,airy among ourselves1 who have simplified and extended the investigation of the formul which determine the best combination of lenses in the object-glasses and eye-glasses of #fh telescopes1 both with reference to spherical and to chromatic aberrations4 ,according to ,dollond's discovery1 the colored spectra produced by prisms of two substances1 as flint-glass and crown-glass1 would be of the same length when the refraction was different4 ,but a question then occurred3 ,when the whole distance from the red to the violet in one spectrum was the same as the whole distance in the other1 were the intermediate colors1 yellow1 green1 c41 in corresponding places in the two8 ,this point also could not be determined any otherwise than by experiment4 ,it appeared that such a correspondence did not exist2 and1 therefore1 when the extreme colors were corrected by combinations of the different media1 there still remained an uncorrected residue of color arising from the rest of the spectrum4 ,this defect was a consequence of the property1 that the spectra belonging to different media were not divided in the same ratio by the same colors1 and was hence termed the irrationality of the spectrum4 ,by using three prisms1 or three lenses1 three colors may be made to coincide instead of two1 and the effects of this irrationality greatly diminished4 ,for the reasons already mentioned1 we do not pursue this subject further1#cei but turn to those optical facts which finally led to a great and comprehensive theory4 ,note #cei3 ,the discovery of the fixed lines in the spectrum1 by ,wollaston and ,fraunhofer1 has more recently supplied the means of determining1 with extreme accuracy1 the corresponding portions of the spectrum in different refracting substances4 #bnd ,ed4 ,mr4 ,chester ,more ,hall1 of ,more ,hall1 in ,essex1 is said to have been led by the study of the human eye1 which he conceived to be achromatic1 to construct achromatic telescopes as early as #agbi4 ,mr4 ,hall1 however1 kept his invention a secret4 ,david ,gregory1 in his ,catoptrics 7#agac71 had suggested that it would perhaps be an improvement of telescopes1 if1 in imitation of the human eye1 the object-glass were composed of different media4 ,encyc4 ,brit4 art4 ,optics4 ,it is said that ,clairaut first discovered the irrationality of the colored spaces in the spectrum4 ,in consequence of this irrationality1 it follows that when two refracting media are so combined as to correct each other's extreme dispersion1 7the separation of the red and violet rays17 this first step of correction still leaves a residue of #fi coloration arising from the unequal dispersion of the intermediate rays 7the green1 c474 ,these outstanding colors1 as they were termed by ,professor ,robison1 form the residual1 or secondary spectrum4 ,dr4 ,blair1 by very ingenious devices1 succeeded in producing an object-glass1 corrected by a fluid lens1 in which this aberration of color was completely corrected1 and which performed wonderfully well4 ,the dispersion produced by a prism may be corrected by another prism of the same substance and of a different angle4 ,in this case also there is an irrationality in the colored spaces1 which prevents the correction of color from being complete2 and hence1 a new residuary spectrum1 which has been called the tertiary spectrum1 by ,sir ,david ,brewster1 who first noticed it4 ,i have omitted1 in the notice of discoveries respecting the spectrum1 many remarkable trains of experimental research1 and especially the investigations respecting the power of various media to absorb the light of different parts of the spectrum1 prosecuted by ,sir ,david ,brewster with extraordinary skill and sagacity4 ,the observations are referred to in chapter iii4 ,sir ,john ,herschel1 ,prof4 ,miller1 ,mr4 ,daniel1 ,dr4 ,faraday1 and ,mr4 ,talbot1 have also contributed to this part of our knowledge4 ,,chapter ,v4 ,,discovery ,,of ,,the ,,laws ,,of ,,double ,,refraction4 ,,the laws of refraction which we have hitherto described1 were simple and uniform1 and had a symmetrical reference to the surface of the refracting medium4 ,it appeared strange to men1 when their attention was drawn to a class of phenomena in which this symmetry was wanting1 and in which a refraction took place which was not even in the plane of incidence4 ,the subject was not unworthy the notice and admiration it attracted2 for the prosecution of it ended in the discovery of the general laws of light4 ,the phenomena of which ,i now speak1 are those exhibited by various kinds of crystalline bodies2 but observed for a long time in one kind only1 namely1 the rhombohedral calc-spar2 or1 as it was usually termed1 from the country which supplied the largest and clearest crystals1 ,iceland spar4 ,these #gj rhombohedral crystals are usually very smooth and transparent1 and often of considerable size2 and it was observed1 on looking through them1 that all objects appeared double4 ,the phenomena1 even as early as #affi1 had been considered so curious1 that ,erasmus ,bartholin published a work upon them at ,copenhagen1#cfi 7,experimenta ,crystalli ,islandici1 ,hafni1 #affi47 ,he analysed the phenomena into their laws1 so far as to discover that one of the two images was produced by refraction after the usual rule1 and the other by an unusual refraction4 ,this latter refraction ,bartholin found to vary in different positions2 to be regulated by a line parallel to the sides of the rhombohedron2 and to be greatest in the direction of a line bisecting two of the angles of the rhombic face of the crystal4 ,note #cfi3 ,priestley's ,optics1 p4 #eej4 ,these rules were exact as far as they went2 and when we consider how geometrically complex the law is1 which really regulates the unusual or extraordinary refraction2--that ,newton altogether mistook it1 and that it was not verified till the experiments of ,hay and ,wollaston in our own time2--we might expect that it would not be soon or easily detected4 ,but ,huyghens possessed a key to the secret1 in the theory1 which he had devised1 of the propagation of light by undulations1 and which he conceived with perfect distinctness and correctness1 so far as its application to these phenomena is concerned4 ,hence he was enabled to lay down the law of the phenomena 7the only part of his discovery which we have here to consider71 with a precision and success which excited deserved admiration1 when the subject1 at a much later period1 regained its due share of attention4 ,his ,treatise was written#cgi in #afgh1 but not published till #afij4 ,note #cgi3 ,see his ,trait de la ,lumire4 ,preface4 ,the laws of the ordinary and the extraordinary refraction in ,iceland spar are related to each other2 they are1 in fact1 similar constructions1 made1 in the one case1 by means of an imaginary sphere1 in the other1 by means of a spheroid2 the spheroid being of such oblateness as to suit the rhombohedral form of the crystal1 and the axis of the spheroid being the axis of symmetry of the crystal4 ,huyghens followed this general conception into particular positions and conditions2 and thus obtained rules1 which he compared with observation1 for cutting the crystal and transmitting the rays in various manners4 ,i have examined in detail1 says he1#ch the properties of the #ga extraordinary refraction of this crystal1 to see if each phenomenon which is deduced from theory1 would agree with what is really observed4 ,and this being so1 it is no slight proof of the truth of our suppositions and principles2 but what ,i am going to add here confirms them still more wonderfully2 that is1 the different modes of cutting this crystal1 in which the surfaces produced give rise to refractions exactly such as they ought to be1 and as ,i had foreseen them1 according to the preceding theory4 ,note #chi3 ,see ,maseres's ,tracts on ,optics1 p4 #bej2 or ,huyghens1 ,tr4 sur la ,lum4 ch4 v4 ,art4 #dc4 ,statements of this kind1 coming from a philosopher like ,huyghens1 were entitled to great confidence2 ,newton1 however1 appears not to have noticed1 or to have disregarded them4 ,in his ,opticks1 he gives a rule for the extraordinary refraction of ,iceland spar which is altogether erroneous1 without assigning any reason for rejecting the law published by ,huyghens2 and1 so far as appears1 without having made any experiments of his own4 ,the ,huyghenian doctrine of double refraction fell1 along with his theory of undulations1 into temporary neglect1 of which we shall have hereafter to speak4 ,but in #aghh1 ,hay showed that ,huyghens's rule agreed much better than ,newton's with the phenomena3 and in #ahjb1 ,wollaston1 applying a method of his own for measuring refraction1 came to the same result4 ,he made1 says ,young1#cii a number of accurate experiments with an apparatus singularly well calculated to examine the phenomena1 but could find no general principle to connect them1 until the work of ,huyghens was pointed out to him4 ,in #ahjh1 the subject of double refraction was proposed as a prize-question by the ,french ,institute2 and ,malus1 whose ,memoir obtained the prize1 says1 ,i began by observing and measuring a long series of phenomena on natural and artificial faces of ,iceland spar4 ,then1 testing by means of these observations the different laws proposed up to the present time by physical writers1 ,i was struck with the admirable agreement of the law of ,huyghens with the phenomena1 and ,i was soon convinced that it is really the law of nature4 ,pursuing the consequences of the law1 he found that it satisfied phenomena which ,huyghens himself had not observed4 ,from this time1 then1 the truth of the ,huyghenian law was universally allowed1 and soon afterwards1 the theory by which it had been suggested was generally received4 ,note #cii3 ,quart4 ,rev4 #ahji1 ,nov4 p4 #cch4 ,the property of double refraction had been first studied only in ,iceland spar1 in which it is very obvious4 ,the same property belongs1 #gb though less conspicuously1 to many other kinds of crystals4 ,huyghens had noticed the same fact in rock-crystal2#dji and ,malus found it to belong to a large list of bodies besides2 for instance1 arragonite1 sulphate of lime1 of baryta1 of strontia1 of iron2 carbonate of lead2 zircon1 corundum1 cymophane1 emerald1 euclase1 felspar1 mesotype1 peridote1 sulphur1 and mellite4 ,attempts were made1 with imperfect success1 to reduce all these to the law which had been established for ,iceland spar4 ,in the first instance1 ,malus took for granted that the extraordinary refraction depended always upon an oblate spheroid2 but ,m4 ,biot#dai pointed out a distinction between two classes of crystals in which this spheroid was oblong and oblate respectively1 and these he called attractive and repulsive crystals4 ,with this correction1 the law could be extended to a considerable number of cases2 but it was afterwards proved by ,sir ,d4 ,brewster's discoveries1 that even in this form1 it belonged only to substances of which the crystallization has relation to a single axis of symmetry1 as the rhombohedron1 or the square pyramid4 ,in other cases1 as the rhombic prism1 in which the form1 considered with reference to its crystalline symmetry1 is biaxal1 the law is much more complicated4 ,in that case1 the sphere and the spheroid1 which are used in the construction for uniaxal crystals1 transform themselves into the two successful convolutions of a single continuous curve surface2 neither of the two rays follows the law of ordinary refraction2 and the formula which determines their position is very complex4 ,it is1 however1 capable of being tested by measures of the refractions of crystals cut in a peculiar manner for the purpose1 and this was done by ,,mm4 ,fresnel and ,arago4 ,but this complex law of double refraction was only discovered through the aid of the theory of a luminiferous ether1 and therefore we must now return to the other facts which led to such a theory4 ,note #dji3 ,trait de la ,lumire1 ch4 v4 ,art4 #bj ,note #dai3 ,biot1 ,trait de ,phys4 iii4 #ccj4 ,,chapter ,,vi4 ,,discovery ,,of ,,the ,,laws ,,of ,,polarization4 ,,if the ,extraordinary ,refraction of ,iceland spar had appeared strange1 another phenomenon was soon noticed in the same #gc substance1 which appeared stranger still1 and which in the sequel was found to be no less important4 ,i speak of the facts which were afterwards described under the term ,polarization4 ,huyghens was the discoverer of this class of facts4 ,at the end of the treatise which we have already quoted1 he says1#dbi ,before ,i quit the subject of this crystal1 ,i will add one other marvellous phenomenon1 which ,i have discovered since writing the above2 for though hitherto ,i have not been able to find out its cause1 ,i will not1 on that account1 omit pointing it out1 that ,i may give occasion to others to examine it4 ,he then states the phenomena2 which are1 that when two rhombohedrons of ,iceland spar are in parallel positions1 a ray doubly refracted by the first1 is not further divided when it falls on the second3 the ordinarily refracted ray is ordinarily refracted only1 and the extraordinary ray is only extraordinarily refracted by the second crystal1 neither ray being doubly refracted4 ,the same is still the case1 if the two crystals have their principal planes parallel1 though they themselves are not parallel4 ,but if the principal plane of the second crystal be perpendicular to that of the first1 the reverse of what has been described takes place2 the ordinarily refracted ray of the first crystal suffers1 at the second1 extraordinary refraction only1 and the extraordinary ray of the first suffers ordinary refraction only at the second4 ,thus1 in each of these positions1 the double refraction of each ray at the second crystal is reduced to single refraction1 though in a different manner in the two cases4 ,but in any other position of the crystals1 each ray1 produced by the first1 is doubly refracted by the second1 so as to produce four rays4 ,note #dbi3 ,tr4 ,opt4 p4 #beb4 ,a step in the right conception of these phenomena was made by ,newton1 in the second edition of his ,opticks 7#agag74 ,he represented them as resulting from this2--that the rays of light have sides1 and that they undergo the ordinary or extraordinary refraction1 according as these sides are parallel to the principal plane of the crystal1 or at right angles to it 7,query #bf74 ,in this way1 it is clear1 that those rays which1 in the first crystal1 had been selected for extraordinary refraction1 because their sides were perpendicular to the principal plane1 would all suffer extraordinary refraction at the second crystal for the same reason1 if its principal plane were parallel to that of the first2 and would all suffer ordinary refraction1 if the principal plane of the second crystal were perpendicular to that of the first1 and #gd consequently parallel to the sides of the refracted ray4 ,this view of the subject includes some of the leading features of the case1 but still leaves several considerable difficulties4 ,no material advance was made in the subject till it was taken up by ,malus1#dci along with the other circumstances of double refraction1 about a hundred years afterwards4 ,he verified what had been observed by ,huyghens and ,newton1 on the subject of the variations which light thus exhibits2 but he discovered that this modification1 in virtue of which light undergoes the ordinary1 or the extraordinary1 refraction1 according to the position of the plane of the crystal1 may be impressed upon it many other ways4 ,one part of this discovery was made accidentally4#ddi ,in #ahjh1 ,malus happened to be observing the light of the setting sun1 reflected from the windows of the ,luxembourg1 through a rhombohedron of ,iceland spar2 and he observed that in turning round the crystal1 the two images varied in their intensity4 ,neither of the images completely vanished1 because the light from the windows was not properly modified1 or1 to use the term which ,malus soon adopted1 was not completely polarized4 ,the complete polarization of light by reflection from glass1 or any other transparent substance1 was found to take place at a certain definite angle1 different for each substance4 ,it was found also that in all crystals in which double refraction occurred1 the separation of the refracted rays was accompanied by polarization2 the two rays1 the ordinary and the extraordinary1 being always polarized oppositely1 that is1 in planes at right angles to each other4 ,the term poles1 used by ,malus1 conveyed nearly the same notion as the term sides which had been employed by ,newton1 with the additional conception of a property which appeared or disappeared according as the poles of the particles were or were not in a certain direction2 a property thus resembling the polarity of magnetic bodies4 ,when a spot of polarized light is looked at through a transparent crystal of ,iceland spar1 each of the two images produced by the double refraction varies in brightness as the crystal is turned round4 ,if1 for the sake of example1 we suppose the crystal to be turned round in the direction of the points of the compass1 ,n1 ,e1 ,s1 ,w1 and if one image be brightest when the crystal marks ,n and ,s1 it will disappear when the crystal marks ,e and ,w3 and on the contrary1 the second image will vanish when the crystal marks ,n and ,s1 #ge and will be brightest when the crystal marks ,e and ,w4 ,the first of these images is polarized in the plane ,,ns passing through the ray1 and the second in the plane ,,ew1 perpendicular to the other4 ,and these rays are oppositely polarized4 ,it was further found that whether the ray were polarized by reflection from glass1 or from water1 or by double refraction1 the modification of light so produced1 or the nature of the polarization1 was identical in all these cases2--that the alternatives of ordinary and extraordinary refraction and non-refraction1 were the same1 by whatever crystal they were tested1 or in whatever manner the polarization had been impressed upon the light2 in short1 that the property1 when once acquired1 was independent of everything except the sides or poles of the ray2 and thus1 in #ahaa1 the term polarization was introduced4#dei ,note #dci3 ,malus1 ,th4 de la ,doub4 ,rf4 p4 #bif4 ,note #ddi3 ,arago1 art4 ,polarization1 ,supp4 ,enc4 ,brit4 ,note #dei3 ,mm4 ,inst4 #ahaj4 ,this being the state of the subject1 it became an obvious question1 by what other means1 and according to what laws1 this property was communicated4 ,it was found that some crystals1 instead of giving1 by double refraction1 two images oppositely polarized1 give a single polarized image4 ,this property was discovered in the agate by ,sir ,d4 ,brewster1 and in tourmaline by ,m4 ,biot and ,dr4 ,seebeck4 ,the latter mineral became1 in consequence1 a very convenient part of the apparatus used in such observations4 ,various peculiarities bearing upon this subject1 were detected by different experimenters4 ,it was in a short time discovered1 that light might be polarized by refraction1 as well as by reflection1 at the surface of uncrystallized bodies1 as glass2 the plane of polarization being perpendicular to the plane of refraction2 further1 that when a portion of a ray of light was polarized by reflection1 a corresponding portion was polarized by transmission1 the planes of the two polarizations being at right angles to each other4 ,it was found also that the polarization which was incomplete with a single plate1 either by reflection or refraction1 might be made more and more complete by increasing the number of plates4 ,among an accumulation of phenomena like this1 it is our business to inquire what general laws were discovered4 ,to make such discoveries without possessing the general theory of the facts1 required no ordinary sagacity and good fortune4 ,yet several laws were detected at this stage of the subject4 ,malus1 in #ahaa1 obtained the important generalization that1 whenever we obtain1 by any means1 a polarized ray of light1 we produce also another ray1 polarized in a contrary #gf direction2 thus when reflection gives a polarized ray1 the companion-ray is refracted polarized oppositely1 along with a quantity of unpolarized light4 ,and we must particularly notice ,sir ,d4 ,brewster's rule for the polarizing angle of different bodies4 ,malus#dfi had said that the angle of reflection from transparent bodies which most completely polarizes the reflected ray1 does not follow any discoverable rule with regard to the order of refractive or dispersive powers of the substances4 ,yet the rule was in reality very simple4 ,in #ahae1 ,sir ,d4 ,brewster stated#dgi as the law1 which in all cases determines this angle1 that the index of refraction is the tangent of the angle of polarization4 ,it follows from this1 that the polarization takes place when the reflected and refracted rays are at right angles to each other4 ,this simple and elegant rule has been fully confirmed by all subsequent observations1 as by those of ,,mm4 ,biot and ,seebeck2 and must be considered one of the happiest and most important discoveries of the laws of phenomena in ,optics4 ,note #dfi3 ,mm4 ,inst4 #ahaj4 ,note #dgi3 ,phil4 ,trans4 #ahae4 ,the rule for polarization by one reflection being thus discovered1 tentative formul were proposed by ,sir ,d4 ,brewster and ,m4 ,biot1 for the cases in which several reflections or refractions take place4 ,fresnel also in #ahag and #ahah1 traced the effect of reflection in modifying the direction of polarization1 which ,malus had done inaccurately in #ahaj4 ,but the complexity of the subject made all such attempts extremely precarious1 till the theory of the phenomena was understood1 a period which now comes under notice4 ,the laws which we have spoken of were important materials for the establishment of the theory2 but in the mean time1 its progress at first had been more forwarded by some other classes of facts1 of a different kind1 and of a longer standing notoriety1 to which we must now turn our attention4 ,,chapter ,,vii4 ,,discovery ,,of ,,the ,,laws ,,of ,,the ,,colours ,,of ,,thin ,,plates4 ,,the facts which we have now to consider are remarkable1 inasmuch as the colours are produced merely by the smallness of dimensions of the bodies employed4 ,the light is not analysed by any peculiar #gg property of the substances1 but dissected by the minuteness of their parts4 ,on this account1 these phenomena give very important indications of the real structure of light2 and at an early period1 suggested views which are1 in a great measure1 just4 ,hooke appears to be the first person who made any progress in discovering the laws of the colors of thin plates4 ,in his ,micrographia1 printed by the ,royal ,society in #affd1 he describes1 in a detailed and systematic manner1 several phenomena of this kind1 which he calls fantastical colors4 ,he examined them in ,muscovy glass or mica1 a transparent mineral which is capable of being split into the exceedingly thin films which are requisite for such colors2 he noticed them also in the fissures of the same substance1 in bubbles blown of water1 rosin1 gum1 glass2 in the films on the surface of tempered steel2 between two plane pieces of glass2 and in other cases4 ,he perceived also1#dhi that the production of each color required a plate of determinate thickness1 and he employed this circumstance as one of the grounds of his theory of light4 ,note #dhi3 ,micrographia1 p4 #ec4 ,newton took up the subject where ,hooke had left it2 and followed it out with his accustomed skill and clearness1 in his ,discourse on ,light and ,colors1 communicated to the ,royal ,society in #afge4 ,he determined1 what ,hooke had not ascertained1 the thickness of the film which was requisite for the production of each color2 and in this way explained1 in a complete and admirable manner1 the colored rings which occur when two lenses are pressed together1 and the scale of color which the rings follow2 a step of the more consequence1 as the same scale occurs in many other optical phenomena4 ,it is not our business here to state the hypothesis with regard to the properties of light which ,newton founded on these facts2--the fits of easy transmission and reflection4 ,we shall see hereafter that his attempted induction was imperfect2 and his endeavor to account1 by means of the laws of thin plates1 for the colors of natural bodies1 is altogether unsatisfactory4 ,but notwithstanding these failures in the speculations on this subject1 he did make in it some very important steps2 for he clearly ascertained that when the thickness of the plate was about #aaghjjjth of an inch1 or three times1 five times1 seven times that magnitude1 there was a bright color produced2 but blackness1 when the thickness was exactly intermediate between those magnitudes4 ,he found1 also1 that the thicknesses which gave red and #gh violet#dii were as fourteen to nine2 and the intermediate colors of course corresponded to intermediate thicknesses1 and therefore1 in his apparatus1 consisting of two lenses pressed together1 appeared as rings of intermediate sizes4 ,his mode of confirming the rule1 by throwing upon this apparatus differently colored homogeneous light1 is striking and elegant4 ,it was very pleasant1 he says1 to see the rings gradually swell and contract as the color of the light was changed4 ,note #dii3 ,opticks1 p4 #ahd4 ,it is not necessary to enter further into the detail of these phenomena1 or to notice the rings seen by transmission1 and other circumstances4 ,the important step made by ,newton in this matter was1 the showing that the rays of light1 in these experiments1 as they pass onwards go periodically through certain cycles of modification1 each period occupying nearly the small fraction of an inch mentioned above2 and this interval being different for different colors4 ,although ,newton did not correctly disentangle the conditions under which this periodical character is manifestly disclosed1 the discovery that1 under some circumstances1 such a periodical character does exist1 was likely to influence1 and did influence1 materially and beneficially1 the subsequent progress of ,optics towards a connected theory4 ,we must now trace this progress2 but before we proceed to this task1 we will briefly notice a number of optical phenomena which had been collected1 and which waited for the touch of sound theory to introduce among them that rule and order which mere observation had sought for in vain4 ,,chapter ,,viii4 ,,attempts ,,to ,,discover ,,the ,,laws ,,of ,,other ,,phenomena4 ,,the phenomena which result from optical combinations1 even of a comparatively simple nature1 are extremely complex4 ,the theory which is now known accounts for these results with the most curious exactness1 and points out the laws which pervade the apparent confusion2 but without this key to the appearances1 it was scarcely possible that any rule or order should be detected4 ,the undertaking was of #gi the same kind as it would have been1 to discover all the inequalities of the moon's motion without the aid of the doctrine of gravity4 ,we will enumerate some of the phenomena which thus employed and perplexed the cultivators of optics4 ,the fringes of shadows were one of the most curious and noted of such classes of facts4 ,these were first remarked by ,grimaldi#eji 7#affe71 and referred by him to a property of light which he called ,diffraction4 ,when shadows are made in a dark room1 by light admitted through a very small hole1 these appearances are very conspicuous and beautiful4 ,hooke1 in #afgb1 communicated similar observations to the ,royal ,society1 as a new property of light not mentioned by any optical writer before2 by which we see that he had not heard of ,grimaldi's experiments4 ,newton1 in his ,opticks1 treats of the same phenomena1 which he ascribes to the inflexion of the rays of light4 ,he asks 7,qu4 #c71 ,are not the rays of light1 in passing by the edges and sides of bodies1 bent several times backward and forward with a motion like that of an eel8 ,and do not the three fringes of colored light in shadows arise from three such bendings8 ,it is remarkable that ,newton should not have noticed1 that it is impossible1 in this way1 to account for the facts1 or even to express their laws2 since the light which produces the fringes must1 on this theory1 be propagated1 even after it leaves the neighborhood of the opake body1 in curves1 and not in straight lines4 ,accordingly1 all who have taken up ,newton's notion of inflexion1 have inevitably failed in giving anything like an intelligible and coherent character to these phenomena4 ,this is1 for example1 the case with ,mr4 7now ,lord7 ,brougham's attempts in the ,philosophical ,transactions for #agif4 ,the same may be said of other experimenters1 as ,mairan#eai and ,du ,four1#ebi who attempted to explain the facts by supposing an atmosphere about the opake body4 ,several authors1 as ,maraldi1#eci and ,comparetti1#edi repeated or varied these experiments in different ways4 ,note #eji3 ,physico-,mathesis1 de ,lumine1 ,coloribus et ,iride4 ,bologna1 #affe4 ,note #eai3 ,ac4 ,par4 #agch4 ,note #ebi3 ,mmoires ,prsents1 vol4 v4 ,note #eci3 ,ac4 ,par4 #agbc4 ,note #edi3 ,observationes ,optic de ,luce ,inflex et ,coloribus4 ,padua1 #aghg4 ,newton had noticed certain rings of color produced by a glass speculum1 which he called colors of thick plates1 and which he attempted to connect with the colors of thin plates4 ,his reasoning is by no means satisfactory2 but it was of use1 by pointing out this as a case in which his fits 7the small periods1 or cycles in the rays of light1 of #hj which we have spoken7 continued to occur for a considerable length of the ray4 ,but other persons1 attempting to repeat his experiments1 confounded with them extraneous phenomena of other kinds2 as the ,duc de ,chaulnes1 who spread muslin before his mirror1#eei and ,dr4 ,herschel1 who scattered hair-powder before his4#efi ,the colors produced by the muslin were those belonging to shadows of gratings1 afterwards examined more successfully by ,fraunhofer1 when in possession of the theory4 ,we may mention here also the colors which appear on finely-striated surfaces1 and on mother-of-pearl1 feathers1 and similar substances4 ,these had been examined by various persons 7as ,boyle1 ,mazeas1 ,lord ,brougham71 but could still1 at this period1 be only looked upon as insulated and lawless facts4 ,note #eei3 ,ac4 ,par4 #agee4 ,note #efi3 ,phil4 ,trans4 #ahjg4 ,,chapter ,,ix4 ,,discovery ,,of ,,the ,,laws ,,of ,,phenomena ,,of ,,dipolarized ,,light4 ,,besides the above-mentioned perplexing cases of colors produced by common light1 cases of periodical colors produced by polarized light began to be discovered1 and soon became numerous4 ,in ,august1 #ahaa1 ,m4 ,arago communicated to the ,institute of ,france an account of colors seen by passing polarized light through mica1 and analysing#egi it with a prism of ,iceland spar4 ,it is remarkable that the light which produced the colors in this case was the light polarized by the sky1 a cause of polarization not previously known4 ,the effect which the mica thus produced was termed depolarization2--not a very happy term1 since the effect is not the destruction of the polarization1 but the combination of a new polarizing influence with the former4 ,the word dipolarization1 which has since been proposed1 is a much more appropriate expression4 ,several other curious phenomena of the same kind were observed in quartz1 and in flint-glass4 ,m4 ,arago was not able to reduce these phenomena to laws1 but he had a full conviction of their value1 and ventures to class them with the great steps in #ha this part of optics4 ,to ,bartholin we owe the knowledge of double refraction2 to ,huyghens1 that of the accompanying polarization2 to ,malus1 polarization by reflection2 to ,arago1 depolarization4 ,sir ,d4 ,brewster was at the same time engaged in a similar train of research2 and made discoveries of the same nature1 which1 though not published till some time after those of ,arago1 were obtained without a knowledge of what had been done by him4 ,sir ,d4 ,brewster's ,treatise on ,new ,philosophical ,instruments1 published in #ahac1 contains many curious experiments on the depolarizing properties of minerals4 ,both these observers noticed the changes of color which are produced by changes in the position of the ray1 and the alternations of color in the two oppositely polarized images2 and ,sir ,d4 ,brewster discovered that1 in topaz1 the phenomena had a certain reference to lines which he called the neutral and depolarizing axes4 ,m4 ,biot had endeavored to reduce the phenomena to a law2 and had succeeded so far1 that he found that in the plates of sulphate of lime1 the place of the tint1 estimated in ,newton's scale 7see ante1 chap4 vii471 was as the square of the sine of the inclination4 ,but the laws of these phenomena became much more obvious when they were observed by ,sir ,d4 ,brewster with a larger field of view4#ehi ,he found that the colors of topaz1 under the circumstances now described1 exhibited themselves in the form of elliptical rings1 crossed by a black bar1 the most brilliant class of phenomena1 as he justly says1 in the whole range of optics4 ,in #ahad1 also1 ,wollaston observed the circular rings with a black cross1 produced by similar means in calc-spar2 and ,m4 ,biot1 in #ahae1 made the same observation4 ,the rings in several of these cases were carefully measured by ,m4 ,biot and ,sir ,d4 ,brewster1 and a great mass of similar phenomena was discovered4 ,these were added to by various persons1 as ,m4 ,seebeck1 and ,sir ,john ,herschel4 ,note #egi3 ,the prism of ,iceland spar produces the colors by separating the transmitted rays according to the laws of double refraction4 ,hence it is said to analyse the light4 ,note #ehi3 ,phil4 ,trans4 #ahad4 ,sir ,d4 ,brewster1 in #ahah1 discovered a general relation between the crystalline form and the optical properties1 which gave an incalculable impulse and a new clearness to these researches4 ,he found that there was a correspondence between the degree of symmetry of the optical phenomena and the crystalline form2 those crystals which are uniaxal in the crystallographical sense1 are also uniaxal in their optical properties1 and give circular rings2 those which are of other forms are1 generally speaking1 biaxal2 they give oval and knotted isochromatic lines1 with two poles4 ,he also discovered a rule for the tint at each point #hb in such cases2 and thus explained1 so far as an empirical law of phenomena went1 the curious and various forms of the colored curves4 ,this law1 when simplified by ,m4 ,biot1#eii made the tint proportional to the product of the distances of the point from the two poles4 ,in the following year1 ,sir ,j4 ,herschel confirmed this law by showing1 from actual measurement1 that the curve of the isochromatic lines in these cases was the curve termed the lemniscata1 which has1 for each point1 the product of the distances from two fixed poles equal to a constant quantity4#fji ,he also reduced to rule some other apparent anomalies in phenomena of the same class4 ,note #eii3 ,mm4 ,inst4 #ahah1 p4 #aib4 ,note #fji3 ,phil4 ,trans4 #ahai4 ,m4 ,biot1 too1 gave a rule for the directions of the planes of polarization of the two rays produced by double refraction in biaxal crystals1 a circumstance which has a close bearing upon the phenomena of dipolarization4 ,his rule was1 that the one plane of polarization bisects the dihedral angle formed by the two planes which pass through the optic axes1 and that the other is perpendicular to such a plane4 ,when1 however1 ,fresnel had discovered from the theory the true laws of double refraction1 it appeared that the above rule is inaccurate1 although in a degree which observation could hardly detect without the aid of theory4#fai ,note #fai3 ,fresnel1 ,mm4 ,inst4 #ahbg1 p4 #afb4 ,there were still other classes of optical phenomena which attracted notice2 especially those which are exhibited by plates of quartz cut perpendicular to the axis4 ,m4 ,arago had observed1 in #ahaa1 that this substance produced a twist of the plane of polarization to the right or left hand1 the amount of this twist being different for different colors2 a result which was afterwards traced to a modification of light different both from common and from polarized light1 and subsequently known as circular polarization4 ,sir ,j4 ,herschel had the good fortune and sagacity to discover that this peculiar kind of polarization in quartz was connected with an equally peculiar modification of crystallization1 the plagihedral faces which are seen1 on some crystals1 obliquely disposed1 and1 as it were1 following each other round the crystal from left to right1 or from right to left4 ,sir ,j4 ,herschel found that the right-handed or left-handed character of the circular polarization corresponded1 in all cases1 to that of the crystal4 ,in #ahae1 ,m4 ,biot1 in his researches on the subject of circular polarization1 was led to the unexpected and curious discovery1 that this #hc property which seemed to require for its very conception a crystalline structure in the body1 belonged nevertheless to several fluids1 and in different directions for different fluids4 ,oil of turpentine1 and an essential oil of laurel1 gave the plane of polarization a rotation to the left hand2 oil of citron1 syrup of sugar1 and a solution of camphor1 gave a rotation to the right hand4 ,soon after1 the like discovery was made independently by ,dr4 ,seebeck1 of ,berlin4 ,it will easily be supposed that all those brilliant phenomena could not be observed1 and the laws of many of the phenomena discovered1 without attempts on the part of philosophers to combine them all under the dominion of some wide and profound theory4 ,endeavors to ascend from such knowledge as we have spoken of1 to the general theory of light1 were1 in fact1 made at every stage of the subject1 and with a success which at last won almost all suffrages4 ,we are now arrived at the point at which we are called upon to trace the history of this theory2 to pass from the laws of phenomena to their causes2--from ,formal to ,physical ,optics4 ,the undulatory theory of light1 the only discovery which can stand by the side of the theory of universal gravitation1 as a doctrine belonging to the same order1 for its generality1 its fertility1 and its certainty1 may properly be treated of with that ceremony which we have hitherto bestowed only on the great advances of astronomy2 and ,i shall therefore now proceed to speak of the ,prelude to this epoch1 the ,epoch itself1 and its ,sequel1 according to the form of the preceding ,book which treats of astronomy4 #bnd ,ed4 ,i ought to have stated1 in the beginning of this chapter1 that ,malus discovered the depolarization of white light in #ahaa4 ,he found that a pencil of light which1 being polarized1 refused to be reflected by a surface properly placed1 recovered its power of being reflected after being transmitted through certain crystals and other transparent bodies4 ,malus intended to pursue this subject1 when his researches were terminated by his death1 ,feb4 #g1 #ahab4 ,m4 ,arago1 about the same time1 announced his important discovery of the depolarization of colors by crystals4 ,i may add1 to what is above said of ,m4 ,biot's discoveries respecting the circular polarizing power of fluids1 that he pursued his researches so as to bring into view some most curious relations among the elements of bodies4 ,it appeared that certain substances1 as sugar of canes1 had a right-handed effect1 and certain other substances1 as gum1 a left-handed effect2 and that the molecular value of this effect was not altered by dilution4 ,it appeared also that a certain element of the #hd substance of fruits1 which had been supposed to be gum1 and which is changed into sugar by the operation of acids1 is not gum1 and has a very energetic right-handed effect4 ,this substance ,m4 ,biot called dextrine1 and he has since traced its effects into many highly curious and important results49999 #he ,,physical ,,optics4 ,,chapter ,x4 ,,prelude ,,to ,,the ,,epoch ,,of ,,young ,,and ,,fresnel4 ,,by ,physical ,optics we mean1 as has already been stated1 the theories which explain optical phenomena on mechanical principles4 ,no such explanation could be given till true mechanical principles had been obtained2 and1 accordingly1 we must date the commencement of the essays towards physical optics from ,descartes1 the founder of the modern mechanical philosophy4 ,his hypothesis concerning light is1 that it consists of small particles emitted by the luminous body4 ,he compares these particles to balls1 and endeavors to explain1 by means of this comparison1 the laws of reflection and refraction4#fbi ,in order to account for the production of colors by refraction1 he ascribes to these balls an alternating rotatory motion4#fci ,this form of the emission theory1 was1 like most of the physical speculations of its author1 hasty and gratuitous2 but was extensively accepted1 like the rest of the ,cartesian doctrines1 in consequence of the love which men have for sweeping and simple dogmas1 and deductive reasonings from them4 ,in a short time1 however1 the rival optical theory of undulations made its appearance4 ,hooke in his ,micrographia 7#affd7 propounds it1 upon occasion of his observations1 already noticed1 7chap4 9999vii417 on the colors of thin plates4 ,he there asserts#fdi light to consist in a quick1 short1 vibrating motion1 and that it is propagated in a homogeneous medium1 in such a way that every pulse or vibration of the luminous body will generate a sphere1 which will continually increase and grow bigger1 just after the same manner 7though indefinitely swifter7 as the waves or rings on the surface of water do swell into bigger and bigger circles about a point in it4#fei ,he applies this to the explanation of refraction1 #hf by supposing that the rays in a denser medium move more easily1 and hence that the pulses become oblique2 a far less satisfactory and consistent hypothesis than that of ,huyghens1 of which we shall next have to speak4 ,but ,hooke has the merit of having also combined with his theory1 though somewhat obscurely1 the ,principle of ,interferences1 in the application which he makes of it to the colors of thin plates4 ,thus#ffi he supposes the light to be reflected at the first surface of such plates2 and he adds1 after two refractions and one reflection 7from the second surface7 there is propagated a kind of fainter ray1 which comes behind the other reflected pulse2 so that hereby 7the surfaces ,,ab and ,,ef being so near together that the eye cannot discriminate them from one71 this compound or duplicated pulse does produce on the retina the sensation of a yellow4 ,the reason for the production of this particular color1 in the case of which he here speaks1 depends on his views concerning the kind of pulses appropriate to each color2 and1 for the same reason1 when the thickness is different1 he finds that the result will be a red or a green4 ,this is a very remarkable anticipation of the explanation ultimately given of these colors2 and we may observe that if ,hooke could have measured the thickness of his thin plates1 he could hardly have avoided making considerable progress in the doctrine of interferences4 ,note #fbi3 ,diopt4 c4 ii4 #d4 ,note #fci3 ,meteor4 c4 viii4 #f4 ,note #fdi3 ,micrographia1 p4 #ef4 ,note #fei3 ,micrographia1 p4 #eg4 ,note #ffi3 ,micrographia1 p4 #ff4 ,but the person who is generally1 and with justice1 looked upon as the great author of the undulatory theory1 at the period now under notice1 is ,huyghens1 whose ,trait de la ,lumire1 containing a developement of his theory1 was written in #afgh1 though not published till #afij4 ,in this work he maintained1 as ,hooke had done1 that light consists in undulations1 and expands itself spherically1 nearly in the same manner as sound does2 and he referred to the observations of ,rmer on ,jupiter's satellites1 both to prove that this difference takes place successively1 and to show its exceeding swiftness4 ,in order to trace the effect of an undulation1 ,huyghens considers that every point of a wave diffuses its motion in all directions2 and hence he draws the conclusion1 so long looked upon as the turning-point of the combat between the rival theories1 that the light will not be diffused beyond the rectilinear space1 when it passes through an aperture2 for1 says he1#fgi although the partial waves1 produced by the particles comprised in the aperture1 do diffuse themselves beyond the rectilinear space1 these waves do not concur anywhere except in front of the #hg aperture4 ,he rightly considers this observation as of the most essential value4 ,this1 he says1 was not known by those who began to consider the waves of light1 among whom are ,mr4 ,hooke in his ,micrography1 and ,father ,pardies2 who1 in a treatise of which he showed me a part1 and which he did not live to finish1 had undertaken to prove1 by these waves1 the effects of reflection and refraction4 ,but the principal foundation1 which consists in the remark ,i have just made1 was wanting in his demonstrations4 ,note #fgi3 ,tracts on ,optics1 p4 #bji4 ,by the help of this view1 ,huyghens gave a perfectly satisfactory and correct explanation of the laws of reflection and refraction2 and he also applied the same theory1 as we have seen1 to the double refraction of ,iceland spar with great sagacity and success4 ,he conceived that in this crystal1 besides the spherical waves1 there might be others of a spheroidal form1 the axis of the spheroid being symmetrically disposed with regard to the faces of the rhombohedron1 for to these faces the optical phenomena are symmetrically related4 ,he found#fhi that the position of the refracted ray1 determined by such spheroidal undulations1 would give an oblique refraction1 which would coincide in its laws with the refraction observed in ,iceland spar2 and1 as we have stated1 this coincidence was long after fully confirmed by other observers4 ,note #fhi3 ,tracts on ,optics1 #bcg4 ,since ,huyghens1 at this early period1 expounded the undulatory theory with so much distinctness1 and applied it with so much skill1 it may be asked why we do not hold him up as the great ,author of the induction of undulations of light2--the person who marks the epoch of the theory8 ,to this we reply1 that though ,huyghens discovered strong presumptions in favor of the undulatory theory1 it was not established till a later era1 when the fringes of shadows1 rightly understood1 made the waves visible1 and when the hypothesis which had been assumed to account for double refraction1 was found to contain also an explanation of polarization4 ,it is then that this theory of light assumes its commanding form2 and the persons who gave it this form1 we must make the great names of our narrative2 without1 however1 denying the genius and merit of ,huyghens1 who is1 undoubtedly1 the leading character in the prelude to the discovery4 ,the undulatory theory1 from this time to our own1 was unfortunate in its career4 ,it was by no means destitute of defenders1 but these were not experimenters2 and none of them thought of applying it to #hh ,grimaldi's experiments on fringes1 of which we have spoken a little while ago4 ,and the great authority of the period1 ,newton1 adopted the opposite hypothesis1 that of emission1 and gave it a currency among his followers which kept down the sounder theory for above a century4 ,newton's first disposition appears to have been by no means averse to the assumption of an ether as the vehicle of luminiferous undulations4 ,when ,hooke brought against his prismatic analysis of light some objections1 founded on his own hypothetical notions1 ,newton1 in his reply1 said1#fii ,the hypothesis has a much greater affinity with his own hypothesis than he seems to be aware of2 the vibrations of the ether being as useful and necessary in this as in his4 ,this was in #afgb2 and we might produce1 from ,newton's writing1 passages of the same kind1 of a much later date4 ,indeed it would seem that1 to the last1 ,newton considered the assumption of an ether as highly probable1 and its vibrations important parts of the phenomena of light2 but he also introduced into his system the hypothesis of emission1 and having followed this hypothesis into mathematical detail1 while he has left all that concerns the ether in the form of queries and conjectures1 the emission theory has naturally been treated as the leading part of his optical doctrines4 ,note #fii3 ,phil4 ,trans4 vii4 #ejhg4 ,the principal propositions of the ,principia which bear upon the question of optical theory are those of the fourteenth ,section of the first ,book1#gji in which the law of the sines in refraction is proved on the hypothesis that the particles of bodies act on light only at very small distances2 and the proposition of the eighth ,section of the second ,book2#gai in which it is pretended to be demonstrated that the motion propagated in a fluid must diverge when it has passed through an aperture4 ,the former proposition shows that the law of refraction1 an optical truth which mainly affected the choice of a theory1 7for about reflection there is no difficulty on any mechanical hypothesis17 follows from the theory of emission3 the latter proposition was intended to prove the inadmissibility of the rival hypothesis1 that of undulations4 ,as to the former point1--the hypothetical explanation of refraction1 on the assumptions there made1--the conclusion is quite satisfactory2 but the reasoning in the latter case1 7respecting the propagation of undulations17 is certainly inconclusive and vague2 and something better might the more reasonably have been expected1 since ,huyghens had at least #hi endeavored to prove the opposite proposition4 ,but supposing we leave these properties1 the rectilinear course1 the reflection1 and the refraction of light1 as problems in which neither theory has a decided advantage1 what is the next material point8 ,the colors of thin plates4 ,now1 how does ,newton's theory explain these8 ,by a new and special supposition2--that of fits of easy transmission and reflection3 a supposition which1 though it truly expresses these facts1 is not borne out by any other phenomena4 ,but1 passing over this1 when we come to the peculiar laws of polarization in ,iceland spar1 how does ,newton's meet this8 ,again by a special and new supposition2--that the rays of light have sides4 ,thus we find no fresh evidence in favor of the emission hypothesis springing out of the fresh demands made upon it4 ,it may be urged1 in reply1 that the same is true of the undulatory theory2 and it must be allowed that1 at the time of which we now speak1 its superiority in this respect was not manifested2 though ,hooke1 as we have seen1 had caught a glimpse of the explanation1 which this theory supplies1 of the colors of thin plates4 ,note #gji3 ,principia1 ,prop4 #id1 et seq4 ,note #gai3 ,ib4 ,prop4 #db4 ,at a later period1 ,newton certainly seems to have been strongly disinclined to believe light to consist in undulations merely4 ,are not1 he says1 in ,question twenty-eight of the ,opticks1 all hypotheses erroneous1 in which light is supposed to consist in pression or motion propagated through a fluid medium8 ,the arguments which most weighed with him to produce this conviction1 appear to have been the one already mentioned1--that1 on the undulatory hypothesis1 undulations passing through an aperture would be diffused2 and again1--his conviction1 that the properties of light1 developed in various optical phenomena1 depend not upon new modifications1 but upon the original and unchangeable properties of the rays4 7,question twenty-seven47 ,but yet1 even in this state of his views1 he was very far from abandoning the machinery of vibrations altogether4 ,he is disposed to use such machinery to produce his fits of easy transmission4 ,in his seventeenth ,query1 he says1#gbi when a ray of light falls upon the surface of any pellucid body1 and is there refracted or reflected2 may not waves of vibrations or tremors be thereby excited in the refracting or reflecting medium at the point of incidence8 4 4 4 4 and do not these vibrations overtake the rays of light1 and by overtaking them successively1 do they not put them into the fits of easy reflection and easy #ij transmission described above8 ,several of the other queries imply the same persuasion1 of the necessity for the assumption of an ether and its vibrations4 ,and it might have been asked1 whether any good reason could be given for the hypothesis of an ether as a part of the mechanism of light1 which would not be equally valid in favor of this being the whole of the mechanism1 especially if it could be shown that nothing more was wanted to produce the results4 ,note #gbi3 ,opticks1 p4 #cbb4 ,the emission theory was1 however1 embraced in the most strenuous manner by the disciples of ,newton4 ,that propositions existed in the ,principia which proceeded on this hypothesis1 was1 with many of these persons1 ground enough for adopting the doctrine2 and it had also the advantage of being more ready of conception1 for though the propagation of a wave is not very difficult to conceive1 at least by a mathematician1 the motion of a particle is still easier4 ,on the other hand1 the undulation theory was maintained by no less a person than ,euler2 and the war between the two opinions was carried on with great earnestness4 ,the arguments on one side and on the other soon became trite and familiar1 for no person explained any new class of facts by either theory4 ,thus it was urged by ,euler against the system of emission1#gci--that the perpetual emanation of light from the sun must have diminished the mass2--that the stream of matter thus constantly flowing must affect the motions of the planets and comets2 that the rays must disturb each other2--that the passage of light through transparent bodies is1 on this system1 inconceivable3 all such arguments were answered by representations of the exceeding minuteness and velocity of the matter of light4 ,on the other hand1 there was urged against the theory of waves1 the favorite ,newtonian argument1 that on this theory the light passing through an aperture ought to be diffused1 as sound is4 ,it is curious that ,euler does not make to this argument the reply which ,huyghens had made before4 ,the fact really was1 that he was not aware of the true ground of the difference of the result in the cases of sound and light2 namely1 that any ordinary aperture bears an immense ratio to the length of an undulation of light1 but does not bear a very great ratio to the length of an undulation of sound4 ,the demonstrable consequence of this difference is1 that light darts through such an orifice in straight rays1 while sound is diffused in all directions4 ,euler1 not perceiving this difference1 rested his answer mainly upon a circumstance by no means #ia unimportant1 that the partitions usually employed are not impermeable to sound1 as opake bodies are to light4 ,he observes that the sound does not all come through the aperture2 for we hear1 though the aperture be stopped4 ,these were the main original points of attack and defence1 and they continued nearly the same for the whole of the last century2 the same difficulties were over and over again proposed1 and the same solutions given1 much in the manner of the disputations of the schoolmen of the middle ages4 ,note #gci3 ,fischer1 iv4 #ddi4 ,the struggle being thus apparently balanced1 the scale was naturally turned by the general ascendancy of the ,newtonian doctrines3 and the emission theory was the one most generally adopted4 ,it was still more firmly established1 in consequence of the turn generally taken by the scientific activity of the latter half of the eighteenth century3 for while nothing was added to our knowledge of optical laws1 the chemical effects of light were studied to a considerable extent by various inquirers2#gdi and the opinions at which these persons arrived1 they found that they could express most readily1 in consistency with the reigning chemical views1 by assuming the materiality of light4 ,it is1 however1 clear1 that no reasonings of the inevitably vague and doubtful character which belong to these portions of chemistry1 ought to be allowed to interfere with the steady and regular progress of induction and generalization1 founded on relations of space and number1 by which procedure the mechanical sciences are formed4 ,we reject1 therefore1 all these chemical speculations1 as belonging to other subjects2 and consider the history of optical theory as a blank1 till we arrive at some very different events1 of which we have now to speak4 #ib ,note #gdi3 ,as ,scheele1 ,selle1 ,lavoisier1 ,de ,luc1 ,richter1 ,leonhardi1 ,gren1 ,girtanner1 ,link1 ,hagen1 ,voigt1 ,de la ,metherie1 ,scherer1 ,diz1 ,brugnatelli4 ,see ,fischer1 vii4 p4 #bj4 ,,chapter ,,xi4 ,,epoch ,,of ,,young ,,and ,,fresnel4 ,sect4 #a4--;,introduction4 ,,the man whose name must occupy the most distinguished place in the history of ,physical ,optics1 in consequence of what he did in reviving and establishing the undulatory theory of light1 is ,dr4 ,thomas ,young4 ,he was born in #aggc1 at ,milverton in ,somersetshire1 of ,quaker parents2 and after distinguishing himself during youth by the variety and accuracy of his attainments1 he settled in ,london as a physician in #ahja2 but continued to give much of his attention to general science4 ,his optical theory1 for a long time1 made few proselytes2 and several years afterwards1 ,auguste ,fresnel1 an eminent ,french mathematician1 an engineer officer1 took up similar views1 proved their truth1 and traced their consequences1 by a series of labors almost independent of those of ,dr4 ,young4 ,it was not till the theory was thus re-echoed from another land1 that it was able to take any strong hold on the attention of the countrymen of its earlier promulgator4 ,the theory of undulations1 like that of universal gravitation1 may be divided into several successive steps of generalization4 ,in both cases1 all these steps were made by the same persons2 but there is this difference3--all the parts of the law of universal gravitation were worked out in one burst of inspiration by its author1 and published at one time2--in the doctrine of light1 on the other hand1 the different steps of the advance were made and published at separate times1 with intervals between4 ,we see the theory in a narrower form1 and in detached portions1 before the widest generalizations and principles of unity are reached2 we see the authors struggling with the difficulties before we see them successful4 ,they appear to us as men like ourselves1 liable to perplexity and failure1 instead of coming before us1 as ,newton does in the history of ,physical ,astronomy1 as the irresistible and almost supernatural hero of a philosophical romance4 #ic ,the main subdivisions of the great advance in physical optics1 of which we have now to give an account1 are the following3-- #a4 ,the explanation of the periodical colors of thin plates1 thick plates1 fringed shadows1 striated surfaces1 and other phenomena of the same kind1 by means of the doctrine of the interference of undulations4 #b4 ,the explanation of the phenomena of double refraction by the propagation of undulations in a medium of which the optical elasticity is different in different directions4 #c4 ,the conception of polarization as the result of the vibrations being transverse2 and the consequent explanation of the production of polarization1 and the necessary connexion between polarization and double refraction1 on mechanical principles4 #d4 ,the explanation of the phenomena of dipolarization1 by means of the interference of the resolved parts of the vibrations after double refraction4 ,the history of each of these discoveries will be given separately to a certain extent2 by which means the force of proof arising from their combination will be more apparent4 ,sect4 #b4--;,explanation of the ,periodical ,colors of ,thin ,plates and ,shadows by the ,undulatory ,theory4 ,,the explanation of periodical colors by the principle of interference of vibrations1 was the first step which ,young made in his confirmation of the undulatory theory4 ,in a paper on ,sound and ,light1 dated ,emmanuel ,college1 ,cambridge1 #ith ,july1 #agii1 and read before the ,royal ,society in ,january following1 he appears to incline strongly to the ,huyghenian theory2 not however offering any new facts or calculations in its favor1 but pointing out the great difficulties of the ,newtonian hypothesis4 ,but in a paper read before the ,royal ,society1 ,november #ab1 #ahja1 he says1 ,a further consideration of the colors of thin plates has converted that prepossession which ,i before entertained for the undulatory theory of light1 into a very strong conviction of its truth and efficiency2 a conviction which has since been most strikingly confirmed by an analysis of the colors of striated surfaces4 ,he here states the general principle of interferences in the form of a proposition4 7,prop4 viii47 ,when two undulations from different origins coincide either perfectly or very nearly in direction1 their joint effect is a combination of the motions belonging to them4 ,he explains1 by the help of this proposition1 the colors which were observed in ,coventry's #id micrometers1 in which instrument lines were drawn on glass at a distance of #aejjth of an inch4 ,the interference of the undulations of the rays reflected from the two sides of these fine lines1 produced periodical colors4 ,in the same manner1 he accounts for the colors of thin plates1 by the interference of the light partially reflected from the two surfaces of the plates4 ,we have already seen that ,hooke had long before suggested the same explanation2 and ,young says at the end of his paper1 ,it was not till ,i had satisfied myself respecting all these phenomena1 that ,i found in ,hooke's ,micrographia a passage which might have led me earlier to a similar opinion4 ,he also quotes from ,newton many passages which assume the existence of an ether2 of which1 as we have already seen1 ,newton suggests the necessity in these very phenomena1 though he would apply it in combination with the emission of material light4 ,in ,july1 #ahjb1 ,young explained1 on the same principle1 some facts in indistinct vision1 and other similar appearances4 ,and in #ahjc1gei he speaks more positively still4 ,in making1 he says1 some experiments on the fringes of colors accompanying shadows1 ,i have found so simple and so demonstrative a proof of the general law of interference of two portions of light1 which ,i have already endeavored to establish1 that ,i think it right to lay before the ,royal ,society a short statement of the facts which appear to me to be thus decisive4 ,the two papers just mentioned certainly ought to have convinced all scientific men of the truth of the doctrine thus urged2 for the number and exactness of the explanations is very remarkable4 ,they include the colored fringes which are seen with the shadows of fibres2 the colors produced by a dew between two pieces of glass1 which1 according to the theory1 should appear when the thickness of the plate is six times that of thin plates1 and which do so2 the changes resulting from the employment of other fluids than water2 the effect of inclining the plates2 also the fringes and bands which accompany shadows1 the phenomena observed by ,grimaldi1 ,newton1 ,maraldi1 and others1 and hitherto never at all reduced to rule4 ,young observes1 very justly1 whatever may be thought of the theory1 we have got a simple and general law of the phenomena4 ,he moreover calculated the length of an undulation from the measurements of fringes of shadows1 as he had done before from the colors of thin plates2 and found a very close accordance of the results of the various cases with one another4 #ie ,note #gei3 ,phil4 ,trans4 ,memoir1 read ,nov4 #bd4 ,there is one difficulty1 and one inaccuracy1 in ,young's views at this period1 which it may be proper to note4 ,the difficulty was1 that he found it necessary to suppose that light1 when reflected at a rarer medium1 is retarded by half an undulation4 ,this assumption1 though often urged at a later period as an argument against the theory1 was fully justified as the mechanical principles of the subject were unfolded2 and the necessity of it was clear to ,young from the first4 ,on the strength of this1 says he1 ,i ventured to predict1 that if the reflections were of the same kind1 made at the surfaces of a thin plate1 of a density intermediate between the densities of the mediums surrounding it1 the central spot would be white2 and ,i have now the pleasure of stating1 that ,i have fully verified this prediction by interposing a drop of oil of sassafras between a prism of flint-glass and a lens of crown-glass4 ,the inaccuracy of his calculations consisted in his considering the external fringe of shadows to be produced by the interference of a ray reflected from the edge of the object1 with a ray which passes clear of it2 instead of supposing all the parts of the wave of light to corroborate or interfere with one another4 ,the mathematical treatment of the question on the latter hypothesis was by no means easy4 ,young was a mathematician of considerable power in the solution of the problems which came before him3 though his methods possessed none of the analytical elegance which1 in his time1 had become general in ,france4 ,but it does not appear that he ever solved the problem of undulations as applied to fringes1 with its true conditions4 ,he did1 however1 rectify his conceptions of the nature of the interference2 and we may add1 that the numerical error of the consequences of the defective hypothesis is not such as to prevent their confirming the undulatory theory4#gfi ,note #gfi3 ,i may mention1 in addition to the applications which ,young made of the principle of interferences1 his ,eriometer1 an instrument invented for the purpose of measuring the thickness of the fibres of wood2 and the explanation of the supernumerary bands of the rainbow4 ,these explanations involve calculations founded on the length of an undulation of light1 and were confirmed by experiment1 as far as experiment went4 ,but though this theory was thus so powerfully recommended by experiment and calculation1 it met with little favor in the scientific world4 ,perhaps this will be in some measure accounted for1 when we come1 in the next chapter1 to speak of the mode of its reception by #if the supposed judges of science and letters4 ,its author went on laboring at the completion and application of the theory in other parts of the subject2 but his extraordinary success in unravelling the complex phenomena of which we have been speaking1 appears to have excited none of the notice and admiration which properly belonged to it1 till ,fresnel's ,memoir ,on ,diffraction was delivered to the ,institute1 in ,october1 #ahae4 ,,mm4 ,arago and ,poinsot were commissioned to make a report upon this ,memoir2 and the former of these philosophers threw himself upon the subject with a zeal and intelligence which peculiarly belonged to him4 ,he verified the laws announced by ,fresnel3 laws1 he says1 which appear to be destined to make an epoch in science4 ,he then cast a rapid glance at the history of the subject1 and recognized1 at once1 the place which ,young occupied in it4 ,grimaldi1 ,newton1 ,maraldi1 he states1 had observed the facts1 and tried in vain to reduce them to rule or cause4 ,such#ggi was the state of our knowledge on this difficult question1 when ,dr4 ,thomas ,young made the very remarkable experiment which is described in the ,philosophical ,transactions for #ahjc2 namely1 that to obliterate all the bands within the shadow1 we need only stop the ray which is going to graze1 or has grazed1 one border of the object4 ,to this1 ,arago added the important observation1 that the same obliteration takes place1 if we stop the ray1 with a transparent plate2 except the plate be very thin1 in which case the bands are displaced1 and not extinguished4 ,fresnel1 says he1 guessed the effect which a thin plate would produce1 when ,i had told him of the effect of a thick glass4 ,fresnel himself declares#ghi that he was not1 at the time1 aware of ,young's previous labors4 ,after stating nearly the same reasonings concerning fringes which ,young had put forward in #ahja1 he adds1 it is therefore the meeting1 the actual crossing of the rays1 which produces the fringes4 ,this consequence1 which is only1 so to speak1 the translation of the phenomena1 seems to me entirely opposed to the hypothesis of emission1 and confirms the system which makes light consist in the vibrations of a peculiar fluid4 ,and thus the ,principle of ,interferences1 and the theory of undulations1 so far as that principle depends upon the theory1 was a second time established by ,fresnel in ,france1 fourteen years after it had been discovered1 fully proved1 and repeatedly published by ,young in ,england4 #ig ,note #ggi3 ,an4 ,chim4 #ahae1 ,febr4 ,note #ghi3 ,ib4 tom4 xvii4 p4 #djb4 ,in this ,memoir of ,fresnel's1 he takes very nearly the same course as ,young had done2 considering the interference of the direct light with that reflected at the edge1 as the cause of the external fringes2 and he observes1 that in this reflection it is necessary to suppose half an undulation lost3 but a few years later1 he considered the propagation of undulations in a more true and general manner1 and obtained the solution of this difficulty of the half-undulation4 ,his more complete ,memoir on ,diffraction was delivered to the ,institute of ,france1 ,july #bi1 #ahah2 and had the prize awarded it in #ahai3gii but by the delays which at that period occurred in the publication of the ,parisian ,academical ,transactions1 it was not published#hji till #ahbf1 when the theory was no longer generally doubtful or unknown in the scientific world4 ,in this ,memoir1 ,fresnel observes1 that we must consider the effect of every portion of a wave of light upon a distant point1 and must1 on this principle1 find the illumination produced by any number of such waves together4 ,hence1 in general1 the process of integration is requisite2 and though the integrals which here offer themselves are of a new and difficult kind1 he succeeded in making the calculation for the cases in which he experimented4 ,his ,table of the ,correspondences of ,theory and ,observation1#hai is very remarkable for the closeness of the agreement2 the errors being generally less than one hundredth of the whole1 in the distances of the black bands4 ,he justly adds1 ,a more striking agreement could not be expected between experiment and theory4 ,if we compare the smallness of the differences with the extent of the breadths measured2 and if we remark the great variations which a and b 7the distance of the object from the luminous point and from the screen7 have received in the different observations1 we shall find it difficult not to regard the integral which has led us to these results as the faithful expression of the law of the phenomena4 ,note #gii3 ,ann4 ,chim4 ,may1 #ahai4 ,note #hji3 ,mm4 ,inst4 for #ahba-b4 ,note #hai3 ,mm4 ,inst4 p4 #dbj-dbd4 ,a mathematical theory1 applied1 with this success1 to a variety of cases of very different kinds1 could not now fail to take strong hold of the attention of mathematicians2 and accordingly1 from this time1 the undulatory doctrine of diffraction has been generally assented to1 and the mathematical difficulties which it involves1 have been duly studied and struggled with4 ,among the remarkable applications of the undulatory doctrine to diffraction1 we may notice those of ,joseph ,fraunhofer1 a #ih mathematical optician of ,munich4 ,he made a great number of experiments on the shadows produced by small holes1 and groups of small holes1 very near each other4 ,these were published#hbi in his ,new ,modifications of ,light1 in #ahbc4 ,the greater part of this ,memoir is employed in tracing the laws of phenomena of the extremely complex and splendid appearances which he obtained2 but at the conclusion he observes1 ,it is remarkable that the laws of the reciprocal influence and of the diffraction of the rays1 can be deduced from the principles of the undulatory theory3 knowing the conditions1 we may1 by means of an extremely simple equation1 determine the extent of a luminous wave for each of the different colors2 and in every case1 the calculation corresponds with observation4 ,this mention of an extremely simple equation1 appears to imply that he employed only ,young's and ,fresnel's earlier mode of calculating interferences1 by considering two portions of light1 and not the method of integration4 ,both from the late period at which they were published1 and from the absence of mathematical details1 ,fraunhofer's labors had not any strong influence on the establishment of the undulatory theory2 although they are excellent verifications of it1 both from the goodness of the observations1 and the complexity and beauty of the phenomena4 ,note #hbi3 ,in ,schumacher's ,astronomische ,abhandlungen1 in ,french2 earlier in ,german4 ,we have now to consider the progress of the undulatory theory in another of its departments1 according to the division already stated4 ,sect4 #c4--;,explanation of ,double ,refraction by the ,undulatory ,theory4 ,,we have traced the history of the undulatory theory applied to diffraction1 into the period when ,young came to have ,fresnel for his fellow-laborer4 ,but in the mean time1 ,young had considered the theory in its reference to other phenomena1 and especially to those of double refraction4 ,in this case1 indeed1 ,huyghens's explanation of the facts of ,iceland spar1 by means of spheroidal undulations1 was so complete1 and had been so fully confirmed by the measurements of ,hay and ,wollaston1 that little remained to be done1 except to connect the ,huyghenian hypothesis with the mechanical views belonging to the theory1 and to extend his law to other cases4 ,the former part of this task ,young executed1 by remarking that we may conceive the elasticity of the #ii crystal1 on which the velocity of propagation of the luminiferous undulation depends1 to be different1 in the direction of the crystallographic axis1 and in the direction of the planes at right angles to this axis2 and from such a difference1 he deduces the existence of spheroidal undulations4 ,this suggestion appeared in the ,quarterly ,review for ,november1 #ahji1 in a critique upon an attempt of ,laplace to account for the same phenomena4 ,laplace had proposed to reduce the double refraction of such crystals as ,iceland spar1 to his favorite machinery of forces which are sensible at small distances only4 ,the peculiar forces which produce the effect in this case1 he conceives to emanate from the crystallographic axis3 so that the velocity of light within the crystal will depend only on the situation of the ray with respect to this axis4 ,but the establishment of this condition is1 as ,young observes1 the main difficulty of the problem4 ,how are we to conceive refracting forces1 independent of the surface of the refracting medium1 and regulated only by a certain internal line8 ,moreover1 the law of force which ,laplace was obliged to assume1 namely1 that it varied as the square of the sine of the angle which the ray made with the axis1 could hardly be reconciled with mechanical principles4 ,in the critique just mentioned1 ,young appears to feel that the undulatory theory1 and perhaps he himself1 had not received justice at the hands of men of science2 he complains that a person so eminent in the world of science as ,laplace then was1 should employ his influence in propagating error1 and should disregard the extraordinary confirmations which the ,huyghenian theory had recently received4 ,the extension of this view1 of the different elasticity of crystals in different directions1 to other than uniaxal crystals1 was a more complex and difficult problem4 ,the general notion was perhaps obvious1 after what ,young had done2 but its application and verification involved mathematical calculations of great generality1 and required also very exact experiments4 ,in fact1 this application was not made till ,fresnel1 a pupil of the ,polytechnic ,school1 brought the resources of the modern analysis to bear upon the problem2--till the phenomena of dipolarized light presented the properties of biaxal crystals in a vast variety of forms2--and till the theory received its grand impulse by the combination of the explanation of polarization with the explanation of double refraction4 ,to the history of this last-mentioned great step we now proceed4 #ajj ,sect4 #d4--;,explanation of ,polarization by the ,undulatory ,theory4 ,,even while the only phenomena of polarization which were known were those which affect the two images in ,iceland spar1 the difficulty which these facts seemed at first to throw in the way of the undulatory theory was felt and acknowledged by ,young4 ,malus's discovery of polarization by reflection increased the difficulty1 and this ,young did not attempt to conceal4 ,in his review of the papers containing this discovery#hci he says1 ,the discovery related in these papers appears to us to be by far the most important and interesting which has been made in ,france concerning the properties of light1 at least since the time of ,huyghens2 and it is so much the more deserving of notice1 as it greatly influences the general balance of evidence in the comparison of the undulatory and projectile theories of the nature of light4 ,he then proceeds to point out the main features in this comparison1 claiming justly a great advantage for the theory of undulations on the two points we have been considering1 the phenomena of diffraction and of double refraction4 ,and he adds1 with reference to the embarrassment introduced by polarization1 that we are not to expect the course of scientific discovery to run smooth and uninterrupted2 but that we are to lay our account with partial obscurity and seeming contradiction1 which we may hope that time and enlarged research will dissipate4 ,and thus he steadfastly held1 with no blind prejudice1 but with unshaken confidence1 his great philosophical trust1 the fortunes of the undulatory theory4 ,it is here1 after the difficulties of polarization had come into view1 and before their solution had been discovered1 that we may place the darkest time of the history of the theory2 and at this period ,young was alone in the field4 ,note #hci3 ,quart4 ,rev4 ,may1 #ahaj4 ,it does not appear that the light dawned upon him for some years4 ,in the mean time1 ,young found that his theory would explain dipolarized colors2 and he had the satisfaction to see ,fresnel re-discover1 and ,m4 ,arago adopt1 his views on diffraction4 ,he became engaged in friendly intercourse with the latter philosopher1 who visited him in ,england in #ahaf4 ,on ,january the #abth1 #ahag1 in writing to this gentleman1 among other remarks on the subject of optics1 he says1 ,i have also been reflecting on the possibility of giving an imperfect explanation of the affection of light which constitutes polarization1 #aja without departing from the genuine doctrine of undulation4 ,he then proceeds to suggest the possibility of a transverse vibration1 propagated in the direction of the radius1 the motions of the particles being in a certain constant direction with respect to that radius2 and this1 he adds1 is polarization4 ,from his further explanation of his views1 it appears that he conceived the motions of the particles to be oblique to the direction of the ray1 and not perpendicular1 as the theory was afterwards framed2 but still1 here was the essential condition for the explanation of the facts of polarization1--the transverse nature of the vibrations4 ,this idea at once made it possible to conceive how the rays of light could have sides2 for the direction in which the vibration was transverse to the ray1 might be marked by peculiar properties4 ,and after the idea was once started1 it was comparatively easy for men like ,young and ,fresnel to pursue and modify it till it assumed its true and distinct form4 ,we may judge of the difficulty of taking firmly hold of the conception of transverse vibrations of the ether1 as those which constitute light1 by observing how long the great philosophers of whom we are speaking lingered within reach of it1 before they ventured to grasp it4 ,fresnel says1 in #ahba1 ,when ,m4 ,arago and ,i had remarked 7in #ahaf7 that two rays polarized at right angles always give the same quantity of light by their union1 ,i thought this might be explained by supposing the vibrations to be transverse1 and to be at right angles when the rays are polarized at right angles4 ,but this supposition was so contrary to the received ideas on the nature of the vibrations of elastic fluids1 that ,fresnel hesitated to adopt it till he could reconcile it better to his mechanical notions4 ,mr4 ,young1 more bold in his conjectures1 and less confiding in the views of geometers1 published it before me1 though perhaps he thought it after me4 ,and ,m4 ,arago was afterwards wont to relate#hdi that when he and ,fresnel had obtained their joint experimental results of the non-interference of oppositely-polarized pencils1 and when ,fresnel pointed out that transverse vibrations were the only possible translation of this fact into the undulatory theory1 he himself protested that he had not courage to publish such a conception2 and accordingly1 the second part of the ,memoir was published in ,fresnel's name alone4 ,what renders this more remarkable is1 that it occurred when ,m4 ,arago had in his possession the very letter of ,young1 in which he proposed the same suggestion4 #ajb ,note #hdi3 ,i take the liberty of stating this from personal knowledge4 ,young's first published statement of the doctrine of transverse vibrations was given in the explanation of the phenomena of dipolarization1 of which we shall have to speak in the next ,section4 ,but the primary and immense value of this conception1 as a step in the progress of the undulatory theory1 was the connexion which it established between polarization and double refraction2 for it held forth a promise of accounting for polarization1 if any conditions could be found which might determine what was the direction of the transverse vibrations4 ,the analysis of these conditions is1 in a great measure1 the work of ,fresnel2 a task performed with profound philosophical sagacity and great mathematical skill4 ,since the double refraction of uniaxal crystals could be explained by undulations of the form of a spheroid1 it was perhaps not difficult to conjecture that the undulations of biaxal crystals would be accounted for by undulations of the form of an ellipsoid1 which differs from the spheroid in having its three axes unequal1 instead of two only2 and consequently has that very relation to the other1 in respect of symmetry1 which the crystalline and optical phenomena have4 ,or1 again1 instead of supposing two different degrees of elasticity in different directions1 we may suppose three such different degrees in directions at right angles to each other4 ,this kind of generalization was tolerably obvious to a practised mathematician4 ,but what shall call into play all these elasticities at once1 and produce waves governed by each of them8 ,and what shall explain the different polarization of the rays which these separate waves carry with them8 ,these were difficult questions1 to the solution of which mathematical calculation had hitherto been unable to offer any aid4 ,it was here that the conception of transverse vibrations came in1 like a beam of sunlight1 to disclose the possibility of a mechanical connexion of all these facts4 ,if transverse vibrations1 travelling through a uniform medium1 come to a medium not uniform1 but constituted so that the elasticity shall be different in different directions1 in the manner we have described1 what will be the course and condition of the waves in the second medium8 ,will the effects of such waves agree with the phenomena of doubly-refracted light in biaxal crystals8 ,here was a problem1 striking to the mathematician for its generality and difficulty1 and of deep interest to the physical philosopher1 because the fate of a great theory depended upon its solution4 ,the solution1 obtained by great mathematical skill1 was laid before the ,french ,institute by ,fresnel in ,november1 #ahba1 and was carried #ajc further in two ,memoirs presented in #ahbb4 ,its import is very curious4 ,the undulations which1 coming from a distant centre1 fall upon such a medium as we have described1 are1 it appears from the principles of mechanics1 propagated in a manner quite different from anything which had been anticipated4 ,the surface of the waves 7that is1 the surface which would bound undulations diverging from a point71 is a very complex1 yet symmetrical curve surface2 which1 in the case of uniaxal crystals1 resolves itself into a sphere and a spheroid2 but which1 in general1 forms a continuous double envelope of the central point to which it belongs1 intersecting itself and returning into itself4 ,the directions of the rays are determined by this curve surface in biaxal crystals1 as in uniaxal crystals they are determined by the sphere and the spheroid2 and the result is1 that in biaxal crystals1 both rays suffer extraordinary refraction according to determinate laws4 ,and the positions of the planes of polarization of the two rays follow from the same investigation2 the plane of polarization in every case being supposed to be that which is perpendicular to the transverse vibrations4 ,now it appeared that the polarization of the two rays1 as determined by ,fresnel's theory1 would be in directions1 not indeed exactly accordant with the law deduced by ,m4 ,biot from experiment1 but deviating so little from those directions1 that there could be small doubt that the empirical formula was wrong1 and the theoretical one right4 ,the theory was further confirmed by an experiment showing that1 in a biaxal crystal 7topaz71 neither of the rays was refracted according to the ordinary law1 though it had hitherto been supposed that one of them was so2 a natural inaccuracy1 since the error was small4#hei ,thus this beautiful theory corrected1 while it explained1 the best of the observations which had previously been made2 and offered itself to mathematicians with an almost irresistible power of conviction4 ,the explanation of laws so strange and diverse as those of double refraction and polarization1 by the same general and symmetrical theory1 could not result from anything but the truth of the theory4 ,note #hei3 ,an4 ,ch4 xxviii4 p4 #bfd4 ,long1 says ,fresnel1#hfi before ,i had conceived this theory1 ,i had convinced myself by a pure contemplation of the facts1 that it was not possible to discover the true explanation of double refraction1 without explaining1 at the same time1 the phenomena of polarization1 which always goes along with it2 and accordingly1 it was after having found #ajd what mode of vibration constituted polarization1 that ,i caught sight of the mechanical causes of double refraction4 ,note #hfi3 ,sur la ,double ,rf41 ,mm4 ,inst4 #ahbf1 p4 #agd4 ,having thus got possession of the principle of the mechanism of polarization1 ,fresnel proceeded to apply it to the other cases of polarized light1 with a rapidity and sagacity which reminds us of the spirit in which ,newton traced out the consequences of the principle of universal gravitation4 ,in the execution of his task1 indeed1 ,fresnel was forced upon several precarious assumptions1 which make1 even yet1 a wide difference between the theory of gravitation and that of light4 ,but the mode in which these were confirmed by experiment1 compels us to admire the happy apparent boldness of the calculator4 ,the subject of polarization by reflection was one of those which seemed most untractable2 but1 by means of various artifices and conjectures1 it was broken up and subdued4 ,fresnel began with the simplest case1 the reflection of light polarized in the plane of reflection2 which he solved by means of the laws of collision of elastic bodies4 ,he then took the reflection of light polarized perpendicularly to this plane2 and here1 adding to the general mechanical principles a hypothetical assumption1 that the communication of the resolved motion parallel to the refracting surface1 takes place according to the laws of elastic bodies1 he obtains his formula4 ,these results were capable of comparison with experiment2 and the comparison1 when made by ,m4 ,arago1 confirmed the formul4 ,they accounted1 too1 for ,sir ,d4 ,brewster's law concerning the polarizing angle 7see ,chap4 vi472 and this could not but be looked upon as a striking evidence of their having some real foundation4 ,another artifice which ,,mm4 ,fresnel and ,arago employed1 in order to trace the effect of reflection upon common light1 was to use a ray polarized in a plane making half a right angle with the plane of reflection2 for the quantities of the oppositely#hgi polarized light in such an incident ray are equal1 as they are in common light2 but the relative quantities of the oppositely polarized light in the reflected ray are indicated by the new plane of polarization2 and thus these relative quantities become known for the case of common light4 ,the results thus obtained were also confirmed by facts2 and in this manner1 all that was doubtful in the process of ,fresnel's reasoning1 seemed to be authorized by its application to real cases4 #aje ,note #hgi3 ,it will be recollected all along1 that oppositely polarized rays are those which are polarized in two planes perpendicular to each other4 ,see above1 chap4 vi4 ,these investigations were published#hhi in #ahba4 ,in succeeding years1 ,fresnel undertook to extend the application of his formul to a case in which they ceased to have a meaning1 or1 in the language of mathematicians1 became imaginary2 namely1 to the case of internal reflection at the surface of a transparent body4 ,it may seem strange to those who are not mathematicians1 but it is undoubtedly true1 that in many cases in which the solution of a problem directs impossible arithmetical or algebraical operations to be performed1 these directions may be so interpreted as to point out a true solution of the question4 ,such an interpretation ,fresnel attempted#hii in the case of which we now speak2 and the result at which he arrived was1 that the reflection of light through a rhomb of glass of a certain form 7since called ,fresnel's rhomb1 would produce a polarization of a kind altogether different from those which his theory had previously considered1 namely1 that kind which we have spoken of as circular polarization4 ,the complete confirmation of this curious and unexpected result by trial1 is another of the extraordinary triumphs which have distinguished the history of the theory at every step since the commencement of ,fresnel's labors4 ,note #hhi3 ,an4 ,chim4 t4 xvii4 ,note #hii3 ,bullet4 des ,sc4 ,feb4 #ahbc4 ,but anything further which has been done in this way1 may be treated of more properly in relating the verification of the theory4 ,and we have still to speak of the most numerous and varied class of facts to which rival theories of light were applied1 and of the establishment of the undulatory doctrine in reference to that department2 ,i mean the phenomena of depolarized1 or rather1 as ,i have already said1 dipolarized light4 ,sect4 #e4--;,explanation of ,dipolarization by the ,undulatory ,theory4 ,,when ,arago1 in #ahaa1 had discovered the colors produced by polarized light passing through certain crystals1#iji it was natural that attempts should be made to reduce them to theory4 ,m4 ,biot1 animated by the success of ,malus in detecting the laws of double refraction1 and ,young1 knowing the resources of his own theory1 were the first persons to enter upon this undertaking4 ,m4 ,biot's theory1 though in the end displaced by its rival1 is well worth notice in the history of the subject4 ,it was what he called the doctrine of moveable polarization4 ,he conceived that when the molecules of light pass through #ajf thin crystalline plates1 the plane of polarization undergoes an oscillation which carries it backwards and forwards through a certain angle1 namely1 twice the angle contained between the original plane of polarization and the principal section of the crystal4 ,the intervals which this oscillation occupies are lengths of the path of the ray1 very minute1 and different for different colors1 like ,newton's fits of easy transmission2 on which model1 indeed1 the new theory was evidently framed4#iai ,the colors produced in the phenomena of dipolarization really do depend1 in a periodical manner1 on the length of the path of the light through the crystal1 and a theory such as ,m4 ,biot's was capable of being modified1 and was modified1 so as to include the leading features of the facts as then known2 but many of its conditions being founded on special circumstances in the experiments1 and not on the real conditions of nature1 there were in it several incongruities1 as well as the general defect of its being an arbitrary and unconnected hypothesis4 ,note #iji3 ,see chap4 ix4 ,note #iai3 ,see ,,mm4 ,arago and ,biot's ,memoirs1 ,mm4 ,inst4 for #ahaa2 the whole volume for #ahab is a ,memoir of ,m4 ,biot's 7published #ahad72 also ,mm4 ,inst4 for #ahag2 ,m4 ,biot's ,mem4 read in #ahah1 published in #ahai and for #ahah4 ,young's mode of accounting for the brilliant phenomena of dipolarization appeared in the ,quarterly ,review for #ahad4 ,after noticing the discoveries of ,,mm4 ,arago1 ,brewster1 and ,biot1 he adds1 ,we have no doubt that the surprise of these gentlemen will be as great as our own satisfaction in finding that they are perfectly reducible1 like other causes of recurrent colors1 to the general laws of the interference of light which have been established in this country2 giving a reference to his former statements4 ,the results are then explained by the interference of the ordinary and extraordinary ray4 ,but1 as ,m4 ,arago properly observes1 in his account of this matter1#ibi ,it must1 however1 be added that ,dr4 ,young had not explained either in what circumstances the interference of the rays can take place1 nor why we see no colors unless the crystallized plates are exposed to light previously polarized4 ,the explanation of these circumstances depends on the laws of interference of polarized light which ,,mm4 ,arago and ,fresnel established in #ahaf4 ,they then proved1 by direct experiment1 that when polarized light was treated so as to bring into view the most marked phenomena of interference1 namely1 the bands of shadows2 pencils of light which have a common origin1 and which are polarized in the parallel planes1 interfere completely1 while those which are #ajg polarized in opposite 7that is1 perpendicular17 planes do not interfere at all4#ici ,taking these principles into the account1 ,fresnel explained very completely1 by means of the interference of undulations1 all the circumstances of colors produced by crystallized plates2 showing the necessity of the polarization in the first instance2 the dipolarizing effect of the crystal2 and the office of the analysing plate1 by which certain portions of each of the two rays in the crystal are made to interfere and produce color4 ,this he did1 as he says1#idi without being aware1 till ,arago told him1 that ,young had1 to some extent1 anticipated him4 ,note #ibi3 ,enc4 ,brit4 ,supp4 art4 ,polarization4 ,note #ici3 ,ann4 ,chim4 tom4 x4 ,note #idi3 ,ib4 tom4 xvii4 p4 #djb4 ,when we look at the history of the emission-theory of light1 we see exactly what we may consider as the natural course of things in the career of a false theory4 ,such a theory may1 to a certain extent1 explain the phenomena which it was at first contrived to meet2 but every new class of facts requires a new supposition1--an addition to the machinery2 and as observation goes on1 these incoherent appendages accumulate1 till they overwhelm and upset the original frame-work4 ,such was the history of the hypothesis of solid epicycles2 such has been the history of the hypothesis of the material emission of light4 ,in its simple form1 it explained reflection and refraction2 but the colors of thin plates added to it the hypothesis of fits of easy transmission and reflection2 the phenomena of diffraction further invested the particles with complex hypothetical laws of attraction and repulsion2 polarization gave them sides2 double refraction subjected them to peculiar forces emanating from the axes of crystals2 finally1 dipolarization loaded them with the complex and unconnected contrivance of moveable polarization2 and even when all this had been assumed1 additional mechanism was wanting4 ,there is here no unexpected success1 no happy coincidence1 no convergence of principles from remote quarters2 the philosopher builds the machine1 but its parts do not fit2 they hold together only while he presses them3 this is not the character of truth4 ,in the undulatory theory1 on the other hand1 all tends to unity and simplicity4 ,we explain reflection and refraction by undulations2 when we come to thin plates1 the requisite fits are already involved in our fundamental hypothesis1 for they are the length of an undulation2 the phenomena of diffraction also require such intervals2 and the intervals thus required agree exactly with the others in magnitude1 #ajh so that no new property is needed4 ,polarization for a moment checks us2 but not long2 for the direction of our vibrations is hitherto arbitrary2--we allow polarization to decide it4 ,having done this for the sake of polarization1 we find that it also answers an entirely different purpose1 that of giving the law of double refraction4 ,truth may give rise to such a coincidence2 falsehood cannot4 ,but the phenomena become more numerous1 more various1 more strange2 no matter3 the ,theory is equal to them all4 ,it makes not a single new physical hypothesis2 but out of its original stock of principles it educes the counterpart of all that observation shows4 ,it accounts for1 explains1 simplifies1 the most entangled cases2 corrects known laws and facts2 predicts and discloses unknown ones2 becomes the guide of its former teacher1 ,observation2 and1 enlightened by mechanical conceptions1 acquires an insight which pierces through shape and color to force and cause4 ,we thus reach the philosophical moral of this history1 so important in reference to our purpose2 and here we shall close the account of the discovery and promulgation of the undulatory theory4 ,any further steps in its development and extension1 may with propriety be noticed in the ensuing chapters1 respecting its reception and verification4 #bnd ,ed4 ,in the ,philosophy of the ,inductive ,sciences1 ,b4 xi4 ch4 iii4 ,sect4 #aa1 ,i have spoken of the ,consilience of ,inductions as one of the characters of scientific truth4 ,we have several striking instances of such consilience in the history of the undulatory theory4 ,the phenomena of fringes of shadows and colored bands in crystals jump together in the ,theory of ,vibrations4 ,the phenomena of polarization and double refraction jump together in the ,theory of ,crystalline ,vibrations4 ,the phenomena of polarization and of the interference of polarized rays jump together in the ,theory of ,transverse ,vibrations4 ,the proof of what is above said of the undulatory theory is contained in the previous history4 ,this theory has accounted for1 explained1 and simplified the most entangled cases2 as the cases of fringes of shadows2 shadows of gratings2 colored bands in biaxal crystals1 and in quartz4 ,there are no optical phenomena more entangled than these4 ,it has corrected experimental laws1 as in the case of ,m4 ,biot's law of the direction of polarization in biaxal crystals4 ,it has done this1 without making any new physical hypothesis2 for the transverse direction of vibrations1 the different optical elasticities of crystals in different directions1 and 7if it be adopted7 the hypothesis of finite #aji intervals of the particles 7see chap4 x4 and hereafter1 chap4 xiii471 are only limitations of what was indefinite in the earlier form of the hypothesis4 ,and so far as the properties of visible radiant light are concerned1 ,i do not think it at all too much to say1 as ,m4 ,schwerd has said1 that the undulation theory accounts for the phenomena as completely as the theory of gravitation does for the facts of the solar system4 ,this we might say1 even if some facts were not yet fully explained2 for there were till very lately1 if there are not still1 such unexplained facts with regard to the theory of gravitation1 presented to us by the solar system4 ,with regard to the undulatory theory1 these exceptions are1 ,i think1 disappearing quite as rapidly and as completely as in the case of gravitation4 ,it is to be observed that no presumption against the theory can with any show of reason be collected from the cases in which classes of phenomena remain unexplained1 the theory having never been applied to them by any mathematician capable of tracing its results correctly4 ,the history of the theory of gravitation may show us abundantly how necessary it is to bear in mind this caution2 and the results of the undulatory theory cannot be traced without great mathematical skill and great labor1 any more than those of gravitation4 ,this remark applies to such cases as that of the transverse fringes of grooved surfaces4 ,the general phenomena of these cases are perfectly explained by the theory4 ,but there is an interruption in the light in an oblique direction1 which has not yet been explained2 but looking at what has been done in other cases1 it is impossible to doubt that this phenomenon depends upon the results of certain integrations1 and would be explained if these were rightly performed4 ,the phenomena of crystallized surfaces1 and especially their effects upon the plane of polarization1 were examined by ,sir ,d4 ,brewster1 and laws of the phenomena made out by him with his usual skill and sagacity4 ,for a time these were unexplained by the theory4 ,but recently ,mr4 ,mac ,cullagh has traced the consequences of the theory in this case1#iei and obtained a law which represents with much exactness1 ,sir ,d4 ,brewster's observation4 ,note #iei3 ,prof4 ,lloyd's ,report1 ,brit4 ,assoc4 #ahcd1 p4 #cgd4 ,the phenomena which ,sir ,d4 ,brewster1 in #ahcg1 called a new property of light1 7certain appearances of the spectrum when the pupil of the eye is half covered with a thin glass or crystal17 have been explained by ,mr4 ,airy in the ,phil4 ,trans4 for #ahdj4 ,mr4 ,airy's explanation of the phenomena termed by ,sir ,d4 #aaj ,brewster a new property of light1 is completed in the ,philosophical ,magazine for ,november1 #ahdf4 ,it is there shown that a dependence of the breadth of the bands upon the aperture of the pupil1 which had been supposed to result from the theory1 and which does not appear in the experiment1 did really result from certain limited conditions of the hypothesis1 which conditions do not belong to the experiment2 and that when the problem is solved without those limitations1 the discrepance of theory and observation vanishes2 so that1 as ,mr4 ,airy says1 this very remarkable experiment1 which long appeared inexplicable1 seems destined to give one of the strongest confirmations to the ,undulatory ,theory4 ,i may remark also that there is no force in the objection which has been urged against the admirers of the undulatory theory1 that by the fulness of their assent to it1 they discourage further researches which may contradict or confirm it4 ,we must1 in this point of view also1 look at the course of the theory of gravitation and its results4 ,the acceptance of that theory did not prevent mathematicians and observers from attending to the apparent exceptions1 but on the contrary1 stimulated them to calculate and to observe with additional zeal1 and still does so4 ,the acceleration of the ,moon1 the mutual disturbances of ,jupiter and ,saturn1 the motions of ,jupiter's ,satellites1 the effect of the ,earth's oblateness on the ,moon's motion1 the motions of the ,moon about her own centre1 and many other phenomena1 were studied with the greater attention1 because the general theory was deemed so convincing3 and the same cause makes the remaining exceptions objects of intense interest to astronomers and mathematicians4 ,the mathematicians and optical experimenters who accept the undulatory theory1 will of course follow out their conviction in the same manner4 ,accordingly1 this has been done and is still doing1 as in ,mr4 ,airy's mathematical investigation of the effect of an annular aperture2 ,mr4 ,earnshaw's1 of the effect of a triangular aperture2 ,mr4 ,talbot's explanation of the effect of interposing a film of mica between a part of the pupil and the pure spectrum1 so nearly approaching to the phenomena which have been spoken of as a new ,polarity of ,light2 besides other labors of eminent mathematicians1 elsewhere mentioned in these pages4 ,the phenomena of the absorption of light have no especial bearing upon the undulatory theory4 ,there is not much difficulty in explaining the possibility of absorption upon the theory4 ,when the light is absorbed1 it ceases to belong to the theory4 #aaa ,for1 as ,i have said1 the theory professes only to explain the phenomena of radiant visible light4 ,we know very well that light has other bearings and properties4 ,it produces chemical effects4 ,the optical polarity of crystals is connected with the chemical polarity of their constitution4 ,the natural colors of bodies1 too1 are connected with their chemical constitution4 ,light is also connected with heat4 ,the undulatory theory does not undertake to explain these properties and their connexion4 ,if it did1 it would be a ,theory of ,heat and of ,chemical ,composition1 as well as a ,theory of ,light4 ,dr4 ,faraday's recent experiments have shown that the magnetic polarity is directly connected with that optical polarity by which the plane of polarization is affected4 ,when the lines of magnetic force pass through certain transparent bodies1 they communicate to them a certain kind of circular polarizing power2 yet different from the circular polarizing power of quartz1 and certain fluids mentioned in chapter ix4 ,perhaps ,i may be allowed to refer to this discovery as a further illustration of the views ,i have offered in the ,philosophy of the ,inductive ,sciences respecting the ,connexion of ,co-existent ,polarities4 7,b4 v4 ,chap4 ii47 ,,chapter ,,xii4 ,,sequel ,,to ,,the ,,epoch ,,of ,,young ,,and ,,fresnel4 ,,reception ,,of ,,the ,,undulatory ,,theory4 ,,when ,young1 in #ahjj1 published his assertion of the ,principle of ,interferences1 as the true theory of optical phenomena1 the condition of ,england was not very favorable to a fair appreciation of the value of the new opinion4 ,the men of science were strongly pre-occupied in favor of the doctrine of emission1 not only from a national interest in ,newton's glory1 and a natural reverence for his authority1 but also from deference towards the geometers of ,france1 who were looked up to as our masters in the application of mathematics to physics1 and who were understood to be ,newtonians in this as in other subjects4 ,a general tendency to an atomic philosophy1 which had begun to appear from the time of ,newton1 operated powerfully2 and #aab the hypothesis of emission was so easily conceived1 that1 when recommended by high authority1 it easily became popular2 while the hypothesis of luminiferous undulations1 unavoidably difficult to comprehend1 even by the aid of steady thought1 was neglected1 and all but forgotten4 ,yet the reception which ,young's opinions met with was more harsh than he might have expected1 even taking into account all these considerations4 ,but there was in ,england no visible body of men1 fitted by their knowledge and character to pronounce judgment on such a question1 or to give the proper impulse and bias to public opinion4 ,the ,royal ,society1 for instance1 had not1 for a long time1 by custom or institution1 possessed or aimed at such functions4 ,the writers of ,reviews alone1 self-constituted and secret tribunals1 claimed this kind of authority4 ,among these publications1 by far the most distinguished about this period was the ,edinburgh ,review2 and1 including among its contributors men of eminent science and great talents1 employing also a robust and poignant style of writing 7often certainly in a very unfair manner71 it naturally exercised great influence4 ,on abstruse doctrines1 intelligible to few persons1 more than on other subjects1 the opinions and feelings expressed in a ,review must be those of the individual reviewer4 ,the criticism on some of ,young's early papers on optics was written by ,mr4 7afterwards ,lord7 ,brougham1 who1 as we have seen1 had experimented on diffraction1 following the ,newtonian view1 that of inflexion4 ,mr4 ,brougham was perhaps at this time young enough#ifi to be somewhat intoxicated with the appearance of judicial authority in matters of science1 which his office of anonymous reviewer gave him3 and even in middle-life1 he was sometimes considered to be prone to indulge himself in severe and sarcastic expressions4 ,in ,january1 #ahjc1 was published#igi his critique on ,dr4 ,young's ,bakerian ,lecture1 ,on the ,theory of ,light and ,colors1 in which lecture the doctrine of undulations and the law of interferences was maintained4 ,this critique was an uninterrupted strain of blame and rebuke4 ,this paper1 the reviewer said1 contains nothing which deserves the name either of experiment or discovery4 ,he charged the writer with dangerous relaxations of the principles of physical logic4 ,we wish1 he cried1 to recall philosophers to the strict and severe methods of investigation1 describing them as those pointed out by ,bacon1 ,newton1 and the like4 ,finally1 ,dr4 ,young's speculations #aac were spoken of as a hypothesis1 which is a mere work of fancy2 and the critic added1 we cannot conclude our review without entreating the attention of the ,royal ,society1 which has admitted of late so many hasty and unsubstantial papers into its ,transactions2 which habit he urged them to reform4 ,the same aversion to the undulatory theory appears soon after in another article by the same reviewer1 on the subject of ,wollaston's measures of the refraction of ,iceland spar2 he says1 ,we are much disappointed to find that so acute and ingenious an experimentalist should have adopted the wild optical theory of vibrations4 ,the reviewer showed ignorance as well as prejudice in the course of his remarks2 and ,young drew up an answer1 which was ably written1 but being published separately had little circulation4 ,we can hardly doubt that these ,edinburgh reviews had their effect in confirming the general disposition to reject the undulatory theory4 ,note #ifi3 ,his age was twenty-four4 ,note #igi3 ,edin4 ,review1 vol4 i4 p4 #dej4 ,we may add1 however1 that ,young's mode of presenting his opinions was not the most likely to win them favor2 for his mathematical reasonings placed them out of the reach of popular readers1 while the want of symmetry and system in his symbolical calculations1 deprived them of attractiveness for the mathematician4 ,he himself gave a very just criticism of his own style of writing1 in speaking on another of his works3#ihi ,the mathematical reasoning1 for want of mathematical symbols1 was not understood1 even by tolerable mathematicians4 ,from a dislike of the affectation of algebraical formality which he had observed in some foreign authors1 he was led into something like an affectation of simplicity1 which was equally inconvenient to a scientific reader4 ,note #ihi3 ,see ,life of ,young1 p4 #ed4 ,young appears to have been aware of his own deficiency in the power of drawing public favor1 or even notice1 to his discoveries4 ,in #ahjb1 ,davy writes to a friend1 ,have you seen the theory of my colleague1 ,dr4 ,young1 on the undulations of an ethereal medium as the cause of light8 ,it is not likely to be a popular hypothesis1 after what has been said by ,newton concerning it4 ,he would be very much flattered if you could offer any observations upon it1 whether for or against it4 ,young naturally felt confident in his power of refuting objections1 and wanted only the opportunity of a public combat4 ,dr4 ,brewster1 who was1 at this period1 enriching optical knowledge with so vast a train of new phenomena and laws1 shared the general aversion to the undulatory theory1 which1 indeed1 he hardly overcame #aad thirty years later4 ,dr4 ,wollaston was a person whose character led him to look long at the laws of phenomena1 before he attempted to determine their causes2 and it does not appear that he had decided the claims of the rival theories in his own mind4 ,herschel 7,i now speak of the son7 had at first the general mathematical prejudice in favor of the emission doctrine4 ,even when he had himself studied and extended the laws of dipolarized phenomena1 he translated them into the language of the theory of moveable polarization4 ,in #ahai1 he refers to1 and corrects1 this theory2 and says1 it is now relieved from every difficulty1 and entitled to rank with the fits of easy transmission and reflection as a general and simple physical law2 a just judgment1 but one which now conveys less of praise than he then intended4 ,at a later period1 he remarked that we cannot be certain that if the theory of emission had been as much cultivated as that of undulation1 it might not have been as successful2 an opinion which was certainly untenable after the fair trial of the two theories in the case of diffraction1 and extravagant after ,fresnel's beautiful explanation of double refraction and polarization4 ,even in #ahbg1 in a ,treatise on ,light1 published in the ,encyclopdia ,metropolitana1 he gives a section to the calculations of the ,newtonian theory2 and appears to consider the rivalry of the theories as still subsisting4 ,but yet he there speaks with a proper appreciation of the advantages of the new doctrine4 ,after tracing the prelude to it1 he says1 ,but the unpursued speculations of ,newton1 and the opinions of ,hooke1 however distinct1 must not be put in competition1 and1 indeed1 ought scarcely to be mentioned1 with the elegant1 simple1 and comprehensive theory of ,young1--a theory which1 if not founded in nature1 is certainly one of the happiest fictions that the genius of man ever invented to grasp together natural phenomena1 which1 at their first discovery1 seemed in irreconcileable opposition to it4 ,it is1 in fact1 in all its applications and details1 one succession of felicities2 insomuch1 that we may almost be induced to say1 if it be not true1 it deserves to be so4 ,in ,france1 ,young's theory was little noticed or known1 except perhaps by ,m4 ,arago1 till it was revived by ,fresnel4 ,and though ,fresnel's assertion of the undulatory theory was not so rudely received as ,young's had been1 it met with no small opposition from the older mathematicians1 and made its way slowly to the notice and comprehension of men of science4 ,m4 ,arago would perhaps have at once adopted the conception of transverse vibrations1 when it was suggested by his fellow-laborer1 ,fresnel1 if it had not been that he was a member of the #aae ,institute1 and had to bear the brunt of the war1 in the frequent discussions on the undulatory theory2 to which theory ,laplace1 and other leading members1 were so vehemently opposed1 that they would not even listen with toleration to the arguments in its favor4 ,i do not know how far influences of this kind might operate in producing the delays which took place in the publication of ,fresnel's papers4 ,we have seen that he arrived at the conception of transverse vibrations in #ahaf1 as the true key to the understanding of polarization4 ,in #ahag and #ahah1 in a memoir read to the ,institute1 he analysed and explained the perplexing phenomena of quartz1 which he ascribed to a circular polarization4 ,this memoir had not been printed1 nor any extract from it inserted in the scientific journals1 in #ahbb1 when he confirmed his views by further experiments4#iii ,his remarkable memoir1 which solved the extraordinary and capital problem of the connexion of double refraction and crystallization1 though written in #ahba1 was not published till #ahbg4 ,he appears by this time to have sought other channels of publication4 ,in #ahbb1 he gave1#ajji in the ,annales de ,chimie et de ,physique1 an explanation of refraction on the principles of the undulatory theory2 alleging1 as the reason for doing so1 that the theory was still little known4 ,and in succeeding years there appeared in the same work1 his theory of reflection4 ,his memoir on this subject 7,mmoire sur la ,loi des ,modifications que la ,rflexion imprime la ,lumire ,polarise17 was read to the ,academy of ,sciences in 9999#ahbc4 ,but the original paper was mislaid1 and1 for a time1 supposed to be lost2 it has since been recovered among the papers of ,m4 ,fourier1 and printed in the eleventh volume of the ,memoirs of the ,academy4#ajai ,some of the speculations to which he refers1 as communicated to the ,academy1 have never yet appeared4#ajbi ,note #iii3 ,hersch4 ,light1 p4 #eci4 ,note #ajji3 ,ann4 de ,chim4 #ahbb1 tom4 xxi4 p4 #bce4 ,note #ajai3 ,lloyd4 ,report on ,optics1 p4 #cfc4 7,fourth ,rep4 of ,brit4 ,ass47 ,note #ajbi3 ,ib4 p4 #caf1 note4 ,still ,fresnel's labors were1 from the first1 duly appreciated by some of the most eminent of his countrymen4 ,his ,memoir on ,diffraction was1 as we have seen1 crowned in #ahai3 and1 in #ahbb1 a ,report upon his ,memoir on ,double ,refraction was drawn up by a commission consisting of ,,mm4 ,ampre1 ,fourier1 and ,arago4 ,in this report#ajci ,fresnel's theory is spoken of as confirmed by the most delicate tests4 ,the reporters add1 respecting his theoretical ideas on the particular kind of undulations which1 according to him1 constitute light1 that it would be impossible for them to pronounce at present a decided #aaf judgment1 but that they have not thought it right to delay any longer making known a work of which the difficulty is attested by the fruitless efforts of the most skilful philosophers1 and in which are exhibited in the same brilliant degree1 the talent for experiment and the spirit of invention4 ,note #ajci3 ,ann4 ,chim4 tom4 xx4 p4 #cdc4 ,in the meantime1 however1 a controversy between the theory of undulations and the theory of moveable polarization which ,m4 ,biot had proposed with a view of accounting for the colors produced by dipolarizing crystals1 had occurred among the ,french men of science4 ,it is clear that in some main features the two theories coincide2 the intervals of interference in the one theory being represented by the intervals of the oscillations in the other4 ,but these intervals in ,m4 ,biot's explanations were arbitrary hypotheses1 suggested by these very facts themselves2 in ,fresnel's theory1 they were essential parts of the general scheme4 ,m4 ,biot1 indeed1 does not appear to have been averse from a coalition2 for he allowed#ajdi to ,fresnel that the theory of undulations took the phenomena at a higher point and carried them further4 ,and ,m4 ,biot could hardly have dissented from ,m4 ,arago's account of the matter1 that ,fresnel's views linked together#ajei the oscillations of moveable polarization4 ,but ,fresnel1 whose hypothesis was all of one piece1 could give up no part of it1 although he allowed the usefulness of ,m4 ,biot's formul4 ,yet ,m4 ,biot's speculations fell in better with the views of the leading mathematicians of ,paris4 ,we may consider as evidence of the favor with which they were looked upon1 the large space they occupy in the volumes of the ,academy for #ahaa1 #ahab1 #ahag1 and #ahah4 ,in #ahab1 the entire volume is filled with a memoir of ,m4 ,biot's on the subject of moveable polarization4 ,this doctrine also had some advantage in coming early before the world in a didactic form1 in his ,trait de ,physique1 which was published in #ahaf1 and was the most complete treatise on general physics which had appeared up to that time4 ,in this and others of this author's writings1 he expresses facts so entirely in the terms of his own hypothesis1 that it is difficult to separate the two4 ,in the sequel ,m4 ,arago was the most prominent of ,m4 ,biot's opponents2 and in his report upon ,fresnel's memoir on the colors of crystalline plates1 he exposed the weaknesses of the theory of moveable polarization with some severity4 ,the details of this controversy need not occupy us2 but we may observe that this may be considered as the last struggle #aag in favor of the theory of emission among mathematicians of eminence4 ,after this crisis of the war1 the theory of moveable polarization lost its ground2 and the explanations of the undulatory theory1 and the calculations belonging to it1 being published in the ,annales de ,chimie et de ,physique1 of which ,m4 ,arago was one of the conductors1 soon diffused it over ,europe4 ,note #ajdi3 ,ann4 ,chim4 tom4 xvii4 p4 #bea4 ,note #ajei3 ,nouait4 ,it was probably in consequence of the delays to which we have referred1 in the publication of ,fresnel's memoirs1 that as late as ,december1 #ahbf1 the ,imperial ,academy at ,st ,petersburg proposed1 as one of their prize-questions for the two following years1 this1--,to deliver the optical system of waves from all the objections which have 7as it appears7 with justice been urged against it1 and to apply it to the polarization and double refraction of light4 ,in the programme to this announcement1 ,fresnel's researches on the subject are not alluded to1 though his memoir on diffraction is noticed2 they were1 therefore1 probably not known to the ,russian ,academy4 ,young was always looked upon as a person of marvellous variety of attainments and extent of knowledge2 but during his life he hardly held that elevated place among great discoverers which posterity will probably assign him4 ,in #ahjb1 he was constituted ,foreign ,secretary of the ,royal ,society1 an office which he held during life2 in #ahbg he was elected one of the eight ,foreign ,members of the ,institute of ,france2 perhaps the greatest honor which men of science usually receive4 ,the fortune of his life in some other respects was of a mingled complexion4 ,his profession of a physician occupied1 sufficiently to fetter1 without rewarding him2 while he was ,lecturer at the ,royal ,institution1 he was1 in his lectures1 too profound to be popular2 and his office of ,superintendent of the ,nautical ,almanac subjected him to much minute labor1 and many petulant attacks of pamphleteers4 ,on the other hand1 he had a leading part in the discovery of the long-sought key to the ,egyptian hieroglyphics2 and thus the age which was marked by two great discoveries1 one in science and one in literature1 owed them both in a great measure to him4 ,dr4 ,young died in #ahbi1 when he had scarcely completed his fifty-sixth year4 ,fresnel was snatched from science still more prematurely1 dying1 in #ahbg1 at the early age of thirty-nine4 ,we need not say that both these great philosophers possessed1 in an eminent degree1 the leading characteristics of the discoverer's mind1 perfect clearness of view1 rich fertility of invention1 and intense love of knowledge4 ,we cannot read without great interest a letter of #aah ,fresnel to ,young1#ajfi in ,november1 #ahbd3 ,for a long time that sensibility1 or that vanity1 which people call love of glory1 is much blunted in me4 ,i labor much less to catch the suffrages of the public1 than to obtain an inward approval which has always been the sweetest reward of my efforts4 ,without doubt ,i have often wanted the spur of vanity to excite me to pursue my researches in moments of disgust and discouragement4 ,but all the compliments which ,i have received from ,,mm4 ,arago1 ,de ,laplace1 or ,biot1 never gave me so much pleasure as the discovery of a theoretical truth1 or the confirmation of a calculation by experiment4 ,note #ajfi3 ,i was able to give this1 and some other extracts1 from the then unedited correspondence of ,young and ,fresnel1 by the kindness of 7the ,dean of ,ely7 ,professor ,peacock1 of ,trinity ,college1 ,cambridge1 whose ,life of ,dr4 ,young has since been published4 ,though ,young and ,fresnel were in years the contemporaries of many who are now alive1 we must consider ourselves as standing towards them in the relation of posterity4 ,the ,epoch of ,induction in ,optics is past2 we have now to trace the ,verification and ,application of the true theory4 ,,chapter ,,xiii4 ,,confirmation ,,and ,,extension ,,of ,,the ,,undulatory ,,theory4 ,,after the undulatory theory had been developed in all its main features1 by its great authors1 ,young and ,fresnel1 although it bore marks of truth that could hardly be fallacious1 there was still here1 as in the case of other great theories1 a period in which difficulties were to be removed1 objections answered1 men's minds familiarized to the new conceptions thus presented to them2 and in which1 also1 it might reasonably be expected that the theory would be extended to facts not at first included in its domain4 ,this period is1 indeed1 that in which we are living2 and we might1 perhaps with propriety1 avoid the task of speaking of our living contemporaries4 ,but it would be unjust to the theory not to notice some of the remarkable events1 characteristic of such a period1 which have already occurred2 and this may be done very simply4 #aai ,in the case of this great theory1 as in that of gravitation1 by far the most remarkable of these confirmatory researches were conducted by the authors of the discovery1 especially ,fresnel4 ,and in looking at what he conceived and executed for this purpose1 we are1 it appears to me1 strongly reminded of ,newton1 by the wonderful inventiveness and sagacity with which he devised experiments1 and applied to them mathematical reasonings4 #a4 ,double ,refraction of ,compressed ,glass4--,one of these confirmatory experiments was the production of double refraction by the compression of glass4 ,fresnel observes1#ajgi that though ,sir ,d4 ,brewster had shown that glass under compression produced colors resembling those which are given by doubly-refracting crystals1 very skilful physicists had not considered those experiments as a sufficient proof of the bifurcation of the light4 ,in the hypothesis of moveable polarization1 it is added1 there is no apparent connexion between these phenomena of coloration and double refraction2 but on ,young's theory1 that the colors arise from two rays which have traversed the crystal with different velocities1 it appears almost unavoidable to admit also a difference of path in the two rays4 ,note #ajgi3 ,ann4 de ,chim4 #ahbb1 tom4 xx4 p4 #cgg4 ,though1 he says1 ,i had long since adopted this opinion1 it did not appear to me so completely demonstrated1 that it was right to neglect an experimental verification of it2 and therefore1 in #ahai1 he proceeded to satisfy himself of the fact1 by the phenomena of diffraction4 ,the trial left no doubt on the subject2 but he still thought it would be interesting actually to produce two images in glass by compression2 and by a highly-ingenious combination1 calculated to exaggerate the effect of the double refraction1 which is very feeble1 even when the compression is most intense1 he obtained two distinct images4 ,this evidence of the dependence of dipolarizing structure upon a doubly-refracting state of particles1 thus excogitated out of the general theory1 and verified by trial1 may well be considered1 as he says1 as a new occasion of proving the infallibility of the principle of interferences4 #b4 ,circular ,polarization4--,fresnel then turned his attention to another set of experiments1 related to this indeed1 but by a tie so recondite1 that nothing less than his clearness and acuteness of view could have detected any connexion4 ,the optical properties of quartz had been perceived to be peculiar1 from the period of the discovery #abj of dipolarized colors by ,,mm4 ,arago and ,biot4 ,at the end of the ,notice just quoted1 ,fresnel says1#ajhi ,as soon as my occupations permit me1 ,i propose to employ a pile of prisms similar to that which ,i have described1 in order to study the double refraction of the rays which traverse crystals of quartz in the direction of the axis4 ,he then ventures1 without hesitation1 to describe beforehand what the phenomena will be4 ,in the ,bulletin des ,sciences#ajii for ,december1 #ahbb1 it is stated that experiment had confirmed what he had thus announced4 ,note #ajhi3 ,ann4 de ,chim4 #ahbb1 tom4 xx4 p4 #chb4 ,note #ajii3 ,ib4 ,ann4 de ,chim4 #ahbb1 tom4 xx4 p4 #aia4 ,the phenomena are those which have since been spoken of as circular polarization2 and the term first occurs in this notice4#aaji ,they are very remarkable1 both by their resemblances to1 and their differences from1 the phenomena of plane-polarized light4 ,and the manner in which ,fresnel was led to this anticipation of the facts is still more remarkable than the facts themselves4 ,having ascertained by observation that two differently-polarized rays1 totally reflected at the internal surface of glass1 suffer different retardations of their undulations1 he applied the formul which he had obtained for the polarizing effect of reflection to this case4 ,but in this case the formul expressed an impossibility2 yet as algebraical formul1 even in such cases1 have often some meaning1 ,i interpreted1 he says1#aaai in the manner which appeared to me most natural and most probable1 what the analysis indicated by this imaginary form2 and by such an interpretation he collected the law of the difference of undulation of the two rays4 ,he was thus able to predict that by two internal reflections in a rhomb1 or parallelopiped of glass1 of a certain form and position1 a polarized ray would acquire a circular undulation of its particles2 and this constitution of the ray1 it appeared1 by reasoning further1 would show itself by its possessing peculiar properties1 partly the same as those of polarized light1 and partly different4 ,this extraordinary anticipation was exactly confirmed2 and thus the apparently bold and strange guess of the author was fully justified1 or at least assented to1 even by the most cautious philosophers4 ,as ,i cannot appreciate the mathematical evidence for the nature of circular polarization1 says ,prof4 ,airy1#aabi ,i shall mention the experimental evidence on which ,i receive it4 ,the conception has since been universally adopted4 ,note #aaji3 ,ib4 p4 #aid4 ,note #aaai3 ,bullet4 des ,sc4 #ahbc1 p4 #cc4 ,note #aabi3 ,camb4 ,trans4 vol4 iv4 p4 #ha1 #ahca4 ,but ,fresnel1 having thus obtained circularly-polarized rays1 saw #aba that he could account for the phenomena of quartz1 already observed by ,m4 ,arago1 as we have noticed in ,chap4 ix41 by supposing two circularly-polarized rays to pass1 with different velocities1 along the axis4 ,the curious succession of colors1 following each other in right-handed or left-handed circular order1 of which we have already spoken1 might thus be hypothetically explained4 ,but was this hypothesis of two circularly-polarized rays1 travelling along the axis of such crystals1 to be received1 merely because it accounted for the phenomena8 ,fresnel's ingenuity again enabled him to avoid such a defect in theorizing4 ,if there were two such rays1 they might be visibly separated#aaci by the same artifice1 of a pile of prisms properly achromatized1 which he had used for compressed glass4 ,the result was1 that he did obtain a visible separation of the rays2 and this result has since been confirmed by others1 for instance4 ,professor ,airy4#aadi ,the rays were found to be in all respects identical with the circularly-polarized rays produced by the internal reflections in ,fresnel's rhomb4 ,this kind of double refraction gave a hypothetical explanation of the laws which ,m4 ,biot had obtained for the phenomena of this class2 for example1#aaei the rule1 that the deviation of the plane of polarization of the emergent ray is inversely as the square of the length of an undulation for each kind of rays4 ,and thus the phenomena produced by light passing along the axis of quartz were reduced into complete conformity with the theory4 ,note #aaci3 ,bull4 des ,sc4 #ahbb1 p4 #aic4 ,note #aadi3 ,cambridge ,trans4 iv4 p4 #hj4 ,note #aaei3 ,bull4 des ,sc4 #ahbb1 p4 #aig4 #bnd ,ed4 ,i believe1 however1 ,fresnel did not deduce the phenomenon from the mathematical formula1 without the previous suggestion of experiment4 ,he observed appearances which implied a difference of retardation in the two differently-polarized rays at total reflection2 as ,sir ,d4 ,brewster observed in reflection of metals phenomena having a like character4 ,the general fact being observed1 ,fresnel used the theory to discover the law of this retardation1 and to determine a construction in which1 one ray being a quarter of an undulation retarded more than the other1 circular polarization would be produced4 ,and this anticipation was verified by the construction of his rhomb4 ,as a still more curious verification of this law1 another of ,fresnel's experiments may be mentioned4 ,he found the proper angles for a circularly-polarizing glass rhomb on the supposition that there were #abb four internal reflections instead of two2 two of the four taking place when the surface of the glass was dry1 and two when it was wet4 ,the rhomb was made2 and when all the points of reflection were dry1 the light was not circularly polarized2 when two points were wet1 the light was circularly polarized2 and when all four were wet1 it was not circularly polarized4 #c4 ,elliptical ,polarization in ,quartz4--,we now come to one of the few additions to ,fresnel's theory which have been shown to be necessary4 ,he had accounted fully for the colors produced by the rays which travel along the axis of quartz crystals2 and thus1 for the colors and changes of the central spot which is produced when polarized light passes through a transverse plate of such crystals4 ,but this central spot is surrounded by rings of colors4 ,how is the theory to be extended to these8 ,this extension has been successfully made by ,professor ,airy4#aafi ,his hypothesis is1 that as rays passing along the axis of a quartz crystal are circularly polarized1 rays which are oblique to the axis are elliptically polarized1 the amount of ellipticity depending1 in some unknown manner1 upon the obliquity2 and that each ray is separated by double refraction into two rays polarized elliptically2 the one right-handed1 the other left-handed4 ,by means of these suppositions1 he not only was enabled to account for the simple phenomena of single plates of quartz2 but for many most complex and intricate appearances which arise from the superposition of two plates1 and which at first sight might appear to defy all attempts to reduce them to law and symmetry2 such as spirals1 curves approaching to a square form1 curves broken in four places4 ,i can hardly imagine1 he says1#aagi very naturally1 that any other supposition would represent the phenomena to such extreme accuracy4 ,i am not so much struck with the accounting for the continued dilatation of circles1 and the general representation of the forms of spirals1 as with the explanations of the minute deviations from symmetry2 as when circles become almost square1 and crosses are inclined to the plane of polarization4 ,and ,i believe that any one who shall follow my investigation1 and imitate my experiments1 will be surprised at their perfect agreement4 ,note #aafi3 ,camb4 ,trans41 iv4 p4 #hc1 c4 ,note #aagi3 ,camb4 ,trans41 iv4 p4 #abb4 #d4 ,differential ,equations of ,elliptical ,polarization4--,although circular and elliptical polarization can be clearly conceived1 and their existence1 it would seem1 irresistibly established by the phenomena1 it #abc is extremely difficult to conceive any arrangement of the particles of bodies by which such motions can mechanically be produced2 and this difficulty is the greater1 because some fluids and some gases impress a circular polarization upon light2 in which cases we cannot imagine any definite arrangement of the particles1 such as might form the mechanism requisite for the purpose4 ,accordingly1 it does not appear that any one has been able to suggest even a plausible hypothesis on that subject4 ,yet1 even here1 something has been done4 ,professor ,mac ,cullagh1 of ,dublin1 has discovered that by slightly modifying the analytical expressions resulting from the common case of the propagation of light1 we may obtain other expressions which would give rise to such motions as produce circular and elliptical polarization4 ,and though we cannot as yet assign the mechanical interpretation of the language of analysis thus generalized1 this generalization brings together and explains by one common numerical supposition1 two distinct classes of facts2--a circumstance which1 in all cases1 entitles an hypothesis to a very favorable consideration4 ,mr4 ,mac ,cullagh's assumption consists in adding to the two equations of motion which are expressed by means of second differentials1 two other terms involving third differentials in a simple and symmetrical manner4 ,in doing this1 he introduces a coefficient1 of which the magnitude determines both the amount of rotation of the polarization of a ray passing along the axis1 as observed and measured by ,biot1 and the ellipticity of the polarization of a ray which is oblique to the axis1 according to ,mr4 ,airy's theory1 of which ellipticity that philosopher also had obtained certain measures4 ,the agreement between the two sets of measures#aahi thus brought into connexion is such as very strikingly to confirm ,mr4 ,mac ,cullagh's hypothesis4 ,it appears probable1 too1 that the confirmation of this hypothesis involves1 although in an obscure and oracular form1 a confirmation of the undulatory theory1 which is the starting-point of this curious speculation4 ,note #aahi3 ,royal ,i4 ,a4 ,trans4 #ahcf4 #e4 ,elliptical ,polarization of ,metals4--,the effect of metals upon the light which they reflect1 was known from the first to be different from that which transparent bodies produce4 ,sir ,david ,brewster1 who has recently examined this subject very fully1#aaii has described the modification thus produced1 as elliptic polarization4 ,in employing this term1 he seems to have been led1 it has been observed1#abji by a #abd desire to avoid as much as possible all reference to theory4 ,the laws which he has obtained1 however1 belong to elliptically-polarized light in the sense in which the term was introduced by ,fresnel4 ,and the identity of the light produced by metallic reflection with the elliptically-polarized light of the wave-theory1 is placed beyond all doubt1 by an observation of ,professor ,airy1 that the rings of uniaxal crystals1 produced by ,fresnel's elliptically-polarized light1 are exactly the same as those produced by ,brewster's metallic light4 ,note #aaii3 ,phil4 ,trans4 #ahcj4 ,note #abji3 ,lloyd1 ,report on ,optics1 p4 #cgb4 7,brit4 ,assoc47 #f4 ,newton's ,rings by ,polarized ,light4--,other modifications of the phenomena of thin plates by the use of polarized light1 supplied other striking confirmations of the theory4 ,these were in one case the more remarkable1 since the result was foreseen by means of a rigorous application of the conception of the vibratory motion of light1 and confirmed by experiment4 ,professor ,airy1 of ,cambridge1 was led by his reasonings to see1 that if ,newton's rings are produced between a lens and a plate of metal1 by polarized light1 then1 up to the polarizing angle1 the central spot will be black1 and instantly beyond this1 it will be white4 ,in a note1#abai in which he announced this1 he says1 ,this ,i anticipated from ,fresnel's expressions2 it is confirmatory of them1 and defies emission4 ,he also predicted that when the rings were produced between two substances of very different refractive powers1 the centre would twice pass from black to white and from white to black1 by increasing the angle2 which anticipation was fulfilled by using a diamond for the higher refraction4#abbi ,note #abai3 ,addressed to myself1 dated ,may #bh1 #ahca4 ,i ought1 however1 to notice1 that this experiment had been made by ,m4 ,arago1 fifteen years earlier1 and published3 though not then recollected by ,mr4 ,airy4 ,note #abbi3 ,camb4 ,trans4 vol4 ii4 p4 #dji4 #g4 ,conical ,refraction4--,in the same manner4 ,professor ,hamilton of ,dublin pointed out that according to the ,fresnelian doctrine of double refraction1 there is a certain direction of a crystal in which a single ray of light will be refracted so as to form a conical pencil4 ,for the direction of the refracted ray is determined by a plane which touches the wave surface1 the rule being that the ray must pass from the centre of the surface to the point of contact2 and though in general this contact gives a single point only1 it so happens1 from the peculiar inflected form of the wave surface1 which has what is called a cusp1 that in one particular position1 the plane can touch the surface in an entire circle4 ,thus the general rule which assigns the path of #abe the refracted ray1 would1 in this case1 guide it from the centre of the surface to every point in the circumference of the circle1 and thus make it a cone4 ,this very curious and unexpected result1 which ,professor ,hamilton thus obtained from the theory1 his friend ,professor ,lloyd verified as an experimental fact4 ,we may notice1 also1 that ,professor ,lloyd found the light of the conical pencil to be polarized according to a law of an unusual kind2 but one which was easily seen to be in complete accordance with the theory4 #h4 ,fringes of ,shadows4--,the phenomena of the fringes of shadows of small holes and groups of holes1 which had been the subject of experiment by ,fraunhofer1 were at a later period carefully observed in a vast variety of cases by ,m4 ,schwerd of ,spires1 and published in a separate work1#abci ,beugungs-erscheinungen 7,phenomena of ,inflection71 #ahcf4 ,in this ,treatise1 the author has with great industry and skill calculated the integrals which1 as we have seen1 are requisite in order to trace the consequences of the theory2 and the accordance which he finds between these and the varied and brilliant results of observation is throughout exact4 ,i shall1 says he1 in the preface1#abdi prove by the present ,treatise1 that all inflection-phenomena1 through openings of any form1 size1 and arrangement1 are not only explained by the undulation-theory1 but that they can be represented by analytical expressions1 determining the intensity of the light in any point whatever4 ,and he justly adds1 that the undulation-theory accounts for the phenomena of light1 as completely as the theory of gravitation does for the facts of the solar system4 ,note #abci3 ,die ,beugungs-erscheinungen1 aus dem ,fundamental-gesetz der ,undulations-,theorie analytisch entwickelt und in ,bildern dargestellt1 von ,f4 ,m4 ,schwerd4 ,mannheim1 #ahce4 ,note #abdi3 ,dated ,speyer1 ,aug4 #ahce4 #i4 ,objections to the ,theory4--,we have hitherto mentioned only cases in which the undulatory theory was either entirely successful in explaining the facts1 or at least hypothetically consistent with them and with itself4 ,but other objections were started1 and some difficulties were long considered as very embarrassing4 ,objections were made to the theory by some ,english experimenters1 as ,mr4 ,potter1 ,mr4 ,barton1 and others4 ,these appeared in scientific journals1 and were afterwards answered in similar publications4 ,the objections depended partly on the measure of the intensity of light in the different points of the phenomena 7a datum which it is very difficult to obtain with accuracy #abf by experiment71 and partly on misconceptions of the theory2 and ,i believe there are none of them which would now be insisted on4 ,we may mention1 also1 another difficulty1 which it was the habit of the opponents of the theory to urge as a reproach against it1 long after it had been satisfactorily explained3 ,i mean the half-undulation which ,young and ,fresnel had found it necessary1 in some cases1 to assume as gained or lost by one of the rays4 ,though they and their followers could not analyse the mechanism of reflection with sufficient exactness to trace out all the circumstances1 it was not difficult to see1 upon ,fresnel's principles1 that reflection from the interior and exterior surface of glass must be of opposite kinds1 which might be expressed by supposing one of these rays to lose half an undulation4 ,and thus there came into view a justification of the step which had originally been taken upon empirical grounds alone4 #aj4 ,dispersion1 on the ,undulatory ,theory4--,a difficulty of another kind occasioned a more serious and protracted embarrassment to the cultivators of this theory4 ,this was the apparent impossibility of accounting1 on the theory1 for the prismatic dispersion of color4 ,for it had been shown by ,newton that the amount of refraction is different for every color2 and the amount of refraction depends on the velocity with which light is propagated4 ,yet the theory suggested no reason why the velocity should be different for different colors3 for1 by mathematical calculation1 vibrations of all degrees of rapidity 7in which alone colors differ7 are propagated with the same speed4 ,nor does analogy lead us to expect this variety4 ,there is no such difference between quick and slow waves of air4 ,the sounds of the deepest and the highest bells of a peal are heard at any distance in the same order4 ,here1 therefore1 the theory was at fault4 ,but this defect was far from being a fatal one4 ,for though the theory did not explain1 it did not contradict1 dispersion4 ,the suppositions on which the calculations had been conducted1 and the analogy of sound1 were obviously in no small degree precarious4 ,the velocity of propagation might differ for different rates of undulation1 in virtue of many causes which would not affect the general theoretical results4 ,many such hypothetical causes were suggested by various eminent mathematicians1 as solutions of this conspicuous difficulty4 ,but without dwelling upon these conjectures1 it may suffice to notice that hypothesis upon which the attention of mathematicians was soon concentrated4 ,this was the hypothesis of finite intervals between the #abg particles of the ether4 ,the length of one of those undulations which produce light1 is a very small quantity1 its mean value being #aej1jjjth of an inch2 but in the previous investigations of the consequences of the theory1 it had been assumed that the distance from each other1 of the particles of the ether1 which1 by their attractions or repulsions1 caused the undulations to be propagated1 is indefinitely less than this small quantity2--so that its amount might be neglected in the cases in which the length of the undulation was one of the quantities which determined the result4 ,but this assumption was made arbitrarily1 as a step of simplification1 and because it was imagined that1 in this way1 a nearer approach was made to the case of a continuous fluid ether1 which the supposition of distinct particles imperfectly represented4 ,it was still free for mathematicians to proceed upon the opposite assumption1 of particles of which the distances were finite1 either as a mathematical basis of calculation1 or as a physical hypothesis2 and it remained to be seen if1 when this was done1 the velocity of light would still be the same for different lengths of undulation1 that is1 for different colors4 ,m4 ,cauchy1 calculating1 upon the most general principles1 the motion of such a collection of particles as would form an elastic medium1 obtained results which included the new extension of the previous hypothesis4 ,professor ,powell1 of ,oxford1 applied himself to reduce to calculation1 and to compare with experiment1 the result of these researches4 ,and it appeared that1 on ,m4 ,cauchy's principles1 a variation in the velocity of light is produced by a variation in the length of the wave1 provided that the interval between the molecules of the ether bears a sensible ratio to the length of an undulation4#abei ,professor ,powell obtained also1 from the general expressions1 a formula expressing the relation between the refractive index of a ray1 and the length of a wave1 or the color of light4#abfi ,it then became his task to ascertain whether this relation obtained experimentally2 and he found a very close agreement between the numbers which resulted from the formula and those observed by ,fraunhofer1 for ten different kinds of media1 namely1 certain glasses and fluids4#abgi ,to these he afterwards added ten other cases of crystals observed by ,m4 ,rudberg4#abhi ,mr4 ,kelland1 of ,cambridge1 also calculated1 in a manner somewhat different1 the results of the same hypothesis of finite intervals2#abii and1 obtaining #abh formul not exactly the same as ,professor ,powell1 found also an agreement between these and ,fraunhofer's observations4 ,note #abei3 ,phil4 ,mag4 vol4 vi4 p4 #bff4 ,note #abfi3 ,ib4 vol4 vii4 #ahce1 p4 #bff4 ,note #abgi3 ,phil4 ,trans4 #ahce1 p4 #bdi4 ,note #abhi3 ,ib4 #ahcf1 p4 #ag4 ,note #abii3 ,camb4 ,trans4 vol4 vi4 p4 #aec4 ,it may be observed1 that the refractive indices observed and employed in these comparisons1 were not those determined by the color of the ray1 which is not capable of exact identification1 but those more accurate measures which ,fraunhofer was enabled to make1 in consequence of having detected in the spectrum the black lines which he called ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h4 ,the agreement between the theoretical formul and the observed numbers is remarkable1 throughout all the series of comparisons of which we have spoken4 ,yet we must at present hesitate to pronounce upon the hypothesis of finite intervals1 as proved by these calculations2 for though this hypothesis has given results agreeing so closely with experiment1 it is not yet clear that other hypotheses may not produce an equal agreement4 ,by the nature of the case1 there must be a certain gradation and continuity in the succession of colors in the spectrum1 and hence1 any supposition which will account for the general fact of the whole dispersion1 may possibly account for the amount of the intermediate dispersions1 because these must be interpolations between the extremes4 ,the result of this hypothetical calculation1 however1 shows very satisfactorily that there is not1 in the fact of dispersion1 anything which is at all formidable to the undulatory theory4 #aa4 ,conclusion4--,there are several other of the more recondite points of the theory which may be considered as1 at present1 too undecided to allow us to speak historically of the discussions which they have occasioned4#acji ,for example1 it was conceived1 for some time1 that the vibrations of polarized light are perpendicular to the plane of polarization4 ,but this assumption was not an essential part of the theory2 and all the phenomena would equally allow us to suppose the vibrations to be in the polarization plane2 the main requisite being1 that light polarized in planes at right angles to each other1 should also have the vibrations at right angles4 ,accordingly1 for some time1 this point was left undecided by ,young and ,fresnel1 and1 more recently1 some mathematicians have come to the opinion that ether vibrates in the plane of polarization4 ,the theory of transverse vibrations is equally stable1 whichever supposition may be finally confirmed4 ,note #acji3 ,for on account of these1 see ,professor ,lloyd's ,report on ,physical ,optics4 7,brit4 ,assoc4 ,report1 #ahcd47 ,we may speak1 in the same manner1 of the suppositions which1 from #abi the time of ,young and ,fresnel1 the cultivators of this theory have been led to make respecting the mechanical constitution of the ether1 and the forces by which transverse vibrations are produced4 ,it was natural that various difficulties should arise upon such points1 for transverse vibrations had not previously been made the subject of mechanical calculation1 and the forces which occasion them must act in a different manner from those which were previously contemplated4 ,still1 we may venture to say1 without entering into these discussions1 that it has appeared1 from all the mathematical reasonings which have been pursued1 that there is not1 in the conception of transverse vibrations1 anything inconsistent either with the principles of mechanics1 or with the best general views which we can form1 of the forces by which the universe is held together4 ,i willingly speak as briefly as the nature of my undertaking allows1 of those points of the undulatory theory which are still under deliberation among mathematicians4 ,with respect to these1 an intimate acquaintance with mathematics and physics is necessary to enable any one to understand the steps which are made from day to day2 and still higher philosophical qualifications would be requisite in order to pronounce a judgment upon them4 ,i shall1 therefore1 conclude this survey by remarking the highly promising condition of this great department of science1 in respect to the character of its cultivators4 ,nothing less than profound thought and great mathematical skill can enable any one to deal with this theory1 in any way likely to promote the interests of science4 ,but there appears1 in the horizon of the scientific world1 a considerable class of young mathematicians1 who are already bringing to these investigations the requisite talents and zeal2 and who1 having acquired their knowledge of the theory since the time when its acceptation was doubtful1 possess1 without effort1 that singleness and decision of view as to its fundamental doctrines1 which it is difficult for those to attain whose minds have had to go through the hesitation1 struggle1 and balance of the epoch of the establishment of the theory4 ,in the hands of this new generation1 it is reasonable to suppose the ,analytical ,mechanics of light will be improved as much as the ,analytical ,mechanics of the solar system was by the successors of ,newton4 ,we have already had to notice many of this younger race of undulationists4 ,for besides ,,mm4 ,cauchy1 ,poisson1 and ,ampre1 ,m4 ,lam has been more recently following these researches in ,france4#acai ,in #acj ,belgium1 ,m4 ,quetelet has given great attention to them2 and1 in our own country1 ,sir ,william ,hamilton1 and ,professor ,lloyd1 of ,dublin1 have been followed by ,mr4 ,mac ,cullagh4 ,professor ,powell1 of ,oxford1 has continued his researches with unremitting industry2 and1 at ,cambridge1 ,professor ,airy1 who did much for the establishment and diffusion of the theory before he was removed to the post of ,astronomer ,royal1 at ,greenwich1 has had the satisfaction to see his labors continued by others1 even to the most recent time2 for ,mr4 ,kelland1#acbi whom we have already mentioned1 and ,mr4 ,archibald ,smith1#acci the two persons who1 in #ahcd and #ahcf1 received the highest mathematical honors which that university can bestow1 have both of them published investigations respecting the undulatory theory4 ,note #acai3 ,prof4 ,lloyd's ,report1 p4 #cib4 ,note #acbi3 ,on the ,dispersion of ,light1 as explained by the ,hypothesis of ,finite ,intervals4 ,camb4 ,trans4 vol4 vi4 p4 #aec4 ,note #acci3 ,investigation of the ,equation to ,fresnel's ,wave ,surface1 ib4 p4 #he4 ,see also1 in the same volume1 ,mathematical ,considerations on the ,problem of the ,rainbow1 showing it to belong to ,physical ,optics1 by ,r4 ,potter1 ,esq41 of ,queen's ,college4 ,we may be permitted to add1 as a reflection obviously suggested by these facts1 that the cause of the progress of science is incalculably benefited by the existence of a body of men1 trained and stimulated to the study of the higher mathematics1 such as exist in the ,british universities1 who are thus prepared1 when an abstruse and sublime theory comes before the world with all the characters of truth1 to appreciate its evidence1 to take steady hold of its principles1 to pursue its calculations1 and thus to convert into a portion of the permanent treasure and inheritance of the civilized world1 discoveries which might otherwise expire with the great geniuses who produced them1 and be lost for ages1 as1 in former times1 great scientific discoveries have sometimes been4 ,the reader who is acquainted with the history of recent optical discovery1 will see that we have omitted much which has justly excited admiration2 as1 for example1 the phenomena produced by glass under heat or pressure1 noticed by ,,mm4 ,lobeck1 and ,biot1 and ,brewster1 and many most curious properties of particular minerals4 ,we have omitted1 too1 all notice of the phenomena and laws of the absorption of light1 which hitherto stand unconnected with the theory4 ,but in this we have not materially deviated from our main design2 for our end1 in what we have done1 has been to trace the advances of ,optics #aca towards perfection as a theory2 and this task we have now nearly executed as far as our abilities allow4 ,we have been desirous of showing that the type of this progress1 in the histories of the two great sciences1 ,physical ,astronomy and ,physical ,optics1 is the same4 ,in both we have many ,laws of ,phenomena detected and accumulated by acute and inventive men2 we have ,preludial guesses which touch the true theory1 but which remain for a time imperfect1 undeveloped1 unconfirmed3 finally we have the ,epoch when this true theory1 clearly apprehended by great philosophical geniuses1 is recommended by its fully explaining what it was first meant to explain1 and confirmed by its explaining what it was not meant to explain4 ,we have then its ,progress struggling for a little while with adverse prepossessions and difficulties2 finally overcoming all these1 and moving onwards1 while its triumphal procession is joined by all the younger and more vigorous men of science4 ,it would1 perhaps1 be too fanciful to attempt to establish a parallelism between the prominent persons who figure in these two histories4 ,if we were to do this1 we must consider ,huyghens and ,hooke as standing in the place of ,copernicus1 since1 like him1 they announced the true theory1 but left it to a future age to give it development and mechanical confirmation2 ,malus and ,brewster1 grouping them together1 correspond to ,tycho ,brahe and ,kepler1 laborious in accumulating observations1 inventive and happy in discovering laws of phenomena2 and ,young and ,fresnel combined1 make up the ,newton of optical science4 #bnd ,ed4 ,in the ,report on ,physical ,optics1 7,brit4 ,ass4 ,reports1 #ahcd17 by ,prof4 ,lloyd1 the progress of the mathematical theory after ,fresnel's labors is stated more distinctly than ,i have stated it1 to the following effect4 ,ampre1 in #ahbh1 proved ,fresnel's mathematical results directly1 which ,fresnel had only proved indirectly1 and derived from his proof ,fresnel's beautiful geometrical construction4 ,prof4 ,mac ,cullagh not long after gave a concise demonstration of the same theorem1 and of the other principal points of ,fresnel's theory4 ,he represents the elastic force by means of an ellipsoid whose axes are inversely proportional to those of ,fresnel's generating ellipsoid1 and deduces ,fresnel's construction geometrically4 ,in the third ,supplement to his ,essay on the ,theory of ,systems of ,rays 7,trans4 ,r4 ,i4 ,acad4 vol4 xvii471 ,sir ,w4 ,hamilton has presented that portion of ,fresnel's theory which relates to the fundamental problem of the determination of the velocity and polarization of a plane wave1 in a very elegant and analytical form4 ,this he does by means of what he calls the #acb characteristic function of the optical system to which the problem belongs4 ,from this function is deduced the surface of wave-slowness of the medium2 and by means of this surface1 the direction of the rays refracted into the medium4 ,from this construction also ,sir ,w4 ,hamilton was led to the anticipation of conical refraction1 mentioned above4 ,the investigations of ,,mm4 ,cauchy and ,lam refer to the laws by which the particles of the ether act upon each other and upon the particles of other bodies2--a field of speculation which appears to me not yet ripe for the final operations of the analyst4 ,among the mathematicians who have supplied defects in ,fresnel's reasoning on this subject1 ,i may mention ,mr4 ,tovey1 who treated it in several papers in the ,philosophical ,magazine 7#ahcg-dj74 ,mr4 ,tovey's early death must be deemed a loss to mathematical science4 ,besides investigating the motion of symmetrical systems of particles which may be supposed to correspond to biaxal crystals1 ,mr4 ,tovey considered the case of unsymmetrical systems1 and found that the undulations propagated would1 in the general case1 be elliptical2 and that in a particular case1 circular undulations would take place1 such as are propagated along the axis of quartz4 ,it appears to me1 however1 that he has not given a definite meaning to those limitations of his general hypothesis which conduct him to this result4 ,perhaps if the hypothetical conditions of this result were traced into detail1 they would be found to reside in a screw-like arrangement of the elementary particles1 in some degree such as crystals of quartz themselves exhibit in their forms1 when they have plagihedral faces at both ends4 ,such crystals of quartz are1 some like a right-handed and some like a left-handed screw2 and1 as ,sir ,john ,herschel discovered1 the circular polarization is right-handed or left-handed according as the plagihedral form is so4 ,in ,mr4 ,tovey's hypothetical investigation it does not appear upon what part of the hypothesis this difference of right and left-handed depends4 ,the definition of this part of the hypothesis is a very desirable step4 ,when crystals of ,quartz are right-handed at one end1 they are right-handed at the other end3 but there is a different kind of plagihedral form1 which occurs in some other crystals1 for instance1 in ,apatite3 in these the plagihedral faces are right-handed at the one extremity and left-handed at the other4 ,for the sake of distinction1 we may call the former homologous plagihedral faces1 since1 at both ends1 they have the same name2 and the latter heterologous plagihedral faces4 #acc ,the homologous plagihedral faces of ,quartz crystals are accompanied by homologous circular polarization of the same name4 ,i do not know that heterologous circular polarization has been observed in any crystal1 but it has been discovered by ,dr4 ,faraday to occur in glass1 c41 when subjected to powerful magnetic action4 ,perhaps it was presumptuous in me to attempt to draw such comparisons1 especially with regard to living persons1 as ,i have done in the preceding pages of this ,book4 ,having published this passage1 however1 ,i shall not now suppress it4 ,but ,i may observe that the immense number and variety of the beautiful optical discoveries which we owe to ,sir ,david ,brewster makes the comparison in his case a very imperfect representation of his triumphs over nature2 and that1 besides his place in the history of the ,theory of ,optics1 he must hold a most eminent position in the history of ,optical ,crystallography1 whenever the discovery of a ,true ,optical ,theory of ,crystals supplies us with the ,epoch to which his labors in this field form so rich a ,prelude4 ,i cordially assent to the expression employed by ,mr4 ,airy in the ,phil4 ,trans4 for #ahdj1 in which he speaks of ,sir ,david ,brewster as the ,father of ,modern ,experimental ,optics4 #ace ,,book ,x4 ,,secondary ,,mechanical ,,sciences4 7,,continued47 ,,history ,,of ,,thermotics ,,and ,,atmology4 ,et primum faciunt ignem se vortere in auras ,aris2 hinc imbrem gigni terramque creari ,ex imbri2 retroque a terr cuncta revorti1 ,humorem primum1 post ara deinde calorem2 ,nec cessare hc inter se mutare1 meare1 ,de clo ad terram de terr ad sidera mundi4 ,,lucretius1 i4 #ghc4 ,water1 and ,air1 and ,fire1 alternate run ,their endless circle1 multiform1 yet one4 ,for1 moulded by the fervor's latent beams1 ,solids flow loose1 and fluids flash to steams1 ,and elemental flame1 with secret force1 ,pursues through earth1 air1 sky1 its stated course4 #acg ,,introduction4 ,of ,thermotics and ,atmology4 ,i ,,employ the term ,thermotics to include all the doctrines respecting ,heat1 which have hitherto been established on proper scientific grounds4 ,our survey of the history of this branch of science must be more rapid and less detailed than it has been in those subjects of which we have hitherto treated3 for our knowledge is1 in this case1 more vague and uncertain than in the others1 and has made less progress towards a general and certain theory4 ,still1 the narrative is too important and too instructive to be passed over4 ,the distinction of ,formal ,thermotics and ,physical ,thermotics1--of the discovery of the mere ,laws of ,phenomena1 and the discovery of their causes1--is applicable here1 as in other departments of our knowledge4 ,but we cannot exhibit1 in any prominent manner1 the latter division of the science now before us2 since no general theory of heat has yet been propounded1 which affords the means of calculating the circumstances of the phenomena of conduction1 radiation1 expansion1 and change of solid1 liquid1 and gaseous form4 ,still1 on each of these subjects there have been proposed1 and extensively assented to1 certain general views1 each of which explains its appropriate class of phenomena2 and1 in some cases1 these principles have been clothed in precise and mathematical conditions1 and thus made bases of calculation4 ,these principles1 thus possessing a generality of a limited kind1 connecting several observed laws of phenomena1 but yet not connecting all the observed classes of facts which relate to heat1 will require our separate attention4 ,they may be described as the ,doctrine of ,conduction1 the ,doctrine of ,radiation1 the ,doctrine of ,specific ,heat1 and the ,doctrine of ,latent ,heat2 and these1 and similar doctrines respecting heat1 make up the science which we may call ,thermotics proper4 ,but besides these collections of principles which regard heat by itself1 the relations of heat and moisture give rise to another and important collection of laws and principles1 which ,i shall treat of in connexion with ,thermotics1 and shall term ,atmology1 borrowing #ach the term from the ,greek word 717 which signifies vapor4 ,the ,atmosphere was so named by the ,greeks1 as being a sphere of vapor2 and1 undoubtedly1 the most general and important of the phenomena which take place in the air1 by which the earth is surrounded1 are those in which water1 of one consistence or other 7ice1 water1 or steam17 is concerned4 ,the knowledge which relates to what takes place in the atmosphere has been called ,meteorology1 in its collective form3 but such knowledge is1 in fact1 composed of parts of many different sciences4 ,and it is useful for our purpose to consider separately those portions of ,meteorology which have reference to the laws of aqueous vapor1 and these we may include under the term ,atmology4 ,the instruments which have been invented for the purpose of measuring the moisture of the air1 that is1 the quantity of vapor which exists in it1 have been termed ,hygrometers2 and the doctrines on which these instruments depend1 and to which they lead1 have been called ,hygrometry2 but this term has not been used in quite so extensive a sense as that which we intend to affix to ,atmology4 ,in treating of ,thermotics1 we shall first describe the earlier progress of men's views concerning ,conduction1 ,radiation1 and the like1 and shall then speak of the more recent corrections and extensions1 by which they have been brought nearer to theoretical generality4 #aci ,,thermotics ,,proper4 ,,chapter ,i4 ,,the ,,doctrines ,,of ,,conduction ,,and ,,radiation4 ,section #a4--;,introduction of the ,doctrine of ,conduction4 ,,by conduction is meant the propagation of heat from one part to another of a continuous body2 or from one body to another in contact with it2 as when one end of a poker stuck in the fire heats the other end1 or when this end heats the hand which takes hold of it4 ,by radiation is meant the diffusion of heat from the surface of a body to points not in contact4 ,it is clear in both these cases1 that1 in proportion as the hot portion is hotter1 it produces a greater effect in warming the cooler portion2 that is1 it communicates more ,heat to it1 if ,heat be the abstract conception of which this effect is the measure4 ,the simplest rule which can be proposed is1 that the heat thus communicated in a given instant is proportional to the excess of the heat of the hot body over that of the contiguous bodies2 there are no obvious phenomena which contradict the supposition that this is the true law2 and it was thence assumed by ,newton as the true law for radiation and by other writers for conduction4 ,this assumption was confirmed approximately1 and afterwards corrected1 for the case of ,radiation2 in its application to ,conduction1 it has been made the basis of calculation up to the present time4 ,we may observe that this statement takes for granted that we have attained to a measure of heat 7or of temperature1 as heat thus measured is termed71 corresponding to the law thus assumed2 and1 in fact1 as we shall have occasion to explain in speaking of the measures of sensible qualities1 #adj the thermometrical scale of heat according to the expansion of liquids 7which is the measure of temperature here adopted71 was constructed with a reference to ,newton's law of radiation of heat2 and thus the law is necessarily consistent with the scale4 ,in any case in which the parts of a body are unequally hot1 the temperature will vary continuously in passing from one part of the body to another2 thus1 a long bar of iron1 of which one end is kept red hot1 will exhibit a gradual diminution of temperature at successive points1 proceeding to the other end4 ,the law of temperature of the parts of such a bar might be expressed by the ordinates of a curve which should run alongside the bar4 ,and1 in order to trace mathematically the consequences of the assumed law1 some of those processes would be necessary1 by which mathematicians are enabled to deal with the properties of curves2 as the method of infinitesimals1 or the differential calculus2 and the truth or falsehood of the law would be determined1 according to the usual rules of inductive science1 by a comparison of results so deduced from the principle1 with the observed phenomena4 ,it was easily perceived that this comparison was the task which physical inquirers had to perform2 but the execution of it was delayed for some time2 partly1 perhaps1 because the mathematical process presented some difficulties4 ,even in a case so simple as that above mentioned1 of a linear bar with a stationary temperature at one end1 partial differentials entered2 for there were three variable quantities1 the time1 as well as the place of each point and its temperature4 ,and at first1 another scruple occurred to ,m4 ,biot when1 about #ahjd1 he undertook this problem4#aaj ,a difficulty1 says ,laplace1#baj in #ahji1 presents itself1 which has not yet been solved4 ,the quantities of heat received and communicated in an instant 7by any point of the bar7 must be infinitely small quantities of the same order as the excess of the heat of a slice of the body over that of the contiguous slice2 therefore the excess of the heat received by any slice over the heat communicated1 is an infinitely small quantity of the second order2 and the accumulation in a finite time 7which depends on this excess7 cannot be finite4 ,i conceive that this difficulty arises entirely from an arbitrary and unnecessary assumption concerning the relation of the infinitesimal parts of the body4 ,laplace resolved the difficulty by further reasoning founded upon the same assumption which occasioned #ada it2 but ,fourier1 who was the most distinguished of the cultivators of this mathematical doctrine of conduction1 follows a course of reasoning in which the difficulty does not present itself4 ,indeed it is stated by ,laplace1 in the ,memoir above quoted1#caj that ,fourier had already obtained the true fundamental equations by views of his own4 ,note #aaj3 ,biot1 ,trait de ,phys4 iv4 p4 #ffi4 ,note #baj3 ,laplace1 ,mm4 ,inst4 for #ahji1 p4 #ccb4 ,note #caj3 ,laplace1 ,mm4 ,inst4 for #ahji1 p4 #ech4 ,the remaining part of the history of the doctrine of conduction is principally the history of ,fourier's labors4 ,attention having been drawn to the subject1 as we have mentioned1 the ,french ,institute1 in ,january1 #ahaj1 proposed1 as their prize question1 ,to give the mathematical theory of the laws of the propagation of heat1 and to compare this theory with exact observations4 ,fourier's ,memoir 7the sequel of one delivered in #ahjg17 was sent in ,september1 #ahaa2 and the prize 7#cjjj francs7 adjudged to it in #ahab4 ,in consequence of the political confusion which prevailed in ,france1 or of other causes1 these important ,memoirs were not published by the ,academy till #ahbd2 but extracts had been printed in the ,bulletin des ,sciences in #ahjh1 and in the ,annales de ,chimie in #ahaf2 and ,poisson and ,m4 ,cauchy had consulted the manuscript itself4 ,it is not my purpose to give1 in this place1#daj an account of the analytical processes by which ,fourier obtained his results4 ,the skill displayed in these ,memoirs is such as to make them an object of just admiration to mathematicians2 but they consist entirely of deductions from the fundamental principle which ,i have noticed1--that the quantity of heat conducted from a hotter to a colder point is proportional to the excess of heat1 modified by the conductivity1 or conducting power of each substance4 ,the equations which flow from this principle assume nearly the same forms as those which occur in the most general problems of hydrodynamics4 ,besides ,fourier's solution1 ,laplace1 ,poisson1 and ,m4 ,cauchy have also exercised their great analytical skill in the management of these formul4 ,we shall briefly speak of the comparison of the results of these reasonings with experiment1 and notice some other consequences to which they lead4 ,but before we can do this1 we must pay some attention to the subject of radiation4 #adb ,note #daj3 ,i have given an account of ,fourier's mathematical results in the ,reports of the ,british ,association for #ahce4 ,sect4 #b4--;,introduction of the ,doctrine of ,radiation4 ,a ,,hot body1 as a mass of incandescent iron1 emits heat1 as we perceive by our senses when we approach it2 and by this emission of heat the hot body cools down4 ,the first step in our systematic knowledge of the subject was made in the ,principia4 ,it was in the destiny of that great work1 says ,fourier1 to exhibit1 or at least to indicate1 the causes of the principal phenomena of the universe4 ,newton assumed1 as we have already said1 that the rate at which a body cools1 that is1 parts with its heat to surrounding bodies1 is proportional to its heat2 and on this assumption he rested the verification of his scale of temperatures4 ,it is an easy deduction from this law1 that if times of cooling be taken in arithmetical progression1 the heat will decrease in geometrical progression4 ,kraft1 and after him ,richman1 tried to verify this law by direct experiments on the cooling of vessels of warm water2 and from these experiments1 which have since been repeated by others1 it appears that for differences of temperature which do not exceed #ej degrees 7boiling water being #ajj71 this geometrical progression represents1 with tolerable 7but not with complete7 accuracy1 the process of cooling4 ,this principle of radiation1 like that of conduction1 required to be followed out by mathematical reasoning4 ,but it required also to be corrected in the first place1 for it was easily seen that the rate of cooling depended1 not on the absolute temperature of the body1 but on the excess of its temperature above the surrounding objects to which it communicated its heat in cooling4 ,and philosophers were naturally led to endeavor to explain or illustrate this process by some physical notions4 ,lambert in #agfe published#eaj an ,essay on the ,force of ,heat1 in which he assimilates the communication of heat to the flow of a fluid out of one vessel into another by an excess of pressure2 and mathematically deduces the laws of the process on this ground4 ,but some additional facts suggested a different view of the subject4 ,it was found that heat is propagated by radiation according to straight lines1 like light2 and that it is1 as light is1 capable of being reflected by mirrors1 and thus brought to a focus of intenser action4 ,in this manner the radiative effect of a body could be more precisely traced4 ,a fact1 however1 came under notice1 which1 at first sight1 appeared to #adc offer some difficulty4 ,it appeared that cold was reflected no less than heat4 ,a mass of ice1 when its effect was concentrated on a thermometer by a system of mirrors1 made the thermometer fall1 just as a vessel of hot water placed in a similar situation made it rise4 ,was cold1 then1 to be supposed a real substance1 no less than heat8 ,note #eaj3 ,act4 ,helvet4 tom4 ii4 p4 #agb4 ,the solution of this and similar difficulties was given by ,pierre ,prevost1 professor at ,geneva1 whose theory of radiant heat was proposed about #agij4 ,according to this theory1 heat1 or caloric1 is constantly radiating from every point of the surface of all bodies in straight lines2 and it radiates the more copiously1 the greater is the quantity of heat which the body contains4 ,hence a constant exchange of heat is going on among neighboring bodies2 and a body grows hotter or colder1 according as it receives more caloric than it emits1 or the contrary4 ,and thus a body is cooled by rectilinear rays from a cold body1 because along these paths it sends rays of heat in greater abundance than those which return the same way4 ,this theory of exchanges is simple and satisfactory1 and was soon generally adopted2 but we must consider it rather as the simplest mode of expressing the dependence of the communication of heat on the excess of temperature1 than as a proposition of which the physical truth is clearly established4 ,a number of curious researches on the effect of the different kinds of surface of the heating and of the heated body1 were made by ,leslie and others4 ,on these ,i shall not dwell2 only observing that the relative amount of this radiative and receptive energy may be expressed by numbers1 for each kind of surface2 and that we shall have occasion to speak of it under the term exterior conductivity2 it is thus distinguished from interior conductivity1 which is the relative rate at which heat is conducted in the interior of bodies4#faj ,note #faj3 ,the term employed by ,fourier1 conductibility or conducibility1 suggests expressions altogether absurd1 as if the bodies could be called conductible1 or conducible1 with respect to heat3 ,i have therefore ventured upon a slight alteration of the word1 and have used the abstract term which analogy would suggest1 if we suppose bodies to be conductive in this respect4 ,sect4 #c4--,verifications of the ,doctrines of ,conduction and ,radiation4 ,,the interior and exterior conductivity of bodies are numbers1 which enter as elements1 or coefficients1 into the mathematical calculations founded on the doctrines of conduction and radiation4 ,these #add coefficients are to be determined for each case by appropriate experiments3 when the experimenters had obtained these data1 as well as the mathematical solutions of the problems1 they could test the truth of their fundamental principles by a comparison of the theoretical and actual results in properly-selected cases4 ,this was done for the law of conduction in the simple cases of metallic bars heated at one end1 by ,m4 ,biot1#gaj and the accordance with experiment was sufficiently close4 ,in the more complex cases of conduction which ,fourier considered1 it was less easy to devise a satisfactory mode of comparison4 ,but some rather curious relations which he demonstrated to exist among the temperatures at different points of an armille1 or ring1 afforded a good criterion of the value of the calculations1 and confirmed their correctness4#haj ,note #gaj3 ,tr4 de ,phys4 iv4 #fga4 ,note #haj3 ,mm4 ,inst4 #ahai1 p4 #aib1 published #ahbd4 ,we may therefore presume these doctrines of radiation and conduction to be sufficiently established2 and we may consider their application to any remarkable case to be a portion of the history of science4 ,we proceed to some such applications4 ,sect4 #d4--,the ,geological and ,cosmological ,application of ,thermotics4 ,,by far the most important case to which conclusions from these doctrines have been applied1 is that of the globe of the earth1 and of those laws of climate to which the modifications of temperature give rise2 and in this way we are led to inferences concerning other parts of the universe4 ,if we had any means of observing these terrestrial and cosmical phenomena to a sufficient extent1 they would be valuable facts on which we might erect our theories2 and they would thus form part1 not of the corollaries1 but of the foundations of our doctrine of heat4 ,in such a case1 the laws of the propagation of heat1 as discovered from experiments on smaller bodies1 would serve to explain these phenomena of the universe1 just as the laws of motion explain the celestial movements4 ,but since we are almost entirely without any definite indications of the condition of the other bodies in the solar system as to heat2 and since1 even with regard to the earth1 we know only the temperature of the parts at or very near the surface1 our knowledge of the part which heat plays in the earth and the heavens must be in a great measure1 not a generalization of observed facts1 but a deduction from theoretical principles4 ,still1 such knowledge1 whether obtained #ade from observation or from theory1 must possess great interest and importance4 ,the doctrines of this kind which we have to notice refer principally to the effect of the sun's heat on the earth1 the laws of climate1--the thermotical condition of the interior of the earth1--and that of the planetary spaces4 #a4 ,effect of ,solar ,heat on the ,earth4--,that the sun's heat passes into the interior of the earth in a variable manner1 depending upon the succession of days and nights1 summers and winters1 is an obvious consequence of our first notions on this subject4 ,the mode in which it proceeds into the interior1 after descending below the surface1 remained to be gathered1 either from the phenomena1 or from reasoning4 ,both methods were employed4#iaj ,saussure endeavored to trace its course by digging1 in #aghe1 and thus found that at the depth of about thirty-one feet1 the annual variation of temperature is about #aabth what it is at the surface4 ,leslie adopted a better method1 sinking the bulbs of thermometers deep in the earth1 while their stems appeared above the surface4 ,in #ahac1 '#af1 and '#ag1 he observed thus the temperatures at the depths of one1 two1 four1 and eight feet1 at ,abbotshall1 in ,fifeshire4 ,the results showed that the extreme annual oscillations of the temperature diminish as we descend4 ,at the depth of one foot1 the yearly range of oscillation was twenty-five degrees 7,fahrenheit72 at two feet it was twenty degrees2 at four feet it was fifteen degrees2 at eight feet it was only nine degrees and a half4 ,and the time at which the heat was greatest was later and later in proceeding to the lower points4 ,at one foot1 the maximum and minimum were three weeks after the solstice of summer and of winter2 at two feet1 they were four or five weeks2 at four feet1 they were two months2 and at eight feet1 three months4 ,the mean temperature of all the thermometers was nearly the same4 ,similar results were obtained by ,ott at ,zurich in #agfb1 and by ,herrenschneider at ,strasburg in #ahba1 '#b1 '#c4ajaj ,note #iaj3 ,leslie1 art4 ,climate1 ,supp4 ,enc4 ,brit4 #agi4 ,note #ajaj3 ,pouillet1 ,mtorol4 t4 ii4 p4 #fdc4 ,these results had already been explained by ,fourier's theory of conduction4 ,he had shown#aaaj that when the surface of a sphere is affected by a periodical heat1 certain alternations of heat travel uniformly into the interior1 but that the extent of the alternation diminishes in geometrical progression in this descent4 ,this conclusion applies to the effect of days and years on the temperature of the earth1 and shows that such facts as those observed by ,leslie are both exemplifications of #adf the general circumstances of the earth1 and are perfectly in accordance with the principles on which ,fourier's theory rests4 ,note #aaaj3 ,mm4 ,inst4 for #ahba 7published #ahbf71 p4 #afb4 #b4 ,climate4--,the term climate1 which means inclination1 was applied by the ancients to denote that inclination of the axis of the terrestrial sphere from which result the inequalities of days in different latitudes4 ,this inequality is obviously connected also with a difference of thermotical condition4 ,places near the poles are colder1 on the whole1 than places near the equator4 ,it was a natural object of curiosity to determine the law of this variation4 ,such a determination1 however1 involves many difficulties1 and the settlement of several preliminary points4 ,how is the temperature of any place to be estimated8 and if we reply1 by its mean temperature1 how are we to learn this mean8 ,the answers to such questions require very multiplied observations1 exact instruments1 and judicious generalizations2 and cannot be given here4 ,but certain first approximations may be obtained without much difficulty2 for instance1 the mean temperature of any place may be taken to be the temperature of deep springs1 which is probably identical with the temperature of the soil below the reach of the annual oscillations4 ,proceeding on such facts1 ,mayer found that the mean temperature of any place was nearly proportional to the square of the cosine of the latitude4 ,this1 as a law of phenomena1 has since been found to require considerable correction2 and it appears that the mean temperature does not depend on the latitude alone1 but on the distribution of land and water1 and on other causes4 ,m4 de ,humboldt has expressed these deviations#abaj by his map of isothermal lines1 and ,sir ,d4 ,brewster has endeavored to reduce them to a law by assuming two poles of maximum cold4 ,note #abaj3 ,british ,assoc4 #ahcc4 ,prof4 ,forbes's ,report on ,meteorology1 p4 #bae4 ,the expression which ,fourier finds#acaj for the distribution of heat in a homogeneous sphere1 is not immediately comparable with ,mayer's empirical formula1 being obtained on a certain hypothesis1 namely1 that the equator is kept constantly at a fixed temperature4 ,but there is still a general agreement2 for1 according to the theory1 there is a diminution of heat in proceeding from the equator to the poles in such a case2 the heat is propagated from the equator and the neighboring parts1 and radiates out from the poles into the surrounding space4 ,and thus1 in the case of the earth1 the solar heat enters in the tropical #adg parts1 and constantly flows towards the polar regions1 by which it is emitted into the planetary spaces4 ,note #acaj3 ,fourier4 ,mm4 ,inst4 tom4 v4 p4 #agc4 ,climate is affected by many thermotic influences1 besides the conduction and radiation of the solid mass of the earth4 ,the atmosphere1 for example1 produces upon terrestrial temperatures effects which it is easy to see are very great2 but these it is not yet in the power of calculation to appreciate2#adaj and it is clear that they depend upon other properties of air besides its power to transmit heat4 ,we must therefore dismiss them1 at least for the present4 ,note #adaj3 ,mm4 ,inst4 tom4 vii4 p4 #ehd #c4 ,temperature of the ,interior of the ,earth4--,the question of the temperature of the interior of the earth has excited great interest1 in consequence of its bearing on other branches of knowledge4 ,the various facts which have been supposed to indicate the fluidity of the central parts of the terrestrial globe1 belong1 in general1 to geological science2 but so far as they require the light of thermotical calculations in order to be rightly reasoned upon1 they properly come under our notice here4 ,the principal problem of this kind which has been treated of is this3--,if in the globe of the earth there be a certain original heat1 resulting from its earlier condition1 and independent of the action of the sun1 to what results will this give rise8 and how far do the observed temperatures of points below the surface lead us to such a supposition8 ,it has1 for instance1 been asserted1 that in many parts of the world the temperature1 as observed in mines and other excavations1 increases in descending1 at the rate of one degree 7centesimal7 in about forty yards4 ,what inference does this justify8 ,the answer to this question was given by ,fourier and by ,laplace4 ,the former mathematician had already considered the problem of the cooling of a large sphere1 in his ,memoirs of #ahjg1 #ahji1 and #ahaa4 ,these1 however1 lay unpublished in the archives of the ,institute for many years4 ,but in #ahbj1 when the accumulation of observations which indicated an increase of the temperature of the earth as we descend1 had drawn observation to the subject1 ,fourier gave1 in the ,bulletin of the ,philomathic ,society1#aeaj a summary of his results1 as far as they bore on this point4 ,his conclusion was1 that such an increase of temperature in proceeding towards the centre of the earth1 can arise from nothing but the remains of a primitive heat2--that the heat which the sun's action would communicate1 would1 in its final and #adh permanent state1 be uniform in the same vertical line1 as soon as we get beyond the influence of the superficial oscillations of which we have spoken2--and that1 before the distribution of temperature reaches this limit1 it will decrease1 not increase1 in descending4 ,it appeared also1 by the calculation1 that this remaining existence of the primitive heat in the interior of the earth's mass1 was quite consistent with the absence of all perceptible traces of it at the surface2 and that the same state of things which produces an increase of one degree of heat in descending forty yards1 does not make the surface a quarter of a degree hotter than it would otherwise be4 ,fourier was led also to some conclusions1 though necessarily very vague ones1 respecting the time which the earth must have taken to cool from a supposed original state of incandescence to its present condition1 which time it appeared must have been very great2 and respecting the extent of the future cooling of the surface1 which it was shown must be insensible4 ,everything tended to prove that1 within the period which the history of the human race embraces1 no discoverable change of temperature had taken place from the progress of this central cooling4 ,laplace further calculated the effect#afaj which any contraction of the globe of the earth by cooling would produce on the length of the day4 ,he had already shown1 by astronomical reasoning1 that the day had not become shorter by #abjjth of a second1 since the time of ,hipparchus2 and thus his inferences agreed with those of ,fourier4 ,as far as regards the smallness of the perceptible effect due to the past changes of the earth's temperature1 there can be no doubt that all the curious conclusions just stated are deduced in a manner quite satisfactory1 from the fact of a general increase of heat in descending below the surface of the earth2 and thus our principles of speculative science have a bearing upon the history of the past changes of the universe1 and give us information concerning the state of things in portions of time otherwise quite out of our reach4 ,note #aeaj3 ,bullet4 des ,sc4 #ahbj1 p4 #eh4 ,note #afaj3 ,conn4 des ,tems1 #ahbc4 #d4 ,heat of the ,planetary ,spaces4--,in the same manner1 this portion of science is appealed to for information concerning parts of space which are utterly inaccessible to observation4 ,the doctrine of heat leads to conclusions concerning the temperatures of the spaces which surround the earth1 and in which the planets of the solar system revolve4 ,in his ,memoir1 published in #ahbg1agaj ,fourier states that he conceives it to follow from his principles1 that these planetary spaces #adi are not absolutely cold1 but have a proper heat independent of the sun and of the planets4 ,if there were not such a heat1 the cold of the polar regions would be much more intense than it is1 and the alternations of cold and warmth1 arising from the influence of the sun1 would be far more extreme and sudden than we find them4 ,as the cause of this heat in the planetary spaces1 he assigns the radiation of the innumerable stars which are scattered through the universe4 ,note #agaj3 ,mm4 ,inst4 tom4 vii4 p4 #ehj4 ,fourier says1#ahaj ,we conclude from these various remarks1 and principally from the mathematical examination of the question1 that this is so4 ,i am not aware that the mathematical calculation which bears peculiarly upon this point has anywhere been published4 ,but it is worth notice1 that ,svanberg has been led#aiaj to the opinion of the same temperature in these spaces which ,fourier had adopted 7#ej centigrade below zero71 by an entirely different course of reasoning1 founded on the relation of the atmosphere to heat4 ,note #ahaj3 ,mm4 ,inst4 tom4 vii4 p4 #eha4 ,note #aiaj3 ,berzel4 ,jahres ,bericht1 xi4 p4 #ej4 ,in speaking of this subject1 ,i have been led to notice incomplete and perhaps doubtful applications of the mathematical doctrine of conduction and radiation4 ,but this may at least serve to show that ,thermotics is a science1 which1 like ,mechanics1 is to be established by experiments on masses capable of manipulation1 but which1 like that1 has for its most important office the solution of geological and cosmological problems4 ,i now return to the further progress of our thermotical knowledge4 ,sect4 #e4--;,correction of ,newton's ,law of ,cooling4 ,,in speaking of the establishment of ,newton's assumption1 that the temperature communicated is proportional to the excess of temperature1 we stated that it was approximately verified1 and afterwards corrected 7chap4 i41 sect4 #a4799994 ,this correction was the result of the researches of ,,mm4 ,dulong and ,petit in #ahag1 and the researches by which they were led to the true law1 are an admirable example both of laborious experiment and sagacious induction4 ,they experimented through a very great range of temperature 7as high as two hundred and forty degrees centigrade71 which was necessary because the inaccuracy of ,newton's law becomes considerable only at high temperatures4 ,they removed the effect of the surrounding medium1 by making their experiments in a vacuum4 ,they selected with great #aej judgment the conditions of their experiments and comparisons1 making one quantity vary while the others remained constant4 ,in this manner they found1 that the quickness of cooling for a constant excess of temperature1 increases in geometrical progression1 when the temperature of the surrounding space increases in arithmetical progression2 whereas1 according to the ,newtonian law1 this quickness would not have varied at all4 ,again1 this variation being left out of the account1 it appeared that the quickness of cooling1 so far as it depends on the excess of temperature of the hot body1 increases as the terms of a geometrical progression diminished by a constant number1 when the temperature of the hot body increases in arithmetical progression4 ,these two laws1 with the coefficients requisite for their application to particular substances1 fully determine the conditions of cooling in a vacuum4 ,starting from this determination1 ,,mm4 ,dulong and ,petit proceeded to ascertain the effect of the medium1 in which the hot body is placed1 upon its rate of cooling2 for this effect became a residual phenomenon1#bjaj when the cooling in the vacuum was taken away4 ,we shall not here follow this train of research2 but we may briefly state1 that they were led to such laws as this2--that the rapidity of cooling due to any gaseous medium in which the body is placed1 is the same1 so long as the excess of the body's temperature is the same1 although the temperature itself vary2--that the cooling power of a gas varies with the elasticity1 according to a determined law2 and other similar rules4 ,note #bjaj3 ,see ,phil4 ,ind4 ,sciences1 ,b4 xiii4 c4 #g1 ,sect4 iv4 ,in reference to the process of their induction1 it is worthy of notice1 that they founded their reasonings upon ,prevost's law of exchanges2 and that1 in this way1 the second of their laws above stated1 respecting the quickness of cooling1 was a mathematical consequence of the first4 ,it may be observed also1 that their temperatures are measured by means of the air-thermometer1 and that if they were estimated on another scale1 the remarkable simplicity and symmetry of their results would disappear4 ,this is a strong argument for believing such a measure of temperature to have a natural prerogative of simplicity4 ,this belief is confirmed by other considerations2 but these1 depending on the laws of expansion by heat1 cannot be here referred to2 and we must proceed to finish our survey of the mathematical theory of heat1 as founded on the phenomena of radiation and conduction1 which alone have as yet been traced up to general principles4 ,we may observe1 before we quit this subject1 that this correction of #aea ,newton's law will materially affect the mathematical calculations on the subject1 which were made to depend on that law both by ,fourier1 ,laplace1 and ,poisson4 ,probably1 however1 the general features of the results will be the same as on the old supposition4 ,m4 ,libri1 an ,italian mathematician1 has undertaken one of the problems of this kind1 that of the armil1 with ,dulong and ,petit's law for his basis1 in a ,memoir read to the ,institute of ,france in #ahbe1 and since published at ,florence4#baaj ,note #baaj3 ,mm4 de ,math4 et de ,phys4 #ahbi4 ,sect4 #f4--,other ,laws of ,phenomena with respect to ,radiation4 ,,the laws of radiation as depending upon the surface of radiating bodies1 and as affecting screens of various kinds interposed between the hot body and the thermometer1 were examined by several inquirers4 ,i shall not attempt to give an account of the latter course of research1 and of the different laws which luminous and non-luminous heat have been found to follow in reference to bodies1 whether transparent or opaque1 which intercept them4 ,but there are two or three laws of the phenomena1 depending upon the effects of the surfaces of bodies1 which are important4 #a4 ,in the first place1 the powers of bodies to emit and to absorb heat1 as far as depends upon their surface1 appear to be in the same proportion4 ,if we blacken the surface of a canister of hot water1 it radiates heat more copiously2 and in the same measure1 it is more readily heated by radiation4 #b4 ,in the next place1 as the radiative power increases1 the power of reflection diminishes1 and the contrary4 ,a bright metal vessel reflects much heat2 on this very account it does not emit much2 and hence a hot fluid which such a vessel contains1 remains hot longer than it does in an unpolished case4 #c4 ,the heat is emitted from every point of the surface of a hot body in all directions2 but by no means in all directions with equal intensity4 ,the intensity of the heating ray is as the sine of the angle which it makes with the surface4 ,the last law is entirely1 the two former in a great measure1 due to the researches of ,leslie1 whose ,experimental ,inquiry into the ,nature and ,propagation of ,heat1 published in #ahjd1 contains a great number of curious and striking results and speculations4 ,the laws now just #aeb stated bear1 in a very important manner1 upon the formation of the theory2 and we must now proceed to consider what appears to have been done in this respect2 taking into account1 it must still be borne in mind1 only the phenomena of conduction and radiation4 ,sect4 #g4--;,fourier's ,theory of ,radiant ,heat4 ,,the above laws of phenomena being established1 it was natural that philosophers should seek to acquire some conception of the physical action by which they might account1 both for these laws1 and for the general fundamental facts of ,thermotics2 as1 for instance1 the fact that all bodies placed in an inclosed space assume1 in time1 the temperature of the inclosure4 ,fourier's explanation of this class of phenomena must be considered as happy and successful2 for he has shown that the supposition to which we are led by the most simple and general of the facts1 will explain1 moreover1 the less obvious laws4 ,it is an obvious and general fact1 that bodies which are included in the space tend to acquire the same temperature4 ,and this identity of temperature of neighboring bodies requires an hypothesis1 which1 it is found1 also accounts for ,leslie's law of the sine1 in radiation4 ,this hypothesis is1 that the radiation takes place1 not from the surface alone of the hot body1 but from all particles situated within a certain small depth of the surface4 ,it is easy to see#bbaj that1 on this supposition1 a ray emitted obliquely from an internal particle1 will be less intense than one sent forth perpendicular to the surface1 because the former will be intercepted in a greater degree1 having a greater length of path within the body2 and ,fourier shows1 that whatever be the law of this intercepting power1 the result will be1 that the radiative intensity is as the sine of the angle made by the ray with the surface4 ,note #bbaj3 ,mm4 ,inst4 t4 v4 #ahba1 p4 #bjd4 ,but this law is1 as ,i have said1 likewise necessary1 in order that neighboring bodies may tend to assume the same temperature3 for instance1 in order that a small particle placed within a spherical shell1 should finally assume the temperature of the shell4 ,if the law of the sines did not obtain1 the final temperature of such a particle would depend upon its place in the inclosure2#bcaj and within a shell of ice we should have1 at certain points1 the temperature of boiling water and of melting iron4 ,note #bcaj3 ,an4 ,chim4 iv4 #ahag1 p4 #abi4 ,this proposition may at first appear strange and unlikely2 but it may #aec be shown to be a necessary consequence of the assumed principle1 by very simple reasoning1 which ,i shall give in a general form in a ,note4#bdaj ,note #bdaj3 ,the following reasoning may show the connexion of the law of the sines in radiant heat with the general principle of ultimate identity of neighboring temperatures4 ,the equilibrium and identity of temperature between an including shell and an included body1 cannot obtain upon the whole1 except it obtain between each pair of parts of the two surfaces of the body and of the shell2 that is1 any part of the one surface1 in its exchanges with any part of the other surface1 must give and receive the same quantity of heat4 ,now the quantity exchanged1 so far as it depends on the receiving surface1 will1 by geometry1 be proportional to the sine of the obliquity of that surface3 and as1 in the exchanges1 each may be considered as receiving1 the quantity transferred must be proportional to the sines of the two obliquities2 that is1 to that of the giving as well as of the receiving surface4 ,nor is this conclusion disturbed by the consideration1 that all the rays of heat which fall upon a surface are not absorbed1 some being reflected according to the nature of the surface4 ,for1 by the other above-mentioned laws of phenomena1 we know that1 in the same measure in which the surface loses the power of admitting1 it loses the power of emitting1 heat2 and the superficial parts gain1 by absorbing their own radiation1 as much as they lose by not absorbing the incident heat2 so that the result of the preceding reasoning remains unaltered4 ,this reasoning is capable of being presented in a manner quite satisfactory1 by the use of mathematical symbols1 and proves that ,leslie's law of the sines is rigorously and mathematically true on ,fourier's hypothesis4 ,and thus ,fourier's theory of molecular extra-radiation acquires great consistency4 ,sect4 #h4--;,discovery of the ,polarization of ,heat4 ,,the laws of which the discovery is stated in the preceding ,sections of this ,chapter1 and the explanations given of them by the theories of conduction and radiation1 all tended to make the conception of a material heat1 or caloric1 communicated by an actual flow and emission1 familiar to men's minds2 and1 till lately1 had led the greater part of thermotical philosophers to entertain such a view1 as the most probable opinion concerning the nature of heat4 ,but some steps have recently been made in thermotics1 which appear to be likely to overturn this belief1 and to make the doctrine of emission as untenable with regard to heat1 as it had been found to be with regard to light4 ,i speak of the discovery of the polarization of heat4 ,it being ascertained that rays of heat are polarized in the same manner as rays of #aed light1 we cannot retain the doctrine that heat radiates by the emanation of material particles1 without supposing those particles of caloric to have poles2 an hypothesis which probably no one would embrace2 for1 besides that the ill fortune which attended that hypothesis in the case of light must deter speculators from it1 the intimate connexion of heat and light would hardly allow us to suppose polarization in the two cases to be produced by two different kinds of machinery4 ,but1 without here tracing further the influence which the polarization of heat must exercise upon the formation of our theories of heat1 we must briefly notice this important discovery1 as a law of phenomena4 ,the analogies and connexions between light and heat are so strong1 that when the polarization of light had been discovered1 men were naturally led to endeavor to ascertain whether heat possessed any corresponding property4 ,but partly from the difficulty of obtaining any considerable effect of heat separated from light1 and partly from the want of a thermometrical apparatus sufficiently delicate1 these attempts led1 for some time1 to no decisive result4 ,m4 ,berard took up the subject in #ahac4 ,he used ,malus's apparatus1 and conceived that he found heat to be polarized by reflection at the surface of glass1 in the same manner as light1 and with the same circumstances4#beaj ,but when ,professor ,powell1 of ,oxford1 a few years later 7#ahcj71 repeated these experiments with a similar apparatus1 he found#bfaj that though the heat which is conveyed along with light is1 of course1 polarizable1 simple radiant heat1 as he terms it1 did not offer the smallest difference in the two rectangular azimuths of the second glass1 and thus showed no trace of polarization4 ,note #beaj3 ,ann4 ,chim4 ,march1 #ahac4 ,note #bfaj3 ,edin4 ,journ4 of ,science1 #ahcj1 vol4 ii4 p4 #cjc4 ,thus1 with the old thermometers1 the point remained doubtful4 ,but soon after this time1 ,,mm4 ,melloni and ,nobili invented an apparatus1 depending on certain galvanic laws1 of which we shall have to speak hereafter1 which they called a thermomultiplier2 and which was much more sensitive to changes of temperature than any previously-known instrument4 ,yet even with this instrument1 ,m4 ,melloni failed2 and did not1 at first1 detect any perceptible polarization of heat by the tourmaline2#bgaj nor did ,m4 ,nobili1#bhaj in repeating ,m4 ,berard's experiment4 ,but in this experiment the attempt was made to polarize heat by reflection from glass1 as light is polarized3 and the quantity #aee reflected is so small that the inevitable errors might completely disguise the whole difference in the two opposite positions4 ,when ,prof4 ,forbes1 of ,edinburgh1 7in #ahcd17 employed mica in the like experiments1 he found a very decided polarizing effect2 first1 when the heat was transmitted through several films of mica at a certain angle1 and afterwards1 when it was reflected from them4 ,in this case1 he found that with non-luminous heat1 and even with the heat of water below the boiling point1 the difference of the heating power in the two positions of opposite polarity 7parallel and crossed7 was manifest4 ,he also detected by careful experiments1#biaj the polarizing effect of tourmaline4 ,this important discovery was soon confirmed by ,m4 ,melloni4 ,doubts were suggested whether the different effect in the opposite positions might not be due to other circumstances2 but ,professor ,forbes easily showed that these suppositions were inadmissible2 and the property of a difference of sides1 which at first seemed so strange when ascribed to the rays of light1 also belongs1 it seems to be proved1 to the rays of heat4 ,professor ,forbes also found1 by interposing a plate of mica to intercept the ray of heat in an intermediate point1 an effect was produced in certain positions of the mica analogous to what was called depolarization in the case of light2 namely1 a partial destruction of the differences which polarization establishes4 ,note #bgaj3 ,ann4 de ,chimie1 vol4 lv4 ,note #bhaj3 ,bibliothque ,universelle4 ,note #biaj3 ,ed4 ,r4 ,s4 ,transactions1 vol4 xiv42 and ,phil4 ,mag4 #ahce1 vol4 v4 p4 #bji4 ,ib4 vol4 vii4 p4 #cdi4 ,before this discovery1 ,m4 ,melloni had already proved by experiment that heat is refracted by transparent substances as light is4 ,in the case of light1 the depolarizing effect was afterwards found to be really1 as we have seen1 a dipolarizing effect1 the ray being divided into two rays by double refraction4 ,we are naturally much tempted to put the same interpretation upon the dipolarizing effect in the case of heat2 but perhaps the assertion of the analogy between light and heat to this extent is as yet insecure4 ,it is the more necessary to be cautious in our attempt to identify the laws of light and heat1 inasmuch as along with all the resemblances of the two agents1 there are very important differences4 ,the power of transmitting light1 the diaphaneity of bodies1 is very distinct from their power of transmitting heat1 which has been called diathermancy by ,m4 ,melloni4 ,thus both a plate of alum and a plate of rock-salt transmit nearly the whole light2 but while the first stops nearly the whole heat1 the second stops very little of it2 and a plate of opake #aef quartz1 nearly impenetrable by light1 allows a large portion of the heat to pass4 ,by passing the rays through various media1 the heat may be1 as it were1 sifted from the light which accompanies it4 #bnd ,ed4 ,the diathermancy of bodies is distinct from their diaphaneity1 in so far that the same bodies do not exercise the same powers of selection and suppression of certain rays on heat and on light2 but it appears to be proved by the investigations of modern thermotical philosophers 7,,mm4 ,de la ,roche1 ,powell1 ,melloni1 and ,forbes71 that there is a close analogy between the absorption of certain colors by transparent bodies1 and the absorption of certain kinds of heat by diathermanous bodies4 ,dark sources of heat emit rays which are analogous to blue and violet rays of light2 and highly luminous sources emit rays which are analogous to red rays4 ,and by measuring the angle of total reflection for heat of different kinds1 it has been shown that the former kind of calorific rays are really less refrangible than the latter4#cjaj ,note #cjaj3 ,see ,prof4 ,forbes's ,third ,series of ,researches on ,heat1 ,edinb4 ,r4,s4 ,trans4 vol4 xiv4 ,m4 ,melloni has assumed this analogy as so completely established1 that he has proposed for this part of thermotics the name ,thermochroology 7,qu4 ,chromothermotics872 and along with this term1 many others derived from the ,greek1 and founded on the same analogy4 ,if it should appear1 in the work which he proposes to publish on this subject1 that the doctrines which he has to state cannot easily be made intelligible without the use of the terms he suggests1 his nomenclature will obtain currency2 but so large a mass of etymological innovations is in general to be avoided in scientific works4 ,m4 ,melloni's discovery of the extraordinary power of rock-salt to transmit heat1 and ,professor ,forbes's discovery of the extraordinary power of mica to polarize and depolarize heat1 have supplied thermotical inquirers with two new and most valuable instruments4#caaj ,note #caaj3 ,for an account of many thermotical researches1 which ,i have been obliged to pass unnoticed here1 see two ,reports by ,prof4 ,powell on the present state of our knowledge respecting ,radiant ,heat1 in the ,reports of the ,british ,association for #ahcb and #ahdj4 ,moreover1 besides the laws of conduction and radiation1 many other laws of the phenomena of heat have been discovered by philosophers2 and these must be taken into account in judging any theory of heat4 ,to these other laws we must now turn our attention4 #aeg ,,chapter ,,ii4 ,,the ,,laws ,,of ,,changes ,,occasioned ,,by ,,heat4 ,sect4 #a4--;,expansion by ,heat4--,the ,law of ,dalton and ,gay-,lussac for ,gases4 ,,almost all bodies expand by heat2 solids1 as metals1 in a small degree2 fluids1 as water1 oil1 alcohol1 mercury1 in a greater degree4 ,this was one of the facts first examined by those who studied the nature of heat1 because this property was used for the measure of heat4 ,in the ,philosophy of the ,inductive ,sciences1 ,book iv41 ,chap4 iv41 ,i have stated that secondary qualities1 such as ,heat1 must be measured by their effects3 and in ,sect4 #d of that ,chapter ,i have given an account of the successive attempts which have been made to obtain measures of heat4 ,i have there also spoken of the results which were obtained by comparing the rate at which the expansion of different substances went on1 under the same degrees of heat2 or as it was called1 the different thermometrical march of each substance4 ,mercury appears to be the liquid which is most uniform in its thermometrical march2 and it has been taken as the most common material of our thermometers2 but the expansion of mercury is not proportional to the heat4 ,de ,luc was led1 by his experiments1 to conclude that the dilatations of mercury follow an accelerated march for equal augmentations of heat4 ,dalton conjectured that water and mercury both expand as the square of the real temperature from the point of greatest contraction3 the real temperature being measured so as to lead to such a result4 ,but none of the rules thus laid down for the expansion of solids and fluids appear to have led1 as yet1 to any certain general laws4 ,with regard to gases1 thermotical inquirers have been more successful4 ,gases expand by heat2 and their expansion is governed by a law which applies alike to all degrees of heat1 and to all gaseous fluids4 ,the law is this3 that for equal increments of temperature they expand by the same fraction of their own bulk2 which fraction is three-eights #aeh in proceeding from freezing to boiling water4 ,this law was discovered by ,dalton and ,m4 ,gay-,lussac independently of each other2#cbaj and is usually called by both their names1 the law of ,dalton and ,gay-,lussac4 ,the latter says1#ccaj ,the experiments which ,i have described1 and which have been made with great care1 prove incontestably that oxygen1 hydrogen1 azotic acid1 nitrous acid1 ammoniacal acid1 muriatic acid1 sulphurous acid1 carbonic acid1 gases1 expand equally by equal increments of heat4 ,therefore1 he adds with a proper inductive generalization1 the result does not depend upon physical properties1 and ,i collect that all gases expand equally by heat4 ,he then extends this to vapors1 as ether4 ,this must be one of the most important foundation-stones of any sound theory of heat4 ,note #cbaj3 ,manch4 ,mem4 vol4 v4 #ahjb2 and ,ann4 ,chim4 xliii4 p4 #acg4 ,note #ccaj3 ,ib4 p4 #bgb4 #bnd ,ed4 ,yet ,,mm4 ,magnus and ,regnault conceive that they have overthrown this law of ,dalton and ,gay-,lussac1 and shown that the different gases do not expand alike for the same increment of heat4 ,magnus found the ratio to be for atmospheric air1 #acff2 for hydrogen1 #acfe2 for carbonic acid1 #acfi2 for sulphurous-acid gas1 #ache4 ,but these differences are not greater than the differences obtained for the same substances by different observers2 and as this law is referred to in ,laplace's hypothesis1 hereafter to be discussed1 ,i do not treat the law as disproved4 ,yet that the rate of expansion of gas in certain circumstances is different for different substances1 must be deemed very probable1 after ,dr4 ,faraday's recent investigations ,on the ,liquefaction and ,solidification of ,bodies generally existing as ,gases1#cdaj by which it appears that the elasticity of vapors in contact with their fluids increases at different rates in different substances4 ,that the force1 he says1 of vapor increases in a geometrical ratio for equal increments of heat is true for all bodies1 but the ratio is not the same for all4 4 4 4 ,for an increase of pressure from two to six atmospheres1 the following number of degrees require to be added to the bodies named3--water #fi1 sulphureous acid #fc1 cyanogen #fde1 ammonia #fj1 arseniuretted hydrogen #ed1 sulphuretted hydrogen #efe1 muriatic acid #dc1 carbonic acid #cbe1 nitrous oxide #cj4 ,note #cdaj3 ,phil4 ,trans4 #ahde1 ,pt4 #a4 ,we have already seen that the opinion that the air-thermometer is a true measure of heat1 is strongly countenanced by the symmetry which1 by using it1 we introduce into the laws of radiation4 ,if we #aei accept the law of ,dalton and ,gay-,lussac1 it follows that this result is independent of any peculiar properties in the air employed2 and thus this measure has an additional character of generality and simplicity which make it still more probable that it is the true standard4 ,this opinion is further supported by the attempts to include such facts in a theory2 but before we can treat of such theories1 we must speak of some other doctrines which have been introduced4 ,sect4 #b4--,specific ,heat4--,change of ,consistence4 ,,in the attempts to obtain measures of heat1 it was found that bodies had different capacities for heat2 for the same quantity of heat1 however measured1 would raise1 in different degrees1 the temperature of different substances4 ,the notion of different capacities for heat was thus introduced1 and each body was thus assumed to have a specific capacity for heat1 according to the quantity of heat which it required to raise it through a given scale of heat4#ceaj ,the term capacity for heat was introduced by ,dr4 ,irvine1 a pupil of ,dr4 ,black4 ,for this term1 ,wilcke1 the ,swedish physicist1 substituted specific heat2 in analogy with specific gravity4 ,note #ceaj3 ,see ,crawford1 ,on ,heat1 for the ,history of ,specific ,heat4 ,it was found1 also1 that the capacity of the same substance was different in the same substance at different temperatures4 ,it appears from experiments of ,,mm4 ,dulong and ,petit1 that1 in general1 the capacity of liquids and solids increases as we ascend in the scale of temperature4 ,but one of the most important thermotic facts is1 that by the sudden contraction of any mass1 its temperature is increased4 ,this is peculiarly observable in gases1 as1 for example1 common air4 ,the amount of the increase of temperature by sudden condensation1 or of the cold produced by sudden rarefaction1 is an important datum1 determining the velocity of sound1 as we have already seen1 and affecting many points of meteorology4 ,the coefficient which enters the calculation in the former case depends on the ratio of two specific heats of air under different conditions2 one belonging to it when1 varying in density1 the pressure is constant by which the air is contained2 the other1 when1 varying in density1 it is contained in a constant space4 ,a leading fact1 also1 with regard to the operation of heat on bodies #afj is1 that it changes their form1 as it is often called1 that is1 their condition as solid1 liquid1 or air4 ,since the term form is employed in too many and various senses to be immediately understood when it is intended to convey this peculiar meaning1 ,i shall use1 instead of it1 the term consistence1 and shall hope to be excused1 even when ,i apply this word to gases1 though ,i must acknowledge such phraseology to be unusual4 ,thus there is a change of consistence when solids become liquid1 or liquids gaseous2 and the laws of such changes must be fundamental facts of our thermotical theories4 ,we are still in the dark as to many of the laws which belong to this change2 but one of them1 of great importance1 has been discovered1 and to that we must now proceed4 ,sect4 #c4--,the ,doctrine of ,latent ,heat4 ,the ,doctrine of ,latent ,heat refers to such changes of consistence as we have just spoken of4 ,it is to this effect2 that during the conversion of solids into liquids1 or of liquids into vapors1 there is communicated to the body heat which is not indicated by the thermometer4 ,the heat is absorbed1 or becomes latent2 and1 on the other hand1 on the condensation of the vapor to a liquid1 or the liquid to a solid consistency1 this heat is again given out and becomes sensible4 ,thus a pound of ice requires twenty times as long a time1 in a warm room1 to raise its temperature seven degrees1 as a pound of ice-cold water does4 ,a kettle placed on a fire1 in four minutes had its temperature raised to the boiling point1 #bab3 and this temperature continued stationary for twenty minutes1 when the whole was boiled away4 ,dr4 ,black inferred from these facts that a large quantity of heat is absorbed by the ice in becoming water1 and by the water in becoming steam4 ,he reckoned from the above experiments1 that ice1 in melting1 absorbs as much heat as would raise ice-cold water through #adj of temperature3 and that water1 in evaporating1 absorbs as much heat as would raise it through #idj4 ,that snow requires a great quantity of heat to melt it2 that water requires a great quantity of heat to convert it into steam2 and that this heat is not indicated by a rise in the thermometer1 are facts which it is not difficult to observe2 but to separate these from all extraneous conditions1 to group the cases together1 and to seize upon the general law by which they are connected1 was an effort of inductive insight1 which has been considered1 and deservedly1 as one of the most striking #afa events in the modern history of physics4 ,of this step the principal merit appears to belong to ,black4 #bnd ,ed4 ,in the first edition ,i had mentioned the names of ,de ,luc and of ,wilcke1 in connexion with the discovery of ,latent ,heat1 along with the name of ,black4 ,de ,luc had observed1 in #agee1 that ice1 in melting1 did not rise above the freezing-point of temperature till the whole was melted4 ,de ,luc has been charged with plagiarizing ,black's discovery1 but1 ,i think1 without any just ground4 ,in his ,ides sur la ,mtorologique 7#aghg71 he spoke of ,dr4 ,black as the first who had attempted the determinations of the quantities of latent heat4 ,and when ,mr4 ,watt pointed out to him that from this expression it might be supposed that ,black had not discovered the fact itself1 he acquiesced1 and redressed the equivocal expression in an ,appendix to the volume4#cfaj ,note #cfaj3 ,see his ,letter to the ,editors of the ,edinburgh ,review1 ,no4 xii4 p4 #ejb1 of the ,review4 ,black never published his own account of the doctrine of ,latent ,heat3 but he delivered it every year after #agfj in his ,lectures4 ,in #aggj1 a surreptitious publication of his ,lectures was made by a ,london bookseller1 and this gave a view of the leading points of ,dr4 ,black's doctrine4 ,in #aggb1 ,wilcke1 of ,stockholm1 read a paper to the ,royal ,society of that city1 in which the absorption of heat by melting ice is described2 and in the same year1 ,de ,luc of ,geneva published his ,recherches sur les ,modifications de l',atmosphre1 which has been alleged to contain the doctrine of latent heat1 and which the author asserts to have been written in ignorance of what ,black had done4 ,at a later period1 ,de ,luc1 adopting1 in part4 ,black's expression1 gave the name of latent fire to the heat absorbed4#cgaj ,note #cgaj3 ,see ,ed4 ,rev4 ,no4 vi4 p4 #bj4 ,it appears that ,cavendish determined the amount of heat produced by condensing steam1 and by thawing snow1 as early as #agfe4 ,he had perhaps already heard something of ,black's investigations1 but did not accept his term latent heat49999#chaj ,note #chaj3 ,see ,mr4 ,v4 ,harcourt's ,address to the ,brit4 ,assoc4 in #ahci1 and the ,appendix4 ,the consequences of ,black's principle are very important1 for upon it is founded the whole doctrine of evaporation2 besides which1 the principle of latent heat has other applications4 ,but the relations of aqueous vapor to air are so important1 and have been so long a #afb subject of speculation1 that we may with advantage dwell a little upon them4 ,the part of science in which this is done may be called1 as we have said1 ,atmology2 and to that division of ,thermotics the following chapters belong4 #afc ,,atmology4 ,,chapter ,,iii4 ,,the ,,relation ,,of ,,vapor ,,and ,,air4 ,sect4 #a4--,the ,boylean ,law of the ,air's ,elasticity4 ,,in the ,sixth ,book 7,chap4 iv4 ,sect4 #a47 we have already seen how the conception on the laws of fluid equilibrium was1 by ,pascal and others1 extended to air1 as well as water4 ,but though air presses and is pressed as water presses and is pressed1 pressure produces upon air an effect which it does not1 in any obvious degree1 produce upon water4 ,air which is pressed is also compressed1 or made to occupy a smaller space2 and is consequently also made more dense1 or condensed2 and on the other hand1 when the pressure upon a portion of air is diminished1 the air expands or is rarefied4 ,these broad facts are evident4 ,they are expressed in a general way by saying that air is an elastic fluid1 yielding in a certain degree to pressure1 and recovering its previous dimensions when the pressure is removed4 ,but when men had reached this point1 the questions obviously offered themselves1 in what degree and according to what law air yields to pressure2 when it is compressed1 what relation does the density bear to the pressure8 ,the use which had been made of tubes containing columns of mercury1 by which the pressure of portions of air was varied and measured1 suggested obvious modes of devising experiments by which this question might be answered4 ,such experiments accordingly were made by ,boyle about #afej2 and the result at which he arrived was1 that when air is thus compressed1 the density is as the pressure4 ,thus if the pressure of the atmosphere in its common state be equivalent to #cj inches of mercury1 as shown by the barometer2 if air included in a tube be pressed by #cj additional inches of #afd mercury1 its density will be doubled1 the air being compressed into one half the space4 ,if the pressure be increased threefold1 the density is also trebled2 and so on4 ,the same law was soon afterwards 7in #afgf7 proved experimentally by ,mariotte4 ,and this law of the air's elasticity1 that the density is as the pressure1 is sometimes called the ,boylean ,law1 and sometimes the ,law of ,boyle and ,mariotte4 ,air retains its aerial character permanently2 but there are other aerial substances which appear as such1 and then disappear or change into some other condition4 ,such are termed vapors4 ,and the discovery of their true relation to air was the result of a long course of researches and speculations4 #bnd ,ed4 ,it was found by ,m4 ,cagniard de la ,tour 7in #ahbc71 that at a certain temperature1 a liquid1 under sufficient pressure1 becomes clear transparent vapor or gas1 having the same bulk as the liquid4 ,this condition ,dr4 ,faraday calls the ,cagniard de la ,tour state1 7the ,tourian state87 ,it was also discovered by ,dr4 ,faraday that carbonic-acid gas1 and many other gases1 which were long conceived to be permanently elastic1 are really reducible to a liquid state by pressure4#ciaj ,and in #ahce1 ,m4 ,thilorier found the means of reducing liquid carbonic acid to a solid form1 by means of the cold produced in evaporation4 ,more recently ,dr4 ,faraday has added several substances usually gaseous to the list of those which could previously be shown in the liquid state1 and has reduced others1 including ammonia1 nitrous oxide1 and sulphuretted hydrogen1 to a solid consistency4#djaj ,after these discoveries1 we may1 ,i think1 reasonably doubt whether all bodies are not capable of existing in the three consistencies of solid1 liquid1 and air4 ,note #ciaj3 ,phil4 ,trans4 #ahbc4 ,note #djaj3 ,ib4 ,pt4 #a4 #ahde4 ,we may note that the law of ,boyle and ,mariotte is not exactly true near the limit at which the air passes to the liquid state in such cases as that just spoken of4 ,the diminution of bulk is then more rapid than the increase of pressure4 ,the transition of fluids from a liquid to an airy consistence appears to be accompanied by other curious phenomena4 ,see ,prof4 ,forbes's papers on the ,color of ,steam under certain circumstances1 and on the ,colors of the ,atmosphere1 in the ,edin4 ,trans4 vol4 xiv4 #afe ,sect4 #b4--,prelude to ,dalton's ,doctrine of ,evaporation4 ,,visible clouds1 smoke1 distillation1 gave the notion of ,vapor2 vapor was at first conceived to be identical with air1 as by ,bacon4#daaj ,it was easily collected1 that by heat1 water might be converted into vapor4 ,it was thought that air was thus produced1 in the instrument called the olipile1 in which a powerful blast is caused by a boiling fluid2 but ,wolfe showed that the fluid was not converted into air1 by using camphorated spirit of wine1 and condensing the vapor after it had been formed4 ,we need not enumerate the doctrines 7if very vague hypotheses may be so termed7 of ,descartes1 ,dechales1 ,borelli4#dbaj ,the latter accounted for the rising of vapor by supposing it a mixture of fire and water2 and thus1 fire being much lighter than air1 the mixture also was light4 ,boyle endeavored to show that vapors do not permanently float in vacuo4 ,he compared the mixture of vapor with air to that of salt with water4 ,he found that the pressure of the atmosphere affected the heat of boiling water2 a very important fact4 ,boyle proved this by means of the air-pump2 and he and his friends were much surprised to find that when air was removed1 water only just warm boiled violently4 ,huyghens mentions an experiment of the same kind made by ,papin about #afgc4 ,note #daaj3 ,bacon's ,hist4 ,nat4 ,cent4 i4 p4 #bg4 ,note #dbaj3 ,they may be seen in ,fischer1 ,geschichte der ,physik1 vol4 ii4 p4 #age4 ,the ascent of vapor was explained in various ways in succession1 according to the changes which physical science underwent4 ,it was a problem distinctly treated of1 at a period when hydrostatics had accounted for many phenomena2 and attempts were naturally made to reduce this fact to hydrostatical principles4 ,an obvious hypothesis1 which brought it under the dominion of these principles1 was1 to suppose that the water1 when converted into vapor1 was divided into small hollow globules2--thin pellicles including air or heat4 ,halley gave such an explanation of evaporation2 ,leibnitz calculated the dimensions of these little bubbles2 ,derham managed 7as he supposed7 to examine them with a magnifying glass3 ,wolfe also examined and calculated on the same subject4 ,it is curious to see so much confidence in so lame a theory2 for if water became hollow globules in order to rise as vapor1 we require1 in order to explain the formation of these globules1 new laws of nature1 which are not even hinted at by #aff the supporters of the doctrine1 though they must be far more complex than the hydrostatical law by which a hollow sphere floats4 ,newton's opinion was hardly more satisfactory2 he#dcaj explained evaporation by the repulsive power of heat2 the parts of vapors1 according to him1 being small1 are easily affected by this force1 and thus become lighter than the atmosphere4 ,note #dcaj3 ,opticks1 ,qu4 #ca4 ,muschenbroek still adhered to the theory of globules1 as the explanation of evaporation2 but he was manifestly discontented with it2 and reasonably apprehended that the pressure of the air would destroy the frail texture of these bubbles4 ,he called to his aid a rotation of the globules 7which ,descartes also had assumed72 and1 not satisfied with this1 threw himself on electrical action as a reserve4 ,electricity1 indeed1 was now in favor1 as hydrostatics had been before2 and was naturally called in1 in all cases of difficulty4 ,desaguliers1 also1 uses this agent to account for the ascent of vapor1 introducing it into a kind of sexual system of clouds2 according to him1 the male fire 7heat7 does a part1 and the female fire 7electricity7 performs the rest4 ,these are speculations of small merit and no value4 ,in the mean time1 ,chemistry made great progress in the estimation of philosophers1 and had its turn in the explanation of the important facts of evaporation4 ,bouillet1 who1 in #agdb1 placed the particles of water in the interstices of those of air1 may be considered as approaching to the chemical theory4 ,in #agdh1 the ,academy of ,sciences of ,bourdeaux proposed the ascent of vapors as the subject of a prize2 which was adjudged in a manner very impartial as to the choice of a theory2 for it was divided between ,kratzenstein1 who advocated the bubbles1 7the coat of which he determined to be #aej1jjjth of an inch thick17 and ,hamberger1 who maintained the truth to be the adhesion of particles of water to those of air and fire4 ,the latter doctrine had become much more distinct in the author's mind when seven years afterwards 7#agej7 he published his ,elementa ,physices4 ,he then gave the explanation of evaporation in a phrase which has since been adopted1--the solution of water in air2 which he conceived to be of the same kind as other chemical solutions4 ,this theory of solution was further advocated and developed by ,le ,roi2#ddaj and in his hands assumed a form which has been extensively adopted up to our times1 and has1 in many instances1 tinged the language commonly used4 ,he conceived that air1 like other solvents1 #afg might be saturated2 and that when the water was beyond the amount required for saturation1 it appeared in a visible form4 ,the saturating quantity was held to depend mainly on warmth and wind4 ,note #ddaj3 ,ac4 ,r4 ,sc4 ,paris1 #agej4 ,this theory was by no means devoid of merit2 for it brought together many of the phenomena1 and explained a number of the experiments which ,le ,roi made4 ,it explained the facts of the transparency of vapor1 7for perfect solutions are transparent17 the precipitation of water by cooling1 the disappearance of the visible moisture by warming it again1 the increased evaporation by rain and wind2 and other observed phenomena4 ,so far1 therefore1 the introduction of the notion of the chemical solution of water in air was apparently very successful4 ,but its defects are of a very fatal kind2 for it does not at all apply to the facts which take place when air is excluded4 ,in ,sweden1 in the mean time1#deaj the subject had been pursued in a different1 and in a more correct manner4 ,wallerius ,ericsen had1 by various experiments1 established the important fact1 that water evaporates in a vacuum4 ,his experiments are clear and satisfactory2 and he inferred from them the falsity of the common explanation of evaporation by the solution of water in air4 ,his conclusions are drawn in a very intelligent manner4 ,he considers the question whether water can be changed into air1 and whether the atmosphere is1 in consequence1 a mere collection of vapors2 and on good reasons1 decides in the negative1 and concludes the existence of permanently-elastic air different from vapor4 ,he judges1 also1 that there are two causes concerned1 one acting to produce the first ascent of vapors1 the other to support them afterwards4 ,the first1 which acts in a vacuum1 he conceives to be the mutual repulsion of the particles2 and since this force is independent of the presence of other substances1 this seems to be a sound induction4 ,when the vapors have once ascended into the air1 it may readily be granted that they are carried higher1 and driven from side to side by the currents of the atmosphere4 ,wallerius conceives that the vapor will rise till it gets into air of the same density as itself1 and being then in equilibrium1 will drift to and fro4 ,note #deaj3 ,fischer1 ,gesch4 ,phys4 vol4 v4 p4 #fc4 ,the two rival theories of evaporation1 that of chemical solution and that of independent vapor1 were1 in various forms1 advocated by the next generation of philosophers4 ,de ,saussure may be considered as the leader on one side1 and ,de ,luc on the other4 ,the former maintained the solution theory1 with some modifications of his own4 ,de #afh ,luc denied all solution1 and held vapor to be a combination of the particles of water with fire1 by which they became lighter than air4 ,according to him1 there is always fire enough present to produce this combination1 so that evaporation goes on at all temperatures4 ,this mode of considering independent vapor as a combination of fire with water1 led the attention of those who adopted that opinion to the thermometrical changes which take place when vapor is formed and condensed4 ,these changes are important1 and their laws curious4 ,the laws belong to the induction of latent heat1 of which we have just spoken2 but a knowledge of them is not absolutely necessary in order to enable us to understand the manner in which steam exists in air4 ,de ,luc's views led him#dfaj also to the consideration of the effect of pressure on vapor4 ,he explains the fact that pressure will condense vapor1 by supposing that it brings the particles within the distance at which the repulsion arising from fire ceases4 ,in this way1 he also explains the fact1 that though external pressure does thus condense steam1 the mixture of a body of air1 by which the pressure is equally increased1 will not produce the same effect2 and therefore1 vapors can exist in the atmosphere4 ,they make no fixed proportion of it2 but at the same temperature we have the same pressure arising from them1 whether they are in air or not4 ,as the heat increases1 vapor becomes capable of supporting a greater and greater pressure1 and at the boiling heat1 it can support the pressure of the atmosphere4 ,note #dfaj3 ,fischer1 vol4 vii4 p4 #dec4 ,nouvelles ,ides sur la ,mtorologie1 #aghg4 ,de ,luc also marked very precisely 7as ,wallerius had done7 the difference between vapor and air2 the former being capable of change of consistence by cold or pressure1 the latter not so4 ,pictet1 in #aghf1 made a hygrometrical experiment1 which appeared to him to confirm ,de ,luc's views2 and ,de ,luc1 in #agib1 published a concluding essay on the subject in the ,philosophical ,transactions4 ,pictet's ,essay on ,fire1 in #agia1 also demonstrated that all the train of hygrometrical phenomena takes place just as well1 indeed rather quicker1 in a vacuum than in air1 provided the same quantity of moisture is present4 ,this essay1 and ,de ,luc's paper1 gave the death-blow to the theory of the solution of water in air4 ,yet this theory did not fall without an obstinate struggle4 ,it was taken up by the new school of ,french chemists1 and connected with their views of heat4 ,indeed1 it long appears as the prevalent opinion4 #afi ,girtanner1#dgaj in his ,grounds of the ,antiphlogistic ,theory1 may be considered as one of the principal expounders of this view of the matter4 ,hube1 of ,warsaw1 was1 however1 the strongest of the defenders of the theory of solution1 and published upon it repeatedly about #agij4 ,yet he appears to have been somewhat embarrassed with the increase of the air's elasticity by vapor4 ,parrot1 in #ahja1 proposed another theory1 maintaining that ,de ,luc had by no means successfully attacked that of solution1 but only ,de ,saussure's superfluous additions to it4 ,note #dgaj3 ,fischer1 vol4 vii4 #dgc4 ,it is difficult to see what prevented the general reception of the doctrine of independent vapor2 since it explained all the facts very simply1 and the agency of air was shown over and over again to be unnecessary4 ,yet1 even now1 the solution of water in air is hardly exploded4 ,m4 ,gay ,lussac1#dhaj in #ahjj1 talks of the quantity of water held in solution by the air2 which1 he says1 varies according to its temperature and density by a law which has not yet been discovered4 ,and ,professor ,robison1 in the article ,steam1 in the ,encyclopdia ,britannica 7published about #ahjj71 says1#diaj ,many philosophers imagine that spontaneous evaporation1 at low temperatures1 is produced in this way 7by elasticity alone74 ,but we cannot be of this opinion2 and must still think that this kind of evaporation is produced by the dissolving power of the air4 ,he then gives some reasons for his opinion4 ,when moist air is suddenly rarefied1 there is always a precipitation of water4 ,but by this new doctrine the very contrary should happen1 because the tendency of water to appear in the elastic form is promoted by removing the external pressure4 ,another main difficulty in the way of the doctrine of the mere mixture of vapor and air was supposed to be this2 that if they were so mixed1 the heavier fluid would take the lower part1 and the lighter the higher part1 of the space which they occupied4 ,note #dhaj3 ,ann4 ,chim4 tom4 xliii4 ,note #diaj3 ,robison's ,works1 ii4 #cg4 ,the former of these arguments was repelled by the consideration that in the rarefaction of air1 its specific heat is changed1 and thus its temperature reduced below the constituent temperature of the vapor which it contains4 ,the latter argument is answered by a reference to ,dalton's law of the mixture of gases4 ,we must consider the establishment of this doctrine in a new section1 as the most material step to the true notion of evaporation4 #agj ,sect4 #c4--;,dalton's ,doctrine of ,evaporation4 ,a ,,portion of that which appears to be the true notion of evaporation was known1 with greater or less distinctness1 to several of the physical philosophers of whom we have spoken4 ,they were aware that the vapor which exists in air1 in an invisible state1 may be condensed into water by cold3 and they had noticed that1 in any state of the atmosphere1 there is a certain temperature lower than that of the atmosphere1 to which1 if we depress bodies1 water forms upon them in fine drops like dew2 this temperature is thence called the dew-point4 ,the vapor of water which exists anywhere may be reduced below the degree of heat which is necessary to constitute it vapor1 and thus it ceases to be vapor4 ,hence this temperature is also called the constituent temperature4 ,this was generally known to the meteorological speculators of the last century1 although1 in ,england1 attention was principally called to it by ,dr4 ,wells's ,essay on ,dew1 in #ahad4 ,this doctrine readily explains how the cold produced by rarefaction of air1 descending below the constituent temperature of the contained vapor1 may precipitate a dew2 and thus1 as we have said1 refutes one obvious objection to the theory of independent vapor4 ,the other difficulty was first fully removed by ,mr4 ,dalton4 ,when his attention was drawn to the subject of vapor1 he saw insurmountable objections to the doctrine of a chemical union of water and air4 ,in fact1 this doctrine was a mere nominal explanation2 for1 on closer examination1 no chemical analogies supported it4 ,after some reflection1 and in the sequel of other generalizations concerning gases1 he was led to the persuasion1 that when air and steam are mixed together1 each follows its separate laws of equilibrium1 the particles of each being elastic with regard to those of their own kind only3 so that steam may be conceived as flowing among the particles of air#ejaj like a stream of water among pebbles2 and the resistance which air offers to evaporation arises1 not from its weight1 but from the inertia of its particles4 ,note #ejaj3 ,manchester ,memoirs1 vol4 v4 p4 #eha4 ,it will be found that the theory of independent vapor1 understood with these conditions1 will include all the facts of the case2--gradual evaporation in air2 sudden evaporation in a vacuum2 the increase of #aga the air's elasticity by vapor2 condensation by its various causes2 and other phenomena4 ,but ,mr4 ,dalton also made experiments to prove his fundamental principle1 that if two different gases communicate1 they will diffuse themselves through each other2#eaaj--slowly1 if the opening of communication be small4 ,he observes also1 that all the gases had equal solvent powers for vapor1 which could hardly have happened1 had chemical affinity been concerned4 ,nor does the density of the air make any difference4 ,note #eaaj3 ,new ,system of ,chemical ,philosophy1 vol4 i4 p4 #aea4 ,taking all these circumstances into the account1 ,mr4 ,dalton abandoned the idea of solution4 ,in the autumn of #ahja1 he says1 ,i hit upon an idea which seemed to be exactly calculated to explain the phenomena of vapor3 it gave rise to a great variety of experiments1 which ended in fixing it in his mind as a true idea4 ,but1 he adds1 the theory was almost universally misunderstood1 and consequently reprobated4 ,mr4 ,dalton answers various objections4 ,berthollet had urged that we can hardly conceive the particles of an elastic substance added to those of another1 without increasing its elasticity4 ,to this ,mr4 ,dalton replies by adducing the instance of magnets1 which repel each other1 but do not repel other bodies4 ,one of the most curious and ingenious objections is that of ,m4 ,gough1 who argues1 that if each gas is elastic with regard to itself alone1 we should hear1 produced by one stroke1 four sounds2 namely1 first1 the sound through aqueous vapor2 second1 the sound through azotic gas2 third1 the sound through oxygen gas2 fourth1 the sound through carbonic acid4 ,mr4 ,dalton's answer is1 that the difference of time at which these sounds would come is very small2 and that1 in fact1 we do hear1 sounds double and treble4 ,in his ,new ,system of ,chemical ,philosophy1 ,mr4 ,dalton considers the objections of his opponents with singular candor and impartiality4 ,he there appears disposed to abandon that part of the theory which negatives the mutual repulsion of the particles of the two gases1 and to attribute their diffusion through one another to the different size of the particles1 which would1 he thinks1#ebaj produce the same effect4 ,note #ebaj3 ,new ,system1 vol4 i4 p4 #ahh4 ,in selecting1 as of permanent importance1 the really valuable part of this theory1 we must endeavor to leave out all that is doubtful or unproved4 ,i believe it will be found that in all theories hitherto #agb promulgated1 all assertions respecting the properties of the particles of bodies1 their sizes1 distances1 attractions1 and the like1 are insecure and superfluous4 ,passing over1 then1 such hypotheses1 the inductions which remain are these2--that two gases which are in communication will1 by the elasticity of each1 diffuse themselves in one another1 quickly or slowly2 and--that the quantity of steam contained in a certain space of air is the same1 whatever be the air1 whatever be its density1 and even if there be a vacuum4 ,these propositions may be included together by saying1 that one gas is mechanically mixed with another2 and we cannot but assent to what ,mr4 ,dalton says of the latter fact1--this is certainly the touchstone of the mechanical and chemical theories4 ,this doctrine of the mechanical mixture of gases appears to supply answers to all the difficulties opposed to it by ,berthollet and others1 as ,mr4 ,dalton has shown2#ecaj and we may1 therefore1 accept it as well established4 ,note #ecaj3 ,new ,system1 vol4 i4 p4 #afj1 c4 ,this doctrine1 along with the principle of the constituent temperature of steam1 is applicable to a large series of meteorological and other consequences4 ,but before considering the applications of theory to natural phenomena1 which have been made1 it will be proper to speak of researches which were carried on1 in a great measure1 in consequence of the use of steam in the arts3 ,i mean the laws which connect its elastic force with its constituent temperature4 ,sect4 #d4--;,determination of the ,laws of the ,elastic ,force of ,steam4 ,,the expansion of aqueous vapor at different temperatures is governed1 like that of all other vapors1 by the law of ,dalton and ,gay-,lussac1 already mentioned2 and from this1 its elasticity1 when its expansion is resisted1 will be known by the law of ,boyle and ,mariotte2 namely1 by the rule that the pressure of airy fluids is as the condensation4 ,but it is to be observed1 that this process of calculation goes on the supposition that the steam is cut off from contact with water1 so that no more steam can be generated2 a case quite different from the common one1 in which the steam is more abundant as the heat is greater4 ,the examination of the force of vapor1 when it is in contact with water1 must be briefly noticed4 ,during the period of which we have been speaking1 the progress of the investigation of the laws of aqueous vapor was much accelerated #agc by the growing importance of the steam-engine1 in which those laws operated in a practical form4 ,james ,watts1 the main improver of that machine1 was thus a great contributor to speculative knowledge1 as well as to practical power4 ,many of his improvements depended on the laws which regulate the quantity of heat which goes to the formation or condensation of steam2 and the observations which led to these improvements enter into the induction of latent heat4 ,measurements of the force of steam1 at all temperatures1 were made with the same view4 ,watts's attention had been drawn to the steam-engine in #agei1 by ,robison1 the former being then an instrument-maker1 and the latter a student at the ,university of ,glasgow4#edaj ,in #agfa or #agfb1 he tried some experiments on the force of steam in a ,papin's ,digester2#eeaj and formed a sort of working model of a steam-engine1 feeling already his vocation to develope the powers of that invention4 ,his knowledge was at that time principally derived from ,desaguliers and ,belidor1 but his own experiments added to it rapidly4 ,in #agfd and #agfe1 he made a more systematical course of experiments1 directed to ascertain the force of steam4 ,he tried this force1 however1 only at temperatures above the boiling-point2 and inferred it at lower degrees from the supposed continuity of the law thus obtained4 ,his friend ,robison1 also1 was soon after led1 by reading the account of some experiments of ,lord ,charles ,cavendish1 and some others of ,mr4 ,nairne1 to examine the same subject4 ,he made out a table of the correspondence of the elasticity and the temperature of vapor1 from thirty-two to two hundred and eighty degrees of ,fahrenheit's thermometer4#efaj ,the thing here to be remarked1 is the establishment of a law of the pressure of steam1 down to the freezing-point of water4 ,ziegler of ,basle1 in #agfi1 and ,achard of ,berlin1 in #aghb1 made similar experiments4 ,the latter examined also the elasticity of the vapor of alcohol4 ,betancourt1 in #agib1 published his ,memoir on the expansive force of vapors2 and his tables were for some time considered the most exact4 #agd ,prony1 in his ,architecture ,hydraulique 7#agif71 established a mathematical formula1#egaj on the experiments of ,betancourt1 who began his researches in the belief that he was first in the field1 although he afterwards found that he had been anticipated by ,ziegler4 ,gren compared the experiments of ,betancourt and ,de ,luc with his own4 ,he ascertained an important fact1 that when water boils1 the elasticity of the steam is equal to that of the atmosphere4 ,schmidt at ,giessen endeavored to improve the apparatus used by ,betancourt2 and ,biker1 of ,rotterdam1 in #ahjj1 made new trials for the same purpose4 ,note #edaj3 ,robison's ,works1 vol4 ii4 p4 #aac4 ,note #eeaj3 ,denis ,papin1 who made many of ,boyle's experiments for him1 had discovered that if the vapor be prevented from rising1 the water becomes hotter than the usual boiling-point2 and had hence invented the instrument called ,papin's ,digester4 ,it is described in his book1 ,la manire d'amolir les os et de faire cuire toutes sorts de viandes en fort peu de temps et peu de frais4 ,paris1 #afhb4 ,note #efaj3 ,these were afterwards published in the ,encyclopdia ,britannica2 in the article ,steam1 written by ,robison4 ,note #egaj3 ,architecture ,hydraulique1 ,seconde ,partie1 p4 #afc4 ,in #ahja1 ,mr4 ,dalton communicated to the ,philosophical ,society of ,manchester his investigations on this subject2 observing truly1 that though the forces at high temperatures are most important when steam is considered as a mechanical agent1 the progress of philosophy is more immediately interested in accurate observations on the force at low temperatures4 ,he also found that his elasticities for equidistant temperatures resembled a geometrical progression1 but with a ratio constantly diminishing4 ,dr4 ,ure1 in #ahah1 published in the ,philosophical ,transactions of ,london1 experiments of the same kind1 valuable from the high temperatures at which they were made1 and for the simplicity of his apparatus4 ,the law which he thus obtained approached1 like ,dalton's1 to a geometrical progression4 ,dr4 ,ure says1 that a formula proposed by ,m4 ,biot gives an error of near nine inches out of seventy-five1 at a temperature of #bff degrees4 ,this is very conceivable1 for if the formula be wrong at all1 the geometrical progress rapidly inflames the error in the higher portions of the scale4 ,the elasticity of steam1 at high temperatures1 has also been experimentally examined by ,mr4 ,southern1 of ,soho1 and ,mr4 ,sharpe1 of ,manchester4 ,mr4 ,dalton has attempted to deduce certain general laws from ,mr4 ,sharpe's experiments2 and other persons have offered other rules1 as those which govern the force of steam with reference to the temperature3 but no rule appears yet to have assumed the character of an established scientific truth4 ,yet the law of the expansive force of steam is not only required in order that the steam-engine may be employed with safety and to the best advantage2 but must also be an important point in every consistent thermotical theory4 #bnd ,ed4 ,to the experiments on steam made by private physicists1 are to be added the experiments made on a grand scale by order of the governments of ,france and of ,america1 with a view to #age legislation on the subject of steam-engines4 ,the ,french experiments were made in #ahbc1 under the direction of a commission consisting of some of the most distinguished members of the ,academy of ,sciences2 namely1 ,,mm4 de ,prony1 ,arago1 ,girard1 and ,dulong4 ,the ,american experiments were placed in the hands of a committee of the ,franklin ,institute of the ,state of ,pennsylvania1 consisting of ,prof4 ,bache and others1 in #ahcj4 ,the ,french experiments went as high as #dce of ,fahrenheit's thermometer1 corresponding to a pressure of #fj feet of mercury1 or #bd atmospheres4 ,the ,american experiments were made up to a temperature of #cdf1 which corresponded to #bgd inches of mercury1 more than #i atmospheres4 ,the extensive range of these experiments affords great advantages for determining the law of the expansive force4 ,the ,french ,academy found that their experiments indicated an increase of the elastic force according to the fifth power of a binominal #a mt1 where t is the temperature4 ,the ,american ,institute were led to a sixth power of a like binominal4 ,other experimenters have expressed their results1 not by powers of the temperature1 but by geometrical ratios4 ,dr4 ,dalton had supposed that the expansion of mercury being as the square of the true temperature above its freezing-point1 the expansive force of steam increases in geometrical ratio for equal increments of temperature4 ,and the author of the article ,steam in the ,seventh ,edition of the ,encyclopdia ,britannica 7,mr4 ,j4 ,s4 ,russell71 has found that the experiments are best satisfied by supposing mercury1 as well as steam1 to expand in a geometrical ratio for equal increments of the true temperature4 ,it appears by such calculation1 that while dry gas increases in the ratio of #h to #aa1 by an increase of temperature from freezing to boiling water2 steam in contact with water1 by the same increase of temperature above boiling water1 has its expansive force increased in the proportion of #a to #ab4 ,by an equal increase of temperature1 mercury expands in about the ratio of #h to #i4 ,recently1 ,,mm4 ,magnus of ,berlin1 ,holzmann and ,regnault1 have made series of observations on the relation between temperature and elasticity of steam4#ehaj ,note #ehaj3 ,see ,taylor's ,scientific ,memoirs1 ,aug4 #ahde1 vol4 iv4 part xiv41 and ,ann4 de ,chimie4 ,prof4 ,magnus measured his temperatures by an air-thermometer2 a process which1 ,i stated in the first edition1 seemed to afford the best promise of simplifying the law of expansion4 ,his result is1 that the #agf elasticity proceeds in a geometric series when the temperature proceeds in an arithmetical series nearly2 the differences of temperature for equal augmentations of the ratio of elasticity being somewhat greater for the higher temperatures4 ,the forces of the vapors of other liquids in contact with their liquids1 determined by ,dr4 ,faraday1 as mentioned in ,chap4 ii4 ,sect4 #a1 are analogous to the elasticity of steam here spoken of4 ,sect4 #e4--;,consequences of the ,doctrine of ,evaporation4--,explanation of ,rain1 ,dew1 and ,clouds4 ,,the discoveries concerning the relations of heat and moisture which were made during the last century1 were principally suggested by meteorological inquiries1 and were applied to meteorology as fast as they rose4 ,still there remains1 on many points of this subject1 so much doubt and obscurity1 that we cannot suppose the doctrines to have assumed their final form2 and therefore we are not here called upon to trace their progress and connexion4 ,the principles of atmology are pretty well understood2 but the difficulty of observing the conditions under which they produce their effects in the atmosphere is so great1 that the precise theory of most meteorological phenomena is still to be determined4 ,we have already considered the answers given to the question3 ,according to what rules does transparent aqueous vapor resume its form of visible water8 ,this question includes1 not only the problems of ,rain and ,dew1 but also of ,clouds2 for clouds are not vapor1 but water1 vapor being always invisible4 ,an opinion which attracted much notice in its time1 was that of ,hutton1 who1 in #aghd1 endeavored to prove that if two masses of air saturated with transparent vapor at different temperatures are mixed together1 the precipitation of water in the form either of cloud or of drops will take place4 ,the reason he assigned for the opinion was this3 that the temperature of the mixture is a mean between the two temperatures1 but that the force of the vapor in the mixture1 which is the mean of the forces of the two component vapors1 will be greater than that which corresponds to the mean temperature1 since the force increases faster than the temperature2#eiaj and hence some part of the vapor will be precipitated4 ,this doctrine1 it will be seen1 speaks of vapor as saturating air1 and is #agg therefore1 in this form1 inconsistent with ,dalton's principle2 but it is not difficult to modify the expression so as to retain the essential part of the explanation4 ,note #eiaj3 ,edin4 ,trans4 vol4 #a4 p4 #db4 ,dew4--,the principle of a constituent temperature of steam1 and the explanation of the dew-point1 were known1 as we have said 7chap4 iii4 sect4 #c17 to the meteorologists of the last century2 but we perceive how incomplete their knowledge was1 by the very gradual manner in which the consequences of this principle were traced out4 ,we have already noticed1 as one of the books which most drew attention to the true doctrine1 in this country at least1 ,dr4 ,wells's ,essay on ,dew1 published in #ahad4 ,in this work the author gives an account of the progress of his opinions2#fjaj ,i was led1 he says1 in the autumn of #aghd1 by the event of a rude experiment1 to think it probable that the formation of dew is attended with the production of cold4 ,this was confirmed by the experiments of others4 ,but some years after1 upon considering the subject more closely1 ,i began to suspect that ,mr4 ,wilson1 ,mr4 ,six1 and myself1 had all committed an error in regarding the cold which accompanies the dew1 as an effect of the formation of the dew4 ,he now considered it rather as the cause3 and soon found that he was able to account for the circumstances of this formation1 many of them curious and paradoxical1 by supposing the bodies on which dew is deposited1 to be cooled down1 by radiation into the clear night-sky1 to the proper temperature4 ,the same principle will obviously explain the formation of mists over streams and lakes when the air is cooler than the water2 which was put forward by ,davy1 even in #ahaj1 as a new doctrine1 or at least not familiar4 ,note #fjaj3 ,essay on ,dew1 p4 #a4 ,hygrometers4--,according as air has more or less of vapor in comparison with that which its temperature and pressure enable it to contain1 it is more or less humid2 and an instrument which measures the degrees of such a gradation is a hygrometer4 ,the hygrometers which were at first invented1 were those which measured the moisture by its effect in producing expansion or contraction in certain organic substances2 thus ,de ,saussure devised a hair-hygrometer1 ,de ,luc a whalebone-hygrometer1 and ,dalton used a piece of whipcord4 ,all these contrivances were variable in the amount of their indications under the same circumstances2 and1 moreover1 it was not easy to know the physical meaning of the degree indicated4 ,the dew-point1 or constituent temperature of the vapor which exists in the air1 is1 on #agh the other hand1 both constant and definite4 ,the determination of this point1 as a datum for the moisture of the atmosphere1 was employed by ,le ,roi1 and by ,dalton 7#ahjb71 the condensation being obtained by cold water3#faaj and finally1 ,mr4 ,daniell 7#ahab7 constructed an instrument1 where the condensing temperature was produced by evaporation of ether1 in a very convenient manner4 ,this invention 7,daniell's ,hygrometer7 enables us to determine the quantity of vapor which exists in a given mass of the atmosphere at any time of observation4 ,note #faaj3 ,daniell1 ,met4 ,ess4 p4 #adb4 ,manch4 ,mem4 vol4 v4 p4 #eha4 #bnd ,ed4 ,as a happy application of the ,atmological ,laws which have been discovered1 ,i may mention the completion of the theory and use of the ,wet-bulb ,hygrometer2 an instrument in which1 from the depression of temperature produced by wetting the bulb of a thermometer1 we infer the further depression which would produce dew4 ,of this instrument the history is thus summed up by ,prof4 ,forbes3--,hutton invented the method2 ,leslie revived and extended it1 giving probably the earliest1 though an imperfect theory2 ,gay-,lussac1 by his excellent experiments and reasoning from them1 completed the theory1 so far as perfectly dry air is concerned2 ,ivory extended the theory2 which was reduced to practice by ,auguste and ,bohnenberger1 who determined the constant with accuracy4 ,english observers have done little more than confirm the conclusions of our industrious ,germanic neighbors2 nevertheless the experiments of ,apjohn and ,prinsep must ever be considered as conclusively settling the value of the coefficient near the one extremity of the scale1 as those of ,kmtz have done for the other4#fbaj ,note #fbaj3 ,second ,report on ,meteorology1 p4 #aja4 ,prof4 ,forbes's two ,reports ,on the ,recent ,progress and ,present ,state of ,meteorology given among the ,reports of the ,british ,association for #ahcb and #ahdj1 contain a complete and luminous account of recent researches on this subject4 ,it may perhaps be asked why ,i have not given ,meteorology a place among the ,inductive ,sciences2 but if the reader refers to these accounts1 or any other adequate view of the subject1 he will see that ,meteorology is not a single ,inductive ,science1 but the application of several sciences to the explanation of terrestrial and atmospheric phenomena4 ,of the sciences so applied1 ,thermotics and ,atmology are the principal ones4 ,but others also come into play2 as ,optics1 in the explanation of ,rainbows1 ,halos1 #agi ,parhelia1 ,coron1 ,glories1 and the like2 ,electricity1 in the explanation of ,thunder and ,lightning1 ,hail1 ,aurora ,borealis2 to which others might be added4 ,clouds4--,when vapor becomes visible by being cooled below its constituent temperature1 it forms itself into a very fine watery powder1 the diameter of the particles of which this powder consists being very small3 they are estimated by various writers1 from #aajj1jjjth to #abj1jjjth of an inch4#fcaj ,such particles1 even if solid1 would descend very slowly2 and very slight causes would suffice for their suspension1 without recurring to the hypothesis of vesicles1 of which we have already spoken4 ,indeed that hypothesis will not explain the fact1 except we suppose these vesicles filled with a rarer air than that of the atmosphere2 and1 accordingly1 though this hypothesis is still maintained by some1#fdaj it is asserted as a fact of observation1 proved by optical or other phenomena1 and not deduced from the suspension of clouds4 ,yet the latter result is still variously explained by different philosophers3 thus1 ,m4 ,gay-,lussac#feaj accounts for it by upward currents of air1 and ,fresnel explains it by the heat and rarefaction of air in the interior of the cloud4 ,note #fcaj3 ,kmtz1 ,met4 i4 #cic4 ,note #fdaj3 ,ib4 i4 #cic4 ,robison1 ii4 #ac4 ,note #feaj3 ,ann4 ,chim4 xxv4 #ahbb4 ,classification of ,clouds4--,a classification of clouds can then only be consistent and intelligible when it rests upon their atmological conditions4 ,such a system was proposed by ,mr4 ,luke ,howard1 in #ahjb-c4 ,his primary modifications are1 ,cirrus1 ,cumulus1 and ,stratus1 which the ,germans have translated by terms equivalent in ,english to feather-cloud1 heap-cloud1 and layer-cloud4 ,the cumulus increases by accumulations on its top1 and floats in the air with a horizontal base2 the stratus grows from below1 and spreads along the earth2 the cirrus consists of fibres in the higher regions of the atmosphere1 which grow every way4 ,between the simple modifications are intermediate ones1 cirro-cumulus and cirro-stratus2 and1 again1 compound ones1 the cumulo-stratus and the nimbus1 or rain-cloud4 ,these distinctions have been generally accepted all over ,europe3 and have rendered a description of all the processes which go on in the atmosphere far more definite and clear than it could be made before their use4 ,i omit a mass of facts and opinions1 supposed laws of phenomena and assigned causes1 which abound in meteorology more than in any other science4 ,the slightest consideration will show us what a great #ahj amount of labor1 of persevering and combined observation1 the progress of this branch of knowledge requires4 ,i do not even speak of the condition of the more elevated parts of the atmosphere4 ,the diminution of temperature as we ascend1 one of the most marked of atmospheric facts1 has been variously explained by different writers4 ,thus ,dalton#ffaj 7#ahjh7 refers it to a principle that each atom of air1 in the same perpendicular column1 is possessed of the same degree of heat1 which principle he conceives to be entirely empirical in this case4 ,fourier says#fgaj 7#ahag71 ,this phenomenon results from several causes3 one of the principal is the progressive extinction of the rays of heat in the successive strata of the atmosphere4 ,note #ffaj3 ,new ,syst4 of ,chem4 vol4 i4 p4 #abe4 ,note #fgaj3 ,ann4 ,chim4 vi4 #bhe4 ,leaving1 therefore1 the application of thermotical and atmological principles in particular cases1 let us consider for a moment the general views to which they have led philosophers4 ,,chapter ,,iv4 ,,physical ,,theories ,,of ,,heat4 ,,when we look at the condition of that branch of knowledge which1 according to the phraseology already employed1 we must call ,physical ,thermotics1 in opposition to ,formal ,thermotics1 which gives us detached laws of phenomena1 we find the prospect very different from that which was presented to us by physical astronomy1 optics1 and acoustics4 ,in these sciences1 the maintainers of a distinct and comprehensive theory have professed at least to show that it explains and includes the principal laws of phenomena of various kinds2 in ,thermotics1 we have only attempts to explain a part of the facts4 ,we have here no example of an hypothesis which1 assumed in order to explain one class of phenomena1 has been found also to account exactly for another2 as when central forces led to the precession of the equinoxes1 or when the explanation of polarization explained also double refraction2 or when the pressure of the atmosphere1 as measured by the barometer1 gave the true velocity of sound4 ,such coincidences1 or consiliences1 as ,i have elsewhere called them1 are the test of truth2 and thermotical theories cannot yet exhibit credentials of this kind4 #aha ,on looking back at our view of this science1 it will be seen that it may be distinguished into two parts2 the ,doctrines of ,conduction and ,radiation1 which we call ,thermotics proper2 and the ,doctrines respecting the relation of ,heat1 ,airs1 and ,moisture1 which we have termed ,atmology4 ,these two subjects differ in their bearing on our hypothetical views4 ,thermotical ,theories4--,the phenomena of radiant heat1 like those of radiant light1 obviously admit of general explanation in two different ways2--by the emission of material particles1 or by the propagation of undulations4 ,both these opinions have found supporters4 ,probably most persons1 in adopting ,prevost's theory of exchanges1 conceive the radiation of heat to be the radiation of matter4 ,the undulation hypothesis1 on the other hand1 appears to be suggested by the production of heat by friction1 and was accordingly maintained by ,rumford and others4 ,leslie#fhaj appears1 in a great part of his ,inquiry1 to be a supporter of some undulatory doctrine1 but it is extremely difficult to make out what his undulating medium is2 or rather1 his opinions wavered during his progress4 ,in page #ca1 he asks1 ,what is this calorific and frigorific fluid8 and after keeping the reader in suspense for a moment1 he replies1 ,quod petis hic est4 ,it is merely the ambient ,,air4 ,but at page #aej1 he again asks the question1 and1 at page #ahh1 he answers1 ,it is the same subtile matter that1 according to its different modes of existence1 constitutes either heat or light4 ,a person thus vacillating between two opinions1 one of which is palpably false1 and the other laden with exceeding difficulties which he does not even attempt to remove1 had little right to protest against#fiaj the sportive freaks of some intangible aura2 to rank all other hypotheses than his own with the occult qualities of the schools2 and to class the prejudices of his opponents with the tenets of those who maintained the fuga vacui in opposition to ,torricelli4 ,it is worth while noticing this kind of rhetoric1 in order to observe1 that it may be used just as easily on the wrong side as on the right4 ,note #fhaj3 ,an ,experimental ,inquiry into the ,nature and ,propagation of ,heat1 #ahjd4 ,note #fiaj3 ,ib4 p4 #dg4 ,till recently1 the theory of material heat1 and of its propagation by emission1 was probably the one most in favor with those who had studied mathematical thermotics4 ,as we have said1 the laws of #ahb conduction1 in their ultimate analytical form1 were almost identical with the laws of motion of fluids4 ,fourier's principle also1 that the radiation of heat takes place from points below the surface1 and is intercepted by the superficial particles1 appears to favor the notion of material emission4 ,accordingly1 some of the most eminent modern ,french mathematicians have accepted and extended the hypothesis of a material caloric4 ,in addition to ,fourier's doctrine of molecular extra-radiation1 ,laplace and ,poisson have maintained the hypothesis of molecular intra-radiation1 as the mode in which conduction takes place2 that is1 they say that the particles of bodies are to be considered as discrete1 or as points separated from each other1 and acting on each other at a distance2 and the conduction of heat from one part to another1 is performed by radiation between all neighboring particles4 ,they hold that1 without this hypothesis1 the differential equations expressing the conditions of conduction cannot be made homogeneous3 but this assertion rests1 ,i conceive1 on an error1 as ,fourier has shown1 by dispensing with the hypothesis4 ,the necessity of the hypothesis of discrete molecular action in bodies1 is maintained in all cases by ,m4 ,poisson2 and he has asserted ,laplace's theory of capillary attraction to be defective on this ground1 as ,laplace asserted ,fourier's reasoning respecting heat to be so4 ,in reality1 however1 this hypothesis of discrete molecules cannot be maintained as a physical truth2 for the law of molecular action1 which is assumed in the reasoning1 after answering its purpose in the progress of calculation1 vanishes in the result2 the conclusion is the same1 whatever law of the intervals of the molecules be assumed4 ,the definite integral1 which expresses the whole action1 no more proves that this action is actually made of the differential parts by means of which it was found1 than the processes of finding the weight of a body by integration1 prove it to be made up of differential weights4 ,and therefore1 even if we were to adopt the emission theory of heat1 we are by no means bound to take along with it the hypothesis of discrete molecules4 ,but the recent discovery of the refraction1 polarization1 and depolarization of heat1 has quite altered the theoretical aspect of the subject1 and1 almost at a single blow1 ruined the emission theory4 ,since heat is reflected and refracted like light1 analogy would lead us to conclude that the mechanism of the processes is the same in the two cases4 ,and when we add to these properties the property of polarization1 it is scarcely possible to believe otherwise than that heat consists in #ahc transverse vibrations2 for no wise philosopher would attempt an explanation by ascribing poles to the emitted particles1 after the experience which ,optics affords1 of the utter failure of such machinery4 ,but here the question occurs1 ,if heat consists in vibrations1 whence arises the extraordinary identity of the laws of its propagation with the laws of the flow of matter8 ,how is it that1 in conducted heat1 this vibration creeps slowly from one part of the body to another1 the part first heated remaining hottest2 instead of leaving its first place and travelling rapidly to another1 as the vibrations of sound and light do8 ,the answer to these questions has been put in a very distinct and plausible form by that distinguished philosopher1 ,m4 ,ampre1 who published a ,note on ,heat and ,light considered as the results of ,vibratory ,motion1#gjaj in #ahcd and #ahce2 and though this answer is an hypothesis1 it at least shows that there is no fatal force in the difficulty4 ,note #gjaj3 ,bibliothque ,universelle de ,genve1 vol4 xlix4 p4 #bbe4 ,ann4 ,chim4 tom4 lvii4 p4 #dcd4 ,m4 ,ampre's hypothesis is this2 that bodies consist of solid molecules1 which may be considered as arranged at intervals in a very rare ether2 and that the vibrations of the molecules1 causing vibrations of the ether and caused by them1 constitute heat4 ,on these suppositions1 we should have the phenomena of conduction explained2 for if the molecules at one end of a bar be hot1 and therefore in a state of vibration1 while the others are at rest1 the vibrating molecules propagate vibrations in the ether1 but these vibrations do not produce heat1 except in proportion as they put the quiescent molecules of the bar in vibration2 and the ether being very rare compared with the molecules1 it is only by the repeated impulses of many successive vibrations that the nearest quiescent molecules are made to vibrate2 after which they combine in communicating the vibration to the more remote molecules4 ,we then find necessarily1 ,m4 ,ampre adds1 the same equations as those found by ,fourier for the distribution of heat1 setting out from the same hypothesis1 that the temperature or heat transmitted is proportional to the difference of the temperatures4 ,since the undulatory hypothesis of heat can thus answer all obvious objections1 we may consider it as upon its trial1 to be confirmed or modified by future discoveries2 and especially by an enlarged knowledge of the laws of the polarization of heat4 #bnd ,ed4 ,since the first edition was written1 the analogies between light and heat have been further extended1 as ,i have already stated4 ,it #ahd has been discovered by ,,mm4 ,biot and ,melloni that quartz impresses a circular polarization upon heat2 and by ,prof4 ,forbes that mica1 of a certain thickness1 produces phenomena such as would be produced by the impression of circular polarization of the supposed transversal vibrations of radiant heat2 and further1 a rhomb of rock-salt1 of the shape of the glass rhomb which verified ,fresnel's extraordinary anticipation of the circular polarization of light1 verified the expectation1 founded upon other analogies1 of the polarization of heat4 ,by passing polarized heat through various thicknesses of mica1 ,prof4 ,forbes has attempted to calculate the length of an undulation for heat4 ,these analogies cannot fail to produce a strong disposition to believe that light and heat1 essences so closely connected that they can hardly be separated1 and thus shown to have so many curious properties in common1 are propagated by the same machinery2 and thus we are led to an ,undulatory ,theory of ,heat4 ,yet such a ,theory has not yet by any means received full confirmation4 ,it depends upon the analogy and the connexion of the ,theory of ,light1 and would have little weight if those were removed4 ,for the separation of the rays in double refraction1 and the phenomena of periodical intensity1 the two classes of facts out of which the ,undulatory ,theory of ,optics principally grew1 have neither of them been detected in thermotical experiments4 ,prof4 ,forbes has assumed alternations of heat for increasing thicknesses of mica1 but in his experiments we find only one maximum4 ,the occurrence of alternate maxima and minima under the like circumstances would exhibit visible waves of heat1 as the fringes of shadows do of light1 and would thus add much to the evidence of the theory4 ,even if ,i conceived the ,undulatory ,theory of ,heat to be now established1 ,i should not venture1 as yet1 to describe its establishment as an event in the history of the ,inductive ,sciences4 ,it is only at an interval of time after such events have taken place that their history and character can be fully understood1 so as to suggest lessons in the ,philosophy of ,science4 ,atmological ,theories4--,hypotheses of the relations of heat and air almost necessarily involve a reference to the forces by which the composition of bodies is produced1 and thus cannot properly be treated of1 till we have surveyed the condition of chemical knowledge4 ,but we may say a few words on one such hypothesis2 ,i mean the hypothesis on the subject of the atmological laws of heat1 proposed by ,laplace1 in the twelfth ,book of the ,mcanique ,clste1 and published in #ahbc4 #ahe ,it will be recollected that the main laws of phenomena for which we have to account1 by means of such an hypothesis1 are the following3-- 7#a47 ,the law of ,boyle and ,mariotte1 that the elasticity of an air varies as its density4 ,see ,chap4 iii41 ,sect4 #a of this ,book4 7#b47 ,the ,law of ,gay-,lussac and ,dalton1 that all airs expand equally by heat4 ,see ,chap4 ii4 ,sect4 #a4 7#c47 ,the production of heat by sudden compression4 ,see ,chap4 ii4 ,sect4 #b4 7#d47 ,dalton's principle of the mechanical mixture of airs4 ,see ,chap4 iii4 ,sect4 #c4 7#e47 ,the ,law of expansion of solids and fluids by heat4 ,see ,chap4 ii4 ,sect4 #a4 7#f47 ,changes of consistence by heat1 and the doctrine of latent heat4 ,see ,chap4 ii4 ,sect4 #c4 7#g47 ,the ,law of the expansive force of steam4 ,see ,chap4 iii4 ,sect4 #d4 ,besides these1 there are laws of which it is doubtful whether they are or are not included in the preceding1 as the low temperature of the air in the higher parts of the atmosphere4 7,see ,chap4 iii4 ,sect4 #e47 ,laplace's hypothesis#gaaj is this3--that bodies consist of particles1 each of which gathers round it1 by its attraction1 a quantity of caloric3 that the particles of the bodies attract each other1 besides attracting the caloric1 and that the particles of the caloric repel each other4 ,note #gaaj3 ,mc4 ,cl4 t4 v4 p4 #hi4 ,in gases1 the particles of the bodies are so far removed1 that their mutual attraction is insensible1 and the matter tends to expand by the mutual repulsion of the caloric4 ,he conceives this caloric to be constantly radiating among the particles2 the density of this internal radiation is the temperature1 and he proves that1 on this supposition1 the elasticity of the air will be as the density1 and as this temperature4 ,hence follow the three first rules above stated4 ,the same suppositions lead to ,dalton's principle of mixtures 7#d71 though without involving his mode of conception2 for ,laplace says that whatever the mutual action of two gases be1 the whole pressure will be equal to the sum of the separate pressures4#gbaj ,expansion 7#e71 and the changes of consistence 7#f71 are explained by supposing#gcaj that in solids1 the mutual attraction of the particles of the body is the greatest force2 in liquids1 the attraction of the particles for the caloric2 in airs1 the repulsion of #ahf the caloric4 ,but the doctrine of latent heat again modifies#gdaj the hypothesis1 and makes it necessary to include latent heat in the calculation2 yet there is not1 as we might suppose there would be if the theory were the true one1 any confirmation of the hypothesis resulting from the new class of laws thus referred to4 ,nor does it appear that the hypothesis accounts for the relation between the elasticity and the temperature of steam4 ,note #gbaj3 ,ib4 p4 #aaj4 ,note #gcaj3 ,ib4 p4 #ib4 ,note #gdaj3 ,mc4 ,cl4 t4 v4 p4 #ic4 ,it will be observed that ,laplace's hypothesis goes entirely upon the materiality of heat1 and is inconsistent with any vibratory theory2 for1 as ,ampre remarks1 ,it is clear that if we admit heat to consist in vibrations1 it is a contradiction to attribute to heat 7or caloric7 a repulsive force of the particles which would be a cause of vibration4 ,an unfavorable judgment of ,laplace's ,theory of ,gases is suggested by looking for that which1 in speaking of ,optics1 was mentioned as the great characteristic of a true theory2 namely1 that the hypotheses1 which were assumed in order to account for one class of facts1 are found to explain another class of a different nature3--the consilience of inductions4 ,thus1 in thermotics1 the law of an intensity of radiation proportional to the sine of the angle of the ray with the surface1 which is founded on direct experiments of radiation1 is found to be necessary in order to explain the tendency of neighboring bodies to equality of temperature2 and this leads to the higher generalization1 that heat is radiant from points below the surface4 ,but in the doctrine of the relation of heat to gases1 as delivered by ,laplace1 there is none of this unexpected confirmation2 and though he explains some of the leading laws1 his assumptions bear a large proportion to the laws explained4 ,thus1 from the assumption that the repulsion of gases arises from the mutual repulsion of the particles of caloric1 he finds that the pressure in any gas is as the square of the density and of the quantity of caloric2#geaj and from the assumption that the temperature is the internal radiation1 he finds that this temperature is as the density and the square of the caloric4#gfaj ,hence he obtains the law of ,boyle and ,mariotte1 and that of ,dalton and ,gay-,lussac4 ,but this view of the subject requires other assumptions when we come to latent heat2 and accordingly1 he introduces1 to express the latent heat1 a new quantity4#ggaj ,yet this quantity produces no effect on his calculations1 nor does he apply his reasoning to any problem in which latent heat is concerned4 #ahg ,note #geaj3 ,p #b ,h ,k #b;c#b 7#a7 p4 #ajg4 ,note #gfaj3 q' 7a7 c#b 7#b7 p4 #ajh4 ,note #ggaj3 ,the quantity i1 p4 #aac4 ,without1 then1 deciding upon this theory1 we may venture to say that it is wanting in all the prominent and striking characteristics which we have found in those great theories which we look upon as clearly and indisputably established4 ,conclusion4--,we may observe1 moreover1 that heat has other bearings and effects1 which1 as soon as they have been analysed into numerical laws of phenomena1 must be attended to in the formation of thermotical theories4 ,chemistry will probably supply many such2 those which occur to us1 we must examine hereafter4 ,but we may mention as examples of such1 ,,mm4 ,de la ,rive and ,marcet's law1 that the specific heat of all gases is the same2#ghaj and ,,mm4 ,dulong and ,petit's law1 that single atoms of all simple bodies have the same capacity for heat4#giaj ,though we have not yet said anything of the relation of different gases1 or explained the meaning of atoms in the chemical sense1 it will easily be conceived that these are very general and important propositions4 ,note #ghaj3 ,ann4 ,chim4 xxxv4 7#ahbg47 ,note #giaj3 ,ib4 x4 #cig4 ,thus the science of ,thermotics1 imperfect as it is1 forms a highly-instructive part of our survey2 and is one of the cardinal points on which the doors of those chambers of physical knowledge must turn which hitherto have remained closed4 ,for1 on the one hand1 this science is related by strong analogies and dependencies to the most complete portions of our knowledge1 our mechanical doctrines and optical theories2 and on the other1 it is connected with properties and laws of a nature altogether different1--those of chemistry2 properties and laws depending upon a new system of notions and relations1 among which clear and substantial general principles are far more difficult to lay hold of and with which the future progress of human knowledge appears to be far more concerned4 ,to these notions and relations we must now proceed2 but we shall find an intermediate stage1 in certain subjects which ,i shall call the ,mechanico-chemical ,sciences2 viz41 those which have to do with ,magnetism1 ,electricity1 and ,galvanism4 #ahi ,,book ,,xi4 ,,the ,,mechanico-,,chemical ,,sciences4 ,,history ,,of ,,electricity4 ,,parva metu primo3 mox sese extollit in auras1 ,ingrediturque solo1 et caput inter nubila condit4 n4 iv4 #agf4 ,a timid breath at first1 a transient touch1 ,how soon it swells from little into much6 ,runs o'er the ground1 and springs into the air1 ,and fills the tempest's gloom1 the lightning's glare2 ,while denser darkness than the central storm ,conceals the secrets of its inward form4 #aia ,,introduction4 ,of the ,mechanico-,chemical ,sciences4 ,,under the title of ,mechanico-,chemical ,sciences1 ,i include the laws of ,magnetism1 ,electricity1 ,galvanism1 and the other classes of phenomena closely related to these1 as ,thermo-electricity4 ,this group of subjects forms a curious and interesting portion of our physical knowledge2 and not the least of the circumstances which give them their interest1 is that double bearing upon mechanical and chemical principles1 which their name is intended to imply4 ,indeed1 at first sight they appear to be purely ,mechanical ,sciences2 the attractions and repulsions1 the pressure and motion1 which occur in these cases1 are referrible to mechanical conceptions and laws1 as completely as the weight or fall of terrestrial bodies1 or the motion of the moon and planets4 ,and if the phenomena of magnetism and electricity had directed us only to such laws1 the corresponding sciences must have been arranged as branches of mechanics4 ,but we find that1 on the other side1 these phenomena have laws and bearings of a kind altogether different4 ,magnetism is associated with ,electricity by its mechanical analogies2 and1 more recently1 has been discovered to be still more closely connected with it by physical influence2 electric is identified with galvanic agency2 but in galvanism1 decomposition1 or some action of that kind1 universally appears2 and these appearances lead to very general laws4 ,now composition and decomposition are the subjects of ,chemistry2 and thus we find that we are insensibly but irresistibly led into the domain of that science4 ,the highest generalizations to which we can look1 in advancing from the elementary facts of electricity and galvanism1 must involve chemical notions2 we must therefore1 in laying out the platform of these sciences1 make provision for that convergence of mechanical and chemical theory1 which they are to exhibit as we ascend4 ,we must begin1 however1 with stating the mechanical phenomena of these sciences1 and the reduction of such phenomena to laws4 ,in this point of view1 the phenomena of which we have to speak are those in which bodies exhibit attractions and repulsions1 peculiarly determined by their nature and circumstances2 as the magnet1 and a #aib piece of amber when rubbed4 ,such results are altogether different from the universal attraction which1 according to ,newton's discovery1 prevails among all particles of matter1 and to which cosmical phenomena are owing4 ,but yet the difference of these special attractions1 and of cosmical attraction1 was at first so far from being recognized1 that the only way in which men could be led to conceive or assent to an action of one body upon another at a distance1 in cosmical cases1 was by likening it to magnetic attraction1 as we have seen in the history of ,physical ,astronomy4 ,and we shall1 in the first part of our account1 not dwell much upon the peculiar conditions under which bodies are magnetic or electric1 since these conditions are not readily reducible to mechanical laws2 but1 taking the magnetic or electric character for granted1 we shall trace its effects4 ,the habit of considering magnetic action as the type or general case of attractive and repulsive agency1 explains the early writers having spoken of ,electricity as a kind of ,magnetism4 ,thus ,gilbert1 in his book ,de ,magnete 7#afjj71 has a chapter1#aaa ,de coitione ,magnitic1 primumque de ,succini attractione1 sive verius corporum ad ,succinum applicatione4 ,the manner in which he speaks1 shows us how mysterious the fact of attraction then appeared2 so that1 as he says1 the magnet and amber were called in aid by philosophers as illustrations1 when our sense is in the dark in abstruse inquiries1 and when our reason can go no further4 ,gilbert speaks of these phenomena like a genuine inductive philosopher1 reproving#baa those who before him had stuffed the booksellers' shops by copying from one another extravagant stories concerning the attraction of magnets and amber1 without giving any reason from experiment4 ,he himself makes some important steps in the subject4 ,he distinguishes magnetic from electric forces1#caa and is the inventor of the latter name1 derived from 1 electron1 amber4 ,he observes rightly1 that the electric force attracts all light bodies1 while the magnetic force attracts iron only2 and he devises a satisfactory apparatus by which this is shown4 ,he gives#daa a considerable list of bodies which possess the electric property2 ,not only amber and agate attract small bodies1 as some think1 but diamond1 sapphire1 carbuncle1 opal1 amethyst1 ,bristol gem1 beryli1 crystal1 glass1 glass of antimony1 spar of various kinds1 sulphur1 mastic1 sealing-wax1 and other substances which he mentions4 ,even his speculations on the general laws of these phenomena1 though vague and erroneous1 as #aic at that period was unavoidable1 do him no discredit when compared with the doctrines of his successors a century and a half afterwards4 ,but such speculations belong to a succeeding part of this history4 ,note #aaa3 ,lib4 ii4 cap4 #b4 ,note #baa3 ,de ,magnete1 p4 #dh4 ,note #caa3 ,ib4 p4 #eb4 ,note #daa3 ,ib4 p4 #dh4 ,in treating of these ,sciences1 ,i will speak of ,electricity in the first place2 although it is thus separated by the interposition of ,magnetism from the succeeding subjects 7,galvanism1 c47 with which its alliance seems1 at first sight1 the closest1 and although some general notions of the laws of magnets were obtained at an earlier period than a knowledge of the corresponding relations of electric phenomena3 for the theory of electric attraction and repulsion is somewhat more simple than of magnetic2 was1 in fact1 the first obtained2 and was of use in suggesting and confirming the generalization of magnetic laws4 ,,chapter #a4 ,,discovery ,,of ,,laws ,,of ,,electric ,,phenomena4 ,,we have already seen what was the state of this branch of knowledge at the beginning of the seventeenth century2 and the advances made by ,gilbert4 ,we must now notice the additions which it subsequently received1 and especially those which led to the discovery of general laws1 and the establishment of the theory2 events of this kind being those of which we have more peculiarly to trace the conditions and causes4 ,among the facts which we have thus especially to attend to1 are the electric attractions of small bodies by amber and other substances when rubbed4 ,boyle1 who repeated and extended the experiments of ,gilbert1 does not appear to have arrived at any new general notions2 but ,otto ,guericke of ,magdeburg1 about the same time1 made a very material step1 by discovering that there was an electric force of repulsion as well as of attraction4 ,he found that when a globe of sulphur had attracted a feather1 it afterwards repelled it1 till the feather had been in contact with some other body4 ,this1 when verified under a due generality of circumstances1 forms a capital fact in our present subject4 ,hawkesbee1 who wrote in #agji 7,physico-,mechanical ,experiments7 also observed various of the effects of attraction and repulsion upon threads hanging loosely4 ,but the person who appears to have first fully seized the general law of these facts1 is #aid ,dufay1 whose experiments appear in the ,memoirs of the ,french ,academy1 in #agcc1 #agcd1 and #agcg4eaa ,i discovered1 he says1 a very simple principle1 which accounts for a great part of the irregularities1 and1 if ,i may use the term1 the caprices that seem to accompany most of the experiments in electricity4 ,this principle is1 that electric bodies attract all those that are not so1 and repel them as soon as they are become electric by the vicinity or contact of the electric body4 4 4 4 ,upon applying this principle to various experiments of electricity1 any one will be surprised at the number of obscure and puzzling facts which it clears up4 ,by the help of this principle1 he endeavors to explain several of ,hawkesbee's experiments4 ,note #eaa3 ,priestley's ,history of ,electricity1 p4 #de1 and the ,memoirs quoted4 ,a little anterior to ,dufay's experiments were those of ,grey1 who1 in #agbi1 discovered the properties of conductors4 ,he found that the attraction and repulsion which appear in electric bodies are exhibited also by other bodies in contact with the electric4 ,in this manner he found that an ivory ball1 connected with a glass tube by a stick1 a wire1 or a packthread1 attracted and repelled a feather1 as the glass itself would have done4 ,he was then led to try to extend this communication to considerable distances1 first by ascending to an upper window and hanging down his ball1 and1 afterwards1 by carrying the string horizontally supported on loops4 ,as his success was complete in the former case1 he was perplexed by failure in the latter2 but when he supported the string by loops of silk instead of hempen cords1 he found it again become a conductor of electricity4 ,this he ascribed at first to the smaller thickness of the silk1 which did not carry off so much of the electric virtue2 but from this explanation he was again driven1 by finding that wires of brass still thinner than the silk destroyed the effect4 ,thus ,grey perceived that the efficacy of the support depended on its being silk1 and he soon found other substances which answered the same purpose4 ,the difference1 in fact1 depended on the supporting substance being electric1 and therefore not itself a conductor2 for it soon appeared from such experiments1 and especially#faa from those made by ,dufay1 that substances might be divided into electrics per se1 and non-electrics1 or conductors4 ,these terms were introduced by ,desaguliers1#gaa and gave a permanent currency to the results of the labors of ,grey and others4 ,note #faa3 ,mm4 ,acad4 ,par4 #agcd4 ,note #gaa3 ,priestley1 p4 #ff4 ,another very important discovery belonging to this period is1 that #aie of the two kinds of electricity4 ,this also was made by ,dufay4 ,chance1 says he1 has thrown in my way another principle more universal and remarkable than the preceding one1 and which casts a new light upon the subject of electricity4 ,the principle is1 that there are two distinct kinds of electricity1 very different from one another2 one of which ,i call vitreous1 the other resinous1 electricity4 ,the first is that of glass1 gems1 hair1 wool1 c42 the second is that of amber1 gum-lac1 silk1 c4 ,the characteristic of these two electricities is1 that they repel themselves and attract each other4 ,this discovery does not1 however1 appear to have drawn so much attention as it deserved4 ,it was published in #agce2 7in the ,memoirs of the ,academy for #agcc27 and yet in #agdg1 ,franklin and his friends at ,philadelphia1 who had been supplied with electrical apparatus and information by persons in ,england well acquainted with the then present state of the subject1 imagined that they were making observations unknown to ,european science1 when they were led to assert two conditions of bodies1 which were in fact the opposite electricities of ,dufay1 though the ,american experimenters referred them to a single element1 of which electrized bodies might have either excess or defect4 ,hence1 ,franklin says1 have arisen some new terms among us3 we say ,b1 who receives a spark from glass1 and bodies in like circumstances1 is electrized positively2 ,a1 who communicates his electricity to glass1 negatively2 or rather ,b is electrized plus1 ,a minus4 ,dr4 7afterwards ,sir ,william7 ,watson had1 about the same time1 arrived at the same conclusions1 which he expresses by saying that the electricity of ,a was more rare1 and that of ,b more dense1 than it naturally would have been4#haa ,but that which gave the main importance to this doctrine was its application to some remarkable experiments1 of which we must now speak4 ,note #haa3 ,priestley1 p4 #aae4 ,electric action is accompanied1 in many cases1 by light and a crackling sound4 ,otto ,guericke#iaa observes that his sulphur-globe1 when rubbed in a dark place1 gave faint flashes1 such as take place when sugar is crushed4 ,and shortly after1 a light was observed at the surface of the mercury in the barometer1 when shaken1 which was explained at first by ,bernoulli1 on the then prevalent ,cartesian principles2 but1 afterwards1 more truly by ,hawkesbee1 as an electrical phenomenon4 ,wall1 in #agjh1 found sparks produced by rubbing amber1 and ,hawkesbee observed the light and the snapping1 as he calls it1 under various modifications4 ,but the electric spark from a living body1 which1 as #aif ,priestley says1#ajaa makes a principal part of the diversion of gentlemen and ladies who come to see experiments in electricity1 was first observed by ,dufay and the ,abb ,nollet4 ,nollet says#aaaa he shall never forget the surprise which the first electric spark ever drawn from the human body excited1 both in ,m4 ,dufay and in himself4 ,the drawing of a spark from the human body was practised in various forms1 one of which was familiarly known as the electrical kiss4 ,other exhibitions of electrical light were the electrical star1 electrical rain1 and the like4 ,note #iaa3 ,experimenta ,magdeburgica1 #afgb1 lib4 iv4 cap4 #ae4 ,note #ajaa3 ,p4 p4 #dg4 ,note #aaaa3 ,priestley1 p4 #dg4 ,nollet1 ,leons de ,physique1 vol4 vi4 p4 #djh4 ,as electricians determined more exactly the conditions of electrical action1 they succeeded in rendering more intense those sudden actions which the spark accompanies1 and thus produced the electric shock4 ,this was especially done in the ,leyden phial4 ,this apparatus received its name1 while the discovery of its property was attributed to ,cunus1 a native of ,leyden1 who1 in #agdf1 handling a vessel containing water in communication with the electrical machine1 and happening thus to bring the inside and the outside into connexion1 received a sudden shock in his arms and breast4 ,it appears1 however1#abaa that a shock had been received under nearly the same circumstances in #agdf1 by ,von ,kleist1 a ,german prelate1 at ,camin1 in ,pomerania4 ,the strangeness of this occurrence1 and the suddenness of the blow1 much exaggerated the estimate which men formed of its force4 ,muschenbroek1 after taking one shock1 declared he would not take a second for the kingdom of ,france2 though ,boze1 with a more magnanimous spirit1 wished#acaa that he might die by such a stroke1 and have the circumstances of the experiment recorded in the ,memoirs of the ,academy4 ,but we may easily imagine what a new fame and interest this discovery gave to the subject of electricity4 ,it was repeated in all parts of the world1 with various modifications3 and the shock was passed through a line of several persons holding hands2 ,nollet1 in the presence of the king of ,france1 sent it through a circle of #ahj men of the guards1 and along a line of men and wires of #ijj toises2#adaa and experiments of the same kind were made in ,england1 principally under the direction of ,watson1 on a scale so large as to excite the admiration of ,muschenbroek2 who says1 in a letter to ,watson1 ,magnificentissimis tuis experimentis superasti conatus omnium4 ,the result was1 that the transmission of electricity through a length of #ab1jjj feet was1 to sense1 instantaneous4 #aig ,note #abaa3 ,fischer1 v4 #dij4 ,note #acaa3 ,fischer1 p4 #hd4 ,note #adaa3 ,ibid4 v4 #eab4 ,the essential circumstances of the electric shock were gradually unravelled4 ,watson found that it did not increase in proportion either to the contents of the phial or the size of the globe by which the electricity was excited2 that the outside coating of the glass 7which1 in the first form of the experiment1 was only a film of water71 and its contents1 might be varied in different ways4 ,to ,franklin is due the merit of clearly pointing out most of the circumstances on which the efficacy of the ,leyden phial depends4 ,he showed1 in #agdg1aeaa that the inside of the bottle is electrized positively1 the outside negatively2 and that the shock is produced by the restoration of the equilibrium1 when the outside and inside are brought into communication suddenly4 ,but in order to complete this discovery1 it remained to be shown that the electric matter was collected entirely at the surface of the glass1 and that the opposite electricities on the two opposite sides of the glass were accumulated by their mutual attraction4 ,monnier the younger discovered that the electricity which bodies can receive1 depends upon their surface rather than their mass1 and ,franklin#afaa soon found that the whole force of the bottle1 and power of giving a shock1 is in the glass itself4 ,this they proved by decanting the water out of an electrized into another bottle1 when it appeared that the second bottle did not become electric1 but the first remained so4 ,thus it was found that the non-electrics1 in contact with the glass1 served only to unite the force of the several parts4 ,note #aeaa3 ,letters1 p4 #ac4 ,note #afaa3 ,letters1 iv4 ,sect4 #af4 ,so far as the effect of the coating of the ,leyden phial is concerned1 this was satisfactory and complete3 but ,franklin was not equally successful in tracing the action of the electric matter upon itself1 in virtue of which it is accumulated in the phial2 indeed1 he appears to have ascribed the effect to some property of the glass4 ,the mode of describing this action varied1 accordingly as two electric fluids were supposed 7with ,dufay17 or one1 which was the view taken by ,franklin4 ,on this latter supposition the parts of the electric fluid repel each other1 and the excess in one surface of the glass expels the fluid from the other surface4 ,this kind of action1 however1 came into much clearer view in the experiments of ,canton1 ,wilcke1 and pinus4 ,it was principally manifested in the attractions and repulsions which objects exert when they are in the neighborhood of electrized bodies2 or in the electrical atmosphere1 using the phraseology of the time4 ,at present we say that bodies are electrized by induction1 when they are #aih thus made electric by the electric attraction and repulsion of other bodies4 ,canton's experiments were communicated to the ,royal ,society in #agec1 and show that the electricity on each body acts upon the electricity of another body1 at a distance1 with a repulsive energy4 ,wilcke1 in like manner1 showed that parts of non-electrics1 plunged in electric atmospheres1 acquire an electricity opposite to that of such atmospheres4 ,and pinus devised a method of examining the nature of the electricity at any part of the surface of a body1 by means of which he ascertained its distribution1 and found that it agreed with such a law of self-repulsion4 ,his attempt to give mathematical precision to this induction was one of the most important steps towards electrical theory1 and must be spoken of shortly1 in that point of view4 ,but in the mean time we may observe1 that this doctrine was applied to the explanation of the ,leyden jar2 and the explanation was confirmed by charging a plate of air1 and obtaining a shock from it1 in a manner which the theory pointed out4 ,before we proceed to the history of the theory1 we must mention some other of the laws of phenomena which were noticed1 and which theory was expected to explain4 ,among the most celebrated of these1 were the effect of sharp points in conductors1 and the phenomena of electricity in the atmosphere4 ,the former of these circumstances was one of the first which ,franklin observed as remarkable4 ,it was found that the points of needles and the like throw off and draw off the electric virtue2 thus a bodkin1 directed towards an electrized ball1 at six or eight inches' distance1 destroyed its electric action4 ,the latter subject1 involving the consideration of thunder and lightning1 and of many other meteorological phenomena1 excited great interest4 ,the comparison of the electric spark to lightning had very early been made2 but it was only when the discharge had been rendered more powerful in the ,leyden jar1 that the comparison of the effects became very plausible4 ,franklin1 about #agej1 had offered a few somewhat vague conjectures#agaa respecting the existence of electricity in the clouds2 but it was not till ,wilcke and pinus had obtained clear notions of the effect of electric matter at a distance1 that the real condition of the clouds could be well understood4 ,in #ageb1 however1#ahaa ,d',alibard1 and other ,french philosophers1 were desirous of verifying ,franklin's conjecture of the analogy of thunder and electricity4 ,this they did by erecting a pointed iron rod1 forty feet high1 #aii at ,marli3 the rod was found capable of giving out electrical sparks when a thunder-cloud passed over the place4 ,this was repeated in various parts of ,europe1 and ,franklin suggested that a communication with the clouds might be formed by means of a kite4 ,by these1 and similar means1 the electricity of the atmosphere was studied by ,canton in ,england1 ,mazeas in ,france1 ,beccaria in ,italy1 and others elsewhere4 ,these essays soon led to a fatal accident1 the death of ,richman at ,petersburg1 while he was1 on ,aug4 #fth1 #agec1 observing the electricity collected from an approaching thunder-cloud1 by means of a rod which he called an electrical gnomon3 a globe of blue fire was seen to leap from the rod to the head of the unfortunate professor1 who was thus struck dead4 ,note #agaa3 ,letter v4 ,note #ahaa3 ,franklin1 p4 #ajg4 #bnd ,ed4 ,as an important application of the doctrines of electricity1 ,i may mention the contrivances employed to protect ships from the effects of lightning4 ,the use of conductors in such cases is attended with peculiar difficulties4 ,in #aghj the ,french began to turn their attention to this subject1 and ,le ,roi was sent to ,brest and the various sea-ports of ,france for that purpose4 ,chains temporarily applied in the rigging had been previously suggested1 but he endeavored to place1 he says1 such conductors in ships as might be fixed and durable4 ,he devised certain long linked rods1 which led from a point in the mast-head along a part of the rigging1 or in divided stages along the masts1 and were fixed to plates of metal in the ship's sides communicating with the sea4 ,but these were either unable to stand the working of the rigging1 or otherwise inconvenient1 and were finally abandoned4#aiaa ,note #aiaa3 ,see ,le ,roi's ,memoir in the ,hist4 ,acad4 ,sc4 for #agij4 ,the conductor commonly used in the ,english ,navy1 till recently1 consisted of a flexible copper chain1 tied1 when occasion required1 to the mast-head1 and reaching down into the sea2 a contrivance recommended by ,dr4 ,watson in #agfb4 ,but notwithstanding this precaution1 the shipping suffered greatly from the effects of lightning4 ,mr4 ,snow ,harris 7now ,sir ,william ,snow ,harris71 whose electrical labors are noticed above1 proposed to the ,admiralty1 in #ahbj1 a plan which combined the conditions of ship-conductors1 so desirable1 yet so difficult to secure3--namely1 that they should be permanently fixed1 and sufficiently large1 and yet should in no way interfere with the motion of the rigging1 or with the sliding masts4 ,the method which he proposed was to make the masts themselves conductors of electricity1 #bjj by incorporating with them1 in a peculiar way1 two lamin of sheet-copper1 uniting these with the metallic masses in the hull by other lamin1 and giving the whole a free communication with the sea4 ,this method was tried experimentally1 both on models and to a large extent in the navy itself2 and a ,commission appointed to examine the result reported themselves highly satisfied with ,mr4 ,harris's plan1 and strongly recommended that it should be fully carried out in the ,navy4#bjaa ,note #bjaa3 ,see ,mr4 ,snow ,harris's paper in ,phil4 ,mag4 ,march1 #ahda4 ,it is not here necessary to trace the study of atmospheric electricity any further3 and we must now endeavor to see how these phenomena and laws of phenomena which we have related1 were worked up into consistent theories2 for though many experimental observations and measures were made after this time1 they were guided by the theory1 and may be considered as having rather discharged the office of confirming than of suggesting it4 ,we may observe also that we have now described the period of most extensive activity and interest in electrical researches4 ,these naturally occurred while the general notions and laws of the phenomena were becoming1 and were not yet become1 fixed and clear4 ,at such a period1 a large and popular circle of spectators and amateurs feel themselves nearly upon a level1 in the value of their trials and speculations1 with more profound thinkers3 at a later period1 when the subject is become a science1 that is1 a study in which all must be left far behind who do not come to it with disciplined1 informed1 and logical minds1 the cultivators are far more few1 and the shout of applause less tumultuous and less loud4 ,we may add1 too1 that the experiments1 which are the most striking to the senses1 lose much of their impressiveness with their novelty4 ,electricity1 to be now studied rightly1 must be reasoned upon mathematically2 how slowly such a mode of study makes its way1 we shall see in the progress of the theory1 which we must now proceed to narrate4 #bnd ,ed4 ,a new mode of producing electricity has excited much notice lately4 ,in ,october1 #ahdj1 one of the workmen in attendance upon a boiler belonging to the ,newcastle and ,durham ,railway1 reported that the boiler was full of fire2 the fact being1 that when he placed his hand near it an electrical spark was given out4 ,this drew the attention of ,mr4 ,armstrong and ,mr4 ,pattinson1 who made the circumstance publicly known4#baaa ,mr4 ,armstrong pursued the investigation #bja with great zeal1 and after various conjectures was able to announce#bbaa that the electricity was excited at the point where the steam is subject to friction in its emission4 ,he found too that he could produce a like effect by the emission of condensed air4 ,following out his views1 he was able to construct1 for the ,polytechnic ,institution in ,london1 a ,hydro-electric ,machine1 of greater power than any electrical machine previously made4 ,dr4 ,faraday took up the investigation as the subject of the ,eighteenth ,series of his ,researches1 sent to the ,royal ,society1 ,jan4 #bf1 #ahdb2 and in this he illustrated1 with his usual command of copious and luminous experiments1 a like view2--that the electricity is produced by the friction of the particles of the water carried along by the 9999steam4 ,and thus this is a new manifestation of that electricity1 which1 to distinguish it from voltaic electricity1 is sometimes called ,friction ,electricity or ,machine ,electricity4 ,dr4 ,faraday has1 however1 in the course of this investigation1 brought to light several new electrical relations of bodies4 ,note #baaa3 ,phil4 ,mag4 ,oct #ahdj4 ,note #bbaa3 ,phil4 ,mag4 ,jan4 #ahdh1 dated ,dec4 #i1 #ahda4 ,,chapter ,,ii4 ,,the ,,progress ,,of ,,electrical ,,theory4 ,,the cause of electrical phenomena1 and the mode of its operation1 were naturally at first spoken of in an indistinct and wavering manner4 ,it was called the electric fire1 the electric fluid2 its effects were attributed to virtues1 effluvia1 atmospheres4 ,when men's mechanical ideas became somewhat more distinct1 the motions and tendencies to motion were ascribed to currents1 in the same manner as the cosmical motions had been in the ,cartesian system4 ,this doctrine of currents was maintained by ,nollet1 who ascribed all the phenomena of electrized bodies to the contemporaneous afflux and efflux of electrical matter4 ,it was an important step towards sound theory1 to get rid of this notion of moving fluids1 and to consider attraction and repulsion as statical forces2 and this appears to have been done by others about the same time4 ,dufay#bcaa considered that he had proved the existence of two electricities1 the vitreous and the resinous1 and conceived each #bjb of these to be a fluid which repelled its own parts and attracted those of the other3 this is1 in fact1 the outline of the theory which recently has been considered as the best established2 but from various causes it was not at once1 or at least not generally adopted4 ,the hypothesis of the excess and defect of a single fluid is capable of being so treated as to give the same results with the hypothesis of two opposite fluids and happened to obtain the preference for some time4 ,we have already seen that this hypothesis1 according to which electric phenomena arose from the excess and defect of a generally diffused fluid1 suggested itself to ,watson and ,franklin about #agdg4 ,watson found that when an electric body was excited1 the electricity was not created1 but collected2 and ,franklin held1 that when the ,leyden jar was charged1 the quantity of electricity was unaltered1 though its distribution was changed4 ,symmer#bdaa maintained the existence of two fluids2 and ,cigna supplied the main defect which belonged to this tenet in the way in which ,dufay held it1 by showing that the two opposite electricities were usually produced at the same time4 ,still the apparent simplicity of the hypothesis of one fluid procured it many supporters4 ,it was that which ,franklin adopted1 in his explanation of the ,leyden experiment2 and though after the first conception of an electrical charge as a disturbance of equilibrium1 there was nothing in the development or details of ,franklin's views which deserved to win for them any peculiar authority1 his reputation1 and his skill as a writer1 gave a considerable influence to his opinions4 ,indeed1 for a time he was considered1 over a large part of ,europe1 as the creator of the science1 and the terms#beaa ,franklinism1 ,franklinist1 ,franklinian system1 occur in almost every page of continental publications on the subject4 ,yet the electrical phenomena to the knowledge of which ,franklin added least1 those of induction1 were those by which the progress of the theory was most promoted4 ,these1 as we have already said1 were at first explained by the hypothesis of electrical atmospheres4 ,lord ,mahon wrote a treatise1 in which this hypothesis was mathematically treated2 yet the hypothesis was very untenable1 for it would not account for the most obvious cases of induction1 such as the ,leyden jar1 except the atmosphere was supposed to penetrate glass4 ,note #bcaa3 ,ac4 ,par4 #agcc1 p4 #dfg ,note #bdaa3 ,phil4 ,trans4 #agei4 ,note #beaa3 ,priestley1 p4 #afj4 ,the phenomena of electricity by induction1 when fairly considered by a person of clear notions of the relations of space and force1 were seen to accommodate themselves very generally to the conception #bjc introduced by ,dufay2#bfaa of two electricities each repelling itself and attracting the other4 ,if we suppose that there is only one fluid1 which repels itself and attracts all other matter1 we obtain1 in many cases1 the same general results as if we suppose two fluids2 thus1 if an electrized body1 overcharged with the single fluid1 act upon a ball1 it drives the electric fluid in the ball to the further side by its repulsion1 and then attracts the ball by attracting the matter of the ball more than it repels the fluid which is upon the ball4 ,if we suppose two fluids1 the positively electrized body draws the negative fluid to the nearer side of the ball1 repels the positive fluid to the opposite side1 and attracts the ball on the whole1 because the attracted fluid is nearer than that which is repelled4 ,the verification of either of these hypotheses1 and the determination of their details1 depended necessarily upon experiment and calculation4 ,it was under the hypothesis of a single fluid that this trial was first properly made4 pinus of ,petersburg published1 in #agei1 his ,tentamen ,theori ,electricitatis et ,magnetismi2 in which he traces mathematically the consequences of the hypothesis of an electric fluid1 attracting all other matter1 but repelling itself2 the law of force of this repulsion and attraction he did not pretend to assign precisely1 confining himself to the supposition that the mutual force of the particles increases as the distance decreases4 ,but it was found1 that in order to make this theory tenable1 an additional supposition was required1 namely1 that the particles of bodies repel each other as much as they attract the electric fluid4#bgaa ,for if two bodies1 ,a and ,b1 be in their natural electrical condition1 they neither attract nor repel each other4 ,now1 in this case1 the fluid in ,a attracts the matter in ,b and repels the fluid in ,b with equal energy1 and thus no tendency to motion results from the fluid in ,a2 and if we further suppose that the matter in ,a attracts the fluid in ,b and repels the matter in ,b with equal energy1 we have the resulting mutual inactivity of the two bodies explained2 but without the latter supposition1 there would be a mutual attraction3 or we may put the truth more simply thus2 two negatively electrized bodies repel each other2 if negative electrization were merely the abstraction of the fluid which is the repulsive element1 this result could not follow except there were a repulsion in the bodies themselves1 independent of the fluid4 ,and thus pinus found himself compelled to assume this mutual repulsion of material particles2 he had1 in fact1 the #bjd alternative of this supposition1 or that of two fluids1 to choose between1 for the mathematical results of both hypotheses are the same4 ,wilcke1 a ,swede1 who had at first asserted and worked out the pinian theory in its original form1 afterwards inclined to the opinion of ,symmer2 and ,coulomb1 when1 at a later period1 he confirmed the theory by his experiments and determined the law of force1 did not hesitate to prefer#bhaa the theory of two fluids1 because1 he says1 it appears to me contradictory to admit at the same time1 in the particles of bodies1 an attractive force in the inverse ratio of the squares of the distances1 which is demonstrated by universal gravitation1 and a repulsive force in the same inverse ratio of the squares of the distances2 a force which would necessarily be infinitely great relatively to the action of gravitation4 ,we may add1 that by forcing us upon this doctrine of the universal repulsion of matter1 the theory of a single fluid seems quite to lose that superiority in the way of simplicity which had originally been its principal recommendation4 ,note #bfaa3 ,mm4 ,a4 ,p4 #agcc1 p4 #dfg4 ,note #bgaa3 ,robison1 vol4 iv4 p4 #ah4 ,note #bhaa3 ,mm4 ,ac4 ,p4 #aghh1 p4 #fga4 ,the mathematical results of the supposition of pinus1 which are1 as ,coulomb observes1#biaa the same as of that of the two fluids1 were traced by the author himself in the work referred to1 and shown to agree1 in a great number of cases1 with the observed facts of electrical induction1 attraction1 and repulsion4 ,apparently this work did not make its way very rapidly through ,europe2 for in #agga1 ,henry ,cavendish stated#cjaa the same hypothesis in a paper read before the ,royal ,society2 which he prefaces by saying1 ,since ,i first wrote the following paper1 ,i find that this way of accounting for the phenomena of electricity is not new4 pinus1 in his ,tentamen ,theori ,electricitatis et ,magnetismi1 has made use of the same1 or nearly the same hypothesis that ,i have2 and the conclusions he draws from it agree nearly with mine as far as he goes4 ,note #biaa3 ,ac4 ,p4 #aghh1 p4 #fgb4 ,note #cjaa3 ,phil4 ,trans4 #agga1 vol4 lxi4 ,the confirmation of the theory was1 of course1 to be found in the agreement of its results with experiment2 and in particular1 in the facts of electrical induction1 attraction1 and repulsion1 which suggested the theory4 pinus showed that such a confirmation appeared in a number of the most obvious cases2 and to these1 ,cavendish added others1 which1 though not obvious1 were of such a nature that the calculations1 in general difficult or impossible1 could in these instances be easily performed2 as1 for example1 cases in which there are plates or globes at the two extremities of a long wire4 ,in all these cases of #bje electrical action the theory was justified4 ,but in order to give it full confirmation1 it was to be considered whether any other facts1 not immediately assumed in the foundation of the theory1 were explained by it2 a circumstance which1 as we have seen1 gave the final stamp of truth to the theories of astronomy and optics4 ,now we appear to have such confirmation1 in the effect of points1 and in the phenomena of the electrical discharge4 ,the theory of neither of these was fully understood by ,cavendish1 but he made an approach to the true view of them4 ,if one part of a conducting body be a sphere of small radius1 the electric fluid upon the surface of this sphere will1 it appears by calculation1 be more dense1 and tend to escape more energetically1 in proportion as the radius of the sphere is smaller2 and1 therefore1 if we consider a point as part of the surface of a sphere of imperceptible radius1 it follows from the theory that the effort of the fluid to escape at that place will be enormous2 so that it may easily be supposed to overcome the resisting causes4 ,and the discharge may be explained in nearly the same manner2 for when a conductor is brought nearer and nearer to an electrized body1 the opposite electricity is more and more accumulated by attraction on the side next to the electrized body2 its tension becomes greater by the increase of its quantity and the diminution of the distance1 and at last it is too strong to be contained1 and leaps out in the form of a spark4 ,the light1 sound1 and mechanical effects produced by the electric discharge1 made the electric fluid to be not merely considered as a mathematical hypothesis1 useful for reducing phenomena to formul 7as for a long time the magnetic fluid was71 but caused it to be at once and universally accepted as a physical reality1 of which we learn the existence by the common use of the senses1 and of which measures and calculations are only wanted to teach us the laws4 ,the applications of the theory of electricity which ,i have principally considered above1 are those which belong to conductors1 in which the electric fluid is perfectly moveable1 and can take that distribution which the forces require4 ,in non-conducting or electric bodies1 the conditions to which the fluid is subject are less easy to determine2 but by supposing that the fluid moves with great difficulty among the particles of such bodies1--that nevertheless it may be dislodged and accumulated in parts of the surface of such bodies1 by friction and other modes of excitement2 and that the earth is an inexhaustible reservoir of electric matter1--the principal facts of excitation and the like receive a tolerably satisfactory explanation4 #bjf ,the theory of pinus1 however1 still required to have the law of action of the particles of the fluid determined4 ,if we were to call to mind how momentous an event in physical astronomy was the determination of the law of the cosmical forces1 the inverse square of the distance1 and were to suppose the importance and difficulty of the analogous step in this case to be of the same kind1 this would be to mistake the condition of science at that time4 ,the leading idea1 the conception of the possibility of explaining natural phenomena by means of the action of forces1 on rigorously mechanical principles1 had already been promulgated by ,newton1 and was1 from the first1 seen to be peculiarly applicable to electrical phenomena2 so that the very material step of clearly proposing the problem1 often more important than the solution of it1 had already been made4 ,moreover the confirmation of the truth of the assumed cause in the astronomical case depended on taking the right law2 but the electrical theory could be confirmed1 in a general manner at least1 without this restriction4 ,still it was an important discovery that the law of the inverse square prevailed in these as well as in cosmical attractions4 ,it was impossible not to conjecture beforehand that it would be so4 ,cavendish had professed in his calculations not to take the exponent of the inverse power1 on which the force depended1 to be strictly #b1 but to leave it indeterminate between #a and #c2 but in his applications of his results1 he obviously inclines to the assumption that it is #b4 ,experimenters tried to establish this in various ways4 ,robison1#caaa in #agfi1 had already proved that the law of force is very nearly or exactly the inverse square2 and ,meyer#cbaa had discovered1 but not published1 the same result4 ,the clear and satisfactory establishment of this truth is due to ,coulomb1 and was one of the first steps in his important series of researches on this subject4 ,in his first paper#ccaa in the ,memoirs of the ,academy for #aghe1 he proves this law for small globes2 in his second ,memoir he shows it to be true for globes one and two feet in diameter4 ,his invention of the torsion-balance1 which measures very small forces with great certainty and exactness1 enabled him to set this question at rest for ever4 ,note #caaa3 ,works1 iv4 p4 #fh4 ,note #cbaa3 ,biog4 ,univ4 art4 ,coulumb1 by ,biot4 ,note #ccaa3 ,mm4 ,a4 ,p4 #aghe1 pp4 #efi1 #egh4 ,the law of force being determined for the particles of the electric fluid1 it now came to be the business of the experimenter and the #bjg mathematician to compare the results of the theory in detail with those of experimental measures4 ,coulomb undertook both portions of the task4 ,he examined the electricity of portions of bodies by means of a little disk 7his tangent plane7 which he applied to them and then removed1 and which thus acted as a sort of electric taster4 ,his numerical results 7the intensity being still measured by the torsion-balance7 are the fundamental facts of the theory of the electrical fluid4 ,without entering into detail1 we may observe that he found the electricity to be entirely collected at the surface of conductors 7which ,beccaria had before shown to be the case71 and that he examined and recorded the electric intensity at the surface of globes1 cylinders1 and other conducting bodies1 placed within each other's influence in various ways4 ,the mathematical calculation of the distribution of two fluids1 all the particles of which attract and repel each other according to the above law1 was a problem of no ordinary difficulty2 as may easily be imagined1 when it is recollected that the attraction and repulsion determine the distribution1 and the distribution reciprocally determines the attraction and repulsion4 ,the problem was of the same nature as that of the figure of the earth2 and its rigorous solution was beyond the powers of the analysis of ,coulomb's time4 ,he obtained1 however1 approximate solutions with much ingenuity2 for instance1 in a case in which it was obvious that the electric fluid would be most accumulated at and near the equator of a certain sphere1 he calculated the action of the sphere on two suppositions3 first1 that the fluid was all collected precisely at the equator2 and next1 that it was uniformly diffused over the surface2 and he then assumed the actual case to be intermediate between these two4 ,by such artifices he was able to show that the results of his experiments and of his calculations gave an agreement sufficiently near to entitle him to consider the theory as established on a solid basis4 ,thus1 at this period1 mathematics was behind experiment2 and a problem was proposed1 in which theoretical numerical results were wanted for comparison with observation1 but could not be accurately obtained2 as was the case in astronomy also1 till the time of the approximate solution of the ,problem of ,three ,bodies1 and the consequent formation of the ,tables of the ,moon and ,planets on the theory of universal gravitation4 ,after some time1 electrical theory was relieved from this reproach1 mainly in consequence of the progress which astronomy had occasioned in pure mathematics4 ,about #ahja1 #bjh there appeared in the ,bulletin des ,sciences1#cdaa an exact solution of the problem of the distribution of electric fluid on a spheroid1 obtained by ,m4 ,biot1 by the application of the peculiar methods which ,laplace had invented for the problem of the figure of the planets4 ,and in #ahaa1 ,m4 ,poisson applied ,laplace's artifices to the case of two spheres acting upon one another in contact1 a case to which many of ,coulomb's experiments were referrible2 and the agreement of the results of theory and observation1 thus extricated from ,coulomb's numbers1 obtained above forty years previously1 was very striking and convincing4#ceaa ,it followed also from ,poisson's calculations1 that when two electrized spheres are brought near each other1 the accumulation of the opposite electricities on their nearest points increases without limit as the spheres approach to contact2 so that before the contact takes place1 the external resistance will be overcome1 and a spark will pass4 ,note #cdaa3 ,no4 li4 ,note #ceaa3 ,mm4 ,a4 ,p4 #ahaa4 ,though the relations of non-conductors to electricity1 and various other circumstances1 leave many facts imperfectly explained by the theory1 yet we may venture to say that1 as a theory which gives the laws of the phenomena1 and which determines the distribution of those elementary forces1 on the surface of electrized bodies1 from which elementary forces 7whether arising from the presence of a fluid or not17 the total effects result1 the doctrine of ,dufay and ,coulomb1 as developed in the analysis of ,poisson1 is securely and permanently established4 ,this part of the subject has been called statical electricity4 ,in the establishment of the theory of this branch of science1 we must1 ,i conceive1 allow to ,dufay more merit than is generally ascribed to him2 since he saw clearly1 and enunciated in a manner which showed that he duly appreciated their capital character1 the two chief principles1--the conditions of electrical attraction and repulsion1 and the apparent existence of two kinds of electricity4 ,his views of attraction are1 indeed1 partly expressed in terms of the ,cartesian hypothesis of vortices1 then prevalent in ,france2 but1 at the time when he wrote1 these forms of speech indicated scarcely anything besides the power of attraction4 ,franklin's real merit as a discoverer was1 that he was one of the first who distinctly conceived the electrical charge as a derangement of equilibrium4 ,the great fame which1 in his day1 he enjoyed1 arose from the clearness and spirit with which he narrated his discoveries2 from his dealing with electricity in the imposing form of thunder and lightning2 and partly1 perhaps1 from his character as an #bji ,american and a politician2 for he was already1 in #agcf1 engaged in public affairs as clerk to the ,general ,assembly of ,pennsylvania1 though it was not till a later period of his life that his admirers had the occasion of saying of him ,eripuit clis fulmen sceptrumque tyrannis2 ,born to control all lawless force1 all fierce and baleful sway1 ,the thunder's bolt1 the tyrant's rod1 alike he wrenched away4 pinus and ,coulomb were two of the most eminent physical philosophers of the last century1 and labored in the way peculiarly required by that generation2 whose office it was to examine the results1 in particular subjects1 of the general conception of attraction and repulsion1 as introduced by ,newton4 ,the reasonings of the ,newtonian period had1 in some measure1 anticipated all possible theories resembling the electrical doctrine of pinus and ,coulomb2 and1 on that account1 this doctrine could not be introduced and confirmed in a sudden and striking manner1 so as to make a great epoch4 ,accordingly1 ,dufay1 ,symmer1 ,watson1 ,franklin1 pinus and ,coulomb1 have all a share in the process of induction4 ,with reference to these founders of the theory of electricity1 ,poisson holds the same place which ,laplace holds with reference to ,newton4 ,the reception of the ,coulombian theory 7so we most call it1 for the pinian theory implies one fluid only17 has hitherto not been so general as might have been reasonably expected from its very beautiful accordance with the facts which it contemplates4 ,this has partly been owing to the extreme abstruseness of the mathematical reasoning which it employs1 and which put it out of the reach of most experimenters and writers of works of general circulation4 ,the theory of pinus was explained by ,robison in the ,encyclopdia ,britannica2 the analysis of ,poisson has recently been presented to the public in the ,encyclopdia ,metropolitana1 but is of a kind not easily mastered even by most mathematicians4 ,on these accounts probably it is1 that in ,english compilations of science1 we find1 even to this day1 the two theories of one and of two fluids stated as if they were nearly on a par in respect of their experimental evidence4 ,still we may say that the ,coulombian theory is probably assented to by all who have examined it1 at least as giving the laws of phenomena2 and ,i have not heard of any denial of it from such a quarter1 or of any attempt to show it to be erroneous by detailed and measured experiments4 ,mr4 ,snow ,harris #baj has recently#cfaa described some important experiments and measures2 but his apparatus was of such a kind that the comparison of the results with the ,coulombian theory was not easy2 and indeed the mathematical problems which ,mr4 ,harris's combinations offered1 require another ,poisson for their solution4 ,still the more obvious results are such as agree with the theory1 even in the cases in which their author considered them to be inexplicable4 ,for example1 he found that by doubling the quantity of electricity of a conductor1 it attracted a body with four times the force2 but the body not being insulated1 would have its electricity also doubled by induction1 and thus the fact was what the theory required4 ,note #cfaa3 ,phil4 ,trans4 #ahcd1 p4 #b4 ,though it is thus highly probable that the ,coulombian theory of electricity 7or the pinian1 which is mathematically equivalent7 will stand as a true representation of the law of the elementary actions1 we must yet allow that it has not received that complete evidence1 by means of experiments and calculations added to those of its founders1 which the precedents of other permanent sciences have led us to look for4 ,the experiments of ,coulomb1 which he used in the establishment of the theory1 were not very numerous1 and they were limited to a peculiar form of bodies1 namely spheres4 ,in order to form the proper sequel to the promulgation of this theory1 to give a full confirmation1 and to ensure its general reception1 we ought to have experiments more numerous and more varied 7such as those of ,mr4 ,harris are7 shown to agree in all respects with results calculated from the theory4 ,this would1 as we have said1 be a task of labor and difficulty2 but the person who shall execute it will deserve to be considered as one of the real founders of the true doctrine of electricity4 ,to show that the coincidence between theory and observation1 which has already been proved for spherical conductors1 obtains also for bodies of other forms1 will be a step in electricity analogous to what was done in astronomy1 when it was shown that the law of gravitation applied to comets as well as to planets4 ,but although we consider the views of pinus or ,coulomb in a very high degree probable as a formal theory1 the question is very different when we come to examine them as a physical theory2--that is1 when we inquire whether there really is a material electric fluid or fluids4 ,question of ,one or ,two ,fluids4--,in the first place as to the question whether the fluids are one or two2--,coulomb's introduction of #baa the hypothesis of two fluids has been spoken of as a reform of the theory of pinus2 it would probably have been more safe to have called his labors an advance in the calculation1 and in the comparison of hypothesis with experiment1 than to have used language which implied that the question1 between the rival hypotheses of one or two fluids1 could be treated as settled4 ,for1 in reality1 if we assume1 as pinus does1 the mutual repulsion of all the particles of matter1 in addition to the repulsion of the particles of the electric fluid for one another and their attraction for the particles of matter1 the one fluid of pinus will give exactly the same results as the two fluids of ,coulomb4 ,the mathematical formul of ,coulomb and of ,poisson express the conditions of the one case as well as of the other2 the interpretation only being somewhat different4 ,the place of the forces of the resinous fluid is supplied by the excess of the forces ascribed to the matter above the forces of the fluid1 in the parts where the electric fluid is deficient4 ,the obvious argument against this hypothesis is1 that we ascribe to the particles of matter a mutual repulsion1 in addition to the mutual attraction of universal gravitation1 and that this appears incongruous4 ,accordingly1 pinus says1 that when he was first driven to this proposition it horrified him4#cgaa ,but we may answer it in this way very satisfactorily3--,if we suppose the mutual repulsion of matter to be somewhat less than the mutual attraction of matter and electric fluid1 it will follow1 as a consequence of the hypothesis1 that besides all obvious electrical action1 the particles of matter would attract each other with forces varying inversely as the square of the distance4 ,thus gravitation itself becomes an electrical phenomenon1 arising from the residual excess of attraction over repulsion2 and the fact which is urged against the hypothesis becomes a confirmation of it4 ,by this consideration the prerogative of simplicity passes over to the side of the hypothesis of one fluid2 and the rival view appears to lose at least all its superiority4 ,note #cgaa3 ,neque diffiteor cum ipsa se mihi offerret 4 4 4 4 me ad ipsam quodammodo exhorruisse4 ,tentamen ,theor4 ,elect4 p4 #ci4 ,very recently1 ,m4 ,mosotti#chaa has calculated the results of the pinian theory in a far more complete manner than had previously been performed2 using ,laplace's coefficients1 as ,poisson had done for the #bab ,coulombian theory4 ,he finds that1 from the supposition of a fluid and of particles of matter exercising such forces as that theory assumes 7with the very allowable additional supposition that the particles are small compared with their distances71 it follows that the particles would exert a force1 repulsive at the smallest distances1 a little further on vanishing1 afterwards attractive1 and at all sensible distances attracting in proportion to the inverse square of the distance4 ,thus there would be a position of stable equilibrium for the particles at a very small distance from each other1 which may be1 ,m4 ,mosotti suggests1 that equilibrium on which their physical structure depends4 ,according to this view1 the resistance of bodies to compression and to extension1 as well as the phenomena of statical electricity and the mutual gravitation of matter1 are accounted for by the same hypothesis of a single fluid or ether4 ,a theory which offers a prospect of such a generalization is worth attention2 but a very clear and comprehensive view of the doctrines of several sciences is requisite to prepare us to estimate its value and probable success4 ,note #chaa3 ,sur les ,forces qui rgissent la ,constitution ,intrieure des ,corps4 ,turin4 #ahcf4 ,question of the ,material ,reality of the ,electric ,fluid4--,at first sight the beautiful accordance of the experiments with calculations founded upon the attractions and repulsions of the two hypothetical fluids1 persuade us that the hypotheses must be the real state of things4 ,but we have already learned that we must not trust to such evidence too readily4 ,it is a curious instance of the mutual influence of the histories of two provinces of science1 but ,i think it will be allowed to be just1 to say that the discovery of the polarization of heat has done much to shake the theory of the electric fluids as a physical reality4 ,for the doctrine of a material caloric appeared to be proved 7from the laws of conduction and radiation7 by the same kind of mathematical evidence 7the agreement of laws respecting the elementary actions with those of fluids71 which we have for the doctrine of material electricity4 ,yet we now seem to see that heat cannot be matter1 since its rays have sides1 in a manner in which a stream of particles of matter cannot have sides without inadmissible hypotheses4 ,we see1 then1 that it will not be contrary to precedent1 if our electrical theory1 representing with perfect accuracy the laws of the actions1 in all their forms1 simple and complex1 should yet be fallacious as a view of the cause of the actions4 ,any true view of electricity must include1 or at least be consistent with1 the other classes of the phenomena1 as well as this statical electrical action2 such as the conditions of excitation and retention of #bac electricity2 to which we may add1 the connexion of electricity with magnetism and with chemistry2--a vast field1 as yet dimly seen4 ,now1 even with regard to the simplest of these questions1 the cause of the retention of electricity at the surface of bodies1 it appears to be impossible to maintain ,coulomb's opinion1 that this is effected by the resistance of air to the passage of electricity4 ,the other questions are such as ,coulomb did not attempt to touch2 they refer1 indeed1 principally to laws not suspected at his time4 ,how wide and profound a theory must be which deals worthily with these1 we shall obtain some indications in the succeeding part of our history4 ,but it may be said on the other side1 that we have the evidence of our senses for the reality of an electric fluid2--we see it in the spark2 we hear it in the explosion2 we feel it in the shock2 and it produces the effects of mechanical violence1 piercing and tearing the bodies through which it passes4 ,and those who are disposed to assert a real fluid on such grounds1 may appear to be justified in doing so1 by one of ,newton's ,rules of ,philosophizing1 in which he directs the philosopher to assume1 in his theories1 causes which are true4 ,the usual interpretation of a vera causa1 has been1 that it implies causes which1 independently of theoretical calculations1 are known to exist by their mechanical effects2 as gravity was familiarly known to exist on the earth1 before it was extended to the heavens4 ,the electric fluid might seem to be such a vera causa4 ,to this ,i should venture to reply1 that this reasoning shows how delusive the ,newtonian rule1 so interpreted1 may be4 ,for a moment's consideration will satisfy us that none of the circumstances1 above adduced1 can really prove material currents1 rather than vibrations1 or other modes of agency4 ,the spark and shock are quite insufficient to supply such a proof4 ,sound is vibrations1--light is vibrations2 vibrations may affect our nerves1 and may rend a body1 as when glasses are broken by sounds4 ,therefore all these supposed indications of the reality of the electric fluid are utterly fallacious4 ,in truth1 this mode of applying ,newton's rule consists in elevating our first rude and unscientific impressions into a supremacy over the results of calculation1 generalization1 and systematic induction49999#ciaa #bad ,note 9999#ciaa3 ,on the subject of this ,newtonian ,rule of ,philosophizing1 see further ,phil4 ,ind4 ,sc4 ,b4 xii4 c4 #ac4 ,i have given an account of the history and evidence of the ,theory of ,electricity in the ,reports of the ,british ,association for #ahce4 ,i may seem there to have spoken more favorably of the ,theory as a ,physical ,theory than ,i have done here4 ,this difference is principally due to a consideration of the present aspect of the ,theory of ,heat4 ,thus our conclusion with regard to this subject is1 that if we wish to form a stable physical theory of electricity1 we must take into account not only the laws of statical electricity1 which we have been chiefly considering1 but the laws of other kinds of agency1 different from the electric1 yet connected with it4 ,for the electricity of which we have hitherto spoken1 and which is commonly excited by friction1 is identical with galvanic action1 which is a result of chemical combinations1 and belongs to chemical philosophy4 ,the connexion of these different kinds of electricity with one another leads us into a new domain2 but we must1 in the first place1 consider their mechanical laws4 ,we now proceed to another branch of the same subject1 ,magnetism4 #bae ,,book ,,xii4 ,,mechanico-,,chemical ,,sciences4 7,,continued47 ,,history ,,of ,,magnetism4 ,,effice1 ut interea fera munera militia ,per maria ac terras omneis sopita quiescant4 ,nam tu sola potes tranquilla pace juvare ,mortales2 quoniam belli fera munera ,mavors ,armipotens regit1 in gremium qui spe tuum se ,rejicit1 terno devictus vulnere amoris2 ,atque ita suspiciens tereti cervice reposta1 ,pascit amore avidos inhians in te1 ,dea1 visus1 ,eque tuo pendet resupini spiritus ore4 ,hunc tu1 ,diva1 tuo recubantem corpore sancto ,circumfusa super1 suaves ex ore loquelas ,funde1 petens placidam ,romanis1 incluta1 pacem4 ,,lucret4 i4 #ca4 ,o charming ,goddess1 whose mysterious sway ,the unseen hosts of earth and sky obey2 ,to whom1 though cold and hard to all besides1 ,the ,iron ,god by strong affection glides4 ,flings himself eager to thy close embrace1 ,and bends his head to gaze upon thy face2 ,do thou1 what time thy fondling arms are thrown ,around his form1 and he is all thy own1 ,do thou1 thy ,rome to save1 thy power to prove1 ,beg him to grant a boon for thy dear love2 ,beg him no more in battle-fields to deal4 ,or crush the nations with his mailed heel4 ,but1 touched and softened by a worthy flame1 ,quit sword and spear1 and seek a better fame4 ,bid him to make all war and slaughter cease1 ,and ply his genuine task in arts of peace2 ,and by thee guided o'er the trackless surge1 ,bear wealth and joy to ocean's farthest verge4 #bag ,,chapter ,i4 ,,discovery ,,of ,,laws ,,of ,,magnetic ,,phenomena4 ,,the history of ,magnetism is in a great degree similar to that of ,electricity1 and many of the same persons were employed in the two trains of research4 ,the general fact1 that the magnet attracts iron1 was nearly all that was known to the ancients1 and is frequently mentioned and referred to2 for instance1 by ,pliny1 who wonders and declaims concerning it1 in his usual exaggerated style4#aab ,the writers of the ,stationary ,period1 in this subject as in others1 employed themselves in collecting and adorning a number of extravagant tales1 which the slightest reference to experiment would have disproved2 as1 for example1 that a magnet1 when it has lost its virtue1 has it restored by goat's blood4 ,gilbert1 whose work ,de ,magnete we have already mentioned1 speaks with becoming indignation and pity of this bookish folly1 and repeatedly asserts the paramount value of experiments4 ,he himself1 no doubt1 acted up to his own precepts2 for his work contains all the fundamental facts of the science1 so fully examined indeed1 that even at this day we have little to add to them4 ,thus1 in his first ,book1 the subjects of the third1 fourth1 and fifth ,chapters are1--that the magnet has poles1--that we may call these poles the north and the south pole1--that in two magnets the north pole of each attracts the south pole and repels the north pole of the other4 ,this is1 indeed1 the cardinal fact on which our generalizations rest2 and the reader will perceive at once its resemblance to the leading phenomena of statical electricity4 ,note #aab3 ,hist4 ,nat4 lib4 xxxvi4 c4 #be4 ,but the doctrines of magnetism1 like those of heat1 have an additional claim on our notice from the manner in which they are exemplified in the globe of the earth4 ,the subject of terrestrial magnetism forms a very important addition to the general facts of magnetic attraction and repulsion4 ,the property of the magnet by which it directs its poles exactly or nearly north and south1 when once discovered1 was of immense importance to the mariner4 ,it does not #bah appear easy to trace with certainty the period of this discovery4 ,passing over certain legends of the ,chinese1 as at any rate not bearing upon the progress of ,european science1#bab the earliest notice of this property appears to be contained in the ,poem of ,guyot de ,provence1 who describes the needle as being magnetized1 and then placed in or on a straw1 7floating on water1 as ,i presume37 ,puis se torne la pointe toute ,contre l'estoile sans doute2 that is1 it turns towards the pole-star4 ,this account would make the knowledge of this property in ,europe anterior to #abjj4 ,it was afterwards found#cab that the needle does not point exactly towards the north4 ,gilbert was aware of this deviation1 which he calls the variation1 and also1 that it is different in different places4#dab ,he maintained on theoretical principles also1#eab that at the same place the variation is constant2 probably in his time there were not any recorded observations by which the truth of this assertion could be tested2 it was afterwards found to be false4 ,the alteration of the variation in proceeding from one place to another was1 it will be recollected1 one of the circumstances which most alarmed the companions of ,columbus in #adib4 ,gilbert says1#fab ,other learned men have1 in long navigations1 observed the differences of magnetic variations1 as ,thomas ,hariot1 ,robert ,hues1 ,edward ,wright1 ,abraham ,kendall1 all ,englishmen3 others have invented magnetic instruments and convenient modes of observation1 such as are requisite for those who take long voyages1 as ,william ,borough in his ,book concerning the variation of the compass1 ,william ,barlo in his supplement1 ,william ,norman in his ,new ,attractive4 ,this is that ,robert ,norman 7a good seaman and an ingenious artificer17 who first discovered the dip of magnetic iron4 ,this important discovery was made#gab in #aegf4 ,from the time when the difference of the variation of the compass in different places became known1 it was important to mariners to register the variation in all parts of the world4 ,halley was appointed to the command of a ship in the ,royal ,navy by the ,government of ,william and ,mary1 with orders to seek by observation the discovery of the rule for the variation of the compass4 ,he published ,magnetic ,charts1 which #bai have been since corrected and improved by various persons4 ,the most recent are those of ,mr4 ,yates in #ahag1 and of ,m4 ,hansteen4 ,the dip1 as well as the variation1 was found to be different in different places4 ,m4 ,humboldt1 in the course of his travels1 collected many such observations4 ,and both the observations of variation and of dip seemed to indicate that the earth1 as to its effect on the magnetic needle1 may1 approximately at least1 be considered as a magnet1 the poles of which are not far removed from the earth's poles of rotation4 ,thus we have a magnetic equator1 in which the needle has no dip1 and which does not deviate far from the earth's equator2 although1 from the best observations1 it appears to be by no means a regular circle4 ,and the phenomena1 both of the dip and of the variation1 in high northern latitudes1 appear to indicate the existence of a pole below the surface of the earth to the north of ,hudson's ,bay4 ,in his second remarkable expedition into those regions1 ,captain ,ross is supposed to have reached the place of this pole2 the dipping-needle there pointing vertically downwards1 and the variation-compass turning towards this point in the adjacent regions4 ,we shall hereafter have to consider the more complete and connected views which have been taken of terrestrial magnetism4 ,note #bab3 ,enc4 ,met4 art4 ,magnetism1 p4 #gcf4 ,note #cab3 ,before #abfi4 ,enc4 ,met4 p4 #gcg4 ,note #dab3 ,de ,magnete1 lib4 iv4 c4 #a4 ,note #eab3 c4 #c4 ,note #fab3 ,lib4 i4 c4 #a4 ,note #gab3 ,enc4 ,met4 p4 #gch4 ,in #afcc1 ,gellibrand discovered that the variation is not constant1 as ,gilbert imagined1 but that at ,london it had diminished from eleven degrees east in #aehj1 to four degrees in #afcc4 ,since that time the variation has become more and more westerly2 it is now about twenty-five degrees west1 and the needle is supposed to have begun to travel eastward again4 ,the next important fact which appeared with respect to terrestrial magnetism was1 that the position of the needle is subject to a small diurnal variation3 this was discovered in #agbb1 by ,graham1 a philosophical instrument-maker1 of ,london4 ,the daily variation was established by one thousand observations of ,graham1 and confirmed by four thousand more made by ,canton1 and is now considered to be out of dispute4 ,it appeared also1 by ,canton's researches1 that the diurnal variation undergoes an annual inequality1 being nearly a quarter of a degree in ,june and ,july1 and only half that quantity in ,december and ,january4 ,having thus noticed the principal facts which belong to terrestrial magnetism1 we must return to the consideration of those phenomena which gradually led to a consistent magnetic theory4 ,gilbert observed that both smelted iron and hammered iron have the magnetic virtue1 #bbj though in a weaker degree than the magnet itself1#hab and he asserted distinctly that the magnet is merely an ore of iron1 7lib4 i4 c4 #af1 ,quod magnes et vena ferri idem sunt47 ,he also noted the increased energy which magnets acquire by being armed2 that is1 fitted with a cap of polished iron at each pole4#iab ,but we do not find till a later period any notice of the distinction which exists between the magnetical properties of soft iron and of hard steel2--the latter being susceptible of being formed into artificial magnets1 with permanent poles2 while soft iron is only passively magnetic1 receiving a temporary polarity from the action of a magnet near it1 but losing this property when the magnet is removed4 ,about the middle of the last century1 various methods were devised of making artificial magnets1 which exceeded in power all magnetic bodies previously known4 ,note #hab3 ,lib4 i4 c4 #i-ac4 ,note #iab3 ,lib4 ii4 c4 #ag4 ,the remaining experimental researches had so close an historical connexion with the theory1 that they will be best considered along with it1 and to that1 therefore1 we now proceed4 ,,chapter ,,ii4 ,,progress ,,of ,,magnetic ,,theory4 ,,theory ,,of ,,magnetic ,,action4--,the assumption of a fluid1 as a mode of explaining the phenomena1 was far less obvious in magnetic than in electric cases1 yet it was soon arrived at4 ,after the usual philosophy of the middle ages1 the forms of ,aquinas1 the efflux of ,cusanus1 the vapors of ,costus1 and the like1 which are recorded by ,gilbert1#ajab we have his own theory1 which he also expresses by ascribing the effects to a formal efficiency2--a form of primary globes2 the proper entity and existence of their homogeneous parts1 which we may call a primary and radical and astral form2--of which forms there is one in the sun1 one in the moon1 one in the earth1 the latter being the magnetic virtue4 ,note #ajab3 ,gilb4 lib4 ii4 c4 #c1 #d ,without attempting to analyse the precise import of these expressions1 we may proceed to ,descartes's explanation of magnetic phenomena4 ,the mode in which he presents this subject#aaab is1 perhaps1 the #bba most persuasive of his physical attempts4 ,if a magnet be placed among iron filings1 these arrange themselves in curved lines1 which proceed from one pole of the magnet to the other4 ,it was not difficult to conceive these to be the traces of currents of ethereal matter which circulate through the magnet1 and which are thus rendered sensible even to the eye4 ,when phenomena could not be explained by means of one vortex1 several were introduced4 ,three ,memoirs on ,magnetism1 written on such principles1 had the prize adjudged#abab by the ,french ,academy of ,sciences in #agdf4 ,note #aaab3 ,prin4 ,phil4 pars c4 iv4 #adf4 ,note #abab3 ,coulomb1 #aghi1 p4 #dhb4 ,but the ,cartesian philosophy gradually declined2 and it was not difficult to show that the magnetic curves1 as well as other phenomena1 would1 in fact1 result from the attraction and repulsion of two poles4 ,the analogy of magnetism with electricity was so strong and clear1 that similar theories were naturally proposed for the two sets of facts2 the distinction of bodies into conductors and electrics in the one case1 corresponding to the distinction of soft and hard steel1 in their relations to magnetism4 pinus published a theory of magnetism and electricity at the same time 7#agei72 and the former theory1 like the latter1 explained the phenomena of the opposite poles as results of the excess and defect of a magnetic fluid1 which was dislodged and accumulated in the ends of the body1 by the repulsion of its own particles1 and by the attraction of iron or steel1 as in the case of induced electricity4 ,the pinian theory of magnetism1 as of electricity1 was recast by ,coulomb1 and presented in a new shape1 with two fluids instead of one4 ,but before this theory was reduced to calculation1 it was obviously desirable1 in the first place1 to determine the law of force4 ,in magnetic1 as in electric action1 the determination of the law of attraction of the particles was attended at first with some difficulty1 because the action which a finite magnet exerts is a compound result of the attractions and repulsions of many points4 ,newton had imagined the attractive force of magnetism to be inversely as the cube of the distance2 but ,mayer in #agfj1 and ,lambert a few years later1 asserted the law to be1 in this as in other forces1 the inverse square4 ,coulomb has the merit of having first clearly confirmed this law1 by the use of his torsion-balance4#acab ,he established1 at the same time1 other very important facts1 for instance1 that the directive magnetic force1 which the earth exerts upon a needle1 is a constant quantity1 parallel #bbb to the magnetic meridian1 and passing through the same point of the needle whatever be its position4 ,this was the more important1 because it was necessary1 in the first place1 to allow for the effect of the terrestrial force1 before the mutual action of the magnets could be extricated from the phenomena4#adab ,coulomb then proceeded to correct the theory of magnetism4 ,note #acab3 ,mem4 ,a4 ,p4 #aghd1 #b;d ,mem4 p4 #eic4 ,note #adab3 p4 #fjc4 ,coulomb's reform of the pinian theory1 in the case of magnetism1 as in that of electricity1 substituted two fluids 7an austral and a boreal fluid17 for the single fluid2 and in this way removed the necessity under which pinus found himself1 of supposing all the particles of iron and steel and other magnetic bodies to have a peculiar repulsion for each other1 exactly equal to their attraction for the magnetic fluid4 ,but in the case of magnetism1 another modification was necessary4 ,it was impossible to suppose here1 as in the electrical phenomena1 that one of the fluids was accumulated on one extremity of a body1 and the other fluid on the other extremity2 for though this might appear1 at first sight1 to be the case in a magnetic needle1 it was found that when the needle was cut into two halves1 the half in which the austral fluid had seemed to predominate1 acquired immediately a boreal pole opposite to its austral pole1 and a similar effect followed in the other half4 ,the same is true1 into however many parts the magnetic body be cut4 ,the way in which ,coulomb modified the theory so as to reconcile it with such facts1 is simple and satisfactory4 ,he supposes#aeab the magnetic body to be made up of molecules or integral parts1 or1 as they were afterwards called by ,m4 ,poisson1 magnetic elements4 ,in each of these elements1 7which are extremely minute17 the fluids can be separated1 so that each element has an austral and a boreal pole2 but the austral pole of an element which is adjacent to the boreal pole of the next1 neutralizes1 or nearly neutralizes1 its effect2 so that the sensible magnetism appears only towards the extremities of the body1 as it would do if the fluids could permeate the body freely4 ,we shall have exactly the same result1 as to sensible magnetic force1 on the one supposition and on the other1 as ,coulomb showed4#afab ,note #aeab3 ,mem4 ,a4 ,p4 #aghi1 p4 #dhh4 ,note #afab3 ,mem4 ,a4 ,p4 p4 #dib4 ,the theory1 thus freed from manifest incongruities1 was to be reduced to calculation1 and compared with experiment2 this was done in ,coulomb's ,seventh ,memoir4#agab ,the difficulties of calculation in this1 as in the electric problem1 could not be entirely surmounted by the analysis of ,coulomb2 but by various artifices1 he obtained theoretically the #bbc relative amount of magnetism at several points of a needle1#ahab and the proposition that the directive force of the earth on similar needles saturated with magnetism1 was as the cube of their dimensions2 conclusions which agreed with experiment4 ,note #agab3 ,a4 ,p4 #aghi4 ,note #ahab3 p4 #dhe4 ,the agreement thus obtained was sufficient to give a great probability to the theory2 but an improvement of the methods of calculation and a repetition of experiments1 was1 in this as in other cases1 desirable1 as a confirmation of the labors of the original theorist4 ,these requisites1 in the course of time1 were supplied4 ,the researches of ,laplace and ,legendre on the figure of the earth had 7as we have already stated17 introduced some very peculiar analytical artifices1 applicable to the attractions of spheroids2 and these methods were employed by ,m4 ,biot in #ahaa1 to show that on an elliptical spheroid1 the thickness of the fluid in the direction of the radius would be as the distance from the centre4#aiab ,but the subject was taken up in a more complete manner in #ahbd by ,m4 ,poisson1 who obtained general expressions for the attractions or repulsions of a body of any form whatever1 magnetized by influence1 upon a given point2 and in the case of spherical bodies was able completely to solve the equations which determine these forces4#bjab ,note #aiab3 ,bull4 des ,sc4 ,no4 li4 ,note #bjab3 ,a4 ,p4 for #ahba and #b1 published #ahbf4 ,previously to these theoretical investigations1 ,mr4 ,barlow had made a series of experiments on the effect of an iron sphere upon a compass needle2 and had obtained empirical formul for the amount of the deviation of the needle1 according to its dependence upon the position and magnitude of the sphere4 ,he afterwards deduced the same formul from a theory which was1 in fact1 identical with that of ,coulomb1 but which he considered as different1 in that it supposed the magnetic fluids to be entirely collected at the surface of the sphere4 ,he had indeed found1 by experiment1 that the surface was the only part in which there was any sensible magnetism2 and that a thin shell of iron would produce the same effect as a solid ball of the same diameter4 ,but this was1 in fact1 a most complete verification of ,coulomb's theory4 ,for though that theory did not suppose the magnetism to be collected solely at the surface1 as ,mr4 ,barlow found it1 it followed from the theory1 that the sensible magnetic intensity assumed the same distribution 7namely1 a surface distribution17 as if the fluids could permeate the whole body1 instead of the magnetic elements only4 ,coulomb1 indeed1 had not expressly noticed the result1 that the sensible #bbd magnetism would be confined to the surface of bodies2 but he had found that1 in a long needle1 the magnetic fluid might be supposed to be concentrated very near the extremities1 just as it is in a long electric body4 ,the theoretical confirmation of this rule among the other consequences of the theory1--that the sensible magnetism would be collected at the surface1--was one of the results of ,poisson's analysis4 ,for it appeared that if the sum of the electric elements of the body was equal to the whole body1 there would be no difference between the action of a solid sphere and very thin shell4 ,we may1 then1 consider the ,coulombian theory to be fully established and verified1 as a representation of the laws of magnetical phenomena4 ,we may add1 as a remarkable and valuable example of an ulterior step in the course of sciences1 the application of the laws of the distribution of magnetism to the purposes of navigation4 ,it had been found that the mass of iron which exists in a ship produces a deviation in the direction of the compass-needle1 which was termed local attraction1 and which rendered the compass an erroneous guide4 ,mr4 ,barlow proposed to correct this by a plate of iron placed near the compass2 the plate being of comparatively small mass1 but1 in consequence of its expanded form1 and its proximity to the needle1 of equivalent effect to the disturbing cause4 #bnd ,ed4 ,this proposed arrangement was not successful1 because as the ship turns into different positions1 it may be considered as revolving round a vertical axis2 and as this does not coincide with the magnetic axis1 the relative magnetic position of the disturbing parts of the ship1 and of the correcting plate1 will be altered1 so that they will not continue to counteract each other4 ,in high magnetic latitudes the correcting plate was used with success4 ,but when iron ships became common1 a correction of the effect of the iron upon the ship's compass in the general case became necessary4 ,mr4 ,airy devised the means of making this correction4 ,by placing a magnet and a mass of iron in certain positions relative to the compass1 the effect of the rest of the iron in the ship is completely counteracted in all positions4#baab ,note #baab3 ,see ,phil4 ,trans4 #ahcf4 ,but we have still to trace the progress of the theory of terrestrial magnetism4 ,theory of ,terrestrial ,magnetism4--,gilbert had begun a plausible course of speculation on this point4 ,we must reject1 he says1#bbab in #bbe the first place1 that vulgar opinion of recent writers concerning magnetic mountains1 or a certain magnetic rock1 or an imaginary pole at a certain distance from the pole of the earth4 ,for1 he adds1 we learn by experience1 that there is no such fixed pole or term in the earth for the variation4 ,gilbert describes the whole earth as a magnetic globe1 and attributes the variation to the irregular form of its protuberances1 the solid parts only being magnetic4 ,it was not easy to confirm or refute this opinion1 but other hypotheses were tried by various writers2 for instance1 ,halley had imagined1 from the forms of the lines of equal variation1 that there must be four magnetic poles2 but ,euler#bcab showed that the ,halleian lines would1 for the most part1 result from the supposition of two magnetic poles1 and assigned their position so as to represent pretty well the known state of the variation all over the world in #agdd4 ,but the variation was not the only phenomenon which required to be taken into account2 the dip at different places1 and also the intensity of the force1 were to be considered4 ,we have already mentioned ,m4 de ,humboldt's collection of observations of the dip4 ,these were examined by ,m4 ,biot1 with the view of reducing them to the action of two poles in the supposed terrestrial magnetic axis4 ,having1 at first1 made the distance of these poles from the centre of the earth indefinite1 he found that his formul agreed more and more nearly with the observations1 as the poles were brought nearer2 and that fact and theory coincided tolerably well when both poles were at the centre4 ,in #ahji1bdab ,krafft simplified this result1 by showing that1 on this supposition1 the tangent of the dip was twice the tangent of the latitude of the place as measured from the magnetic equator4 ,but ,m4 ,hansteen1 who has devoted to the subject of terrestrial magnetism a great amount of labor and skill1 has shown that1 taking together all the observations which we possess1 we are compelled to suppose four magnetic poles2 two near the north pole1 and two near the south pole1 of the terrestrial globe2 and that these poles1 no two of which are exactly opposite each other1 are all in motion1 with different velocities1 some moving to the east and some to the west4 ,this curious collection of facts awaits the hand of future theorists1 when the ripeness of time shall invite them to the task4 ,note #bbab3 ,lib4 iv4 c4 #a4 ,de ,variatione4 ,note #bcab3 ,ac4 ,berlin1 #ageg4 ,note #bdab3 ,enc4 ,met4 p4 #gdb4 #bnd ,ed4 ,i had thus written in the first edition4 ,the theorist who was needed to reduce this accumulation of facts to their laws1 #bbf had already laid his powerful hand upon them2 namely1 ,m4 ,gauss1 a mathematician not inferior to any of the great men who completed the theory of gravitation4 ,and institutions had been established for extending the collection of the facts pertaining to it1 on a scale which elevates ,magnetism into a companionship with ,astronomy4 ,m4 ,hansteen's ,magnetismus der ,erde was published in #ahai4 ,his conclusions respecting the position of the four magnetic poles excited so much interest in his own country1 that the ,norwegian ,storthing1 or parliament1 by a unanimous vote1 provided funds for a magnetic expedition which he was to conduct along the north of ,europe and ,asia2 and this they did at the very time when they refused to make a grant to the king for building a palace at ,christiania4 ,the expedition was made in #ahbh-cj1 and verified ,hansteen's anticipations as to the existence of a region of magnetic convergence in ,siberia1 which he considered as indicating a pole to the north of that country4 ,m4 ,erman also travelled round the earth at the same time1 making magnetic observations4 ,about the same time another magnetical phenomenon attracted attention4 ,besides the general motion of the magnetic poles1 and the diurnal movements of the needle1 it was found that small and irregular disturbances take place in its position1 which ,m4 de ,humboldt termed magnetic storms4 ,and that which excited a strong interest on this subject was the discovery that these magnetic storms1 seen only by philosophers who watch the needle with microscopic exactness1 rage simultaneously over large tracts of the surface of our globe4 ,this was detected about #ahbe by a comparison of the observations of ,m4 ,arago at ,paris with simultaneous observations of ,m4 ,kupffer at ,kasan in ,russia1 distant more than #dg degrees of longitude4 ,at the instance of ,m4 de ,humboldt1 the ,imperial ,academy of ,russia adopted with zeal the prosecution of this inquiry1 and formed a chain of magnetic stations across the whole of the ,russian empire4 ,magnetic observations were established at ,petersburg and at ,kasan1 and corresponding observations were made at ,moscow1 at ,nicolaieff in the ,crimea1 and ,barnaoul and ,nertchinsk in ,siberia1 at ,sitka in ,russian ,america1 and even at ,pekin4 ,to these magnetic stations the ,russian government afterwards added1 ,catharineburg in ,russia ,proper1 ,helsingfors in ,finland1 ,teflis in ,georgia4 ,a comparison of the results obtained at four of these stations made by ,,mm4 de ,humboldt and ,dove1 in the year #ahcj1 showed that the magnetic disturbances were simultaneous1 and were for the most parallel in their progress4 #bbg ,important steps in the prosecution of this subject were soon after made by ,m4 ,gauss1 the great mathematician of ,gttingen4 ,he contrived instruments and modes of observation far more perfect than any before employed1 and organized a system of comparative observations throughout ,europe4 ,in #ahce1 stations for this purpose were established at ,altona1 ,augsburg1 ,berlin1 ,breda1 ,breslau1 ,copenhagen1 ,dublin1 ,freiberg1 ,gttingen1 ,greenwich1 ,hanover1 ,leipsic1 ,marburg1 ,milan1 ,munich1 ,petersburg1 ,stockholm1 and ,upsala4 ,at these places1 six times in the year1 observations were taken simultaneously1 at intervals of five minutes for #bd hours4 ,the ,results of the ,magnetic ,association 7,resultaten des ,magnetischen ,vereins7 were published by ,,mm4 ,gauss and ,weber1 beginning in #ahcf4 ,british physicists did not at first take any leading part in these plans4 ,but in #ahcf1 ,baron ,humboldt1 who by his long labors and important discoveries in this subject might be considered as peculiarly entitled to urge its claims1 addressed a letter to the ,duke of ,sussex1 then ,president of the ,royal ,society1 asking for the co-operation of this country in so large and hopeful a scheme for the promotion of science4 ,the ,royal ,society willingly entertained this appeal2 and the progress of the cause was still further promoted when it was zealously taken up by the ,british ,association for the ,advancement of ,science1 assembled at ,newcastle in #ahch4 ,the ,association there expressed its strong interest in the ,german system of magnetic observations2 and at the instigation of this body1 and of the ,royal ,society1 four complete magnetical observatories were established by the ,british government1 at ,toronto1 ,st4 ,helena1 the ,cape of ,good ,hope1 and ,van ,diemen's ,land4 ,the munificence of the ,directors of the ,east ,india ,company founded and furnished an equal number at ,simla 7in the ,himalayah71 ,madras1 ,bombay1 and ,sincapore4 ,sir ,thomas ,brisbane added another at his own expense at ,kelso1 in ,scotland4 ,besides this1 the government sent out a naval expedition to make discoveries 7magnetic among others71 in the ,antarctic regions1 under the command of ,sir ,james ,ross4 ,other states lent their assistance also1 and founded or reorganized their magnetic observatories4 ,besides those already mentioned1 one was established by the ,french government at ,algiers2 one by the ,belgian1 at ,brussels2 two by ,austria1 at ,prague and ,milan2 one by ,prussia1 at ,breslau2 one by ,bavaria1 at ,munich2 one by ,spain1 at ,cadiz2 there are two in the ,united ,states1 at ,philadelphia and ,cambridge2 one at ,cairo1 founded by the ,pasha of ,egypt2 and in ,india1 one at ,trevandrum1 established by the ,rajah of ,travancore2 and one by #bbh the ,king of ,oude1 at ,lucknow4 ,at all these distant stations the same plan was followed out1 by observations strictly simultaneous1 made according to the same methods1 with the same instrumental means4 ,such a scheme1 combining world-wide extent with the singleness of action of an individual mind1 is hitherto without parallel4 ,at first1 the ,british stations were established for three years only2 but it was thought advisable to extend this period three years longer1 to end in #ahde4 ,and when the termination of that period arrived1 a discussion was held among the magneticians themselves1 whether it was better to continue the observations still1 or to examine and compare the vast mass of observations already collected1 so as to see to what results and improvements of methods they pointed4 ,this question was argued at the meeting of the ,british ,association at ,cambridge in that year2 and the conference ended in the magneticians requesting to have the observations continued1 at some of the observatories for an indefinite period1 at others1 till the year #ahdh4 ,in the mean time the ,antarctic expedition had brought back a rich store of observations1 fitted to disclose the magnetic condition of those regions which it had explored4 ,these were discussed1 and their results exhibited1 in the ,philosophical ,transactions for #ahdc1 by ,col4 ,sabine1 who had himself at various periods1 made magnetic observations in the ,arctic regions1 and in several remote parts of the globe1 and had always been a zealous laborer in this fruitful field4 ,the general mass of the observations was placed under the management of ,professor ,lloyd1 of ,dublin1 who has enriched the science of magnetism with several valuable instruments and methods1 and who1 along with ,col4 ,sabine1 made a magnetic survey of the ,british ,isles in #ahce and #ahcf4 ,i do not dwell upon magnetic surveys of various countries made by many excellent observers2 as ,,mm4 ,quetelet1 ,forbes1 ,fox1 ,bache and others4 ,the facts observed at each station were1 the intensity of the magnetic force2 the declination of the needle from the meridian1 sometimes called the variation2 and its inclination to the horizon1 the dip2--or at least1 some elements equivalent to these4 ,the values of these elements at any given time1 if known1 can be expressed by charts of the earth's surface1 on which are drawn the isodynamic1 isogonal1 and isoclinal curves4 ,the second of these kinds of charts contain the ,halleian lines spoken of in a previous page4 ,moreover the magnetic elements at each place are to be observed in such a #bbi manner as to determine both their periodical variations 7the changes which occur in the period of a day1 and of a year71 the secular changes1 as the gradual increase or diminution of the declination at the same place for many years2 and the irregular fluctuations which1 as we have said1 are simultaneous over a large part1 or the whole1 of the earth's surface4 ,when these ,facts have been ascertained over the whole extent of the earth's surface1 we shall still have to inquire what is the ,cause of the changes in the forces which these phenomena disclose4 ,but as a basis for all speculation on that subject1 we must know the law of the phenomena1 and of the forces which immediately produce them4 ,i have already said that ,euler tried to account for the ,halleian lines by means of two magnetic poles1 but that ,m4 ,hansteen conceived it necessary to assume four4 ,but an entirely new light has been thrown upon this subject by the beautiful investigations of ,gauss1 in his ,theory of ,terrestrial ,magnetism1 published in #ahci4 ,he remarks that the term poles1 as used by his predecessors1 involves an assumption arbitrary1 and1 as it is now found1 false2 namely1 that certain definite points1 two1 four1 or more1 acting according to the laws of ordinary magnetical poles1 will explain the phenomena4 ,he starts from a more comprehensive assumption1 that magnetism is distributed throughout the mass of the earth in an unknown manner4 ,on this assumption he obtains a function ,v1 by the differentials of which the elements of the magnetic force at any point will be expressed4 ,this function ,v is well known in physical astronomy1 and is obtained by summing all the elements of magnetic force in each particle1 each multiplied by the reciprocal of its distance2 or as we may express it1 by taking the sum of each element and its proximity jointly4 ,hence it has been proposed#beab to term this function the integral proximity of the attracting mass4#bfab ,by using the most refined #bcj mathematical artifices for deducing the values of ,v and its differentials in converging series1 he is able to derive the coefficients of these series from the observed magnetic elements at certain places1 and hence1 to calculate them for all places4 ,the comparison of the calculation with the observed results is1 of course1 the test of the truth of the theory4 ,note #beab3 ,quart4 ,rev4 ,no4 #aca1 p4 #bhc4 ,note #bfab3 ,the function ,v is of constant occurrence in investigations respecting attractions4 ,it is introduced by ,laplace in his investigations respecting the attractions of spheroids1 ,mc4 ,cl4 ,livr4 ,,iii4 ,art4 #d4 ,mr4 ,green and ,professor ,mac ,cullagh have proposed to term this function the ,potential of the system2 but this term 7though suggested1 ,i suppose1 by analogy with the substantive ,exponential71 does not appear convenient in its form4 ,on the other hand1 the term ,integral ,proximity does not indicate that which gives the function its peculiar claim to distinction2 namely1 that its differentials express the power or attraction of the system4 ,perhaps ,integral ,potentiality1 or ,integral ,attractivity1 would be a term combining the recommendations of both the others4 ,the degree of convergence of the series depends upon the unknown distribution of magnetism within the earth4 ,if we could venture to assume1 says ,m4 ,gauss1 that the members have a sensible influence only as far as the fourth order1 complete observations from eight points would be sufficient1 theoretically considered1 for the determination of the coefficients4 ,and under certain limitations1 making this assumption1 as the best we can do at present1 ,m4 ,gauss obtains from eight places1 #bd coefficients 7each supplying three elements71 and hence calculates the magnetic elements 7intensity1 variation and dip7 at #ia places in all parts of the earth4 ,he finds his calculations approach the observed values with a degree of exactness which appears to be quite convincing as to the general truth of his results2 especially taking into account how entirely unlimited is his original hypothesis4 ,it is one of the most curious results of this investigation that according to the most simple meaning which we can give to the term pole the earth has only two magnetic poles2 that is1 two points where the direction of the magnetic force is vertical4 ,and thus the isogonal curves may be looked upon as deformations of the curves deduced by ,euler from the supposition of two poles1 the deformation arising from this1 that the earth does not contain a single definite magnet1 but irregularly diffused magnetical elements1 which still have collectively a distinct resemblance to a single magnet4 ,and instead of ,hansteen's ,siberian pole1 we have a ,siberian region in which the needles converge2 but if the apparent convergence be pursued it nowhere comes to a point2 and the like is the case in the ,antarctic region4 ,when the #bd ,gaussian elements at any time are known the magnetic condition of the globe is known1 just as the mechanical condition of the solar system is known1 when we know the elements of the orbits of the satellites and planets and the mass of each4 ,and the comparison of this magnetic condition of the globe at distant periods of time cannot fail to supply materials for future researches and speculations with regard to the agencies by which the condition of the earth is determined4 ,the condition of which we here speak must necessarily be its mechanico-chemical condition1 being expressed1 as it will be1 in terms of the mechanico-chemical sciences4 ,the #bca investigations ,i have been describing belong to the mechanical side of the subject3 but when philosophers have to consider the causes of the secular changes which are found to occur in this mechanical condition1 they cannot fail to be driven to electrical1 that is1 chemical agencies and laws4 ,i can only allude to ,gauss's investigations respecting the ,absolute ,measure of the ,earth's ,magnetic ,force4 ,to determine the ratio of the magnetic force of the earth to that of a known magnet1 ,poisson proposed to observe the time of vibration of a second magnet4 ,the method of ,gauss1 now universally adopted1 consists in observing the position of equilibrium of the second magnet when deflected by the first4 ,the manner in which the business of magnetic observation has been taken up by the governments of our time makes this by far the greatest scientific undertaking which the world has ever seen4 ,the result will be that we shall obtain in a few years a knowledge of the magnetic constitution of the earth which otherwise it might have required centuries to accumulate4 ,the secular magnetic changes must still require a long time to reduce to their laws of phenomena1 except observation be anticipated or assisted by some happy discovery as to the cause of these changes4 ,but besides the special gain to magnetic science by this great plan of joint action among the nations of the earth1 there is thereby a beginning made in the recognition and execution of the duty of forwarding science in general by national exertions4 ,for at most of the magnetic observatories1 meteorological observations are also carried on2 and such observations1 being far more extensive1 systematic1 and permanent than those which have usually been made1 can hardly fail to produce important additions to science4 ,but at any rate they do for science that which nations can do1 and individuals cannot2 and they seek for scientific truths in a manner suitable to the respect now professed for science and to the progress which its methods have made4 ,nor are we to overlook the effect of such observations as means of training men in the pursuit of science4 ,there is amongst us1 says one of the magnetic observers1 a growing recognition of the importance1 both for science and for practical life1 of forming exact observers of nature4 ,hitherto astronomy alone has afforded a very partial opportunity for the formation of fine observers1 of which few could avail themselves4 ,experience has shown that magnetic observations may serve as excellent training schools in this respect4#bgab #bcb ,note #bgab3 ,letter of ,w4 ,weber4 ,brit4 ,assoc4 ,rep4 #ahde1 p4 #ag4 ,the various other circumstances which terrestrial magnetism exhibits1--the diurnal and annual changes of the position of the compass-needle2--the larger secular change which affects it in the course of years2--the difference of intensity at different places1 and other facts1 have naturally occupied philosophers with the attempt to determine1 both the laws of the phenomena and their causes4 ,but these attempts necessarily depend1 not upon laws of statical magnetism1 such as they have been explained above2 but upon the laws by which the production and intensity of magnetism in different cases are regulated2--laws which belong to a different province1 and are related to a different set of principles4 ,thus1 for example1 we have not attempted to explain the discovery of the laws by which heat influences magnetism2 and therefore we cannot now give an account of those theories of the facts relating to terrestrial magnetism1 which depend upon the influence of temperature4 ,the conditions of excitation of magnetism are best studied by comparing this force with other cases where the same effects are produced by very different apparent agencies2 such as galvanic and thermo-electricity4 ,to the history of these we shall presently proceed4 ,conclusion4--,the hypothesis of magnetic fluids1 as physical realities1 was never widely or strongly embraced1 as that of electric fluids was4 ,for though the hypothesis accounted1 to a remarkable degree of exactness1 for large classes of the phenomena1 the presence of a material fluid was not indicated by facts of a different kind1 such as the spark1 the discharge from points1 the shock1 and its mechanical effects4 ,thus the belief of a peculiar magnetic fluid or fluids was not forced upon men's minds2 and the doctrine above stated was probably entertained by most of its adherents1 chiefly as a means of expressing the laws of phenomena in their elementary form4 ,one other observation occurs here4 ,we have seen that the supposition of a fluid moveable from one part of bodies to another1 and capable of accumulation in different parts of the surface1 appeared at first to be as distinctly authorized by magnetic as by electric phenomena2 and yet that it afterwards appeared1 by calculation1 that this must be considered as a derivative result2 no real transfer of fluid taking place except within the limits of the insensible particles of the body4 ,without attempting to found a formula of philosophizing on this circumstance1 we may observe1 that this occurrence1 like the disproof of heat as a material fluid1 shows the possibility of an hypothesis which shall very exactly satisfy many phenomena1 and yet be incomplete3 it #bcc shows1 too1 the necessity of bringing facts of all kinds to bear on the hypothesis2 thus1 in this case it was requisite to take into account the facts of junction and separation of magnetic bodies1 as well as their attractions and repulsions4 ,if we have seen reason to doubt the doctrine of electric fluids as physical realities1 we cannot help pronouncing upon the magnetic fluids as having still more insecure claims to a material existence1 even on the grounds just stated4 ,but we may add considerations still more decisive2 for at a further stage of discovery1 as we shall see1 magnetic and electric action were found to be connected in the closest manner1 so as to lead to the persuasion of their being different effects of one common cause4 ,after those discoveries1 no philosopher would dream of assuming electric fluids and magnetic fluids as two distinct material agents4 ,yet even now the nature of the dependence of magnetism upon any other cause is extremely difficult to conceive4 ,but till we have noticed some of the discoveries to which we have alluded1 we cannot even speculate about that dependence4 ,we now1 therefore1 proceed to sketch the history of these discoveries4 #bce ,,book ,,xiii4 ,,mechanico-,,chemical ,,sciences4 7,,continued47 ,,history ,,of ,,galvanism1 ,,or ,,voltaic ,,electricity4 ,percusss gelido trepidant sub pectore fibr1 ,et nova desuetis subrepens vita medullis ,miscetur morti3 tunc omnis palpitat artus ,tenduntur nervi2 nec se tellure cadaver ,paullatim per membra levat2 terrque repulsum est ,erectumque simul4 ,,lucan4 vi4 #geb4 ,the form which lay before inert and dead1 ,sudden a piercing thrill of change o'erspread2 ,returning life gleams in the stony face1 ,the fibres quiver and the sinews brace1 ,move the stiff limbs2--nor did the body rise ,with tempered strength which genial life supplies1 ,but upright starting1 its full stature held1 ,as though the earth the supine corse repelled4 #bcg ,,chapter ,i4 ,,discovery ,,of ,,voltaic ,,electricity4 ,,we have given the name of mechanico-chemical to the class of sciences now under our consideration2 for these sciences are concerned with cases in which mechanical effects1 that is1 attractions and repulsions1 are produced2 while the conditions under which these effects occur1 depend1 as we shall hereafter see1 on chemical relations4 ,in that branch of these sciences which we have just treated of1 ,magnetism1 the mechanical phenomena were obvious1 but their connexion with chemical causes was by no means apparent1 and1 indeed1 has not yet come under our notice4 ,the subject to which we now proceed1 ,galvanism1 belongs to the same group1 but1 at first sight1 exhibits only the other1 the chemical1 portion of the features of the class2 for the connexion of galvanic phenomena with chemical action was soon made out1 but the mechanical effects which accompany them were not examined till the examination was required by a new train of discovery4 ,it is to be observed1 that ,i do not include in the class of mechanical effects the convulsive motions in the limbs of animals which are occasioned by galvanic action2 for these movements are produced1 not by attraction and repulsion1 but by muscular irritability2 and though they indicate the existence of a peculiar agency1 cannot be used to measure its intensity and law4 ,the various examples of the class of agents which we here consider1--magnetism1 electricity1 galvanism1 electro-magnetism1 thermo-electricity1--differ from each other principally in the circumstances by which they are called into action2 and these differences are in reality of a chemical nature1 and will have to be considered when we come to treat of the inductive steps by which the general principles of chemical theory are established4 ,in the present part of our task1 therefore1 we must take for granted the chemical conditions on which the excitation of these various kinds of action depends1 and trace the history of the discovery of their mechanical laws only4 ,this rule will much abridge the account we have here to give of the progress of discovery in the provinces to which ,i have just referred4 #bch ,the first step in this career of discovery was that made by ,galvani1 ,professor of ,anatomy at ,bologna4 ,in #agij1 electricity1 as an experimental science1 was nearly stationary4 ,the impulse given to its progress by the splendid phenomena of the ,leyden phial had almost died away2 ,coulomb was employed in systematizing the theory of the electric fluid1 as shown by its statical effects2 but in all the other parts of the subject1 no great principle or new result had for some time been detected4 ,the first announcement of ,galvani's discovery in #agia excited great notice1 for it was given forth as a manifestation of electricity under a new and remarkable character2 namely1 as residing in the muscles of animals4#aac ,the limbs of a dissected frog were observed to move1 when touched with pieces of two different metals2 the agent which produced these motions was conceived to be identified with electricity1 and was termed animal electricity2 and ,galvani's experiments were repeated1 with various modifications1 in all parts of ,europe1 exciting much curiosity1 and giving rise to many speculations4 ,note #aac3 ,de ,viribus ,electricis in ,motu ,musculari1 ,comm4 ,bonon4 t4 vii4 #agib4 ,it is our business to determine the character of each great discovery which appears in the progress of science4 ,men are fond of repeating that such discoveries are most commonly the result of accident2 and we have seen reason to reject this opinion1 since that preparation of thought by which the accident produces discovery is the most important of the conditions on which the successful event depends4 ,such accidents are like a spark which discharges a gun already loaded and pointed4 ,in the case of ,galvani1 indeed1 the discovery may1 with more propriety than usual1 be said to have been casual2 but in the form in which it was first noted1 it exhibited no important novelty4 ,his frog was lying on a table near the conductor of an electrical machine1 and the convulsions appeared only when a spark was taken from the machine4 ,if ,galvani had been as good a physicist as he was an anatomist1 he would probably have seen that the movements so occasioned proved only that the muscles or nerves1 or the two together1 formed a very sensitive indicator of electrical action4 ,it was when he produced such motions by contact of metals alone1 that he obtained an important and fundamental fact in science4 ,the analysis of this fact into its real and essential conditions was the work of ,alexander ,volta1 another ,italian professor4 ,volta1 indeed1 possessed that knowledge of the subject of electricity which made a hint like that of ,galvani the basis of a new science4 ,galvani appears #bci never to have acquired much general knowledge of electricity3 ,volta1 on the other hand1 had labored at this branch of knowledge from the age of eighteen1 through a period of nearly thirty years2 and had invented an electrophorus and an electrical condenser1 which showed great experimental skill4 ,when he turned his attention to the experiments made by ,galvani1 he observed that the author of them had been far more surprised than he needed to be1 at those results in which an electrical spark was produced2 and that it was only in the cases in which no such apparatus was employed1 that the observations could justly be considered as indicating a new law1 or a new kind of electricity4#bac ,he soon satisfied himself#cac 7about #agid7 that the essential conditions of this kind of action depended on the metals2 that it is brought into play most decidedly when two different metals touch each other1 and are connected by any moist body2--and that the parts of animals which had been used discharged the office both of such moist bodies1 and of very sensitive electrometers4 ,the animal electricity of ,galvani might1 he observed1 be with more propriety called metallic electricity4 ,note #bac3 ,phil4 ,trans4 #agic1 p4 #ba4 ,note #cac3 ,see ,fischer1 viii4 #fbe4 ,the recognition of this agency as a peculiar kind of electricity1 arose in part perhaps1 at first1 from the confusion made by ,galvani between the cases in which his electrical machine was1 and those in which it was not employed4 ,but the identity was confirmed by its being found that the known difference of electrical conductors and non-conductors regulated the conduction of the new influence4 ,the more exact determination of the new facts to those of electricity was a succeeding step of the progress of the subject4 ,the term animal electricity has been superseded by others1 of which galvanism is perhaps the most familiar4 ,i think it will appear from what has been said1 that ,volta's office in this discovery is of a much higher and more philosophical kind than that of ,galvani2 and it would1 on this account1 be more fitting to employ the term voltaic electricity2 which1 indeed1 is very commonly used1 especially by our most recent and comprehensive writers4 ,volta more fully still established his claim as the main originator of this science by his next step4 ,when some of those who repeated the experiments of ,galvani had expressed a wish that there was some method of multiplying the effect of this electricity1 such as the ,leyden phial supplies for common electricity1 they probably thought their wishes far from a realization4 ,but the voltaic pile1 which ,volta #bdj described in the ,philosophical ,transactions for #ahjj1 completely satisfies this aspiration2 and was1 in fact1 a more important step in the history of electricity than the ,leyden jar had been4 ,it has since undergone various modifications1 of which the most important was that introduced by 9999,cruickshanks1 who#dac substituted a trough for a pile4 ,but in all cases the principle of the instrument was the same2--a continued repetition of the triple combination of two metals and a fluid in contact1 so as to form a circuit which returns into itself4 ,note #dac3 ,fischer1 viii4 p4 #fhc4 ,such an instrument is capable of causing effects of great intensity2 as seen both in the production of light and heat1 and in chemical changes4 ,but the discovery with which we are here concerned1 is not the details and consequences of the effects1 7which belong to chemistry17 but the analysis of the conditions under which such effects take place2 and this we may consider as completed by ,volta at the epoch of which we speak4 ,,chapter ,,ii4 ,,reception ,,and ,,confirmation ,,of ,,the ,,discovery ,,of ,,voltaic ,,electricity4 ,,galvani',s experiments excited a great interest all over ,europe1 in consequence partly of a circumstance which1 as we have seen1 was unessential1 the muscular contractions and various sensations which they occasioned4 ,galvani himself had not only considered the animal element of the circuit as the origin of the electricity1 but had framed a theory1#eac in which he compared the muscles to charged jars1 and the nerves to the discharging wires2 and a controversy was1 for some time1 carried on1 in ,italy1 between the adherents of ,galvani and those of ,volta4#fac ,note #eac3 ,ib4 viii4 #fac4 ,note #fac3 ,ib4 viii4 #fai4 ,the galvanic experiments1 and especially those which appeared to have a physiological bearing1 were verified and extended by a number of the most active philosophers of ,europe1 and especially ,william von ,humboldt4 ,a commission of the ,institute of ,france1 appointed in #agig1 repeated many of the known experiments1 but does not seem to have decided any disputed points4 ,the researches of this #bda commission referred rather to the discoveries of ,galvani than to those of ,volta3 the latter were1 indeed1 hardly known in ,france till the conquest of ,italy by ,bonaparte1 in #ahja4 ,france was1 at the period of these discoveries1 separated from all other countries by war1 and especially from ,england1#gac where ,volta's ,memoirs were published4 ,note #gac3 ,biog4 ,univ41 art4 ,volta1 7by ,biot47 ,the political revolutions of ,italy affected1 in very different manners1 the two discoverers of whom we speak4 ,galvani refused to take an oath of allegiance to the ,cisalpine republic1 which the ,french conqueror established2 he was consequently stripped of all his offices2 and deprived1 by the calamities of the times1 of most of his relations1 he sank into poverty1 melancholy1 and debility4 ,at last his scientific reputation induced the republican rulers to decree his restoration to his professorial chair2 but his claims were recognised too late1 and he died without profiting by this intended favor1 in #agih4 ,volta1 on the other hand1 was called to ,paris by ,bonaparte as a man of science1 and invested with honors1 emoluments1 and titles4 ,the conqueror himself1 indeed1 was strongly interested by this train of research4#hac ,he himself founded valuable prizes1 expressly with a view to promote its prosecution4 ,at this period1 there was something in this subject peculiarly attractive to his ,italian mind2 for the first glimpses of discoveries of great promise have always excited an enthusiastic activity of speculation in the philosophers of ,italy1 though generally accompanied with a want of precise thought4 ,it is narrated#iac of ,bonaparte1 that after seeing the decomposition of the salts by means of the voltaic pile1 he turned to ,corvisart1 his physician1 and said1 ,here1 doctor1 is the image of life2 the vertebral column is the pile1 the liver is the negative1 the bladder the positive1 pole4 ,the importance of voltaic researches is not less than it was estimated by ,bonaparte2 but the results to which it was to lead were of a kind altogether different from those which thus suggested themselves to his mind4 ,the connexion of mechanical and chemical action was the first great point to be dealt with2 and for this purpose the laws of the mechanical action of voltaic electricity were to be studied4 ,note #hac3 ,becquerel1 ,trait d',electr4 t4 i4 p4 #ajg4 ,note #iac3 ,ib4 t4 i4 p4 #ajh4 ,it will readily be supposed that the voltaic researches1 thus begun1 opened a number of interesting topics of examination and discussion4 ,these1 however1 it does not belong to our place to dwell upon at present2 since they formed parts of the theory of the subject1 which #bdb was not completed till light had been thrown upon it from other quarters4 ,the identity of galvanism with electricity1 for instance1 was at first1 as we have intimated1 rather conjectured than proved4 ,it was denied by ,dr4 ,fowler1 in #agic2 was supposed to be confirmed by ,dr4 ,wells two years later2 but was1 still later1 questioned by ,davy4 ,the nature of the operation of the pile was variously conceived4 ,volta himself had obtained a view of it which succeeding researches confirmed1 when he asserted1#ajac in #ahjj1 that it resembled an electric battery feebly charged and constantly renewing its charge4 ,in pursuance of this view1 the common electrical action was1 at a later period 7for instance by ,ampre1 in #ahbj71 called electrical tension1 while the voltaic action was called the electrical current1 or electromotive action4 ,the different effects produced1 by increasing the size and the number of the plates in the voltaic trough1 were also very remarkable4 ,the power of producing heat was found to depend on the size of the plates2 the power of producing chemical changes1 on the other hand1 was augmented by the number of plates of which the battery consisted4 ,the former effect was referred to the increased quantity1 the latter to the intensity1 of the electric fluid4 ,we mention these distinctions at present1 rather for the purpose of explaining the language in which the results of the succeeding investigations are narrated1 than with the intention of representing the hypotheses and measures which they imply1 as clearly established1 at the period of which we speak4 ,for that purpose new discoveries were requisite1 which we have soon to relate4 ,note #ajac3 ,phil4 ,trans4 p4 #djc4 ,,chapter ,,iii4 ,,discovery ,,of ,,the ,,laws ,,of ,,the ,,mutual ,,attraction ,,and ,,repulsion ,,of ,,voltaic ,,currents4--,,amp,,re4 ,,in order to show the place of voltaic electricity among the mechanico-chemical sciences1 we must speak of its mechanical laws as separate from the laws of electro-magnetic action2 although1 in fact1 it was only in consequence of the forces which conducting voltaic wires exert upon magnets1 that those forces were detected which they exert upon each #bdc other4 ,this latter discovery was made by ,m4 ,ampre2 and the extraordinary rapidity and sagacity with which he caught the suggestion of such forces1 from the electro-magnetic experiments of ,m4 ,oersted1 7of which we shall speak in the next chapter17 well entitle him to be considered as a great and independent discoverer4 ,as he truly says1#aaac it by no means followed1 that because a conducting wire exerted a force on a magnet1 two conducting wires must exert a force on each other2 for two pieces of soft iron1 both of which affect a magnet1 do not affect each other4 ,but immediately on the promulgation of ,oersted's experiments1 in #ahbj1 ,ampre leapt forwards to a general theory of the facts1 of which theory the mutual attraction and repulsion of conducting voltaic wires was a fundamental supposition4 ,the supposition was immediately verified by direct trial2 and the laws of this attraction and repulsion were soon determined1 with great experimental ingenuity1 and a very remarkable command of the resources of analysis4 ,but the experimental and analytical investigation of the mutual action of voltaic or electrical currents1 was so mixed up with the examination of the laws of electro-magnetism1 which had given occasion to the investigation1 that we must not treat the two provinces of research as separate4 ,the mention in this place1 premature as it might appear1 of the labors of ,ampre1 arises inevitably from his being the author of a beautiful and comprehensive generalization1 which not only included the phenomena exhibited by the new combinations of ,oersted1 but also disclosed forces which existed in arrangements already familiar1 although they had never been detected till the theory pointed out how they were to be looked for4 ,note #aaac3 ,thorie des ,phnom4 ,electrodynamiques1 p4 #aac4 ,,chapter ,,iv4 ,,discovery ,,of ,,electro-,,magnetic ,,action4--,,oersted4 ,,the impulse which the discovery of galvanism1 in #agia1 and that of the voltaic pile1 in #ahjj1 had given to the study of electricity as a mechanical science1 had nearly died away in #ahbj4 ,it was in that year that ,m4 ,oersted1 of ,copenhagen1 announced that the conducting #bdd wire of a voltaic circuit1 acts upon a magnetic needle2 and thus recalled into activity that endeavor to connect magnetism with electricity1 which1 though apparently on many accounts so hopeful1 had hitherto been attended with no success4 ,oersted found that the needle has a tendency to place itself at right angles to the wire2--a kind of action altogether different from any which had been suspected4 ,this observation was of vast importance2 and the analysis of its conditions and consequences employed the best philosophers in ,europe immediately on its promulgation4 ,it is impossible1 without great injustice1 to refuse great merit to ,oersted as the author of the discovery4 ,we have already said that men appear generally inclined to believe remarkable discoveries to be accidental1 and the discovery of ,oersted has been spoken of as a casual insulated experiment4#abac ,yet ,oersted had been looking for such an accident probably more carefully and perseveringly than any other person in ,europe4 ,in #ahjg1 he had published#acac a work1 in which he professed that his purpose was to ascertain whether electricity1 in its most latent state1 had any effect on the magnet4 ,and he1 as ,i know from his own declaration1 considered his discovery as the natural sequel and confirmation of his early researches2 as1 indeed1 it fell in readily and immediately with speculations on these subjects then very prevalent in ,germany4 ,it was an accident like that by which a man guesses a riddle on which his mind has long been employed4 ,note #abac3 ,see ,schelling ueber ,faraday's ,entdeckung1 p4 #bg4 ,note #acac3 ,ampre1 p4 #fi4 ,besides the confirmation of ,oersted's observations by many experimenters1 great additions were made to his facts3 of these1 one of the most important was due to ,ampre4 ,since the earth is in fact magnetic1 the voltaic wire ought to be affected by terrestrial magnetism alone1 and ought to tend to assume a position depending on the position of the compass-needle4 ,at first1 the attempts to produce this effect failed1 but soon1 with a more delicate apparatus1 the result was found to agree with the anticipation4 ,it is impossible here to dwell on any of the subsequent researches1 except so far as they are essential to our great object1 the progress towards a general theory of the subject4 ,i proceed1 therefore1 immediately to the attempts made towards this object4 #bde ,,chapter ,v4 ,,discovery ,,of ,,the ,,laws ,,of ,,electro-,,magnetic ,,action4 ,,on attempting to analyse the electro-magnetic phenomena observed by ,oersted and others into their simplest forms1 they appeared1 at least at first sight1 to be different from any mechanical actions which had yet been observed4 ,it seemed as if the conducting wire exerted on the pole of the magnet a force which was not attractive or repulsive1 but transverse2--not tending to draw the point acted on nearer1 or to push it further off1 in the line which reached from the acting point1 but urging it to move at right angles to this line4 ,the forces appeared to be such as ,kepler had dreamt of in the infancy of mechanical conceptions2 rather than such as those of which ,newton had established the existence in the solar system1 and such as he1 and all his successors1 had supposed to be the only kinds of force which exist in nature4 ,the north pole of the needle moved as if it were impelled by a vortex revolving round the wire in one direction1 while the south pole seemed to be driven by an opposite vortex4 ,the case seemed novel1 and almost paradoxical4 ,it was soon established by experiments1 made in a great variety of forms1 that the mechanical action was really of this transverse kind4 ,and a curious result was obtained1 which a little while before would have been considered as altogether incredible2--that this force would cause a constant and rapid revolution of either of the bodies about the other2--of the conducting wire about the magnet1 or of the magnet about the conducting wire4 ,this was effected by ,mr4 ,faraday in #ahba4 ,the laws which regulated the intensity of this force1 with reference to the distance and position of the bodies1 now naturally came to be examined4 ,,mm4 ,biot and ,savart in ,france1 and ,mr4 ,barlow in ,england1 instituted such measures2 and satisfied themselves that the elementary force followed the law of magnitude of all known elementary forces1 in being inversely as the square of the distance2 although1 in its direction1 it was so entirely different from other forces4 ,but the investigation of the laws of phenomena of the subject was too closely connected with the choice of a mechanical theory1 to be established #bdf previously and independently1 as had been done in astronomy4 ,the experiments gave complex results1 and the analysis of these into their elementary actions was almost an indispensable step in order to disentangle their laws4 ,we must1 therefore1 state the progress of this analysis4 ,,chapter ,,vi4 ,,theory ,,of ,,electrodynamical ,,action4 ,,amp,,re',s ,,theory4--,nothing can show in a more striking manner the advanced condition of physical speculation in #ahbj1 than the reduction of the strange and complex phenomena of electromagnetism to a simple and general theory as soon as they were published4 ,instead of a gradual establishment of laws of phenomena1 and of theories more and more perfect1 occupying ages1 as in the case of astronomy1 or generations1 as in the instances of magnetism and electricity1 a few months sufficed for the whole process of generalization2 and the experiments made at ,copenhagen were announced at ,paris and ,london1 almost at the same time with the skilful analysis and comprehensive inductions of ,ampre4 ,yet we should err if we should suppose1 from the celerity with which the task was executed1 that it was an easy one4 ,there were required in the author of such a theory1 not only those clear conceptions of the relations of space and force1 which are the first conditions of all sound theory1 and a full possession of the experiments2 but also a masterly command of the mathematical arms by which alone the victory could be gained1 and a sagacious selection of proper experiments which might decide the fate of the proposed hypothesis4 ,it is true1 that the nature of the requisite hypothesis was not difficult to see in a certain vague and limited way4 ,the conducting-wire and the magnetic needle had a tendency to arrange themselves at right angles to one another4 ,this might be represented by supposing the wire to be made up of transverse magnetic needles1 or by supposing the needle to be made up of transverse conducting-wires2 for it was easy to conceive forces which should bring corresponding elements1 either magnetic or voltaic1 into parallel positions2 and then the #bdg general phenomena above stated would be accounted for4 ,and the choice between the two modes of conception1 appeared at first sight a matter of indifference4 ,the majority of philosophers at first adopted1 or at least employed1 the former method1 as ,oersted in ,germany1 ,berzelius in ,sweden1 ,wollaston in ,england4 ,ampre adopted the other view1 according to which the magnet is made up of conducting-wires in a transverse position4 ,but he did for his hypothesis what no one did or could do for the other3 he showed that it was the only one which would account1 without additional and arbitrary suppositions1 for the facts of continued motion in electromagnetic cases4 ,and he further elevated his theory to a higher rank of generality1 by showing that it explained1--not only the action of a conducting-wire upon a magnet1 but also two other classes of facts1 already spoken of in this history1--the action of magnets upon each other1--and the action of conducting-wires upon each other4 ,the deduction of such particular cases from the theory1 required1 as may easily be imagined1 some complex calculations3 but the deduction being satisfactory1 it will be seen that ,ampre's theory conformed to that description which we have repeatedly had to point out as the usual character of a true and stable theory2 namely1 that besides accounting for the class of phenomena which suggested it1 it supplies an unforeseen explanation of other known facts4 ,for the mutual action of magnets1 which was supposed to be already reduced to a satisfactory theoretical form by ,coulomb1 was not contemplated by ,ampre in the formation of his hypothesis2 and the mutual action of voltaic currents1 though tried only in consequence of the suggestion of the theory1 was clearly a fact distinct from electromagnetic action2 yet all these facts flowed alike from the theory4 ,and thus ,ampre brought into view a class of forces for which the term electromagnetic was too limited1 and which he designated#adac by the appropriate term electrodynamic2 distinguishing them by this expression1 as the forces of an electric current1 from the statical effects of electricity which we had formerly to treat of4 ,this term has passed into common use among scientific writers1 and remains the record and stamp of the success of the ,amperian induction4 ,note #adac3 ,ann4 de ,chim41 tom4 xx4 p4 #fj 7#ahbb74 ,the first promulgation of ,ampre's views was by a communication to the ,french ,academy of ,sciences1 ,september the #ahth1 #ahbj2 ,oersted's discoveries having reached ,paris only in the preceding ,july4 #bdh ,at almost every meeting of the ,academy during the remainder of that year and the beginning of the following one1 he had new developements or new confirmations of his theory to announce4 ,the most hypothetical part of his theory1--the proposition that magnets might be considered in their effects as identical with spiral voltaic wires1--he asserted from the very first4 ,the mutual attraction and repulsion of voltaic wires1--the laws of this action1--the deduction of the observed facts from it by calculation1--the determination1 by new experiments1 of the constant quantities which entered into his formul1--followed in rapid succession4 ,the theory must be briefly stated4 ,it had already been seen that parallel voltaic currents attracted each other2 when1 instead of being parallel1 they were situate in any directions1 they still exerted attractive and repulsive forces depending on the distance1 and on the directions of each element of both currents4 ,add to this doctrine the hypothetical constitution of magnets1 namely1 that a voltaic current runs round the axis of each particle1 and we have the means of calculating a vast variety of results which may be compared with experiment4 ,but the laws of the elementary forces required further fixation4 ,what functions are the forces of the distance and the directions of the elements8 ,to extract from experiment an answer to this inquiry was far from easy1 for the elementary forces were mathematically connected with the observed facts1 by a double mathematical integration2--a long1 and1 while the constant coefficients remained undefined1 hardly a possible operation4 ,ampre made some trials in this way1 but his happier genius suggested to him a better path4 ,it occurred to him1 that if his integrals1 without being specially found1 could be shown to vanish upon the whole1 under certain conditions of the problem1 this circumstance would correspond to arrangements of his apparatus in which a state of equilibrium was preserved1 however the form of some of the parts might be changed4 ,he found two such cases1 which were of great importance to the theory4 ,the first of these cases proved that the force exerted by any element of the voltaic wire might be resolved into other forces by a theorem resembling the well-known proposition of the parallelogram of forces4 ,this was proved by showing that the action of a straight wire is the same with that of another wire which joins the same extremities1 but is bent and contorted in any way whatever4 ,but it still remained necessary to determine two fundamental quantities2 one which expressed the power of the distance according to which the force varied2 the other1 the #bdi degree in which the force is affected by the obliquity of the elements4 ,one of the general causes of equilibrium1 of which we have spoken1 gave a relation between these two quantities2#aeac and as the power was naturally1 and1 as it afterwards appeared1 rightly conjectured to be the inverse square1 the other quantity also was determined2 and the general problem of electrodynamical action was fully solved4 ,note #aeac3 ,communication to the ,acad4 ,sc41 ,june #aj1 #ahbb4 ,see ,ampre1 ,recueil1 p4 #bib4 ,if ,ampre had not been an accomplished analyst1 he would not have been able to discover the condition on which the nullity of the integral in this case depended4#afac ,and throughout his labors1 we find reason to admire1 both his mathematical skill1 and his steadiness of thought2 although these excellences are by no means accompanied throughout with corresponding clearness and elegance of exposition in his writings4 ,note #afac3 ,recueil1 p4 #cad4 ,reception of ,ampre's ,theory4--,clear mathematical conceptions1 and some familiarity with mathematical operations1 were needed by readers also1 in order to appreciate the evidence of the theory2 and1 therefore1 we need not feel any surprise if it was1 on its publication and establishment1 hailed with far less enthusiasm than so remarkable a triumph of generalizing power might appear to deserve4 ,for some time1 indeed1 the greater portion of the public were naturally held in suspense by the opposing weight of rival names4 ,the ,amperian theory did not make its way without contention and competition4 ,the electro-magnetic experiments1 from their first appearance1 gave a clear promise of some new and wide generalization2 and held out a prize of honor and fame to him who should be first in giving the right interpretation of the riddle4 ,in ,france1 the emulation for such reputation is perhaps more vigilant and anxious than it is elsewhere2 and we see1 on this as on other occasions1 the scientific host of ,paris springing upon a new subject with an impetuosity which1 in a short time1 runs into controversies for priority or for victory4 ,in this case1 ,m4 ,biot1 as well as ,ampre1 endeavored to reduce the electro-magnetic phenomena to general laws4 ,the discussion between him and ,ampre turned on some points which are curious4 ,m4 ,biot was disposed to consider as an elementary action1 the force which an element of a voltaic wire exerts upon a magnetic particle1 and which is1 as we have seen1 at right angles to their mutual distance2 and he conceived that #bej the equal reaction which necessarily accompanies this action acts oppositely to the action1 not in the same line1 but in a parallel line1 at the other extremity of the distance2 thus forming a primitive couple1 to use a technical expression borrowed from mechanics4 ,to this ,ampre objected1#agac that the direct opposition of all elementary action and reaction was a universal and necessary mechanical law4 ,he showed too that such a couple as had been assumed1 would follow as a derivative result from his theory4 ,and in comparing his own theory with that in which the voltaic wire is assimilated to a collection of transverse magnets1 he was also able to prove that no such assemblage of forces acting to and from fixed points1 as the forces of magnets do act1 could produce a continued motion like that discovered by ,faraday4 ,this1 indeed1 was only the well-known demonstration of the impossibility of a perpetual motion4 ,if1 instead of a collection of magnets1 the adverse theorists had spoken of a magnetic current1 they might probably interpret their expressions so as to explain the facts2 that is1 if they considered every element of such a current as a magnet1 and consequently1 every point of it as being a north and a south point at the same instant4 ,but to introduce such a conception of a magnetic current was to abandon all the laws of magnetic action hitherto established2 and consequently to lose all that gave the hypothesis its value4 ,the idea of an electric current1 on the other hand1 was so far from being a new and hazardous assumption1 that it had already been forced upon philosophers from the time of ,volta2 and in this current1 the relation of preceding and succeeding1 which necessarily existed between the extremities of any element1 introduced that relative polarity on which the success of the explanations of the facts depended4 ,and thus in this controversy1 the theory of ,ampre has a great and undeniable superiority over the rival hypotheses4 ,note #agac3 ,ampre1 ,thorie1 p4 #aed4 ,,chapter ,,vii4 ,,consequences ,,of ,,the ,,electrodynamic ,,theory4 ,,it is not necessary to state the various applications which were soon made of the electro-magnetic discoveries4 ,but we may notice one #bea of the most important1--the ,galvanometer1 an instrument which1 by enabling the philosopher to detect and to measure extremely minute electrodynamic actions1 gave an impulse to the subject similar to that which it received from the invention of the ,leyden ,phial1 or the ,voltaic ,pile4 ,the strength of the voltaic current was measured1 in this instrument1 by the deflection produced in a compass-needle2 and its sensibility was multiplied by making the wire pass repeatedly above and below the needle4 ,schweigger1 of ,halle1 was one of the first devisers of this apparatus4 ,the substitution of electro-magnets1 that is1 of spiral tubes composed of voltaic wires1 for common magnets1 gave rise to a variety of curious apparatus and speculations1 some of which ,i shall hereafter mention4 #bnd ,ed4 ,when a voltaic apparatus is in action1 there may be conceived to be a current of electricity running through its various elements1 as stated in the text4 ,the force of this current in various parts of the circuit has been made the subject of mathematical investigation by ,m4 ,ohm4#ahac ,the problem is in every respect similar to that of the flow of heat through a body1 and taken generally1 leads to complex calculations of the same kind4 ,but ,dr4 ,ohm1 by limiting the problem in the first place by conditions which the usual nature and form of voltaic apparatus suggest1 has been able to give great simplicity to his reasonings4 ,these conditions are1 the linear form of the conductors 7wires7 and the steadiness of the electric state4 ,for this part of the problem ,dr4 ,ohm's reasonings are as simple and as demonstrative as the elementary propositions of ,mechanics4 ,the formul for the electric force of a voltaic current to which he is led have been experimentally verified by others1 especially ,fechner1#aiac ,gauss1#bjac ,lenz1 ,jacobi1 ,poggendorf1 and ,pouillet4 ,note #ahac3 ,die ,galvanische ,kette ,mathematisch bearbeitet von ,dr4 ,g4 ,s4 ,ohm1 ,berlin1 #ahbg4 ,note #aiac3 9999,mass-bestimmungen ber die ,galvanische ,kette4 ,leipzig1 #ahca4 ,note #bjac3 ,results of the ,magnetic ,association4 ,among ourselves1 ,mr4 ,wheatstone has confirmed and applied the views of ,m4 ,ohm1 in a ,memoir#baac ,on ,new ,instruments and ,processes for determining the ,constants of a ,voltaic ,circuit4 ,he there remarks that the clear ideas of electromotive forces and resistances1 substituted by ,ohm for the vague notions of quantity and intensity which have long been prevalent1 give satisfactory explanations of the most important difficulties1 and express the laws of a vast number of phenomena #beb in formul of remarkable simplicity and generality4 ,in this ,memoir1 ,professor ,wheatstone describes an instrument which he terms ,rheostat1 because it brings to a common standard the voltaic currents which are compared by it4 ,he generalizes the language of the subject by employing the term rheomotor for any apparatus which originates an electric current 7whether voltaic or thermoelectric1 c47 and rheometer for any instrument to measure the force of such a current4 ,it appears that the idea of constructing an instrument of the nature of the ,rheostat had occurred also to ,prof4 ,jacobi1 of ,st ,petersburg4 ,note #baac3 ,phil4 ,trans4 #ahdc4 ,pt4 #aa4 ,the galvanometer led to the discovery of another class of cases in which the electrodynamical action was called into play1 namely1 those in which a circuit1 composed of two metals only1 became electro-magnetic by heating one part of it4 ,this discovery of thermo-electricity was made by ,professor ,seebeck of ,berlin1 in #ahbb1 and prosecuted by various persons2 especially by ,prof4 ,cumming#bbac of ,cambridge1 who1 early in #ahbc1 extended the examination of this property to most of the metals1 and determined their thermo-electric order4 ,but as these investigations exhibited no new mechanical effects of electromotive forces1 they do not now further concern us2 and we pass on1 at present1 to a case in which such forces act in a manner different from any of those already described4 ,note #bbac3 ,camb4 ,trans4 vol4 ii4 p4 #fb4 ,on the ,development of ,electro-,magnetism by ,heat4 ,,discovery ,,of ,,diamagnetism4 #bnd ,ed4 ,by the discoveries just related1 a cylindrical spiral of wire through which an electric current is passing is identified with a magnet2 and the effect of such a spiral is increased by placing in it a core of soft iron4 ,by the use of such a combination under the influence of a voltaic battery1 magnets are constructed far more powerful than those which depend upon the permanent magnetism of iron4 ,the electro-magnet employed by ,dr4 ,faraday in some of his experiments would sustain a hundred-weight at either end4 ,by the use of such magnets ,dr4 ,faraday discovered that1 besides iron1 nickel and cobalt1 which possess magnetism in a high degree1 many bodies are magnetic in a slight degree4 ,and he made the further very important discovery1 that of those substances which are not magnetic1 many1 perhaps all1 possess an opposite property1 in virtue of which he terms them diamagnetic4 ,the opposition is of this #bec kind2--that magnetic bodies in the form of bars or needles1 if free to move1 arrange themselves in the axial line joining the poles2 diamagnetic bodies under the same circumstances arrange themselves in an equatorial position1 perpendicular to the axial line4 ,and this tendency he conceives to be the result of one more general2 that whereas magnetic bodies are attracted to the poles of a magnet1 diamagnetic bodies are repelled from the poles4 ,the list of diamagnetic bodies includes all kinds of substances2 not only metals1 as antimony1 bismuth1 gold1 silver1 lead1 tin1 zinc1 but many crystals1 glass1 phosphorus1 sulphur1 sugar1 gum1 wood1 ivory2 and even flesh and fruit4 ,it appears that ,m4 le ,bailli had shown1 in #ahbi1 that both bismuth and antimony and bismuth repelled the magnetic needle2 and as ,dr4 ,faraday remarks1 it is astonishing that such an experiment should have remained so long without further results4 ,m4 ,becquerel in #ahbg observed1 and quoted ,coulomb as having also observed1 that a needle of wood under certain conditions pointed across the magnetic curves2 and also stated that he had found a needle of wood place itself parallel to the wires of a galvanometer4 ,this he referred to a magnetism transverse to the length4 ,but he does not refer the phenomena to elementary repulsive action1 nor show that they are common to an immense class of bodies1 nor distinguish this diamagnetic from the magnetic class1 as ,faraday has taught us to do4 ,i do not dwell upon the peculiar phenomena of copper which1 in the same series of researches1 are traced by ,dr4 ,faraday to the combined effect of its diamagnetic character1 and the electric currents excited in it by the electro-magnet2 nor to the optical phenomena manifested by certain transparent diamagnetic substances under electric action2 as already stated in ,book ix4#bcac ,note #bcac3 ,see the ,twentieth ,series of ,experimental ,researches in ,electricity1 read to the ,royal ,society1 ,dec4 #ah1 #ahde4 ,,chapter ,,viii4 ,,discovery ,,of ,,the ,,laws ,,of ,,magneto-,,electric ,,induction4--,,faraday4 ,,it was clearly established by ,ampre1 as we have seen1 that magnetic action is a peculiar form of electromotive actions1 and that1 in #bed this kind of agency1 action and reaction are equal and opposite4 ,it appeared to follow almost irresistibly from these considerations1 that magnetism might be made to produce electricity1 as electricity could be made to imitate all the effects of magnetism4 ,yet for a long time the attempts to obtain such a result were fruitless4 ,faraday1 in #ahbe1 endeavored to make the conducting-wire of the voltaic circuit excite electricity in a neighboring wire by induction1 as the conductor charged with common electricity would have done1 but he obtained no such effect4 ,if this attempt had succeeded1 the magnet1 which1 for all such purposes1 is an assemblage of voltaic circuits1 might also have been made to excite electricity4 ,about the same time1 an experiment was made in ,france by ,m4 ,arago1 which really involved the effect thus sought2 though this effect was not extricated from the complex phenomenon1 till ,faraday began his splendid career of discovery on this subject in #ahcb4 ,arago's observation was1 that the rapid revolution of a conducting-plate in the neighborhood of a magnet1 gave rise to a force acting on the magnet4 ,in ,england1 ,messrs4 ,barlow and ,christie1 ,herschel and ,babbage1 repeated and tried to analyse this experiment2 but referring the forces only to conditions of space and time1 and overlooking the real cause1 the electrical currents produced by the motion1 these philosophers were altogether unsuccessful in their labors4 ,in #ahca1 ,faraday again sought for electro-dynamical induction1 and after some futile trials1 at last found it in a form different from that in which he had looked for it4 ,it was then seen1 that at the precise time of making or breaking the contact which closed the galvanic circuit1 a momentary effect was induced in a neighboring wire1 but disappeared instantly4#bdac ,once in possession of this fact1 ,mr4 ,faraday ran rapidly up the ladder of discovery1 to the general point of view4--,instead of suddenly making or breaking the contact of the inducing circuit1 a similar effect was produced by removing the inducible wire nearer to or further from the circuit2#beac--the effects were increased by the proximity of soft iron2#bfac--when the soft iron was affected by an ordinary magnet instead of the voltaic wire1 the same effect still recurred2#bgac--;and thus it appeared1 that by making and breaking magnetic contact1 a momentary electric current was produced4 ,it was produced also by moving the magnet2#bhac--or by moving the wire with reference to the magnet4#biac ,finally1 it was found that the earth might supply the place of a magnet #bee in this as in other experiments2#cjac and the mere motion of a wire1 under proper circumstances1 produced in it1 it appeared1 a momentary electric current4#caac ,these facts were curiously confirmed by the results in special cases4 ,they explained ,arago's experiments3 for the momentary effect became permanent by the revolution of the plate4 ,and without using the magnet1 a revolving plate became an electrical machine2#cbac--;a revolving globe exhibited electro-magnetic action1#ccac the circuit being complete in the globe itself without the addition of any wire2--and a mere motion of the wire of a galvanometer produced an electro-dynamic effect upon its needle4#cdac ,note #bdac3 ,phil4 ,trans4 #ahcb1 p4 #abg1 ,first ,series1 ,art4 #aj4 ,note #beac3 ,art4 #ah4 ,note #bfac3 ,art4 #bh4 ,note #bgac3 ,art4 #cg4 ,note #bhac3 ,art4 #ci4 ,note #biac3 ,art4 #ec4 ,note #cjac3 ,second ,series1 ,phil4 ,trans4 p4 #afc4 ,note #caac3 ,art4 #ada4 ,note #cbac3 ,art4 #aej4 ,note #ccac3 ,art4 #afd4 ,note #cdac3 ,art4 #aga4 ,but the question occurs1 ,what is the general law which determines the direction of electric currents thus produced by the joint effects of motion and magnetism8 ,nothing but a peculiar steadiness and clearness in his conceptions of space1 could have enabled ,mr4 ,faraday to detect the law of this phenomenon4 ,for the question required that he should determine the mutual relations in space which connect the magnetic poles1 the position of the wire1 the direction of the wire's motion1 and the electrical current produced in it4 ,this was no easy problem2 indeed1 the mere relation of the magnetic to the electric forces1 the one set being perpendicular to the other1 is of itself sufficient to perplex the mind2 as we have seen in the history of the electrodynamical discoveries4 ,but ,mr4 ,faraday appears to have seized at once the law of the phenomena4 ,the relation1 he says1#ceac which holds between the magnetic pole1 the moving wire or metal1 and the direction of the current evolved1 is very simple 7so it seemed to him7 although rather difficult to express4 ,he represents it by referring position and motion to the magnetic curves1 which go from a magnetic pole to the opposite pole4 ,the current in the wire sets one way or the other1 according to the direction in which the motion of the wire cuts these curves4 ,and thus he was enabled1 at the end of his ,second ,series of ,researches 7,december1 #ahca71 to give1 in general terms1 the law of nature to which may be referred the extraordinary number of new and curious experiments which he has stated2#cfac--namely1 that if a wire move so as to cut a magnetic curve1 a power is called into action which tends to urge a magnetic current through the wire2 and that if a mass move so that its parts do not move in the same direction across the magnetic curves1 #bef and with the same angular velocity1 electrical currents are called into play in the mass4 ,note #ceac3 ,first ,series1 ,art4 #aad4 ,note #cfac3 ,art4 #bef-bfd4 ,this rule1 thus simple from its generality1 though inevitably complex in every special case1 may be looked upon as supplying the first demand of philosophy1 the law of the phenomena2 and accordingly ,dr4 ,faraday has1 in all his subsequent researches on magneto-electric induction1 applied this law to his experiments2 and has thereby unravelled an immense amount of apparent inconsistency and confusion1 for those who have followed him in his mode of conceiving the subject4 ,but yet other philosophers have regarded these phenomena in other points of view1 and have stated the laws of the phenomena in a manner different from ,faraday's1 although for the most part equivalent to his4 ,and these attempts to express1 in the most simple and general form1 the law of the phenomena of magneto-electrical induction1 have naturally been combined with the expression of other laws of electrical and magnetical phenomena4 ,further1 these endeavors to connect and generalize the ,facts have naturally been clothed in the garb of various ,theories3--the laws of phenomena have been expressed in terms of the supposed causes of the phenomena2 as fluids1 attractions and repulsions1 particles with currents running through them or round them1 physical lines of force1 and the like4 ,such views1 and the conflict of them1 are the natural and hopeful prognostics of a theory which shall harmonize their discords and include all that each contains of ,truth4 ,the fermentation at present is perhaps too great to allow us to see clearly the truth which lies at the bottom4 ,but a few of the leading points of recent discussions on these subjects will be noticed in the ,additions to this volume4 ,,chapter ,,ix4 ,,transition ,,to ,,chemical ,,science4 ,,the preceding train of generalization may justly appear extensive1 and of itself well worthy of admiration4 ,yet we are to consider all that has there been established as only one-half of the science to which it belongs1--one limb of the colossal form of ,chemistry4 ,we #beg have ascertained1 we will suppose1 the laws of ,electric ,polarity2 but we have then to ask1 ,what is the relation of this ,polarity to ,chemical ,composition8 ,this was the great problem which1 constantly present to the minds of electro-chemical inquirers1 drew them on1 with the promise of some deep and comprehensive insight into the mechanism of nature4 ,long tasks of research1 though only subsidiary to this1 were cheerfully undertaken4 ,thus ,faraday#cgac describes himself as compelled to set about satisfying himself of the identity of common1 animal1 and voltaic electricity1 as the decision of a doubtful point which interfered with the extension of his views1 and destroyed the strictness of reasoning4 ,having established this identity1 he proceeded with his grand undertaking of electro-chemical research4 ,note #cgac3 ,dec4 #ahcb4 ,researches1 #bff4 ,the connexion of electrical currents with chemical action1 though kept out of sight in the account we have hitherto given1 was never forgotten by the experimenters2 for1 in fact1 the modes in which electrical currents were excited1 were chemical actions2--the action of acids and metals on each other in the voltaic trough1 or in some other form4 ,the dependence of the electrical effect on these chemical actions1 and still more1 the chemical actions produced by the agency of the poles of the circuit1 had been carefully studied2 and we must now relate with what success4 ,but in what terms shall we present this narration8 ,we have spoken of chemical actions1--but what kind of actions are these8 ,decomposition2 the resolution of compounds into their ingredients2 the separation of acids from bases2 the reduction of bodies to simple elements4 ,these names open to us a new drama2 they are words which belong to a different set of relations of things1 a different train of scientific inductions1 a different system of generalizations1 from any with which we have hitherto been concerned4 ,we must learn to understand these phrases1 before we can advance in our history of human knowledge4 ,and how are we to learn the meaning of this collection of words8 ,in what other language shall it be explained8 ,in what terms shall we define these new expressions8 ,to this we are compelled to reply1 that we cannot translate these terms into any ordinary language2--that we cannot define them in any terms already familiar to us4 ,here1 as in all other branches of knowledge1 the meaning of words is to be sought in the progress of thought2 the history of science is our #beh dictionary2 the steps of scientific induction are our definitions4 ,it is only by going back through the successful researches of men respecting the composition and elements of bodies1 that we can learn in what sense such terms must be understood1 so as to convey real knowledge4 ,in order that they may have a meaning for us1 we must inquire what meaning they had in the minds of the authors of our discoveries4 ,and thus we cannot advance a step1 till we have brought up our history of ,chemistry to the level of our history of ,electricity2--till we have studied the progress of the analytical1 as well as the mechanical sciences4 ,we are compelled to pause and look backwards here2 just as happened in the history of astronomy1 when we arrived at the brink of the great mechanical inductions of ,newton1 and found that we must trace the history of ,mechanics1 before we could proceed to mechanical ,astronomy4 ,the terms force1 attraction1 inertia1 momentum1 sent us back into preceding centuries then1 just as the terms composition and element send us back now4 ,nor is it to a small extent that we have thus to double back upon our past advance4 ,next to ,astronomy1 ,chemistry is one of the most ancient of sciences2--the field of the earliest attempts of man to command and understand nature4 ,it has held men for centuries by a kind of fascination2 and innumerable and endless are the various labors1 the failures and successes1 the speculations and conclusions1 the strange pretences and fantastical dreams1 of those who have pursued it4 ,to exhibit all these1 or give any account of them1 would be impossible2 and for our design1 it would not be pertinent4 ,to extract from the mass that which is to our purpose1 is difficult2 but the attempt must be made4 ,we must endeavor to analyse the history of ,chemistry1 so far as it has tended towards the establishment of general principles4 ,we shall thus obtain a sight of generalizations of a new kind1 and shall prepare ourselves for others of a higher order4 #bei ,,book ,,xiv4 ,,the ,,analytical ,,science4 ,,history ,,of ,,chemistry4 4 4 4 4 4 4 4 ,soon had his crew ,opened into the hill a spacious wound1 ,and digged out ribs of gold 4 4 4 4 ,anon out of the earth a fabric huge ,rose like an exhalation1 with the sound ,of dulcet symphonies and voices sweet1 ,built like a temple4 ,,milton4 ,paradise ,lost1 i4 #bfa ,,chapter ,i4 ,,improvement ,,of ,,the ,,notion ,,of ,,chemical ,,analysis1 ,,and ,,recognition ,,of ,,it ,,as ,,the ,,spagiric ,,art4 ,,the doctrine of the four elements is one of the oldest monuments of man's speculative nature2 goes back1 perhaps1 to times anterior to ,greek philosophy2 and as the doctrine of ,aristotle and ,galen1 reigned for fifteen hundred years over the ,gentile1 ,christian1 and ,mohammedan world4 ,in medicine1 taught as the doctrine of the four elementary qualities1 of which the human body and all other substances are compounded1 it had a very powerful and extensive influence upon medical practice4 ,but this doctrine never led to any attempt actually to analyse bodies into their supposed elements3 for composition was inferred from the resemblance of the qualities1 not from the separate exhibition of the ingredients2 the supposed analysis was1 in short1 a decomposition of the body into adjectives1 not into substances4 ,this doctrine1 therefore1 may be considered as a negative state1 antecedent to the very beginning of chemistry2 and some progress beyond this mere negation was made1 as soon as men began to endeavor to compound and decompound substances by the use of fire or mixture1 however erroneous might be the opinions and expectations which they combined with their attempts4 ,alchemy is a step in chemistry1 so far as it implies the recognition of the work of the cupel and the retort1 as the produce of analysis and synthesis4 ,how perplexed and perverted were the forms in which this recognition was clothed1--how mixed up with mythical follies and extravagancies1 we have already seen2 and the share which ,alchemy had in the formation of any sounder knowledge1 is not such as to justify any further notice of that pursuit4 ,the result of the attempts to analyse bodies by heat1 mixture1 and the like processes1 was the doctrine that the first principles of things are three1 not four2 namely1 salt1 sulphur1 and mercury2 and that1 of these three1 all things are compounded4 ,in reality1 the doctrine1 as thus stated1 contained no truth which was of any value2 for1 though the chemist could extract from most bodies portions which he called salt1 #bfb and sulphur1 and mercury1 these names were given1 rather to save the hypothesis1 than because the substances were really those usually so called3 and thus the supposed analyses proved nothing1 as ,boyle justly urged against them4#aad ,note #aad3 ,shaw's ,boyle4 ,skeptical ,chymist1 pp4 #cab1 #cac4 c4 ,the only real advance in chemical theory1 therefore1 which we can ascribe to the school of the three principles1 as compared with those who held the ancient dogma of the four elements1 is1 the acknowledgment of the changes produced by the chemist's operations1 as being changes which were to be accounted for by the union and separation of substantial elements1 or1 as they were sometimes called1 of hypostatical principles4 ,the workmen of this school acquired1 no doubt1 a considerable acquaintance with the results of the kinds of processes which they pursued2 they applied their knowledge to the preparation of new medicines2 and some of them1 as ,paracelsus and ,van ,helmont1 attained1 in this way1 to great fame and distinction3 but their merits1 as regards theoretical chemistry1 consist only in a truer conception of the problem1 and of the mode of attempting its solution1 than their predecessors had entertained4 ,this step is well marked by a word which1 about the time of which we speak1 was introduced to denote the chemist's employment4 ,it was called the ,spagiric art1 7often misspelt ,spagyric17 from two ,greek words1 71 17 which mean to separate parts1 and to unite them4 ,these two processes1 or in more modern language1 analysis and synthesis1 constitute the whole business of the chemist4 ,we are not making a fanciful arrangement1 therefore1 when we mark the recognition of this object as a step in the progress of chemistry4 ,i now proceed to consider the manner in which the conditions of this analysis and synthesis were further developed4 ,,chapter ,,ii4 ,,doctrine ,,of ,,acid ,,and ,,alkali4--,,sylvius4 ,,among the results of mixture observed by chemists1 were many instances in which two ingredients1 each in itself pungent or destructive1 being put together1 became mild and inoperative2 each #bfc counteracting and neutralizing the activity of the other4 ,the notion of such opposition and neutrality is applicable to a very wide range of chemical processes4 ,the person who appears first to have steadily seized and generally applied this notion is ,francis de la ,bo ,sylvius2 who was born in #afad1 and practised medicine at ,amsterdam1 with a success and reputation which gave great currency to his opinions on that art4#bad ,his chemical theories were propounded as subordinate to his medical doctrines2 and from being thus presented under a most important practical aspect1 excited far more attention than mere theoretical opinions on the composition of bodies could have done4 ,sylvius is spoken of by historians of science1 as the founder of the iatro-chemical sect among physicians2 that is1 the sect which considers the disorders in the human frame as the effects of chemical relations of the fluids1 and applies to them modes of cure founded upon this doctrine4 ,we have here to speak1 not of his physiological1 but of his chemical views4 ,note #bad3 ,sprengel4 ,geschichte der ,arzneykunde1 vol4 iv4 ,thomson's ,history of ,chemistry in the corresponding part is translated from ,sprengel4 ,the distinction of acid and alkaline bodies 7acidum1 lixivum7 was familiar before the time of ,sylvius2 but he framed a system1 by considering them both as eminently acrid and yet opposite1 and by applying this notion to the human frame4 ,thus#cad the lymph contains an acid1 the bile an alkaline salt4 ,these two opposite acrid substances1 when they are brought together1 neutralize each other 7infringunt71 and are changed into an intermediate and milder substance4 ,note #cad3 ,de ,methodo ,medendi1 ,amst4 #afgi4 ,lib4 ii4 cap4 #bh1 sects4 #h and #ec4 ,the progress of this doctrine1 as a physiological one1 is an important part of the history of medical science in the seventeenth century2 but with that we are not here concerned4 ,but as a chemical doctrine1 this notion of the opposition of acid and alkali1 and of its very general applicability1 struck deep root1 and has not been eradicated up to our own time4 ,boyle1 indeed1 whose disposition led him to suspect all generalities1 expressed doubts with regard to this view2#dad and argued that the supposition of acid and alkaline parts in all bodies was precarious1 their offices arbitrary1 and the notion of them unsettled4 ,indeed it was not difficult to show1 that there was no one certain criterion to which all supposed acids conformed4 ,yet the general conception of such a combination as that of acid and alkali was supposed to #bfd be1 served so well to express many chemical facts1 that it kept its ground4 ,it is found1 for instance1 in ,lemery's ,chemistry1 which was one of those in most general use before the introduction of the phlogistic theory4 ,in this work 7which was translated into ,english by ,keill1 in #afih7 we find alkalies defined by their effervescing with acids4#ead ,they were distinguished as the mineral alkali 7soda71 the vegetable alkali 7potassa71 and the volatile alkali 7ammonia74 ,again1 in ,macquer's ,chemistry1 which was long the text-book in ,europe during the reign of phlogiston1 we find acids and alkalies1 and their union1 in which they rob each other of their characteristic properties1 and form neutral salts1 stated among the leading principles of the science4#fad ,note #dad3 ,shaw's ,boyle1 iii4 p4 #dcb4 ,note #ead3 ,lemery1 p4 #be4 ,note #fad3 ,macquer1 p4 #ai4 ,in truth1 the mutual relation of acids to alkalies was the most essential part of the knowledge which chemists possessed concerning them4 ,the importance of this relation arose from its being the first distinct form in which the notion of chemical attraction or affinity appeared4 ,for the acrid or caustic character of acids and alkalies is1 in fact1 a tendency to alter the bodies they touch1 and thus to alter themselves2 and the neutral character of the compounds 9999is the absence of any such proclivity to change4 ,acids and alkalies have a strong disposition to unite4 ,they combine1 often with vehemence1 and produce neutral salts2 they exhibit1 in short1 a prominent example of the chemical attraction1 or affinity1 by which two ingredients are formed into a compound4 ,the relation of acid and base in a salt is1 to this day1 one of the main grounds of all theoretical reasonings4 ,the more distinct development of the notion of such chemical attraction1 gradually made its way among the chemists of the latter part of the seventeenth and the beginning of the eighteenth century1 as we may see in the writings of ,boyle1 ,newton1 and their followers4 ,beecher speaks of this attraction as a magnetism2 but ,i do not know that any writer in particular1 can be pointed out as the person who firmly established the general notion of chemical attraction4 ,but this idea of chemical attraction became both more clear and more extensively applicable1 when it assumed the form of the doctrine of elective attractions1 in which shape we must now speak of it4 #bfe ,,chapter ,,iii4 ,,doctrine ,,of ,,elective ,,attractions4 ,,geoffroy4 ,,bergman4 ,,though the chemical combinations of bodies had already been referred to attraction1 in a vague and general manner1 it was impossible to explain the changes that take place1 without supposing the attraction to be greater or less1 according to the nature of the body4 ,yet it was some time before the necessity of such a supposition was clearly seen4 ,in the history of the ,french ,academy for #agah 7published #agai71 the writer of the introductory notice 7probably ,fontenelle7 says1 ,that a body which is united to another1 for example1 a solvent which has penetrated a metal1 should quit it to go and unite itself with another which we present to it1 is a thing of which the possibility had never been guessed by the most subtle philosophers1 and of which the explanation even now is not easy4 ,the doctrine had1 in fact1 been stated by ,stahl1 but the assertion just quoted shows1 at least1 that it was not familiar4 ,the principle1 however1 is very clearly stated#gad in a memoir in the same volume1 by ,geoffroy1 a ,french physician of great talents and varied knowledge1 ,we observe in chemistry1 he says1 certain relations amongst different bodies1 which cause them to unite4 ,these relations have their degrees and their laws4 ,we observe their different degrees in this2--that among different matters jumbled together1 which have a certain disposition to unite1 we find that one of these substances always unites constantly with a certain other1 preferably to all the rest4 ,he then states that those which unite by preference1 have plus de rapport1 or1 according to a phrase afterwards used1 more affinity4 ,and ,i have satisfied myself1 he adds1 that we may deduce1 from these observations1 the following proposition1 which is very extensively true1 though ,i cannot enunciate it as universal1 not having been able to examine all the possible combinations1 to assure myself that ,i should find no exception4 ,the proposition which he states in this admirable spirit of philosophical caution1 is this3 ,in all cases where two substances1 #bff which have any disposition to combine1 are united2 if there approaches them a third1 which has more affinity with one of the two1 this one unites with the third and lets go the other4 ,he then states these affinities in the form of a ,table2 placing a substance at the head of each column1 and other substances in succession below it1 according to the order of their affinities for the substance which stands at the head4 ,he allows that the separation is not always complete 7an imperfection which he ascribes to the glutinosity of fluids and other causes71 but1 with such exceptions1 he defends very resolutely and successfully his ,table1 and the notions which it implies4 ,note #gad3 ,mm4 ,acad4 ,par4 #agah1 p4 #bjb4 ,the value of such a tabulation was immense at the time1 and is even still very great2 it enabled the chemist to trace beforehand the results of any operation2 since1 when the ingredients were given1 he could see which were the strongest of the affinities brought into play1 and1 consequently1 what compounds would be formed4 ,geoffroy himself gave several good examples of this use of his table4 ,it was speedily adopted into works on chemistry4 ,for instance1 ,macquer#had places it at the end of his book2 taking it1 as he says1 to be of great use at the end of an elementary tract1 as it collects into one point of view1 the most essential and fundamental doctrines which are dispersed through the work4 ,note #had3 ,pref41 p4 #ac4 ,the doctrine of ,elective ,attraction1 as thus promulgated1 contained so large a mass of truth1 that it was never seriously shaken1 though it required further development and correction4 ,in particular the celebrated work of ,torbern ,bergman1 professor at ,upsala1 ,on ,elective ,attractions1 published in #agge1 introduced into it material improvements4 ,bergman observed1 that not only the order of attractions1 but the sum of those attractions which had to form the new compounds1 must be taken account of1 in order to judge of the result4 ,thus1#iad if we have a combination of two elements1 ,p1 s1 7potassa and vitriolic acid71 and another combination1 ,l1 m1 7lime and muriatic acid17 though s has a greater affinity for ,p than for ,l1 yet the sum of the attractions of ,p to m1 and of ,l to s1 is greater than that of the original compounds1 and therefore if the two combinations are brought together1 the new compounds1 ,p1 m1 and ,l1 s1 are formed4 ,note #iad3 ,elect4 ,attract41 p4 #ai4 ,the ,table of ,elective ,attractions1 modified by ,bergman in pursuance of these views1 and corrected according to the advanced knowledge of the time1 became still more important than before4 ,the next step #bfg was to take into account the quantities of the elements which combined2 but this leads us into a new train of investigation1 which was1 indeed1 a natural sequel to the researches of ,geoffroy and ,bergman4 ,in #ahjc1 however1 a chemist of great eminence1 ,berthollet1 published a work 7,essai de ,statique ,chimique71 the tendency of which appeared to be to throw the subject back into the condition in which it had been before ,geoffroy4 ,for ,berthollet maintained that the rules of chemical combination were not definite1 and dependent on the nature of the substances alone1 but indefinite1 depending on the quantity present1 and other circumstances4 ,proust answered him1 and as ,berzelius says1#ajad ,berthollet defended himself with an acuteness which makes the reader hesitate in his judgment2 but the great mass of facts finally decided the point in favor of ,proust4 ,before1 however1 we trace the result of these researches1 we must consider ,chemistry as extending her inquiries to combustion as well as mixture1 to airs as well as fluids and solids1 and to weight as well as quality4 ,these three steps we shall now briefly treat of4 ,note #ajad3 ,chem4 t4 iii4 p4 #bc4 ,,chapter ,,iv4 ,,doctrine ,,of ,,acidification ,,and ,,combustion4--,,phlogistic ,,theory4 ,,publication of the ,theory by ,beccher and ,stahl4--,it will be recollected that we are tracing the history of the progress only of ,chemistry1 not of its errors2--that we are concerned with doctrines only so far as they are true1 and have remained part of the received system of chemical truths4 ,the ,phlogistic ,theory was deposed and succeeded by the ,theory of ,oxygen4 ,but this circumstance must not lead us to overlook the really sound and permanent part of the opinions which the founders of the phlogistic theory taught4 ,they brought together1 as processes of the same kind1 a number of changes which at first appeared to have nothing in common2 as acidification1 combustion1 respiration4 ,now this classification is true2 and its importance remains undiminished1 whatever are the explanations which we adopt of the processes themselves4 ,the two chemists to whom are to be ascribed the merit of this step1 and the establishment of the phlogistic theory which they connected #bfh with it1 are ,john ,joachim ,beccher and ,george ,ernest ,stahl2 the former of whom was professor at ,mentz1 and physician to the ,elector of ,bavaria 7born #afbe1 died #afhb72 the latter was professor at ,halle1 and afterwards royal physician at ,berlin 7born #affj1 died #agcd74 ,these two men1 who thus contributed to a common purpose1 were very different from each other4 ,the first was a frank and ardent enthusiast in the pursuit of chemistry1 who speaks of himself and his employments with a communicativeness and affection both amusing and engaging4 ,the other was a teacher of great talents and influence1 but accused of haughtiness and moroseness2 a character which is well borne out by the manner in which1 in his writings1 he anticipates an unfavorable reception1 and defies it4 ,but it is right to add to this that he speaks of ,beccher1 his predecessor1 with an ungrudging acknowledgment of obligations to him1 and a vehement assertion of his merit as the founder of the true system1 which give a strong impression of ,stahl's justice and magnanimity4 ,beccher's opinions were at first promulgated rather as a correction than a refutation of the doctrine of the three principles1 salt1 sulphur1 and mercury4 ,the main peculiarity of his views consists in the offices which he ascribes to his sulphur1 these being such as afterwards induced ,stahl to give the name of ,phlogiston to this element4 ,beccher had the sagacity to see that the reduction of metals to an earthy form 7calx71 and the formation of sulphuric acid from sulphur1 are operations connected by a general analogy1 as being alike processes of combustion4 ,hence the metal was supposed to consist of an earth1 and of something which1 in the process of combustion1 was separated from it2 and1 in like manner1 sulphur was supposed to consist of the sulphuric acid1 which remained after its combustion1 and of the combustible part or true sulphur1 which flew off in the burning4 ,beccher insists very distinctly upon this difference between his element sulphur and the sulphur of his ,paracelsian predecessors4 ,it must be considered as indicating great knowledge and talent in ,stahl1 that he perceived so clearly what part of the views of ,beccher was of general truth and permanent value4 ,though he#aaad everywhere gives to ,beccher the credit of the theoretical opinions which he promulgates1 7,beccheriana sunt qu profero17 it seems certain that he had the merit1 not only of proving them more completely1 and applying them more widely than his forerunner1 but also of conceiving them #bfi with a distinctness which ,beccher did not attain4 ,in #afig1 appeared ,stahl's ,zymotechnia ,fundamentalis 7the ,doctrine of ,fermentation71 simulque experimentum novum sulphur verum arte producendi4 ,in this work 7besides other tenets which the author considered as very important71 the opinion published by ,beccher was now maintained in a very distinct form2--namely1 that the process of forming sulphur from sulphuric acid1 and of restoring the metals from their calces1 are analogous1 and consist alike in the addition of some combustible element1 which ,stahl termed phlogiston 71 combustible74 ,the experiment most insisted on in the work now spoken of1#abad was the formation of sulphur from sulphate of potass 7or of soda7 by fusing the salt with an alkali1 and throwing in coals to supply phlogiston4 ,this is the experimentum novum4 ,though ,stahl published an account of this process1 he seems to have regretted his openness4 ,he denies not1 he says1 that he should peradventure have dissembled this experiment as the true foundation of the ,beccherian assertion concerning the nature of sulphur1 if he had not been provoked by the pretending arrogance of some of his contemporaries4 ,note #aaad3 9999,stahl1 ,prf4 ad ,specim4 ,becch4 #agjc4 ,note #abad3 ,p4 #aag4 ,from this time1 ,stahl's confidence in his theory may be traced becoming more and more settled in his succeeding publications4 ,it is hardly necessary to observe here1 that the explanations which his theory gives are easily transformed into those which the more recent theory supplies4 ,according to modern views1 the addition of oxygen takes place in the formation of acids and of calces1 and in combustion1 instead of the subtraction of phlogiston4 ,the coal which ,stahl supposed to supply the combustible in his experiment1 does in fact absorb the liberated oxygen4 ,in like manner1 when an acid corrodes a metal1 and1 according to existing theory1 combines with and oxidates it1 ,stahl supposed that the phlogiston separated from the metal and combined with the acid4 ,that the explanations of the phlogistic theory are so generally capable of being translated into the oxygen theory1 merely by inverting the supposed transfer of the combustible element1 shows us how important a step towards the modern doctrines the phlogistic theory really was4 ,the question1 whether these processes were in fact addition or subtraction1 was decided by the balance1 and belongs to a succeeding period of the science4 ,but we may observe1 that both ,beccher and ,stahl were aware of the increase of weight which metals undergo in #bgj calcination2 although the time had not yet arrived in which this fact was to be made one of the bases of the theory4 ,it has been said1#acad that in the adoption of the phlogistic theory1 that is1 in supposing the above-mentioned processes to be addition rather than subtraction1 of two possible roads the wrong was chosen1 as if to prove the perversity of the human mind4 ,but we must not forget how natural it was to suppose that some part of a body was destroyed or removed by combustion2 and we may observe1 that the merit of ,beccher and ,stahl did not consist in the selection of one road or two1 but in advancing so far as to reach this point of separation4 ,that1 having done this1 they went a little further on the wrong line1 was an error which detracted little from the merit or value of the progress really made4 ,it would be easy to show1 from the writings of phlogistic chemists1 what important and extensive truths their theory enabled them to express simply and clearly4 ,note #acad3 ,herschel's ,introd4 to ,nat4 ,phil4 p4 #cjj4 ,that an enthusiastic temper is favorable to the production of great discoveries in science1 is a rule which suffers no exception in the character of ,beccher4 ,in his preface#adad addressed to the benevolent reader of his ,physica ,subterranea1 he speaks of the chemists as a strange class of mortals1 impelled by an almost insane impulse to seek their pleasure among smoke and vapor1 soot and flame1 poisons and poverty4 ,yet among all these evils1 he says1 ,i seem to myself to live so sweetly1 that1 may ,i die if ,i would change places with the ,persian king4 ,he is1 indeed1 well worthy of admiration1 as one of the first who pursued the labors of the furnace and the laboratory1 without the bribe of golden hopes4 ,my kingdom1 he says1 is not of this world4 ,i trust that ,i have got hold of my pitcher by the right handle1--the true method of treating this study4 ,for the ,pseudochymists seek gold2 but the true philosophers1 science1 which is more precious than any gold4 ,note #adad3 ,frankfort1 #afha4 ,the ,physica ,subterranea made no converts4 ,stahl1 in his indignant manner1 says1#aead ,no one will wonder that it never yet obtained a physician or a chemist as a disciple1 still less as an advocate4 ,and again1 ,this work obtained very little reputation or estimation1 or1 to speak ingenuously1 as far as ,i know1 none whatever4 ,in #afga1 ,beccher published a supplement to his work1 in which he showed how metal might be extracted from mud and sand4 ,he offered to execute #bga this at ,vienna2 but found that people there cared nothing about such novelties4 ,he was then induced1 by ,baron ,d',isola1 to go to ,holland for similar purposes4 ,after various delays and quarrels1 he was obliged to leave ,holland for fear of his creditors2 and then1 ,i suppose1 came to ,great ,britain1 where he examined the ,scottish and ,cornish mines4 ,he is said to have died in ,london in #afhb4 ,note #aead3 ,prf4 ,phys4 ,sub4 #agjc4 ,stahl's publications appear to have excited more notice1 and led to controversy on the so-called sulphur4 ,the success of the experiment had been doubted1 which1 as he remarks1 it was foolish to make a matter of discussion1 when any one might decide the point by experiment2 and finally1 it had been questioned whether the substance obtained by this process were pure sulphur4 ,the originality of his doctrine was also questioned1 which1 as he says1 could not with any justice be impugned4 ,he published in defence and development of his opinion at various intervals1 as the ,specimen ,beccherianum in #agjc1 the ,documentum ,theori ,beecherian1 a ,dissertation ,de ,anatomia ,sulphuris ,artificialis2 and finally1 ,casual ,thoughts on the so-called ,sulphur1 in #agah1 in which he gave 7in ,german7 both a historical and a systematic view of his opinions on the nature of salts and of his ,phlogiston4 ,reception and ,application of the ,theory4--,the theory that the formation of sulphuric acid1 and the restoration of metals from their calces1 are analogous processes1 and consist in the addition of phlogiston1 was soon widely received2 and the ,phlogistic ,school was thus established4 ,from ,berlin1 its original seat1 it was diffused into all parts of ,europe4 ,the general reception of the theory may be traced1 not only in the use of the term phlogiston1 and of the explanations which it implies2 but in the adoption of a nomenclature founded on those explanations1 which1 though not very extensive1 is sufficient evidence of the prevalence of the theory4 ,thus when ,priestley1 in #aggd1 discovered oxygen1 and when ,scheele1 a little later1 discovered chlorine1 these gases were termed dephlogisticated air1 and dephlogisticated marine acid2 while azotic acid gas1 having no disposition to combustion1 was supposed to be saturated with phlogiston1 and was called phlogisticated air4 ,this phraseology kept its ground1 till it was expelled by the antiphlogistic1 or oxygen theory4 ,for instance4 ,cavendish's papers on the chemistry of the airs are expressed in terms of it1 although his researches led him to the confines of the new theory4 ,we must now give an account of such researches1 and of the consequent revolution in the science4 #bgb ,,chapter ,v4 ,,chemistry ,,of ,,gases4--,,black4 ,,cavendish4 ,,the study of the properties of ariform substances1 or ,pneumatic ,chemistry1 as it was called1 occupied the chemists of the eighteenth century1 and was the main occasion of the great advances which the science made at that period4 ,the most material general truths which came into view in the course of these researches1 were1 that gases were to be numbered among the constituent elements of solid and fluid bodies2 and that1 in these1 as in all other cases of composition1 the compound was equal to the sum of its elements4 ,the latter proposition1 indeed1 cannot be looked upon as a discovery1 for it had been frequently acknowledged1 though little applied2 in fact1 it could not be referred to with any advantage1 till the ariform elements1 as well as others1 were taken into the account4 ,as soon as this was done1 it produced a revolution in chemistry4 #bnd ,ed4 ,though the view of the mode in which gaseous elements become fixed in bodies and determine their properties1 had great additional light thrown upon it by ,dr4 ,black's discoveries1 as we shall see1 the notion that solid bodies involve such gaseous elements was not new at that period4 ,mr4 ,vernon ,harcourt has shown#afad that ,newton and ,boyle admitted into their speculations airs of various kinds1 capable of fixation in bodies4 ,i have1 in the succeeding chapter 7chap4 vi471 spoken of the views of ,rey1 ,hooke1 and ,mayow1 connected with the function of airs in chemistry1 and forming a prelude to the ,oxygen ,theory4 ,note #afad3 ,phil4 ,mag4 #ahdf4 ,notwithstanding these preludes1 the credit of the first great step in pneumatic chemistry is1 with justice1 assigned to ,dr4 ,black1 afterwards professor at ,edinburgh1 but a young man of the age of twenty-four at the time when he made his discovery4#agad ,he found that the difference between caustic lime and common limestone arose from this1 that the latter substance consists of the former1 combined with a certain air1 which1 being thus fixed in the solid body1 he called fixed air 7carbonic #bgc acid gas74 ,he found1 too1 that magnesia1 caustic potash1 and caustic soda1 would combine with the same air1 with similar results4 ,this discovery consisted1 of course1 in a new interpretation of observed changes4 ,alkalies appeared to be made caustic by contact with quicklime3 at first ,black imagined that they underwent this change by acquiring igneous matter from the quicklime2 but when he perceived that the lime gained1 not lost1 in magnitude as it became mild1 he rightly supposed that the alkalies were rendered caustic by imparting their air to the lime4 ,this discovery was announced in ,black's inaugural dissertation1 pronounced in #agee1 on the occasion of his taking his degree of ,doctor in the ,university of ,edinburgh4 ,note #agad3 ,thomson's ,hist4 ,chem4 i4 #cag4 ,the chemistry of airs was pursued by other experimenters4 ,the ,honorable ,henry ,cavendish1 about #agfe1 invented an apparatus1 in which arial fluids are confined by water1 so that they can be managed and examined4 ,this hydro-pneumatic apparatus1 or as it is sometimes called1 the pneumatic trough1 from that time was one of the most indispensable parts of the chemist's apparatus4 ,cavendish1#ahad in #agff1 showed the identity of the properties of fixed air derived from various sources2 and pointed out the peculiar qualities of inflammable air 7afterwards called hydrogen gas71 which1 being nine times lighter than common air1 soon attracted general notice by its employment for raising balloons4 ,the promise of discovery which this subject now offered1 attracted the confident and busy mind of ,priestley1 whose ,experiments and ,observations on different kinds of ,air appeared in #agdd-gi4 ,in these volumes1 he describes an extraordinary number of trials of various kinds2 the results of which were1 the discovery of new kinds of air1 namely1 phlogisticated air 7azotic gas71 nitrous air 7nitrous gas71 and dephlogisticated air 7oxygen gas74 ,note #ahad3 ,phil4 ,trans4 #agff4 ,but the discovery of new substances1 though valuable in supplying chemistry with materials1 was not so important as discoveries respecting their modes of composition4 ,among such discoveries1 that of ,cavendish1 published in the ,philosophical ,transactions for #aghd1 and disclosing the composition of water by the union of two gases1 oxygen and hydrogen1 must be considered as holding a most distinguished place4 ,he states1#aiad that his experiments were made principally with a view to find out the cause of the diminution which common air is well known to suffer1 by all the various ways in which it is phlogisticated4 ,and1 after describing various unsuccessful attempts1 he finds #bgd that when inflammable air is used in this phlogistication 7or burning71 the diminution of the common air is accompanied by the formation of a dew in the apparatus4#bjad ,and thus he infers#baad that almost all the inflammable air1 and one-fifth of the common air1 are turned into pure water4 ,note #aiad3 ,phil4 ,trans4 #aghd1 p4 #aai4 ,note #bjad3 ,phil4 ,trans4 #aghd1 p4 #abh4 ,note #baad3 ,ib4 p4 #abi4 ,lavoisier1 to whose researches this result was1 as we shall soon see1 very important1 was employed in a similar attempt at the same time 7#aghc71 and had already succeeded1#bbad when he learned from ,dr4 ,blagden1 who was present at the experiment1 that ,cavendish had made the discovery a few months sooner4 ,monge had1 about the same time1 made the same experiments1 and communicated the result to ,lavoisier and ,laplace immediately afterwards4 ,the synthesis was soon confirmed by a corresponding analysis4 ,indeed the discovery undoubtedly lay in the direct path of chemical research at the time4 ,it was of great consequence in the view it gave of experiments in composition2 for the small quantity of water produced in many such processes1 had been quite overlooked2 though1 as it now appeared1 this water offered the key to the whole interpretation of the change4 ,note #bbad3 ,a4 ,p4 #agha1 p4 #dgb ,though some objections to ,mr4 ,cavendish's view were offered by ,kirwan1#bcad on the whole they were generally received with assent and admiration4 ,but the bearing of these discoveries upon the new theory of ,lavoisier1 who rejected phlogiston1 was so close1 that we cannot further trace the history of the subject without proceeding immediately to that theory4 ,note #bcad3 ,p4 ,t4 #aghd1 p4 #aed4 #bnd ,ed4 ,i have elsewhere stated1#bdad--with reference to recent attempts to deprive ,cavendish of the credit of his discovery of the composition of water1 and to transfer it to ,watt1--that ,watt not only did not anticipate1 but did not fully appreciate the discovery of ,cavendish and ,lavoisier2 and ,i have expressed my concurrence with ,mr4 ,vernon ,harcourt's views1 when he says1#bead that ,cavendish pared off from the current hypotheses their theory of combustion1 and their affinities of imponderable for ponderable matter1 as complicating chemical with physical considerations2 and he then corrected and adjusted them with admirable skill to the actual phenomena1 not binding the facts to the theory1 but adapting the theory to the facts4 ,note #bdad3 ,philosophy1 b4 vi4 c4 #d4 ,note #bead3 ,address to the ,british ,association1 #ahci4 ,i conceive that the discussion which the subject has recently received1 has left no doubt on the mind of any one who has perused the #bge documents1 that ,cavendish is justly entitled to the honor of this discovery1 which in his own time was never contested4 ,the publication of his ,journals of ,experiments#bfad shows that he succeeded in establishing the point in question in ,july1 #agha4 ,his experiments are referred to in an abstract of a paper of ,priestley's1 made by ,dr4 ,maty1 the secretary of the ,royal ,society1 in ,june1 #aghc4 ,in ,june1 #aghc1 also1 ,dr4 ,blagden communicated the result of ,cavendish's experiments to ,lavoisier1 at ,paris4 ,watt's letter1 containing his hypothesis that water is composed of dephlogisticated air and phlogiston deprived of part of their latent or elementary heat2 and that phlogisticated or pure air is composed of water deprived of its phlogiston and united to elementary heat and light1 was not read till ,nov4 #aghc2 and even if it could have suggested such an experiment as ,cavendish's 7which does not appear likely71 is proved1 by the dates1 to have had no share in doing so4 ,note #bfad3 ,appendix to ,mr4 ,v4 ,harcourt's ,address ,mr4 ,cavendish's experiment was suggested by an experiment in which ,warltire1 a lecturer on chemistry at ,birmingham1 exploded a mixture of hydrogen and common air in a close vessel1 in order to determine whether heat were ponderable4 ,,chapter ,,vi4 ,,epoch ,,of ,,the ,,theory ,,of ,,oxygen4--,,lavoisier4 ,sect4 #a4--,prelude to the ,theory4--,its ,publication4 ,,we arrive now at a great epoch in the history of ,chemistry4 ,few revolutions in science have immediately excited so much general notice as the introduction of the theory of oxygen4 ,the simplicity and symmetry of the modes of combination which it assumed2 and1 above all1 the construction and universal adoption of a nomenclature which applied to all substances1 and which seemed to reveal their inmost constitution by their name1 naturally gave it an almost irresistible sway over men's minds4 ,we must1 however1 dispassionately trace the course of its introduction4 #bgf ,antoine ,laurent ,lavoisier1 an accomplished ,french chemist1 had pursued1 with zeal and skill1 researches such as those of ,black1 ,cavendish1 and ,priestley1 which we have described above4 ,in #aggd1 he showed that1 in the calcination of metals in air1 the metal acquires as much weight as the air loses4 ,it might appear that this discovery at once overturned the view which supposed the metal to be phlogiston added to the calx4 ,lavoisier's contemporaries were1 however1 far from allowing this2 a greater mass of argument was needed to bring them to this conclusion4 ,convincing proofs of the new opinion were1 however1 rapidly supplied4 ,thus1 when ,priestley had discovered dephlogisticated air1 in #aggd1 ,lavoisier showed1 in #aggf1 that fixed air consisted of charcoal and the dephlogisticated or pure air2 for the mercurial calx which1 heated by itself1 gives out pure air1 gives out1 when heated with charcoal1 fixed air1#bgad which has1 therefore1 since been called carbonic acid gas4 ,note #bgad3 ,mm4 ,ac4 ,par4 #agge4 ,again1 ,lavoisier showed that the atmospheric air consists of pure or vital air1 and of an unvital air1 which he thence called azot4 ,the vital air he found to be the agent in combustion1 acidification1 calcination1 respiration2 all of these processes were analogous3 all consisted in a decomposition of the atmospheric air1 and a fixation of the pure or vital portion of it4 ,but he thus arrived at the conclusion1 that this pure air was added1 in all the cases in which1 according to the received theory1 phlogiston was subtracted1 and vice vers4 ,he gave the name#bhad of oxygen 7principe oxygne7 to the substance which thus unites itself with metals to form their calces1 and with combustible substances to form acids4 ,note #bhad3 ,mm4 ,ac4 ,par4 #agha1 p4 #ddh4 ,a new theory was thus produced1 which would account for all the facts which the old one would explain1 and had besides the evidence of the balance in its favor4 ,but there still remained some apparent objections to be removed4 ,in the action of dilute acids on metals1 inflammable air was produced4 ,whence came this element8 ,the discovery of the decomposition of water sufficiently answered this question1 and converted the objection into an argument on the side of the theory3 and thus the decomposition of water was1 in fact1 one of the most critical events for the fortune of the ,lavoisierian doctrine1 and one which1 more than any other1 decided chemists in its favor4 ,in succeeding years1 ,lavoisier showed the consistency of his theory with #bgg all that was discovered concerning the composition of alcohol1 oil1 animal and vegetable substances1 and many other bodies4 ,it is not necessary for us to consider any further the evidence for this theory1 but we must record a few circumstances respecting its earlier history4 ,rey1 a ,french physician1 had in #afcj1 published a book1 in which he inquires into the grounds of the increase of the weight of metals by calcination4#biad ,he says1 ,to this question1 then1 supported on the grounds already mentioned1 ,i answer1 and maintain with confidence1 that the increase of weight arises from the air1 which is condensed1 rendered heavy and adhesive1 by the heat of the furnace4 ,hooke and ,mayow had entertained the opinion that the air contains a nitrous spirit1 which is the supporter of combustion4 ,but ,lavoisier disclaimed the charge of having derived anything from these sources2 nor is it difficult to understand how the received generalizations of the phlogistic theory had thrown all such narrower explanations into obscurity4 ,the merit of ,lavoisier consisted in his combining the generality of ,stahl with the verified conjectures of ,rey and ,mayow4 ,note #biad3 ,thomson1 ,hist4 ,chem4 ii4 #ie4 ,no one could have a better claim1 by his early enthusiasm for science1 his extensive knowledge1 and his zealous labors1 to hope that a great discovery might fall to his share1 than ,lavoisier4 ,his father1#cjad a man of considerable fortune1 had allowed him to make science his only profession2 and the zealous philosopher collected about him a number of the most active physical inquirers of his time1 who met and experimented at his house one day in the week4 ,in this school1 the new chemistry was gradually formed4 ,a few years after the publication of ,priestley's first experiments1 ,lavoisier was struck with the presentiment of the theory which he was afterwards to produce4 ,in #aggb1 he deposited#caad with the secretary of the ,academy1 a note which contained the germ of his future doctrines4 ,at that time1 he says1 in explaining this step1 there was a kind of rivalry between ,france and ,england in science1 which gave importance to new experiments1 and which sometimes was the cause that the writers of the one or other of the nations disputed the discovery with the real author4 ,in #aggg1 the editor of the ,memoirs of the ,academy speaks of his theory as overturning that of ,stahl2 but the general acceptance of the new opinion did not take place till later4 #bgh ,note #cjad3 ,biogr4 ,univ4 7,cuvier47 ,note #caad3 ,thomson1 ii4 #ii4 ,sect4 #b4--,reception and ,confirmation of the ,theory of ,oxygen4 ,,the ,oxygen ,theory made its way with extraordinary rapidity among the best philosophers4#cbad ,in #aghe1 that is1 soon after ,cavendish's synthesis of water had removed some of the most formidable objections to it1 ,berthollet1 already an eminent chemist1 declared himself a convert4 ,indeed it was so soon generally adopted in ,france1 that ,fourcroy promulgated its doctrines under the name of ,la ,chimie ,franaise1 a title which ,lavoisier did not altogether relish4 ,the extraordinary eloquence and success of ,fourcroy as a lecturer at the ,jardin des ,plantes1 had no small share in the diffusion of the oxygen theory2 and the name of the apostle of the new chemistry which was at first given him in ridicule1 was justly held by him to be a glorious distinction4#ccad ,note #cbad3 ,thomson1 ii4 #acj4 ,note #ccad3 ,cuvier1 ,eloges1 i4 p4 #bj4 ,guyton de ,morveau1 who had at first been a strenuous advocate of the phlogistic theory1 was invited to ,paris1 and brought over to the opinions of ,lavoisier2 and soon joined in the formation of the nomenclature founded upon the theory4 ,this step1 of which we shall shortly speak1 fixed the new doctrine1 and diffused it further4 ,delametherie alone defended the phlogistic theory with vigor1 and indeed with violence4 ,he was the editor of the ,journal de ,physique1 and to evade the influence which this gave him1 the antiphlogistians#cdad established1 as the vehicle of their opinions1 another periodical1 the ,annales de ,chimie4 ,note #cdad3 ,thomson1 ii4 #acc4 ,in ,england1 indeed1 their success was not so immediate4 ,cavendish1#cead in his ,memoir of #aghd1 speaks of the question between the two opinions as doubtful4 ,there are1 he says1 several ,memoirs of ,m4 ,lavoisier1 in which he entirely discards phlogiston2 and as not only the foregoing experiments1 but most other phenomena of nature1 seem explicable as well1 or nearly as well1 upon this as upon the commonly believed principle of phlogiston1 ,cavendish proceeds to explain his experiments according to the new views1 expressing no decided preference1 however1 for either system4 ,but ,kirwan1 another ,english chemist1 contested the point much more resolutely4 ,his theory identified inflammable air1 or hydrogen1 with phlogiston2 and in this view1 he wrote a work which was intended as a confutation of #bgi the essential part of the oxygen theory4 ,it is a strong proof of the steadiness and clearness with which the advocates of the new system possessed their principles1 that they immediately translated this work1 adding1 at the end of each chapter1 a refutation of the phlogistic doctrines which it contained4 ,lavoisier1 ,berthollet1 ,de ,morveau1 ,fourcroy1 and ,monge1 were the authors of this curious specimen of scientific polemics4 ,it is also remarkable evidence of the candor of ,kirwan1 that notwithstanding the prominent part he had taken in the controversy1 he allowed himself at last to be convinced4 ,after a struggle of ten years1 he wrote#cfad to ,berthollet in #agif1 ,i lay down my arms1 and abandon the cause of phlogiston4 ,black followed the same course4 ,priestley alone1 of all the chemists of great name1 would never assent to the new doctrines1 though his own discoveries had contributed so much to their establishment4 ,he saw1 says ,cuvier1#cgad without flinching1 the most skilful defenders of the ancient theory go over to the enemy in succession2 and when ,kirwan had1 almost the last of all1 abjured phlogiston1 ,priestley remained alone on the field of battle1 and threw out a new challenge1 in a memoir addressed to the principal ,french chemists4 ,it happened1 curiously enough1 that the challenge was accepted1 and the arguments answered by ,m4 ,adet1 who was at that time 7#agih17 the ,french ambassador to the ,united ,states1 in which country ,priestley's work was published4 ,even in ,germany1 the birth-place and home of the phlogistic theory1 the struggle was not long protracted4 ,there was1 indeed1 a controversy1 the older philosophers being1 as usual1 the defenders of the established doctrines2 but in #agib1 ,klaproth repeated1 before the ,academy of ,berlin1 all the fundamental experiments2 and the result was a full conviction on the part of ,klaproth and the ,academy1 that the ,lavoisierian theory was the true one4#chad ,upon the whole1 the introduction of the ,lavoisierian theory in the scientific world1 when compared with the great revolution of opinion to which it comes nearest in importance1 the introduction of the ,newtonian theory1 shows1 by the rapidity and temper with which it took place1 a great improvement1 both in the means of arriving at truth1 and in the spirit with which they were used4 ,note #cead3 ,phil4 ,trans4 #aghd1 p4 #aej4 ,note #cfad3 ,pref4 to ,fourcroy's ,chemistry1 xiv4 ,note #cgad3 ,cuvier1 ,eloge de ,priestley1 p4 #bjh4 ,note #chad3 ,thomson1 vol4 ii4 p4 #acf4 ,some ,english writers#ciad have expressed an opinion that there was #bhj little that was original in the new doctrines4 ,but if they were so obvious1 what are we to say of eminent chemists1 as ,black and ,cavendish1 who hesitated when they were presented1 or ,kirwan and ,priestley1 who rejected them8 ,this at least shows that it required some peculiar insight to see the evidence of these truths4 ,to say that most of the materials of ,lavoisier's theory existed before him1 is only to say that his great merit was1 that which must always be the great merit of a new theory1 his generalization4 ,the effect which the publication of his doctrines produced1 shows us that he was the first person who1 possessing clearly the idea of quantitative composition1 applied it steadily to a great range of well-ascertained facts4 ,this is1 as we have often had to observe1 precisely the universal description of an inductive discoverer4 ,it has been objected1 in like manner1 to the originality of ,newton's discoveries1 that they were contained in those of ,kepler4 ,they were so1 but they needed a ,newton to find them there4 ,the originality of the theory of oxygen is proved by the conflict1 short as it was1 which accompanied its promulgation2 its importance is shown by the changes which it soon occasioned in every part of the science4 ,note #ciad3 ,brande1 ,hist4 ,diss4 in ,enc1 ,brit4 p4 #ahb4 ,lunn1 ,chem4 in ,enc4 ,met4 p4 #eif4 ,thus ,lavoisier1 far more fortunate than most of those who had1 in earlier ages1 produced revolutions in science1 saw his theory accepted by all the most eminent men of his time1 and established over a great part of ,europe within a few years from its first promulgation4 ,in the common course of events1 it might have been expected that the later years of his life would have been spent amid the admiration and reverence which naturally wait upon the patriarch of a new system of acknowledged truths4 ,but the times in which he lived allowed no such euthanasia to eminence of any kind4 ,the democracy which overthrew the ancient political institutions of ,france1 and swept away the nobles of the land1 was not1 as might have been expected1 enthusiastic in its admiration of a great revolution in science1 and forward to offer its homage to the genuine nobility of a great discoverer4 ,lavoisier was thrown into prison on some wretched charge of having1 in the discharge of a public office which he had held1 adulterated certain tobacco2 but in reality1 for the purpose of confiscating his property4#djad ,in his imprisonment1 his philosophy was his resource2 and he employed himself in the preparation of his papers for printing4 ,when he was brought before the revolutionary tribunal1 he begged for a respite of a few days1 in order to complete some researches1 the results of which #bha were1 he said1 important to the good of humanity4 ,the brutish idiot1 whom the state of the country at that time had placed in the judgment-seat1 told him that the republic wanted no savans4 ,he was dragged to the guillotine1 ,may the #hth1 #agid1 and beheaded1 in the fifty-second year of his age2 a melancholy proof that1 in periods of political ferocity1 innocence and merit1 private virtues and public services1 amiable manners and the love of friends1 literary fame and exalted genius1 are all as nothing to protect their possessor from the last extremes of violence and wrong1 inflicted under judicial forms4 ,note #djad3 ,biog4 ,univ4 7,cuvier47 ,sect4 #c4--,nomenclature of the ,oxygen ,theory4 ,,as we have already said1 a powerful instrument in establishing and diffusing the new chemical theory1 was a ,systematic ,nomenclature founded upon it1 and applicable to all chemical compounds1 which was soon constructed and published by the authors of the theory4 ,such a nomenclature made its way into general use the more easily1 in that the want of such a system had already been severely felt2 the names in common use being fantastical1 arbitrary1 and multiplied beyond measure4 ,the number of known substances had become so great1 that a list of names with no regulative principle1 founded on accident1 caprice1 and error1 was too cumbrous and inconvenient to be tolerated4 ,even before the currency which ,lavoisier's theory obtained1 these evils had led to attempts towards a more convenient set of names4 ,bergman and ,black had constructed such lists2 and ,guyton de ,morveau1 a clever and accomplished lawyer of ,dijon1 had formed a system of nomenclature in #aghb1 before he had become a convert to ,lavoisier's theory1 in which task he had been exhorted and encouraged by ,bergman and ,macquer4 ,in this system1#daad we do not find most of the characters of the method which was afterwards adopted4 ,but a few years later1 ,lavoisier1 ,de ,morveau1 ,berthollet and ,fourcroy1 associated themselves for the purpose of producing a nomenclature which should correspond to the new theoretical views4 ,this appeared in #aghg1 and soon made its way into general use4 ,the main features of this system are1 a selection of the simplest radical words1 by which substances are designated1 and a systematic distribution of terminations1 to express their relations4 ,thus1 sulphur1 combined with oxygen in two different proportions1 forms two acids1 the #bhb sulphurous and the sulphuric2 and these acids form1 with earthy or alkaline bases1 sulphides and sulphates2 while sulphur directly combined with another element1 forms a sulphuret4 ,the term oxyd 7now usually written oxide7 expressed a lower degree of combination with oxygen than the acids4 ,the ,mthode de ,nomenclature ,chimique was published in #aghg2 and in #aghi1 ,lavoisier published a treatise on chemistry in order further to explain this method4 ,in the preface to this volume1 he apologizes for the great amount of the changes1 and pleads the authority of ,bergman1 who had exhorted ,de ,morveau to spare no improper names2 those who are learned will always be learned1 and those who are ignorant will thus learn sooner4 ,to this maxim they so far conformed1 that their system offers few anomalies2 and though the progress of discovery1 and the consequent changes of theoretical opinion1 which have since gone on1 appear now to require a further change of nomenclature1 it is no small evidence of the skill with which this scheme was arranged1 that for half a century it was universally used1 and felt to be far more useful and effective than any nomenclature in any science had ever been before4 ,note #daad3 ,journal de ,physique1 #aghb1 p4 #cgj4 ,,chapter ,,vii4 ,,application ,,and ,,correction ,,of ,,the ,,oxygen ,,theory4 ,,since a chemical theory1 as far as it is true1 must enable us to obtain a true view of the intimate composition of all bodies whatever1 it will readily be supposed that the new chemistry led to an immense number of analyses and researches of various kinds4 ,these it is not necessary to dwell upon2 nor will ,i even mention the names of any of the intelligent and diligent men who have labored in this field4 ,perhaps one of the most striking of such analyses was ,davy's decomposition of the earths and alkalies into metallic bases and oxygen1 in #ahjg and #ahjh2 thus extending still further that analogy between the earths and the calces of the metals1 which had had so large a share in the formation of chemical theories4 ,this discovery1 however1 both in the means by which it was made1 and in the views to which it led1 bears upon subjects hereafter to be treated of4 ,the ,lavoisierian theory also1 wide as was the range of truth which it embraced1 required some limitation and correction4 ,i do not now #bhc speak of some erroneous opinions entertained by the author of the theory2 as1 for instance1 that the heat produced in combustion1 and even in respiration1 arose from the conversion of oxygen gas to a solid consistence1 according to the doctrine of latent heat4 ,such opinions not being necessarily connected with the general idea of the theory1 need not here be considered4 ,but the leading generalization of ,lavoisier1 that acidification was always combination with oxygen1 was found untenable4 ,the point on which the contest on this subject took place was the constitution of the oxymuriatic and muriatic acids2--as they had been termed by ,berthollet1 from the belief that muriatic acid contained oxygen1 and oxymuriatic a still larger dose of oxygen4 ,in opposition to this1 a new doctrine was put forward in #ahji by ,gay-,lussac and ,thenard in ,france1 and by ,davy in ,england2--namely1 that oxymuriatic acid was a simple substance1 which they termed chlorine1 and that muriatic acid was a combination of chlorine with hydrogen1 which therefore was called hydrochloric acid4 ,it may be observed1 that the point in dispute in the controversy on this subject was nearly the same which had been debated in the course of the establishment of the oxygen theory2 namely1 whether in the formation of muriatic acid from chlorine1 oxygen is subtracted1 or hydrogen added1 and the water concealed4 ,in the course of this dispute1 it was allowed on both sides1 that the combination of dry muriatic acid and ammonia afforded an experimentum crucis2 since1 if water was produced from these elements1 oxygen must have existed in the acid4 ,davy being at ,edinburgh in #ahab1 this experiment was made in the presence of several eminent philosophers2 and the result was found to be1 that though a slight dew appeared in the vessel1 there was not more than might be ascribed to unavoidable imperfection in the process1 and certainly not so much as the old theory of muriatic acid required4 ,the new theory1 after this period1 obtained a clear superiority in the minds of philosophical chemists1 and was further supported by new analogies4#dbad ,note #dbad3 ,paris1 ,life of ,davy1 i4 #ccg4 ,for1 the existence of one hydracid being thus established1 it was found that other substances gave similar combinations2 and thus chemists obtained the hydriodic1 hydrofluoric1 and hydrobromic acids4 ,these acids1 it is to be observed1 form salts with bases1 in the same manner as the oxygen acids do4 ,the analogy of the muriatic and fluoric compounds was first clearly urged by a philosopher who was #bhd not peculiarly engaged in chemical research1 but who was often distinguished by his rapid and happy generalizations1 ,m4 ,ampre4 ,he supported this analogy by many ingenious and original arguments1 in letters written to ,davy1 while that chemist was engaged in his researches on fluor spar1 as ,davy himself declares4#dcad ,note #dcad3 ,paris1 ,life of ,davy1 i4 #cgj4 ,still further changes have been proposed1 in that classification of elementary substances to which the oxygen theory led4 ,it has been held by ,berzelius and others1 that other elements1 as1 for example1 sulphur1 form salts with the alkaline and earthy metals1 rather than sulphurets4 ,the character of these sulpho-salts1 however1 is still questioned among chemists2 and therefore it does not become us to speak as if their place in history were settled4 ,of course1 it will easily be understood that1 in the same manner in which the oxygen theory introduced its own proper nomenclature1 the overthrow or material transformation of the theory would require a change in the nomenclature2 or rather1 the anomalies which tended to disturb the theory1 would1 as they were detected1 make the theoretical terms be felt as inappropriate1 and would suggest the necessity of a reformation in that respect4 ,but the discussion of this point belongs to a step of the science which is to come before us hereafter4 ,it may be observed1 that in approaching the limits of this part of our subject1 as we are now doing1 the doctrine of the combination of acids and bases1 of which we formerly traced the rise and progress1 is still assumed as a fundamental relation by which other relations are tested4 ,this remark connects the stage of chemistry now under our notice with its earliest steps4 ,but in order to point out the chemical bearing of the next subjects of our narrative1 we may further observe1 that metals1 earths1 salts1 are spoken of as known classes of substances2 and in like manner the newly-discovered elements1 which form the last trophies of chemistry1 have been distributed into such classes according to their analogies2 thus potassium1 sodium1 barium1 have been asserted to be metals2 iodine1 bromine1 fluorine1 have been arranged as analogical to chlorine4 ,yet there is something vague and indefinite in the boundaries of such classifications and analogies2 and it is precisely where this vagueness falls1 that the science is still obscure or doubtful4 ,we are led1 therefore1 to see the dependence of ,chemistry upon ,classification2 and it is to ,sciences of ,classification which we shall next proceed2 as soon as we have noticed the most general views #bhe which have been given of chemical relations1 namely1 the views of the electro-chemists4 ,but before we do this1 we must look back upon a law which obtains in the combination of elements1 and which we have hitherto not stated2 although it appears1 more than any other1 to reveal to us the intimate constitution of bodies1 and to offer a basis for future generalizations4 ,i speak of the ,atomic ,theory1 as it is usually termed2 or1 as we might rather call it1 the ,doctrine of ,definite1 ,reciprocal1 and ,multiple ,proportions4 ,,chapter ,,viii4 ,,theory ,,of ,,definite1 ,,reciprocal1 ,,and ,,multiple ,,proportions4 ,sect4 #a4--,prelude to the ,atomic ,theory1 and its ,publication by ,dalton4 ,,the general laws of chemical combination announced by ,mr4 ,dalton are truths of the highest importance in the science1 and are now nowhere contested2 but the view of matter as constituted of atoms1 which he has employed in conveying those laws1 and in expressing his opinion of their cause1 is neither so important nor so certain4 ,in the place which ,i here assign to his discovery1 as one of the great events of the history of chemistry1 ,i speak only of the law of phenomena1 the rules which govern the quantities in which elements combine4 ,this law may be considered as consisting of three parts1 according to the above description of it2--that elements combine in definite proportions2--that these determining proportions operate reciprocally2--and that when1 between the same elements1 several combining proportions occur1 they are related as multiples4 ,that elements combine in certain definite proportions of quantity1 and in no other1 was implied1 as soon as it was supposed that chemical compounds had any definite properties4 ,those who first attempted to establish regular formul#ddad for the constitution of salts1 minerals1 and #bhf other compounds1 assumed1 as the basis of this process1 that the elements in different specimens had the same proportion4 ,wenzel1 in #aggg1 published his ,lehre von der ,verwandschaft der ,krper2 or1 ,doctrine of the ,affinities of ,bodies2 in which he gave many good and accurate analyses4 ,his work1 it is said1 never grew into general notice4 ,berthollet1 as we have already stated1 maintained that chemical compounds were not definite2 but this controversy took place at a later period4 ,it ended in the establishment of the doctrine1 that there is1 for each combination1 only one proportion of the elements1 or at most only two or three4 ,note #ddad3 ,thomson1 ,hist4 ,chem4 vol4 ii4 p4 #bgi4 ,not only did ,wenzel1 by his very attempt1 presume the first law of chemical composition1 the definiteness of the proportions1 but he was also led1 by his results1 to the second rule1 that they are reciprocal4 ,for he found that when two neutral salts decompose each other1 the resulting salts are also neutral4 ,the neutral character of the salts shows that they are definite compounds2 and when the two elements of the one salt1 ,p and s1 are presented to those of the other1 ,b and n1 if ,p be in such quantity as to combine definitely with n1 ,b will also combine definitely with s4#dead ,note #dead3 ,i am told that ,wenzel 7whose book ,i have not seen71 though he adduces many cases in which double decomposition gives neutral salts1 does not express the proposition in a general form1 nor use letters in expressing it4 ,views similar to those of ,wenzel were also published by ,jeremiah ,benjamin ,richter#dfad in #agib1 in his ,anfangsgrnde der ,stchyometrie1 oder ,messkunst ,chymischer ,elemente1 7,principles of the ,measure of ,chemical ,elements7 in which he took the law1 just stated1 of reciprocal proportions1 as the basis of his researches1 and determined the numerical quantities of the common bases and acids which would saturate each other4 ,it is clear that1 by these steps1 the two first of our three rules may be considered as fully developed4 ,the change of general views which was at this time going on1 probably prevented chemists from feeling so much interest as they might have done otherwise1 in these details2 the ,french and ,english chemists1 in particular1 were fully employed with their own researches and controversies4 ,note #dfad3 ,thomson1 ,hist4 ,chem4 vol4 ii4 p4 #bhc4 ,thus the rules which had already been published by ,wenzel and ,richter had attracted so little notice1 that we can hardly consider ,mr4 ,dalton as having been anticipated by those writers1 when1 in #ahjc1 he began to communicate his views on the chemical constitution of #bhg bodies2 these views being such as to include both these two rules in their most general form1 and further1 the rule1 at that time still more new to chemists1 of multiple proportions4 ,he conceived bodies as composed of atoms of their constituent elements1 grouped1 either one and one1 or one and two1 or one and three1 and so on4 ,thus1 if ,c represent an atom of carbon and ,o one of oxygen1 ,o ,c will be an atom of carbonic oxide1 and ,o ,c ,o an atom of carbonic acid2 and hence it follows1 that while both these bodies have a definite quantity of oxygen to a given quantity of carbon1 in the latter substance this quantity is double of what it is in the former4 ,the consideration of bodies as consisting of compound atoms1 each of these being composed of elementary atoms1 naturally led to this law of multiple proportions4 ,in this mode of viewing bodies1 ,mr4 ,dalton had been preceded 7unknown to himself7 by ,mr4 ,higgins1 who1 in #aghi1 published#dgad his ,comparative ,view of the ,phlogistic and ,antiphlogistic ,theories4 ,he there says1#dhad ,that in volatile vitriolic acid1 a single ultimate particle of sulphur is united only to a single particle of dephlogisticated air2 and that in perfect vitriolic acid1 every single particle of sulphur is united to two of dephlogisticated air1 being the quantity necessary to saturation2 and he reasons in the same manner concerning the constitution of water1 and the compounds of nitrogen and oxygen4 ,these observations of ,higgins were1 however1 made casually1 and not followed out1 and cannot affect ,dalton's claim to original merit4 ,note #dgad3 ,turner's ,chem4 p4 #bag4 ,note #dhad3 ,p4 #cf and #cg4 ,mr4 ,dalton's generalization was first suggested#diad during his examination of olefiant gas and carburetted hydrogen gas2 and was asserted generally1 on the strength of a few facts1 being1 as it were1 irresistibly recommended by the clearness and simplicity which the notion possessed4 ,mr4 ,dalton himself represented the compound atoms of bodies by symbols1 which professed to exhibit the arrangement of the elementary atoms in space as well as their numerical proportion2 and he attached great importance to this part of his scheme4 ,it is clear1 however1 that this part of his doctrine is not essential to that numerical comparison of the law with facts1 on which its establishment rests4 ,these hypothetical configurations of atoms have no value till they are confirmed by corresponding facts1 such as the optical or crystalline properties of bodies may perhaps one day furnish4 #bhh ,note #diad3 ,thomson1 vol4 ii4 p4 #bia4 ,sect4 #b4--,reception and ,confirmation of the ,atomic ,theory4 ,,in order to give a sketch of the progress of the ,atomic ,theory into general reception1 we cannot do better than borrow our information mainly from ,dr4 ,thomson1 who was one of the earliest converts and most effective promulgators of the doctrine4 ,mr4 ,dalton1 at the time when he conceived his theory1 was a teacher of mathematics at ,manchester1 in circumstances which might have been considered narrow1 if he himself had been less simple in his manner of life1 and less moderate in his worldly views4 ,his experiments were generally made with apparatus of which the simplicity and cheapness corresponded to the rest of his habits4 ,in #ahjd1 he was already in possession of his atomic theory1 and explained it to ,dr4 ,thomson1 who visited him at that time4 ,it was made known to the chemical world in ,dr4 ,thomson's ,chemistry1 in #ahjg2 and in ,dalton's own ,system of ,chemistry 7#ahjh7 the leading ideas of it were very briefly stated4 ,dr4 ,wollaston's memoir1 on superacid and subacid salts1 which appeared in the ,philosophical ,transactions for #ahjh1 did much to secure this theory a place in the estimation of chemists4 ,here the author states1 that he had observed1 in various salts1 the quantities of acid combined with the base in the neutral and in the superacid salts to be as one to two3 and he says that1 thinking it likely this law might obtain generally in such compounds1 it was his design to have pursued this subject1 with the hope of discovering the cause to which so regular a relation may be ascribed4 ,but he adds1 that this appears to be superfluous after the publication of ,dalton's theory by ,dr4 ,thomson1 since all such facts are but special cases of the general law4 ,we cannot but remark here1 that the scrupulous timidity of ,wollaston was probably the only impediment to his anticipating ,dalton in the publication of the rule of multiple proportions2 and the forwardness to generalize1 which belongs to the character of the latter1 justly secured him1 in this instance1 the name of the discoverer of this law4 ,the rest of the ,english chemists soon followed ,wollaston and ,thomson1 though ,davy for some time resisted4 ,they objected1 indeed1 to ,dalton's assumption of atoms1 and1 to avoid this hypothetical step1 ,wollaston used the phrase chemical equivalents1 and ,davy the word proportions1 for the numbers which expressed ,dalton's atomic weights4 ,we may1 however1 venture to say that the term atom is the most convenient1 and it need not be understood as claiming our assent to the hypothesis of indivisible molecules4 #bhi ,as ,wollaston and ,dalton were thus arriving independently at the same result in ,england1 other chemists1 in other countries1 were1 unknown to each other1 travelling towards the same point4 ,in #ahjg1 ,berzelius1#ejad intending to publish a system of chemistry1 went through several works little read1 and among others the treatises of ,richter4 ,he was astonished1 he tells us1 at the light which was there thrown upon composition and decomposition1 and which had never been turned to profit4 ,he was led to a long train of experimental research1 and1 when he received information of ,dalton's ideas concerning multiple proportions1 he found1 in his own collection of analyses1 a full confirmation of this theory4 ,note #ejad3 ,berz4 ,chem4 ,b4 iii4 p4 #bg4 ,some of the ,germans1 indeed1 appear discontented with the partition of reputation which has taken place with respect to the ,theory of ,definite ,proportions4 ,one#eaad of them says1 ,dalton has only done this2--he has wrapt up the good ,richter 7whom he knew2 compare ,schweigger1 ,t1 older series1 vol4 x41 p4 #cha27 in a ragged suit1 patched together of atoms2 and now poor ,richter comes back to his own country in such a garb1 like ,ulysses1 and is not recognized4 ,it is to be recollected1 however1 that ,richter says nothing of multiple proportions4 ,note #eaad3 ,marx4 ,gesch4 der ,cryst4 p4 #bjb4 ,the general doctrine of the atomic theory is now firmly established over the whole of the chemical world4 ,there remain still several controverted points1 as1 for instance1 whether the atomic weights of all elements are exact multiples of the atomic weight of hydrogen4 ,dr4 ,prout advanced several instances in which this appeared to be true1 and ,dr4 ,thomson has asserted the law to be of universal application4 ,but1 on the other hand1 ,berzelius and ,dr4 ,turner declare that this hypothesis is at variance with the results of the best analyses4 ,such controverted points do not belong to our history1 which treats only of the progress of scientific truths already recognized by all competent judges4 ,though ,dalton's discovery was soon generally employed1 and universally spoken of with admiration1 it did not bring to him anything but barren praise1 and he continued in the humble employment of which we have spoken1 when his fame had filled ,europe1 and his name become a household word in the laboratory4 ,after some years he was appointed a corresponding member of the ,institute of ,france2 which may be considered as a ,european recognition of the importance #bij of what he had done2 and1 in #ahbf1 two medals for the encouragement of science having been placed at the disposal of the ,royal ,society by the ,king of ,england1 one of them was assigned to ,dalton1 for his development of the atomic theory4 ,in #ahcc1 at the meeting of the ,british ,association for the ,advancement of ,science1 which was held in ,cambridge1 it was announced that the ,king had bestowed upon him a pension of #aejl42 at the preceding meeting at ,oxford1 that university had conferred upon him the degree of ,doctor of ,laws1 a step the more remarkable1 since he belonged to the sect of ,quakers4 ,at all the meetings of the ,british ,association he has been present1 and has always been surrounded by the reverence and admiration of all who feel any sympathy with the progress of science4 ,may he long remain among us thus to remind us of the vast advance which ,chemistry owes to him6 #bnd ,ed4 ,soon after ,i wrote these expressions of hope1 the period of ,dalton's sojourn among us terminated4 ,he died on the #bgth of ,july1 #ahdd1 aged #gh4 ,his fellow-townsmen1 the inhabitants of ,manchester1 who had so long taken a pride in his residence among them1 soon after his death came to a determination to perpetuate his memory by establishing in his honor a ,professor of ,chemistry at ,manchester4 ,sect4 #c4--,the ,theory of ,volumes4--,gay-,lussac4 ,,the atomic theory1 at the very epoch of its introduction into ,france1 received a modification in virtue of a curious discovery then made4 ,soon after the publication of ,dalton's system1 ,gay-,lussac and ,humboldt found a rule for the combination of substances1 which includes that of ,dalton as far as it goes1 but extends to combinations of gases only4 ,this law is the theory of volumes2 namely1 that gases unite together by volume in very simple and definite proportions4 ,thus water is composed exactly of #ajj measures of oxygen and #bjj measures of hydrogen4 ,and since these simple ratios #a and #a1 #a and #b1 #a and #c1 alone prevail in such combinations1 it may easily be shown that laws like ,dalton's law of multiple proportions1 must obtain in such cases as he considered4 #bnd ,ed4 ,m4 ,schrder1 of ,mannheim1 has endeavored to extend to solids a law in some degree resembling ,gay-,lussac's law of the volumes of gases4 ,according to him1 the volumes of the chemical equivalents #bia of simple substances and their compounds are as whole numbers4#ebad ,,mm4 ,kopp1 ,playfair1 and ,joule have labored in the same field4 ,note #ebad3 ,die molecular-volume der ,chemischen ,verbindungen in festen und flssingen ,zustande1 #ahdc4 ,i cannot now attempt to trace other bearings and developments of this remarkable discovery4 ,i hasten on to the last generalization of chemistry2 which presents to us chemical forces under a new aspect1 and brings us back to the point from which we departed in commencing the history of this science4 ,,chapter ,,ix4 ,,epoch ,,of ,,davy ,,and ,,faraday4 ,sect4 #a4--,promulgation of the ,electro-chemical ,theory by ,davy4 ,,the reader will recollect that the ,history of ,chemistry1 though highly important and instructive in itself1 has been an interruption of the ,history of ,electro-dynamic ,research3--a necessary interruption1 however2 for till we became acquainted with ,chemistry in general1 we could not follow the course of ,electro-chemistry3 we could not estimate its vast yet philosophical theories1 nor even express its simplest facts4 ,we have now to endeavor to show what has thus been done1 and by what steps2--to give a fitting view of the ,epoch of ,davy and ,faraday4 ,this is1 doubtless1 a task of difficulty and delicacy4 ,we cannot execute it at all1 except we suppose that the great truths1 of which the discovery marks this epoch1 have already assumed their definite and permanent form4 ,for we do not learn the just value and right place of imperfect attempts and partial advances in science1 except by seeing to what they lead4 ,we judge properly of our trials and guesses only when we have gained our point and guessed rightly4 ,we might personify philosophical theories1 and might represent them to ourselves as figures1 all pressing eagerly onwards in the same #bib direction1 whom we have to pursue3 and it is only in proportion as we ourselves overtake those figures in the race1 and pass beyond them1 that we are enabled to look back upon their faces2 to discern their real aspects1 and to catch the true character of their countenances4 ,except1 therefore1 ,i were of opinion that the great truths which ,davy brought into sight have been firmly established and clearly developed by ,faraday1 ,i could not pretend to give the history of this striking portion of science4 ,but ,i trust1 by the view ,i have to offer of these beautiful trains of research and their result1 to justify the assumption on which ,i thus proceed4 ,i must1 however1 state1 as a further appeal to the reader's indulgence1 that1 even if the great principles of electro-chemistry have now been brought out in their due form and extent1 the discovery is but a very few years1 ,i might rather say a few months1 old1 and that this novelty adds materially to the difficulty of estimating previous attempts from the point of view to which we are thus led4 ,it is only slowly and by degrees that the mind becomes sufficiently imbued with those new truths1 of which the office is1 to change the face of a science4 ,we have to consider familiar appearances under a new aspect2 to refer old facts to new principles2 and it is not till after some time1 that the struggle and hesitation which this employment occasions1 subsides into a tranquil equilibrium4 ,in the newly acquired provinces of man's intellectual empire1 the din and confusion of conquest pass only gradually into quiet and security4 ,we have seen1 in the history of all capital discoveries1 how hardly they have made their way1 even among the most intelligent and candid philosophers of the antecedent schools3 we must1 therefore1 not expect that the metamorphosis of the theoretical views of chemistry which is now going on1 will be effected without some trouble and delay4 ,i shall endeavor to diminish the difficulties of my undertaking1 by presenting the earlier investigations in the department of which ,i have now to speak1 as much as possible according to the most deliberate view taken of them by the great discoverers themselves1 ,davy and ,faraday2 since these philosophers are they who have taught us the true import of such investigations4 ,there is a further difficulty in my task1 to which ,i might refer2--the difficulty of speaking1 without error and without offence1 of men now alive1 or who were lately members of social circles which exist still around us4 ,but the scientific history in which such persons play a part1 is so important to my purpose1 that ,i do not hesitate to incur #bic the responsibility which the narration involves2 and ,i have endeavored earnestly1 and ,i hope not in vain1 to speak as if ,i were removed by centuries from the personages of my story4 ,the phenomena observed in the ,voltaic apparatus were naturally the subject of many speculations as to their cause1 and thus gave rise to ,theories of the ,pile4 ,among these phenomena there was one class which led to most important results3 it was discovered by ,nicholson and ,carlisle1 in #ahjj1 that water was decomposed by the pile of ,volta2 that is1 it was found that when the wires of the pile were placed with their ends near each other in the fluid1 a stream of bubbles of air arose from each wire1 and these airs were found on examination to be oxygen and hydrogen3 which1 as we have had to narrate1 had already been found to be the constituents of water4 ,this was1 as ,davy says1#ecad the true origin of all that has been done in electro-chemical science4 ,it was found that other substances also suffered a like decomposition under the same circumstances4 ,certain metallic solutions were decomposed1 and an alkali was separated on the negative plates of the apparatus4 ,cruickshank1 in pursuing these experiments1 added to them many important new results2 such as the decomposition of muriates of magnesia1 soda1 and ammonia by the pile2 and the general observation that the alkaline matter always appeared at the negative1 and the acid at the positive1 pole4 ,note #ecad3 ,phil4 ,trans4 #ahbf1 p4 #chf4 ,such was the state of the subject when one who was destined to do so much for its advance1 first contributed his labors to it4 ,humphry ,davy was a young man who had been apprenticed to a surgeon at ,penzance1 and having shown an ardent love and a strong aptitude for chemical research1 was1 in #agih1 made the superintendent of a ,pneumatic ,institution1 established at ,bristol by ,dr4 ,beddoes1 for the purpose of discovering medical powers of factitious airs4#edad ,but his main attention was soon drawn to galvanism2 and when1 in consequence of the reputation he had acquired1 he was1 in #ahja1 appointed lecturer at the ,royal ,institution in ,london 7then recently established71 he was soon put in possession of a galvanic apparatus of great power2 and with this he was not long in obtaining the most striking results4 ,note #edad3 ,paris1 ,life of ,davy1 i4 #eh4 ,his first paper on the subject#eead is sent from ,bristol1 in ,september1 #ahjj2 and describes experiments1 in which he had found that the decompositions observed by ,nicholson and ,carlisle go on1 although the #bid water1 or other substance in which the two wires are plunged1 be separated into two portions1 provided these portions are connected by muscular or other fibres4 ,this use of muscular fibres was1 probably1 a remnant of the original disposition1 or accident1 by which galvanism had been connected with physiology1 as much as with chemistry4 ,davy1 however1 soon went on towards the conclusion1 that the phenomena were altogether chemical in their nature4 ,he had already conjectured1#efad in #ahjb1 that all decompositions might be polar2 that is1 that in all cases of chemical decomposition1 the elements might be related to each other as electrically positive and negative2 a thought which it was the peculiar glory of his school to confirm and place in a distinct light4 ,at this period such a view was far from obvious2 and it was contended by many1 on the contrary1 that the elements which the voltaic apparatus brought to view1 were not liberated from combinations1 but generated4 ,in #ahjf1 ,davy attempted the solution of this question2 he showed that the ingredients which had been supposed to be produced by electricity1 were due to impurities in the water1 or to the decomposition of the vessel2 and thus removed all preliminary difficulties4 ,and then he says1#egad referring to my experiments of #ahjj1 #ahja1 and #ahjb1 and to a number of new facts1 which showed that inflammable substances and oxygen1 alkalies and acids1 and oxidable and noble metals1 were in electrical relations of positive and negative1 ,i drew the conclusion1 that the combinations and decompositions by electricity were referrible to the law of electrical attractions and repulsions1 and advanced the hypothesis1 that chemical and electrical attractions were produced by the same cause1 acting in the one case on particles1 in the other on masses2 4 4 4 and that the same property1 under different modifications1 was the cause of all the phenomena exhibited by different voltaic combinations4 ,note #eead3 ,nicholson's ,journal1 #dto4 iv4 #bge4 ,note #efad3 ,phil4 ,trans4 #ahbf4 ,note #egad3 ,ib4 #ahbf1 p4 #chi4 ,although this is the enunciation1 in tolerably precise terms1 of the great discovery of his epoch1 it was1 at the period of which we speak1 conjectured rather than proved2 and we shall find that neither ,davy nor his followers1 for a considerable period1 apprehended it with that distinctness which makes a discovery complete4 ,but in a very short time afterwards1 ,davy drew great additional notice to his researches by effecting1 in pursuance1 as it appeared1 of his theoretical views1 the decomposition of potassa into a metallic base and oxygen4 ,this was1 as he truly said1 in the memorandum written in his journal at the #bie instant1 a capital experiment4 ,this discovery was soon followed by that of the decomposition of soda2 and shortly after1 of other bodies of the same kind2 and the interest and activity of the whole chemical world were turned to the subject in an intense degree4 ,at this period1 there might be noticed three great branches of speculation on this subject2 the theory of the pile1 the theory of electrical decomposition1 and 9999the theory of the identity of chemical and electrical forces2 which last doctrine1 however1 was found to include the other two1 as might have been anticipated from the time of its first suggestion4 ,it will not be necessary to say much on the theories of the voltaic pile1 as separate from other parts of the subject4 ,the contact-theory1 which ascribed the action to the contact of different metals1 was maintained by ,volta himself2 but gradually disappeared1 as it was proved 7by ,wollaston#ehad especially17 that the effect of the pile was inseparably connected with oxidation or other chemical changes4 ,the theories of electro-chemical decomposition were numerous1 and especially after the promulgation of ,davy's ,memoir in #ahjf2 and1 whatever might be the defects under which these speculations for a long time labored1 the subject was powerfully urged on in the direction in which truth lay1 by ,davy's discoveries and views4 ,that there remained something still to be done1 in order to give full evidence and consistency to the theory1 appears from this2--that some of the most important parts of ,davy's results struck his followers as extraordinary paradoxes2--for instance1 the fact that the decomposed elements are transferred from one part of the circuit to another1 in a form which escapes the cognizance of our senses1 through intervening substances for which they have a strong affinity4 ,it was found afterwards that the circumstance which appeared to make the process so wonderful1 was1 in fact1 the condition of its going on at all4 ,davy's expressions often seem to indicate the most exact notions3 for instance1 he says1 ,it is very natural to suppose that the repellent and attractive energies are communicated from one particle to another of the same kind1 so as to establish a conducting chain in the fluid2 and that the locomotion takes place in consequence2#eiad and yet at other times he speaks of the element as attracted and repelled by the metallic surfaces which form the poles2--a different1 and1 as it appeared afterwards1 an untenable view4 ,mr4 ,faraday1 who supplied what was wanting1 justly notices this vagueness4 #bif ,he says1#fjad that though1 in ,davy's celebrated ,memoir of #ahjf1 the points established are of the utmost value1 the mode of action by which the effects take place is stated very generally2 so generally1 indeed1 that probably a dozen precise schemes of electro-chemical action might be drawn up1 differing essentially from each other1 yet all agreeing with the statement there given4 ,and at a period a little later1 being reproached by ,davy's brother with injustice in this expression1 he substantiated his assertion by an enumeration of twelve such schemes which had been published4 ,note #ehad3 ,phil4 ,trans4 #ahja1 p4 #dbg4 ,note #eiad3 ,paris1 i4 #aed4 ,note #fjad3 ,researches1 #dhb4 ,but yet we cannot look upon this ,memoir of #ahjf1 otherwise than as a great event1 perhaps the most important event of the epoch now under review4 ,and as such it was recognized at once all over ,europe4 ,in particular1 it received the distinguished honor of being crowned by the ,institute of ,france1 although that country and ,england were then engaged in fierce hostility4 ,buonaparte had proposed a prize of sixty thousand francs to the person who by his experiments and discoveries should advance the knowledge of electricity and galvanism1 as much as ,franklin and ,volta did2 and of three thousand francs for the best experiment which should be made in the course of each year on the galvanic fluid2 the latter prize was1 by the ,first ,class of the ,institute1 awarded to ,davy4 ,from this period he rose rapidly to honors and distinctions1 and reached a height of scientific fame as great as has ever fallen to the lot of a discoverer in so short a time4 ,i shall not1 however1 dwell on such circumstances1 but confine myself to the progress of my subject4 ,sect4 #b4--;,establishment of the ,electro-chemical ,theory by ,faraday4 ,,the defects of ,davy's theoretical views will be seen most clearly by explaining what ,faraday added to them4 ,michael ,faraday was in every way fitted and led to become ,davy's successor in his great career of discovery4 ,in #ahab1 being then a bookseller's apprentice1 he attended the lectures of ,davy1 which at that period excited the highest admiration4#faad ,my desire to escape from trade1 ,mr4 ,faraday says1 which ,i thought vicious and selfish1 and to enter into the service of science1 which ,i imagined made its pursuers amiable and liberal1 induced me at last to take the bold and simple step of writing to ,sir ,h4 ,davy4 ,he was favorably received1 and1 in the next year1 became #big ,davy's assistant at the ,institution2 and afterwards his successor4 ,the ,institution which produced such researches as those of these two men1 may well be considered as a great school of exact and philosophical chemistry4 ,mr4 ,faraday1 from the beginning of his course of inquiry1 appears to have had the consciousness that he was engaged on a great connected work4 ,his ,experimental ,researches1 which appeared in a series of ,memoirs in the ,philosophical ,transactions1 are divided into short paragraphs1 numbered into a continued order from #a up to #aafj1 at the time at which ,i write2#fbad and destined1 probably1 to extend much further4 ,these paragraphs are connected by a very rigorous method of investigation and reasoning which runs through the whole body of them4 ,yet this unity of purpose was not at first obvious4 ,his first two ,memoirs were upon subjects which we have already treated of 7,b4 xiii4 c4 #e and c4 #h71 ,voltaic ,induction1 and the evolution of ,electricity from ,magnetism4 ,his ,third ,series has also been already referred to4 ,its object was1 as a preparatory step towards further investigation1 to show the identity of voltaic and animal electricity with that of the electrical machine2 and as machine electricity differs from other kinds in being successively in a state of tension and explosion1 instead of a continued current1 ,mr4 ,faraday succeeded in identifying it with them1 by causing the electrical discharge to pass through a bad conductor into a discharging-train of vast extent2 nothing less1 indeed1 than the whole fabric of the metallic gas-pipes and water-pipes of ,london4 ,in this ,memoir#fcad it is easy to see already traces of the general theoretical views at which he had arrived2 but these are not expressly stated till his ,fifth ,series2 his intermediate ,fourth ,series being occupied by another subsidiary labor on the conditions of conduction4 ,at length1 however1 in the ,fifth ,series1 which was read to the ,royal ,society in ,june1 #ahcc1 he approaches the theory of electro-chemical decomposition4 ,most preceding theorists1 and ,davy amongst the number1 had referred this result to attractive powers residing in the poles of the apparatus2 and had even pretended to compare the intensity of this attraction at different distances from the poles4 ,by a number of singularly beautiful and skilful experiments1 ,mr4 ,faraday shows that the phenomena can with no propriety be #bih ascribed to the attraction of the poles4#fdad ,as the substances evolved in cases of electro-chemical decomposition may be made to appear against air1#fead which1 according to common language1 is not a conductor1 nor is decomposed2 or against water1#ffad which is a conductor1 and can be decomposed2 as well as against the metal poles1 which are excellent conductors1 but undecomposable2 there appears but little reason to consider this phenomenon generally as due to the attraction or attractive powers of the latter1 when used in the ordinary way1 since similar attractions can hardly be imagined in the former instances4 ,note #faad3 ,paris1 ii4 #c4 ,note #fbad3 ,december1 #ahce4 7,at present1 when ,i am revising the second edition1 ,september1 #ahdf1 ,dr4 ,faraday has recently published the ,twenty-first ,series of his ,researches ending with paragraph #bdec47 ,note #fcad3 ,phil4 ,trans4 #ahcc4 ,note #fdad3 ,researches1 ,art4 #dig ,note #fead3 ,researches1 ,arts4 #dfe1 #dfi4 ,note #ffad3 #die4 ,faraday's opinion1 and1 indeed1 the only way of expressing the results of his experiments1 was1 that the chemical elements1 in obedience to the direction of the voltaic currents established in the decomposing substance1 were evolved1 or1 as he prefers to say1 ejected at its extremities4#fgad ,he afterwards states that the influence which is present in the electric current may be described#fhad as an axis of power1 having at each point contrary forces exactly equal in amount in contrary directions4 ,note #fgad3 #dic4 ,note #fhad3 #eag4 ,having arrived at this point1 ,faraday rightly wished to reject the term poles1 and other words which could hardly be used without suggesting doctrines now proved to be erroneous4 ,he considered1 in the case of bodies electrically decomposed1 or1 as he termed them1 electrolytes1 the elements as travelling in two opposite directions2 which1 with reference to the direction of terrestrial magnetism1 might be considered as naturally east and west2 and he conceived elements as1 in this way1 arriving at the doors or outlets at which they finally made their separate appearance4 ,the doors he called electrodes1 and1 separately1 the anode and the cathode2#fiad and the elements which thus travel he termed the anon and the caton 7or cathon74#gjad ,by means of this nomenclature he was able to express his general results with much more distinctness and facility4 ,note #fiad3 #ffc4 ,note #gjad3 ,the analogy of the ,greek derivation requires caton2 but to make the relation to cathode obvious to the ,english reader1 and to avoid a violation of the habits of ,english pronunciation1 ,i should prefer cathon4 ,but this general view of the electrolytical process required to be pursued further1 in order to explain the nature of the action4 ,the identity of electrical and chemical forces1 which had been hazarded as #bii a conjecture by ,davy1 and adopted as the basis of chemistry by ,berzelius1 could only be established by exact measures and rigorous proofs4 ,faraday had1 in his proof of the identity of voltaic and electric agency1 attempted also to devise such a measure as should give him a comparison of their quantity2 and in this way he proved that#gaad a voltaic group of two small wires of platinum and zinc1 placed near each other1 and immersed in dilute acid for three seconds1 yields as much electricity as the electrical battery1 charged by ten turns of a large machine2 and this was established both by its momentary electro-magnetic effect1 and by the amount of its chemical action4#gbad ,note #gaad3 ,researches1 ,art4 #cga4 ,note #gbad3 #ecg4 ,it was in his ,seventh ,series1 that he finally established a principle of definite measurement of the amount of electrolytical action1 and described an instrument which he termed#gcad a volta-electrometer4 ,in this instrument the amount of action was measured by the quantity of water decomposed3 and it was necessary1 in order to give validity to the mensuration1 to show 7as ,faraday did show7 that neither the size of the electrodes1 nor the intensity of the current1 nor the strength of the acid solution which acted on the plates of the pile1 disturbed the accuracy of this measure4 ,he proved1 by experiments upon a great variety of substances1 of the most different kinds1 that the electro-chemical action is definite in amount according to the measurement of the new instrument4#gdad ,he had already1 at an earlier period1#gead asserted1 that the chemical power of a current of electricity is in direct proportion to the absolute quantity of electricity which passes2 but the volta-electrometer enabled him to fix with more precision the meaning of this general proposition1 as well as to place it beyond doubt4 ,note #gcad3 #gci4 ,note #gdad3 ,arts4 #geh1 #had4 ,note #gead3 #cgg4 ,the vast importance of this step in chemistry soon came into view4 ,by the use of the volta-electrometer1 ,faraday obtained1 for each elementary substance1 a number which represented the relative amount of its decomposition1 and which might properly#gfad be called its electro-chemical equivalent4 ,and the question naturally occurs1 whether these numbers bore any relation to any previously established chemical measures4 ,the answer is remarkable4 ,they were no other than the atomic weights of the ,daltonian theory1 which formed the climax of the previous ascent of chemistry2 and thus here1 as everywhere in #cjj the progress of science1 the generalizations of one generation are absorbed in the wider generalizations of the next4 ,note #gfad3 #gib4 ,but in order to reach securely this wider generalization1 ,faraday combined the two branches of the subject which we have already noticed2--the theory of electrical decomposition with the theory of the pile4 ,for his researches on the origin of activity of the voltaic circuit 7his ,eighth ,series71 led him to see more clearly than any one before him1 what1 as we have said1 the most sagacious of preceding philosophers had maintained1 that the current in the pile was due to the mutual chemical action of its elements4 ,he was led to consider the processes which go on in the exciting-cell and in the decomposing place as of the same kind1 but opposite in direction4 ,the chemical composition of the fluid with the zinc1 in the common apparatus1 produces1 when the circuit is completed1 a current of electric influence in the wire2 and this current1 if it pass through an electrolyte1 manifests itself by decomposition1 overcoming the chemical affinity which there resists it4 ,an electrolyte cannot conduct without being decomposed4 ,the forces at the point of composition and the point of decomposition are of the same kind1 and are opposed to each other by means of the conducting-wire2 the wire may properly be spoken of#ggad as conducting chemical affinity3 it allows two forces of the same kind to oppose one another2#ghad electricity is only another mode of the exertion of chemical forces2#giad and we might express all the circumstances of the voltaic pile without using any other term than chemical affinity1 though that of electricity may be very convenient4#hjad ,bodies are held together by a definite power1 which1 when it ceases to discharge that office1 may be thrown into the condition of an electric current4#haad ,note #ggad3 ,researches ,art4 #iah4 ,note #ghad3 #iaj4 ,note #giad3 #iae4 ,note #hjad3 #iag4 ,note #haad3 #hee4 ,thus the great principle of the identity of electrical and chemical action was completely established4 ,it was1 as ,faraday with great candor says1#hbad a confirmation of the general views put forth by ,davy1 in #ahjf1 and might be expressed in his terms1 that chemical and electrical attractions are produced by the same cause2 but it is easy to see that neither was the full import of these expressions understood nor were the quantities to which they refer conceived as measurable quantities1 nor was the assertion anything but a sagacious conjecture1 till ,faraday gave the interpretation1 measure1 and proof1 of which we have spoken4 ,the evidence of the incompleteness of the views of his predecessor we have already adduced1 in speaking of his vague and #cja inconsistent theoretical account of decomposition4 ,the confirmation of ,davy's discoveries by ,faraday is of the nature of ,newton's confirmation of the views of ,borelli and ,hooke respecting gravity1 or like ,young's confirmation of the undulatory theory of ,huyghens4 ,note #hbad3 #ife4 ,we must not omit to repeat here the moral which we wish to draw from all great discoveries1 that they depend upon the combination of exact facts with clear ideas4 ,the former of these conditions is easily illustrated in the case of ,davy and ,faraday1 both admirable and delicate experimenters4 ,davy's rapidity and resource in experimenting were extraordinary1#hcad and extreme elegance and ingenuity distinguish almost every process of ,faraday4 ,he had published1 in #ahbi1 a work on ,chemical ,manipulation1 in which directions are given for performing in the neatest manner all chemical processes4 ,manipulation1 as he there truly says1 is to the chemist like the external senses to the mind2#hdad and without the supply of fit materials which such senses only can give1 the mind can acquire no real knowledge4 ,note #hcad3 ,paris1 i4 #ade4 ,note #hdad3 ,pref4 p4 ii4 ,but still the operations of the mind as well as the information of the senses1 ideas as well as facts1 are requisite for the attainment of any knowledge2 and all great steps in science require a peculiar distinctness and vividness of thought in the discoverer4 ,this it is difficult to exemplify in any better way than by the discoveries themselves4 ,both ,davy and ,faraday possessed this vividness of mind2 and it was a consequence of this endowment1 that ,davy's 9999lectures upon chemistry1 and ,faraday's upon almost any subject of physical philosophy1 were of the most brilliant and captivating character4 ,in discovering the nature of voltaic action1 the essential intellectual requisite was to have a distinct conception of that which ,faraday expressed by the remarkable phrase1#head an axis of power having equal and opposite forces2 and the distinctness of this idea in ,faraday's mind shines forth in every part of his writings4 ,thus he says1 the force which determines the decomposition of a body is in the body1 not in the poles4#hfad ,but for the most part he can of course only convey this fundamental idea by illustrations4 ,thus#hgad he represents the voltaic circuit by a double circle1 studded with the elements of the circuit1 and shows how the anons travel round it in one direction1 and the cathons in the opposite4 ,he considers#hhad the powers at the two places of action as balancing against each other through the medium of the conductors1 in a manner #cjb analogous to that in which mechanical forces are balanced against each other by the intervention of the lever4 ,it is impossible to him#hiad to resist the idea1 that the voltaic current must be preceded by a state of tension in its interrupted condition1 which is relieved when the circuit is completed4 ,he appears to possess the idea of this kind of force with the same eminent distinctness with which ,archimedes in the ancient1 and ,stevinus in the modern history of science1 possessed the idea of pressure1 and were thus able to found the science of mechanics4#ijad ,and when he cannot obtain these distinct modes of conception1 he is dissatisfied1 and conscious of defect4 ,thus in the relation between magnetism and electricity1#iaad there appears to be a link in the chain of effects1 a wheel in the physical mechanism of the action1 as yet unrecognized4 ,all this variety of expression shows how deeply seated is the thought4 ,this conception of ,chemical ,affinity as a peculiar influence of force1 which1 acting in opposite directions1 combines and resolves bodies2--which may be liberated and thrown into the form of a voltaic current1 and thus be transferred to remote points1 and applied in various ways2 is essential to the understanding1 as it was to the making1 of these discoveries4 ,note #head3 ,art4 #eag4 ,note #hfad3 ,art4 #ffa4 ,note #hgad3 9999#ifc4 ,note #hhad3 #iag4 ,note #hiad3 ,art4 #iej4 ,note #ijad3 #iij4 ,note #iaad3 #aaad4 ,by those to whom this conception has been conveyed1 ,i venture to trust that ,i shall be held to have given a faithful account of this important event in the history of science4 ,we may1 before we quit the subject1 notice one or two of the remarkable subordinate features of ,faraday's discoveries4 ,sect4 #c4--;,consequences of ,faraday's ,discoveries4 ,,faraday',s volta-electrometer1 in conjunction with the method he had already employed1 as we have seen1 for the comparison of voltaic and common electricity1 enabled him to measure the actual quantity of electricity which is exhibited1 in given cases1 in the form of chemical affinity4 ,his results appeared in numbers of that enormous amount which so often comes before us in the expression of natural laws4 ,one grain of water#ibad will require for its decomposition as much electricity as would make a powerful flash of lightning4 ,by further calculation1 he finds this quantity to be not less than #hjj1jjj charges of his ,leyden battery2#icad and this is1 by his theory of the identity of the combining with the decomposing force1 the quantity of electricity #cjc which is naturally associated with the elements of the grain of water1 endowing them with their mutual affinity4 ,note #ibad3 9999#hec4 ,note #icad3 #hfa4 ,many of the subordinate facts and laws which were brought to light by these researches1 clearly point to generalizations1 not included in that which we have had to consider1 and not yet discovered3 such laws do not properly belong to our main plan1 which is to make our way up to the generalizations4 ,but there is one which so evidently promises to have an important bearing on future chemical theories1 that ,i will briefly mention it4 ,the class of bodies which are capable of electrical decomposition is limited by a very remarkable law3 they are such binary compounds only as consist of single proportionals of their elementary principles4 ,it does not belong to us here to speculate on the possible import of this curious law2 which1 if not fully established1 ,faraday has rendered1 at least1 highly probable3#idad but it is impossible not to see how closely it connects the ,atomic with the ,electro-chemical ,theory2 and in the connexion of these two great members of ,chemistry1 is involved the prospect of its reaching wider generalizations1 and principles more profound than we have yet caught sight of4 ,note #idad3 ,art4 #fig4 ,as another example of this connexion1 ,i will1 finally1 notice that ,faraday has employed his discoveries in order to decide1 in some doubtful cases1 what is the true chemical equivalent2#iead ,i have such conviction1 he says1 that the power which governs electro-decomposition and ordinary chemical attractions is the same2 and such confidence in the overruling influence of those natural laws which render the former definite1 as to feel no hesitation in believing that the latter must submit to them too4 ,such being the case1 ,i can have no doubt that1 assuming hydrogen as #a1 and dismissing small fractions for the simplicity of expression1 the equivalent number or atomic weight of oxygen is #h1 of chlorine #cf1 of bromine #ghd1 of lead #ajce1 of tin #ei1 c42 notwithstanding that a very high authority doubles several of these numbers4 ,note #iead3 #hea4 ,sect4 #d4--,reception of the ,electro-chemical ,theory4 ,,the epoch of establishment of the electro-chemical theory1 like other great scientific epochs1 must have its sequel1 the period of its reception and confirmation1 application and extension4 ,in that period we #cjd are living1 and it must be the task of future historians to trace its course4 ,we may1 however1 say a word on the reception which the theory met with1 in the forms which it assumed1 anterior to the labors of ,faraday4 ,even before the great discovery of ,davy1 ,grotthuss1 in #ahje1 had written upon the theory of electro-chemical decomposition2 but he and1 as we have seen1 ,davy1 and afterwards other writers1 as ,riffault and ,chompr1 in #ahjg1 referred the effects to the poles4#ifad ,but the most important attempt to appropriate and employ the generalization which these discoveries suggested1 was that of ,berzelius2 who adopted at once the view of the identity1 or at least the universal connexion1 of electrical relations with chemical affinity4 ,he considered1#igad that in all chemical combinations the elements may be considered as electro-positive and electro-negative2 and made this opposition the basis of his chemical doctrines2 in which he was followed by a large body of the chemists of ,germany4 ,he held too that the heat and light1 evolved during cases of powerful combination1 are the consequence of the electric discharge which is at that moment taking place3 a conjecture which ,faraday at first spoke of with praise4#ihad ,but at a later period he more sagely says1#iiad that the flame which is produced in such cases exhibits but a small portion of the electric power which really acts4 ,these therefore may not1 cannot1 be taken as evidences of the nature of the action2 but are merely incidental results1 incomparably small in relation to the forces concerned1 and supplying no information of the way in which the particles are active on each other1 or in which their forces are finally arranged4 ,and comparing the evidence which he himself had given of the principle on which ,berzelius's speculations rested1 with the speculations themselves1 ,faraday justly conceived1 that he had transferred the doctrine from the domain of what he calls doubtful knowledge1 to that of inductive certainty4 ,note #ifad3 ,faraday 7,researches1 ,art4 #dha1 #dib74 ,note #igad3 ,ann4 ,chim4 lxxxvi4 #adf1 for #ahac4 ,note #ihad3 ,researches1 ,art4 #hgj ,note #iiad3 #ifj4 ,now that we are arrived at the starting-place1 from which this well-proved truth1 the identity of electric and chemical forces1 must make its future advances1 it would be trifling to dwell longer on the details of the diffusion of that doubtful knowledge which preceded this more certain science4 ,our history of chemistry is1 therefore1 here at an end4 ,i have1 as far as ,i could1 executed my task2 which was1 to mark all the #cje great steps of its advance1 from the most unconnected facts and the most imperfect speculations1 to the highest generalization at which chemical philosophers have yet arrived4 ,yet it will appear to our purpose to say a few words on the connexion of this science with those of which we are next to treat2 and that ,i now proceed to do4 ,,chapter ,x4 ,,transition ,,from ,,the ,,chemical ,,to ,,the ,,classificatory ,,sciences4 ,,it is the object and the boast of chemistry to acquire a knowledge of bodies which is more exact and constant than any knowledge borrowed from their sensible qualities can be2 since it penetrates into their intimate constitution1 and discloses to us the invariable laws of their composition4 ,but yet it will be seen1 on a little reflection1 that such knowledge could not have any existence1 if we were not also attentive to their sensible qualities4 ,the whole fabric of chemistry rests1 even at the present day1 upon the opposition of acids and bases3 an acid was certainly at first known by its sensible qualities1 and how otherwise1 even now1 do we perceive its quality8 ,it was a great discovery of modern times that earths and alkalies have for their bases metals3 but what are metals8 or how1 except from lustre1 hardness1 weight1 and the like1 do we recognize a body as a metal8 ,and how1 except by such characters1 even before its analysis1 was it known to be an earth or an alkali8 ,we must suppose some classification established1 before we can make any advance by experiment or observation4 ,it is easy to see that all attempts to avoid this difficulty by referring to processes and analogies1 as well as to substances1 bring us back to the same point in a circle of fallacies4 ,if we say that an acid and alkali are known by combining with each other1 we still must ask1 ,what is the criterion that they have combined8 ,if we say that the distinctive qualities of metals and earths are1 that metals become earths by oxidation1 we must still inquire how we recognize the process of oxidation8 ,we have seen how important a part combustion plays in the history of chemical speculation2 and we may usefully form such classes of #cjf bodies as combustibles and supporters of combustion4 ,but even combustion is not capable of being infallibly known1 for it passes by insensible shades into oxidation4 ,we can find no basis for our reasonings1 which does not assume a classification of obvious facts and qualities4 ,but any classification of substances on such grounds1 appears1 at first sight1 to involve us in vagueness1 ambiguity1 and contradiction4 ,do we really take the sensible qualities of an acid as the criterion of its being an acid8--for instance1 its sourness8 ,prussic acid1 arsenious acid1 are not sour4 ,i remember1 says ,dr4 ,paris1#ajjad a chemist having been exposed to much ridicule from speaking of a sweet acid1--why not8 ,when ,davy had discovered potassium1 it was disputed whether it was a metal2 for though its lustre and texture are metallic1 it is so light as to swim on water4 ,and if potassium be allowed to be a metal1 is silicium one1 a body which wants the metallic lustre1 and is a non-conductor of electricity8 ,it is clear that1 at least1 the obvious application of a classification by physical characters1 is attended with endless perplexity4 ,note #ajjad3 ,life of ,davy1 i4 #bfc4 ,but since we cannot even begin our researches without assuming a classification1 and since the forms of such a classification which first occur1 end in apparent confusion1 it is clear that we must look to our philosophy for a solution of this difficulty2 and must avoid the embarrassments and contradictions of casual and unreflective classification1 by obtaining a consistent and philosophical arrangement4 ,we must employ external characters and analogies in a connected and systematic manner2 we must have ,classificatory ,sciences1 and these must have a bearing even on ,chemistry4 ,accordingly1 the most philosophical chemists now proceed upon this principle4 ,the method which ,i have followed1 says ,m4 ,thenard1 in his ,trait de ,chimie1 published in #ahbd1 is1 to unite in one group all analogous bodies2 and the advantage of this method1 which is that employed by naturalists1 is very great1 especially in the study of the metals and their compounds4#ajaad ,in this1 as in all good systems of chemistry1 which have appeared since the establishment of the phlogistic theory1 combustion1 and the analogous processes1 are one great element in the arrangement1 while the difference of metallic and non-metallic1 is another element4 ,thus ,thenard1 in the first place1 speaks of ,oxygen2 in the next place1 of the ,non-metallic ,combustibles1 as ,hydrogen1 ,carbon1 ,sulphur1 ,chlorine2 and in the next place1 of ,metals4 ,but the ,metals are again divided into six ,sections1 with reference1 #cjg principally1 to their facility of combination with oxygen4 ,thus1 the ,first ,section is the ,metals of the ,earths2 the ,second1 the ,metals of the ,alkalies2 the ,third1 the ,easily ,oxidable ,metals1 as ,iron2 the ,fourth1 ,metals ,less ,oxidable1 as ,copper and ,lead2 the ,fifth ,section contains only ,mercury and ,osmium2 and the ,sixth1 what were at an earlier period termed the ,noble ,metals1 ,gold1 ,silver1 ,platinum1 and others4 ,note #ajaad3 ,pref41 p4 viii4 ,how such principles are to be applied1 so as to produce a definite and consistent arrangement1 will be explained in speaking of the philosophy of the ,classificatory ,sciences2 but there are one or two peculiarities in the classes of bodies thus recognized by modern chemistry1 which it may be useful to notice4 #a4 ,the distinction of ,metallic and ,non-metallic is still employed1 as of fundamental importance4 ,the discovery of new metals is so much connected with the inquiries concerning chemical elements1 that we may notice the general progress of such discoveries4 ,gold1 ,silver1 ,iron1 ,copper1 ,quicksilver1 ,lead1 ,tin1 were known from the earliest antiquity4 ,in the beginning of the sixteenth century1 mine-directors1 like ,george ,agricola1 had advanced so far in practical metallurgy1 that they had discovered the means of extracting three additional metals1 ,zinc1 ,bismuth1 ,antimony4 ,after this1 there was no new metal discovered for a century1 and then such discoveries were made by the theoretical chemists1 a race of men who had not existed before ,beccher and ,stahl4 ,thus ,arsenic and ,cobalt were made known by ,brandt1 in the middle of the eighteenth century1 and we have a long list of similar discoveries belonging to the same period2 ,nickel1 ,manganese1 and ,tungsten1 which were detected by ,cronstedt1 ,gahn1 and ,scheele1 and ,delhuyart1 respectively2 metals of a very different kind1 ,tellurium and ,molybdenum1 which were brought to light by ,mller1 ,scheele1 ,bergman1 and ,hielm2 ,platinum1 which was known as early as #agda1 but with the ore of which1 in #ahjb and #ahjc1 the ,english chemists1 ,wollaston and ,tennant1 found that no less than four other new metals 7,palladium1 ,rhodium1 ,iridium and ,osmium7 were associated4 ,finally1 7omitting some other new metals17 we have another period of discovery1 opened in #ahjg1 by ,davy's discovery of ,potassium1 and including the resolution of all1 or almost all1 the alkalies and earths into metallic bases4 #bnd ,ed4 ,the next few years made some1 at least some conjectural1 additions to the list of simple substances1 detected by a more minute scrutiny of known substances4 ,thorium was discovered by ,berzelius in #ahbh2 and ,vanadium by ,professor ,sefstrm in #ahcj4 ,a #cjh metal named ,cerium1 was discovered in #ahjc1 by ,hisinger and ,berzelius1 in a rare ,swedish mineral known by the name of ,cerit4 ,mosander more recently has found combined with ,cerium1 other new metals which he has called ,lanthanium1 ,didymium1 ,erbium1 and ,terbium3 ,m4 ,klaus has found a new metal1 ,ruthenium1 in the ore of ,platinum2 and ,rose has discovered in ,tantalite two other new metals1 which he has announced under the names of ,pelopium and ,niobium4 ,svanberg is said to have discovered a new earth in ,eudialyt1 which is supposed to have1 like the rest1 a new radical4 ,if these last discoveries be confirmed1 the number of simple substances will be raised to sixty-two4 #b4 ,attempts have been made to indicate the classification of chemical substances by some peculiarity in the ,name2 and the ,metals1 for example1 have been designated generally by names in um1 like the ,latin names of the ancient metals1 aurum1 ferrum4 ,this artifice is a convenient nomenclature for the purpose of marking a recognized difference2 and it would be worth the while of chemists to agree to make it universal1 by writing molybdenum and platinum2 which is sometimes done1 but not always4 #c4 ,i am not now to attempt to determine how far this class1--,metals1--extends2 but where the analogies of the class cease to hold there the nomenclature must also change4 ,thus1 some chemists1 as ,dr4 ,thomson1 have conceived that the base of ,silica is more analogous to ,carbon and ,boron1 which form acids with oxygen1 than it is to the metals3 and he has accordingly associated this base with these substances1 and has given it the same termination1 ,silicon4 ,but on the validity of this analogy chemists appear not to be generally agreed4 #d4 ,there is another class of bodies which have attracted much notice among modern chemists1 and which have also been assimilated to each other in the form of their names2 the ,english writers calling them ,chlorine1 ,fluorine1 ,iodine1 ,bromine1 while the ,french use the terms ,chlore1 ,phtore1 ,iode1 ,brome4 ,we have already noticed the establishment of the doctrine--that muriatic acid is formed of a base1 chlorine1 and of hydrogen1--as a great reform in the oxygen theory2 with regard to which rival claims were advanced by ,davy1 and by ,,mm4 ,gay-,lussac and ,thenard in #ahjj4 ,iodine1 a remarkable body which1 from a dark powder1 is converted into a violet-colored gas by the application of heat1 was also1 in #ahac1 the subject of a similar rivalry between the same ,english and ,french chemists4 ,bromine #cji was only discovered as late as #ahbf2 and ,fluorine1 or ,phtore1 as1 from its destructive nature1 it has been proposed to term it1 has not been obtained as a separate substance1 and is inferred to exist by analogy only4 ,the analogies of these bodies 7,chlore1 ,phtore1 c47 are very peculiar2 for instance1 by combination with metals they form salts2 by combination with hydrogen they form very strong acids2 and all1 at the common temperature of the atmosphere1 operate on other bodies in the most energetic manner4 ,berzelius#ajbad proposes to call them halogenous bodies1 or halogenes4 ,note #ajbad3 ,chem4 i4 #bfb4 #e4 ,the number of ,elementary ,substances which are at present presented in our treatises of chemistry#ajcad is fifty-three1 or rather1 as we have said above1 sixty-two4 ,it is naturally often asked what evidence we have1 that all these are elementary1 and what evidence that they are all the elementary bodies2--how we know that new elements may not hereafter be discovered1 or these supposed simple bodies resolved into simpler still8 ,to these questions we can only answer1 by referring to the history of chemistry2--by pointing out what chemists have understood by analysis1 according to the preceding narrative4 ,they have considered1 as the analysis of a substance1 that elementary constitution of it which gives the only intelligible explanation of the results of chemical manipulation1 and which is proved to be complete as to quantity1 by the balance1 since the whole can only be equal to all its parts4 ,it is impossible to maintain that new substances may not hereafter be discovered2 for they may lurk1 even in familiar substances1 in doses so minute that they have not yet been missed amid the inevitable slight inaccuracies of all analysis2 in the way in which iodine and bromine remained so long undetected in sea-water2 and new minerals1 or old ones not yet sufficiently examined1 can hardly fail to add something to our list4 ,as to the possibility of a further analysis of our supposed simple bodies1 we may venture to say that1 in regard to such supposed simple bodies as compose a numerous and well-characterized class1 no such step can be made1 except through some great change in chemical theory1 which gives us a new view of all the general relations which chemistry has yet discovered4 ,the proper evidence of the reality of any supposed new analysis is1 that it is more consistent with the known analogies of chemistry1 to suppose the process analytical than synthetical4 ,thus1 as has already been said1 chemists admit the existence of fluorine1 from the analogy of chlorine2 and ,davy1 when it was found #caj that ammonia formed an amalgam with mercury1 was tempted to assign to it a metallic basis4 ,but then he again hesitates1#ajdad and doubts whether the analogies of our knowledge are not better preserved by supposing that ammonia1 as a compound of hydrogen and another principle1 is a type of the composition of the metals4 ,note #ajcad3 ,turner1 p4 #iga4 ,note #ajdad3 ,elem4 ,chem4 ,phil4 #ahab1 p4 #dha4 ,our history1 which is the history of what we know1 has little to do with such conjectures4 ,there are1 however1 some not unimportant principles which bear upon them1 and which1 as they are usually employed1 belong to the science which next comes under our review1 ,mineralogy4 #caa ,,book ,,xv4 ,,the ,,analytico-,,classificatory ,,science4 ,,history ,,of ,,mineralogy4 1 1 ' 4 ' 1 1 4 ,,orpheus4 ,lithica4 ,now1 if the bold but pious thought be thine1 ,to reach our spacious temple's inner shrine1 ,take in thy reverent hands the crystal stone1 ,where heavenly light in earthy shroud is shown3-- ,where1 moulded into measured form1 with rays ,complex yet clear1 the eternal ,ether plays2 ,this if thou firmly hold and rightly use1 ,not long the gods thy ardent wish refuse4 #cac ,,introduction4 ,sect4 #a4--,of the ,classificatory ,sciences4 ,,the horizon of the sciences spreads wider and wider before us1 as we advance in our task of taking a survey of the vast domain4 ,we have seen that the existence of ,chemistry as a science which declares the ingredients and essential constitution of all kinds of bodies1 implies the existence of another corresponding science1 which shall divide bodies into kinds1 and point out steadily and precisely what bodies they are which we have analysed4 ,but a science thus dividing and defining bodies1 is but one member of an order of sciences1 different from those which we have hitherto described2 namely1 of the classificatory sciences4 ,such sciences there must be1 not only having reference to the bodies with which chemistry deals1 but also to all things respecting which we aspire to obtain any general knowledge1 as1 for instance1 plants and animals4 ,indeed it will be found1 that it is with regard to these latter objects1 to organized beings1 that the process of scientific classification has been most successfully exercised2 while with regard to inorganic substances1 the formation of a satisfactory system of arrangement has been found extremely difficult2 nor has the necessity of such a system been recognised by chemists so distinctly and constantly as it ought to be4 ,the best exemplification of these branches of knowledge1 of which we now have to speak1 will1 therefore1 be found in the organic world1 in ,botany and ,zoology2 but we will1 in the first place1 take a brief view of the science which classifies inorganic bodies1 and of which ,mineralogy is hitherto the very imperfect representative4 ,the principles and rules of the ,classificatory ,sciences1 as well as of those of the other orders of sciences1 must be fully explained when we come to treat of the ,philosophy of the ,sciences2 and cannot be introduced here1 where we have to do with history only4 ,but ,i may observe very briefly1 that with the process of classing1 is joined the process of naming2--that names imply classification2--and that even the rudest and earliest application of language presupposes a distribution of objects according to their kinds2--but that such a spontaneous #cad and unsystematic distribution cannot1 in the cases we now have to consider1 answer the purposes of exact and general knowledge4 ,our classification of objects must be made consistent and systematic1 in order to be scientific2 we must discover marks and characters1 properties and conditions1 which are constant in their occurrence and relations2 we must form our classes1 we must impose our names1 according to such marks4 ,we can thus1 and thus alone1 arrive at that precise1 certain1 and systematic knowledge1 which we seek2 that is1 at science4 ,the object1 then1 of the classificatory sciences is to obtain ,,fixed ,,characters of the kinds of things2 and the criterion of the fitness of names is1 that ,,they ,,make ,,general ,,propositions ,,possible4 ,i proceed to review the progress of certain sciences on these principles1 and first1 though briefly1 the science of ,mineralogy4 ,sect4 #b4--,mineralogy as the ,analytico-classificatory ,science4 ,,mineralogy1 as it has hitherto been cultivated1 is1 as ,i have already said1 an imperfect representative of the department of human knowledge to which it belongs4 ,the attempts at the science have generally been made by collecting various kinds of information respecting mineral bodies2 but the science which we require is a complete and consistent classified system of all inorganic bodies4 ,for chemistry proceeds upon the principle that the constitution of a body invariably determines its properties2 and1 consequently1 its kind3 but we cannot apply this principle1 except we can speak with precision of the kind of a body1 as well as of its composition4 ,we cannot attach any sense to the assertion1 that soda or baryta has a metal for its base1 except we know what a metal is1 or at least what properties it implies4 ,it may not be1 indeed it is not1 possible1 to define the kinds of bodies by words only2 but the classification must proceed by some constant and generally applicable process2 and the knowledge which has reference to the classification will be precise as far as this process is precise1 and vague as far as this is vague4 ,there must be1 then1 as a necessary supplement to ,chemistry1 a ,science of those properties of bodies by which we divide them into kinds4 ,mineralogy is the branch of knowledge which has discharged the office of such a science1 so far as it has been discharged2 and1 indeed1 ,mineralogy has been gradually approaching to a clear consciousness of her real place1 and of her whole task2 ,i shall give the history of some of the advances which have thus been made4 ,they are1 principally1 #cae the establishment and use of ,external ,characters1 especially of ,crystalline ,form1 as a fixed character of definite substances2 and the attempts to bring into view the connexion of ,chemical ,constitution and ,external ,properties1 made in the shape of mineralogical ,systems2 both those in which chemical methods of arrangement are adopted1 and those which profess to classify by the natural-history method4 #caf ,,crystallography4 ,,chapter ,i4 ,,prelude ,,to ,,the ,,epoch ,,of ,,de ,,lisle ,,and ,,ha,y4 ,,of all the physical properties of bodies1 there is none so fixed1 and in every way so remarkable1 as this2--that the same chemical compound always assumes1 with the utmost precision1 the same geometrical form4 ,this identity1 however1 is not immediately obvious2 it is often obscured by various mixtures and imperfections in the substance2 and even when it is complete1 it is not immediately recognized by a common eye1 since it consists1 not in the equality of the sides or faces of the figures1 but in the equality of their angles4 ,hence it is not surprising that the constancy of form was not detected by the early observers4 ,pliny says1#aae ,why crystal is generated in a hexagonal form1 it is difficult to assign a reason2 and the more so1 since1 while its faces are smoother than any art can make them1 the pyramidal points are not all of the same kind4 ,the quartz crystals of the ,alps1 to which he refers1 are1 in some specimens1 very regular1 while in others1 one side of the pyramid becomes much the largest2 yet the angles remain constantly the same4 ,but when the whole shape varied so much1 the angles also seemed to vary4 ,thus ,conrad ,gessner1 a very learned naturalist1 who1 in #aefd1 published at ,zurich his work1 ,de rerum ,fossilium1 ,lapidum et ,gemmarum maxime1 ,figuris1 says1#bae ,one crystal differs from another in its angles1 and consequently in its figure4 ,and ,csalpinus1 who1 as we shall find1 did so much in establishing fixed characters in botany1 was led by some of his general views to disbelieve the fixity of the form of crystals4 ,in his work ,de ,metallicis1 published at ,nuremberg in #afjb1 he says1#cae ,to ascribe to inanimate bodies a definite form1 does not appear consentaneous to reason2 for it is the office of organization to produce a definite form2 #cag an opinion very natural in one who had been immersed in the study of the general analogies of the forms of plants4 ,but though this is excusable in ,csalpinus1 the rejection of this definiteness of form a hundred years later1 when its existence had been proved1 and its laws developed by numerous observers1 cannot be ascribed to anything but strong prejudice2 yet this was the course taken by no less a person than ,buffon4 ,the form of crystallization1 says he1#dae is not a constant character1 but is more equivocal and more variable than any other of the characters by which minerals are to be distinguished4 ,and accordingly1 he makes no use of this most important feature in his history of minerals4 ,this strange perverseness may perhaps be ascribed to the dislike which ,buffon is said to have entertained for ,linnus1 who had made crystalline form a leading character of minerals4 ,note #aae3 ,nat4 ,hist4 xxvii4 #b4 ,note #bae3 p4 #be4 ,note #cae3 p4 #ig4 ,note #dae3 ,hist4 des ,min4 p4 #cdc4 ,it is not necessary to mark all the minute steps by which mineralogists were gradually led to see clearly the nature and laws of the fixity of crystalline forms4 ,these forms were at first noticed in that substance which is peculiarly called rock-crystal or quartz2 and afterwards in various stones and gems1 in salts obtained from various solutions1 and in snow4 ,but those who observed the remarkable regular figures which these substances assume1 were at first impelled onwards in their speculations by the natural tendency of the human mind to generalize and guess1 rather than to examine and measure4 ,they attempted to snatch at once the general laws of geometrical regularity of these occurrences1 or to connect them with some doctrine concerning formative causes4 ,thus ,kepler1#eae in his ,harmonics of the ,world1 asserts a formatrix facultas1 which has its seat in the entrails of the earth1 and1 after the manner of a pregnant woman1 expresses the five regular geometrical solids in the forms of gems4 ,but ,philosophers1 in the course of time1 came to build more upon observation1 and less upon abstract reasonings4 ,nicolas ,steno1 a ,dane1 published1 in #affi1 a dissertation ,de ,solido intra ,solidum ,naturaliter contento1 in which he says1#fae that though the sides of the hexagonal crystal may vary1 the angles are not changed4 ,and ,dominic ,gulielmini1 in a ,dissertation on ,salts1 published in #agjg1 says1#gae in a true inductive spirit1 ,nature does not employ all figures1 but only certain ones of those which are possible2 and of these1 the determination is not to be fetched from the brain1 or proved priori1 but obtained by experiments and observations4 ,and #cah he speaks#hae with entire decision on this subject3 ,nevertheless since there is here a principle of crystallization1 the inclination of the planes and of the angles is always constant4 ,he even anticipates1 very nearly1 the views of later crystallographers as to the mode in which crystals are formed from elementary molecules4 ,from this time1 many persons labored and speculated on this subject2 as ,cappeller1 whose ,prodromus ,crystallographi appeared at ,lucern in #agbc2 ,bourguet1 who published ,lettres ,philosophiques sur la ,formation de ,sels et de ,cristaux1 at ,amsterdam1 in #agib2 and ,henckel1 the ,physicus of the ,elector of ,saxony1 whose ,pyritologia came forth in #agbe4 ,in this last work we have an example of the description of the various forms of special classes of minerals1 7iron pyrites1 copper pyrites1 and arsenic pyrites27 and an example of the enthusiasm which this apparently dry and laborious study can excite3 ,neither tongue nor stone1 he exclaims1#iae can express the satisfaction which ,i received on setting eyes upon this sinter covered with galena2 and thus it constantly happens1 that one must have more pleasure in what seems worthless rubbish1 than in the purest and most precious ores1 if we know aught of minerals4 ,note #eae3 ,linz4 #afai1 p4 #afa4 ,note #fae3 p4 #fi4 ,note #gae3 p4 #ai4 ,note #hae3 p4 #hc4 ,note #iae3 p4 #cdc4 ,still1 however1 ,henckel#ajae disclaims the intention of arranging minerals according to their mathematical forms2 and this1 which may be considered as the first decided step in the formation of crystallographic mineralogy1 appears to have been first attempted by ,linnus4 ,in this attempt1 however1 he was by no means happy2 nor does he himself appear to have been satisfied4 ,he begins his preface by saying1 ,lithology is not what ,i plume myself upon4 7,lithologia mihi cristas non eriget47 ,though his sagacity1 as a natural historian1 led him to see that crystalline form was one of the most definite1 and therefore most important1 characters of minerals1 he failed in profiting by this thought1 because1 in applying it1 he did not employ the light of geometry1 but was regulated by what appeared to him resemblances1 arbitrarily selected1 and often delusive4#aaae ,thus he derived the form of pyrites from that of vitriol2#abae and brought together alum and diamond on account of their common octohedral form4 ,but he had the great merit of animating to this study one to whom1 more perhaps than to any other person1 it owes its subsequent progress2 ,i mean ,rom de ,lisle4 ,instructed1 this writer says1 in his preface to his ,essais de ,crystallographie1 by the works of the celebrated ,von ,linne1 how #cai greatly the study of the angular form of crystals might become interesting1 and fitted to extend the sphere of our mineralogical knowledge1 ,i have followed them in all their metamorphoses with the most scrupulous attention4 ,the views of ,linnus1 as to the importance of this character1 had indeed been adopted by several others2 as ,john ,hill1 the ,king's gardener at ,kew1 who1 in #aggg1 published his ,spathogenesia2 and ,grignon1 who1 in #agge1 says1 ,these crystallizations may give the means of finding a new theory of the generation of crystalline gems4 ,note #ajae3 p4 #afg4 ,note #aaae3 ,marx4 ,gesch4 p4 #ig4 ,note #abae3 ,syst4 ,nat4 vi4 p4 #bbj4 ,the circumstance which threw so much difficulty in the way of those who tried to follow out his thought was1 that in consequence of the apparent irregularity of crystals1 arising from the extension or contraction of particular sides of the figure1 each kind of substance may really appear under many different forms1 connected with each other by certain geometrical relations4 ,these may be conceived by considering a certain fundamental form to be cut into new forms in particular ways4 ,thus if we take a cube1 and cut off all the eight corners1 till the original faces disappear1 we make it an octohedron2 and if we stop short of this1 we have a figure of fourteen faces1 which has been called a cubo-octohedron4 ,the first person who appears distinctly to have conceived this truncation of angles and edges1 and to have introduced the word1 is ,dmeste2#acae although ,wallerius#adae had already said1 in speaking of the various crystalline forms of calcspar1 ,i conceive it would be better not to attend to all differences1 lest we be overwhelmed by the number4 ,and ,werner1 in his celebrated work ,on the ,external ,characters of ,minerals1#aeae had formally spoken of truncation1 acuation1 and acumination1 or replacement by a plane1 an edge1 a point respectively1 7abstumpfung1 zuschrfung1 zuspitzung17 as ways in which the forms of crystals are modified and often disguised4 ,he applied this process in particular to show the connexion of the various forms which are related to the cube4 ,but still the extension of the process to the whole range of minerals and other crystalline bodies1 was due to ,rom de ,lisle4 #cbj ,note #acae3 ,lettres1 #aggi1 i4 #dh4 ,note #adae3 ,systema ,mineralogicum1 #aggb-e1 i4 #adc4 ,note #aeae3 ,leipzig1 #aggd4 ,,chapter ,,ii4 ,,epoch ,,of ,,rom ,,de ,,lisle ,,and ,,ha,y4--,,establishment ,,of ,,the ,,fixity ,,of ,,crystalline ,,angles1 ,,and ,,the ,,simplicity ,,of ,,the ,,laws ,,of ,,derivation4 ,,we have already seen that1 before #aghj1 several mineralogists had recognized the constancy of the angles of crystals1 and had seen 7as ,dmeste and ,werner17 that the forms were subject to modifications of a definite kind4 ,but neither of these two thoughts was so apprehended and so developed1 as to supersede the occasion for a discoverer who should put forward these principles as what they really were1 the materials of a new and complete science4 ,the merit of this step belongs jointly to ,rom de ,lisle and to ,hay4 ,the former of these two men had already1 in #aggb1 published an ,essai de ,crystallographie1 in which he had described a number of crystals4 ,but in this work his views are still rude and vague2 he does not establish any connected sequence of transitions in each kind of substance1 and lays little or no stress on the angles4 ,but in #aghc1 his ideas#afae had reached a maturity which1 by comparison1 excites our admiration4 ,in this he asserts1 in the most distinct manner1 the invariability of the angles of crystals of each kind1 under all the changes of relative dimension which the faces may undergo2#agae and he points out that this invariability applies only to the primitive forms1 from each of which many secondary forms are derived by various changes4#ahae ,thus we cannot deny him the merit of having taken steady hold on both the handles of this discovery1 though something still remained for another to do4 ,rom pursues his general ideas into detail with great labor and skill4 ,he gives drawings of more than five hundred regular forms 7in his first work he had inserted only one hundred and ten2 ,linnus only knew forty72 and assigns them to their proper substances2 for instance1 thirty to calcspar1 and sixteen to felspar4 ,he also invented and used a goniometer4 ,we cannot doubt that he would have been #cba looked upon as a great discoverer1 if his fame had not been dimmed by the more brilliant success of his contemporary ,hay4 ,note #afae3 ,cristallographie1 ou ,description de ,formes propres tous les ,corps du ,rgne ,minral4 #c vols4 and #a vol4 of plates4 ,note #agae3 p4 #fh4 ,note #ahae3 p4 #gc4 ,rn-,just ,hay is rightly looked upon as the founder of the modern school of crystallography2 for all those who have1 since him1 pursued the study with success1 have taken his views for their basis4 ,besides publishing a system of crystallography and of mineralogy1 far more complete than any which had yet appeared1 the peculiar steps in the advance which belong to him are1 the discovery of the importance of cleavage1 and the consequent expression of the laws of derivation of secondary from primary forms1 by means of the decrements of the successive layers of integrant molecules4 ,the latter of these discoveries had already been1 in some measure1 anticipated by ,bergman1 who had1 in #aggc1 conceived a hexagonal prism to be built up by the juxtaposition of solid rhombs on the planes of a rhombic nucleus4#aiae ,it is not clear#bjae whether ,hay was acquainted with ,bergman's ,memoir1 at the time when the cleavage of a hexagonal prism of calcspar1 accidentally obtained1 led him to the same conception of its structure4 ,but however this might be1 he had the indisputable credit of following out this conception with all the vigor of originality1 and with the most laborious and persevering earnestness2 indeed he made it the business of his life4 ,the hypothesis of a solid1 built up of small solids1 had this peculiar advantage in reference to crystallography2 it rendered a reason of this curious fact2--that a certain series of forms occur in crystals of the same kind1 while other forms1 apparently intermediate between those which actually occur1 are rigorously excluded4 ,the doctrine of decrements explained this2 for by placing a number of regularly-decreasing rows of equal solids1 as1 for instance1 of bricks1 upon one another1 we might form a regular equal-sided triangle1 as the gable of a house2 and if the breadth of the gable were one hundred bricks1 the height of the triangle might be one hundred1 or fifty1 or twenty-five2 but it would be found that if the height were an intermediate number1 as fifty-seven1 or forty-three1 the edge of the wall would become irregular2 and such irregularity is assumed to be inadmissible in the regular structure of crystals4 ,thus this mode of conceiving crystals allows of certain definite secondary forms1 and no others4 ,note #aiae3 ,de ,formis ,crystallorum4 ,nov4 ,act4 ,reg4 ,soc4 ,sc4 ,ups4 #aggc4 ,note #bjae3 ,trait de ,minr4 #ahbb1 i4 #ae4 ,the mathematical deduction of the dimensions and proportions #cbb of these secondary forms2--the invention of a notation to express them2--the examination of the whole mineral kingdom in accordance with these views2--the production of a work#baae in which they are explained with singular clearness and vivacity2--are services by which ,hay richly earned the admiration which has been bestowed upon him4 ,the wonderful copiousness and variety of the forms and laws to which he was led1 thoroughly exercised and nourished the spirit of deduction and calculation which his discoveries excited in him4 ,the reader may form some conception of the extent of his labors1 by being told--that the mere geometrical propositions which he found it necessary to premise to his special descriptions1 occupy a volume and a half of his work2--that his diagrams are nearly a thousand in number2--that in one single substance 7calcspar7 he has described forty-seven varieties of form2--and that he has described one kind of crystal 7called by him fer sulfur paralllique7 which has one hundred and thirty-four faces4 ,note #baae3 ,trait de ,minralogie1 #ahja1 #e vols4 ,in the course of a long life1 he examined1 with considerable care1 all the forms he could procure of all kinds of mineral2 and the interpretation which he gave of the laws of those forms was1 in many cases1 fixed1 by means of a name applied to the mineral in which the form occurred2 thus1 he introduced such names as quiaxe1 mtastatique1 unibinaire1 perihexahdre1 bisalterne1 and others4 ,it is not now desirable to apply separate names to the different forms of the same mineral species1 but these terms answered the purpose1 at the time1 of making the subjects of study more definite4 ,a symbolical notation is the more convenient mode of designating such forms1 and such a notation ,hay invented2 but the symbols devised by him had many inconveniences1 and have since been superseded by the systems of other crystallographers4 ,another of ,hay's leading merits was1 as we have already intimated1 to have shown1 more clearly than his predecessors had done1 that the crystalline angles of substances are a criterion of the substances2 and that this is peculiarly true of the angles of cleavage2--that is1 the angles of those edges which are obtained by cleaving a crystal in two different directions2--a mode of division which the structure of many kinds of crystals allowed him to execute in the most complete manner4 ,as an instance of the employment of this criterion1 ,i may mention his separation of the sulphates of baryta and strontia1 which had #cbc previously been confounded4 ,among crystals which in the collections were ranked together as heavy spar1 and which were so perfect as to admit of accurate measurement1 he found that those which were brought from ,sicily1 and those of ,derbyshire1 differed in their cleavage angle by three degrees and a half4 ,i could not suppose1 he says1#bbae that this difference was the effect of any law of decrement2 for it would have been necessary to suppose so rapid and complex a law1 that such an hypothesis might have been justly regarded as an abuse of the theory4 ,he was1 therefore1 in great perplexity4 ,but a little while previous to this1 ,klaproth had discovered that there is an earth which1 though in many respects it resembles baryta1 is different from it in other respects2 and this earth1 from the place where it was found 7in ,scotland71 had been named ,strontia4 ,the ,french chemists had ascertained that the two earths had1 in some cases1 been mixed or confounded2 and ,vauquelin1 on examining the ,sicilian crystals1 found that their base was strontia1 and not1 as in the ,derbyshire ones1 baryta4 ,the riddle was now read2 all the crystals with the larger angle belong to the one1 all those with the smaller1 to the other1 of these two sulphates2 and crystallometry was clearly recognized as an authorized test of the difference of substances which nearly resemble each other4 ,note #bbae3 ,trait1 ii4 #cbj4 ,enough has been said1 probably1 to enable the reader to judge how much each of the two persons1 now under review1 contributed to crystallography4 ,it would be unwise to compare such contributions to science with the great discoveries of astronomy and chemistry2 and we have seen how nearly the predecessors of ,rom and ,hay had reached the point of knowledge on which these two crystallographers took their stand4 ,but yet it is impossible not to allow1 that in these discoveries1 which thus gave form and substance to the science of crystallography1 we have a manifestation of no common sagacity and skill4 ,here1 as in other discoveries1 were required ideas and facts2--clearness of geometrical conception which could deal with most complex relations of form2 a minute and extensive acquaintance with actual crystals2 and the talent and habit of referring these facts to the general ideas4 ,hay1 in particular1 was happily endowed for his task4 ,without being a great mathematician1 he was sufficiently a geometer to solve all the problems which his undertaking demanded2 and though the mathematical reasoning might have been made more compendious #cbd by one who was more at home in mathematical generalization1 probably this could hardly have been done without making the subject less accessible and less attractive to persons moderately disciplined in mathematics4 ,in all his reasonings upon particular cases1 ,hay is acute and clear2 while his general views appear to be suggested rather by a lively fancy than by a sage inductive spirit3 and though he thus misses the character of a great philosopher1 the vivacity of style1 and felicity and happiness of illustration1 which grace his book1 and which agree well with the character of an ,abb of the old ,french monarchy1 had a great and useful influence on the progress of the subject4 ,unfortunately ,rom de ,lisle and ,hay were not only rivals1 but in some measure enemies4 ,the former might naturally feel some vexation at finding himself1 in his later years 7he died in #agij71 thrown into shade by his more brilliant successor4 ,in reference to ,hay's use of cleavage1 he speaks#bcae of innovators in crystallography1 who may properly be called crystalloclasts4 ,yet he adopted1 in great measure1 the same views of the formation of crystals by lamin1#bdae which ,hay illustrated by the destructive process at which he thus sneers4 ,his sensitiveness was kept alive by the conduct of the ,academy of ,sciences1 which took no notice of him and his labors2#beae probably because it was led by ,buffon1 who disliked ,linnus1 and might dislike ,rom as his follower2 and who1 as we have seen1 despised crystallography4 ,hay revenged himself by rarely mentioning ,rom in his works1 though it was manifest that his obligations to him were immense2 and by recording his errors while he corrected them4 ,more fortunate than his rival1 ,hay was1 from the first1 received with favor and applause4 ,his lectures at ,paris were eagerly listened to by persons from all quarters of the world4 ,his views were1 in this manner1 speedily diffused2 and the subject was soon pursued1 in various ways1 by mathematicians and mineralogists in every country of ,europe4 ,note #bcae3 ,pref4 p4 xxvii4 ,note #bdae3 ,t4 ii4 p4 #ba4 ,note #beae3 ,marx4 ,gesch4 d4 ,cryst4 #acj4 ,,chapter ,,iii4 ,,reception ,,and ,,corrections ,,of ,,the ,,hau,,an ,,crystallography4 ,i ,,have not hitherto noticed the imperfections of the crystallographic views and methods of ,hay1 because my business in the last section #cbe was to mark the permanent additions he made to the science4 ,his system did1 however1 require completion and rectification in various points2 and in speaking of the crystallographers of the subsequent time1 who may all be considered as the cultivators of the ,hauan doctrines1 we must also consider what they did in correcting them4 ,the three main points in which this improvement was needed were2--a better determination of the crystalline forms of the special substances2--a more general and less arbitrary method of considering crystalline forms according to their symmetry2 and a detection of more general conditions by which the crystalline angle is regulated4 ,the first of these processes may be considered as the natural sequel of the ,hauan epoch3 the other two must be treated as separate steps of discovery4 ,when it appeared that the angle of natural or of cleavage faces could be used to determine the differences of minerals1 it became important to measure this angle with accuracy4 ,hay's measurements were found very inaccurate by many succeeding crystallographers3 ,mohs says#bfae that they are so generally inaccurate1 that no confidence can be placed in them4 ,this was said1 of course1 according to the more rigorous notions of accuracy to which the establishment of ,hay's system led4 ,among the persons who principally labored in ascertaining1 with precision1 the crystalline angles of minerals1 were several ,englishmen1 especially ,wollaston1 ,phillips1 and ,brooke4 ,wollaston1 by the invention of his ,reflecting ,goniometer1 placed an entirely new degree of accuracy within the reach of the crystallographer2 the angle of two faces being1 in this instrument1 measured by means of the reflected images of bright objects seen in them1 so that the measure is the more accurate the more minute the faces are4 ,in the use of this instrument1 no one was more laborious and successful than ,william ,phillips1 whose power of apprehending the most complex forms with steadiness and clearness1 led ,wollaston to say that he had a geometrical sense4 ,phillips published a ,treatise on ,mineralogy1 containing a great collection of such determinations2 and ,mr4 ,brooke1 a crystallographer of the same exact and careful school1 has also published several works of the same kind4 ,the precise measurement of crystalline angles must be the familiar employment of all who study crystallography2 and1 therefore1 any further enumeration of those #cbf who have added in this way to the stock of knowledge1 would be superfluous4 ,note #bfae3 ,marx4 p4 #aec4 ,nor need ,i dwell long on those who added to the knowledge which ,hay left1 of derived forms4 ,the most remarkable work of this kind was that of ,count ,bournon1 who published a work on a single mineral 7calcspar7 in three quarto volumes4#bgae ,he has here given representations of seven hundred forms of crystals1 of which1 however1 only fifty-six are essentially different4 ,from this example the reader may judge what a length of time1 and what a number of observers and calculators1 were requisite to exhaust the subject4 ,note #bgae3 ,trait complet de la ,chaux ,carbonate et d',aragonite1 par ,m4 le ,comte de ,bournon4 ,london1 #ahjh4 ,if the calculations1 thus occasioned1 had been conducted upon the basis of ,hay's system1 without any further generalization1 they would have belonged to that process1 the natural sequel of inductive discoveries1 which we call deduction2 and would have needed only a very brief notice here4 ,but some additional steps were made in the upward road to scientific truth1 and of these we must now give an account4 ,,chapter ,,iv4 ,,establishment ,,of ,,the ,,distinction ,,of ,,systems ,,of ,,crystallization4--,,weiss ,,and ,,mohs4 ,,in ,hay's views1 as generally happens in new systems1 however true1 there was involved something that was arbitrary1 something that was false or doubtful1 something that was unnecessarily limited4 ,the principal points of this kind were2--his having made the laws of crystalline derivation depend so much upon cleavage2--his having assumed an atomic constitution of bodies as an essential part of his system2 and his having taken a set of primary forms1 which1 being selected by no general view1 were partly superfluous1 and partly defective4 ,how far evidence1 such as has been referred to by various philosophers1 has proved1 or can prove1 that bodies are constituted of indivisible atoms1 will be more fully examined in the work which treats of the ,philosophy of this subject4 ,there can be little doubt that the #cbg portion of ,hay's doctrine which most riveted popular attention and applause1 was his dissection of crystals1 in a manner which was supposed to lead actually to their ultimate material elements4 ,yet it is clear1 that since the solids given by cleavage are1 in many cases1 such as cannot make up a solid space1 the primary conception of a necessary geometrical identity between the results of division and the elements of composition1 which is the sole foundation of the supposition that crystallography points out the actual elements1 disappears on being scrutinized3 and when ,hay1 pressed by this difficulty1 as in the case of fluor-spar1 put his integrant octohedral molecules together1 touching by the edges only1 his method became an empty geometrical diagram1 with no physical meaning4 ,the real fact1 divested of the hypothesis which was contained in the fiction of decrements1 was1 that when the relation of the derivative to the primary faces is expressed by means of numerical indices1 these numbers are integers1 and generally very small ones2 and this was the form which the law gradually assumed1 as the method of derivation was made more general and simple by ,weiss and others4 ,when1 in #ahji1 ,i published my ,dissertation1 says ,weiss1#bhae ,i shared the common opinion as to the necessity of the assumption and the reality of the existence of a primitive form1 at least in a sense not very different from the usual sense of the expression4 ,while ,i sought1 he adds1 referring to certain doctrines of general philosophy which he and others entertained1 a dynamical ground for this1 instead of the untenable atomistic view1 ,i found that1 out of my primitive forms1 there was gradually unfolded to my hands1 that which really governs them1 and is not affected by their casual fluctuations1 the fundamental relations of those ,dimensions according to which a multiplicity of internal oppositions1 necessarily and mutually interdependent1 are developed in the mass1 each having its own polarity2 so that the crystalline character is co-extensive with these polarities4 ,note #bhae3 ,mem4 ,acad4 ,berl4 #ahaf1 p4 #cjg4 ,the ,dimensions of which ,weiss here speaks1 are the ,axes of ,symmetry of the crystal2 that is1 those lines in reference to which1 every face is accompanied by other faces1 having like positions and properties4 ,thus a rhomb1 or more properly a rhombohedron1#biae of #cbh calcspar may be placed with one of its obtuse corners uppermost1 so that all the three faces which meet there are equally inclined to the vertical line4 ,in this position1 every derivative face1 which is obtained by any modification of the faces or edges of the rhombohedron1 implies either three or six such derivative faces2 for no one of the three upper faces of the rhombohedron has any character or property different from the other two2 and1 therefore1 there is no reason for the existence of a derivative from one of these primitive faces1 which does not equally hold for the other primitive faces4 ,hence the derivative forms will1 in all cases1 contain none but faces connected by this kind of correspondence4 ,the axis thus made vertical will be an ,axis of ,symmetry1 and the crystal will consist of three divisions1 ranged round this axis1 and exactly resembling each other4 ,according to ,weiss's nomenclature1 such a crystal is three-and-three-membered4 ,note #biae3 ,i use this name for the solid figure1 since rhomb has always been used for a plane figure4 ,but this is only one of the kinds of symmetry which crystalline forms may exhibit4 ,they may have three axes of complete and equal symmetry at right angles to each other1 as the cube and the regular octohedron2--or1 two axes of equal symmetry1 perpendicular to each other and to a third axis1 which is not affected with the same symmetry with which they are2 such a figure is a square pyramid2--or they may have three rectangular axes1 all of unequal symmetry1 the modifications referring to each axis separately from the other two4 ,these are essential and necessary distinctions of crystalline form2 and the introduction of a classification of forms founded on such relations1 or1 as they were called1 ,systems of ,crystallization1 was a great improvement upon the divisions of the earlier crystallographers1 for those divisions were separated according to certain arbitrarily-assumed primary forms4 ,thus ,rom de ,lisle's fundamental forms were1 the tetrahedron1 the cube1 the octohedron1 the rhombic prism1 the rhombic octohedron1 the dodecahedron with triangular faces3 ,hay's primary forms are the cube1 the rhombohedron1 the oblique rhombic prism1 the right rhombic prism1 the rhombic dodecahedron1 the regular octohedron1 tetrahedron1 and six-sided prism1 and the bipyramidal dodecahedron4 ,this division1 as ,i have already said1 errs both by excess and defect1 for some of these primary forms might be made derivatives from others2 and no solid reason could be assigned why they were not4 ,thus the cube may be derived from the tetrahedron1 by truncating the edges2 and the rhombic dodecahedron again from the cube1 by truncating its edges2 while the square pyramid could not be legitimately identified with the derivative of any of these forms2 for if we were to #cbi derive it from the rhombic prism1 why should the acute angles always suffer decrements corresponding in a certain way to those of the obtuse angles1 as they must do in order to give rise to a square pyramid8 ,the introduction of the method of reference to ,systems of ,crystallization has been a subject of controversy1 some ascribing this valuable step to ,weiss1 and some to ,mohs4#cjae ,it appears1 ,i think1 on the whole1 that ,weiss first published works in which the method is employed2 but that ,mohs1 by applying it to all the known species of minerals1 has had the merit of making it the basis of real crystallography4 ,weiss1 in #ahji1 published a ,dissertation ,on the mode of investigating the principal geometrical character of crystalline forms1 in which he says1#caae ,no part1 line1 or quantity1 is so important as the axis2 no consideration is more essential or of a higher order than the relation of a crystalline plane to the axis2 and again1 ,an axis is any line governing the figure1 about which all parts are similarly disposed1 and with reference to which they correspond mutually4 ,this he soon followed out by examination of some difficult cases1 as ,felspar and ,epidote4 ,in the ,memoirs of the ,berlin ,academy1#cbae for #ahad-ae1 he published ,an ,exhibition of the natural ,divisions of ,systems of ,crystallization4 ,in this ,memoir1 his divisions are as follows3--,the regular system1 the four-membered1 the two-and-two-membered1 the three-and-three-membered1 and some others of inferior degrees of symmetry4 ,these divisions are by ,mohs 7,outlines of ,mineralogy1 #ahbb71 termed the tessular1 pyramidal1 prismatic1 and rhombohedral systems respectively4 ,hausmann1 in his ,investigations concerning the ,forms of ,inanimate ,nature1#ccae makes a nearly corresponding arrangement2--the isometric1 monodimetric1 trimetric1 and monotrimetic2 and one or other of these sets of terms have been adopted by most succeeding writers4 ,note #cjae3 ,edin4 ,phil4 ,trans4 #ahbc1 vols4 xv4 and xvi4 ,note #caae3 pp4 #af1 #db4 ,note #cbae3 ,ibid4 ,note #ccae3 ,gttingen1 #ahba4 ,in order to make the distinctions more apparent1 ,i have purposely omitted to speak of the systems which arise when the prismatic system loses some part of its symmetry2--when it has only half or a quarter its complete number of faces2--or1 according to ,mohs's phraseology1 when it is hemihedral or tetartohedral4 ,such systems are represented by the singly-oblique or doubly-oblique prism2 they are termed by ,weiss two-and-one-membered1 and one-and-one-membered2 by other writers1 ,monoklinometric1 and ,triklinometric ,systems4 ,there are also other #ccj peculiarities of ,symmetry1 such1 for instance1 as that of the plagihedral faces of quartz1 and other minerals4 ,the introduction of an arrangement of crystalline forms into systems1 according to their degree of symmetry1 was a step which was rather founded on a distinct and comprehensive perception of mathematical relations1 than on an acquaintance with experimental facts1 beyond what earlier mineralogists had possessed4 ,this arrangement was1 however1 remarkably confirmed by some of the properties of minerals which attracted notice about the time now spoken of1 as we shall see in the next chapter4 ,,chapter ,v4 ,,reception ,,and ,,confirmation ,,of ,,the ,,distinction ,,of ,,systems ,,of ,,crystallization4 ,,diffusion ,,of ,,the ,,distinction ,,of ,,systems4--,the distinction of systems of crystallization was so far founded on obviously true views1 that it was speedily adopted by most mineralogists4 ,i need not dwell on the steps by which this took place4 ,mr4 ,haidinger's translation of ,mohs was a principal occasion of its introduction in ,england4 ,as an indication of dates1 bearing on this subject1 perhaps ,i may be allowed to notice1 that there appeared in the ,philosophical ,transactions for #ahbe1 ,a ,general ,method of ,calculating the 9999,angles of ,crystals1 which ,i had written1 and in which ,i referred only to ,hay's views2 but that in #ahbf1cdae ,i published a ,memoir ,on the ,classification of ,crystalline ,combinations1 founded on the methods of ,weiss and ,mohs1 especially the latter2 with which ,i had in the mean time become acquainted1 and which appeared to me to contain their own evidence and recommendation4 ,general methods1 such as was attempted in the ,memoir just quoted1 are part of that process in the history of sciences1 by which1 when the principles are once established1 the mathematical operation of deducing their consequences is made more and more general and symmetrical3 which we have seen already exemplified in the history of celestial mechanics after the time of ,newton4 ,it does not enter into our plan1 to dwell upon the various steps in this way #cca made by ,levy1 ,naumann1 ,grassmann1 ,kupffer1 ,hessel1 and by ,professor ,miller among ourselves4 ,i may notice that one great improvement was1 the method introduced by ,monteiro and ,levy1 of determining the laws of derivation of forces by means of the parallelisms of edges2 which was afterwards extended so that faces were considered as belonging to zones4 ,nor need ,i attempt to enumerate 7what indeed it would be difficult to describe in words7 the various methods of notation by which it has been proposed to represent the faces of crystals1 and to facilitate the calculations which have reference to them4 ,note #cdae3 ,camb4 ,trans4 vol4 ii4 p4 #cia4 #bnd ,ed4 ,my ,memoir of #ahbe depended on the views of ,hay in so far as that ,i started from his primitive forms2 but being a general method of expressing all forms by co-ordinates1 it was very little governed by these views4 ,the mode of representing crystalline forms which ,i proposed seemed to contain its own evidence of being more true to nature than ,hay's theory of decrements1 inasmuch as my method expressed the faces at much lower numbers4 ,i determine a face by means of the dimensions of the primary form divided by certain numbers2 ,hay had expressed the face virtually by the same dimensions multiplied by numbers4 ,in cases where my notation gives such numbers as 7#c1 #d1 #a71 7#a1 #c1 #g71 7#e1 #a1 #ai71 his method involves the higher numbers 7#d1 #c1 #ab71 7#ba1 #g1 #c71 7#ai1 #ie1 #e74 ,my method however has1 ,i believe1 little value as a method of calculating the angles of crystals4 ,m4 ,neumann1 of ,knigsberg1 introduced a very convenient and elegant mode of representing the position of faces of crystals by corresponding points on the surface of a circumscribing sphere4 ,he gave 7in #ahbc7 the laws of the derivation of crystalline faces1 expressed geometrically by the intersection of zones1 7,beitrge zur ,krystallonomie47 ,the same method of indicating the position of faces of crystals was afterwards1 together with the notation1 re-invented by ,m4 ,grassmann1 7,zur ,krystallonomie und ,geometrischen ,combinationslehre1 #ahbi47 ,aiding himself by the suggestions of these writers1 and partly adopting my method1 ,prof4 ,miller has produced a work on ,crystallography remarkable for mathematical elegance and symmetry2 and has given expressions really useful for calculating the angles of crystalline faces1 7,a ,treatise on ,crystallography4 ,cambridge1 #ahci47 ,confirmation of the ,distinction of ,systems by the ,optical ,properties of ,minerals4--,brewster4--,i must not omit to notice the striking confirmation which the distinction of systems of crystallization received from optical discoveries1 especially those of ,sir ,d4 ,brewster4 ,of the #ccb history of this very rich and beautiful department of science1 we have already given some account1 in speaking of ,optics4 ,the first facts which were noticed1 those relating to double refraction1 belonged exclusively to crystals of the rhombohedral system4 ,the splendid phenomena of the rings and lemniscates produced by dipolarizing crystals1 were afterwards discovered2 and these were1 in #ahag1 classified by ,sir ,david ,brewster1 according to the crystalline forms to which they belong4 ,this classification1 on comparison with the distinction of ,systems of ,crystallization1 resolved itself into a necessary relation of mathematical symmetry3 all crystals of the pyramidal and rhombohedral systems1 which from their geometrical character have a single axis of symmetry1 are also optically uniaxal1 and produce by dipolarization circular rings2 while the prismatic system1 which has no such single axis1 but three unequal axes of symmetry1 is optically biaxal1 gives lemniscates by dipolarized light1 and according to ,fresnel's theory1 has three rectangular axes of unequal elasticity4 #bnd ,ed4 ,i have placed ,sir ,david ,brewster's arrangement of crystalline forms in this chapter1 as an event belonging to the confirmation of the distinctions of forms introduced by ,weiss and ,mohs2 because that arrangement was established1 not on crystallographical1 but on optical grounds4 ,but ,sir ,david ,brewster's optical discovery was a much greater step in science than the systems of the two ,german crystallographers2 and even in respect to the crystallographical principle1 ,sir ,d4 ,brewster had an independent share in the discovery4 ,he divided crystalline forms into three classes1 enumerating the ,hauan primitive forms which belonged to each2 and as he found some exceptions to this classification1 7such as idocrase1 c417 he ventured to pronounce that in those substances the received primitive forms were probably erroneous2 a judgment which was soon confirmed by a closer crystallographical scrutiny4 ,he also showed his perception of the mineralogical importance of his discovery by publishing it1 not only in the ,phil4 ,trans4 7#ahah71 but also in the ,transactions of the ,wernerian ,society of ,natural ,history4 ,in a second paper inserted in this later series1 read in #ahbj1 he further notices ,mohs's ,system of ,crystallography1 which had then recently appeared1 and points out its agreement with his own4 ,another reason why ,i do not make his great optical discovery a cardinal point in the history of crystallography is1 that as a crystallographical system it is incomplete4 ,although we are thus led to distinguish the tessular and the prismatic systems 7using ,mohs's terms7 #ccc from the rhombohedral and the square prismatic1 we are not led to distinguish the latter two from each other2 inasmuch as they have no optical difference of character4 ,but this distinction is quite essential in crystallography2 for these two systems have faces formed by laws as different as those of the other two systems4 ,moreover1 ,weiss and ,mohs not only divided crystalline forms into certain classes1 but showed that by doing this1 the derivation of all the existing forms from the fundamental ones assumed a new aspect of simplicity and generality2 and this was the essential part of what they did4 ,on the other hand1 ,i do not think it is too much to say as ,i have elsewhere said#ceae that ,sir ,d4 ,brewster's optical experiments must have led to a classification of crystals into the above systems1 or something nearly equivalent1 even if crystals had not been so arranged by attention to their forms4 ,note #ceae3 ,philosophy of the ,inductive ,sciences1 ,b4 viii4 ,c4 iii4 ,art4 #c4 ,many other most curious trains of research have confirmed the general truth1 that the degree and kind of geometrical symmetry corresponds exactly with the symmetry of the optical properties4 ,as an instance of this1 eminently striking for its singularity1 we may notice the discovery of ,sir ,john ,herschel1 that the plagihedral crystallization of quartz1 by which it exhibits faces twisted to the right or the left1 is accompanied by right-handed or left-handed circular polarization respectively4 ,no one acquainted with the subject can now doubt1 that the correspondence of geometrical and optical symmetry is of the most complete and fundamental kind4 #bnd ,ed4 ,our knowledge with respect to the positions of the optical axes of the oblique prismatic crystals is still imperfect4 ,it appears to be ascertained that1 in singly oblique crystals1 one of the axes of optical elasticity coincides with the rectangular crystallographic axis4 ,in doubly oblique crystals1 one of the axes of optical elasticity is1 in many cases1 coincident with the axis of a principal zone4 ,i believe no more determinate laws have been discovered4 ,thus the highest generalization at which mathematical crystallographers have yet arrived1 may be considered as fully established2 and the science of ,crystallography1 in the condition in which these place it1 is fit to be employed as one of the members of ,mineralogy1 and thus to fill its appropriate place and office4 #ccd ,,chapter ,,vi4 ,,correction ,,of ,,the ,,law ,,of ,,the ,,same ,,angle ,,for ,,the ,,same ,,substance4 ,,discovery ,,of ,,isomorphism4 ,,mitscherlich4--,the discovery of which we now have to speak may appear at first sight too large to be included in the history of crystallography1 and may seem to belong rather to chemistry4 ,but it is to be recollected that crystallography1 from the time of its first assuming importance in the hands of ,hay1 founded its claim to notice entirely upon its connexion with chemistry2 crystalline forms were properties of something2 but what that something was1 and how it might be modified without becoming something else1 no crystallographer could venture to decide1 without the aid of chemical analysis4 ,hay had assumed1 as the general result of his researches1 that the same chemical elements1 combined in the same proportions1 would always exhibit the same crystalline form2 and reciprocally1 that the same form and angles 7except in the obvious case of the tessular system1 in which the angles are determined by its being the tessular system17 implied the same chemical constitution4 ,but this dogma could only be considered as an approximate conjecture2 for there were many glaring and unexplained exceptions to it4 ,the explanation of several of these was beautifully described by the discovery that there are various elements which are isomorphous to each other2 that is1 such that one may take the place of another without altering the crystalline form2 and thus the chemical composition may be much changed1 while the crystallographic character is undisturbed4 ,this truth had been caught sight of1 probably as a guess only1 by ,fuchs as early as #ahae4 ,in speaking of a mineral which had been called ,gehlenite1 he says1 ,i hold the oxide of iron1 not for an essential component part of this genus1 but only as a vicarious element1 replacing so much lime4 ,we shall find it necessary to consider the results of several analyses of mineral bodies in this point of view1 if we wish1 on the one hand1 to bring them into agreement with the doctrine of chemical proportions1 and on the other1 to avoid unnecessarily splitting up genera4 ,in a lecture ,on the ,mutual ,influence of #cce ,chemistry and ,mineralogy1#cfae he again draws attention to his term vicarious 7vicarirende71 which undoubtedly expresses the nature of the general law afterwards established by ,mitscherlich in #ahbb4 ,note #cfae3 ,munich1 #ahbj4 ,but ,fuchs's conjectural expression was only a prelude to ,mitscherlich's experimental discovery of isomorphism4 ,till many careful analyses had given substance and signification to this conception of vicarious elements1 it was of small value4 ,perhaps no one was more capable than ,berzelius of turning to the best advantage any ideas which were current in the chemical world2 yet we find him1#cgae in #ahbj1 dwelling upon a certain vague view of these cases1--that oxides which contain equal doses of oxygen must have their general properties common2 without tracing it to any definite conclusions4 ,but his scholar1 ,mitscherlich1 gave this proposition a real crystallographical import4 ,thus he found that the carbonates of lime 7calcspar17 of magnesia1 of protoxide of iron1 and of protoxide of manganese1 agree in many respects of form1 while the homologous angles vary through one or two degrees only2 so again the carbonates of baryta1 strontia1 lead1 and lime 7arragonite71 agree nearly2 the different kinds of felspar vary only by the substitution of one alkali for another2 the phosphates are almost identical with the arseniates of several bases4 ,these1 and similar results1 were expressed by saying that1 in such cases1 the bases1 lime1 protoxide of iron1 and the rest1 are isomorphous2 or in the latter instance1 that the arsenic and phosphoric acids are isomorphous4 ,note #cgae3 ,essay on the ,theory of ,chemical ,proportions1 p4 #abb4 ,since1 in some of these cases1 the substitution of one element of the isomorphous group for another does alter the angle1 though slightly1 it has since been proposed to call such groups plesiomorphous4 ,this discovery of isomorphism was of great importance1 and excited much attention among the chemists of ,europe4 ,the history of its reception1 however1 belongs1 in part1 to the classification of minerals2 for its effect was immediately to metamorphose the existing chemical systems of arrangement4 ,but even those crystallographers and chemists who cared little for general systems of classification1 received a powerful impulse by the expectation1 which was now excited1 of discovering definite laws connecting chemical constitution with crystalline form4 ,such investigations were soon carried on with great activity4 ,thus1 at a recent period1 ,abich analysed a number of tessular minerals1 spinelle1 pleonaste1 gahnite1 franklinite1 and chromic iron oxide2 and #ccf seems to have had some success in 9999giving a common type to their chemical formul1 as there is a common type in their crystallization4 #bnd ,ed4 ,it will be seen by the above account that ,prof4 ,mitscherlich's merit in the great discovery of ,isomorphism is not at all narrowed by the previous conjectures of ,m4 ,fuchs4 ,i am informed1 moreover1 that ,m4 ,fuchs afterwards 7in ,schweigger's ,journal7 retracted the opinions he had put forward on this subject4 ,dimorphism4--,my business is1 to point out the connected truths which have been obtained by philosophers1 rather than insulated difficulties which still stand out to perplex them4 ,i need not1 therefore1 dwell on the curious cases of dimorphism2 cases in which the same definite chemical compound of the same elements appears to have two different forms2 thus the carbonate of lime has two forms1 calcspar and arragonite1 which belong to different systems of crystallization4 ,such facts may puzzle us2 but they hardly interfere with any received general truths1 because we have as yet no truths of very high order respecting the connexion of chemical constitution and crystalline form4 ,dimorphism does not interfere with isomorphism2 the two classes of facts stand at the same stage of inductive generalization1 and we wait for some higher truth which shall include both1 and rise above them4 #bnd ,ed4 ,for additions to our knowledge of the ,dimorphism of ,bodies1 see ,professor ,johnstone's valuable ,report on that subject in the ,reports of the ,british ,association for #ahcg4 ,substances have also been found which are trimorphous4 ,we owe to ,professor ,mitscherlich the discovery of dimorphism1 as well as of isomorphism3 and to him also we owe the greater part of the knowledge to which these discoveries have led4 ,,chapter ,,vii4 ,,attempts ,,to ,,establish ,,the ,,fixity ,,of ,,other ,,physical ,,properties4--,,werner4 ,,the reflections from which it appeared1 7at the end of the last ,book17 that in order to obtain general knowledge respecting bodies1 we must give scientific fixity to our appreciation of their properties1 applies to their other properties as well as to their crystalline #ccg form4 ,and though none of the other properties have yet been referred to standards so definite as that which geometry supplies for crystals1 a system has been introduced which makes their measures far more constant and precise than they are to a common undisciplined sense4 ,the author of this system was ,abraham ,gottlob ,werner1 who had been educated in the institutions which the ,elector of ,saxony had established at the mines of ,freiberg4 ,of an exact and methodical intellect1 and of great acuteness of the senses1 ,werner was well fitted for the task of giving fixity to the appreciation of outward impressions2 and this he attempted in his ,dissertation on the external ,characters of ,fossils1 which was published at ,leipzig in #aggd4 ,of the precision of his estimation of such characters1 we may judge from the following story1 told by his biographer ,frisch4#chae ,one of his companions had received a quantity of pieces of amber1 and was relating to ,werner1 then very young1 that he had found in the lot one piece from which he could extract no signs of electricity4 ,werner requested to be allowed to put his hand in the bag which contained these pieces1 and immediately drew out the unelectrical piece4 ,it was yellow chalcedony1 which is distinguishable from amber by its weight and coldness4 ,note #chae3 ,werner's ,leben1 p4 #bf4 ,the principal external characters which were subjected by ,werner to a systematic examination were color1 lustre1 hardness1 and specific gravity4 ,his subdivisions of the first character 7,color71 were very numerous2 yet it cannot be doubted that if we recollect them by the eye1 and not by their names1 they are definite and valuable characters1 and especially the metallic colors4 ,breithaupt1 merely by the aid of this character1 distinguished two new compounds among the small grains found along with the grains of platinum1 and usually confounded with them4 ,the kinds of ,lustre1 namely1 glassy1 fatty1 adamantine1 metallic1 are1 when used in the same manner1 equally valuable4 ,specific ,gravity obviously admits of a numerical measure2 and the ,hardness of a mineral was pretty exactly defined by the substances which it would scratch1 and by which it was capable of being scratched4 ,werner soon acquired a reputation as a mineralogist1 which drew persons from every part of ,europe to ,freiberg in order to hear his lectures2 and thus diffused very widely his mode of employing external characters4 ,it was1 indeed1 impossible to attend so closely to #cch these characters as the ,wernerian method required1 without finding that they were more distinctive than might at first sight be imagined2 and the analogy which this mode of studying ,mineralogy established between that and other branches of ,natural ,history1 recommended the method to those in whom a general inclination to such studies was excited4 ,thus ,professor ,jameson of ,edinburgh1 who had been one of the pupils of ,werner at ,freiberg1 not only published works in which he promulgated the mineralogical doctrines of his master1 but established in ,edinburgh a ,wernerian ,society1 having for its object the general cultivation of ,natural ,history4 ,werner's standards and nomenclature of external characters were somewhat modified by ,mohs1 who1 with the same kinds of talents and views1 succeeded him at ,freiberg4 ,mohs reduced hardness to numerical measure by selecting ten known minerals1 each harder than the other in order1 from talc to corundum and diamond1 and by making the place which these minerals occupy in the list1 the numerical measure of the hardness of those which are compared with them4 ,the result of the application of this fixed measurement and nomenclature of external characters will appear in the ,history of ,classification1 to which we now proceed4 #cci ,,systematic ,,mineralogy4 ,,chapter ,,viii4 ,,attempts ,,at ,,the ,,classification ,,of ,,minerals4 ,sect4 #a4--,proper object of ,classification4 ,,the fixity of the crystalline and other physical properties of minerals is turned to account by being made the means of classifying such objects4 ,to use the language of ,aristotle1#ciae ,classification is the architectonic science1 to which ,crystallography and the ,doctrine of ,external ,characters are subordinate and ministerial1 as the art of the bricklayer and carpenter are to that of the architect4 ,but classification itself is useful only as subservient to an ulterior science1 which shall furnish us with knowledge concerning things so classified4 ,to classify is to divide and to name2 and the value of the ,divisions which we thus make1 and of the names which we give them1 is this2--that they render exact knowledge and general propositions possible4 ,now the knowledge which we principally seek concerning minerals is a knowledge of their chemical composition2 the general propositions to which we hope to be led are such as assert relations between their intimate constitution and their external attributes4 ,thus our ,mineralogical ,classification must always have an eye turned towards ,chemistry4 ,we cannot get rid of the fundamental conviction1 that the elementary composition of bodies1 since it fixes their essence1 must determine their properties4 ,hence all mineralogical arrangements1 whether they profess it or not1 must be1 in effect1 chemical2 they must have it for their object to bring into view a set of relations1 which1 whatever else they may be1 are at least chemical relations4 ,we may begin with the outside1 but it is only in order to reach the inner #cdj structure4 ,we may classify without reference to chemistry2 but if we do so1 it is only that we may assert chemical propositions with reference to our classification4 ,note #ciae3 ,eth4 ,nicom4 i4 #b4 ,but1 as we have already attempted to show1 we not only may1 but we must classify1 by other than chemical characters1 in order to be able to make our classification the basis of chemical knowledge4 ,in order to assert chemical truths concerning bodies1 we must have the bodies known by some tests not chemical4 ,the chemist cannot assert that ,arragonite does or does not contain ,strontia1 except the mineralogist can tell him whether any given specimen is or is not ,arragonite4 ,if chemistry be called upon to supply the definitions as well as the doctrines of mineralogy1 the science can only consist of identical propositions4 ,yet chemistry has been much employed in mineralogical classifications1 and1 it is generally believed1 with advantage to the science3 ,how is this consistent with what has been said8 ,to this the answer is1 that when this has been done with advantage1 the authority of external characters1 as well as of chemical constitution1 has really been brought into play4 ,we have two sets of properties to compare1 chemical and physical2 to exhibit the connexion of these is the object of scientific mineralogy4 ,and though this connexion would be most distinctly asserted1 if we could keep the two sets of properties distinct1 yet it may be brought into view in a great degree1 by classifications in which both are referred to as guides4 ,since the governing principle of the attempts at classification is the conviction that the chemical constitution and the physical properties have a definite relation to each other1 we appear entitled to use both kinds of evidence1 in proportion as we can best obtain each2 and then the general consistency and convenience of our system will be the security for its containing substantial knowledge1 though this be not presented in a rigorously logical or systematic form4 ,such mixed systems of classification1 resting partly on chemical and partly on physical characters1 naturally appeared as the earliest attempts in this way1 before the two members of the subject had been clearly separated in men's minds2 and these systems1 therefore1 we must first give an account of4 ,sect4 #b4--,mixed ,systems of ,classification4 ,early ,systems4--,the first attempts at classifying minerals went upon the ground of those differences of general aspect which had been #cda recognized in the formation of common language2 as earths1 stones1 metals4 ,but such arrangements were manifestly vague and confused2 and when chemistry had advanced to power and honor1 her aid was naturally called in to introduce a better order4 ,hiarne and ,bromell were1 as far as ,i know1 says#djae ,cronstedt1 the first who founded any mineral system upon chemical principles2 to them we owe the three known divisions of the most simple mineral bodies2 viz41 the calcarei1 vitrescentes1 and apyri4 ,but ,cronstedt's own ,essay towards a ,system of ,mineralogy1 published in ,swedish in #ageh1 had perhaps more influence than any other1 upon succeeding systems4 ,in this1 the distinction of earths and stones1 and also of vitrescent and non-vitrescent earths 7apyri71 is rejected4 ,the earths are classed as calcareous1 siliceous1 argillaceous1 and the like4 ,again1 calcareous earth is pure 7calc spar71 or united with acid of vitriol 7gypsum71 or united with the muriatic add 7sal ammoniac71 and the like4 ,it is easy to see that this is the method1 which1 in its general principle1 has been continued to our own time4 ,in such methods1 it is supposed that we can recognize the substance by its general appearance1 and on this assumption1 its place in the system conveys to us chemical knowledge concerning it4 ,note #djae3 ,mineralogy1 ,pref4 p4 viii4 ,but as the other branches of ,natural ,history1 and especially ,botany1 assumed a systematic form1 many mineralogists became dissatisfied with this casual and superficial mode of taking account of external characters2 they became convinced1 that in ,mineralogy as in other sciences1 classification must have its system and its rules4 ,the views which ,werner ascribes to his teacher1 ,pabst van ,ohain1#daae show the rise of those opinions which led through ,werner to ,mohs3 ,he was of opinion that a natural mineral system must be constructed by chemical determinations1 and external characters at the same time 7methodus mixta72 but that along with this1 mineralogists ought also to construct and employ what he called an artificial system1 which might serve us as a guide 7loco indicis7 how to introduce newly-discovered fossils into the system1 and how to find easily and quickly those already known and introduced4 ,such an artificial system1 containing not the grounds of classification1 but marks for recognition1 was afterwards attempted by ,mohs1 and termed by him the ,characteristic of his system4 ,note #daae3 ,frisch4 ,werner's ,leben1 p4 #ae4 ,werner's ,system4--,but1 in the mean time1 ,werner's classification had an extensive reign1 and this was still a mixed system4 ,werner himself1 indeed1 never published a system of mineralogy4 ,we might #cdb almost imagine1 ,cuvier says1#dbae that when he had produced his nomenclature of external characters1 he was affrighted with his own creation2 and that the reason of his writing so little after his first essay1 was to avoid the shackles which he had imposed upon others4 ,his system was1 indeed1 made known both in and out of ,germany1 by his pupils2 but in consequence of ,werner's unwillingness to give it on his own authority1 it assumed1 in its published forms1 the appearance of an extorted secret imperfectly told4 ,a ,notice of the ,mineralogical ,cabinet of ,mine-,director ,pabst von ,ohain1 was1 in #agib1 published by ,karsten and ,hoffman1 under ,werner's direction2 and conveyed by example1 his views of mineralogical arrangement2 and#dcae in #ahaf his ,doctrine of ,classification was surreptitiously copied from his manuscript1 and published in a ,german ,journal1 termed ,the ,hesperus4 ,but it was only in #ahag1 after his death1 that there appeared ,werner's ,last ,mineral ,system1 edited from his papers by ,breithaupt and ,khler3 and by this time1 as we shall soon see1 other systems were coming forwards on the stage4 ,note #dbae3 ,cuv4 ,el4 ii4 #cad4 ,note #dcae3 ,frisch4 p4 #eb4 ,a very slight notice of ,werner's arrangement will suffice to show that it was1 as we have termed it1 a ,mixed ,system4 ,he makes four great ,classes of fossils1 ,earthy1 ,saline1 ,combustible1 ,metallic3 the earthy fossils are in eight ,genera--,diamond1 ,zircon1 ,silica1 ,alumina1 ,talc1 ,lime1 ,baryta1 ,hallites4 ,it is clear that these genera are in the main chemical1 for chemistry alone can definitely distinguish the different ,earths which characterize them4 ,yet the ,wernerian arrangement supposed the distinctions to be practically made by reference to those external characters which the teacher himself could employ with such surpassing skill4 ,and though it cannot be doubted1 that the chemical views which prevailed around him had a latent influence on his classification in some cases1 he resolutely refused to bend his system to the authority of chemistry4 ,thus1#ddae when he was blamed for having1 in opposition to the chemists1 placed diamond among the earthy fossils1 he persisted in declaring that1 mineralogically considered1 it was a stone1 and could not be treated as anything else4 ,note #ddae3 ,frisch4 p4 #fb4 ,this was an indication to that tendency1 which1 under his successor1 led to a complete separation of the two grounds of classification4 ,but before we proceed to this1 we must notice what was doing at this period in other parts of ,europe4 ,hay's ,system4--,though ,werner1 on his own principles1 ought to #cdc have been the first person to see the immense value of the most marked of external characters1 crystalline form1 he did not1 in fact1 attach much importance to it4 ,perhaps he was in some measure fascinated by a fondness for those characters which he had himself systematized1 and the study of which did not direct him to look for geometrical relations4 ,however this may be1 the glory of giving to ,crystallography its just importance in ,mineralogy is due to ,france3 and the ,treatise of ,hay1 published in #ahja1 is the basis of the best succeeding works of mineralogy4 ,in this work1 the arrangement is professedly chemical2 and the classification thus established is employed as the means of enunciating crystallographic and other properties4 ,the principal object of this ,treatise1 says the author1#deae is the exposition and development of a method founded on certain principles1 which may serve as a frame-work for all the knowledge which ,mineralogy can supply1 aided by the different sciences which can join hands with her and march on the same line49999 ,it is worthy of notice1 as characteristic of this period of ,mixed ,systems1 that the classification of ,hay1 though founded on principles so different from the ,wernerian ones1 deviates little from it in the general character of the divisions4 ,thus1 the first ,order of the first ,class of ,hay is ,acidiferous ,earthy ,substances2 the first genus is ,lime2 the species are1 ,carbonate of ,lime1 ,phosphate of ,lime1 ,fluate of ,lime1 ,sulphate of ,lime1 and so on4 ,note #deae3 ,disc4 ,prl4 p4 xvii4 ,other ,systems4--,such mixed methods were introduced also into this country1 and have prevailed1 we may say1 up to the present time4 ,the ,mineralogy of ,william ,phillips1 which was published in #ahbd1 and which was an extraordinary treasure of crystallographic facts1 was arranged by such a mixed system2 that is1 by a system professedly chemical2 but1 inasmuch as a rigid chemical system is impossible1 and the assumption of such a one leads into glaring absurdities1 the system was1 in this and other attempts of the same kind1 corrected by the most arbitrary and lax application of other considerations4 ,it is a curious example of the difference of national intellectual character1 that the manifest inconsistencies of the prevalent systems1 which led in ,germany1 as we shall see1 to bold and sweeping attempts at reform1 produced in ,england a sort of contemptuous despair with regard to systems in general2--a belief that no system could be consistent or useful2--and a persuasion that the only valuable knowledge is the accumulation of particular facts4 ,this is not the place to #cdd explain how erroneous and unphilosophical such an opinion is4 ,but we may notice that while such a temper prevails among us1 our place in this science can never be found in advance of that position which we are now considering as exemplified in the period of ,werner and ,hay4 ,so long as we entertain such views respecting the objects of ,mineralogy1 we can have no share in the fortunes of the succeeding period of its history1 to which ,i now proceed4 ,,chapter ,,ix4 ,,attempts ,,at ,,the ,,reform ,,of ,,mineralogical ,,systems4--,,separation ,,of ,,the ,,chemical ,,and ,,natural ,,history ,,methods4 ,sect4 #a4--,natural ,history ,system of ,mohs4 ,,the chemical principle of classification1 if pursued at random1 as in the cases just spoken of leads to results at which a philosophical spirit revolts2 it separates widely substances which are not distinguishable2 joins together bodies the most dissimilar2 and in hardly any instance does it bring any truth into view4 ,the vices of classifications like that of ,hay could not long be concealed2 but even before time had exposed the weakness of his system1 ,hay himself had pointed out1 clearly and without reserve1#dfae that a chemical system is only one side of the subject1 and supposes1 as its counterpart1 a science of external characters4 ,in the mean time1 the ,wernerians were becoming more and more in love with the form which they had given to such a science4 ,indeed1 the expertness which ,werner and his scholars acquired in the use of external characters1 justified some partiality for them4 ,it is related of him1#dgae that1 by looking at a piece of iron-ore1 and poising it in his hand1 he was able to tell1 almost precisely1 the proportion of pure metal which it contained4 ,and in the last year of his life1#dhae he had marked out1 as the employment of the ensuing winter1 the study of the system of ,berzelius1 with a view to find out the laws of combination as disclosed by external characters4 ,in the same spirit1 his pupil #cde ,breithaupt#diae attempted to discover the ingredients of minerals by their peculiarities of crystallization4 ,the persuasion that there must be some connexion between composition and properties1 transformed itself1 in their minds1 into a belief that they could seize the nature of the connexion by a sort of instinct4 ,note #dfae3 ,see his ,disc4 ,prl4 ,note #dgae3 ,frisch4 ,werner's ,leben1 p4 #gh4 ,note #dhae3 ,frisch4 #c4 ,note #diae3 ,dresdn4 ,auswahl1 vol4 ii4 p4 #ig4 ,this opinion of the independency of the science of external characters1 and of its sufficiency for its own object1 at last assumed its complete form in the bold attempt to construct a system which should borrow nothing from chemistry4 ,this attempt was made by ,frederick ,mohs1 who had been the pupil of ,werner1 and was afterwards his successor in the school of ,freiberg2 and who1 by the acute and methodical character of his intellect1 and by his intimate knowledge of minerals1 was worthy of his predecessor4 ,rejecting altogether all divisions of which the import was chemical1 ,mohs turned for guidance1 or at least for the light of analogy1 to botany4 ,his object was to construct a ,natural ,system of mineralogy4 ,what the conditions and advantages of a natural system of any province of nature are1 we must delay to explain till we have before us1 in botany1 a more luminous example of such a scheme4 ,but further2 in mineralogy1 as in botany1 besides the ,natural ,system1 by which we form our classes1 it is necessary to have an ,artificial ,system by which we recognize them2--a principle which1 we have seen1 had already taken root in the school of ,freiberg4 ,such an artificial system ,mohs produced in his ,characteristic of the ,mineral ,kingdom1 which was published at ,dresden in #ahbj2 and which1 though extending only to a few pages1 excited a strong interest in ,germany1 where men's minds were prepared to interpret the full import of such a work4 ,some of the traits of such a ,characteristic had1 indeed1 been previously drawn by others2 as for example1 by ,hay1 who notices that each of his ,classes has peculiar characters4 ,for instance1 his ,first ,class 7acidiferous substances17 alone possesses these combinations of properties2 division into a regular octohedron1 without being able to scratch glass2 specific gravity above #ce1 without being able to scratch glass4 ,the extension of such characters into a scheme which should exhaust the whole mineral kingdom1 was the undertaking of ,mohs4 ,such a collection of marks of classes1 implied a classification previously established1 and accordingly1 ,mohs had created his own mineral system4 ,his aim was to construct it1 as we shall hereafter see that other natural systems are constructed1 by taking into account all the #cdf resemblances and differences of the objects classified4 ,it is obvious that to execute such a work1 implied a most intimate and universal acquaintance with minerals2--a power of combining in one vivid survey the whole mineral kingdom4 ,to illustrate the spirit in which ,professor ,mohs performed his task1 ,i hope ,i may be allowed to refer to my own intercourse with him4 ,at an early period of my mineralogical studies1 when the very conception of a ,natural ,system was new to me1 he1 with great kindliness of temper1 allowed me habitually to propose to him the scruples which arose in my mind1 before ,i could admit principles which appeared to me then so vague and indefinite2 and answered my objections with great patience and most instructive clearness4 ,among other difficulties1 ,i one day propounded to him this2--,you have published a ,treatise on ,mineralogy1 in which you have described all the important properties of all known minerals4 ,on your principles1 then1 it ought to be possible1 merely by knowing the descriptions in your book1 and without seeing any minerals1 to construct a natural system2 and this natural system ought to turn out identical with that which you have produced1 by so careful an examination of the minerals themselves4 ,he pondered a moment1 and then he answered1 ,it is true2 but what an enormous imagination 7einbildungskraft1 power of inward imagining71 a man must have for such a work6 ,vividness of conception of sensible properties1 and the steady intuition 7anschauung7 of objects1 were deemed by him1 and by the ,wernerian school in general1 to be the most essential conditions of complete knowledge4 ,it is not necessary to describe ,mohs's system in detail2 it may sufficiently indicate its form to state that the following substances1 such as ,i before gave as examples of other arrangements1 calcspar1 gypsum1 fluor spar1 apatite1 heavy spar1 are by ,mohs termed respectively1 ,rhombohedral ,lime ,haloide1 ,gyps ,haloide1 ,octohedral ,fluor ,haloide1 ,rhombohedral ,fluor ,haloide1 ,prismatic ,hal ,baryte4 ,these substances are thus referred to the ,orders ,haloide1 and ,baryte2 to ,genera ,lime ,haloide1 ,fluor ,haloide1 ,hal ,baryte2 and the ,species is an additional particularization4 ,mohs not only aimed at framing such a system1 but was also ambitious of giving to all minerals ,names which should accord with the system4 ,this design was too bold to succeed4 ,it is true1 that a new nomenclature was much needed in mineralogy3 it is true1 too1 that it was reasonable to expect1 from an improved classification1 an improved nomenclature1 such as had been so happily obtained in botany by the #cdg reform of ,linnus4 ,but besides the defects of ,mohs's system1 he had not prepared his verbal novelties with the temperance and skill of the great botanical reformer4 ,he called upon mineralogists to change the name of almost every mineral with which they were acquainted2 and the proposed appellations were mostly of a cumbrous form1 as the above example may serve to show4 ,such names could have obtained general currency1 only after a general and complete acceptance of the system2 and the system did not possess1 in a sufficient degree1 that evidence which alone could gain it a home in the belief of philosophers1--the coincidence of its results with those of ,chemistry4 ,but before ,i speak finally of the fortunes of the ,natural-history ,system1 ,i will say something of the other attempt which was made about the same time to introduce a ,reform into ,mineralogy from the opposite extremity of the science4 ,sect4 #b4--;,chemical ,system of ,berzelius and others4 ,,if the students of external characters were satisfied of the independence of their method1 the chemical analysts were naturally no less confident of the legitimate supremacy of their principles3 and when the beginning of the present century had been distinguished by the establishment of the theory of definite proportions1 and by discoveries which pointed to the electro-chemical theory1 it could not appear presumption to suppose1 that the classification of bodies1 so far as it depended on chemistry1 might be presented in a form more complete and scientific than at any previous time4 ,the attempt to do this was made by the great ,swedish chemist ,jacob ,berzelius4 ,in #ahaf1 he published his ,essay to establish a purely ,scientific ,system of ,mineralogy1 by means of the ,application of the ,electro-chemical ,theory and the ,chemical ,doctrine of ,definite ,proportions4 ,it is manifest that1 for minerals which are constituted by the law of ,definite ,proportions1 this constitution must be a most essential part of their character4 ,the electro-chemical theory was called in aid1 in addition to the composition1 because1 distinguishing the elements of all compounds as electro-positive and electro-negative1 and giving to every element a place in a series1 and a place defined by the degree of these relations1 it seemed to afford a rigorous and complete principle of arrangement4 ,accordingly1 ,berzelius1 in his ,first ,system1 arranged minerals according to their electro-positive element1 and the elements according to their electro-positive rank2 #cdh and supposed that he had thus removed all that was arbitrary and vague in the previous chemical systems of mineralogy4 ,though the attempt appeared so well justified by the state of chemical science1 and was so plausible in its principle1 it was not long before events showed that there was some fallacy in these specious appearances4 ,in #ahbj1 ,mitscherlich discovered ,isomorphism3 by that discovery it appeared that bodies containing very different electro-positive elements could not be distinguished from each other2 it was impossible1 therefore1 to put them in distant portions of the classification2--and thus the first system of ,berzelius crumbled to pieces4 ,but ,berzelius did not so easily resign his project4 ,with the most unhesitating confession of his first failure1 but with undaunted courage1 he again girded himself to the task of rebuilding his edifice4 ,defeated at the electro-positive position1 he now resolved to make a stand at the electro-negative element4 ,in #ahbd1 he published in the ,transactions of the ,swedish ,academy1 a ,memoir ,on the ,alterations in the ,chemical ,mineral ,system1 which necessarily follow from the ,property exhibited by ,isomorphous ,bodies1 of replacing each other in given ,proportions4 ,the alteration was1 in fact1 an inversion of the system1 with an attempt still to preserve the electro-chemical principle of arrangement4 ,thus1 instead of arranging metallic minerals according to the metal1 under iron1 copper1 c41 all the sulphurets were classed together1 all the oxides together1 all the sulphates together1 and so in other respects4 ,that such an order was a great improvement on the preceding one1 cannot be doubted2 but we shall see1 ,i think1 that as a strict scientific system it was not successful4 ,the discovery of isomorphism1 however1 naturally led to such attempts4 ,thus ,gmelin also1 in #ahbe1 published a mineral system1#ejae which1 like that of ,berzelius1 founded its leading distinctions on the electro-negative1 or1 as it was sometimes termed1 the formative element of bodies2 and1 besides this1 took account of the numbers of atoms or proportions which appear in the composition of the body2 distinguishing1 for instance1 ,silicates1 as simple silicates1 double silicates1 and so on1 to quintuple silicate 7,pechstein7 and sextuple silicate 7,perlstein74 ,in like manner1 ,nordenskild devised a system resting on the same bases1 taking into account also the crystalline form4 ,in #ahbd1 ,beudant published his ,trait ,elmentaire de ,minralogie1 in which he professes to found his arrangement on the electro-negative element1 and on ,ampre's circular #cdi arrangement of elementary substances4 ,such schemes exhibit rather a play of the mere logical faculty1 exercising itself on assumed principles1 than any attempt at the real interpretation of nature4 ,other such pure chemical systems may have been published1 but it is not necessary to accumulate instances4 ,i proceed to consider their result4 ,note #ejae3 ,zeitsch4 der ,min4 #ahbe1 p4 #dce4 ,sect4 #c4--;,failure of the ,attempts at ,systematic ,reform4 ,,it may appear presumptuous to speak of the failure of those whom1 like ,berzelius and ,mohs1 we acknowledge as our masters1 at a period when1 probably1 they and some of their admirers still hold them to have succeeded in their attempt to construct a consistent system4 ,but ,i conceive that my office as an historian requires me to exhibit the fortunes of this science in the most distinct form of which they admit1 and that ,i cannot evade the duty of attempting to seize the true aspect of recent occurrences in the world of science4 ,hence ,i venture to speak of the failure of both the attempts at framing a pure scientific system of mineralogy1--that founded on the chemical1 and that founded on the natural-history principle2 because it is clear that they have not obtained that which alone we could1 according to the views here presented1 consider as success1--a coincidence of each with the other4 ,a ,chemical ,system of arrangement1 which should bring together1 in all cases1 the substances which come nearest each other in external properties2--a ,natural-history ,system1 which should be found to arrange bodies in complete accordance with their chemical constitution3--if such systems existed1 they might1 with justice1 claim to have succeeded4 ,their agreement would be their verification4 ,the interior and exterior system are the type and the antitype1 and their entire correspondence would establish the mode of interpretation beyond doubt4 ,but nothing less than this will satisfy the requisitions of science4 ,and when1 therefore1 the chemical and the natural-history system1 though evidently1 as ,i conceive1 tending towards each other1 are still far from coming together1 it is impossible to allow that either method has been successful in regard to its proper object4 ,but we may1 ,i think1 point out the fallacy of the principles1 as well as the imperfection of the results1 of both of those methods4 ,with regard to that of ,berzelius1 indeed1 the history of the subject obviously betrays its unsoundness4 ,the electro-positive principle was1 in a very short time after its adoption1 proved and acknowledged to be utterly untenable3 what security have we that the electro-negative element is #cej more trustworthy8 ,was not the necessity of an entire change of system1 a proof that the ground1 whatever that was1 on which the electro-chemical principle was adopted1 was an unfounded assumption8 ,and1 in fact1 do we not find that the same argument which was allowed to be fatal to the ,first ,system of ,berzelius1 applies in exactly the same manner against the ,second8 ,if the electro-positive elements be often isomorphous1 are not the electro-negative elements sometimes isomorphous also8 for instance1 the arsenic and phosphoric acids4 ,but to go further1 what is the ground on which the electro-chemical arrangement is adopted8 ,granted that the electrical relations of bodies are important2 but how do we come to know that these relations have anything to do with mineralogy8 ,how does it appear that on them1 principally1 depend those external properties which mineralogy must study8 ,how does it appear that because sulphur is the electro-negative part of one body1 and an acid the electro-negative part of another1 these two elements similarly affect the compounds8 ,how does it appear that there is any analogy whatever in their functions8 ,we allow that the composition must1 in some way1 determine the classified place of the mineral1--but why in this way8 ,i do not dwell on the remark which ,berzelius himself#eaae makes on ,nordenskild's system2--that it assumes a perfect knowledge of the composition in every case2 although1 considering the usual discrepancies of analyses of minerals1 this objection must make all pure chemical systems useless4 ,but ,i may observe1 that mineralogists have not yet determined what characters are sufficiently affixed to determine a species of minerals4 ,we have seen that the ancient notion of the composition of a species1 has been unsettled by the discovery of isomorphism4 ,the tenet of the constancy of the angle is rendered doubtful by cases of plesiomorphism4 ,the optical properties1 which are so closely connected with the crystalline1 are still so imperfectly known1 that they are subject to changes which appear capricious and arbitrary4 ,both the chemical and the optical mineralogists have constantly1 of late1 found occasion to separate species which had been united1 and to bring together those which had been divided4 ,everything shows that1 in this science1 we have our classification still to begin4 ,the detection of that fixity of characters1 on which a right establishment of species must rest1 is not yet complete1 great as the progress is which we have made1 by acquiring a knowledge of the laws of crystallization and of #cea definite chemical constitution4 ,our ignorance may surprise us2 but it may diminish our surprise to recollect1 that the knowledge which we seek is that of the laws of the physical constitution of all bodies whatever2 for to us1 as mineralogists1 all chemical compounds are minerals4 ,note #eaae3 ,jahres ,bericht4 viii4 #ahh4 ,the defect of the principle of the natural-history classifiers may be thus stated3--in studying the external characters of bodies1 they take for granted that they can1 without any other light1 discover the relative value and importance of those characters4 ,the grouping of ,species into a ,genus1 of ,genera into an ,order1 according to the method of this school1 proceeds by no definite rules1 but by a latent talent of appreciation1--a sort of classifying instinct4 ,but this course cannot reasonably be expected to lead to scientific truth2 for it can hardly be hoped1 by any one who looks at the general course of science1 that we shall discover the relation between external characters and chemical composition1 otherwise than by tracing their association in cases where both are known4 ,it is urged that in other classificatory sciences1 in botany1 for example1 we obtain a natural classification from external characters without having recourse to any other source of knowledge4 ,but this is not true in the sense here meant4 ,in framing a natural system of botany1 we have constantly before our eyes the principles of physiology2 and we estimate the value of the characters of a plant by their bearing on its functions1--by their place in its organization4 ,in an unorganic body1 the chemical constitution is the law of its being2 and we shall never succeed in framing a science of such bodies but by studiously directing our efforts to the interpretation of that law4 ,on these grounds1 then1 ,i conceive1 that the bold attempts of ,mohs and of ,berzelius to give new forms to mineralogy1 cannot be deemed successful in the manner in which their authors aspired to succeed4 ,neither of them can be marked as a permanent reformation of the science4 ,i shall not inquire how far they have been accepted by men of science1 for ,i conceive that their greatest effect has been to point out improvements which might be made in mineralogy without going the whole length either of the pure chemical1 or of the pure natural-history system4 ,sect4 #d4--,return to ,mixed ,systems with ,improvements4 ,,in spite of the efforts of the purists1 mineralogists returned to mixed systems of classification2 but these systems are much better than they were before such efforts were made4 #ceb ,the ,second ,system of ,berzelius1 though not tenable in its rigorous form1 approaches far nearer than any previous system to a complete character1 bringing together like substances in a large portion of its extent4 ,the ,system of ,mohs also1 whether or not unconsciously swayed by chemical doctrines1 forms orders which have a community of chemical character2 thus1 the minerals of the order ,haloide are salts of oxides1 and those of the order ,pyrites are sulphurets of metals4 ,thus the two methods appear to be converging to a common centre2 and though we are unable to follow either of them to this point of union1 we may learn from both in what direction we are to look for it4 ,if we regard the best of the pure systems hitherto devised as indications of the nature of that system1 perfect both as a chemical and as a natural-history system1 to which a more complete condition of mineralogical knowledge may lead us1 we may obtain1 even at present1 a tolerably good approximation to a complete classification2 and such a one1 if we recollect that it must be imperfect1 and is to be held as provisional only1 may be of no small value and use to us4 ,the best of the mixed systems produced by this compromise again comes from ,freiberg1 and was published by ,professor ,naumann in #ahbh4 ,most of his orders have both a chemical character and great external resemblances4 ,thus his ,haloides1 divided into ,unmetallic and ,metallic1 and these again into ,hydrous and ,anhydrous1 give good natural groups4 ,the most difficult minerals to arrange in all systems are the siliceous ones4 ,these ,m4 ,naumann calls ,silicides1 and subdivides them into ,metallic1 ,unmetallic1 and ,amphoteric or mixed2 and again1 into ,hydrous and ,anhydrous4 ,such a system is at least a good basis for future researches2 and this is1 as we have said1 all that we can at present hope for4 ,and when we recollect that the natural-history principle of classification has begun1 as we have already seen1 to make its appearance in our treatises of chemistry1 we cannot doubt that some progress is making towards the object which ,i have pointed out4 ,but we know not yet how far we are from the end4 ,the combination of chemical1 crystallographical1 physical and optical properties into some lofty generalization1 is probably a triumph reserved for future and distant years4 ,conclusion4--,the history of ,mineralogy1 both in its successes and by its failures1 teaches us this lesson2--that in the sciences of classification1 the establishment of the fixity of characters1 and the discovery of such characters as are fixed1 are steps of the first importance in the progress of these sciences4 ,the recollection of this maxim may aid us in #cec shaping our course through the history of other sciences of this kind2 in which1 from the extent of the subject1 and the mass of literature belonging to it1 we might at first almost despair of casting the history into distinct epochs and periods4 ,to the most prominent of such sciences1 ,botany1 ,i now proceed4 #cee ,,book ,,xvi4 ,,classificatory ,,sciences4 ,,history ,,of ,,systematic ,,botany ,,and ,,zoology4 4 4 4 4 4 ,vatem aspicies qu rupe sub alt ,fata canit1 foliisque notas et nomina mandat4 ,qucunque in foliis descripsit carmina virgo ,digerit in numerum atque antro seclusa relinquit ,illa manent immorta locis neque ab ordine cedunt4 ,,virgil4 n4 iii4 #ddc4 ,behold the ,sibyl6--,her who weaves a long1 ,a tangled1 full1 yet sweetly flowing song4 ,wondrous her skill2 for leaf on leaf she frames ,unerring symbols and enduring names2 ,and as her nicely measured line she binds1 ,for leaf on leaf a fitting place she finds2 ,their place once found1 no more the leaves depart1 ,but fixed rest3--such is her magic art4 #ceg ,,introduction4 ,,we now arrive at that study which offers the most copious and complete example of the sciences of classification1 ,i mean ,botany4 ,and in this case1 we have before us a branch of knowledge of which we may say1 more properly than of any of the sciences which we have reviewed since ,astronomy1 that it has been constantly advancing1 more or less rapidly1 from the infancy of the human race to the present day4 ,one of the reasons of this resemblance in the fortunes of two studies so widely dissimilar1 is to be found in a simplicity of principle which they have in common2 the ideas of ,likeness and ,difference1 on which the knowledge of plants depends1 are1 like the ideas of ,space and ,time1 which are the foundation of astronomy1 readily apprehended with clearness and precision1 even without any peculiar culture of the intellect4 ,but another reason why1 in the history of ,botany1 as in that of ,astronomy1 the progress of knowledge forms an unbroken line from the earliest times1 is precisely the great difference of the kind of knowledge which has been attained in the two cases4 ,in ,astronomy1 the discovery of general truths began at an early period of civilization2 in ,botany1 it has hardly yet begun2 and thus1 in each of these departments of study1 the lore of the ancient is homogeneous with that of the modern times1 though in the one case it is science1 in the other1 the absence of science1 which pervades all ages4 ,the resemblance of the form of their history arises from the diversity of their materials4 ,i shall not here dwell further upon this subject1 but proceed to trace rapidly the progress of ,systematic ,botany1 as the classificatory science is usually denominated1 when it is requisite to distinguish between that and ,physiological ,botany4 ,my own imperfect acquaintance with this study admonishes me not to venture into its details1 further than my purpose absolutely requires4 ,i trust that1 by taking my views principally from writers who are generally allowed to possess the best insight into the science1 ,i may be able to draw the larger features of its history with tolerable correctness2 and if ,i succeed in this1 ,i shall attain an object of great importance in my general scheme4 #ceh ,,chapter ,i4 ,,imaginary ,,knowledge ,,of ,,plants4 ,,the apprehension of such differences and resemblances as those by which we group together and discriminate the various kinds of plants and animals1 and the appropriation of words to mark and convey the resulting notions1 must be presupposed1 as essential to the very beginning of human knowledge4 ,in whatever manner we imagine man to be placed on the earth by his ,creator1 these processes must be conceived to be1 as our ,scriptures represent them1 contemporaneous with the first exertion of reason1 and the first use of speech4 ,if we were to indulge ourselves in framing a hypothetical account of the origin of language1 we should probably assume as the first-formed words1 those which depend on the visible likeness or unlikeness of objects2 and should arrange as of subsequent formation1 those terms which imply1 in the mind1 acts of wider combination and higher abstraction4 ,at any rate1 it is certain that the names of the kinds of vegetables and animals are very abundant even in the most uncivilized stages of man's career4 ,thus we are informed#aaf that the inhabitants of ,new ,zealand have a distinct name of every tree and plant in their island1 of which there are six or seven hundred or more different kinds4 ,in the accounts of the rudest tribes1 in the earliest legends1 poetry1 and literature of nations1 pines and oaks1 roses and violets1 the olive and the vine1 and the thousand other productions of the earth1 have a place1 and are spoken of in a manner which assumes1 that in such kinds of natural objects1 permanent and infallible distinctions had been observed and universally recognized4 ,note #aaf3 ,yate's ,new ,zealand1 p4 #bch4 ,for a long period1 it was not suspected that any ambiguity or confusion could arise from the use of such terms2 and when such inconveniences did occur1 7as even in early times they did17 men were far from divining that the proper remedy was the construction of a science of classification4 ,the loose and insecure terms of the language of common life retained their place in botany1 long after their #cei defects were severely felt3 for instance1 the vague and unscientific distinction of vegetables into trees1 shrubs1 and herbs1 kept its ground till the time of ,linnus4 ,while it was thus imagined that the identification of a plant1 by means of its name1 might properly be trusted to the common uncultured faculties of the mind1 and to what we may call the instinct of language1 all the attention and study which were bestowed on such objects1 were naturally employed in learning and thinking upon such circumstances respecting them as were supplied by any of the common channels through which knowledge and opinion flow into men's minds4 ,the reader need hardly be reminded that in the earlier periods of man's mental culture1 he acquires those opinions on which he loves to dwell1 not by the exercise of observation subordinate to reason2 but1 far more1 by his fancy and his emotions1 his love of the marvellous1 his hopes and fears4 ,it cannot surprise us1 therefore1 that the earliest lore concerning plants which we discover in the records of the past1 consists of mythological legends1 marvellous relations1 and extraordinary medicinal qualities4 ,to the lively fancy of the ,greeks1 the ,narcissus1 which bends its head over the stream1 was originally a youth who in such an attitude became enamored of his own beauty3 the hyacinth1#baf on whose petals the notes of grief were traced 7,a ,i1 ,a ,i71 recorded the sorrow of ,apollo for the death of his favorite ,hyacinthus3 the beautiful lotus of ,india1#caf which floats with its splendid flower on the surface of the water1 is the chosen seat of the goddess ,lackshmi1 the daughter of ,ocean4#daf ,in ,egypt1 too1#eaf ,osiris swam on a lotus-leaf and ,harpocrates was cradled in one4 ,the lotus-eaters of ,homer lost immediately their love of home4 ,every one knows how easy it would be to accumulate such tales of wonder or religion4 ,note #baf3 ,lilium martagon4 ,ipse suos gemitus foliis inscribit et ,a ,i1 ,a ,i1 ,flos habet inscriptum funestaque litera ducta est4--,,ovid4 ,note #caf3 ,nelumbium speciosum4 ,note #daf3 ,sprengel1 ,geschichte der ,botanik1 i4 #bg4 ,note #eaf3 ,ib4 i4 #bh4 ,those who attended to the effects of plants1 might discover in them some medicinal properties1 and might easily imagine more2 and when the love of the marvellous was added to the hope of health1 it is easy to believe that men would be very credulous4 ,we need not dwell upon the examples of this4 ,in ,pliny's ,introduction to that book of his #cfj ,natural ,history which treats of the medicinal virtues of plants1 he says1#faf ,antiquity was so much struck with the properties of herbs1 that it affirmed things incredible4 ,xanthus1 the historian1 says1 that a man killed by a dragon1 will be restored to life by an herb which he calls balin2 and that ,thylo1 when killed by a dragon1 was recovered by the same plant4 ,democritus asserted1 and ,theophrastus believed1 that there was an herb1 at the touch of which1 the wedge which the woodman had driven into a tree would leap out again4 ,though we cannot credit these stories1 most persons believe that almost anything might be effected by means of herbs1 if their virtues were fully known4 ,how far from a reasonable estimate of the reality of such virtues were the persons who entertained this belief we may judge from the many superstitious observances which they associated with the gathering and using of medicinal plants4 ,theophrastus speaks of these2#gaf ,the drug-sellers and the rhizotomists 7root-cutters7 tell us1 he says1 some things which may be true1 but other things which are merely solemn quackery2#haf thus they direct us to gather some plants1 standing from the wind1 and with our bodies anointed2 some by night1 some by day1 some before the sun falls on them4 ,so far there may be something in their rules4 ,but others are too fantastical and far fetched4 ,it is1 perhaps1 not absurd to use a prayer in plucking a plant2 but they go further than this4 ,we are to draw a sword three times round the mandragora1 and to cut it looking to the west3 again1 to dance round it1 and to use obscene language1 as they say those who sow cumin should utter blasphemies4 ,again1 we are to draw a line round the black hellebore1 standing to the east and praying2 and to avoid an eagle either on the right or on the left2 for1 say they1 'if an eagle be near1 the cutter will die in a year4' ,note #faf3 ,lib4 xxv4 #e4 ,note #gaf3 ,de ,plantis1 ix4 #i4 ,note #haf3 4 ,this extract may serve to show the extent to which these imaginations were prevalent1 and the manner in which they were looked upon by ,theophrastus1 our first great botanical author4 ,and we may now consider that we have given sufficient attention to these fables and superstitions1 which have no place in the history of the progress of real knowledge1 except to show the strange chaos of wild fancies and legends out of which it had to emerge4 ,we proceed to trace the history of the knowledge of plants4 #cfa ,,chapter ,,ii4 ,,unsystematic ,,knowledge ,,of ,,plants4 ,a ,,step was made towards the formation of the ,science of ,plants1 although undoubtedly a slight one1 as soon as men began to collect information concerning them and their properties1 from a love and reverence for knowledge1 independent of the passion for the marvellous and the impulse of practical utility4 ,this step was very early made4 ,the wisdom of ,solomon1 and the admiration which was bestowed upon it1 prove1 even at that period1 such a working of the speculative faculty3 and we are told1 that among other evidences of his being wiser than all men1 he spake of trees1 from the cedar-tree that is in ,lebanon even unto the hyssop that springeth out of the wall4#iaf ,the father of history1 ,herodotus1 shows us that a taste for natural history had1 in his time1 found a place in the minds of the ,greeks4 ,in speaking of the luxuriant vegetation of the ,babylonian plain1#ajaf he is so far from desiring to astonish merely1 that he says1 the blades of wheat and barley are full four fingers wide2 but as to the size of the trees which grow from millet and sesame1 though ,i could mention it1 ,i will not2 knowing well that those who have not been in that country will hardly believe what ,i have said already4 ,he then proceeds to describe some remarkable circumstances respecting the fertilization of the date-palms in ,assyria4 ,note #iaf3 #a ,kings iv4 #cc4 ,note #ajaf3 ,herod4 i4 #aic4 ,this curious and active spirit of the ,greeks led rapidly1 as we have seen in other instances1 to attempts at collecting and systematizing knowledge on almost every subject3 and in this1 as in almost every other department1 ,aristotle may be fixed upon1 as the representative of the highest stage of knowledge and system which they ever attained4 ,the vegetable kingdom1 like every other province of nature1 was one of the fields of the labors of this universal philosopher4 ,but though his other works on natural history have come down to us1 and are a most valuable monument of the state of such knowledge in his time1 his ,treatise on ,plants is lost4 ,the book ,de ,plantis #cfb which appears with his name1 is an imposture of the middle ages1 full of errors and absurdities4#aaaf ,note #aaaf3 ,mirbel1 ,botanique1 ii4 #eje4 ,his disciple1 friend1 and successor1 ,theophrastus of ,eresos1 is1 as we have said already1 the first great writer on botany whose works we possess2 and1 as may be said in most cases of the first great writer1 he offers to us a richer store of genuine knowledge and good sense than all his successors4 ,but we find in him that the ,greeks of his time1 who aspired1 as we have said1 to collect and systematize a body of information on every subject1 failed in one half of their object1 as far as related to the vegetable world4 ,their attempts at a systematic distribution of plants were altogether futile4 ,although ,aristotle's divisions of the animal kingdom are1 even at this day1 looked upon with admiration by the best naturalists1 the arrangements and comparisons of plants which were contrived by ,theophrastus and his successors1 have not left the slightest trace in the modern form of the science2 and1 therefore1 according to our plan1 are of no importance in our history4 ,and thus we can treat all the miscellaneous information concerning vegetables which was accumulated by the whole of this school of writers1 in no other way than as something antecedent to the first progress towards systematic knowledge4 ,the information thus collected by the unsystematic writers is of various kinds2 and relates to the economical and medicinal uses of plants1 their habits1 mode of cultivation1 and many other circumstances3 it frequently includes some description2 but this is always extremely imperfect1 because the essential conditions of description had not been discovered4 ,of works composed of materials so heterogeneous1 it can be of little use to produce specimens2 but ,i may quote a few words from ,theophrastus1 which may serve to connect him with the future history of the science1 as bearing upon one of the many problems respecting the identification of ancient and modern plants4 ,it has been made a question whether the following description does not refer to the potato4#abaf ,he is speaking of the differences of roots3 ,some roots1 he says1 are still different from those which have been described2 as that of the arachidna#acaf plant3 for this bears fruit underground as well as above3 the fleshy part sends one thick root deep into the ground1 but the others1 which bear the fruit1 are more slender #cfc and higher up1 and ramified4 ,it loves a sandy soil1 and has no leaf whatever4 ,note #abaf3 ,theoph4 i4 #aa4 ,note #acaf3 ,most probably the ,arachnis hypoga1 or ground-nut4 ,the books of ,aristotle and ,theophrastus soon took the place of the ,book of ,nature in the attention of the degenerate philosophers who succeeded them4 ,a story is told by ,strabo#adaf concerning the fate of the works of these great naturalists4 ,in the case of the wars and changes which occurred among the successors of ,alexander1 the heirs of ,theophrastus tried to secure to themselves his books1 and those of his master1 by burying them in the ground4 ,there the manuscripts suffered much from damp and worms2 till ,apollonicon1 a book-collector of those days1 purchased them1 and attempted1 in his own way1 to supply what time had obliterated4 ,when ,sylla marched the ,roman troops into ,athens1 he took possession of the library of ,apollonicon2 and the works which it contained were soon circulated among the learned of ,rome and ,alexandria1 who were thus enabled to ,aristotelize#aeaf on botany as on other subjects4 ,note #adaf3 ,strabo1 lib4 xiii4 c4 i4 #ed4 ,note #aeaf3 4 ,the library collected by the ,attalic kings of ,pergamus1 and the ,alexandrian ,museum1 founded and supported by the ,ptolemies of ,egypt1 rather fostered the commentatorial spirit than promoted the increase of any real knowledge of nature4 ,the ,romans1 in this as in other subjects1 were practical1 not speculative4 ,they had1 in the times of their national vigor1 several writers on agriculture1 who were highly esteemed2 but no author1 till we come to ,pliny1 who dwells on the mere knowledge of plants4 ,and even in ,pliny1 it is easy to perceive that we have before us a writer who extracted his information principally from books4 ,this remarkable man1#afaf in the middle of a public and active life1 of campaigns and voyages1 contrived to accumulate1 by reading and study1 an extraordinary store of knowledge of all kinds4 ,so unwilling was he to have his reading and note-making interrupted1 that1 even before day-break in winter1 and from his litter as he travelled1 he was wont to dictate to his amanuensis1 who was obliged to preserve his hand from the numbness which the cold occasioned1 by the use of gloves4#agaf ,note #afaf3 ,sprengel1 i4 #afc4 ,note #agaf3 ,plin4 ,jun4 ,epist4 #c1 #e4 ,it has been ingeniously observed1 that we may find traces in the botanical part of his ,natural ,history1 of the errors which this hurried and broken habit of study produced2 and that he appears frequently to have had books read to him and to have heard them amiss4#ahaf ,thus1 #cfd among several other instances1 ,theophrastus having said that the plane-tree is in ,italy rare1#aiaf ,pliny1 misled by the similarity of the ,greek word 7spanian1 rare71 says that the tree occurs in ,italy and ,spain4#bjaf ,his work has1 with great propriety1 been called the ,encyclopdia of ,antiquity2 and1 in truth1 there are few portions of the learning of the times to which it does not refer4 ,of the thirty-seven ,books of which it consists1 no less than sixteen 7from the twelfth to the twenty-seventh7 relate to plants4 ,the information which is collected in these books1 is of the most miscellaneous kind2 and the author admits1 with little distinction1 truth and error1 useful knowledge and absurd fables4 ,the declamatory style1 and the comprehensive and lofty tone of thought which we have already spoken of as characteristic of the ,roman writers1 are peculiarly observable in him4 ,the manner of his death is well known3 it was occasioned by the eruption of ,vesuvius1 ,a4,d4 #gi1 to which1 in his curiosity1 he ventured so near as to be suffocated4 ,note #ahaf3 ,sprengel1 i4 #afc4 ,note #aiaf3 ,theoph4 iv4 #g4 1 ,note #bjaf3 ,plin4 ,nat4 ,hist4 xii4 #c4 ,et alias 7platanos7 fuisse in ,italia1 ac nominatim ,hispania1 apud auctores invenitur4 ,pliny's work acquired an almost unlimited authority1 as one of the standards of botanical knowledge1 in the middle ages2 but even more than his1 that of his contemporary1 ,pedanius ,dioscorides1 of ,anazarbus in ,cilicia4 ,this work1 written in ,greek1 is held by the best judges#baaf to offer no evidence that the author observed for himself4 ,yet he says expressly in his ,preface1 that his love of natural history1 and his military life1 have led him into many countries1 in which he has had opportunity to become acquainted with the nature of herbs and trees4#bbaf ,he speaks of six hundred plants1 but often indicates only their names and properties1 giving no description by which they can be identified4 ,the main cause of his great reputation in subsequent times was1 that he says much of the medicinal virtues of vegetables4 ,note #baaf3 ,mirbel1 #eaj4 ,note #bbaf3 ,sprengel1 i4 #acf4 ,we come now to the ages of darkness and lethargy1 when the habit of original thought seems to die away1 as the talent of original observation had done before4 ,commentators and mystics succeed to the philosophical naturalists of better times4 ,and though a new race1 altogether distinct in blood and character from the ,greek1 appropriates to itself the stores of ,grecian learning1 this movement does not1 as might be expected1 break the chains of literary slavery4 ,the ,arabs #cfe bring1 to the cultivation of the science of the ,greeks1 their own oriental habit of submission1 their oriental love of wonder2 and thus1 while they swell the herd of commentators and mystics1 they produce no philosopher4 ,yet the ,arabs discharged an important function in the history of human knowledge1#bcaf by preserving1 and transmitting to more enlightened times1 the intellectual treasures of antiquity4 ,the unhappy dissensions which took place in the ,christian church had scattered these treasures over the ,east1 at a period much antecedent to the rise of the ,saracen power4 ,in the fifth century1 the adherents of ,nestorius1 bishop of ,constantinople1 were declared heretical by the ,council of ,ephesus 7,a4,d4 #dca71 and driven into exile4 ,in this manner1 many of the most learned and ingenious men of the ,christian world were removed to the ,euphrates1 where they formed the ,chaldean church1 erected the celebrated ,nestorian school of ,edessa1 and gave rise to many offsets from this in various regions4 ,already1 in the fifth century1 ,hibas1 ,cumas1 and ,probus1 translated the writings of ,aristotle into ,syriac4 ,but the learned ,nestorians paid an especial attention to the art of medicine1 and were the most zealous students of the works of the ,greek physicians4 ,at ,djondisabor1 in ,khusistan1 they became an ostensible medical school1 who distributed academical honors as the result of public disputations4 ,the califs of ,bagdad heard of the fame and the wisdom of the doctors of ,djondisabor1 summoned some of them to ,bagdad1 and took measures for the foundation of a school of learning in that city4 ,the value of the skill1 the learning1 and the virtues of the ,nestorians1 was so strongly felt1 that they were allowed by the ,mohammedans the free exercise of the ,christian religion1 and intrusted with the conduct of the studies of those of the ,moslemin1 whose education was most cared for4 ,the affinity of the ,syriac and ,arabic languages made the task of instruction more easy4 ,the ,nestorians translated the works of the ancients out of the former into the latter language3 hence there are still found ,arabic manuscripts of ,dioscorides1 with ,syriac words in the margin4 ,pliny and ,aristotle likewise assumed an ,arabic dress2 and were1 as well as ,dioscorides1 the foundation of instruction in all the ,arabian academies2 of which a great number were established throughout the ,saracen empire1 from ,bokhara in the remotest east1 to ,marocco and ,cordova in the west4 ,after some time1 the ,mohammedans themselves began to translate and #cff extract from their ,syriac sources2 and at length to write works of their own4 ,and thus arose vast libraries1 such as that of ,cordova1 which contained #bej1jjj volumes4 ,note #bcaf3 ,sprengel1 i4 #bjc4 ,the ,nestorians are stated#bdaf to have first established among the ,arabs those collections of medicinal substances 7,apothec71 from which our term ,apothecary is taken2 and to have written books 7,dispensatoria7 containing systematic instructions for the employment of these medicaments2 a word which long continued to be implied in the same sense1 and which we also retain1 though in a modified application 7,dispensary74 ,note #bdaf3 ,sprengel1 i4 #bje4 ,the directors of these collections were supposed to be intimately acquainted with plants2 and yet1 in truth1 the knowledge of plants owed but little to them2 for the ,arabic ,dioscorides was the source and standard of their knowledge4 ,the flourishing commerce of the ,arabians1 their numerous and distant journeys1 made them1 no doubt1 practically acquainted with the productions of lands unknown to the ,greeks and ,romans4 ,their ,nestorian teachers had established ,christianity even as far as ,china and ,malabar2 and their travellers mention#beaf the camphor of ,sumatra1 the aloe-wood of ,socotra near ,java1 the tea of ,china4 ,but they never learned the art of converting their practical into speculative knowledge4 ,they treat of plants only in so far as their use in medicine is concerned1#bfaf and followed ,dioscorides in the description1 and even in the order of the plants1 except when they arrange them according to the ,arabic alphabet4 ,with little clearness of view1 they often mistake what they read3#bgaf thus when ,dioscorides says that ligusticon grows on the ,apennine1 a mountain not far from the ,alps2 ,avicenna1 misled by a resemblance of the ,arabic letters1 quotes him as saying that the plant grows on ,akabis1 a mountain near ,egypt4 ,note #beaf3 ,sprengel1 i4 #bjf4 ,note #bfaf3 ,ib4 i4 #bjg4 ,note #bgaf3 ,ib4 i4 #baa4 ,it is of little use to enumerate such writers4 ,one of the most noted of them was ,mesu1 physician of the ,calif of ,kahirah4 ,his work1 which was translated into ,latin at a later period1 was entitled1 ,on ,simple ,medicines2 a title which was common to many medical treatises1 from the time of ,galen in the second century4 ,indeed1 of this opposition of simple and compound medicines1 we still have traces in our language3 #cfg ,he would ope his leathern scrip1 ,and show me simples of a thousand names1 ,telling their strange and vigorous faculties4 ,,milton1 ,comus4 ,where the subject of our history is so entirely at a stand1 it is unprofitable to dwell on a list of names4 ,the ,arabians1 small as their science was1 were able to instruct the ,christians4 ,their writings were translated by learned ,europeans1 for instance ,michael ,scot1 and ,constantine of ,africa1 a ,carthaginian who had lived forty years among the ,saracens#bhaf and who died ,a4,d4 #ajhg4 ,among his works1 is a ,treatise1 ,de ,gradibus1 which contains the ,arabian medicinal lore4 ,in the thirteenth century occur ,encyclopdias1 as that of ,albertus ,magnus1 and of ,vincent of ,beauvais2 but these contain no natural history except traditions and fables4 ,even the ancient writers were altogether perverted and disfigured4 ,the ,dioscorides of the middle ages varied materially from ours4#biaf ,monks1 merchants1 and adventurers travelled far1 but knowledge was little increased4 ,simon of ,genoa1#cjaf a writer on plants in the fourteenth century1 boasts that he perambulated the ,east in order to collect plants4 ,yet in his ,clavis ,sanationis1 says a modern botanical writer1#caaf we discover no trace of an acquaintance with nature4 ,he merely compares the ,greek1 ,arabic1 and ,latin names of plants1 and gives their medicinal effect after his predecessors3--so little true is it1 that the use of the senses alone necessarily leads to real knowledge4 ,note #bhaf3 ,sprengel1 i4 #bcj4 ,note #biaf3 ,ib4 i4 #bci4 ,note #cjaf3 ,ib4 i4 #bda4 ,note #caaf3 ,ib4 ib4 ,though the growing activity of thought in ,europe1 and the revived acquaintance with the authors of ,greece in their genuine form1 were gradually dispelling the intellectual clouds of the middle ages1 yet during the fifteenth century1 botany makes no approach to a scientific form4 ,the greater part of the literature of this subject consisted of ,herbals1 all of which were formed on the same plan1 and appeared under titles such as ,hortus1 or ,ortus ,sanitatis4 ,there are1 for example1 three#cbaf such ,german ,herbals1 with woodcuts1 which date about #adij4 ,but an important peculiarity in these works is that they contain some indigenous species placed side by side with the old ones4 ,in #aeaf1 ,the ,grete ,herbal was published in ,england1 also with woodcuts4 ,it contains an account of more than four hundred vegetables1 and their #cfh products2 of which one hundred and fifty are ,english1 and are no way distinguished from the exotics by the mode in which they are inserted in the work4 ,note #cbaf3 ,augsburg1 #adhh4 ,mainz1 #adia4 ,lubec1 #adib4 ,we shall see1 in the next chapter1 that when the intellect of ,europe began really to apply itself to the observation of nature1 the progress towards genuine science soon began to be visible1 in this as in other subjects2 but before this tendency could operate freely1 the history of botany was destined to show1 in another instance1 how much more grateful to man1 even when roused to intelligence and activity1 is the study of tradition than the study of nature4 ,when the scholars of ,europe had become acquainted with the genuine works of the ancients in the original languages1 the pleasure and admiration which they felt1 led them to the most zealous endeavors to illustrate and apply what they read4 ,they fell into the error of supposing that the plants described by ,theophrastus1 ,dioscorides1 ,pliny1 must be those which grew in their own fields4 ,and thus ,ruellius1#ccaf a ,french physician1 who only travelled in the environs of ,paris and ,picardy1 imagined that he found there the plants of ,italy and ,greece4 ,the originators of genuine botany in ,germany1 ,brunfels and ,tragus 7,bock71 committed the same mistake2 and hence arose the misapplication of classical names to many genera4 ,the labors of many other learned men took the same direction1 of treating the ancient writers as if they alone were the sources of knowledge and truth4 ,note #ccaf3 ,de ,natura ,stirpium1 #aecf4 ,but the philosophical spirit of ,europe was already too vigorous to allow this superstitious erudition to exercise a lasting sway4 ,leonicenus1 who taught at ,ferrara till he was almost a hundred years old1 and died in #aebd1cdaf disputed1 with great freedom1 the authority of the ,arabian writers1 and even of ,pliny4 ,he saw1 and showed by many examples1 how little ,pliny himself knew of nature1 and how many errors he had made or transmitted4 ,the same independence of thought with regard to other ancient writers1 was manifested by other scholars4 ,yet the power of ancient authority melted away but gradually4 ,thus ,antonius ,brassavola1 who established on the banks of the ,po the first botanical garden of modern times1 published in #aecf1 his ,examen omnium ,simplicium ,medicamentorum2 and1 as ,cuvier says1#ceaf though he studied plants in nature1 his book 7written in the #cfi ,platonic form of dialogue71 has still the character of a commentary on the ancients4 ,note #cdaf3 ,sprengel1 i4 #beb4 ,note #ceaf3 ,hist4 des ,sc4 ,nat4 partie ii4 #afi4 ,the ,germans appear to have been the first to liberate themselves from this thraldom1 and to publish works founded mainly on actual observation4 ,the first of the botanists who had this great merit is ,otho ,brunfels of ,mentz1 whose work1 ,herbarum ,viv ,icones1 appeared in #aecj4 ,it consists of two volumes in folio1 with wood-cuts2 and in #aecb1 a ,german edition was published4 ,the plants which it contains are given without any arrangement1 and thus he belongs to the period of unsystematic knowledge4 ,yet the progress towards the formation of a system manifested itself so immediately in the series of ,german botanists to which he belongs1 that we might with almost equal propriety transfer him to the history of that progress2 to which we now proceed4 ,,chapter ,,iii4 ,,formation ,,of ,a ,,system ,,of ,,arrangement ,,of ,,plants4 ,sect4 #a4--,prelude to the ,epoch of ,csalpinus4 ,,the arrangement of plants in the earliest works was either arbitrary1 or according to their use1 or some other extraneous circumstance1 as in ,pliny4 ,this and the division of vegetables by ,dioscorides into aromatic1 alimentary1 medicinal1 vinous1 is1 as will be easily seen1 a merely casual distribution4 ,the ,arabian writers1 and those of the middle ages1 showed still more clearly their insensibility to the nature of system1 by adopting an alphabetical arrangement2 which was employed also in the ,herbals of the sixteenth century4 ,brunfels1 as we have said1 adopted no principle of order2 nor did his successor1 ,fuchs4 ,yet the latter writer urged his countrymen to put aside their ,arabian and barbarous ,latin doctors1 and to observe the vegetable kingdom for themselves2 and he himself set the example of doing this1 examined plants with zeal and accuracy1 and made above fifteen hundred drawings of them4#cfaf #cgj ,note #cfaf3 ,his ,historia ,stirpium was published at ,basil in #aedb4 ,the difficulty of representing plants in any useful way by means of drawings1 is greater1 perhaps1 than it at first appears4 ,so long as no distinction was made of the importance of different organs of the plant1 a picture representing merely the obvious general appearance and larger parts1 was of comparatively small value4 ,hence we are not to wonder at the slighting manner in which ,pliny speaks of such records4 ,those who gave such pictures of plants1 he says1 ,crateuas1 ,dionysius1 ,metrodorus1 have shown nothing clearly1 except the difficulty of their undertaking4 ,a picture may be mistaken1 and is changed and disfigured by copyists2 and1 without these imperfections1 it is not enough to represent the plant in one state1 since it has four different aspects in the four seasons of the year4 ,the diffusion of the habit of exact drawing1 especially among the countrymen of ,albert ,durer and ,lucas ,cranach1 and the invention of wood-cuts and copper-plates1 remedied some of these defects4 ,moreover1 the conviction gradually arose in men's minds that the structure of the flower and the fruit are the most important circumstances in fixing the identity of the plant4 ,theophrastus speaks with precision of the organs which he describes1 but these are principally the leaves1 roots1 and stems4 ,fuchs uses the term apices for the anthers1 and gluma for the blossom of grasses1 thus showing that he had noticed these parts as generally present4 ,in the next writer whom we have to mention1 we find some traces of a perception of the real resemblances of plants beginning to appear4 ,it is impossible to explain the progress of such views without assuming in the reader some acquaintance with plants2 but a very few words may suffice to convey the requisite notions4 ,even in plants which most commonly come in our way1 we may perceive instances of the resemblances of which we speak4 ,thus1 ,mint1 ,marjoram1 ,basil1 ,sage1 ,lavender1 ,thyme1 ,dead-nettle1 and many other plants1 have a tubular flower1 of which the mouth is divided into two lips2 hence they are formed into a family1 and termed ,labiat4 ,again1 the ,stock1 the ,wall-flower1 the ,mustard1 the ,cress1 the ,lady-smock1 the ,shepherd's purse1 have1 among other similarities1 their blossoms with four petals arranged crosswise2 these are all of the order ,crucifer4 ,other flowers1 apparently more complex1 still resemble each other1 as ,daisy4 ,marigold1 ,aster1 and ,chamomile2 these belong to the order ,composit4 ,and though the members of each such family may differ widely in their larger parts1 their stems and leaves1 the close study of nature leads the botanist irresistibly to consider their resemblances as #cga occupying a far more important place than their differences4 ,it is the general establishment of this conviction and its consequences which we have now to follow4 ,the first writer in whom we find the traces of an arrangement depending upon these natural resemblances1 is ,hieronymus ,tragus1 7,jerom ,bock17 a laborious ,german botanist1 who1 in #aeea1 published a herbal4 ,in this work1 several of the species included in those natural families to which we have alluded1#cgaf as for instance the ,labiat1 the ,crucifer1 the ,composit1 are for the most part brought together2 and thus1 although with many mistakes as to such connexions1 a new principle of order is introduced into the subject4 ,note #cgaf3 ,sprengel1 i4 #bgj4 ,in pursuing the development of such principles of natural order1 it is necessary to recollect that the principles lead to an assemblage of divisions and groups1 successively subordinate1 the lower to the higher1 like the brigades1 regiments1 and companies of an army1 or the provinces1 towns1 and parishes of a kingdom4 ,species are included in ,genera1 ,genera in ,families or ,orders1 and orders in ,classes4 ,the perception that there is some connexion among the species of plants1 was the first essential step2 the detection of different marks and characters which should give1 on the one hand1 limited groups1 on the other1 comprehensive divisions1 were other highly important parts of this advance4 ,to point out every successive movement in this progress would be a task of extreme difficulty1 but we may note1 as the most prominent portions of it1 the establishment of the groups which immediately include ,species1 that is1 the formation of ,genera2 and the invention of a method which should distribute into consistent and distinct divisions the whole vegetable kingdom1 that is1 the construction of a ,system4 ,to the second of these two steps we have no difficulty in assigning its proper author4 ,it belongs to ,csalpinus1 and marks the first great epoch of this science4 ,it is less easy to state to what botanist is due the establishment of ,genera2 yet we may justly assign the greater part of the merit of this invention1 as is usually done1 to ,conrad ,gessner of ,zurich4 ,this eminent naturalist1 after publishing his great work on animals1 died#chaf of the plague in #aefe1 at the age of forty-nine1 while he was preparing to publish a ,history of ,plants1 a sequel to his ,history of ,animals4 ,the fate of the work thus left #cgb unfinished was remarkable4 ,it fell into the hands of his pupil1 ,gaspard ,wolf1 who was to have published it1 but wanting leisure for the office1 sold it to ,joachim ,camerarius1 a physician and botanist of ,nuremberg1 who made use of the engravings prepared by ,gessner1 in an ,epitome which he published in #aehf4 ,the text of ,gessner's work1 after passing through various hands1 was published in #aged under the title of ,gessneri ,opera ,botanica per duo ,scula desiderata1 c41 but is very incomplete4 ,note #chaf3 ,cuvier1 ,leons sur l',hist4 des ,sciences ,naturelles1 partie ii4 p4 #aic4 ,the imperfect state in which ,gessner left his botanical labors1 makes it necessary to seek the evidence of his peculiar views in scattered passages of his correspondence and other works4 ,one of his great merits was1 that he saw the peculiar importance of the flower and fruit as affording the characters by which the affinities of plants were to be detected2 and that he urged this view upon his contemporaries4 ,his plates present to us1 by the side of each plant1 its flower and its fruit1 carefully engraved4 ,and in his communications with his botanical correspondents1 he repeatedly insists on these parts4 ,thus#ciaf in #aefe he writes to ,zuinger concerning some foreign plants which the latter possessed3 ,tell me if your plants have fruit and flower1 as well as stalk and leaves1 for those are of much the greater consequence4 ,by these three marks1--flower1 fruit1 and seed1--,i find that ,saxifraga and ,consolida ,regalis are related to ,aconite4 ,these characters1 derived from the fructification 7as the assemblage of flower and fruit is called71 are the means by which genera are established1 and hence1 by the best botanists1 ,gessner is declared to be the inventor of genera4#djaf #cgc ,note #ciaf3 ,epistol1 fol4 #aac a2 see also fol4 #fe b4 ,note #djaf3 ,haller1 ,biblio ,botanica1 i4 #bhd4 ,methodi ,botanic rationem primus pervidit2--dari nempe et genera qu plures species comprehenderent et classes qu multa genera4 ,varias etiam classes naturales expressit4 ,characterem in flore inque semine posuit1 c4--,rauwolfio ,socio ,epist4 ,wolf1 p4 #ci4 ,linnus1 ,genera ,plantarum1 ,pref4 xiii4 ,a fructificatione plantas distinguere in genera1 infinit sapienti placuisse1 detexit posterior tas1 et quidem primus1 sculi sui ornamentum1 ,conradus ,gessnerus1 uti patet ex ,epistolis ejus postremis1 et ,tabulis per ,carmerarium editis4 ,cuvier says 7,hist4 des ,sc4 ,nat4 #b;e pe1 p4 #aic71 after speaking to the same effect1 ,il fit voir encore que toutes les plantes qui ont des fleurs et des fruits semblables se ressemblent par leurs proprits1 et que quand on rapproche ces plantes on obtient ainsi une classification naturelle4 ,i do not know if he here refers to any particular passages of ,gessner's work4 ,the labors of ,gessner in botany1 both on account of the unfinished state in which he left the application of his principles1 and on account of the absence of any principles manifestly applicable to the whole extent of the vegetable kingdom1 can only be considered as a prelude to the epoch in which those defects were supplied4 ,to that epoch we now proceed4 ,sect4 #b4--;,epoch of ,csalpinus4--,formation of a ,system of ,arrangement4 ,,if any one were disposed to question whether ,natural ,history truly belongs to the domain of ,inductive ,science2--whether it is to be prosecuted by the same methods1 and requires the same endowments of mind as those which lead to the successful cultivation of the ,physical ,sciences1--the circumstances under which ,botany has made its advance appear fitted to remove such doubts4 ,the first decided step in this study was merely the construction of a classification of its subjects4 ,we shall1 ,i trust1 be able to show that such a classification includes1 in reality1 the establishment of one general principle1 and leads to more4 ,but without here dwelling on this point1 it is worth notice that the person to whom we owe this classification1 ,andreas ,csalpinus of ,arezzo1 was one of the most philosophical men of his time1 profoundly skilled in the ,aristotelian lore which was then esteemed1 yet gifted with courage and sagacity which enabled him to weigh the value of the ,peripatetic doctrines1 to reject what seemed error1 and to look onwards to a better philosophy4 ,how are we to understand1 he inquires1 that we must proceed from universals to particulars 7as ,aristotle directs71 when particulars are better known8#daaf ,yet he treats the ,master with deference1 and1 as has been observed1#dbaf we see in his great botanical work deep traces of the best features of the ,aristotelian school1 logic and method2 and1 indeed1 in this work he frequently refers to his ,qustiones ,peripatetic4 ,his book1 entitled ,de ,plantis libri xvi4 appeared at ,florence in #aehc4 ,the aspect under which his task presented itself to his mind appears to me to possess so much interest1 that ,i will transcribe a few of his reflections4 ,after speaking of the splendid multiplicity of the productions of nature1 and the confusion which has hitherto prevailed among writers on plants1 #cgd the growing treasures of the botanical world2 he adds1#dcaf ,in this immense multitude of plants1 ,i see that want which is most felt in any other unordered crowd3 if such an assemblage be not arranged into brigades like an army1 all must be tumult and fluctuation4 ,and this accordingly happens in the treatment of plants3 for the mind is overwhelmed by the confused accumulation of things1 and thus arise endless mistake and angry altercation4 ,he then states his general view1 which1 as we shall see1 was adopted by his successors4 ,since all science consists in the collection of similar1 and the distinction of dissimilar things1 and since the consequence of this is a distribution into genera and species1 which are to be natural classes governed by real differences1 ,i have attempted to execute this task in the whole range of plants2--ut si quid pro ingenii mei tenuitate in hujusmodi studio profecerim1 ad communem utilitatem proferam4 ,we see here how clearly he claims for himself the credit of being the first to execute this task of arrangement4 ,note #daaf3 ,qustiones ,peripatetic1 7#aefi17 lib4 i4 qust4 i4 ,note #dbaf3 ,cuvier1 p4 #aih4 ,note #dcaf3 ,dedicatio1 a #b4 ,after certain preparatory speculations1 he says1#ddaf ,let us now endeavor to mark the kinds of plants by essential circumstances in the fructification4 ,he then observes1 ,in the constitution of organs three things are mainly important--the number1 the position1 the figure4 ,and he then proceeds to exemplify this3 ,some have under one flower1 ,,one seed1 as ,amygdala1 or ,,one seed-receptacle1 as ,rosa2 or ,,two seeds1 as ,ferularia1 or ,,two seed-receptacles1 as ,nasturtium2 or three1 as the ,tithymalum kind have ,,three seeds1 the ,bulbace ,,three receptacles2 or four1 as ,marrubium1 ,,four seeds1 ,siler ,,four receptacles2 or more1 as ,cicorace1 and ,acanace have ,,more seeds1 ,pinus1 ,,more receptacles4 ,note #ddaf3 ,lib4 i4 c4 #ac1 #ad4 ,it will be observed that we have here ten classes made out by means of number alone1 added to the consideration of whether the seed is alone in its covering1 as in a cherry1 or contained in a receptacle with several others1 as in a berry1 pod1 or capsule4 ,several of these divisions are1 however1 further subdivided according to other circumstances1 and especially according as the vital part of the seed1 which he called the heart 7cor#deaf71 is situated in the upper or lower part of the seed4 ,as our object here is only to indicate the principle of the method of ,csalpinus1 ,i need not further dwell on the details1 and still less on the defects by which it is disfigured1 as1 for instance1 the retention of the old distinction of ,trees1 ,shrubs1 and ,herbs4 #cge ,note #deaf3 ,corculum1 of ,linnus4 ,to some persons it may appear that this arbitrary distribution of the vegetable kingdom1 according to the number of parts of a particular kind1 cannot deserve to be spoken of as a great discovery4 ,and if1 indeed1 the distribution had been arbitrary1 this would have been true2 the real merit of this and of every other system is1 that while it is artificial in its form1 it is natural in its results4 ,the plants which are associated by the arrangement of ,csalpinus1 are those which have the closest resemblances in the most essential points4 ,thus1 as ,linnus says1 though the first in attempting to form natural orders1 he observed as many as the most successful of later writers4 ,thus his ,legumina#dfaf correspond to the natural order ,leguminos2 his genus ,ferulaceum#dgaf to the ,umbellat2 his ,bulbace#dhaf to ,liliace2 his ,anthemides#diaf to the ,composit2 in like manner1 the ,boragine are brought together1#ejaf and the ,labiat4 ,that such assemblages are produced by the application of his principles1 is a sufficient evidence that they have their foundation in the general laws of the vegetable world4 ,if this had not been the case1 the mere application of number or figure alone as a standard of arrangement1 would have produced only intolerable anomalies4 ,if1 for instance1 ,csalpinus had arranged plants by the number of flowers on the same stalk1 he would have separated individuals of the same species2 if he had distributed them according to the number of leaflets which compose the leaves1 he would have had to place far asunder different species of the same genus4 ,or1 as he himself says1#eaaf ,if we make one genus of those which have a round root1 as ,rapum1 ,aristolochia1 ,cyclaminus1 ,aton1 we shall separate from this genus those which most agree with it1 as ,napum and ,raphanum1 which resemble ,rapum1 and the long ,aristolochia1 which resembles the round2 while we shall join the most remote kinds1 for the nature of ,cyclaminus and ,rapum is altogether diverse in all other respects4 ,or if we attend to the differences of stalk1 so as to make one genus of those which have a naked stalk1 as the ,junci1 ,cpe1 ,aphac1 along with ,cicorace1 ,viol1 we shall still connect the most unlike things1 and disjoin the closest affinities4 ,and if we note the differences of leaves1 or even flowers1 we fall into the same difficulty2 for many plants very different in kind have leaves very similar1 as ,polygonum and ,hypericum1 ,ernea and ,sesamois1 ,apium and ,ranunculus2 and plants of the same genus have sometimes very different #cgf leaves1 as the several species of ,ranunculus and of ,lactuca4 ,nor will color or shape of the flowers help us better2 for what has ,vitis in common with nanthe1 except the resemblance of the flower8 ,he then goes on to say1 that if we seek a too close coincidence of all the characters we shall have no ,species2 and thus shows us that he had clearly before his view the difficulty1 which he had to attack1 and which it is his glory to have overcome1 that of constructing ,natural ,orders4 ,note #dfaf3 ,lib4 vi4 ,note #dgaf3 ,lib4 vii4 ,note #dhaf3 ,lib4 x4 ,note #diaf3 ,lib4 xii4 ,note #ejaf3 ,lib4 xi4 ,note #eaaf3 ,lib4 i4 cap4 xii4 p4 #be4 ,but as the principles of ,csalpinus are justified1 on the one hand1 by their leading to ,natural ,orders1 they are recommended on the other by their producing a ,system which applies through the whole extent of the vegetable kingdom4 ,the parts from which he takes his characters must occur in all flowering-plants1 for all such plants have seeds4 ,and these seeds1 if not very numerous for each flower1 will be of a certain definite number and orderly distribution4 ,and thus every plant will fall into one part or other of the same system4 ,it is not difficult to point out1 in this induction of ,csalpinus1 the two elements which we have so often declared must occur in all inductive processes2 the exact acquaintance with facts1 and the general and applicable ideas by which these facts are brought together4 ,csalpinus was no mere dealer in intellectual relations or learned traditions1 but a laborious and persevering collector of plants and of botanical knowledge4 ,for many years1 he says in his ,dedication1 ,i have been pursuing my researches in various regions1 habitually visiting the places in which grew the various kinds of herbs1 shrubs1 and trees2 ,i have been assisted by the labors of many friends1 and by gardens established for the public benefit1 and containing foreign plants collected from the most remote regions4 ,he here refers to the first garden directed to the public study of ,botany1 which was that of ,pisa1#ebaf instituted in #aedc1 by order of the ,grand ,duke ,cosmo the ,first4 ,the management of it was confided first to ,lucas ,ghini1 and afterwards to ,csalpinus4 ,he had collected also a herbarium of dried plants1 which he calls the rudiment of his work4 ,tibi enim1 he says1 in his dedication to ,francis ,medici1 ,grand ,duke of ,etruria1 apud quem extat ejus rudimentum ex plantis libro agglutinatis a me compositum4 ,and1 throughout1 he speaks with the most familiar and vivid acquaintance of the various vegetables which he describes4 ,note #ebaf3 ,cuv4 #ahg4 ,but ,csalpinus also possessed fixed and general views concerning the relation and functions of the parts of plants1 and ideas of symmetry #cgg and system2 without which1 as we see in other botanists of his and succeeding times1 the mere accumulation of a knowledge of details does not lead to any advance in science4 ,we have already mentioned his reference to general philosophical principles1 both of the ,peripatetics and of his own4 ,the first twelve chapters of his work are employed in explaining the general structure of plants1 and especially that point to which he justly attaches so much importance1 the results of the different situation of the cor or corculum of the seed4 ,he shows#ecaf that if we take the root1 or stem1 or leaves1 or blossom1 as our guide in classification1 we shall separate plants obviously alike1 and approximate those which have merely superficial resemblances4 ,and thus we see that he had in his mind ideas of fixed resemblance and symmetrical distribution1 which he sedulously endeavored to apply to plants2 while his acquaintance with the vegetable kingdom enabled him to see in what manner these ideas were not1 and in what manner they were1 really applicable4 ,note #ecaf3 ,lib4 i4 cap4 xii4 ,the great merit and originality of ,csalpinus have been generally allowed1 by the best of the more modern writers on ,botany4 ,linnus calls him one of the founders of the science2 ,primus verus systematicus2#edaf and1 as if not satisfied with the expression of his admiration in prose1 hangs a poetical garland on the tomb of his hero4 ,the following distich concludes his remarks on this writer3 ,quisquis hic extiterit primos concedet honores ,csalpine tibi2 primaque serta dabit3 and similar language of praise has been applied to him by the best botanists up to ,cuvier1#eeaf who justly terms his book a work of genius4 ,note #edaf3 ,philosoph4 ,bot4 p4 #ai4 ,note #eeaf3 ,cuv4 ,hist4 #aic4 ,perhaps the great advance made in this science by ,csalpinus1 is most strongly shown by this2 that no one appeared1 to follow the path which he had opened to system and symmetry1 for nearly a century4 ,moreover1 when the progress of this branch of knowledge was resumed1 his next successor1 ,morison1 did not choose to acknowledge that he had borrowed so much from so old a writer2 and thus1 hardly mentions his name1 although he takes advantage of his labors1 and even transcribes his words without acknowledgement1 as ,i shall show4 ,the pause between the great invention of ,csalpinus1 and its natural sequel1 the developement and improvement of his method1 is so marked1 that ,i #cgh will1 in order to avoid too great an interruption of chronological order1 record some of its circumstances in a separate section4 ,sect4 #c4--,stationary ,interval4 ,,the method of ,csalpinus was not1 at first1 generally adopted4 ,it had1 indeed1 some disadvantages4 ,employed in drawing the boundary-lines of the larger divisions of the vegetable kingdom1 he had omitted those smaller groups1 ,genera1 which were both most obvious to common botanists1 and most convenient in the description and comparison of plants4 ,he had also neglected to give the ,synonyms of other authors for the plants spoken of by him2 an appendage to botanical descriptions1 which the increase of botanical information and botanical books had now rendered indispensable4 ,and thus it happened1 that a work1 which must always be considered as forming a great epoch in the science to which it refers1 was probably little read1 and in a short time could be treated as if it were quite forgotten4 ,in the mean time1 the science was gradually improved in its details4 ,clusius1 or ,charles de l',ecluse1 first taught botanists to describe well4 ,before him1 says ,mirbel1#efaf the descriptions were diffuse1 obscure1 indistinct2 or else concise1 incomplete1 vague4 ,clusius introduced exactitude1 precision1 neatness1 elegance1 method3 he says nothing superfluous2 he omits nothing necessary4 ,he travelled over great part of ,europe1 and published various works on the more rare of the plants which he had seen4 ,among such plants1 we may note now one well known1 the potato2 which he describes as being commonly used in ,italy in #aehf2egaf thus throwing doubt1 at least1 on the opinion which ascribes the first introduction of it into ,europe to ,sir ,walter ,raleigh1 on his return from ,virginia1 about the same period4 ,as serving to illustrate1 both this point1 and the descriptive style of ,clusius1 ,i quote1 in a note1 his description of the flower of this plant4#ehaf #cgi ,note #efaf3 ,physiol4 ,veg4 p4 #ebe4 ,note #egaf3 ,clusius4 ,exotic4 iv4 c4 #eb1 p4 lxxix4 ,note #ehaf3 ,papas ,peruanorum4 ,arachidna1 ,theoph4 forte4 ,flores elegantes1 uncialis amplitudinis aut majores1 angulosi1 singulari folio constantes1 sed ita complicato ut quinque folia discreta videantur1 coloris exterius ex purpura candicantis1 interius purpurascentis1 radiis quinque herbaceis ex umbilico stell instar prodeuntibus1 et totidem staminibus flavis in umbonem coeuntibus4 ,he says that the ,italians do not know whence they had the plant1 and that they call it ,taratouffli4 ,the name ,potato was1 in ,england1 previously applied to the ,sweet ,potato 7,convolvulus batatas71 which was the common ,potato1 in distinction to the ,virginian ,potato1 at the time of ,gerard's ,herbal4 7#aeig87 ,gerard's figures of both plants are copied from those of ,clusius4 ,it may be seen by the description of ,arachidna1 already quoted from ,theophrastus1 7above17 that there is little plausibility in ,clusius's conjecture of the plant being known to the ancients4 ,i need not inform the botanist that this opinion is untenable4 ,the addition of exotic species to the number of known plants was indeed going on rapidly during the interval which we are now considering4 ,francis ,hernandez1 a ,spaniard1 who visited ,america towards the end of the sixteenth century1 collected and described many plants of that country1 some of which were afterwards published by ,recchi4#eiaf ,barnabas ,cobo1 who went as a missionary to ,america in #aeif1 also described plants4#fjaf ,the ,dutch1 among other exertions which they made in their struggle with the tyranny of ,spain1 sent out an expedition which1 for a time1 conquered the ,brazils2 and among other fruits of this conquest1 they published an account of the natural history of the country4#faaf ,to avoid interrupting the connexion of such labors1 ,i will here carry them on a little further in the order of time4 ,paul ,herman1 of ,halle1 in ,saxony1 went to the ,cape of ,good ,hope and to ,ceylon2 and on his return1 astonished the botanists of ,europe by the vast quantity of remarkable plants which he introduced to their knowledge4#fbaf ,rheede1 the ,dutch governor of ,malabar1 ordered descriptions and drawings to be made of many curious species1 which were published in a large work in twelve folio volumes4#fcaf ,rumphe1 another ,dutch consul at ,amboyna1#fdaf labored with zeal and success upon the plants of the ,moluccas4 ,some species which occur in ,madagascar figured in a description of that island composed by the ,french ,commandant ,flacourt4#feaf ,shortly afterwards1 ,engelbert ,kmpfer1#ffaf a ,westphalian of great acquirements and undaunted courage1 visited ,persia1 ,arabia ,felix1 the ,mogul ,empire1 ,ceylon1 ,bengal1 ,sumatra1 ,java1 ,siam1 ,japan2 ,wheler travelled in ,greece and ,asia ,minor2 and ,sherard1 the ,english consul1 published an account of the plants of the neighborhood of ,smyrna4 #chj ,note #eiaf3 ,nova ,plantarum ,regni ,mexicana ,historia1 ,rom4 #afea1 fol4 ,note #fjaf3 ,sprengel1 ,gesch4 der ,botanik1 ii4 #fb4 ,note #faaf3 ,historia ,naturalis ,brasili1 ,l4 ,b4 #afdh1 fol4 7,piso and ,maregraf74 ,note #fbaf3 ,museum ,zeylanicum1 ,l4 ,b4 #agbf4 ,note #fcaf3 ,hortus ,malabaricus1 #afgj-agjc4 ,note #fdaf3 ,herbarium ,amboinense1 ,amsterdam1 #agda-ea1 fol4 ,note #feaf3 ,histoire de la grande ,isle ,madagascar1 ,paris1 #affa4 ,note #ffaf3 ,amnitates ,exotic1 ,lemgov4 #agab4 #dto4 ,at the same time1 the ,new ,world excited also the curiosity of botanists4 ,hans ,sloane collected the plants of ,jamaica2 ,john ,banister those of ,virginia2 ,william ,vernon1 also an ,englishman1 and ,david ,kriege1 a ,saxon1 those of ,maryland2 two ,frenchmen1 ,surian and ,father ,plumier1 those of ,saint ,domingo4 ,we may add that public botanical gardens were about this time established all over ,europe4 ,we have already noticed the institution of that of ,pisa in #aedc2 the second was that of ,padua in #aede2 the next1 that of ,florence in #aeef2 the fourth1 that of ,bologna1 #aefh2 that of ,rome1 in the ,vatican1 dates also from #aefh4 ,the first transalpine garden of this kind arose at ,leyden in #aegg2 that of ,leipzig in #aehj4 ,henry the ,fourth of ,france established one at ,montpellier in #aeig4 ,several others were instituted in ,germany2 but that of ,paris did not begin to exist till #afbf2 that of ,upsal1 afterwards so celebrated1 took its rise in #afeg1 that of ,amsterdam in #afhd4 ,morison1 whom we shall soon have to mention1 calls himself1 in #afhj1 the first ,director of the ,botanical ,garden at ,oxford4 #bnd ,ed4 ,to what is above said of ,botanical ,gardens and ,botanical ,writers1 between the times of ,csalpinus and ,morison1 ,i may add a few circumstances4 ,the first academical garden in ,france was that at ,montpellier1 which was established by ,peter ,richier de ,belleval1 at the end of the sixteenth century4 ,about the same period1 rare flowers were cultivated at ,paris1 and pictures of them made1 in order to supply the embroiderers of the court-robes with new patterns4 ,thus figures of the most beautiful flowers in the garden of ,peter ,robins were published by the court-embroiderer ,peter ,vallet1 in #afjh1 under the title of ,le ,jardin du ,roi ,henry ,,iv4 ,but ,robins' works were of great service to botany2 and his garden assisted the studies of ,renealmus 7,paul ,reneaulme71 whose ,specimen ,histori ,plantarum 7,paris1 #afaa71 is highly spoken of by the best botanists4 ,recently1 ,mr4 ,robert ,brown has named after him a new genus of ,iride 7,,renealmia72 adding1 ,dixi in memoriam ,,pauli ,,renealmi1 botanici sui vi accuratissimi1 atque staminum primi scrutatoris2 qui non modo eorum numerum et situm1 sed etiam filamentorum proportionem passim descripsit1 et characterem tetradynamicum siliquosarum perspexit4 7,prodromus ,flor ,nov ,hollandi1 p4 #ddh47 ,the oldest ,botanical ,garden in ,england is that at ,hampton ,court1 founded by ,queen ,elizabeth1 and much enriched by ,charles ,,ii4 and ,william ,,iii4 7,sprengel1 ,gesch4 d4 ,bot4 vol4 ii4 p4 #if47 ,in the mean time1 although there appeared no new system which #cha commanded the attention of the botanical world1 the feeling of the importance of the affinities of plants became continually more strong and distinct4 ,lobel1 who was botanist to ,james the ,first1 and who published his ,stirpium ,adversaria ,nova in #aega1 brings together the natural families of plants more distinctly than his predecessors1 and even distinguishes 7as ,cuvier states1#fgaf7 monocotyledonous from dicotyledonous plants2 one of the most comprehensive division-lines of botany1 of which succeeding times discovered the value more completely4 ,fabius ,columna1#fhaf in #afaf1 gave figures of the fructification of plants on copper1 as ,gessner had before done on wood4 ,but the elder ,bauhin 7,john71 notwithstanding all that ,csalpinus had done1 retrograded1 in a work published in #afai1 into the less precise and scientific distinctions of--trees with nuts2 with berries2 with acorns2 with pods2 creeping plants1 gourds1 c43 and no clear progress towards a system was anywhere visible among the authors of this period4 ,note #fgaf3 ,cuv4 ,leons1 c4 #aih4 ,note #fhaf3 ,ib4 #bjf4 ,while this continued to be the case1 and while the materials1 thus destitute of order1 went on accumulating1 it was inevitable that the evils which ,csalpinus had endeavored to remedy1 should become more and more grievous4 ,the nomenclature of the subject#fiaf was in such disorder1 it was so impossible to determine with certainty the plants spoken of by preceding writers1 that thirty or forty different botanists had given to the same plant almost as many different names4 ,bauhin called by one appellation1 a species which ,lobel or ,matheoli designated by another4 ,there was an actual chaos1 a universal confusion1 in which it was impossible for men to find their way4 ,we can the better understand such a state of things1 from having1 in our own time1 seen another classificatory science1 ,mineralogy1 in the very condition thus described4 ,for such a state of confusion there is no remedy but the establishment of a true system of classification2 which by its real foundation renders a reason for the place of each species2 and which1 by the fixity of its classes1 affords a basis for a standard nomenclature1 as finally took place in ,botany4 ,but before such a remedy is obtained1 men naturally try to alleviate the evil by tabulating the synonyms of different writers1 as far as they are able to do so4 ,the task of constructing such a ,synonymy of botany at the period of which we speak1 was undertaken by ,gaspard ,bauhin1 the brother of ,john1 but nineteen years younger4 ,this work1 the ,pinax ,theatri ,botanici1 was printed #chb at ,basil in #afbc4 ,it was a useful undertaking at the time2 but the want of any genuine order in the ,pinax itself1 rendered it impossible that it should be of great permanent utility4 ,note #fiaf3 ,ib4 #bab4 ,after this period1 the progress of almost all the sciences became languid for a while2 and one reason of this interruption was1 the wars and troubles which prevailed over almost the whole of ,europe4 ,the quarrels of ,charles the ,first and his parliament1 the civil wars and the usurpation1 in ,england2 in ,france1 the war of the ,league1 the stormy reign of ,henry the ,fourth1 the civil wars of the minority of ,louis the ,thirteenth1 the war against the ,protestants and the war of the ,fronde in the minority of ,louis the ,fourteenth2 the bloody and destructive ,thirty ,years' ,war in ,germany2 the war of ,spain with the ,united ,provinces and with ,portugal2--all these dire agitations left men neither leisure nor disposition to direct their best thoughts to the promotion of science4 ,the baser spirits were brutalized2 the better were occupied by high practical aims and struggles of their moral nature4 ,amid such storms1 the intellectual powers of man could not work with their due calmness1 nor his intellectual objects shine with their proper lustre4 ,at length a period of greater tranquillity gleamed forth1 and the sciences soon expanded in the sunshine4 ,botany was not inert amid this activity1 and rapidly advanced in a new direction1 that of physiology2 but before we speak of this portion of our subject1 we must complete what we have to say of it as a classificatory science4 ,sect4 #d4--,sequel to the ,epoch of ,csalpinus4 ,further ,formation and ,adoption of ,systematic ,arrangement4 ,,soon after the period of which we now speak1 that of the restoration of the ,stuarts to the throne of ,england1 systematic arrangements of plants appeared in great numbers2 and in a manner such as to show that the minds of botanists had gradually been ripening for this improvement1 through the influence of preceding writers1 and the growing acquaintance with plants4 ,the person whose name is usually placed first on this list1 ,robert ,morison1 appears to me to be much less meritorious than many of those who published very shortly after him2 but ,i will give him the precedence in my narrative4 ,he was a ,scotchman1 who was wounded fighting on the royalist side in the civil wars of ,england4 ,on the triumph of the republicans1 he withdrew to ,france1 when he became director of the garden of ,gaston1 ,duke of ,orlans at ,blois2 and there he came under the notice of our ,charles #chc the ,second2 who1 on his restoration1 summoned ,morison to ,england1 where he became ,superintendent of the ,royal ,gardens1 and also of the ,botanic ,garden at ,oxford4 ,in #affi1 he published ,remarks on the ,mistakes of the two ,bauhins1 in which he proves that many plants in the ,pinax are erroneously placed1 and shows considerable talent for appreciating natural families and genera4 ,his great systematic work appeared from the ,university press at ,oxford in #afhj4 ,it contains a system1 but a system1 ,cuvier says1#gjaf which approaches rather to a natural method than to a rigorous distribution1 like that of his predecessor ,csalpinus1 or that of his successor ,ray4 ,thus the herbaceous plants are divided into climbers1 leguminous1 siliquose1 unicapsalar1 bicapsular1 tricapsular1 quadricapsular1 quinquecapsular2 this division being combined with characters derived from the number of petals4 ,but along with these numerical elements1 are introduced others of a loose and heterogeneous kind1 for instance1 the classification of herbs as lactescent and emollient4 ,it is not unreasonable to say1 that such a scheme shows no talent for constructing a complete system2 and that the most distinct part of it1 that dependent on the fruit1 was probably borrowed from ,csalpinus4 ,that this is so1 we have1 ,i think1 strong proof2 for though ,morison nowhere1 ,i believe1 mentions ,csalpinus1 except in one place in a loose enumeration of botanical writers1#gaaf he must have made considerable use of his work4 ,for he has introduced into his own preface a passage copied literally#gbaf from the dedication of ,csalpinus2 which passage we have already quoted 7p4 #cgd17 beginning1 ,since all science consists in the collection of similar1 and the distinction of dissimilar things4 ,and that the mention of the original is not omitted by accident1 appears from this2 that ,morison appropriates also the conclusion of the passage1 which has a personal reference1 ,conatus sum id prstare in universa plantarum historia1 ut si quid pro ingenii mei tenuitate in hujusmodi studio profecerim1 ad communem utilitatem proferrem4 ,that ,morison1 thus1 at so long an interval after the publication of the work of ,csalpinus1 borrowed from him without acknowledgement1 and adopted his system so as to mutilate it1 proves that he had neither the temper nor the talent of a discoverer2 and justifies us withholding from him the credit which belongs to those1 who1 in his time1 resumed the great undertaking of constructing a vegetable system4 ,note #gjaf3 ,cuv4 ,leons1 c4 p4 #dhf4 ,note #gaaf3 ,pref4 p4 i4 ,note #gbaf3 ,ib4 p4 ii4 ,among those whose efforts in this way had the greatest and earliest #chd influence1 was undoubtedly our countryman1 ,john ,ray1 who was ,fellow of ,trinity ,college1 ,cambridge1 at the same time with ,isaac ,newton4 ,but though ,cuvier states#gcaf that ,ray was the model of the systematists during the whole of the eighteenth century1 the ,germans claim a part of his merit for one of their countrymen1 ,joachim ,jung1 of ,lubeck1 professor at ,hamburg4#gdaf ,concerning the principles of this botanist1 little was known during his life4 ,but a manuscript of his book was communicated#geaf to ,ray in #affj1 and from this time forwards1 says ,sprengel1 there might be noticed in the writings of ,englishmen1 those better and clearer views to which ,jung's principles gave birth4 ,five years after the death of ,jung1 his ,doxoscopia ,physica was published1 in #affb2 and in #afgh1 his ,isagoge ,phytoscopica4 ,but neither of these works was ever much read2 and even ,linnus1 whom few things escaped which concerned botany1 had1 in #agga1 seen none of ,jung's works4 ,note #gcaf3 ,leons ,hist4 ,sc4 p4 #dhg4 ,note #gdaf3 ,sprengel1 ii4 #bg4 ,note #geaf3 ,ray acknowledges this in his ,index ,plant4 ,agri ,cantab4 p4 #hg1 and quotes from it the definition of caulis4 ,i here pass over ,jung's improvements of botanical language1 and speak only of those which he is asserted to have suggested in the arrangement of plants4 ,he examines1 says ,sprengel1#gfaf the value of characters of species1 which1 he holds1 must not be taken from the thorns1 nor from color1 taste1 smell1 medicinal effects1 time and place of blossoming4 ,he shows1 in numerous examples1 what plants must be separated1 though called by a common name1 and what most be united1 though their names are several4 ,note #gfaf3 ,sprengel1 ii4 #bi4 ,i do not see in this much that interferes with the originality of ,ray's method1#ggaf of which1 in consequence of the importance ascribed to it by ,cuvier1 as we have already seen1 ,i shall give an account1 following that great naturalist4#ghaf ,i confine myself to the ordinary plants1 and omit the more obscure vegetables1 as mushrooms1 mosses1 ferns1 and the like4 ,note #ggaf3 ,methodus ,plantarum ,nova1 #afhb4 ,historia ,plantarum1 #afhf4 ,note #ghaf3 ,cuv4 ,leons ,hist4 ,sc4 #dhh4 ,such plants are composite or simple4 ,the composite flowers are those which contain many florets in the same calyx4#giaf ,these are subdivided according as they are composed altogether of complete florets1 #che or of half florets1 or of a centre of complete florets1 surrounded by a circumference or ray of demi-florets4 ,such are the divisions of the corymbifer1 or composit4 ,note #giaf3 ,involucrum1 in modern terminology4 ,in the simple flowers1 the seeds are naked1 or in a pericarp4 ,those with naked seeds are arranged according to the number of the seeds1 which may be one1 two1 three1 four1 or more4 ,if there is only one1 no subdivision is requisite3 if there are two1 ,ray makes a subdivision1 according as the flower has five petals1 or a continuous corolla4 ,here we come to several natural families4 ,thus1 the flowers with two seeds and five petals are the ,umbelliferous plants2 the monopetalous flowers with two seeds are the ,stellat4 ,he founds the division of four-seeded flowers on the circumstance of the leaves being opposite1 or alternate2 and thus again1 we have the natural families of ,asperifoli1 as ,echium1 c41 which have the leaves alternate1 and the ,verticillat1 as ,salvia1 in which the leaves are opposite4 ,when the flower has more than four seeds1 he makes no subdivision4 ,so much for simple flowers with naked seeds4 ,in those where the seeds are surrounded by a pericarp1 or fruit1 this fruit is large1 soft1 and fleshy1 and the plants are pomiferous2 or it is small and juicy1 and the fruit is a berry1 as a ,gooseberry4 ,if the fruit is not juicy1 but dry1 it is multiple or simple4 ,if it be simple1 we have the leguminose plants4 ,if it be multiple1 the form of the flower is to be attended to4 ,the flower may be monopetalous1 or tetrapetalous1 or pentapetalous1 or with still more divisions4 ,the monopetalous may be regular or irregular2 so may the tetrapetalous4 ,the regular tetrapetalous flowers are1 for example1 the ,crucifer1 as ,stock and ,cauliflower2 the irregular1 are the papilionaceous plants1 ,peas1 ,beans1 and ,vetches2 and thus we again come to natural families4 ,the remaining plants are divided in the same way1 into those with imperfect1 and those with perfect1 flowers4 ,those with imperfect flowers are the ,grasses1 the ,rushes 7,junci71 and the like2 among those with perfect flowers1 are the ,palmace1 and the ,liliace4 ,we see that the division of plants is complete as a system2 all flowers must belong to one or other of the divisions4 ,fully to explain the characters and further subdivisions of these families1 would be to write a treatise on botany2 but it is easily seen that they exhaust the subject as far as they go4 ,thus ,ray constructed his system partly on the fruit and partly on the flower2 or more properly1 according to the expression of ,linnus1 #chf comparing his earlier with his later system1 he began by being a fructicist1 and ended by being a corollist4#hjaf ,note #hjaf3 ,ray was a most industrious herbalizer1 and ,i cannot understand on what ground ,mirbel asserts 7,physiol4 ,veg41 tom4 ii4 p4 #eca17 that he was better acquainted with books than with plants4 ,as we have said1 a number of systems of arrangement of plants were published about this time1 some founded on the fruit1 some on the corolla1 some on the calyx1 and these employed in various ways4 ,rivinus#haaf 7whose real name was ,bachman17 classified by the flower alone2 instead of combining it with the fruit1 as ,ray had done4#hbaf ,he had the further merit of being the first who rejected the old division1 of woody and herbaceous plants2 a division which1 though at variance with any system founded upon the structure of the plants was employed even by ,tournefort1 and only finally expelled by ,linnus4 ,note #haaf3 ,cuv4 ,leons1 #dia4 ,note #hbaf3 ,historia ,generalis ad rem ,herbariam1 #afij4 ,it would throw little light upon the history of botany1 especially for our purpose1 to dwell on the peculiarities of these transitory systems4 ,linnus1#hcaf after his manner1 has given a classification of them4 ,rivinus1 as we have just seen1 was a corollist1 according to the regularity and number of the petals2 ,hermann was a fructicist4 ,christopher ,knaut#hdaf adopted the system of ,ray1 but inverted the order of its parts2 ,christian ,knaut did nearly the same with regard to that of ,rivinus1 taking number before regularity in the flower4#heaf ,note #hcaf3 ,philos4 ,bot4 p4 #ba4 ,note #hdaf3 ,enumeratio ,plantarum1 c41 #afhg4 ,note #heaf3 ,linn4 ,of the systems which prevailed previous to that of ,linnus1 ,tournefort's was by far the most generally accepted4 ,joseph ,pitton de ,tournefort was of a noble family in ,provence1 and was appointed professor at the ,jardin du ,roi in #afhc4 ,his well-known travels in the ,levant are interesting on other subjects1 as well as botany4 ,his ,institutio ,rei ,herbari1 published in #agjj1 contains his method1 which is that of a corollist4 ,he is guided by the regularity or irregularity of the flowers1 by their form1 and by the situation of the receptacle of the seeds below the calyx1 or within it4 ,thus his classes are--those in which the flowers are campaniform1 or bell-shaped2 those in which they are infundibuliform1 or funnel-shaped1 as ,tobacco2 then the irregular flowers1 as the ,personat1 which resemble an ancient mask2 the ,labiat1 with their two lips2 the ,cruciform2 the ,rosace1 with flowers like a rose2 the ,umbellifer2 the ,caryophylle1 as the #chg ,pink2 the ,liliace1 with six petals1 as the ,tulip1 ,narcissus1 ,hyacinth1 ,lily2 the ,papilionace1 which are leguminous plants1 the flower of which resembles a butterfly1 as ,peas and ,beans2 and finally1 the ,anomalous1 as ,violet1 ,nasturtium1 and others4 ,though this system was found to be attractive1 as depending1 in an evident way1 on the most conspicuous part of the plant1 the flower1 it is easy to see that it was much less definite than systems like that of ,rivinus1 ,hermann1 and ,ray1 which were governed by number4 ,but ,tournefort succeeded in giving to the characters of genera a degree of rigor never before attained1 and abstracted them in a separate form4 ,we have already seen that the reception of botanical ,systems has depended much on their arrangement into ,genera4 ,tournefort's success was also much promoted by the author inserting in his work a figure of a flower and fruit belonging to each genus2 and the figures1 drawn by ,aubriet1 were of great merit4 ,the study of botany was thus rendered easy1 for it could be learned by turning over the leaves of a book4 ,in spite of various defects1 these advantages gave this writer an ascendancy which lasted1 from #agjj1 when his book appeared1 for more than half a century4 ,for though ,linnus began to publish in #agce1 his method and his nomenclature were not generally adopted till #agfj4 ,,chapter ,,iv4 ,,the ,,reform ,,of ,,linn,,us4 ,sect4 #a4--;,introduction of the ,reform4 ,,although1 perhaps1 no man of science ever exercised a greater sway than ,linnus1 or had more enthusiastic admirers1 the most intelligent botanists always speak of him1 not as a great discoverer1 but as a judicious and strenuous ,reformer4 ,indeed1 in his own lists of botanical writers1 he places himself among the ,reformatores2 and it is apparent that this is the nature of his real claim to admiration2 for the doctrine of the sexes of plants1 even if he had been the first to establish it1 was a point of botanical physiology1 a province of the #chh science which no one would select as the peculiar field of ,linnus's glory2 and the formation of a system of arrangement on the basis of this doctrine1 though attended with many advantages1 was not an improvement of any higher order than those introduced by ,ray and ,tournefort4 ,but as a ,reformer of the state of ,natural ,history in his time1 ,linnus was admirable for his skill1 and unparalleled in his success4 ,and we have already seen1 in the instance of the reform of mineralogy1 as attempted by ,mohs and ,berzelius1 that men of great talents and knowledge may fail in such an undertaking4 ,it is1 however1 only by means of the knowledge which he displays1 and of the beauty and convenience of the improvements which he proposes1 that any one can acquire such an influence as to procure his suggestions to be adopted4 ,and even if original circumstances of birth or position could invest any one with peculiar prerogatives and powers in the republic of science1 ,karl ,linn began his career with no such advantages4 ,his father was a poor curate in ,smaland1 a province of ,sweden2 his boyhood was spent in poverty and privation2 it was with great difficulty that1 at the age of twenty-one1 he contrived to subsist at the ,university of ,upsal1 whither a strong passion for natural history had urged him4 ,here1 however1 he was so far fortunate1 that ,olaus ,rudbeck1 the professor of botany1 committed to him the care of the ,botanic ,garden4#hfaf ,the perusal of the works of ,vaillant and ,patrick ,blair suggested to him the idea of an arrangement of plants1 formed upon the sexual organs1 the stamens and pistils2 and of such an arrangement he published a sketch in #agca1 at the age of twenty-four4 ,note #hfaf3 ,sprengel1 ii4 #bcb4 ,but we must go forwards a few years in his life1 to come to the period to which his most important works belong4 ,university and family quarrels induced him to travel2 and1 after various changes of scene1 he was settled in ,holland1 as the curator of the splendid botanical garden of ,george ,clifford1 an opulent banker4 ,here it was#hgaf that he laid the foundation of his future greatness4 ,in the two years of his residence at ,harlecamp1 he published nine works4 ,the first1 the ,systema ,natur1 which contained a comprehensive sketch of the whole domain of ,natural ,history1 excited general astonishment1 by the acuteness of the observations1 the happy talent of combination1 and the clearness of the systematic views4 ,such a work could not fail to procure considerable respect for its author4 ,his ,hortus ,cliffortiana #chi and ,musa ,cliffortiana added to this impression4 ,the weight which he had thus acquired1 he proceeded to use for the improvement of botany4 ,his ,fundamenta ,botanica and ,bibliotheca ,botanica appeared in #agcf2 his ,critica ,botanica and ,genera ,plantarum in #agcg2 his ,classes ,plantarum in #agch2 his ,species ,plantarum was not published till #agec2 and all these works appeared in many successive editions1 materially modified4 ,note #hgaf3 ,ibid4 #bcd4 ,this circulation of his works showed that his labors were producing their effect4 ,his reputation grew2 and he was soon enabled to exert a personal1 as well as a literary1 influence1 on students of natural history4 ,he became ,botanist ,royal1 ,president of the ,academy of ,sciences at ,stockholm1 and ,professor in the ,university of ,upsal2 and this office he held for thirty-six years with unrivalled credit2 exercising1 by means of his lectures1 his constant publications1 and his conversation1 an extraordinary power over a multitude of zealous naturalists1 belonging to every part of the world4 ,in order to understand more clearly the nature and effect of the reforms introduced by ,linnus into botany1 ,i shall consider them under the four following heads2--,terminology1 ,nomenclature1 ,artificial ,system1 and ,natural ,system4 ,sect4 #b4--,linnan ,reform of ,botanical ,terminology4 ,,it must be recollected that ,i designate as ,terminology1 the system of terms employed in the description of objects of natural history2 while by ,nomenclature1 ,i mean the collection of the names of species4 ,the reform of the descriptive part of botany was one of the tasks first attempted by ,linnus2 and his terminology was the instrument by which his other improvements were effected4 ,though most readers1 probably1 entertain1 at first1 a persuasion that a writer ought to content himself with the use of common words in their common sense1 and feel a repugnance to technical terms and arbitrary rules of phraseology1 as pedantic and troublesome2 it is soon found1 by the student of any branch of science that1 without technical terms and fixed rules1 there can be no certain or progressive knowledge4 ,the loose and infantine grasp of common language cannot hold objects steadily enough for scientific examination1 or lift them from one stage of generalization to another4 ,they must be secured by the rigid mechanism of a scientific phraseology4 ,this necessity had been felt in all the sciences1 from the earliest periods of their progress4 ,but the #cij conviction had never been acted upon so as to produce a distinct and adequate descriptive botanical language4 ,jung1 indeed1#hhaf had already attempted to give rules and precepts which should answer this purpose2 but it was not till the ,fundamenta ,botanica appeared1 that the science could be said to possess a fixed and complete terminology4 ,note #hhaf3 ,isagoge ,phytoscopica1 #afgi4 ,to give an account of such a terminology1 is1 in fact1 to give a description of a dictionary and grammar1 and is therefore what cannot here be done in detail4 ,linnus's work contains about a thousand terms of which the meaning and application are distinctly explained2 and rules are given1 by which1 in the use of such terms1 the botanist may avoid all obscurity1 ambiguity1 unnecessary prolixity and complexity1 and even inelegance and barbarism4 ,of course the greater part of the words which ,linnus thus recognized had previously existed in botanical writers2 and many of them had been defined with technical precision4 ,thus ,jung#hiaf had already explained what was a composite1 what a pinnate leaf2 what kind of a bunch of flowers is a spike1 a panicle1 an umbel1 a corymb1 respectively4 ,linnus extended such distinctions1 retaining complete clearness in their separation4 ,thus1 with him1 composite leaves are further distinguished as digitate1 pinnate1 bipinnate1 pedate1 and so on2 pinnate leaves are abruptly so1 or with an odd one1 or with a tendril2 they are pinnate oppositely1 alternately1 interruptedly1 articulately1 decursively4 ,again1 the inflorescence1 as the mode of assemblage of the flowers is called1 may be a tuft 7fasciculus71 a head 7capitulum71 a cluster 7racemus71 a bunch 7thyrsus71 a panicle1 a spike1 a catkin 7amentum71 a corymb1 an umbel1 a cyme1 a whorl 7verticillus74 ,and the rules which he gives1 though often apparently arbitrary and needless1 are found1 in practice1 to be of great service by their fixity and connexion4 ,by the good fortune of having had a teacher with so much delicacy of taste as ,linnus1 in a situation of so much influence1 ,botany possesses a descriptive language which will long stand as a model for all other subjects4 ,note #hiaf3 ,sprengel1 ii4 #bh4 ,it may1 perhaps1 appear to some persons1 that such a terminology as we have here described must be enormously cumbrous2 and that1 since the terms are arbitrarily invested with their meaning1 the invention of them requires no knowledge of nature4 ,with respect to the former doubt1 we may observe1 that technical description is1 in reality1 the only description which is clearly intelligible2 but that technical language cannot be understood without being learnt as any other #cia language is learnt2 that is1 the reader must connect the terms immediately with his own sensations and notions1 and not mediately1 through a verbal explanation2 he must not have to guess their meaning1 or to discover it by a separate act of interpretation into more familiar language as often as they occur4 ,the language of botany must be the botanist's most familiar tongue4 ,when the student has thus learnt to think in botanical language1 it is no idle distinction to tell him that a bunch of grapes is not a cluster2 that is1 a thyrsus not a raceme4 ,and the terminology of botany is then felt to be a useful implement1 not an oppressive burden4 ,it is only the schoolboy that complains of the irksomeness of his grammar and vocabulary4 ,the accomplished student possesses them without effort or inconvenience4 ,as to the other question1 whether the construction of such a botanical grammar and vocabulary implies an extensive and accurate acquaintance with the facts of nature1 no one can doubt who is familiar with any descriptive science4 ,it is true1 that a person might construct an arbitrary scheme of distinctions and appellations1 with no attention to natural objects2 and this is what shallow and self-confident persons often set about doing1 in some branch of knowledge with which they are imperfectly acquainted4 ,but the slightest attempt to use such a phraseology leads to confusion2 and any continued use of it leads to its demolition4 ,like a garment which does not fit us1 if we attempt to work in it we tear it in pieces4 ,the formation of a good descriptive language is1 in fact1 an inductive process of the same kind as those which we have already noticed in the progress of natural history4 ,it requires the discovery of fixed characters1 which discovery is to be marked and fixed1 like other inductive steps1 by appropriate technical terms4 ,the characters must be so far fixed1 that the things which they connect must have a more permanent and real association than the things which they leave unconnected4 ,if one bunch of grapes were really a racemus1 and another a thyrsus1 according to the definition of these terms1 this part of the ,linnan language would lose its value2 because it would no longer enable us to assert a general proposition with respect to one kind of plants4 ,sect4 #c4--,linnan ,reform of ,botanical ,nomenclature4 ,,in the ancient writers each recognized kind of plants had a distinct name4 ,the establishment of ,genera led to the practice of designating #cib ,species by the name of the genus1 with the addition of a phrase to distinguish the species4 ,these phrases1 7expressed in ,latin in the ablative case17 were such as not only to mark1 but to describe the species1 and were intended to contain such features of the plant as were sufficient to distinguish it from others of the same genus4 ,but in this way the designation of a plant often became a long and inconvenient assemblage of words4 ,thus different kinds of ,rose were described as1 ,rosa campestris1 spinis carens1 biflora 7,rosa alpina47 ,rosa aculeata1 foliis odoratis subtus rubiginosis 7,r4 eglanteria47 ,rosa carolina fragrans1 foliis medio tenus serratis 7,r4 carolina47 ,rosa sylvestris vulgaris1 flore odorato incarnato 7,r4 canina47 ,and several others4 ,the prolixity of these appellations1 their variety in every different author1 the insufficiency and confusion of the distinctions which they contained1 were felt as extreme inconveniences4 ,the attempt of ,bauhin to remedy this evil by a ,synonymy1 had1 as we have seen1 failed at the time1 for want of any directing principle2 and was become still more defective by the lapse of years and the accumulation of fresh knowledge and new books4 ,haller had proposed to distinguish the species of each genus by the numbers #a1 #b1 #c1 and so on2 but botanists found that their memory could not deal with such arbitrary abstractions4 ,the need of some better nomenclature was severely felt4 ,the remedy which ,linnus finally introduced was the use of trivial names2 that is1 the designation of each species by the name of the genus along with a single conventional word1 imposed without any general rule4 ,such names are added above in parentheses1 to the specimens of the names previously in use4 ,but though this remedy was found to be complete and satisfactory1 and is now universally adopted in every branch of natural history1 it was not one of the reforms which ,linnus at first proposed4 ,perhaps he did not at first see its full value2 or1 if he did1 we may suppose that it required more self-confidence than he possessed1 to set himself to introduce and establish ten thousand new names in the botanical world4 ,accordingly1 the first attempts of ,linnus at the improvement of the nomenclature of botany were1 the proposal of fixed and careful rules for the generic name1 and for the descriptive phrase4 ,thus1 in his ,critica ,botanica1 he gives many precepts concerning the selection of the names of #cic genera1 intended to secure convenience or elegance4 ,for instance1 that they are to be single words2#ijaf he substitutes atropa for bella donna1 and leontodon for dens leonis2 that they are not to depend upon the name of another genus1#iaaf as acriviola1 agrimonoides2 that they are not#ibaf to be sesquipedalia2 and1 says he1 any word is sesquipedalian to me1 which has more than twelve letters1 as kalophyllodendron1 for which he substitutes calophyllon4 ,though some of these rules may seem pedantic1 there is no doubt that1 taken altogether1 they tend exceedingly1 like the labors of purists in other languages1 to exclude extravagance1 caprice1 and barbarism in botanical speech4 ,note #ijaf3 ,phil4 ,bot4 #bbd4 ,note #iaaf3 ,ib4 #bbh1 #bbi4 ,note #ibaf3 ,ib4 #beb4 ,the precepts which he gives for the matter of the descriptive phrase1 or1 as it is termed in the language of the ,aristotelian logicians1 the differentia1 are1 for the most part1 results of the general rule1 that the most fixed characters which can be found are to be used2 this rule being interpreted according to all the knowledge of plants which had then been acquired4 ,the language of the rules was1 of course1 to be regulated by the terminology1 of which we have already spoken4 ,thus1 in the ,critica ,botanica1 the name of a plant is considered as consisting of a generic word and a specific phrase2 and these are1 he says1#icaf the right and left hands of the plant4 ,but he then speaks of another kind of name2 the trivial name1 which is opposed to the scientific4 ,such names were1 he says1#idaf those of his predecessors1 and especially of the most ancient of them4 ,hitherto#ieaf no rules had been given for their use4 ,he manifestly1 at this period1 has small regard for them4 ,yet1 he says1 trivial names may1 perhaps1 be used on this account1--that the differentia often turns out too long to be convenient in common use1 and may require change as new species are discovered4 ,however1 he continues1 in this work we set such names aside altogether1 and attend only to the differenti4 ,note #icaf3 ,ib4 #bff4 ,note #idaf3 ,ib4 #bfa4 ,note #ieaf3 ,ib4 #bfj4 ,even in the ,species ,plantarum1 the work which gave general currency to these trivial names1 he does not seem to have yet dared to propose so great a novelty4 ,they only stand in the margin of the work4 ,i have placed them there1 he says in his ,preface1 that1 without circumlocution1 we may call every herb by a single name2 ,i have done this without selection1 which would require more time4 ,and ,i beseech all sane botanists to avoid most religiously ever #cid proposing a trivial name without a sufficient specific distinction1 lest the science should fall into its former barbarism4 ,it cannot be doubted1 that the general reception of these trivial names of ,linnus1 as the current language among botanists1 was due1 in a very great degree1 to the knowledge1 care1 and skill with which his characters1 both of genera and of species1 were constructed4 ,the rigorous rules of selection and expression which are proposed in the ,fundamenta ,botanica and ,critica ,botanica1 he himself conformed to2 and this scrupulosity was employed upon the results of immense labor4 ,in order that ,i might make myself acquainted with the species of plants1 he says1 in the preface to his work upon them1 ,i have explored the ,alps of ,lapland1 the whole of ,sweden1 a part of ,norway1 ,denmark1 ,germany1 ,belgium1 ,england1 ,france3 ,i have examined the ,botanical ,gardens of ,paris1 ,oxford1 ,chelsea1 ,harlecamp1 ,leyden1 ,utrecht1 ,amsterdam1 ,upsal1 and others3 ,i have turned over the ,herbals of ,burser1 ,hermann1 ,clifford1 ,burmann1 ,oldenland1 ,gronovius1 ,royer1 ,sloane1 ,sherard1 ,bobart1 ,miller1 ,tournefort1 ,vaillant1 ,jussieu1 9999,surian1 ,beck1 ,brown1 c43 my dear disciples have gone to distant lands1 and sent me plants from thence2 ,kerlen to ,canada1 ,hasselquist to ,egypt1 ,asbech to ,china1 ,toren to ,surat1 ,solander to ,england1 ,alstrmer to ,southern ,europe1 ,martin to ,spitzbergen1 ,pontin to ,malabar1 ,khler to ,italy1 ,forskhl to the ,east1 ,lfling to ,spain1 ,montin to ,lapland3 my botanical friends have sent me many seeds and dried plants from various countries3 ,lagerstrm many from the ,east ,indies2 ,gronovius most of the ,virginian2 ,gmelin all the ,siberian2 ,burmann those of the ,cape4 ,and in consistency with this habit of immense collection of materials1 is his maxim1#ifaf that a person is a better botanist in proportion as he knows more species4 ,it will easily be seen that this maxim1 like ,newton's declaration that discovery requires patient thought alone1 refers only to the exertions of which the man of genius is conscious2 and leaves out of sight his peculiar endowments1 which he does not see because they are part of his power of vision4 ,with the taste for symmetry which dictated the ,critica ,botanica1 and the talent for classification which appears in the ,genera ,plantarum1 and the ,systema ,natur1 a person must undoubtedly rise to higher steps of classificatory knowledge and skill1 as he became acquainted with a greater number of facts4 ,note #ifaf3 ,phil4 ,bot4 #bei4 ,the acknowledged superiority of ,linnus in the knowledge of the #cie matter of his science1 induced other persons to defer to him in what concerned its form2 especially when his precepts were1 for the most part1 recommended strongly both by convenience and elegance4 ,the trivial names of the ,species ,plantarum were generally received2 and though some of the details may have been altered1 the immense advantage of the scheme ensures its permanence4 ,sect4 #d4--,linnus's ,artificial ,system4 ,,we have already seen1 that1 from the time of ,csalpinus1 botanists had been endeavoring to frame a systematic arrangement of plants4 ,all such arrangements were necessarily both artificial and natural3 they were artificial1 inasmuch as they depended upon assumed principles1 the number1 form1 and position of certain parts1 by the application of which the whole vegetable kingdom was imperatively subdivided2 they were natural1 inasmuch as the justification of this division was1 that it brought together those plants which were naturally related4 ,no system of arrangement1 for instance1 would have been tolerated which1 in a great proportion of cases1 separated into distant parts of the plan the different species of the same genus4 ,as far as the main body of the genera1 at least1 all systems are natural4 ,but beginning from this line1 we may construct our systems with two opposite purposes1 according as we endeavor to carry our assumed principle of division rigorously and consistently through the system1 or as we wish to associate natural families of a wider kind than genera4 ,the former propensity leads to an artificial1 the latter to a natural method4 ,each is a ,system of ,plants2 but in the first1 the emphasis is thrown on the former word of the title1 in the other1 on the latter4 ,the strongest recommendation of an artificial system1 7besides its approaching to a natural method17 is1 that it shall be capable of easy use2 for which purpose1 the facts on which it depends must be apparent in their relations1 and universal in their occurrence4 ,the system of ,linnus1 founded upon the number1 position1 and other circumstances of the stamina and pistils1 the reproductive organs of the plants1 possessed this merit in an eminent degree1 as far as these characters are concerned2 that is1 as far as the classes and orders4 ,in its further subdivision into genera1 its superiority was mainly due to the exact observation and description1 which we have already had to notice as talents which ,linnus peculiarly possessed4 ,the ,linnan system of plants was more definite than that of #cif ,tournefort1 which was governed by the corolla2 for number is more definite than irregular form4 ,it was more readily employed than any of those which depend on the fruit1 for the flower is a more obvious object1 and more easily examined4 ,still1 it can hardly be doubted1 that the circumstance which gave the main currency to the system of ,linnus was its physiological signification3 it was the ,sexual ,system4 ,the relation of the parts to which it directed the attention1 interested both the philosophical faculty and the imagination4 ,and when1 soon after the system had become familiar in our own country1 the poet of ,the ,botanic ,garden peopled the bell of every flower with ,nymphs and ,swains1 his imagery was felt to be by no means forced and far-fetched4 ,the history of the doctrine of the sexes of plants1 as a point of physiology1 does not belong to this place2 and the ,linnan system of classification need not be longer dwelt upon for our present purpose4 ,i will only explain a little further what has been said1 that it is1 up to a certain point1 a natural system4 ,several of ,linnus's classes are1 in a great measure1 natural associations1 kept together in violation of his own artificial rules4 ,thus the class ,diadelphia1 in which1 by the system1 the filaments of the stamina should be bound together in two parcels1 does1 in fact1 contain many genera which are monadelphous1 the filaments of the stamina all cohering so as to form one bundle only2 as in ,genista1 ,spartium1 ,anthyllis1 ,lupinus1 c4 ,and why is this violation of rule8 ,precisely because these genera all belong to the natural tribe of ,papilionaceous plants1 which the author of the system could not prevail upon himself to tear asunder4 ,yet in other cases ,linnus was true to his system1 to the injury of natural alliances1 as he was1 for instance1 in another portion of this very tribe of ,papilionace2 for there are plants which undoubtedly belong to the tribe1 but which have ten separate stamens2 and these he placed in the order ,decandria4 ,upon the whole1 however1 he inclines rather to admit transgression of art than of nature4 ,the reason of this inclination was1 that he rightly considered an artificial method as instrumental to the investigation of a natural one2 and to this part of his views we now proceed4 ,sect4 #e4--,linnus's ,views on a ,natural ,method4 ,,the admirers of ,linnus1 the ,english especially1 were for some time in the habit of putting his ,sexual ,system in opposition to the ,natural ,method1 which about the same time was attempted in ,france4 ,and #cig as they often appear to have imagined that the ultimate object of botanical methods was to know the name of plants1 they naturally preferred the ,swedish method1 which is excellent as a finder4 ,no person1 however1 who wishes to know botany as a science1 that is1 as a body of general truths1 can be content with making names his ultimate object4 ,such a person will be constantly and irresistibly led on to attempt to catch sight of the natural arrangement of plants1 even before he discovers1 as he will discover by pursuing such a course of study1 that the knowledge of the natural arrangement is the knowledge of the essential construction and vital mechanism of plants4 ,he will consider an artificial method as a means of arriving at a natural method4 ,accordingly1 however much some of his followers may have overlooked this1 it is what ,linnus himself always held and taught4 ,and though what he executed with regard to this object was but little1#igaf the distinct manner in which he presented the relations of an artificial and natural method1 may justly be looked upon as one of the great improvements which he introduced into the study of his science4 ,note #igaf3 ,the natural orders which he proposed are a bare enumeration of genera1 and have not been generally followed4 ,thus in the ,classes ,plantarum 7#agdg71 he speaks of the difficulty of the task of discovering the natural orders1 and of the attempts made by others4 ,yet1 he adds1 ,i too have labored at this1 have done something1 have much still to do1 and shall labor at the object as long as ,i live4 ,he afterwards proposed sixty-seven orders1 as the fragments of a natural method1 always professing their imperfection4#ihaf ,and in others of his works#iiaf he lays down some antitheses on the subject after his manner4 ,the natural orders teach us the nature of plants2 the artificial orders enable us to recognize plants4 ,the natural orders1 without a key1 do not constitute a ,method2 the ,method ought to be available without a master4 ,note #ihaf3 ,phil4 ,bot4 p4 #hj4 ,note #iiaf3 ,genera ,plantarum1 #agfd4 ,see ,prlect4 in ,ord4 ,nat4 p4 xlviii4 ,that extreme difficulty must attend the formation of a ,natural ,method1 may be seen from the very indefinite nature of the ,aphorisms upon this subject which ,linnus has delivered1 and which the best botanists of succeeding times have assented to4 ,such are these2--the ,natural ,orders must be formed by attention1 not to one or two1 but to all the parts of plants2--the same organs are of great importance in regulating the divisions of one part of the system1 and #cih of small importance in another part2#ajjaf--the ,character does not constitute the ,genus1 but the ,genus the ,character2--the ,character is necessary1 not to make the ,genus1 but to recognize it4 ,the vagueness of these maxims is easily seen2 the rule of attending to all the parts1 implies1 that we are to estimate their relative importance1 either by physiological considerations 7and these again lead to arbitrary rules1 as1 for instance1 the superiority of the function of nutrition to that of reproduction71 or by a sort of latent naturalist instinct1 which ,linnus in some passages seems to recognize4 ,the ,habit of a plant1 he says1#ajaaf must be secretly consulted4 ,a practised botanist will distinguish1 at the first glance1 the plants of different quarters of the globe1 and yet will be at a loss to tell by what mark he detects them4 ,there is1 ,i know not what look1--sinister1 dry1 obscure in ,african plants2 superb and elevated1 in the ,asiatic2 smooth and cheerful1 in the ,american2 stunted and indurated1 in the ,alpine4 ,note #ajjaf3 ,phil4 ,bot4 p4 #agb4 ,note #ajaaf3 ,ib4 p4 #aga4 ,again1 the rule that the same parts are of very different value in different ,orders1 not only leaves us in want of rules or reasons which may enable us to compare the marks of different ,orders1 but destroys the systematic completeness of the natural arrangement4 ,if some of the ,orders be regulated by the flower and others by the fruit1 we may have plants1 of which the flower would place them in one ,order1 and the fruit in another4 ,the answer to this difficulty is the maxim already stated2--that no ,character makes the ,order2 and that if a ,character do not enable us to recognize the ,order1 it does not answer its purpose1 and ought to be changed for another4 ,this doctrine1 that the ,character is to be employed as a servant and not as a master1 was a stumbling-block in the way of those disciples who looked only for dogmatical and universal rules4 ,one of ,linnus's pupils1 ,paul ,dietrich ,giseke1 has given us a very lively account of his own perplexity on having this view propounded to him1 and of the way in which he struggled with it4 ,he had complained of the want of intelligible grounds1 in the collection of natural orders given by ,linnus4 ,linnus#ajbaf wrote in answer1 ,you ask me for the characters of the ,natural ,orders3 ,i confess ,i cannot give them4 ,such a reply naturally increased ,giseke's difficulties4 ,but afterwards1 in #agga1 he had the good fortune to spend some time at ,upsal2 and he narrates a conversation which he held with the great #cii teacher on this subject1 and which ,i think may serve to show the nature of the difficulty2--one by no means easily removed1 and by the general reader1 not even readily comprehended with distinctness4 ,giseke began by conceiving that an ,order must have that attribute from which its name is derived2--that the ,umbellat must have their flower disposed in an umbel4 ,the mighty master smiled1#ajcaf and told him not to look at names1 but at nature4 ,but 7said the pupil7 what is the use of the name1 if it does not mean what it professes to mean8 ,it is of small import 7replied ,linnus7 what you call the ,order1 if you take a proper series of plants and give it some name1 which is clearly understood to apply to the plants which you have associated4 ,in such cases as you refer to1 ,i followed the logical rule1 of borrowing a name a potiori1 from the principal member4 ,can you 7he added7 give me the character of any single ,order8 ,giseke4 ,surely1 the character of the ,umbellat is1 that they have an umbel8 ,linnus4 ,good2 but there are plants which have an umbel1 and are not of the ,umbellat4 ,g4 ,i remember4 ,we must therefore add1 that they have two naked seeds4 ,l4 ,then1 ,echinophora1 which has only one seed1 and ,eryngium1 which has not an umbel1 will not be ,umbellat2 and yet they are of the ,order4 ,g4 ,i would place ,eryngium among the ,aggregat4 ,l4 ,no2 both are beyond dispute ,umbellat4 ,eryngium has an involucrum1 five stamina1 two pistils1 c4 ,try again for your ,character4 ,g4 ,i would transfer such plants to the end of the ,order1 and make them form the transition to the next ,order4 ,eryngium would connect the ,umbellat with the ,aggregat4 ,l4 ,ah6 my good friend1 the ,transition from ,order to ,order is one thing2 the ,character of an ,order is another4 ,the ,transitions ,i could indicate2 but a ,character of a ,natural ,order is impossible4 ,i will not give my reasons for the distribution of ,natural ,orders which ,i have published4 ,you or some other person1 after twenty or after fifty years1 will discover them1 and see ,i was in the right4 ,note #ajbaf3 ,linni ,prlectiones1 ,pref4 p4 xv4 ,note #ajcaf3 ,subrisit 4 ,i have given a portion of this curious conversation in order to show that the attempt to establish ,natural ,orders leads to convictions which are out of the domain of the systematic grounds on which they profess to proceed4 ,i believe the real state of the case to be that the systematist1 in such instances1 is guided by an unformed and undeveloped apprehension of physiological functions4 ,the ideas of the form1 #djj number1 and figure of parts are1 in some measure1 overshadowed and superseded by the rising perception of organic and vital relations2 and the philosopher who aims at a ,natural ,method1 while he is endeavoring merely to explore the apartment in which he had placed himself1 that of ,arrangement1 is led beyond it1 to a point where another light begins1 though dimly1 to be seen2 he is brought within the influence of the ideas of ,organization and ,life4 ,the sciences which depend on these ideas will be the subject of our consideration hereafter4 ,but what has been said may perhaps serve to explain the acknowledged and inevitable imperfection of the unphysiological ,linnan attempts towards a natural method4 ,artificial ,glasses are1 ,linnus says1 a substitute for ,natural1 till ,natural are detected4 ,but we have not yet a ,natural ,method4 ,nor1 he says1 in the conversation above cited1 can we have a ,natural ,method2 for a ,natural ,method implies ,natural ,classes and ,orders2 and these ,orders must have ,characters4 ,and they1 he adds in another place1#ajdaf who1 though they cannot obtain a complete ,natural ,method1 arrange plants according to the fragments of such a method1 to the rejection of the ,artificial1 seem to me like persons who pull down a convenient vaulted room1 and set about building another1 though they cannot turn the vault which is to cover it4 ,note #ajdaf3 ,gen4 ,plant4 in ,prlect4 p4 xii4 ,how far these considerations deterred other persons from turning their main attention to a natural method1 we shall shortly see2 but in the mean time1 we must complete the history of the ,linnan ,reform4 ,sect4 #f4--,reception and ,diffusion of the ,linnan ,reform4 ,,we have already seen that ,linnus received1 from his own country1 honors and emoluments which mark his reputation as established1 as early as #agdj2 and by his publications1 his lectures1 and his personal communications1 he soon drew round him many disciples1 whom he impressed strongly with his own doctrines and methods4 ,it would seem that the sciences of classification tend1 at least in modern times more than other sciences1 to collect about the chair of the teacher a large body of zealous and obedient pupils2 ,linnus and ,werner were by far the most powerful heads of schools of any men who appeared in the course of the last century4 ,perhaps one reason of this is1 that in these sciences1 consisting of such an enormous multitude of species1 of descriptive #dja particulars1 and of previous classifications1 the learner is dependent upon the teacher more completely1 and for a longer time than in other subjects of speculation3 he cannot so soon or so easily cast off the aid and influence of the master1 to pursue reasonings and hypotheses of his own4 ,whatever the cause may be1 the fact is1 that the reputation and authority of ,linnus1 in the latter part of his life1 were immense4 ,he enjoyed also royal favor1 for the ,king and ,queen of ,sweden were both fond of natural history4 ,in #agec1 ,linnus received from the hand of his sovereign the knighthood of the ,polar ,star1 an honor which had never before been conferred for literary merit2 and in #agef1 was raised to the rank of ,swedish nobility by the title of ,von ,linn2 and this distinction was confirmed by the ,diet in #agfb4 ,he lived1 honored and courted1 to the age of seventy-one2 and in #aggh was buried in the cathedral of ,upsal1 with many testimonials of public respect and veneration4 ,de ,candolle#ajeaf assigns1 as the causes of the successes of the ,linnan system1--the specific names1--the characteristic phrase1--the fixation of descriptive language1--the distinction of varieties and species1--the extension of the method to all the kingdoms of nature1--and the practice of introducing into it the species most recently discovered4 ,this last course ,linnus constantly pursued2 thus making his works the most valuable for matter1 as they were the most convenient in form4 ,the general diffusion of his methods over ,europe may be dated1 perhaps1 a few years after #agfj1 when the tenth and the succeeding editions of the ,systema ,natur were in circulation1 professing to include every species of organized beings4 ,but his pupils and correspondents effected no less than his books1 in giving currency to his system4 ,in ,germany1#ajfaf it was defended by ,ludwig1 ,gesner1 ,fabricius4 ,but ,haller1 whose reputation in physiology was as great as that of ,linnus in methodology1 rejected it as too merely artificial4 ,in ,france1 it did not make any rapid or extensive progress3 the best ,french botanists were at this time occupied with the solution of the great problem of the construction of a ,natural ,method4 ,and though the rhetorician ,rousseau charmed1 we may suppose1 with the elegant precision of the ,philosophia ,botanica1 declared it to be the most philosophical work he had ever read in his life1 ,buffon and ,andanson1 describers and philosophers of a more ambitious school1 felt a repugnance to the rigorous rules1 and limited1 but finished1 undertakings of the ,swedish naturalist4 ,to resist his #djb criticism and his influence1 they armed themselves with dislike and contempt4 ,note #ajeaf3 ,thor4 ,elm4 p4 #dj4 ,note #ajfaf3 ,sprengel1 ii4 #bdd4 ,in ,england the ,linnan system was very favorably received3--perhaps the more favorably1 for being a strictly artificial system4 ,for the indefinite and unfinished form which almost inevitably clings to a natural method1 appears to be peculiarly distasteful to our countrymen4 ,it might seem as if the suspense and craving which comes with knowledge confessedly incomplete were so disagreeable to them1 that they were willing to avoid it1 at any rate whatever2 either by rejecting system altogether1 or by accepting a dogmatical system without reserve4 ,the former has been their course in recent times with regard to ,mineralogy2 the latter was their proceeding with respect to the ,linnan ,botany4 ,it is in this country alone1 ,i believe1 that ,wernerian and ,linnan ,societies have been instituted4 ,such appellations somewhat remind us of the ,aristotelian and ,platonic schools of ancient ,greece4 ,in the same spirit it was1 that the ,artificial ,system was at one time here considered1 not as subsidiary and preparatory to the ,natural ,orders1 but as opposed to them4 ,this was much as if the disposition of an army in a review should be considered as inconsistent with another arrangement of it in a battle4 ,when ,linnus visited ,england in #agcf1 ,sloane1 then the patron of natural history in this country1 is said to have given him a cool reception1 such as was perhaps most natural from an old man to a young innovator2 and ,dillenius1 the ,professor at ,oxford1 did not accept the sexual system4 ,but as ,pulteney1 the historian of ,english ,botany1 says1 when his works became known1 the simplicity of the classical characters1 the uniformity of the generic notes1 all confined to the parts of the fructification1 and the precision which marked the specific distinctions1 merits so new1 soon commanded the assent of the unprejudiced4 ,perhaps the progress of the introduction of the ,linnan ,system into ,england will be best understood from the statement of ,t4 ,martyn1 who was ,professor of ,botany in the ,university of ,cambridge1 from #agfa to #ahbe4 ,about the year #agej1 he says1#ajgaf ,i was a pupil of the school of our great countryman ,ray2 but the rich vein of knowledge1 the profoundness and precision1 which ,i remarked everywhere in the ,philosophia ,botanica1 7published in #agea17 withdrew me from my first master1 and ,i became a decided convert to that system of botany which has since been generally received4 ,in #agec1 the ,species #djc ,plantarum1 which first introduced the specific names1 made me a ,linnan completely4 ,in #agfc1 he introduced the system in his lectures at ,cambridge1 and these were the first ,linnan lectures in ,england4 ,stillingfleet had already1 in #ageg1 and ,lee1 in #agfj1 called the attention of ,english readers to ,linnus4 ,sir ,j4 ,hill1 7the king's gardener at ,kew17 in his ,flora ,britannica1 published in #agfj1 had employed the classes and generic characters1 but not the nomenclature2 but the latter was adopted by ,hudson1 in #agfb1 in the ,flora ,anglica4 ,note #ajgaf3 ,pref4 to ,language of ,botany1 #crd edit4 #ahjg4 ,two young ,swedes1 pupils of ,linnus1 ,dryander and ,solander1 settled in ,england1 and were in intimate intercourse with the most active naturalists1 especially with ,sir ,joseph ,banks1 of whom the former was librarian1 and the latter a fellow-traveller in ,cook's celebrated voyage4 ,james ,edward ,smith was also one of the most zealous disciples of the ,linnan school2 and1 after the death of ,linnus1 purchased his ,herbariums and ,collections4 ,it is related1#ajhaf as a curious proof of the high estimation in which ,linnus was held1 that when the ,swedish government heard of this bargain1 they tried1 though too late1 to prevent these monuments of their countryman's labor and glory being carried from his native land1 and even went so far as to send a frigate in pursuit of the ship which conveyed them to ,england4 ,smith had1 however1 the triumph of bringing them home in safety4 ,on his death they were purchased by the ,linnan ,society4 ,such relics serve1 as will easily be imagined1 not only to warm the reverence of his admirers1 but to illustrate his writings3 and since they have been in this country1 they have been the object of the pilgrimage of many a botanist1 from every part of ,europe4 ,note #ajhaf3 ,trapp's ,transl4 of ,stower's ,life of ,linnus1 p4 #cad4 ,i have purposely confined myself to the history of the ,linnan system in the cases in which it is most easily applicable1 omitting all consideration of more obscure and disputed kinds of vegetables1 as ferns1 mosses1 fungi1 lichens1 sea-weeds1 and the like4 ,the nature and progress of a classificatory science1 which it is our main purpose to bring into view1 will best be understood by attending1 in the first place1 to the cases in which such a science has been pursued with the most decided success2 and the advances which have been made in the knowledge of the more obscure vegetables1 are1 in fact1 advances in artificial classification1 only in as far as they are advances in natural classification1 and in physiology4 ,to these subjects we now proceed4 #djd ,,chapter ,v4 ,,progress ,,towards ,a ,,natural ,,system ,,of ,,botany4 ,,we have already said1 that the formation of a ,natural ,system of classification must result from a comparison of all the resemblances and differences of the things classed2 but that1 in acting upon this maxim1 the naturalist is necessarily either guided by an obscure and instinctive feeling1 which is1 in fact1 an undeveloped recognition of physiological relations1 or else acknowledges physiology for his guide1 though he is obliged to assume arbitrary rules in order to interpret its indications4 ,thus all ,natural ,classification of organized beings1 either begins or soon ends in ,physiology2 and can never advance far without the aid of that science4 ,still1 the progress of the ,natural ,method in botany went to such a length before it was grounded entirely on the anatomy of plants1 that it will be proper1 and ,i hope instructive1 to attempt a sketch of it here4 ,as ,i have already had occasion to remark1 the earlier systems of plants were natural2 and they only ceased to be so1 when it appeared that the problem of constructing a system admitted of a very useful solution1 while the problem of devising a natural system remained insoluble4 ,but many botanists did not so easily renounce the highest object of their science4 ,in ,france1 especially1 a succession of extraordinary men labored at it with no inconsiderable success3 and they were seconded by worthy fellow-laborers in ,germany and elsewhere4 ,the precept of taking into account all the parts of plants according to their importance1 may be applied according to arbitrary rules4 ,we may1 for instance1 assume that the fruit is the most important part2 or we may make a long list of parts1 and look for agreement in the greatest possible number of these1 in order to construct our natural orders4 ,the former course was followed by ,grtner2#ajiaf the latter by ,adanson4 ,grtner's principles1 deduced from the dissection of more than a thousand kinds of fruits1#aajaf exercised1 in the sequel1 a great and #dje permanent influence on the formation of natural classes4 ,adanson's attempt1 bold and ingenious1 belonged1 both in time and character1 to a somewhat earlier stage of the subject4#aaaaf ,enthusiastic and laborious beyond belief but self-confident1 and contemptuous of the labors of others1 ,michael ,adanson had collected1 during five years spent in ,senegal1 an enormous mass of knowledge and materials2 and had formed plans for the systems which he conceived himself thus empowered to reach1 far beyond the strength and the lot of man4#aabaf ,in his ,families of ,plants1 however1 all agree that his labors were of real value to the science4 ,the method which he followed is thus described by his eloquent and philosophical eulogist4#aacaf ,note #ajiaf3 ,de ,fructibus et ,seminibus ,plantarum4 ,stuttg4 #aghh-agia4 ,note #aajaf3 ,sprengel1 ii4 #bij4 ,note #aaaaf3 ,familles des ,plantes1 #agfc4 ,note #aabaf3 ,cuvier's ,eloge4 ,note #aacaf3 ,cuv4 ,eloges1 tom4 i4 p4 #bhb4 ,considering each organ by itself1 he formed1 by pursuing its various modifications1 a system of division1 in which he arranged all known species according to that organ alone4 ,doing the same for another organ1 and another1 and so for many1 he constructed a collection of systems of arrangement1 each artificial1--each founded upon one assumed organ4 ,the species which come together in all these systems are1 of all1 naturally the nearest to each other2 those which are separated in a few of the systems1 but contiguous in the greatest number1 are naturally near to each other1 though less near than the former2 those which are separated in a greater number1 are further removed from each other in nature2 and they are the more removed1 the fewer are the systems in which they are associated4 ,thus1 by this method1 we obtain the means of estimating precisely the degree of natural affinity of all the species which our systems include1 independent of a physiological knowledge of the influence of the organs4 ,but the method has1 ,cuvier adds1 the inconvenience of presupposing another kind of knowledge1 which1 though it belongs only to descriptive natural history1 is no less difficult to obtain2--the knowledge1 namely1 of all species1 and of all the organs of each4 ,a single one neglected1 may lead to relations the most false2 and ,adanson himself1 in spite of the immense number of his observations1 exemplifies this in some instances4 ,we may add1 that in the division of the structure into organs1 and in the estimation of the gradations of these in each artificial system1 there is still room for arbitrary assumption4 ,in the mean time1 the two ,jussieus had presented to the world a ,natural ,method1 which produced a stronger impression than the #djf ,universal ,method of ,adanson4 ,the first author of the system was ,bernard de ,jussieu1 who applied it in the arrangement of the garden of the ,trianon1 in #agei1 though he never published upon it4 ,his nephew1 ,antoine ,laurent de ,jussieu1 in his ,treatise of the ,arrangement of the ,trianon1#aadaf gave an account of the principles and orders of his uncle1 which he adopted when he succeeded him2 and1 at a later period1 published his ,genera ,plantarum secundum ,ordines ,naturales disposita2 a work1 says ,cuvier1 which perhaps forms as important an epoch in the sciences of observation1 as the ,chimie of ,lavoisier does in the sciences of experiment4 ,the object of the ,jussieus was to obtain a system which should be governed by the natural affinities of the plants1 while1 at the same time1 the characters by which the orders were ostensibly determined1 should be as clear1 simple1 and precise1 as those of the best artificial system4 ,the main points in these characters were the number of the cotyledons1 and the structure of the seed3 and subordinate to this1 the insertion of the stamina1 which they distinguished as epigynous1 perigynous1 and hypogynous1 according as they were inserted over1 about1 or under1 the germen4 ,and the classes which were formed by the ,jussieus1 though they have since been modified by succeeding writers1 have been so far retained by the most profound botanists1 notwithstanding all the new care and new light which have been bestowed upon the subject1 as to show that what was done at first1 was a real and important step in the solution of the problem4 ,note #aadaf3 ,mm4 ,ac4 ,p4 #aggd4 ,the merit of the formation of this natural method of plants must be divided between the two ,jussieus4 ,it has been common to speak of the nephew1 ,antoine ,laurent1 as only the publisher of his uncle's work4#aaeaf ,but this appears1 from a recent statement1#aafaf to be highly unjust4 ,bernard left nothing in writing but the catalogues of the garden of the ,trianon1 which he had arranged according to his own views2 but these catalogues consist merely of a series of names without explanation or reason added4 ,the nephew1 in #aggc1 undertook and executed for himself the examination of a natural family1 the ,ranunculace2 and he was wont to relate 7as his son informs us7 that it #djg was this employment which first opened his eyes and rendered him a botanist4 ,in the memoir which he wrote1 he explained fully the relative importance of the characters of plants1 and the subordination of some to others2--an essential consideration1 which ,adanson's scheme had failed to take account of4 ,the uncle died in #aggg2 and his nephew1 in speaking of him1 compares his arrangement to the ,ordines ,naturales of ,linnus3 ,both these authors1 he says1 have satisfied themselves with giving a catalogue of genera which approach each other in different points1 without explaining the motives which induced them to place one order before another1 or to arrange a genus under a certain order4 ,these two arrangements may be conceived as problems which their authors have left for botanists to solve4 ,linnus published his2 that of ,m4 de ,jussieu is only known by the manuscript catalogues of the garden of the ,trianon4 ,note #aaeaf3 ,prodromus ,flor ,penins4 ,ind4 ,orient4 ,wight and ,walker-,arnott1 ,introd4 p4 xxxv4 ,note #aafaf3 ,by ,adrien de ,jussieu1 son of ,antoine ,laurent1 in the ,annales des ,sc4 ,nat41 ,nov4 #ahcd4 ,it was not till the younger ,jussieu had employed himself for nineteen years upon botany1 that he published1 in #aghi1 his ,genera ,plantarum2 and by this time he had so entirely formed his scheme in his head1 that he began the impression without having written the book1 and the manuscript was never more than two pages in advance of the printer's type4 ,when this work appeared1 it was not received with any enthusiasm2 indeed1 at that time1 the revolution of states absorbed the thoughts of all ,europe1 and left men little leisure to attend to the revolutions of science4 ,the author himself was drawn into the vortex of public affairs1 and for some years forgot his book4 ,the method made its way slowly and with difficulty3 it was a long time before it was comprehended and adopted in ,france1 although the botanists of that country had1 a little while before1 been so eager in pursuit of a natural system4 ,in ,england and ,germany1 which had readily received the ,linnan method1 its progress was still more tardy4 ,there is only one point1 on which it appears necessary further to dwell4 ,a main and fundamental distinction in all natural systems1 is that of the ,monocotyledonous and ,dicotyledonous plants2 that is1 plants which unfold themselves from an embryo with two little leaves1 or with one leaf only4 ,this distinction produces its effects in the systems which are regulated by numbers2 for the flowers and fruit of the monocotyledons are generally referrible to some law in which the number three prevails2 a type which rarely occurs in dicotyledons1 these affecting most commonly an arrangement founded on the number five4 ,but it appears1 when we attempt to rise towards a natural #djh method1 that this division according to the cotyledons is of a higher order than the other divisions according to number2 and corresponds to a distinction in the general structure and organization of the plant4 ,the apprehension of the due rank of this distinction has gradually grown clearer4 ,cuvier#aagaf conceives that he finds such a division clearly marked in ,lobel1 in #aeha1 and employed by ,ray as the basis of his classification a century later4 ,this difference has had its due place assigned it in more recent systems of arrangement2 but it is only later still that its full import has been distinctly brought into view4 ,desfontaines discovered#aahaf that the ligneous fibre is developed in an opposite manner in vegetables with one and with two cotyledons2--towards the inside in the former case1 and towards the outside in the latter2 and hence these two great classes have been since termed endogenous and exogenous4 ,note #aagaf3 ,hist4 ,sc4 ,nat4 ii4 #aig4 ,note #aahaf3 ,hist4 ,sc4 ,nat4 i4 pp4 #aif1 #bij4 ,thus this division1 according to the cotyledons1 appears to have the stamp of reality put upon it1 by acquiring a physiological meaning4 ,yet we are not allowed to forget1 even at this elevated point of generalization1 that no one character can be imperative in a natural method4 ,lamarck1 who employed his great talents on botany1 before he devoted himself exclusively to other branches of natural history1 published his views concerning methods1 systems1#aaiaf and characters4 ,his main principle is1 that no single part of a plant1 however essential1 can be an absolute rule for classification2 and hence he blames the ,jussieuian method1 as giving this inadmissible authority to the cotyledons4 ,roscoe#abjaf further urges that some plants1 as ,orchis morio1 and ,limodorum verecundum1 have no visible cotyledons4 ,yet ,de ,candolle1 who labored along with ,lamarck1 in the new edition of the ,flore ,franaise1 has1 as we have already intimated1 been led1 by the most careful application of the wisest principles1 to a system of ,natural ,orders1 of which ,jussieu's may be looked upon as the basis2 and we shall find the greatest botanists1 up to the most recent period1 recognizing1 and employing themselves in improving1 ,jussieu's ,natural ,families2 so that in the progress of this part of our knowledge1 vague and perplexing as it is1 we have no exception to our general aphorism1 that no real acquisition in science is ever discarded4 #dji ,note #aaiaf3 ,sprengel1 ii4 #bif2 and1 there quoted1 ,flore ,franaise1 t4 i4 #c1 #aggh4 ,mm4 ,ac4 ,p4 #aghe4 ,journ4 ,hist4 ,nat4 t4 i4 ,for ,lamarck's ,mthode ,analytique1 see ,dumeril1 ,sc4 ,nat4 i4 ,art4 #cij4 ,note #abjaf3 ,roscoe1 ,linn4 ,tr4 vol4 xi4 ,cuscuta also has no cotyledons4 ,the reception of the system of ,jussieu in this country was not so ready and cordial as that of ,linnus4 ,as we have already noticed1 the two systems were looked upon as rivals4 ,thus ,roscoe1 in #ahaj1abaaf endeavored to show that ,jussieu's system was not more natural than the ,linnan1 and was inferior as an artificial system3 but he argues his points as if ,jussieu's characters were the grounds of his distribution2 which1 as we have said1 is to mistake the construction of a natural system4 ,in #ahjc1 ,salisbury#abbaf had already assailed the machinery of the system1 maintaining that there are no cases of perigynous stamens1 as ,jussieu assumes2 but this he urges with great expressions of respect for the author of the method4 ,and the more profound botanists of ,england soon showed that they could appreciate and extend the natural method4 ,robert ,brown1 who had accompanied ,captain ,flinders to ,new ,holland in #ahja1 and who1 after examining that country1 brought home1 in #ahje1 nearly four thousand species of plants1 was the most distinguished example of this4 ,in his preface to the ,prodromus ,flor ,nov ,hollandi1 he says1 that he found himself under the necessity of employing the natural method1 as the only way of avoiding serious error1 when he had to deal with so many new genera as occur in ,new ,holland2 and that he has1 therefore1 followed the method of ,jussieu2 the greater part of whose orders are truly natural1 although their arrangement in classes1 as is1 he says1 conceded by their author1 no less candid than learned1 is often artificial1 and1 as appears to me1 rests on doubtful grounds4 ,note #abaaf3 ,linn4 ,tr4 vol4 xi4 p4 #ej4 ,note #abbaf3 ,ibid4 vol4 viii4 ,from what has already been said1 the reader will1 ,i trust1 see what an extensive and exact knowledge of the vegetable world1 and what comprehensive views of affinity1 must be requisite in a person who has to modify the natural system so as to make it suited to receive and arrange a great number of new plants1 extremely different from the genera on which the arrangement was first formed1 as the ,new ,holland genera for the most part were4 ,he will also see how impossible it must be to convey by extract or description any notion of the nature of these modifications3 it is enough to say1 that they have excited the applause of botanists wherever the science is studied1 and that they have induced ,m4 de ,humboldt and his fellow-laborers1 themselves botanists of the first rank1 to dedicate one of their works to him in terms of the strongest admiration4#abcaf ,mr4 ,brown has also published #daj special disquisitions on parts of the ,natural ,system2 as on ,jussieu's ,proteace2#abdaf on the ,asclepiade1 a natural family of plants which must be separated from ,jussieu's ,apocyne2#abeaf and other similar labors4 ,note #abcaf3 ,roberto ,brown1 ,britanniarum glori atque ornamento1 totam ,botanices scientiam ingenio mirifico complectenti4 c4 ,note #abdaf3 ,linn4 ,tr4 vol4 x4 #ahji4 ,note #abeaf3 ,mem4 of ,wernerian ,n4 ,h4 ,soc4 vol4 i4 #ahji4 ,we have1 ,i think1 been led1 by our survey of the history of ,botany1 to this point2--that a ,natural ,method directs us to the study of ,physiology1 as the only means by which we can reach the object4 ,this conviction1 which in botany comes at the end of a long series of attempts at classification1 offers itself at once in the natural history of animals1 where the physiological signification of the resemblances and differences is so much more obvious4 ,i shall not1 therefore1 consider any of these branches of natural history in detail as examples of mere classification4 ,they will come before us1 if at all1 more properly when we consider the classifications which depend on the functions of organs1 and on the corresponding modifications which they necessarily undergo2 that is1 when we trace the results of ,physiology4 ,but before we proceed to sketch the history of that part of our knowledge1 there are a few points in the progress of ,zoology1 understood as a mere classificatory science1 which appear to me sufficiently instructive to make it worth our while to dwell upon them4 #bnd ,ed4 ,mr4 ,lindley's recent work1 ,the ,vegetable ,kingdom 7#ahdf71 may be looked upon as containing the best view of the recent history of ,systematic ,botany4 ,in the ,introduction to this work1 ,mr4 ,lindley has given an account of various recent works on the subject2 as ,agardh's ,classes ,plantarum 7#ahbf72 ,perleb's ,lehrbuch der ,naturgeschichte der ,pflanzenreich 7#ahbf72 ,dumortier's ,florula ,belgica 7#ahbg72 ,bartling's ,ordines ,naturales ,plantarum 7#ahcj72 ,hess's ,uebersicht der ,phanerogenischen ,natrlichen ,pflanzenfamilien 7#ahcb72 ,schulz's ,natrliches ,system des ,pflanzenreich's 7#ahcb72 ,horaninow's ,prim ,line ,systematis ,natur 7#ahcd72 ,fries's ,corpus ,florarum provincialium ,sueci 7#ahce72 ,martins's ,conspectus ,regni ,vegetablis secundum ,characteres ,morphologicos 7#ahce72 ,sir ,edward ,f4 ,bromhead's ,system1 as published in the ,edinburgh ,journal and other ,journals 7#ahcf-ahdj72 ,endlicher's ,genera ,plantarum secundum ,ordines ,naturales disposita 7#ahcf-ahdj72 ,perleb's ,clavis ,classicum ,ordinum et ,familiarum 7#ahch72 ,adolphe ,brongniart's ,enumration des ,genres de ,plantes 7#ahdc72 ,meisner's ,plantarum vascularium ,genera secundum ,ordines ,naturales digesta 7#ahdc72 ,horaninow's ,tetractys ,natur1 seu ,systema quinquemembre omnium ,naturalium #daa 7#ahdc72 ,adrien de ,jussieu's 9999,cours ,elmentaire d',histoire ,naturelle4 ,botanique 7#ahdd74 ,mr4 ,lindley1 in this as in all his works1 urges strongly the superior value of natural as compared with artificial systems2 his principles being1 ,i think1 nearly such as ,i have attempted to establish in the ,philosophy of the ,sciences1 ,book viii41 ,chapter ii4 ,he states that the leading idea which has been kept in view in the compilation of his work is this maxim of ,fries3 ,singula sphra 7sectio7 ideam quandam exponit1 indeque ejus character notione simplici optime exprimitur2 and he is hence led to think that the true characters of all natural assemblages are extremely simple4 ,one of the leading features in ,mr4 ,lindley's system is that he has thrown the ,natural ,orders into groups subordinate to the higher divisions of ,classes and ,sub-classes4 ,he had already attempted this1 in imitation of ,agardh and ,bartling1 in his ,nixus ,plantarum 7#ahch74 ,the groups of ,natural ,orders were there called ,nixus 7tendencies72 and they were denoted by names ending in ales2 but these groups were further subordinated to ,cohorts4 ,thus the first member of the arrangement was ,class #a4 ,,exogen4 ,sub-class #a4 ,,polypetal4 ,cohort #a4 ,,albuminos4 ,nixus #a4 ,ranales4 ,natural ,orders included in this ,nixus1 ,ranunculace1 ,saracenice1 ,papaverace1 c4 ,in the ,vegetable ,kingdom1 the groups of ,natural ,orders are termed ,alliances4 ,in this work1 the ,sub-classes of the ,,exogens are four3 ,i4 ,,diclinous2 ,,ii4 ,,hypogynous2 ,,iii4 ,,perigynous2 ,,iv4 ,,epigynous2 and the ,alliances are subordinated to these without the intervention of ,cohorts4 ,mr4 ,lindley has also1 in this as in other works1 given ,english names for the ,natural ,orders4 ,thus for ,nymphace1 ,ranunculace1 ,tamaricace1 ,zygophyllace1 ,eleatrinace1 he substitutes ,water-,lilies1 ,crowfoots1 ,tamarisks1 ,bean-,capers1 and ,water-,peppers2 for ,malvace1 ,aurantiace1 ,gentianace1 ,primulace1 ,urtiace1 ,euphorbiace1 he employs ,mallow-worts1 ,citron-worts1 ,gentian-worts1 ,prim-worts1 ,nettle-worts1 ,spurge-worts2 and the terms ,orchids1 ,hippurids1 ,amaryllids1 ,irids1 ,typhads1 ,arads1 ,cucurbits1 are taken as ,english equivalents for ,orchidace1 ,haloragace1 ,amaryllidace1 ,iridace1 ,typhace1 ,arace1 ,cucurbitace4 ,all persons who wish success to the study of botany in ,england must rejoice to see it tend to assume this idiomatic shape4 #dab ,,chapter ,,vi4 ,,the ,,progress ,,of ,,systematic ,,zoology4 ,,the history of ,systematic ,botany1 as we have presented it1 may be considered as a sufficient type of the general order of progression in the sciences of classification4 ,it has appeared1 in the survey which we have had to give1 that this science1 no less than those which we first considered1 has been formed by a series of inductive processes1 and has1 in its history1 ,epochs at which1 by such processes1 decided advances were made4 ,the important step in such cases is1 the seizing upon some artificial mark which conforms to natural resemblances2--some basis of arrangement and nomenclature by means of which true propositions of considerable generality can be enunciated4 ,the advance of other classificatory sciences1 as well as botany1 must consist of such steps2 and their course1 like that of botany1 must 7if we attend only to the real additions made to knowledge17 be gradual and progressive1 from the earliest times to the present4 ,to exemplify this continued and constant progression in the whole range of ,zoology1 would require vast knowledge and great labor2 and is1 perhaps1 the less necessary1 after we have dwelt so long on the history of ,botany1 considered in the same point of view4 ,but there are a few observations respecting ,zoology in general which we are led to make in consequence of statements recently promulgated2 for these statements seem to represent the history of ,zoology as having followed a course very different from that which we have just ascribed to the classificatory sciences in general4 ,it is held by some naturalists1 that not only the formation of a systematic classification in ,zoology dates as far back as ,aristotle2 but that his classification is1 in many respects1 superior to some of the most admired and recent attempts of modern times4 ,if this were really the case1 it would show that at least the idea of a ,systematic ,classification had been formed and developed long previous to the period to which we have assigned such a step2 and it would be difficult to reconcile such an early maturity of ,zoology with the conviction1 which we have had impressed upon us by the other #dac parts of our history1 that not only labor but time1 not only one man of genius but several1 and those succeeding each other1 are requisite to the formation of any considerable science4 ,but1 in reality1 the statements to which we refer1 respecting the scientific character of ,aristotle's ,zoological system1 are altogether without foundation2 and this science confirms the lessons taught us by all the others4 ,the misstatements respecting ,aristotle's doctrines are on this account so important1 and are so curious in themselves1 that ,i must dwell upon them a little4 ,aristotle's nine ,books ,on ,animals are a work enumerating the differences of animals in almost all conceivable respects2--in the organs of sense1 of motion1 of nutrition1 the interior anatomy1 the exterior covering1 the manner of life1 growth1 generation1 and many other circumstances4 ,these differences are very philosophically estimated4 ,the corresponding parts of animals1 he says1#abfaf besides the differences of quality and circumstance1 differ in being more or fewer1 greater or smaller1 and1 speaking generally1 in excess and defect4 ,thus some animals have crustaceous coverings1 others hard shells2 some have long beaks1 some short2 some have many wings1 some have few2 ,some again have parts which others want1 as crests and spurs4 ,he then makes the following important remark3 ,some animals have parts which correspond to those of others1 not as being the same in species1 nor by excess and defect1 but by analogy2 thus a claw is analogous to a thorn1 and a nail to a hoof1 and a hand to the nipper of a lobster1 and a feather to a scale2 for what a feather is in a bird1 that is a scale in a fish4 ,note #abfaf3 ,lib4 i4 c4 i4 ,it will not1 however1 be necessary1 in order to understand ,aristotle for our present purpose1 that we should discuss his notion of ,analogy4 ,he proceeds to state his object1#abgaf which is1 as we have said1 to describe the differences of animals in their structure and habits4 ,he then observes1 that for structure1 we may take ,man for our type1#abhaf as being best known to us2 and the remainder of the first ,book is occupied with a description of man's body1 beginning from the head1 and proceeding to the extremities4 ,note #abgaf3 ,lib4 i4 c4 ii4 ,note #abhaf3 c4 iii4 ,in the next ,book1 7from which are taken the principal passages in which his modern commentators detect his system17 he proceeds to compare the differences of parts in different animals1 according to the order which he had observed in man4 ,in the first chapter he speaks #dad of the head and neck of animals2 in the second1 of the parts analogous to arms and hands2 in the third1 of the breast and paps1 and so on2 and thus he comes1 in the seventh chapter1 to the legs1 feet1 and toes3 and in the eleventh1 to the teeth1 and so to other parts4 ,the construction of a classification consists in the selection of certain parts1 as those which shall eminently and peculiarly determine the place of each species in our arrangement4 ,it is clear1 therefore1 that such an enumeration of differences as we have described1 supposing it complete1 contains the materials of all possible classifications4 ,but we can with no more propriety say that the author of such an enumeration of differences is the author of any classification which can be made by means of them1 than we can say that a man who writes down the whole alphabet writes down the solution of a given riddle or the answer to a particular question4 ,yet it is on no other ground than this enumeration1 so far as ,i can discover1 that ,aristotle's ,system has been so decidedly spoken of1#abiaf and exhibited in the most formal tabular shape4 ,the authors of this ,systema ,aristotelicum1 have selected1 ,i presume1 the following passages from the work ,on ,animals1 as they might have selected any other2 and by arranging them according to a subordination unknown to ,aristotle himself have made for him a scheme which undoubtedly bears a great resemblance to the most complete systems of modern times4 ,note #abiaf3 ,linnan ,transactions1 vol4 xvi4 p4 #bd4 ,book ,i41 chap4 v4--,some animals are viviparous1 some oviparous1 some vermiparous4 ,the viviparous are such as man1 and the horse1 and all those animals which have hair2 and of aquatic animals1 the whale kind1 as the dolphin and cartilaginous fishes4 ,book ,,ii41 chap4 vii4--,of quadrupeds which have blood and are viviparous1 some are 7as to their extremities17 many-cloven1 as the hands and feet of man4 ,for some are many-toed1 as the lion1 the dog1 the panther2 some are bifid1 and have hoofs instead of nails1 as the sheep1 the goat1 the elephant1 the hippopotamus2 and some have undivided feet1 as the solid-hoofed animals1 the horse and ass4 ,the swine kind share both characters4 ,chap4 ii4--,animals have also great differences in the teeth1 both when compared with each other and with man4 ,for all quadrupeds which have blood and are viviparous1 have teeth4 ,and in the first place1 some are ambidental1#acjaf 7having teeth in both jaws27 and some #dae are not so1 wanting the front teeth in the upper jaw4 ,some have neither front teeth nor horns1 as the camel2 some have tusks1#acaaf as the boar1 some have not4 ,some have serrated#acbaf teeth1 as the lion1 the panther1 the dog2 some have the teeth unvaried1#accaf as the horse and the ox2 for the animals which vary their cutting-teeth have all serrated teeth4 ,no animal has both tusks and horns2 nor has any animal with serrated teeth either of those weapons4 ,the greater part have the front teeth cutting1 and those within broad4 ,note #acjaf3 4 ,note #acaaf3 4 ,note #acbaf3 4 ,note #accaf3 4 ,these passages undoubtedly contain most of the differences on which the asserted ,aristotelian classification rests2 but the classification is formed by using the characters drawn from the teeth1 in order to subdivide those taken from the feet2 whereas in ,aristotle these two sets of characters stand side by side1 along with dozens of others2 any selection of which1 employed according to any arbitrary method of subordination1 might with equal justice be called ,aristotle's system4 ,why1 for instance1 in order to form subdivisions of animals1 should we not go on with ,aristotle's continuation of the second of the above quoted passages1 instead of capriciously leaping to the third8 ,of these some have horns1 some have none 4 4 4 ,some have a fetlock-joint1#acdaf some have none 4 4 4 ,of those which have horns1 some have them solid throughout1 as the stag2 others1 for the most part1 hollow 4 4 4 ,some cast their horns1 some do not4 ,if it be replied1 that we could not1 by means of such characters1 form a tenable zoological system2 we again ask by what right we assume ,aristotle to have made or attempted a systematic arrangement1 when what he has written1 taken in its natural order1 does not admit of being construed into a system4 ,note #acdaf3 4 ,again1 what is the object of any classification8 ,this1 at least1 among others4 ,to enable the person who uses it to study and describe more conveniently the objects thus classified4 ,if1 therefore1 ,aristotle had formed or adopted any system of arrangement1 we should see it in the order of the subjects in his work4 ,accordingly1 so far as he has a system1 he professes to make this use of it4 ,at the beginning of the fifth ,book1 where he is proceeding to treat of the different modes of generation of animals1 he says1 ,as we formerly made a ,division of animals according to their kinds1 we must now1 in the same manner1 give a general survey of their ,history 774 ,except1 indeed1 that in the former case we made our commencement by a description #daf of man1 but in the present instance we must speak of him last1 because he requires most study4 ,we must begin then with those animals which have shells2 we must go on to those which have softer coverings1 as crustacea1 soft animals1 and insects2 after these1 fishes1 both viviparous and oviparous2 then birds2 then land animals1 both viviparous and oviparous4 ,it is clear from this passage that ,aristotle had certain wide and indefinite views of classification1 which though not very exact1 are still highly creditable to him2 but it is equally clear that he was quite unconscious of the classification that has been ascribed to him4 ,if he had adopted that or any other system1 this was precisely the place in which he must have referred to and employed it4 ,the honor due to the stupendous accumulation of zoological knowledge which ,aristotle's works contain1 cannot be tarnished by our denying him the credit of a system which he never dreamt of and which1 from the nature of the progress of science1 could not possibly be constructed at that period4 ,but1 in reality1 we may exchange the mistaken claims which we have been contesting for a better1 because a truer praise4 ,aristotle does show1 as far as could be done at his time1 a perception of the need of groups1 and of names of groups1 in the study of the animal kingdom2 and thus may justly be held up as the great figure in the ,prelude to the ,formation of ,systems which took place in more advanced scientific times4 ,this appears1 in some measure1 from the passage last quoted4 ,for not only is there1 in that1 a clear recognition of the value and object of a method in natural history2 but the general arrangement of the animal kingdom there proposed has considerable scientific merit1 and is1 for the time1 very philosophical4 ,but there are passages in his work in which he shows a wish to carry the principle of arrangement more into detail4 ,thus1 in the first ,book1 before proceeding to his survey of the differences of animals1#aceaf after speaking of such classes as ,quadrupeds4 ,birds1 ,fishes1 ,cetaceous1 ,testaceous1 ,crustaceous ,animals1 ,mollusks1 ,insects1 he says1 7chap4 vii47 ,animals cannot be divided into large genera1 in which one kind includes many kinds4 ,for some kinds are unique1 and have no difference of species1 as man4 ,some have such kinds1 but have no names for them4 ,thus all quadrupeds which have not wings1 have blood4 ,but of these1 some are viviparous1 some oviparous4 ,those which are #dag viviparous have not all hair2 those which are oviparous have scales4 ,we have here a manifestly intentional subordination of characters3 and a kind of regret that we have not names for the classes here indicated2 such1 for instance1 as viviparous quadrupeds having hair4 ,but he follows the subject into further detail4 ,of the class of viviparous quadrupeds1 he continues1 there are many genera1#acfaf but these again are without names1 except specific names1 such as man1 lion1 stag1 horse1 dog1 and the like4 ,yet there is a genus of animals that have names1 as the horse1 the ass1 the oreus1 the ginnus1 the innus1 and the animal which in ,syria is called heminus 7mule72 for these are called mules1 from their resemblance only2 not being mules1 for they breed of their own kind4 ,wherefore1 he adds1 that is1 because we do not possess recognized genera and generic names of this kind1 we must take the species separately1 and study the nature of each4 ,note #aceaf3 4 ,note #acfaf3 99994 ,these passages afford us sufficient ground for placing ,aristotle at the head of those naturalists to whom the first views of the necessity of a zoological system are due4 ,it was1 however1 very long before any worthy successor appeared1 for no additional step was made till modern times4 ,when ,natural ,history again came to be studied in ,nature1 the business of ,classification1 as we have seen1 forced itself upon men's attention1 and was pursued with interest in animals1 as in plants4 ,the steps of its advance were similar in the two cases2--by successive naturalists1 various systems of artificial marks were selected with a view to precision and convenience2--and these artificial systems assumed the existence of certain natural groups1 and of a natural system to which they gradually tended4 ,but there was this difference between botany and zoology3--the reference to physiological principles1 which1 as we have remarked1 influenced the natural systems of vegetables in a latent and obscure manner1 botanists being guided by its light1 but hardly aware that they were so1 affected the study of systematic zoology more directly and evidently4 ,for men can neither overlook the general physiological features of animals1 nor avoid being swayed by them in their judgments of the affinities of different species4 ,thus the classifications of zoology tended more and more to a union with comparative anatomy1 as the science was more and more improved4#acgaf ,but comparative anatomy belongs to the subject of the next ,book2 and anything it may be proper to say respecting its influence upon zoological arrangements1 will properly find a place there4 #dah ,note #acgaf3 ,cuvier1 ,le4 d',anat4 ,comp4 vol4 i4 p4 #ag4 ,it will appear1 and indeed it hardly requires to be proved1 that those steps in systematic zoology which are due to the light thrown upon the subject by physiology1 are the result of a long series of labors by various naturalists1 and have been1 like other advances in science1 led to and produced by the general progress of such knowledge4 ,we can hardly expect that the classificatory sciences can undergo any material improvement which is not of this kind4 ,very recently1 however1 some authors have attempted to introduce into these sciences certain principles which do not1 at first sight1 appear as a continuation and extension of the previous researches of comparative anatomists4 ,i speak1 in particular1 of the doctrines of a ,circular ,progression in the series of affinity2 of a ,quinary ,division of such circular groups2 and of a relation of ,analogy between the members of such groups1 entirely distinct from the relation of ,affinity4 ,the doctrine of ,circular ,progression has been propounded principally by ,mr4 ,macleay2 although1 as he has shown1#achaf there are suggestions of the same kind to be found in other writers4 ,so far as this view negatives the doctrine of a mere linear progression in nature1 which would place each genus in contact only with the preceding and succeeding ones1 and so far as it requires us to attend to more varied and ramified resemblances1 there can be no doubt that it is supported by the result of all the attempts to form natural systems4 ,but whether that assemblage of circles of arrangement which is now offered to naturalists1 be the true and only way of exhibiting the natural relations of organized bodies1 is a much more difficult question1 and one which ,i shall not here attempt to examine2 although it will be found1 ,i think1 that those analogies of science which we have had to study1 would not fail to throw some light upon such an inquiry4 ,the prevalence of an invariable numerical law in the divisions of natural groups1 7as the number five is asserted to prevail by ,mr4 ,macleay1 the number ten by ,fries1 and other numbers by other writers71 would be a curious fact1 if established2 but it is easy to see that nothing short of the most consummate knowledge of natural history1 joined with extreme clearness of view and calmness of judgment1 could enable any one to pronounce on the attempts which have been made to establish such a principle4 ,but the doctrine of a relation of ,analogy distinct from ,affinity1 in the manner which has recently been taught1 seems to be obviously at variance with that gradual approximation of the classificatory to the #dai physiological sciences1 which has appeared to us to be the general tendency of real knowledge4 ,it seems difficult to understand how a reference to such relations as those which are offered as examples of analogy#aciaf can be otherwise than a retrograde step in science4 ,note #achaf3 ,linn4 ,trans4 vol4 xvi4 p4 #i4 ,note #aciaf3 ,for example1 the goatsucker has an affinity with the swallow2 but it has an analogy with the bat1 because both fly at the same hour of the day1 and feed in the same manner4--,swainson1 ,geography and ,classification of ,animals1 p4 #abi4 ,without1 however1 now dwelling upon these points1 ,i will treat a little more in detail of one of the branches of ,zoology4 #bnd ,ed4 ,for the more recent progress of ,systematic ,zoology1 see in the ,reports of the ,british ,association1 in #ahcd1 ,mr4 ,l4 ,jenyns's ,report an the ,recent ,progress and ,present ,state of ,zoology1 and in #ahdd1 ,mr4 ,strickland's ,report on the ,recent ,progress and ,present ,state of ,ornithology4 ,in these ,reports1 the questions of the ,circular ,arrangement1 the ,quinary ,system1 and the relation of ,analogy and ,affinity are discussed4 ,,chapter ,,vii4 ,,the ,,progress ,,of ,,ichthyology4 ,,if it had been already observed and admitted that sciences of the same kind follow1 and must follow1 the same course in the order of their development1 it would be unnecessary to give a history of any special branch of ,systematic ,zoology2 since botany has already afforded us a sufficient example of the progress of the classificatory sciences4 ,but we may be excused for introducing a sketch of the advance of one department of zoology1 since we are led to the attempt by the peculiar advantage we possess in having a complete history of the subject written with great care1 and brought up to the present time1 by a naturalist of unequalled talents and knowledge4 ,i speak of ,cuvier's ,historical ,view of ,ichthyology1 which forms the first chapter of his great work on that part of natural history4 ,the place and office in the progress of this science1 which is assigned to each person by ,cuvier1 will probably not be lightly contested4 ,it will1 therefore1 be no small confirmation of the justice of the views on which the #dbj distribution of the events in the history of botany was founded1 if ,cuvier's representation of the history of ichthyology offers to us obviously a distribution almost identical4 ,we shall find that this is so2--that we have1 in zoology as in botany1 a period of unsystematic knowledge2 a period of misapplied erudition2 an epoch of the discovery of fixed characters2 a period in which many systems were put forward2 a struggle of an artificial and a natural method2 and a gradual tendency of the natural method to a manifestly physiological character4 ,a few references to ,cuvier's history will enable us to illustrate these and other analogies4 ,period of ,unsystematic ,knowledge4--,it would be easy to collect a number of the fabulous stories of early times1 which formed a portion of the imaginary knowledge of men concerning animals as well as plants4 ,but passing over these1 we come to a long period and a great collection of writers1 who1 in various ways1 and with various degrees of merit1 contributed to augment the knowledge which existed concerning fish1 while as yet there was hardly ever any attempt at a classification of that province of the animal kingdom4 ,among these writers1 ,aristotle is by far the most important4 ,indeed he carried on his zoological researches under advantages which rarely fall to the lot of the naturalist2 if it be true1 as ,athenus and ,pliny state1#adjaf that ,alexander gave him sums which amounted to nine hundred talents1 to enable him to collect materials for his history of animals1 and put at his disposal several thousands of men to be employed in hunting1 fishing1 and procuring information for him4 ,the works of his on ,natural ,history which remain to us are1 nine ,books ,of the ,history of ,animals2 four1 ,on the ,parts of ,animals2 five1 ,on the ,generation of ,animals2 one1 ,on the ,going of ,animals2 one1 ,of the ,sensations1 and the ,organs of them2 one1 ,on ,sleeping and ,waking2 one1 ,on the ,motion of ,animals2 one1 ,on the ,length and ,shortness of ,life2 one1 ,on ,youth and ,old ,age2 one1 ,on ,life and ,death2 one1 ,on ,respiration4 ,the knowledge of the external and internal conformation of animals1 their habits1 instincts1 and uses1 which ,aristotle displays in these works1 is spoken of as something wonderful even to the naturalists of our own time4 ,and he may be taken as a sufficient representative of the whole of the period of which we speak2 for he is1 says ,cuvier1#adaaf not only the first1 but the only one of the ancients who has treated of the natural history of fishes 7the province to which #dba we now confine ourselves17 in a scientific point of view1 and in a way which shows genius4 ,note #adjaf3 ,cuv4 ,hist4 ,nat4 des ,poissons1 i4 #ac4 ,note #adaaf3 ,cuv4 p4 #ah4 ,we may pass over1 therefore1 the other ancient authors from whose writings ,cuvier1 with great learning and sagacity1 has levied contributions to the history of ichthyology2 as ,theophrastus1 ,ovid1 ,pliny1 ,oppian1 ,athenus1 lian1 ,ausonius1 ,galen4 ,we may1 too1 leave unnoticed the compilers of the middle ages1 who did little but abstract and disfigure the portions of natural history which they found in the ancients4 ,ichthyological1 like other knowledge1 was scarcely sought except in books1 and on that very account was not understood when it was found4 ,period of ,erudition4--,better times at length came1 and men began to observe nature for themselves4 ,the three great authors who are held to be the founders of modern ichthyology1 appeared in the middle of the sixteenth century2 these were ,blon1 ,rondelet1 and ,salviani1 who all published about #aeee4 ,all the three1 very different from the compilers who filled the interval from ,aristotle to them1 themselves saw and examined the fishes which they describe1 and have given faithful representations of them4 ,but1 resembling in that respect the founders of modern botany1 ,briassavola1 ,ruellius1 ,tragus1 and others1 they resembled them in this also1 that they attempted to make their own observations a commentary upon the ancient writers4 ,faithful to the spirit of their time1 they are far more careful to make out the names which each fish bore in the ancient world1 and to bring together scraps of their history from the authors in whom these names occur1 than to describe them in a lucid manner2 so that without their figures1 says ,cuvier1 it would be almost as difficult to discover their species as those of the ancients4 ,the difficulty of describing and naming species so that they can be recognized1 is little appreciated at first1 although it is in reality the main-spring of the progress of the sciences of classification4 ,aristotle never dreamt that the nomenclature which was in use in his time could ever become obscure2#adbaf hence he has taken no precaution to enable his readers to recognize the species of which he speaks2 and in him and in other ancient authors1 it requires much labor and great felicity of divination to determine what the names mean4 ,the perception of this difficulty among modern naturalists led to systems1 and to nomenclature founded upon system2 but these did not come into #dbb being immediately at the time of which we speak2 nor till the evil had grown to a more inconvenient magnitude4 ,note #adbaf3 ,cuvier1 p4 #ag4 ,period of ,accumulation of ,materials4 ,exotic ,collections4--,the fishes of ,europe were for some time the principal objects of study2 but those of distant regions soon came into notice4#adcaf ,in the seventeenth century the ,dutch conquered ,brazil1 and ,george ,margrave1 employed by them1 described the natural productions of the country1 and especially the fishes4 ,bontius1 in like manner1 described some of those of ,batavia4 ,thus these writers correspond to ,romphius and ,rheede in the history of botany4 ,many others might be mentioned2 but we must hasten to the formation of systems1 which is our main object of attention4 ,note #adcaf3 ,cuv4 p4 #dc4 ,epoch of the ,fixation of ,characters4 ,ray and ,willoughby4--,in botany1 as we have seen1 though ,ray was one of the first who invented a connected system1 he was preceded at a considerable interval by ,csalpinus1 who had given a genuine solution of the same problem4 ,it is not difficult to assign reasons why a sound classification should be discovered for plants at an earlier period than for fishes4 ,the vastly greater number of the known species1 and the facilities which belong to the study of vegetables1 give the botanist a great advantage2 and there are numerical relations of a most definite kind 7for instance1 the number of parts of the seed-vessel employed by ,csalpinus as one of the bases of his system71 which are tolerably obvious in plants1 but which are not easily discovered in animals4 ,and thus we find that in ichthyology1 ,ray1 with his pupil and friend ,willoughby1 appears as the first founder of a tenable system4#addaf ,note #addaf3 ,francisci ,willoughbeii1 ,armigeri1 de ,historia ,piscium1 libri iv4 jussu et sumptibus ,societatis ,regi ,londinensis editi1 c4 ,totum opus recognovit1 coaptavit1 supplevit1 librum etiam primum et secundum adjecit ,joh4 ,raius4 ,oxford1 #affh4 ,the first great division in this system is into cartilaginous and bony fishes2 a primary division1 which had been recognized by ,aristotle1 and is retained by ,cuvier in his latest labors4 ,the subdivisions are determined by the general form of the fish 7as long or flat71 by the teeth1 the presence or absence of ventral fins1 the number of dorsal fins1 and the nature of the spines of the fins1 as soft or prickly4 ,most of these characters have preserved their importance in later systems2 especially the last1 which1 under the terms malacopterygian and acanthopterygian1 holds a place in the best recent arrangements4 #dbc ,that this system was a true first approximation to a solution of the problem1 appears to be allowed by naturalists4 ,although1 says ,cuvier1#adeaf there are in it no genera well defined and well limited1 still in many places the species are brought together very naturally1 and in such a way that a few words of explanation would suffice to form1 from the groups thus presented to us1 several of the genera which have since been received4 ,even in botany1 as we have seen1 genera were hardly maintained with any degree of precision1 till the binary nomenclature of ,linnus made this division a matter of such immense convenience4 ,note #adeaf3 ,cuvier1 p4 #eg4 ,the amount of this convenience1 the value of a brief and sure nomenclature1 had not yet been duly estimated4 ,the work of ,willoughby forms an epoch1#adfaf and a happy epoch1 in the history of ichthyology2 for the science1 once systematized1 could distinguish the new from the old1 arrange methodically1 describe clearly4 ,yet1 because ,willoughby had no nomenclature of his own1 and no fixed names for his genera1 his immediate influence was not great4 ,i will not attempt to trace this influence in succeeding authors1 but proceed to the next important step in the progress of system4 ,note #adfaf3 p4 #eh4 ,improvement of the ,system4 ,artedi4--,peter ,artedi was a countryman and intimate friend of ,linnus2 and rendered to ichthyology nearly the same services which ,linnus rendered to botany4 ,in his ,philosophia ,ichthyologica1 he analysed#adgaf all the interior and exterior parts of animals2 he created a precise terminology for the different forms of which these parts are susceptible2 he laid down rules for the nomenclature of genera and species2 besides his improvements of the subdivisions of the class4 ,it is impossible not to be struck with the close resemblance between these steps1 and those which are due to the ,fundamenta ,botanica4 ,the latter work appeared in #agcf1 the former was published by ,linnus1 after the death of the author1 in #agch2 but ,linnus had already1 as early as #agce1 made use of ,artedi's manuscripts in the ichthyological part of his ,systema ,natur4 ,we cannot doubt that the two young naturalists 7they were nearly of the same age71 must have had a great influence upon each other's views and labors2 and it would be difficult now to ascertain what portion of the peculiar merits of the ,linnan reform was derived from ,artedi4 ,but we may remark that1 in ichthyology at least1 ,artedi appears to have been a naturalist of more original views and profounder philosophy than his friend and editor1 who afterwards himself took up the subject4 #dbd ,the reforms of ,linnus1 in all parts of natural history1 appear as if they were mainly dictated by a love of elegance1 symmetry1 clearness1 and definiteness2 but the improvement of the ichthyological system by ,artedi seems to have been a step in the progress to a natural arrangement4 ,his genera1#adhaf which are forty-five in number1 are so well constituted1 that they have almost all been preserved2 and the subdivisions which the constantly-increasing number of species has compelled his successors to introduce1 have very rarely been such that they have led to the transposition of his genera4 ,note #adgaf3 p4 #bj4 ,note #adhaf3 ,cuvier1 p4 #ga4 ,in its bases1 however1 ,artedi's was an artificial system4 ,his characters were positive and decisive1 founded in general upon the number of rays of the membrane of the gills1 of which he was the first to mark the importance2--upon the relative position of the fins1 upon their number1 upon the part of the mouth where the teeth are found1 upon the conformation of the scales4 ,yet1 in some cases1 he has recourse to the interior anatomy4 ,linnus himself at first did not venture to deviate from the footsteps of a friend1 who1 in this science1 had been his master4 ,but in #ageh1 in the tenth edition of the ,systema ,natur1 he chose to depend upon himself and devised a new ichthyological method4 ,he divided some genera1 united others1 gave to the species trivial names and characteristic phrases1 and added many species to those of ,artedi4 ,yet his innovations are for the most part disapproved of by ,cuvier2 as his transferring the chondropterygian fishes of ,artedi to the class of reptiles1 under the title of ,amphybia nantes2 and his rejecting the distinction of acanthopterygian and malacopterygian1 which1 as we have seen1 had prevailed from the time of ,willoughby1 and introducing in its stead a distribution founded on the presence or absence of the ventral fins1 and on their situation with regard to the pectoral fins4 ,nothing1 says ,cuvier1 more breaks the true connexions of genera than these orders of apodes1 jugulares1 thoracici1 and abdominales4 ,thus ,linnus1 though acknowledging the value and importance of natural orders1 was not happy in his attempts to construct a system which should lead to them4 ,in his detection of good characters for an artificial system he was more fortunate4 ,he was always attentive to number1 as a character2 and he had the very great merit#adiaf of introducing into the classification the number of rays of the fins of each species4 ,this mark is one of great importance and use4 ,and this1 as well as #dbe other branches of natural history1 derived incalculable advantages from the more general merits of the illustrious ,swede2#aejaf--the precision of the characters1 the convenience of a well-settled terminology1 the facility afforded by the binary nomenclature4 ,these recommendations gave him a pre-eminence which was acknowledged by almost all the naturalists of his time1 and displayed by the almost universal adoption of his nomenclature1 in zoology1 as well as in botany2 and by the almost exclusive employment of his distributions of classes1 however imperfect and artificial they might be4 ,note #adiaf3 p4 #gd4 ,note #aejaf3 ,cuvier1 p4 #he4 ,and even#aeaaf if ,linnus had had no other merit than the impulse he gave to the pursuit of natural science1 this alone would suffice to immortalize his name4 ,in rendering natural history easy1 or at least in making it appear so1 he diffused a general taste for it4 ,the great took it up with interest2 the young1 full of ardor1 rushed forwards in all directions1 with the sole intention of completing his system4 ,the civilized world was eager to build the edifice which ,linnus had planned4 ,note #aeaaf3 ,ib4 p4 #hh4 ,this spirit1 among other results1 produced voyages of natural historical research1 sent forth by nations and sovereigns4 ,george the ,third of ,england had the honor of setting the example in this noble career1 by sending out the expeditions of ,byron1 ,wallis1 and ,carteret1 in #agfe4 ,these were followed by those of ,bougainville1 ,cook1 ,forster1 and others4 ,russia also scattered several scientific expeditions through her vast dominions2 and pupils of ,linnus sought the icy shores of ,greenland and ,iceland1 in order to apply his nomenclature to the productions of those climes4 ,but we need not attempt to convey any idea of the vast stores of natural historical treasures which were thus collected from every part of the globe4 ,i shall not endeavor to follow ,cuvier in giving an account of the great works of natural history to which this accumulation of materials gave rise2 such as the magnificent work of ,bloch on ,fishes1 which appeared in #aghb-aghe2 nor need ,i attempt1 by his assistance1 to characterize or place in their due position the several systems of classification proposed about this time4 ,but in the course of these various essays1 the distinction of the artificial and natural methods of classification came more clearly into view than before2 and this is a point so important to the philosophy of the subject1 that we must devote a few words to it4 #dbf ,separation of the ,artificial and ,natural ,methods in ,ichthyology4--,it has already been said that all so-called artificial methods of classification must be natural1 at least as to the narrowest members of the system2 thus the artificial ,linnan method is natural as to species1 and even as to genera4 ,and on the other hand1 all proposed natural methods1 so long as they remain unmodified1 are artificial as to their characteristic marks4 ,thus a ,natural ,method is an attempt to provide positive and distinct characters for the wider as well as for the narrower natural groups4 ,these considerations are applicable to zoology as well as to botany4 ,but the question1 how we know natural groups before we find marks for them1 was1 in botany1 as we have seen1 susceptible only of vague and obscure answers3--the mind forms them1 it was said1 by taking the aggregate of all the characters2 or by establishing a subordination of characters4 ,and each of these answers had its difficulty1 of which the solution appeared to be1 that in attempting to form natural orders we are really guided by a latent undeveloped estimate of physiological relations4 ,now this principle1 which was so dimly seen in the study of vegetables1 shines out with much greater clearness when we come to the study of animals1 in which the physiological relations of the parts are so manifest that they cannot be overlooked1 and have so strong an attraction for our curiosity that we cannot help having our judgments influenced by them4 ,hence the superiority of natural systems in zoology would probably be far more generally allowed than in botany2 and no arrangement of animals which1 in a large number of instances1 violated strong and clear natural affinities1 would be tolerated because it answered the purpose of enabling us easily to find the name and place of the animal in the artificial system4 ,every system of zoological arrangement may be supposed to aspire to be a natural system4 ,but according to the various habits of the minds of systematizers1 this object was pursued more or less steadily and successfully2 and these differences came more and more into view with the increase of knowledge and the multiplication of attempts4 ,bloch1 whose ichthyological labors have been mentioned1 followed in his great work the method of ,linnus4 ,but towards the end of his life he had prepared a general system1 founded upon one single numerical principle2--the number of fins2 just as the sexual system of ,linnus is founded upon the number of stamina2 and he made his subdivisions according to the position of the ventral and pectoral fins2 the same character which ,linnus had employed for his primary #dbg division4 ,he could not have done better1 says ,cuvier1#aebaf if his object had been to turn into ridicule all artificial methods1 and to show to what absurd combinations they may lead4 ,note #aebaf3 p4 #ajh4 ,cuvier himself who always pursued natural systems with a singularly wise and sagacious consistency1 attempted to improve the ichthyological arrangements which had been proposed before him4 ,in his ,rgne ,animal1 published in #ahag1 he attempts the problem of arranging this class2 and the views suggested to him1 both by his successes and his failures1 are so instructive and philosophical1 that ,i cannot illustrate the subject better than by citing some of them4 ,the class of fishes1 he says1#aecaf is1 of all1 that which offers the greatest difficulties1 when we wish to subdivide it into orders1 according to fixed and obvious characters4 ,after many trials1 ,i have determined on the following distribution1 which in some instances is wanting in precision1 but which possesses the advantage of keeping the natural families entire4 ,note #aecaf3 ,rgne ,animal1 vol4 ii4 p4 #aaj4 ,fish form two distinct series2--that of chondropterygians or cartilaginous fish1 and that of fish properly so called4 ,the first of these series has for its character1 that the palatine bones replace1 in it1 the bones of the upper jaw3 moreover the whole of its structure has evident analogies1 which we shall explain4 ,it divides itself into three ,,orders3 ,the ,,cyclostomes1 in which the jaws are soldered 7soudes7 into an immovable ring1 and the bronchi are open in numerous holes4 ,the ,,selacians1 which have the bronchi like the preceding1 but not the jaws4 ,the ,,sturonians1 in which the bronchi are open as usual by a slit furnished with an operculum4 ,the second series1 or that of ordinary fishes1 offers me1 in the first place1 a primary division1 into those of which the maxillary bone and the palatine arch are dovetailed 7engrens7 to the skull4 ,of these ,i make an order of ,,pectognaths1 divided into two families2 the gymnodonts and the scleroderms4 ,after these ,i have the fishes with complete jaws1 but with bronchi which1 instead of having the form of combs1 as in all the others1 have the form of a series of little tufts 7houppes74 ,of these ,i again form an order1 which ,i call ,,lophobranchs1 which only includes one family4 #dbh ,there then remains an innumerable quantity of fishes1 to which we can no longer apply any characters except those of the exterior organs of motion4 ,after long examination1 ,i have found that the least bad of these characters is1 after all1 that employed by ,ray and ,artedi1 taken from the nature of the first rays of the dorsal and of the anal fin4 ,thus ordinary fishes are divided into ,,malacopterygians1 of which all the rays are soft1 except sometimes the first of the dorsal fin or the pectorals2--and ,,acanthopterygians1 which have always the first portion of the dorsal1 or of the first dorsal when there are two1 supported by spinous rays1 and in which the anal has also some such rays1 and the ventrals1 at least1 each one4 ,the former may be subdivided without inconvenience1 according to their ventral fins1 which are sometimes situate behind the abdomen1 sometimes adherent to the apparatus of the shoulder1 or1 finally1 are sometimes wanting altogether4 ,we thus arrive at the three orders of ,,abdominal ,,malacopterygians1 of ,,subbrachians1 and of ,,apodes2 each of which includes some natural families which we shall explain3 the first1 especially1 is very numerous4 ,but this basis of division is absolutely impracticable with the ,acanthopterygians2 and the problem of establishing among these any other subdivision than that of the natural families has hitherto remained for me insoluble4 ,fortunately several of these families offer characters almost as precise as those which we could give to true orders4 ,in truth1 we cannot assign to the families of fishes1 ranks as marked1 as for example1 to those of mammifers4 ,thus the ,chondropterygians on the one hand hold to reptiles by the organs of the senses1 and by those of generation in some2 and they are related to mollusks and worms by the imperfection of the skeleton in others4 ,as to ,ordinary ,fishes1 if any part of the organization is found more developed in some than in others1 there does not result from this any pre-eminence sufficiently marked1 or of sufficient influence upon their whole system1 to oblige us to consult it in the methodical arrangement4 ,we shall place them1 therefore1 nearly in the order in which we have just explained their characters4 ,i have extracted the whole of this passage1 because1 though it is too technical to be understood in detail by the general reader1 those who have followed with any interest the history of the attempts at a natural classification in any department in nature1 will see here a fine example of the problems which such attempts propose1 of the #dbi difficulties which it may present1 and of the reasonings1 labors1 cautions1 and varied resources1 by means of which its solution is sought1 when a great philosophical naturalist girds himself to the task4 ,we see here1 most instructively1 how different the endeavor to frame such a natural system1 is from the procedure of an artificial system1 which carries imperatively through the whole of a class of organized beings1 a system of marks either arbitrary1 or conformable to natural affinities in a partial degree4 ,and we have not often the advantage of having the reasons for a systematic arrangement so clearly and fully indicated1 as is done here1 and in the descriptions of the separate orders4 ,this arrangement ,cuvier adhered to in all its main points1 both in the second edition of the ,rgne ,animal1 published in #ahba1 and in his ,histoire ,naturelle des ,poissons1 of which the first volume was published in #ahbh1 but which unfortunately was not completed at the time of his death4 ,it may be supposed1 therefore1 to be in accordance with those views of zoological philosophy1 which it was the business of his life to form and to apply2 and in a work like the present1 where1 upon so large a question of natural history1 we must be directed in a great measure by the analogy of the history of science1 and by the judgments which seem most to have the character of wisdom1 we appear to be justified in taking ,cuvier's ichthyological system as the nearest approach which has yet been made to a natural method in that department4 ,the true natural method is only one3 artificial methods1 and even good ones1 there may be many1 as we have seen in botany2 and each of these may have its advantages for some particular use4 ,on some methods of this kind1 on which naturalists themselves have hardly yet had time to form a stable and distinct opinion1 it is not our office to decide4 ,but judging1 as ,i have already said1 from the general analogy of the natural sciences1 ,i find it difficult to conceive that the ichthyological method of ,m4 ,agassiz1 recently propounded with an especial reference to fossil fishes1 can be otherwise than an artificial method4 ,it is founded entirely on one part of the animal1 its scaly covering1 and even on a single scale4 ,it does not conform to that which almost all systematic ichthyologists hitherto have considered as a permanent natural distinction of a high order2 the distinction of bony and cartilaginous fishes2 for it is stated that each order contains examples of both4#aedaf ,i do not know what general anatomical or physiological #dcj truths it brings into view2 but they ought to be very important and striking ones1 to entitle them to supersede those which led ,cuvier to his system4 ,to this ,i may add1 that the new ichthyological classification does not seem to form1 as we should expect that any great advance towards a natural system would form1 a connected sequel to the past history of ichthyology2--a step to which anterior discoveries and improvements have led1 and in which they are retained4 ,note #aedaf3 ,dr4 ,buckland's ,bridgewater ,treatise1 p4 #bgj4 ,but notwithstanding these considerations1 the method of ,m4 ,agassiz has probably very great advantages for his purpose2 for in the case of fossil fish1 the parts which are the basis of his system often remain1 when even the skeleton is gone4 ,and we may here again refer to a principle of the classificatory sciences which we cannot make too prominent2--all arrangements and nomenclatures are good1 which enable us to assert general propositions4 ,tried by this test1 we cannot fail to set a high value on the arrangement of ,m4 ,agassiz2 for propositions of the most striking generality respecting fossil remains of fish1 of which geologists before had never dreamt1 are enunciated by means of his groups and names4 ,thus only the two first orders1 the ,placodians and ,ganodians1 existed before the commencement of the cretaceous formation3 the third and fourth orders1 the ,ctenodians and ,cyclodians1 which contain three-fourths of the eight thousand known species of living ,fishes1 appear for the first time in the cretaceous formation3 and other geological relations of these orders1 no less remarkable1 have been ascertained by ,m4 ,agassiz4 ,but we have now1 ,i trust1 pursued these sciences of classification sufficiently far2 and it is time for us to enter upon that higher domain of ,physiology to which1 as we have said4 ,zoology so irresistibly directs us4 #bnd ,ed4 ,i have retained the remarks which ,i ventured at first to make on the ,system of ,m4 ,agassiz2 but ,i believe the opinion of the most philosophical ichthyologists to be that ,cuvier's ,system was too exclusively based on the internal skeleton1 as ,agassiz's was on the external skeleton4 ,in some degree both systems have been superseded1 while all that was true in each has been retained4 ,mr4 ,owen1 in his ,lectures on ,vertebrata 7#ahdf71 takes ,cuvierian characters from the endo-skeleton1 ,agassizian ones from the exo-skeleton1 ,linnan ones from the ventral fins1 ,mllerian ones from the air-bladder1 and combines them by the light of his own researches1 with the view of forming a system more truly natural than any preceding one4 ,as ,i have said above1 naturalists1 in their progress towards a ,natural #dca ,system1 are guided by physiological relations1 latently in ,botany1 but conspicuously in ,zoology4 ,from the epoch of ,cuvier's ,rgne ,animal1 the progress of ,systematic ,zoology is inseparably dependent on the progress of ,comparative ,anatomy4 ,hence ,i have placed ,cuvier's ,classification of animal forms in the next ,book1 which treats of ,physiology4 #dcc ,,book ,,xvii4 ,,organical ,,sciences4 ,,history ,,of ,,physiology ,,and ,,comparative ,,anatomy4 ,fearful and wondrous is the skill which moulds ,our body's vital plan1 ,and from the first dim hidden germ unfolds ,the perfect limbs of man4 ,who1 who can pierce the secret8 tell us how ,something is drawn from naught1 ,life from the inert mass8 ,who1 ,lord6 but thou1 ,whose hand the whole has wrought8 ,of this corporeal substance1 still to be1 ,thine eye a survey took2 ,and all my members1 yet unformed by thee1 ,were written in thy book4 ,,psalm cxxxix4 #ac-af4 #dce ,,introduction4 ,of the ,organical ,sciences ,,though the general notion of life is acknowledged by the most profound philosophers to be dim and mysterious1 even up to the present time2 and must1 in the early stages of human speculation1 have been still more obscure and confused2 it was sufficient1 even then1 to give interest and connexion to men's observations upon their own bodies and those of other animals4 ,it was seen1 that in living things1 certain peculiar processes were constantly repeated1 as those of breathing and of taking food1 for example2 and that a certain conformation of the parts of the animal was subservient to these processes2 and thus were gradually formed the notions of ,function and of ,organization4 ,and the sciences of which these notions formed the basis are clearly distinguishable from all those which we have hitherto considered4 ,we conceive an organized body to be one in which the parts are there for the sake of the whole1 in a manner different from any mechanical or chemical connexion2 we conceive a function to be not merely a process of change1 but of change connected with the general vital process4 ,when mechanical or chemical processes occur in the living body1 they are instrumental to1 and directed by1 the peculiar powers of life4 ,the sciences which thus consider organization and vital functions may be termed organical sciences4 ,when men began to speculate concerning such subjects1 the general mode of apprehending the process in the cases of some functions1 appeared to be almost obvious2 thus it was conceived that the growth of animals arose from their frame appropriating to itself a part of the substance of the food through the various passages of the body4 ,under the influence of such general conceptions1 speculative men were naturally led to endeavor to obtain more clear and definite views of the course of each of such processes1 and of the mode in which the separate parts contributed to it4 ,along with the observation of the living person1 the more searching examination which could be carried on in the dead body1 and the comparison of various kinds of animals1 soon showed that this pursuit was rich in knowledge and in interest4 #dcf ,moreover1 besides the interest which the mere speculative faculty gave to this study1 the ,art of ,healing added to it a great practical value2 and the effects of diseases and of medicines supplied new materials and new motives for the reasonings of the philosopher4 ,in this manner anatomy or physiology may be considered as a science which began to be cultivated in the earliest periods of civilization4 ,like most other ancient sciences1 its career has been one of perpetual though variable progress2 and as in others1 so in this1 each step has implied those which had been previously made1 and cannot be understood aright except we understand them4 ,moreover1 the steps of this advance have been very many and diverse2 the cultivators of anatomy have in all ages been numerous and laborious2 the subject is one of vast extent and complexity2 almost every generation had added something to the current knowledge of its details2 and the general speculations of physiologists have been subtle1 bold1 and learned4 ,it must1 therefore1 be difficult or impossible for a person who has not studied the science with professional diligence and professional advantages1 to form just judgments of the value of the discoveries of various ages and persons1 and to arrange them in their due relation to each other4 ,to this we may add1 that though all the discoveries which have been made with respect to particular functions or organizations are understood to be subordinate to one general science1 the ,philosophy of ,life1 yet the principles and doctrines of this science nowhere exist in a shape generally received and assented to among physiologists2 and thus we have not1 in this science1 the advantage which in some others we have possessed2--of discerning the true direction of its first movements1 by knowing the point to which they ultimately tend2--of running on beyond the earlier discoveries1 and thus looking them in the face1 and reading their true features4 ,with these disadvantages1 all that we can have to say respecting the history of ,physiology must need great indulgence on the part of the reader4 ,yet here1 as in other cases1 we may1 by guiding our views by those of the greatest and most philosophical men who have made the subject their study1 hope to avoid material errors4 ,nor can we well evade making the attempt4 ,to obtain some simple and consistent view of the progress of physiological science1 is in the highest degree important to the completion of our views of the progress of physical science4 ,for the physiological or organical sciences form a class to which the classes already treated of1 the mechanical1 chemical1 and classificatory sciences1 are subordinate and auxiliary4 ,again1 another #dcg circumstance which makes physiology an important part of our survey of human knowledge is1 that we have here a science which is concerned1 indeed1 about material combinations1 but in which we are led almost beyond the borders of the material world1 into the region of sensation and perception1 thought and will4 ,such a contemplation may offer some suggestions which may prepare us for the transition from physical to metaphysical speculations4 ,in the survey which we must1 for such purposes1 take of the progress of physiology1 it is by no means necessary that we should exhaust the subject1 and attempt to give the history of every branch of the knowledge of the phenomena and laws of living creatures4 ,it will be sufficient1 if we follow a few of the lines of such researches1 which may be considered as examples of the whole4 ,we see that life is accompanied and sustained by many processes1 which at first offer themselves to our notice as separate functions1 however they may afterwards be found to be connected and identified2 such are feeling1 digestion1 respiration1 the action of the heart and pulse1 generation1 perception1 voluntary motion4 ,the analysis of any one of these functions may be pursued separately4 ,and since in this1 as in all genuine sciences1 our knowledge becomes real and scientific1 only in so far as it is verified in particular facts1 and thus established in general propositions1 such an original separation of the subjects of research is requisite to a true representation of the growth of real knowledge4 ,the loose hypotheses and systems1 concerning the connexion of different vital faculties and the general nature of living things1 which have often been promulgated1 must be excluded from this part of our plan4 ,we do not deny all value and merit to such speculations2 but they cannot be admitted in the earlier stages of the history of physiology1 treated of as an inductive science4 ,if the doctrine so propounded have a solid and permanent truth1 they will again come before us when we have travelled through the range of more limited truths1 and are prepared to ascend with security and certainty into the higher region of general physiological principles4 ,if they cannot be arrived at by such a road1 they are then1 however plausible and pleasing1 no portion of that real and progressive science with which alone our history is concerned4 ,we proceed1 therefore1 to trace the establishment of some of the more limited but certain doctrines of physiology4 #dch ,,chapter ,i4 ,,discovery ,,of ,,the ,,organs ,,of ,,voluntary ,,motion4 ,sect4 #a4--,knowledge of ,galen and his ,predecessors4 ,,in the earliest conceptions which men entertained of their power of moving their own members1 they probably had no thought of any mechanism or organization by which this was effected4 ,the foot and the hand1 no less than the head1 were seen to be endowed with life2 and this pervading life seemed sufficiently to explain the power of motion in each part of the frame1 without its being held necessary to seek out a special seat of the will1 or instruments by which its impulses were made effective4 ,but the slightest inspection of dissected animals showed that their limbs were formed of a curious and complex collection of cordage1 and communications of various kinds1 running along and connecting the bones of the skeleton4 ,these cords and communications we now distinguish as muscles1 nerves1 veins1 arteries1 c42 and among these1 we assign to the muscles the office of moving the parts to which they are attached1 as cords move the parts of a machine4 ,though this action of the muscles on the bones may now appear very obvious1 it was1 probably1 not at first discerned4 ,it is observed that ,homer1 who describes the wounds which are inflicted in his battles with so much apparent anatomical precision1 nowhere employs the word muscle4 ,and even ,hippocrates of ,cos1 the most celebrated physician of antiquity1 is held to have had no distinct conception of such an organ4#aag ,he always employs the word flesh when he means muscle1 and the first explanation of the latter word 77 occurs in a spurious work ascribed to him4 ,for nerves1 sinews1 ligaments1#bag he used indiscriminately the same terms2 7 or 27 and of these nerves 77 he asserts that they contract the limbs4 ,nor do we find much more distinctness on this subject even in ,aristotle1 a generation or two later4 ,the origin of the 1 he says1#cag is from the heart2 they connect #dci the bones1 and surround the joints4 ,it is clear that he means here the muscles1 and therefore it is with injustice that he has been accused of the gross error of deriving the nerves from the heart4 ,and he is held to have really had the merit#dag of discovering the nerves of sensation1 which he calls the canals of the brain 7 72 but the analysis of the mechanism of motion is left by him almost untouched4 ,perhaps his want of sound mechanical notions1 and his constant straining after verbal generalities1 and systematic classifications of the widest kind1 supply the true account of his thus missing the solution of one of the simplest problems of ,anatomy4 ,note #aag3 ,sprengel1 ,geschichte der ,arzneikunde1 i4 #chb4 ,note #bag3 ,sprengel1 ,gesch4 ,arz4 i4 #che4 ,note #cag3 ,hist4 ,anim4 iii4 #e4 ,note #dag3 ,ib4 i4 #def4 ,in this1 however1 as in other subjects1 his immediate predecessors were far from remedying the deficiencies of his doctrines4 ,those who professed to study physiology and medicine were1 for the most part1 studious only to frame some general system of abstract principles1 which might give an appearance of connexion and profundity to their tenets4 ,in this manner the successors of ,hippocrates became a medical school1 of great note in its day1 designated as the ,dogmatic school2#eag in opposition to which arose an ,empiric sect1 who professed to deduce their modes of cure1 not from theoretical dogmas1 but from experience4 ,these rival parties prevailed principally in ,asia ,minor and ,egypt1 during the time of ,alexander's successors1--a period rich in names1 but poor in discoveries2 and we find no clear evidence of any decided advance in anatomy1 such as we are here attempting to trace4 ,note #eag3 ,sprengel1 ,gesch4 ,arz4 i4 #ehc4 ,the victories of ,lucullus and ,pompeius1 in ,greece and ,asia1 made the ,romans acquainted with the ,greek philosophy2 and the consequence soon was1 that shoals of philosophers1 rhetoricians1 poets1 and physicians#fag streamed from ,greece1 ,asia ,minor1 and ,egypt1 to ,rome and ,italy1 to traffic their knowledge and their arts for ,roman wealth4 ,among these1 was one person whose name makes a great figure in the history of medicine1 ,asclepiades of ,prusa in ,bithynia4 ,this man appears to have been a quack1 with the usual endowments of his class2--boldness1 singularity1 a contemptuous rejection of all previously esteemed opinions1 a new classification of diseases1 a new list of medicines1 and the assertion of some wonderful cures4 ,he would not1 on such accounts1 deserve a place in the history of science1 but that he became the founder of a new school1 the ,methodic1 which professed to hold itself separate both from the ,dogmatics and the ,empirics4 #ddj ,note #fag3 ,sprengel1 ,gesch4 ,arz4 ii4 #e4 ,i have noticed these schools of medicine1 because1 though ,i am not able to state distinctly their respective merits in the cultivation of anatomy1 a great progress in that science was undoubtedly made during their domination1 of which the praise must1 ,i conceive1 be in some way divided among them4 ,the amount of this progress we are able to estimate1 when we come to the works of ,galen1 who flourished under the ,antonines1 and died about ,a4,d4 #bjc4 ,the following passage from his works will show that this progress in knowledge was not made without the usual condition of laborious and careful experiment1 while it implies the curious fact of such experiment being conducted by means of family tradition and instruction1 so as to give rise to a caste of dissectors4 ,in the opening of his ,second ,book ,on ,anatomical ,manipulations1 he speaks thus of his predecessors3 ,i do not blame the ancients1 who did not write books on anatomical manipulation2 though ,i praise ,marinus1 who did4 ,for it was superfluous for them to compose such records for themselves or others1 while they were1 from their childhood1 exercised by their parents in dissecting1 just as familiarly as in writing and reading2 so that there was no more fear of their forgetting their anatomy1 than of forgetting their alphabet4 ,but when grown men1 as well as children1 were taught1 this thorough discipline fell off2 and1 the art being carried out of the family of the ,asclepiads1 and declining by repeated transmission1 books became necessary for the student4 ,that the general structure of the animal frame1 as composed of bones and muscles1 was known with great accuracy before the time of ,galen1 is manifest from the nature of the mistakes and deficiencies of his predecessors which he finds it necessary to notice4 ,thus he observes1 that some anatomists have made one muscle into two1 from its having two heads2--that they have overlooked some of the muscles in the face of an ape1 in consequence of not skinning the animal with their own hands2--and the like4 ,such remarks imply that the current knowledge of this kind was tolerably complete4 ,galen's own views of the general mechanical structure of an animal are very clear and sound4 ,the skeleton1 he observes1 discharges#gag the office of the pole of a tent1 or the walls of a house4 ,with respect to the action of the muscles1 his views were anatomically and mechanically correct2 in some instances1 he showed what this action was1 by severing the muscle4#hag ,he himself added considerably to the existing knowledge of #dda this subject2 and his discoveries and descriptions1 even of very minute parts of the muscular system1 are spoken of with praise by modern anatomists4#iag ,note #gag3 ,de ,anatom4 ,administ4 i4 #b4 ,note #hag3 ,sprengel1 ii4 #aeg4 ,note #iag3 ,sprengel1 ii4 #aej4 ,we may consider1 therefore1 that the doctrine of the muscular system1 as a collection of cords and sheets1 by the contraction of which the parts of the body are moved and supported1 was firmly established1 and completely followed into detail1 by ,galen and his predecessors4 ,but there is another class of organs connected with voluntary motion1 the nerves1 and we must for a moment trace the opinions which prevailed respecting these4 ,aristotle1 as we have said1 noticed some of the nerves of sensation4 ,but ,herophilus1 who lived in ,egypt in the time of the first ,ptolemy1 distinguished nerves as the organs of the will1#ajag and ,rufus1 who lived in the time of ,trajan1#aaag divides the nerves into sensitive and motive1 and derives them all from the brain4 ,but this did not imply that men had yet distinguished the nerves from the muscles4 ,even ,galen maintained that every muscle consists of a bundle of nerves and sinews4#abag ,but the important points1 the necessity of the nerve1 and the origination of all this apparatus of motion from the brain1 he insists upon with great clearness and force4 ,thus he proved the necessity experimentally1 by cutting through some of the bundles of nerves1#acag and thus preventing the corresponding motions4 ,and it is1 he says1#adag allowed by all1 both physicians and philosophers1 that where the origin of the nerve is1 there the seat of the soul 7 7 must be3 now this1 he adds1 is in the brain1 and not in the heart4 ,note #ajag3 ,ib4 i4 #ecd4 ,note #aaag3 ,ib4 ii4 #fg4 ,note #abag3 ,ibid4 ii4 #aeb4 ,galen1 ,de ,motu ,musc41 p4 #eec4 ,note #acag3 ,ib4 #aeg4 ,note #adag3 ,de ,hippocr4 et ,plat4 ,dog4 viii4 #a4 ,thus the general construction and arrangement of the organization by which voluntary motion is effected1 was well made out at the time of ,galen1 and is found distinctly delivered in his works4 ,we cannot1 perhaps1 justly ascribe any large portion of the general discovery to him3 indeed1 the conception of the mechanism of the skeleton and muscles was probably so gradually unfolded in the minds of anatomical students1 that it would be difficult1 even if we knew the labors of each person1 to select one1 as peculiarly the author of the discovery4 ,but it is clear that all those who did materially contribute to the establishment of this doctrine1 must have possessed the qualifications which we find in ,galen for such a task2 namely1 clear mechanical views of what the #ddb tensions of collections of strings could do1 and an exact practical acquaintance with the muscular cordage which exists in the animal frame2--in short1 in this as in other instances of real advance in science1 there must have been clear ideas and real facts1 unity of thought and extent of observation1 brought into contact4 ,sect4 #b4--,recognition of ,final ,causes in ,physiology4 ,galen4 ,,there is one idea which the researches of the physiologist and the anatomist so constantly force upon him1 that he cannot help assuming it as one of the guides of his speculations2 ,i mean1 the idea of a purpose1 or1 as it is called in ,aristotelian phrase1 a final cause1 in the arrangements of the animal frame4 ,it is impossible to doubt that the motive nerves run along the limbs1 in order that they may convey to the muscles the impulses of the will2 and that the muscles are attached to the bones1 in order that they may move and support them4 ,this conviction prevails so steadily among anatomists1 that even when the use of any part is altogether unknown1 it is still taken for granted that it has some use4 ,the developement of this conviction1--of a purpose in the parts of animals1--of a function to which each portion of the organization is subservient1--contributed greatly to the progress of physiology2 for it constantly urged men forwards in their researches respecting each organ1 till some definite view of its purpose was obtained4 ,the assumption of hypothetical final causes in ,physics may have been1 as ,bacon asserts it to have been1 prejudicial to science2 but the assumption of unknown final causes in ,physiology1 has given rise to the science4 ,the two branches of speculation1 ,physics and ,physiology1 were equally led1 by every new phenomenon1 to ask their question1 ,why8 ,but1 in the former case1 why meant through what cause8 in the latter1 for what end8 ,and though it may be possible to introduce into physiology the doctrine of efficient causes1 such a step can never obliterate the obligations which the science owes to the pervading conception of a purpose contained in all organization4 ,this conception makes its appearance very early4 ,indeed1 without any special study of our structure1 the thought1 that we are fearfully and wonderfully made1 forces itself upon men1 with a mysterious impressiveness1 as a suggestion of our ,maker4 ,in this bearing1 the thought is developed to a considerable extent in the well-known passage in ,xenophon's ,conversations of ,socrates4 ,nor did it ever lose its hold on sober-minded and instructed men4 ,the ,epicureans1 indeed1 #ddc held that the eye was not made for seeing1 nor the ear for hearing2 and ,asclepiades1 whom we have already mentioned as an impudent pretender1 adopted this wild dogma4#aeag ,such assertions required no labor4 ,it is easy1 says ,galen1#afag for people like ,asclepiades1 when they come to any difficulty1 to say that ,nature has worked to no purpose4 ,the great anatomist himself pursues his subject in a very different temper4 ,in a well-known passage1 he breaks out into an enthusiastic scorn of the folly of the atheistical notions4#agag ,try1 he says1 if you can imagine a shoe made with half the skill which appears in the skin of the foot4 ,some one had spoken of a structure of the human body which he would have preferred to that which it now has4 ,see1 ,galen exclaims1 after pointing out the absurdity of the imaginary scheme1 see what brutishness there is in this wish4 ,but if ,i were to spend more words on such cattle1 reasonable men might blame me for desecrating my work1 which ,i regard as a religious hymn in honor of the ,creator4 ,note #aeag3 ,sprengel1 ii4 #ae4 ,note #afag3 ,de ,usu ,part4 v4 #e1 7on the kidneys47 ,note #agag3 ,de ,usu ,part4 iii4 #aj4 ,galen was from the first highly esteemed as an anatomist4 ,he was originally of ,pergamus2 and after receiving the instructions of many medical and philosophical professors1 and especially of those of ,alexandria1 which was then the metropolis of the learned and scientific world1 he came to ,rome1 where his reputation was soon so great as to excite the envy and hatred of the ,roman physicians4 ,the emperors ,marcus ,aurelius and ,lucius ,verus would have retained him near them2 but he preferred pursuing his travels1 directed principally by curiosity4 ,when he died1 he left behind him numerous works1 all of them of great value for the light they throw on the history of anatomy and medicine2 and these were for a long period the storehouse of all the most important anatomical knowledge which the world possessed4 ,in the time of intellectual barrenness and servility1 among the ,arabians and the ,europeans of the dark ages1 the writings of ,galen had almost unquestioned authority2#ahag and it was only by an uncommon effort of independent thinking that ,abdollatif ventured to assert1 that even ,galen's assertions must give way to the evidence of the senses4 ,in more modern times1 when ,vesalius1 in the sixteenth century1 accused ,galen of mistakes1 he drew upon himself the hostility of the whole body of physicians4 ,yet the mistakes were such as might have #ddd been pointed out and confessed#aiag without acrimony1 if1 in times of revolution1 mildness and moderation were possible2 but an impatience of the superstition of tradition on the part of the innovators1 and an alarm of the subversion of all recognized truths on the part of the established teachers1 inflame and pervert all such discussions4 ,vesalius's main charge against ,galen is1 that his dissections were performed upon animals1 and not upon the human body4 ,galen himself speaks of the dissection of apes as a very familiar employment1 and states that he killed them by drowning4 ,the natural difficulties which1 in various ages1 have prevented the unlimited prosecution of human dissection1 operated strongly among the ancients1 and it would have been difficult1 under such circumstances1 to proceed more judiciously than ,galen did4 ,note #ahag3 ,sprengel1 ii4 #cei4 ,note #aiag3 ,cuv4 ,leons sur l',hist4 des ,sc4 ,nat4 p4 #be4 ,i shall now proceed to the history of the discovery of another and less obvious function1 the circulation of the blood1 which belongs to modern times4 ,,chapter ,,ii4 ,,discovery ,,of ,,the ,,circulation ,,of ,,the ,,blood4 ,sect4 #a4--,prelude to the ,discovery4 ,,the blood-vessels1 the veins and arteries1 are as evident and peculiar in their appearance as the muscles2 but their function is by no means so obvious4 ,hippocrates#bjag did not discriminate ,veins and ,arteries2 both are called by the same name 77 and the word from which artery comes 77 means1 in his works1 the windpipe4 ,aristotle1 scanty as was his knowledge of the vessels of the body1 has yet the merit of having traced the origin of all the veins to the heart4 ,he expressly contradicts those of his predecessors who had derived the veins from the head2#baag and refers to dissection for the proof4 ,if the book ,on the ,breath be genuine 7which is doubted71 ,aristotle was aware of the distinction between veins and arteries4 ,every artery1 #dde it is there asserted1 is accompanied by a vein2 the former are filled only with breath or air4#bbag ,but whether or no this passage be ,aristotle's1 he held opinions equally erroneous2 as1 that the windpipe conveys air into the heart4#bcag ,galen#bdag was far from having views respecting the blood-vessels1 as sound as those which he entertained concerning the muscles4 ,he held the liver to be the origin of the veins1 and the heart of the arteries4 ,he was1 however1 acquainted with their junctions1 or anastomoses4 ,but we find no material advance in the knowledge of this subject1 till we overleap the blank of the middle ages1 and reach the dawn of modern science4 ,note #bjag3 ,sprengel1 i4 #chc4 ,note #baag3 ,hist4 ,animal4 iii4 #c4 ,note #bbag3 ,de ,spiritu1 v4 #ajgh4 ,note #bcag3 ,spr4 i4 #eja4 ,note #bdag3 ,ib4 ii4 #aeb4 ,the father of modern anatomy is held to be ,mondino1#beag who dissected and taught at ,bologna in #acae4 ,some writers have traced in him the rudiments of the doctrine of the circulation of the blood2 for he says that the heart transmits blood to the lungs4 ,but it is allowed1 that he afterwards destroys the merit of his remark1 by repeating the old assertion that the left ventricle ought to contain spirit or air1 which it generates from the blood4 ,note #beag3 ,encyc4 ,brit4 #fib4 ,anatomy4 ,anatomy was cultivated with great diligence and talent in ,italy by ,achillini1 ,carpa1 and ,messa1 and in ,france by ,sylvius and ,stephanus 7,dubois and ,etienne74 ,yet still these empty assumptions respecting the heart and blood-vessels kept their ground4 ,vesalius1 a native of ,brussels1 has been termed the founder of human anatomy1 and his great work ,de ,humani ,corporis ,fabric is1 even yet1 a splendid monument of art1 as well as science4 ,it is said that his figures were designed by ,titian2 and if this be not exactly true1 says ,cuvier1#bfag they must1 at least1 be from the pencil of one of the most distinguished pupils of the great painter2 for to this day1 though we have more finished drawings1 we have no designs that are more artist-like4 ,fallopius1 who succeeded ,vesalius at ,padua1 made some additions to the researches of his predecessor2 but in his treatise ,de ,principio ,venarum1 it is clearly seen#bgag that the circulation of the blood was unknown to him4 ,eustachius also1 whom ,cuvier groups with ,vesalius and ,fallopius1 as the three great founders of modern anatomy1 wrote a treatise on the vein azygos#bhag which is a little treatise on comparative anatomy2 but the discovery of the functions of the veins came from a different quarter4 #ddf ,note #bfag3 ,leons sur l',hist4 des ,sc4 ,nat4 p4 #ba4 ,note #bgag3 ,cuv4 ,sc4 ,nat4 p4 #cb4 ,note #bhag3 ,ib4 p4 #cd4 ,the unfortunate ,servetus1 who was burnt at ,geneva as a heretic in #aeec1 is the first person who speaks distinctly of the small circulation1 or that which carries the blood from the heart to the lungs1 and back again to the heart4 ,his work entitled ,christianismi ,restitutio was also burnt2 and only two copies are known to have escaped the flames4 ,it is in this work that he asserts the doctrine in question1 as a collateral argument or illustration of his subject4 ,the communication between the right and left ventricle of the heart1 is made1 he says1 not as is commonly believed1 through the partition of the heart1 but by a remarkable artifice 7magno artificio7 the blood is carried from the right ventricle by a long circuit through the lungs2 is elaborated by the lungs1 made yellow1 and transfused from the vena arteriosa into the arteria venosa4 ,this truth is1 however1 mixed with various of the traditional fancies concerning the vital spirit1 which has its origin in the left ventricle4 ,it may be doubted1 also1 how far ,servetus formed his opinion upon conjecture1 and on a hypothetical view of the formation of this vital spirit4 ,and we may1 perhaps1 more justly ascribe the real establishment of the pulmonary circulation as an inductive truth1 to ,realdus ,columbus1 a pupil and successor of ,vesalius at ,padua1 who published a work ,de ,re ,anatomic in #aeei1 in which he claims this discovery as his own4#biag ,note #biag3 ,encyc4 ,brit4 ,andrew ,csalpinus1 who has already come under our notice as one of the fathers of modern inductive science1 both by his metaphysical and his physical speculations1 described the pulmonary circulation still more completely in his ,qustiones ,peripatetic1 and even seemed to be on the eve of discovering the great circulation2 for he remarked the swelling of veins below ligatures1 and inferred from it a refluent motion of blood in these vessels4#cjag ,but another discovery of structure was needed1 to prepare the way for this discovery of function2 and this was made by ,fabricius of ,acquapendente1 who succeeded in the grand list of great professors at ,padua1 and taught there for fifty years4#caag ,sylvius had discovered the existence of the valves of the veins2 but ,fabricius remarked that they are all turned towards the heart4 ,combining this disposition with that of the valves of the heart1 and with the absence of valves in the arteries1 he might have come to the conclusion#cbag that the blood moves in a different direction in the arteries and in the veins1 and might thus have discovered the circulation3 but this glory was reserved for ,william ,harvey3 so true #ddg is it1 observes ,cuvier1 that we are often on the brink of a discovery without suspecting that we are so2--so true is it1 we may add1 that a certain succession of time and of persons is generally necessary to familiarize men with one thought1 before they can advance to that which is the next in order4 ,note #cjag3 ,ib4 ,note #caag3 ,cuv4 p4 #dd4 ,note #cbag3 p4 #de4 ,sect4 #b4--,the ,discovery of the ,circulation made by ,harvey4 ,,william ,,harvey was born in #aegh1 at ,folkestone in ,kent4#ccag ,he first studied at ,cambridge3 he afterwards went to ,padua1 where the celebrity of ,fabricius of ,acquapendente attracted from all parts those who wished to be instructed in anatomy and physiology4 ,in this city1 excited by the discovery of the valves of the veins1 which his master had recently made1 and reflecting on the direction of the valves which are at the entrance of the veins into the heart1 and at the exit of the arteries from it1 he conceived the idea of making experiments1 in order to determine what is the course of the blood in its vessels4 ,he found that when he tied up veins in various animals1 they swelled below the ligature1 or in the part furthest from the heart2 while arteries1 with a like ligature1 swelled on the side next the heart4 ,combining these facts with the direction of the valves1 he came to the conclusion that the blood is impelled1 by the left side of the heart1 in the arteries to the extremities1 and thence returns by the veins into the right side of the heart4 ,he showed1 too1 how this was confirmed by the phenomena of the pulse1 and by the results of opening the vessels4 ,he proved1 also1 that the circulation of the lungs is a continuation of the larger circulation2 and thus the whole doctrine of the double circulation was established4 ,note #ccag3 ,cuv4 p4 #ea4 ,harvey's experiments had been made in #afaf and #afah2 it is commonly said that he first promulgated his opinion in #afai2 but the manuscript of the lectures1 delivered by him as lecturer to the ,college of ,physicians1 is extant in the ,british ,museum1 and1 containing the propositions on which the doctrine is founded1 refers them to ,april1 #afaf4 ,it was not till #afbh that he published1 at ,frankfort1 his ,exercitatio ,anatomica de ,motu ,cordis et ,sanguinis2 but he there observes that he had for above nine years confirmed and illustrated his opinion in his lectures1 by arguments grounded upon ocular demonstrations4 #ddh ,sect4 #c4--,reception of the ,discovery4 ,,without dwelling long upon the circumstances of the general reception of this doctrine1 we may observe that it was1 for the most part1 readily accepted by his countrymen1 but that abroad it had to encounter considerable opposition4 ,although1 as we have seen1 his predecessors had approached so near to the discovery1 men's minds were by no means as yet prepared to receive it4 ,several physicians denied the truth of the opinion1 among whom the most eminent was ,riolan1 professor at the ,collge de ,france4 ,other writers1 as usually happens in the case of great discoveries1 asserted that the doctrine was ancient1 and even that it was known to ,hippocrates4 ,harvey defended his opinion with spirit and temper2 yet he appears to have retained a lively recollection of the disagreeable nature of the struggles in which he was thus involved4 ,at a later period of his life1 ,ent1#cdag one of his admirers1 who visited him1 and urged him to publish the researches on generation1 on which he had long been engaged1 gives this account of the manner in which he received the proposal3 ,and would you then advise me1 7smilingly replies the doctor17 to quit the tranquillity of this haven1 wherein ,i now calmly spend my days1 and again commit myself to the unfaithful ocean8 ,you are not ignorant how great troubles my lucubrations1 formerly published1 have raised4 ,better it is1 certainly1 at some time1 to endeavor to grow wise at home in private1 than by the hasty divulgation of such things to the knowledge whereof you have attained with vast labor1 to stir up tempests that may deprive you of your leisure and quiet for the future4 ,note #cdag3 ,epist4 ,dedic4 to ,anatom4 ,exercit4 ,his merits were1 however1 soon generally recognized4 ,he was#ceag made physician to ,james the ,first1 and afterwards to ,charles the ,first1 and attended that unfortunate monarch in the civil war4 ,he had the permission of the parliament to accompany the king on his leaving ,london2 but this did not protect him from having his house plundered in his absence1 not only of its furniture1 but1 which he felt more1 of the records of his experiments4 ,in #afeb1 his brethren of the ,college of ,physicians placed a marble bust of him in their hall1 with an inscription recording his discoveries2 and two years later1 he was nominated to the office of ,president of the ,college1 which however he #ddi declined in consequence of his age and infirmities4 ,his doctrine soon acquired popular currency2 it was1 for instance1 taken by ,descartes#cfag as the basis of his physiology in his work ,on ,man2 and ,harvey had the pleasure1 which is often denied to discoverers1 of seeing his discovery generally adopted during his lifetime4 ,note #ceag3 ,biog4 ,brit4 ,note #cfag3 ,cuv4 #ec4 ,sect4 #d4--;,bearing of the ,discovery on the ,progress of ,physiology4 ,,in considering the intellectual processes by which ,harvey's discoveries were made1 it is impossible not to notice1 that the recognition of a creative purpose1 which1 as we have said1 appears in all sound physiological reasonings1 prevails eminently here4 ,i remember1 says ,boyle1 that when ,i asked our famous ,harvey what were the things that induced him to think of a circulation of the blood1 he answered me1 that when he took notice that the valves in the veins of so many parts of the body were so placed1 that they gave a free passage to the blood towards the heart1 but opposed the passage of the venal blood the contrary way2 he was incited to imagine that so provident a cause as ,nature had not placed so many valves without design2 and no design seemed more probable than that the blood should be sent through the arteries1 and return through the veins1 whose valves did not oppose its course that way4 ,we may notice further1 that this discovery implied the usual conditions1 distinct general notions1 careful observation of many facts1 and the mental act of bringing together these elements of truth4 ,harvey must have possessed clear views of the motions and pressures of a fluid circulating in ramifying tubes1 to enable him to see how the position of valves1 the pulsation of the heart1 the effects of ligatures1 of bleeding1 and of other circumstances1 ought to manifest themselves in order to confirm his view4 ,that he referred to a multiplied and varied experience for the evidence that it was so confirmed1 we have already said4 ,like all the best philosophers of his time1 he insists rigidly upon the necessity of such experience4 ,in every science1 he says1#cgag be it what it will1 a diligent observation is requisite1 and sense itself must be frequently consulted4 ,we must not rely upon other men's experience1 but our own1 without which no man is a proper disciple of any part of natural knowledge4 ,and by publishing his experiments1 he trusts1 he adds1 that he has enabled his reader to be an equitable #dej umpire between ,aristotle and ,galen2 or rather1 he might have said1 to see how1 in the promotion of science1 sense and reason1 observation and invention1 have a mutual need of each other4 ,note #cgag3 ,generation of ,animals1 ,pref4 ,we may observe further1 that though ,harvey's glory1 in the case now before us1 rested upon his having proved the reality of certain mechanical movements and actions in the blood1 this discovery1 and all other physiological truths1 necessarily involved the assumption of some peculiar agency belonging to living things1 different both from mechanical agency1 and from chemical2 and in short1 something vital1 and not physical merely4 ,for when it was seen that the pulsation of the heart1 its systole and diastole1 caused the circulation of the blood1 it might still be asked1 what force caused this constantly-recurring contraction and expansion4 ,and again1 circulation is closely connected with respiration2 the blood is1 by the circulation1 carried to the lungs1 and is there1 according to the expression of ,columbus and ,harvey1 mixed with air4 ,but by what mechanism does this mixture take place1 and what is the real nature of it8 ,and when succeeding researches had enabled physiologists to give an answer to this question1 as far as chemical relations go1 and to say1 that the change consists in the abstraction of the carbon from the blood by means of the oxygen of the atmosphere2 they were still only led to ask further1 how this chemical change was effected1 and how such a change of the blood fitted it for its uses4 ,every function of which we explain the course1 the mechanism1 or the chemistry1 is connected with other functions1--is subservient to them1 and they to it2 and all together are parts of the general vital system of the animal1 ministering to its life1 but deriving their activity from the life4 ,life is not a collection of forces1 or polarities1 or affinities1 such as any of the physical or chemical sciences contemplate2 it has powers of its own1 which often supersede those subordinate relations2 and in the cases where men have traced such agents in the animal frame1 they have always seen1 and usually acknowledged1 that these agents were ministerial to some higher agency1 more difficult to trace than these1 but more truly the cause of the phenomena4 ,the discovery of the mechanical and chemical conditions of the vital functions1 as a step in physiology1 may be compared to the discovery of the laws of phenomena in the heavens by ,kepler and his predecessors1 while the discovery of the force by which they were produced was still reserved in mystery for ,newton to bring to light4 ,the subordinate relation of the facts1 their 9999dependence on space and time1 their reduction to order and cycle1 had been fully performed2 but the #dea reference of them to distinct ideas of causation1 their interpretation as the results of mechanical force1 was omitted or attempted in vain4 ,the very notion of such ,force1 and of the manner in which motions were determined by it1 was in the highest degree vague and vacillating2 and a century was requisite1 as we have seen1 to give to the notion that clearness and fixity which made the ,mechanics of the ,heavens a possible science4 ,in like manner1 the notion of ,life1 and of ,vital ,forces1 is still too obscure to be steadily held4 ,we cannot connect it distinctly with severe inductions from facts4 ,we can trace the motions of the animal fluids as ,kepler traced the motions of the planets2 but when we seek to render a reason for these motions1 like him1 we recur to terms of a wide and profound1 but mysterious import2 to ,virtues1 ,influences1 undefined ,powers4 ,yet we are not on this account to despair4 ,the very instance to which ,i am referring shows us how rich is the promise of the future4 ,why1 says ,cuvier1#chag may not ,natural ,history one day have its ,newton8 ,the idea of the vital forces may gradually become so clear and definite as to be available in science2 and future generations may include1 in their physiology1 propositions elevated as far above the circulation of the blood1 as the doctrine of universal gravitation goes beyond the explanation of the heavenly motions by epicycles4 ,note #chag3 ,ossem4 ,foss4 ,introd4 ,if1 by what has been said1 ,i have exemplified sufficiently the nature of those steps in physiology1 which1 like the discovery of the ,circulation1 give an explanation of the process of some of the animal functions1 it is not necessary for me to dwell longer on the subject2 for to write a history1 or even a sketch of the history of ,physiology1 would suit neither my powers nor my purpose4 ,some further analysis of the general views which have been promulgated by the most eminent physiologists1 may perhaps be attempted in treating of the ,philosophy of ,inductive ,science2 but the estimation of the value of recent speculations and investigations must be left to those who have made this vast subject the study of their lives4 ,a few brief notices may1 however1 be here introduced4 #deb ,,chapter ,,iii4 ,,discovery ,,of ,,the ,,motion ,,of ,,the ,,chyle1 ,,and ,,consequent ,,speculations4 ,sect4 #a4--,the ,discovery of the ,motion of the ,chyle4 ,,it may have been observed in the previous course of this ,history of the ,sciences1 that the discoveries in each science have a peculiar physiognomy3 something of a common type may be traced in the progress of each of the theories belonging to the same department of knowledge4 ,we may notice something of this common form in the various branches of physiological speculation4 ,in most1 or all of them1 we have1 as we have noticed the case to be with respect to the circulation of the blood1 clear and certain discoveries of mechanical and chemical processes1 succeeded by speculations far more obscure1 doubtful1 and vague1 respecting the relation of these changes to the laws of life4 ,this feature in the history of physiology may be further instanced1 7it shall be done very briefly71 in one or two other cases4 ,and we may observe1 that the lesson which we are to collect from this narrative1 is by no means that we are to confine ourselves to the positive discovery1 and reject all the less clear and certain speculations4 ,to do this1 would be to lose most of the chances of ulterior progress2 for though it may be1 that our conceptions of the nature of organic life are not yet sufficiently precise and steady to become the guides to positive inductive truths1 still the only way in which these peculiar physiological ideas can be made more distinct and precise1 and thus brought more nearly into a scientific form1 is by this struggle with our ignorance or imperfect knowledge4 ,this is the lesson we have learnt from the history of physical astronomy and other sciences4 ,we must strive to refer facts which are known and understood1 to higher principles1 of which we cannot doubt the existence1 and of which1 in some degree1 we can see the place2 however dim and shadowy may be the glimpses we have hitherto been able to obtain of their forms4 ,we may often fail in such attempts1 but without the attempt we can never succeed4 #dec ,that the food is received into the stomach1 there undergoes a change of its consistence1 and is then propelled along the intestines1 are obvious facts in the animal economy4 ,but a discovery made in the course of the seventeenth century brought into clearer light the sequel of this series of processes1 and its connexion with other functions4 ,in the year #afbb1 ,asellius or ,aselli#ciag discovered certain minute vessels1 termed lacteals1 which absorb a white liquid 7the chyle7 from the bowels1 and pour it into the blood4 ,these vessels had1 in fact1 been discovered by ,eristratus1 in the ancient world1#djag in the time of ,ptolemy2 but ,aselli was the first modern who attended to them4 ,he described them in a treatise entitled ,de ,venis ,lacteis1 cum figuris elegantissimis1 printed at ,milan in #afbg1 the year after the death of the author4 ,the work is remarkable as the first which exhibits colored anatomical figures2 the arteries and veins are represented in red1 the lacteals in black4 ,note #ciag3 ,mayo1 ,physiology1 p4 #aef4 ,note #djag3 ,cuv4 ,hist4 ,sc4 p4 #ej4 ,eustachius1#daag at an earlier period1 had described 7in the horse7 the thoracic duct by which the chyle is poured into the subclavian vein1 on the right side of the neck4 ,but this description did not excite so much notice as to prevent its being forgotten1 and rediscovered in #aeej1 after the knowledge of the circulation of the blood had given more importance to such a discovery4 ,up to this time1#dbag it had been supposed that the lacteals carried the chyle to the liver1 and that the blood was manufactured there4 ,this opinion had prevailed in all the works of the ancients and moderns2 its falsity was discovered by ,pecquet1 a ,french physician1 and published in #afea1 in his ,new ,anatomical ,experiments2 in which are discovered a receptacle of the chyle1 unknown till then1 and the vessel which conveys it to the subclavian vein4 ,pecquet himself and other anatomists1 soon connected this discovery with the doctrine1 then recently promulgated1 of the circulation of the blood4 ,in #affe1 these vessels1 and the lymphatics which are connected with them1 were further illustrated by ,ruysch in his exhibition of their valves4 7,dilucidatio valvularum in vasis lymphaticis et lacteis47 ,note #daag3 ,cuv4 ,hist4 p4 #cd4 ,note #dbag3 ,ib4 p4 #cfe4 ,sect4 #b4--,the ,consequent ,speculations4 ,hypotheses of ,digestion4 ,,thus it was shown that aliments taken into the stomach are1 by its action1 made to produce chyme2 from the chyme1 gradually changed #ded in its progress through the intestines1 chyle is absorbed by the lacteals2 and this1 poured into the blood by the thoracic duct1 repairs the waste and nourishes the growth of the animal4 ,but by what powers is the food made to undergo these transformations8 ,can we explain them on mechanical or on chemical principles8 ,here we come to a part of physiology less certain than the discovery of vessels1 or of the motion of fluids4 ,we have a number of opinions on this subject1 but no universally acknowledged truth4 ,we have a collection of ,hypotheses of ,digestion and ,nutrition4 ,i shall confine myself to the former class2 and without dwelling long upon these1 ,i shall mention some of them4 ,the philosophers of the ,academy del ,cimento1 and several others1 having experimented on the stomach of gallinaceous birds1 and observed the astonishing force with which it breaks and grinds substances1 were led to consider the digestion which takes place in the stomach as a kind of trituration4#dcag ,other writers thought it was more properly described as fermentation2 others again spoke of it as a putrefaction4 ,varignon gave a merely physical account of the first part of the process1 maintaining that the division of the aliments was the effect of the disengagement of the air introduced into the stomach1 and dilated by the heat of the body4 ,the opinion that digestion is a solution of the food by the gastric juice has been more extensively entertained4 ,note #dcag3 ,bourdon1 ,physiol4 ,comp4 p4 #ead4 ,spallanzani and others made many experiments on this subject4 ,yet it is denied by the best physiologists1 that the changes of digestion can be adequately represented as chemical changes only4 ,the nerves of the stomach 7the pneumo-gastric7 are said to be essential to digestion4 ,dr4 ,wilson ,philip has asserted that the influence of these nerves1 when they are destroyed1 may be replaced by a galvanic current4#ddag ,this might give rise to a supposition that digestion depends on galvanism4 ,yet we cannot doubt that all these hypotheses1--mechanical1 physical1 chemical1 galvanic--are altogether insufficient4 ,the stomach must have1 as ,dr4 ,prout says1#deag the power of #dee organizing and vitalizing the different elementary substances4 ,it is impossible to imagine that this organizing agency of the stomach can be chemical4 ,this agency is vital1 and its nature completely unknown4 ,note #ddag3 ,mller 7,manual of ,physiology1 ,b4 iii4 ,sect4 #a1 ,chap4 iii47 speaks of ,dr4 ,wilson ,philip's assertion that the nerves of the stomach being cut1 and a galvanic current kept up in them1 digestion is still accomplished4 ,he states that he and other physiologists have repeated such experiments on an extensive scale1 and have found no effect of this kind4 ,note #deag3 ,bridgewater ,tr4 p4 #dic4 ,,chapter ,,iv4 ,,examination ,,of ,,the ,,process ,,of ,,reproduction ,,in ,,animals ,,and ,,plants1 ,,and ,,consequent ,,speculations4 ,sect4 #a4--,the ,examination of the ,process of ,reproduction in ,animals4 ,,it would not1 perhaps1 be necessary to give any more examples of what has hitherto been the general process of investigations on each branch of physiology2 or to illustrate further the combination which such researches present1 of certain with uncertain knowledge2--of solid discoveries of organs and processes1 succeeded by indefinite and doubtful speculation concerning vital forces4 ,but the reproduction of organized beings is not only a subject of so much interest as to require some notice1 but also offers to us laws and principles which include both the vegetable and the animal kingdom2 and which1 therefore1 are requisite to render intelligible the most general views to which we can attain1 respecting the world of organization4 ,the facts and laws of reproduction were first studied in detail in animals4 ,the subject appears to have attracted the attention of some of the philosophers of antiquity in an extraordinary degree3 and indeed we may easily imagine that they hoped1 by following this path1 if any1 to solve the mystery of creation4 ,aristotle appears to have pursued it with peculiar complacency2 and his great work ,on animals contains#dfag an extraordinary collection of curious observations relative to this subject4 ,he had learnt the modes of reproduction of most of the animals with which he was acquainted2 and his work is still1 as a writer of our own times has said1#dgag original after so many copies1 and young after two thousand years4 ,his observations referred principally to the external circumstances of generation3 the anatomical examination was #def left to his successors4 ,without dwelling on the intermediate labors1 we come to modern times1 and find that this examination owes its greatest advance to those who had the greatest share in the discovery of the circulation of the blood2--,fabricius of ,acquapendente1 and ,harvey4 ,the former#dhag published a valuable work on the ,egg and the ,chick4 ,in this are given1 for the first time1 figures representing the developement of the chick1 from its almost imperceptible beginning1 to the moment when it breaks the shell4 ,harvey pursued the researches of his teacher4 ,charles#diag the ,first had supplied him with the means of making the experiments which his purpose required1 by sacrificing a great number of the deer in ,windsor ,park in the state of gestation3 but his principal researches were those respecting the egg1 in which he followed out the views of ,fabricius4 ,in the troubles which succeeded the death of the unfortunate ,charles the house of ,harvey was pillaged2 and he lost the whole of the labors he had bestowed on the generation of insects4 ,his work1 ,exercitationes de ,generatione ,animalium1 was published at ,london in #afea2 it is more detailed and perfect than that of ,fabricius2 but the author was prevented by the unsettled condition of the country from getting figures engraved to accompany his descriptions4 ,note #dfag3 ,bourdon1 p4 #afa4 ,note #dgag3 ,ib4 p4 #aja4 ,note #dhag3 ,cuv4 ,hist4 ,sc4 ,nat4 p4 #df4 ,note #diag3 ,ib4 p4 #ec4 ,many succeeding anatomists pursued the examination of the series of changes in generation1 and of the organs which are concerned in them1 especially ,malpighi1 who employed the microscope in this investigation1 and whose work on the ,chick was published in #afgc4 ,it is impossible to give here any general view of the result of these laborious series of researches3 but we may observe1 that they led to an extremely minute and exact survey of all the parts of the ftus1 its envelopes and appendages1 and1 of course1 to a designation of these by appropriate names4 ,these names afterwards served to mark the attempts which were made to carry the analogy of animal generation into the vegetable kingdom4 ,there is one generalization of ,harvey which deserves notice4#ejag ,he was led by his researches to the conclusion1 that all living things may be properly said to come from eggs3 ,omne vivum ex ovo4 ,thus not only do oviparous animals produce by means of eggs1 but in those which are viviparous1 the process of generation begins with the developement of a small vesicle1 which comes from the ovary1 and which exists before the embryo3 and thus viviparous or suckling-beasts1 #deg notwithstanding their name1 are born from eggs1 as well as birds1 fishes1 and reptiles4#eaag ,this principle also excludes that supposed production of organized beings without parents 7of worms in corrupted matter1 for instance17 which was formerly called spontaneous generation2 and the best physiologists of modern times agree in denying the reality of such a mode of generation4#ebag ,note #ejag3 ,exerc4 lxiii4 ,note #eaag3 ,bourdon1 p4 #bba4 ,note #ebag3 ,ib4 p4 #di4 ,sect4 #b4--,the ,examination of the ,process of ,reproduction in ,vegetables4 ,,the extension of the analogies of animal generation to the vegetable world was far from obvious4 ,this extension was however made2--with reference to the embryo plant1 principally by the microscopic observers1 ,nehemiah ,grew1 ,marcello ,malpighi1 and ,antony ,leeuwenhoek2--with respect to the existence of the sexes1 by ,linnus and his predecessors4 ,the microscopic labors of ,grew and ,malpighi were patronized by the ,royal ,society of ,london in its earliest youth4 ,grew's book1 ,the ,anatomy of ,plants1 was ordered to be printed in #afgj4 ,it contains plates representing extremely well the process of germination in various seeds1 and the author's observations exhibit a very clear conception of the relation and analogies of different portions of the seed4 ,on the day on which the copy of this work was laid before the ,society1 a communication from ,malpighi of ,bologna1 ,anatomes ,plantarum ,idea1 stated his researches1 and promised figures which should illustrate them4 ,both authors afterwards went on with a long train of valuable observations1 which they published at various times1 and which contain much that has since become a permanent portion of the science4 ,both ,grew and ,malpighi were1 as we have remarked1 led to apply to vegetable generation many terms which imply an analogy with the generation of animals4 ,thus1 ,grew terms the innermost coat of the seed1 the secundine2 speaks of the navel-fibres1 c4 ,many more such terms have been added by other writers4 ,and1 as has been observed by a modern physiologist1#ecag the resemblance is striking4 ,both in the vegetable seed and in the fertilized animal egg1 we have an embryo1 chalaz1 a placenta1 an umbilical cord1 a cicatricula1 an amnios1 membranes1 nourishing vessels4 ,the cotyledons of the seed are the equivalent of the vitellus of birds1 or of the umbilical vesicle of 9999suckling-beasts3 #deh the albumen or perisperm of the grain is analogous to the white of the egg of birds1 or the allantoid of viviparous animals4 ,note #ecag3 ,ib4 p4 #chd4 ,sexes of ,plants4--,the attribution of sexes to plants1 is a notion which was very early adopted2 but only gradually unfolded into distinctness and generality4#edag ,the ancients were acquainted with the fecundation of vegetables4 ,empedocles1 ,aristotle1 ,theophrastus1 ,pliny1 and some of the poets1 make mention of it2 but their notions were very incomplete1 and the conception was again lost in the general shipwreck of human knowledge4 ,a ,latin poem1 composed in the fifteenth century by ,jovianus ,pontanus1 the preceptor of ,alphonso1 ,king of ,naples1 is the first modern work in which mention is made of the sex of plants4 ,pontanus sings the loves of two date-palms1 which grew at the distance of fifteen leagues from each other3 the male at ,brundusium1 the female at ,otranto4 ,the distance did not prevent the female from becoming fruitful1 as soon as the palms had raised their heads above the surrounding trees1 so that nothing intervened directly between them1 or1 to speak with the poet1 so that they were able to see each other4 ,note #edag3 ,mirbel1 ,el4 ii4 #ech4 ,zaluzian1 a botanist who lived at the end of the fifteenth century1 says that the greater part of the species of plants are androgynes1 that is1 have the properties of the male and of the female united in the same plant2 but that some species have the two sexes in separate individuals2 and he adduces a passage of ,pliny relative to the fecundation of the date-palm4 ,john ,bauhin1 in the middle of the seventeenth century1 cites the expressions of ,zaluzian2 and forty years later1 a professor of ,tbingen1 ,rudolph ,jacob ,camerarius1 pointed out clearly the organs of generation1 and proved by experiments on the mulberry1 on maize1 and on the plant called ,mercury 7mercurialis71 that when by any means the action of the stamina upon the pistils is intercepted1 the seeds are barren4 ,camerarius1 therefore1 a philosopher in other respects of little note1 has the honor assigned him of being the author of the discovery of the sexes of plants in modern times4#eeag ,note #eeag3 ,mirbel1 ii4 #eci4 ,the merit of this discovery will1 perhaps1 appear more considerable when it is recollected that it was rejected at first by very eminent botanists4 ,thus ,tournefort1 misled by insufficient experiments1 maintained that the stamina are excretory organs2 and ,reaumur1 at the beginning of the eighteenth century1 inclined to the same doctrine4 #dei ,upon this1 ,geoffroy1 an apothecary at ,paris1 scrutinized afresh the sexual organs2 he examined the various forms of the pollen1 already observed by ,grew and ,malpighi2 he pointed out the excretory canal1 which descends through the style1 and the micropyle1 or minute orifice in the coats of the ovule1 which is opposite to the extremity of this canal2 though he committed some mistakes with regard to the nature of the pollen4 ,soon afterwards1 ,sebastian ,vaillant1 the pupil of ,tournefort1 but the corrector of his error on this subject1 explained in his public lectures the phenomenon of the fecundation of plants1 described the explosion of the anthers1 and showed that the florets of composite flowers1 though formed on the type of an androgynous flower1 are sometimes male1 sometimes female1 and sometimes neuter4 ,but though the sexes of plants had thus been noticed1 the subject drew far more attention when ,linnus made the sexual parts the basis of his classification4 ,camerarius and ,burkard had already entertained such a thought1 but it was ,linnus who carried into effect1 and thus made the notion of the sexes of vegetables almost as familiar to us as that of the sexes of animals4 ,sect4 #c4--,the ,consequent ,speculations4--,hypotheses of ,generation4 ,,the views of the processes of generation1 and of their analogies throughout the whole of the organic world1 which were thus established and diffused1 form an important and substantial part of our physiological knowledge4 ,that a number of curious but doubtful hypotheses should be put forward1 for the purpose of giving further significance and connexion to these discoveries1 was to be expected4 ,we must content ourselves with speaking of these very briefly4 ,we have such hypotheses in the earliest antiquity of ,greece2 for as we have already said1 the speculations of cosmogony were the source of the ,greek philosophy2 and the laws of generation appeared to offer the best promise of knowledge respecting the mystery of creation4 ,hippocrates explained the production of a new animal by the mixture of seed of the parents2 and the offspring was male or female as the seminal principle of the father or of the mother was the more powerful4 ,according to ,aristotle1 the mother supplied the matter1 and the father the form4 ,harvey's doctrine was1 that the ovary of the female is fertilized by a seminal contagion produced by the seed of the male4 ,but an opinion which obtained far more general reception was1 that #dfj the embryo pre-existed in the mother1 before any union of the sexes4#efag ,it is easy to see that this doctrine is accompanied with great difficulties2#egag for if the mother1 at the beginning of life1 contain in her the embryos of all her future children2 these embryos again must contain the children which they are capable of producing2 and so on indefinitely2 and thus each female of each species contains in herself the germs of infinite future generations4 ,the perplexity which is involved in this notion of an endless series of creatures1 thus encased one within another1 has naturally driven inquirers to attempt other suppositions4 ,the microscopic researches of ,leeuwenhoek and others led them to the belief that there are certain animalcules contained in the seed of the male1 which are the main agents in the work of reproduction4 ,this system ascribes almost everything to the male1 as the one last mentioned does to the female4 ,finally1 we have the system of ,buffon2--the famous hypothesis of organic molecules4 ,that philosopher asserted that he found1 by the aid of the microscope1 all nature full of moving globules1 which he conceived to be1 not animals as ,leeuwenhoek imagined1 but bodies capable of producing1 by their combination1 either animals or vegetables1 in short1 all organized bodies4 ,these globules he called organic molecules4#ehag ,and if we inquire how these organic molecules1 proceeding from all parts of the two parents1 unite into a whole1 as perfect as either of the progenitors1 ,buffon answers1 that this is the effect of the interior mould2 that is1 of a system of internal laws and tendencies which determine the form of the result as an external mould determines the shape of the cast4 ,note #efag3 ,bourdon1 p4 #bjd4 ,note #egag3 ,ib4 p4 #bji4 ,note #ehag3 ,ib4 p4 #bai4 ,an admirer of ,buffon1 who has well shown the untenable character of this system1 has urged1 as a kind of apology for the promulgation of the hypothesis1#eiag that at the period when its author wrote1 he could not present his facts with any hope of being attended to1 if he did not connect them by some common tie1 some dominant idea which might gratify the mind2 and that1 acting under this necessity1 he did well to substitute for the extant theories1 already superannuated and confessedly imperfect1 conjectures more original and more probable4 ,without dissenting from this view1 we may observe1 that ,buffon's theory1 like those which preceded it1 is excusable1 and even deserving of admiration1 so far as it groups the facts consistently2 because in doing this1 it exhibits the necessity1 which the physiological speculator ought to feel1 of aspiring to definite and solid general principles2 and that thus1 though #dfa the theory may not be established as true1 it may be useful by bringing into view the real nature and application of such principles4 ,note #eiag3 ,ib4 p4 #bba4 ,it is1 therefore1 according to our views1 unphilosophical to derive despair1 instead of hope1 from the imperfect success of ,buffon and his predecessors4 ,yet this is what is done by the writer to whom we refer4 ,for me1 says he1#fjag ,i vow that1 after having long meditated on the system of ,buffon1--a system so remarkable1 so ingenious1 so well matured1 so wonderfully connected in all its parts1 at first sight so probable2--,i confess that1 after this long study1 and the researches which it requires1 ,i have conceived in consequence1 a distrust of myself a skepticism1 a disdain of hypothetical systems1 a decided predilection and exclusive taste for pure and rational observation1 in short1 a disheartening1 which ,i had never felt before4 ,note #fjag3 ,bourdon1 p4 #bgd4 ,the best remedy of such feelings is to be found in the history of science4 ,kepler1 when he had been driven to reject the solid epicycles of the ancients1 or a person who had admired ,kepler as ,m4 ,bourdon admires ,buffon1 but who saw that his magnetic virtue was an untenable fiction1 might1 in the same manner1 have thrown up all hope of a sound theory of the causes of the celestial motions4 ,but astronomers were too wise and too fortunate to yield to such despondency4 ,the predecessors of ,newton substituted a solid science of ,mechanics for the vague notions of ,kepler2 and the time soon came when ,newton himself reduced the motions of the heavens to a ,law as distinctly conceived as the ,motions had been before4 ,,chapter ,v4 ,,examination ,,of ,,the ,,nervous ,,system1 ,,and ,,consequent ,,speculations4 ,sect4 #a4--,the ,examination of the ,nervous ,system4 ,,it is hardly necessary to illustrate by further examples the manner in which anatomical observation has produced conjectural and hypothetical attempts to connect structure and action with some #dfb higher principle1 of a more peculiarly physiological kind4 ,but it may still be instructive to notice a case in which the principle1 which is thus brought into view1 is far more completely elevated above the domain of matter and mechanism than in those we have yet considered2--a case where we have not only ,irritation1 but ,sensation2--not only ,life1 but ,consciousness and ,will4 ,a part of science in which suggestions present themselves1 brings us1 in a very striking manner1 to the passage from the physical to the hyperphysical sciences4 ,we have seen already 7chap4 i47 that ,galen and his predecessors had satisfied themselves that the nerves are the channels of perception2 a doctrine which had been distinctly taught by ,herophilus#faag in the ,alexandrian school4 ,herophilus1 however1 still combined1 under the common name of ,nerves1 the ,tendons2 though he distinguished such ,nerves from those which arise from the brain and the spinal marrow1 and which are subservient to the will4 ,in ,galen's time this subject had been prosecuted more into detail4 ,that anatomist has left a ,treatise expressly upon ,the ,anatomy of the ,nerves2 in which he describes the successive ,pairs of ,nerves3 thus1 the ,first ,pair are the visual nerves3 and we see1 in the language which ,galen uses1 the evidence of the care and interest with which he had himself examined them4 ,these nerves1 he says1 are not resolved into many fibres1 like all the other nerves1 when they reach the organs to which they belong2 but spread out in a different and very remarkable manner1 which it is not easy to describe or to believe1 without actually seeing it4 ,he then gives a description of the retina4 ,in like manner he describes the ,second ,pair1 which is distributed to the muscles of the eyes2 the ,third and ,fourth ,pairs1 which go to the tongue and palate2 and so on to the ,seventh ,pair4 ,this division into ,seven ,pairs was established by ,marinus1#fbag but ,vesalius found it to be incomplete4 ,the examination which is the basis of the anatomical enumeration of the ,nerves at present recognized was that of ,willis4 ,his book1 entitled ,cerebri ,anatome1 cui accessit ,nervorum descriptio et usus1 appeared at ,london in #affd4 ,he made important additions to the knowledge of this subject4#fcag ,thus he is the first who describes in a distinct manner what has been called the ,nervous ,centre1#fdag the pyramidal eminences which1 according to more recent anatomists1 are the communication of the brain with the spinal marrow3 and of which the ,decussation1 described by ,santorini1 affords the explanation of the action of a part #dfc of the brain upon the nerves of the opposite side4 ,willis proved also that the ,rete ,mirabile1 the remarkable net-work of arteries at the base of the brain1 observed by the ancients in ruminating animals1 does not exist in man4 ,he described the different ,pairs of ,nerves with more care than his predecessors2 and his mode of numbering them is employed up to the present time4 ,he calls the ,olfactory ,nerves the ,first ,pair2 previously to him1 these were not reckoned a ,pair3 and thus the optic nerves were1 as we have seen1 called the first4 ,he added the ,sixth and the ,ninth ,pairs1 which the anatomists who preceded him did not reckon4 ,willis also examined carefully the different ,ganglions1 or knots which occur upon the nerves4 ,he traced them wherever they were to be found1 and he gave a general figure of what ,cuvier calls the nervous skeleton1 very superior to that of ,vesalius1 which was coarse and inexact4 ,willis also made various efforts to show the connexion of the parts of the brain4 ,in the earlier periods of anatomy1 the brain had been examined by slicing it1 so as to obtain a section4 ,varolius endeavored to unravel it1 and was followed by ,willis4 ,vicq d',azyr1 in modern times1 has carried the method of section to greater perfection than had before been given it2#feag as ,vieussens and ,gall have done with respect to the method of ,varolius and ,willis4 ,recently ,professor ,chaussier#ffag makes three kinds of ,nerves3--the ,encephalic1 which proceed from the head1 and are twelve on each side2--the ,rachidian1 which proceed from the spinal marrow1 and are thirty on each side2--and ,compound ,nerves1 among which is the ,great ,sympathetic ,nerve4 ,note #faag3 ,spr4 i4 #ecd4 ,note #fbag3 ,dic4 ,sc4 ,med4 xxxv4 #dfg4 ,note #fcag3 ,cuv4 ,sc4 ,nat4 p4 #che4 ,note #fdag3 ,ibid4 ,note #feag3 ,cuv4 p4 #dj4 ,note #ffag3 ,dict4 ,sc4 ,nat4 xxxv4 #dfg4 ,one of the most important steps ever made in our knowledge of the nerves is1 the distinction which ,bichat is supposed to have established1 of a ganglionic system1 and a cerebral system4 ,and we may add1 to the discoveries in nervous anatomy1 the remarkable one1 made in our own time1 that the two offices--of conducting the motive impressions from the central seat of the will to the muscles1 and of propagating sensations from the surface of the body and the external organs of sense to the sentient mind--reside in two distinct portions of the nervous substance3--a discovery which has been declared#fgag to be doubtless the most important accession to physiological 7anatomical7 knowledge since the time of ,harvey4 ,this doctrine was first published and taught by ,sir ,charles ,bell3 after an interval of some #dfd years1 it was more distinctly delivered in the publications of ,mr4 ,john ,shaw1 ,sir ,c4 ,bell's pupil4 ,soon afterwards it was further confirmed1 and some part of the evidence corrected1 by ,mr4 ,mayo1 another pupil of ,sir ,c4 ,bell1 and by ,m4 ,majendie4#fhag ,note #fgag3 ,dr4 ,charles ,henry's ,report of ,brit4 ,assoc4 iii4 p4 #fb4 ,note #fhag3 ,as authority for the expressions which ,i have now used in the text1 ,i will mention ,mller's ,manual of ,physiology 7#dth edition1 #ahdd74 ,in ,book iii4 ,section #b1 ,chap4 i41 ,on the ,nerves of ,sensation and ,motion1 ,mller says1 ,charles ,bell was the first who had the ingenious thought that the posterior roots of the nerves of the spine--those which are furnished with a ganglion--govern sensation only2 that the anterior roots are appointed for motion2 and that the primitive fibres of these roots1 after being united in a single nervous cord1 are mingled together in order to supply the wants of the skin and muscles4 ,he developed this idea in a little work 7,an ,idea of a new ,anatomy of the ,brain1 ,london1 #ahaa71 which was not intended to travel beyond the circle of his friends4 ,mller goes on to say1 that eleven years later1 ,majendie prosecuted the same theory4 ,but ,mr4 ,alexander ,shaw1 in #ahci1 published ,a ,narrative of the ,discoveries of ,sir ,charles ,bell in the ,nervous ,system1 in which it appears that ,sir ,charles ,bell had further expounded his views in his lectures to his pupils 7p4 #hi71 and that one of these1 ,mr4 ,john ,shaw1 had in various publications1 in #ahba and #ahbb1 further insisted upon the same views2 especially in a ,memoir ,on ,partial ,paralysis 7p4 #ge74 ,,mm4 ,mayo and ,majendie both published ,memoirs in ,august1 #ahbb2 and these and subsequent works confirmed the doctrine of ,bell4 ,mr4 ,alexander ,shaw states 7p4 #ig71 that a mistake of ,sir ,charles ,bell's1 in an experiment which he had made to prove his doctrine1 was discovered through the joint labors of ,m4 ,majendie and ,mr4 ,mayo4 ,sect4 #b4--,the ,consequent ,speculations4 ,hypotheses respecting ,life1 ,sensation1 and ,volition4 ,i ,,shall not attempt to explain the details of these anatomical investigations2 and ,i shall speak very briefly of the speculations which have been suggested by the obvious subservience of the nerves to life1 sensation1 and volition4 ,some general inferences from their distribution were sufficiently obvious2 as1 that the seat of sensation and volition is in the brain4 ,galen begins his work1 ,on the ,anatomy of the ,nerves1 thus3 ,that none of the members of the animal either exercises voluntary motion1 or receives sensation1 and that if the nerve be cut1 the part immediately becomes inert and insensible1 is acknowledged by all physicians4 ,but that the origin of the nerves is partly from the brain1 and partly from the spinal marrow1 ,i proceed to explain4 ,and in his work ,on the ,doctrines of ,plato and ,hippocrates1 he proves at #dfe great length#fiag that the brain is the origin of sensation and motion1 refuting the opinions of earlier days1 as that of ,chrysippus1#gjag who placed the hegemonic or master-principle of the soul1 in the heart4 ,but though ,galen thought that the rational soul resides in the brain1 he was disposed to agree with the poets and philosophers1 according to whom the heart is the seat of courage and anger1 and the liver the seat of love4#gaag ,the faculties of the soul were by succeeding physiologists confined to the brain2 but the disposition still showed itself1 to attribute to them distinct localities4 ,thus ,willis#gbag places the imagination in the corpus callosum1 the memory in the folds of the hemispheres1 the perception in the corpus striatum4 ,in more recent times1 a system founded upon a similar view has been further developed by ,gall and his followers4 ,the germ of ,gall's system may be considered as contained in that of ,willis2 for ,gall represents the hemispheres as the folds of a great membrane which is capable of being unwrapped and spread out1 and places the different faculties of man in the different regions of this membrane4 ,the chasm which intervenes between matter and motion on the one side1 and thought and feeling on the other1 is brought into view by all such systems2 but none of the hypotheses which they involve can effectually bridge it over4 ,note #fiag3 ,lib4 vii4 ,note #gjag3 ,lib4 iii4 c4 #a4 ,note #gaag3 ,lib4 vi4 c4 #h4 ,note #gbag3 ,cuv4 ,sc4 ,nat4 p4 #chd4 ,the same observation may be made respecting the attempts to explain the manner in which the nerves operate as the instruments of sensation and volition4 ,perhaps a real step was made by ,glisson1#gcag professor of medicine in the ,university of ,cambridge1 who distinguished in the fibres of the muscles of motion a peculiar property1 different from any merely mechanical or physical action4 ,his work ,on the ,nature of the ,energetic ,substance1 or on the ,life of ,nature and of its ,three ,first ,faculties1 ,the ,perceptive1 ,appetitive1 and ,motive1 which was published in #afgb1 is rather metaphysical than physiological4 ,but the principles which he establishes in this treatise he applies more specially to physiology in a treatise ,on the ,stomach and ,intestines 7,amsterdam1 #afgg74 ,in this he ascribes to the fibres of the animal body a peculiar power which he calls ,irritability4 ,he divides irritation into natural1 vital1 and animal2 and he points out1 though briefly1 the gradual differences of irritability in different organs4 ,it is hardly comprehensible1 says ,sprengel1#gdag how this #dff lucid and excellent notion of the ,cambridge teacher was not accepted with greater alacrity1 and further unfolded by his contemporaries4 ,it has1 however1 since been universally adopted4 ,note #gcag3 ,cuv4 ,sc4 ,nat4 p4 #dcd4 ,note #gdag3 ,spr4 iv4 #dg4 ,but though the discrimination of muscular irritability as a peculiar power might be a useful step in physiological research1 the explanations hitherto offered1 of the way in which the nerves operate on this irritability1 and discharge their other offices1 present only a series of hypotheses4 ,glisson#geag assumed the existence of certain vital spirits1 which1 according to him1 are a mild1 sweet fluid1 resembling the spirituous part of white of egg1 and residing in the nerves4--,this hypothesis1 of a very subtle humor or spirit existing in the nerves1 was indeed very early taken up4#gfag ,this nervous spirit had been compared to air by ,erasistratus1 ,asclepiades1 ,galen1 and others4 ,the chemical tendencies of the seventeenth century led to its being described as acid1 sulphureous or nitrous4 ,at the end of that century1 the hypothesis of an ether attracted much notice as a means of accounting for many phenomena2 and this ether was identified with the nervous fluid4 ,newton himself inclines to this view1 in the remarkable ,queries which are annexed to his ,opticks4 ,after ascribing many physical effects to his ether1 he adds 7,query #bc71 ,is not vision performed chiefly by the vibrations of this medium1 excited in the bottom of the eye by the rays of light1 and propagated through the solid1 pellucid1 and uniform capillamenta of the nerves into the place of sensation8 ,and 7,query #bd71 ,is not animal motion performed by the vibrations of this medium1 excited in the brain by the power of the will1 and propagated from thence through the capillamenta of the nerves into the muscles for contracting and dilating them8 ,and an opinion approaching this has been adopted by some of the greatest of modern physiologists2 as ,haller1 who says1#ggag that1 though it is more easy to find what this nervous spirit is not than what it is1 he conceives that1 while it must be far too fine to be perceived by the sense1 it must yet be more gross than fire1 magnetism1 or electricity2 so that it may be contained in vessels1 and confined by boundaries4 ,and ,cuvier speaks to the same effect3#ghag ,there is a great probability that it is by an imponderable fluid that the nerve acts on the fibre1 and that this nervous fluid is drawn from the blood1 and secreted by the medullary matter4 ,note #geag3 ,spr4 iv4 #ch4 ,note #gfag3 ,haller1 ,physiol4 iv4 #cfe4 ,note #ggag3 ,physiol4 iv4 #cha1 lib4 x4 sect4 viii4 #ae4 ,note #ghag3 ,rgne ,animal1 ,introd4 p4 #cj4 ,without presuming to dissent from such authorities on a point of #dfg anatomical probability1 we may venture to observe1 that these hypotheses do not tend at all to elucidate the physiological principle which is here involved2 for this principle cannot be mechanical1 chemical1 or physical1 and therefore cannot be better understood by embodying it in a fluid2 the difficulty we have in conceiving what the moving force is1 is not got rid of by explaining the machinery by which it is merely transferred4 ,in tracing the phenomena of sensation and volition to their cause1 it is clear that we must call in some peculiar and hyperphysical principle4 ,the hypothesis of a fluid is not made more satisfactory by attenuating the fluid2 it becomes subtle1 spirituous1 ethereal1 imponderable1 to no purpose2 it must cease to be a fluid1 before its motions can become sensation and volition4 ,this1 indeed1 is acknowledged by most physiologists2 and strongly stated by ,cuvier4#giag ,the impression of external objects upon the ,,me1 the production of a sensation1 of an image1 is a mystery impenetrable for our thoughts4 ,and in several places1 by the use of this peculiar phrase1 the me1 7le moi7 for the sentient and volent faculty1 he marks1 with peculiar appropriateness and force1 that phraseology borrowed from the world of matter will1 in this subject1 no longer answer our purpose4 ,we have here to go from ,nouns to ,pronouns1 from ,things to ,persons4 ,we pass from the ,body to the ,soul1 from ,physics to ,metaphysics4 ,we are come to the borders of material philosophy2 the next step is into the domain of ,thought and ,mind4 ,here1 therefore1 we begin to feel that we have reached the boundaries of our present subject4 ,the examination of that which lies beyond them must be reserved for a philosophy of another kind1 and for the labors of the future2 if we are ever enabled to make the attempt to extend into that loftier and wider scene1 the principles which we gather on the ground we are now laboriously treading4 ,note #giag3 ,rgne ,animal1 ,introd4 p4 #dg4 ,such speculations as ,i have quoted respecting the nervous fluid1 proceeding from some of the greatest philosophers who ever lived1 prove only that hitherto the endeavor to comprehend the mystery of perception and will1 of life and thought1 have been fruitless and vain4 ,many anatomical truths have been discovered1 but1 so far as our survey has yet gone1 no genuine physiological principle4 ,all the trains of physiological research which we have followed have begun in exact examination of organization and function1 and have ended in wide conjectures and arbitrary hypotheses4 ,the stream of knowledge in all such cases is #dfh clear and lively at its outset2 but1 instead of reaching the great ocean of the general truths of science1 it is gradually spread abroad among sands and deserts till its course can be traced no longer4 ,hitherto1 therefore1 we must consider that we have had to tell the story of the failures of physiological speculation4 ,but of late there have come into view and use among physiologists certain principles which may be considered as peculiar to organized subjects2 and of which the introduction forms a real advance in organical science4 ,though these have hitherto been very imperfectly developed1 we must endeavor to exhibit1 in some measure1 their history and bearing4 #bnd ,ed4 ,in order to show that ,i am not unaware how imperfect the sketch given in this work is1 as a ,history of ,physiology1 ,i may refer to the further discussions on these subjects contained in the ,philosophy of the ,inductive ,sciences1 ,book ix4 ,i have there 7,chap4 ii47 noticed the successive ,biological ,hypotheses of the ,mystical1 the ,iatrochemical1 and ,iatromathematical ,schools1 the ,vital-,fluid ,school1 and the ,psychical ,school4 ,i have 7,chaps4 iii41 iv41 v47 examined several of the attempts which have been made to analyze the ,idea of ,life1 to classify ,vital ,functions1 and to form ,ideas of ,separate ,vital ,forces4 ,i have considered in particular1 the attempts to form a distinct conception of ,assimilation and ,secretion1 of ,generation1 and of ,voluntary ,motion2 and ,i have 7,chap4 vi47 further discussed the ,idea of ,final ,causes as employed in ,biology4 ,,chapter ,,vi4 ,,introduction ,,of ,,the ,,principle ,,of ,,developed ,,and ,,metamorphosed ,,symmetry4 ,sect4 #a4--,vegetable ,morphology4 ,gthe4 ,de ,candolle4 ,,before we proceed to consider the progress of principles which belong to animal and human life1 such as have just been pointed at1 we must look round for such doctrines1 if any such there be1 as apply alike to all organized beings1 conscious or unconscious1 fixed or locomotive2--to the laws which regulate vegetable as well as animal forms and functions4 ,though we are very far from being able to present a #dfi clear and connected code of such laws1 we may refer to one law1 at least1 which appears to be of genuine authority and validity2 and which is worthy our attention as an example of a properly organical or physiological principle1 distinct from all mechanical1 chemical1 or other physical forces2 and such as cannot even be conceived to be resolvable into those4 ,i speak of the tendency which produces such results as have been brought together in recent speculations upon ,morphology4 ,it may perhaps be regarded as indicating how peculiar are the principles of organic life1 and how far removed from any mere mechanical action1 that the leading idea in these speculations was first strongly and effectively apprehended1 not by a laborious experimenter and reasoner1 but by a man of singularly brilliant and creative fancy2 not by a mathematician or chemist1 but by a poet4 ,and we may add further1 that this poet had already shown himself incapable of rightly apprehending the relation of physical facts to their principles2 and had1 in trying his powers on such subjects1 exhibited a signal instance of the ineffectual and perverse operation of the method of philosophizing to which the constitution of his mind led him4 ,the person of whom we speak1 is ,john ,wolfgang ,gthe1 who is held1 by the unanimous voice of ,europe1 to have been one of the greatest poets of our own1 or of any time1 and whose ,doctrine of ,colors we have already had to describe1 in the ,history of ,optics1 as an entire failure4 ,yet his views on the laws which connect the forms of plants into one simple system1 have been generally accepted and followed up4 ,we might almost be led to think that this writer's poetical endowments had contributed to this scientific discovery2--the love of beauty of form1 by fixing the attention upon the symmetry of plants2 and the creative habit of thought1 by making constant developement of a familiar process4#hjag #dgj ,note #hjag3 ,we may quote some of the poet's own verses as an illustration of his feelings on this subject4 ,they are addressed to a lady4 ,dich verwirret1 geliebte1 die tausendfltige mischung ,dieses blumengewhls ber dem garten umher2 ,viele namen hrest du an1 und immer verdrnget1 ,mit barbarischem klang1 einer den andern im ohr4 ,alle gestalten sind 9999hnlich und keine gleichet der andern2 ,und so deutet das chor auf ein geheimes gesetz1 ,auf ein heiliges rthsel4 ,o6 knnte ich dich1 liebliche freundinn1 ,ueberliefern so gleich glcklich das lsende wort4 ,thou1 my love1 art perplext with the endless seeming confusion ,of the luxuriant wealth which in the garden is spread2 ,name upon name thou hearest1 and in thy dissatisfied hearing1 ,with a barbarian noise one drives another along4 ,all the forms resemble1 yet none is the same as another2 ,thus the whole of the throng points at a deep hidden law4 ,points at a sacred riddle4 ,oh6 could ,i to thee1 my beloved friend1 ,whisper the fortunate word by which the riddle is read6 ,but though we cannot but remark the peculiarity of our being indebted to a poet for the discovery of a scientific principle1 we must not forget that he himself held1 that in making this step1 he had been guided1 not by his invention1 but by observation4 ,he repelled1 with extreme repugnance1 the notion that he had substituted fancy for fact1 or imposed ideal laws on actual things4 ,while he was earnestly pursuing his morphological speculations1 he attempted to impress them upon ,schiller4 ,i expounded to him1 in as lively a manner as possible1 the metamorphosis of plants1 drawing on paper1 with many characteristic strokes1 a symbolic plant before his eyes4 ,he heard me1 ,gthe says1#haag with much interest and distinct comprehension2 but when ,i had done1 he shook his head1 and said1 ',that is not ,experience2 that is an ,idea3' ,i stopt with some degree of irritation2 for the point which separated us was marked most luminously by this expression4 ,and in the same work he relates his botanical studies and his habit of observation1 from which it is easily seen that no common amount of knowledge and notice of details1 were involved in the course of thought which led him to the principle of the ,metamorphosis of ,plants4 ,note #haag3 ,zur ,morphologie1 p4 #bd4 ,before ,i state the history of this principle1 ,i may be allowed to endeavor to communicate to the reader1 to whom this subject is new1 some conception of the principle itself4 ,this will not be difficult1 if he will imagine to himself a flower1 for instance1 a common wild-rose1 or the blossom of an apple-tree1 as consisting of a series of parts disposed in whorls1 placed one over another on an axis4 ,the lowest whorl is the calyx with its five sepals2 above this is the corolla with its five petals2 above this are a multitude of stamens1 which may be considered as separate whorls of five each1 often repeated2 above these is a whorl composed of the ovaries1 or what become the seed-vessels in the fruit1 which are five united together in the apple1 but indefinite in number and separate in the rose4 ,now the morphological view is #dga this2--that the members of each of these whorls are in their nature identical1 and the same as if they were whorls of ordinary leaves1 brought together by the shortening their common axis1 and modified in form by the successive elaboration of their nutriment4 ,further1 according to this view1 a whorl of leaves itself is to be considered as identical with several detached leaves dispersed spirally along the axis1 and brought together because the axis is shortened4 ,thus all the parts of a plant are1 or at least represent1 the successive metamorphoses of the same elementary member4 ,the root-leaves thus pass into the common leaves2--these into bracte2--these into the sepals2--these into the petals2--these into the stamens with their anthers2--these into the ovaries with their styles and stigmas2--these ultimately become the fruit2 and thus we are finally led to the seed of a new plant4 ,moreover the same notion of metamorphosis may be applied to explain the existence of flowers which are not symmetrical like those we have just referred to1 but which have an irregular corolla or calyx4 ,the papilionaceous flower of the pea tribe1 which is so markedly irregular1 may be deduced by easy gradations from the regular flower1 7through the mimose17 by expanding one petal1 joining one or two others1 and modifying the form of the intermediate ones4 ,without attempting to go into detail respecting the proofs of that identity of all the different organs1 and all the different forms of plants1 which is thus asserted1 we may observe1 that it rests on such grounds as these2--the transformations which the parts of flowers undergo by accidents of nutriment or exposure4 ,such changes1 considered as monstrosities where they are very remarkable1 show the tendencies and possibilities belonging to the organization in which they occur4 ,for instance1 the single wild-rose1 by culture1 transforms many of its numerous stamens into petals1 and thus acquires the deeply folded flower of the double garden-rose4 ,we cannot doubt of the reality of this change1 for we often see stamens in which it is incomplete4 ,in other cases we find petals becoming leaves1 and a branch growing out of the centre of the flower4 ,some pear-trees1 when in blossom1 are remarkable for their tendencies to such monstrosities4#hbag ,again1 we find that flowers which are usually irregular1 occasionally become regular1 and conversely4 ,the common snap-dragon 7,linaria vulgaris7 affords a curious instance of this4#hcag ,the usual form of this plant is personate1 the corolla being divided into two lobes1 which differ in form1 and #dgb together present somewhat the appearance of an animal's face2 and the upper portion of the corolla is prolonged backwards into a tube-like spur4 ,no flower can be more irregular2 but there is a singular variety of this plants termed ,peloria1 in which the corolla is strictly symmetrical1 consisting of a conical tube1 narrowed in front1 elongated behind into five equal spurs1 and containing five stamens of equal length1 instead of the two unequal pairs of the didynamous ,linaria4 ,these and the like appearances show that there is in nature a capacity for1 and tendency to1 such changes as the doctrine of metamorphosis asserts4 ,note #hbag3 ,lindley1 ,nat4 ,syst4 p4 #hd4 ,note #hcag3 ,henslow1 ,principles of ,botany1 p4 #aaf4 ,gthe's ,metamorphosis of ,plants was published #agij3 and his system was the result of his own independent course of thoughts4 ,the view which it involved was not1 however1 absolutely new1 though it had never before been unfolded in so distinct and persuasive a manner4 ,linnus considered the leaves1 calyx1 corolla1 stamens1 each as evolved in succession from the other2 and spoke of it as prolepsis or anticipation1#hdag when the leaves changed accidentally into bracte1 these into a calyx1 this into a corolla1 the corolla into stamens1 or these into the pistil4 ,and ,caspar ,wolf apprehended in a more general manner the same principle4 ,in the whole plant1 says he1#heag we see nothing but leaves and stalk2 and in order to prove what is the situation of the leaves in all their later forms1 he adduces the cotyledons as the first leaves4 ,note #hdag3 ,sprengel1 ,bot4 ii4 #cjb4 ,amn4 ,acad4 vi4 #cbd1 #cfe4 ,note #heag3 ,nov4 ,con4 ,ac4 ,petrop4 xii4 #djc1 xiii4 #dgh4 ,gthe was led to his system on this subject by his general views of nature4 ,he saw1 he says1#hfag that a whole life of talent and labor was requisite to enable any one to arrange the infinitely copious organic forms of a single kingdom of nature4 ,yet ,i felt1 he adds1 that for me there must be another way1 analogous to the rest of my habits4 ,the appearance of the changes1 round and round1 of organic creatures had taken strong hold on my mind4 ,imagination and ,nature appeared to me to vie with each other which could go on most boldly yet most consistently4 ,his observation of nature1 directed by such a thought1 led him to the doctrine of the metamorphosis4 ,note #hfag3 ,zur ,morph4 i4 #cj4 ,in a later republication of his work 7,zur ,morphologie1 #ahag17 he gives a very agreeable account of the various circumstances which affected the reception and progress of his doctrine4 ,willdenow#hgag quoted #dgc him thus3--,the life of plants is1 as ,mr4 ,gthe very prettily says1 an expansion and contraction1 and these alternations make the various periods of life4 ,this 'prettily1' says ,gthe1 ,i can be well content with1 but the 'egregie1' of ,usteri is much more pretty and obliging4 ,usteri had used this term respecting ,gthe in an edition of ,jussieu4 ,note #hgag3 ,zur ,morph4 i4 #aba4 ,the application of the notion of metamorphosis to the explanation of double and monstrous flowers had been made previously by ,jussieu4 ,gthe's merit was1 to have referred to it the regular formation of the flower4 ,and as ,sprengel justly says1#hhag his view had so profound a meaning1 made so strong an appeal by its simplicity1 and was so fruitful in the most valuable consequences1 that it was not to be wondered at if it occasioned further examination of the subject2 although many persons pretend to slight it4 ,the task of confirming and verifying the doctrine by a general application of it to all cases1--a labor so important and necessary after the promulgation of any great principle1--,gthe himself did not execute4 ,at first he collected specimens and made drawings with some such view1#hiag but he was interrupted and diverted to other matters4 ,and now1 says he1 in his later publication1 when ,i look back on this undertaking1 it is easy to see that the object which ,i had before my eyes was1 for me1 in my position1 with my habits and mode of thinking1 unattainable4 ,for it was no less than this3 that ,i was to take that which ,i had stated in general1 and presented to the conception1 to the mental intuition1 in words2 and that ,i should1 in a particularly visible1 orderly1 and gradual manner1 present it to the eye2 so as to show to the outward sense that out of the germ of this idea might grow a tree of physiology fit to overshadow the world4 ,note #hhag3 ,gesch4 ,botan4 ii4 #cjd4 ,note #hiag3 ,zur ,morph4 i4 9999#abi4 ,voigt1 professor at ,jena1 was one of the first who adopted ,gthe's view into an elementary work1 which he did in #ahjh4 ,other botanists labored in the direction which had thus been pointed out4 ,of those who have thus contributed to the establishment and developement of the metamorphic doctrine4 ,professor ,de ,candolle1 of ,geneva1 is perhaps the most important4 ,his ,theory of ,developement rests upon two main principles1 abortion and adhesion4 ,by considering some parts as degenerated or absent through the abortion of the buds which might have formed them1 and other parts as adhering together1 he holds that all plants may be reduced to perfect symmetry3 and the actual and constant occurrence of such incidents is shown beyond #dgd all doubt4 ,and thus the snap-dragon1 of which we have spoken above1 is derived from the ,peloria1 which is the normal condition of the flower1 by the abortion of one stamen1 and the degeneration of two others4 ,such examples are too numerous to need to be dwelt on4 ,sect4 #b4--;,application of ,vegetable ,morphology4 ,,the doctrine1 being thus fully established1 has been applied to solve different problems in botany2 for instance1 to explain the structure of flowers which appear at first sight to deviate widely from the usual forms of the vegetable world4 ,we have an instance of such an application in ,mr4 ,robert ,brown's explanation of the real structure of various plants which had been entirely misunderstood3 as1 for example1 the genus ,euphorbia4 ,in this plant he showed that what had been held to be a jointed filament1 was a pedicel with a filament above it1 the intermediate corolla having evanesced4 ,in ,orchide 7the orchis tribe71 he showed that the peculiar structure of the plant arose from its having six stamens 7two sets of three each71 of which five are usually abortive4 ,in ,conifer 7the cone-bearing trees71 it was made to appear that the seed was naked1 while the accompanying appendage1 corresponding to a seed-vessel1 assumed all forms1 from a complete leaf to a mere scale4 ,in like manner it was proved that the pappus1 or down of composite plants 7as thistles71 is a transformed calyx4 ,along with this successful application of a profound principle1 it was natural that other botanists should make similar attempts4 ,thus ,mr4 ,lindley was led to take a view#ijag of the structure of ,reseda 7mignonette7 different from that usually entertained2 which1 when published1 attracted a good deal of attention1 and gained some converts among the botanists of ,germany and ,france4 ,but in #ahcc1 ,mr4 ,lindley says1 with great candor1 ,lately1 ,professor ,henslow has satisfactorily proved1 in part by the aid of a monstrosity in the common ,mignonette1 in part by a severe application of morphological rules1 that my hypothesis must necessarily be false4 ,such an agreement of different botanists respecting the consequences of morphological rules1 proves the reality and universality of the rules4 ,note #ijag3 ,lindley1 ,brit4 ,assoc4 ,report1 iii4 #ej4 ,we find1 therefore1 that a principle which we may call the ,principle of ,developed and ,metamorphosed ,symmetry1 is firmly established #dge and recognized1 and familiarly and successfully applied by botanists4 ,and it will be apparent1 on reflection1 that though symmetry is a notion which applies to inorganic as well as to organic things1 and is1 in fact1 a conception of certain relations of space and position1 such developement and metamorphosis as are here spoken of1 are ideas entirely different from any of those to which the physical sciences have led us in our previous survey2 and are1 in short1 genuine organical or physiological ideas2--real elements of the philosophy of life4 ,we must1 however imperfectly1 endeavor to trace the application of this idea in the other great department of the world of life2 we must follow the history of ,animal ,morphology4 ,,chapter ,,vii4 ,,progress ,,of ,,animal ,,morphology4 ,sect4 #a4--,rise of ,comparative ,anatomy4 ,,the most general and constant relations of the form of the organs1 both in plants and animals1 are the most natural grounds of classification4 ,hence the first scientific classifications of animals are the first steps in animal morphology4 ,at first1 a zoology was constructed by arranging animals1 as plants were at first arranged1 according to their external parts4 ,but in the course of the researches of the anatomists of the seventeenth century1 it was seen that the internal structure of animals offered resemblances and transitions of a far more coherent and philosophical kind1 and the ,science of ,comparative ,anatomy rose into favor and importance4 ,among the main cultivators of this science#iaag at the period just mentioned1 we find ,francis ,redi1 of ,arezzo2 ,guichard-,joseph ,duvernay1 who was for sixty years ,professor of ,anatomy at the ,jardin du ,roi at ,paris1 and during this lapse of time had for his pupils almost all the greatest anatomists of the greater part of the eighteenth century2 ,nehemiah ,grew1 secretary to the ,royal ,society of ,london1 whose ,anatomy of ,plants we have already noticed4 ,note #iaag3 ,cuv4 ,leons sur l',hist4 des ,sc4 ,nat4 #dad1 #dbj4 ,but ,comparative ,anatomy1 which had been cultivated with ardor #dgf to the end of the seventeenth century1 was1 in some measure1 neglected during the first two-thirds of the eighteenth4 ,the progress of botany was1 ,cuvier sagaciously suggests1#ibag one cause of this2 for that science had made its advances by confining itself to external characters1 and rejecting anatomy2 and though ,linnus acknowledged the dependence of zoology upon anatomy#icag so far as to make the number of teeth his characters1 even this was felt1 in his method1 as a bold step4 ,but his influence was soon opposed by that of ,buffon1 ,daubenton1 and ,pallas2 who again brought into view the importance of comparative anatomy in ,zoology2 at the same time that ,haller proved how much might be learnt from it in ,physiology4 ,john ,hunter in ,england1 the two ,monros in ,scotland1 ,camper in ,holland1 and ,vicq d',azyr in ,france1 were the first to follow the path thus pointed out4 ,camper threw the glance of genius on a host of interesting objects1 but almost all that he produced was a number of sketches2 ,vicq d',azyr1 more assiduous1 was stopt in the midst of a most brilliant career by a premature death4 ,note #ibag3 ,cuv4 ,hist4 ,sc4 ,nat4 i4 #cja4 ,note #icag3 ,ib4 ,such is ,cuvier's outline of the earlier history of comparative anatomy4 ,we shall not go into detail upon this subject2 but we may observe that such studies had fixed in the minds of naturalists the conviction of the possibility and the propriety of considering large divisions of the animal kingdom as modifications of one common type4 ,belon1 as early as #aeee1 had placed the skeleton of a man and a bird side by side1 and shown the correspondence of parts4 ,so far as the case of vertebrated animals extends1 this correspondence is generally allowed2 although it required some ingenuity to detect its details in some cases2 for instance1 to see the analogy of parts between the head of a man and a fish4 ,in tracing these less obvious correspondencies1 some curious steps have been made in recent times4 ,and here we must1 ,i conceive1 again ascribe no small merit to the same remarkable man who1 as we have already had to point out1 gave so great an impulse to vegetable morphology4 ,gthe1 whose talent and disposition for speculating on all parts of nature were truly admirable1 was excited to the study of anatomy by his propinquity to the ,duke of ,weimar's cabinet of natural history4 ,in #aghf1 he published a little essay1 the object of which was to show that in man1 as well as in beasts1 the upper jaw contains an intermaxillary bone1 although the sutures are obliterated4 ,after #agij1idag animated and impelled by the same passion for natural #dgg observation and for general views1 which had produced his ,metamorphosis of ,plants1 he pursued his speculations on these subjects eagerly and successfully4 ,and in #agie1 he published a ,sketch of a ,universal ,introduction into ,comparative ,anatomy1 beginning with ,osteology2 in which he attempts to establish an osteological type1 to which skeletons of all animals may be referred4 ,i do not pretend that ,gthe's anatomical works have had any influence on the progress of the science comparable with that which has been exercised by the labors of professional anatomists2 but the ingenuity and value of the views which they contained was acknowledged by the best authorities2 and the clearer introduction and application of the principle of developed and metamorphosed symmetry may be dated from about this time4 ,gthe declares that1 at an early period of these speculations1 he was convinced#ieag that the bony head of beasts is to be derived from six vertebr4 ,in #ahjg1 ,oken published a ,program ,on the ,signification of the ,bones of the ,skull1 in which he maintained that these bones are equivalent to four vertebr72 and ,meckel1 in his ,comparative ,anatomy1 in #ahaa1 also resolved the skull into vertebr4 ,but ,spix1 in his elaborate work ,cephalogenesis1 in #ahae1 reduced the vertebr of the head to three4 ,oken1 he says1#ifag published opinions merely theoretical1 and consequently contrary to those maintained in this work1 which are drawn from observation4 ,this resolution of the head into vertebr is assented to by many of the best physiologists1 as explaining the distribution of the nerves1 and other phenomena4 ,spix further extended the application of the vertebral theory to the heads of all classes of vertebrate animals2 and ,bojanus published a ,memoir expressly on the vertebral structure of the skulls of fishes in ,oken's ,isis for #ahah4 ,geoffroy ,saint-,hilaire presented a lithographic plate to the ,french ,academy in ,february #ahbd1 entitled ,composition de la ,tte 9999osseuse chez l',homme et les ,animaux1 and developed his views of the vertebral composition of the skull in two ,memoirs published in the ,annales des ,sciences ,naturelles for #ahbd4 ,we cannot fail to recognize here the attempt to apply to the skeleton of animals the principle which leads botanists to consider all the parts of a flower as transformations of the same organs4 ,how far the application of the principle1 as here proposed1 is just1 ,i must leave philosophical physiologists to decide4 ,note #idag3 ,zur ,morphologie1 i4 #bcd4 ,note #ieag3 ,zur ,morphologie1 #bej4 ,note #ifag3 ,spix1 ,cephalogenesis4 ,by these and similar researches1 it is held by the best physiologists #dgh that the skull of all vertebrate animals is pretty well reduced to a uniform structure1 and the laws of its variations nearly determined4#igag ,note #igag3 ,cuv4 ,hist4 ,sc4 ,nat4 iii4 #ddb4 ,the vertebrate animals being thus reduced to a single type1 the question arises how far this can be done with regard to other animals1 and how many such types there are4 ,and here we come to one of the important services which ,cuvier rendered to natural history4 ,sect4 #b4--;,distinction of the ,general ,types of the ,forms of ,animals4--,cuvier4 ,,animals were divided by ,lamarck into vertebrate and invertebrate2 and the general analogies of all vertebrate animals are easily made manifest4 ,but with regard to other animals1 the point is far from clear4 ,cuvier was the first to give a really philosophical view of the animal world in reference to the plan on which each animal is constructed4 ,there are1#ihag he says1 four such plans2--four forms on which animals appear to have been modelled2 and of which the ulterior divisions1 with whatever titles naturalists have decorated them1 are only very slight modifications1 founded on the development or addition of some parts which do not produce any essential change in the plan4 ,note #ihag3 ,rgne ,animal1 p4 #eg4 ,these four great branches of the animal world are the vertebrata1 mollusca1 articulata1 radiata2 and the differences of these are so important that a slight explanation of them may be permitted4 ,the vertebrata are those animals which 7as man and other sucklers1 birds1 fishes1 lizards1 frogs1 serpents7 have a backbone and a skull with lateral appendages1 within which the viscera are included1 and to which the muscles are attached4 ,the mollusca1 or soft animals1 have no bony skeleton2 the muscles are attached to the skin1 which often includes stony plates called shells2 such molluscs are shell-fish2 others are cuttle-fish1 and many pulpy sea-animals4 ,the articulata consist of crustacea 7lobsters1 c471 insects1 spiders1 and annulose worms1 which consist of a head and a number of successive annular portions of the body jointed together 7to the interior of which the muscles are attached71 whence the name4 ,finally1 the radiata include the animals known under the name of zoophytes4 ,in the preceding three branches the organs of motion and of sense were distributed symmetrically on the two sides of an axis1 #dgi so that the animal has a right and a left side4 ,in the radiata the similar members radiate from the axis in a circular manner1 like the petals of a regular flower4 ,the whole value of such a classification cannot be understood without explaining its use in enabling us to give general descriptions1 and general laws of the animal functions of the classes which it includes2 but in the present part of our work our business is to exhibit it as an exemplification of the reduction of animals to laws of ,symmetry4 ,the bipartite ,symmetry of the form of vertebrate and articulate animals is obvious2 and the reduction of the various forms of such animals to a common type has been effected1 by attention to their anatomy1 in a manner which has satisfied those who have best studied the subject4 ,the molluscs1 especially those in which the head disappears1 as oysters1 or those which are rolled into a spiral1 as snails1 have a less obvious ,symmetry1 but here also we can apply certain general types4 ,and the ,symmetry of the radiated zoophytes is of a nature quite different from all the rest1 and approaching1 as we have suggested1 to the kind of ,symmetry found in plants4 ,some naturalists have doubted whether#iiag these zoophytes are not referrible to two types 7acrita or polypes1 and true radiata17 rather than to one4 ,note #iiag3 ,brit4 ,assoc4 ,rep4 iv4 #bbg4 ,this fourfold division was introduced by ,cuvier4#ajjag ,before him1 naturalists followed ,linnus1 and divided non-vertebrate animals into two classes1 insects and worms4 ,i began1 says ,cuvier1 to attack this view of the subject1 and offered another division1 in a ,memoir read at the ,society of ,natural ,history of ,paris1 the #bast of ,floreal1 in the year ,,iii4 of the ,republic 7,may #aj1 #agie17 printed in the ,dcade ,philosophique3 in this1 ,i mark the characters and the limits of molluscs1 insects1 worms1 echinoderms1 and zoophytes4 ,i distinguish the red-blooded worms or annelides1 in a ,memoir read to the ,institute1 the #aath ,nivose1 year ,x4 7,december #ca1 #ahja47 ,i afterwards distributed these different classes into three branches1 each co-ordinate to the branch formed by the vertebrate animals1 in a ,memoir read to the ,institute in ,july1 #ahab1 printed in the ,annales du ,musum d',histoire ,naturelle1 tom4 xix4 ,his great systematic work1 the ,rgne ,animal1 founded on this distribution1 was published in #ahag2 and since that time the division has been commonly accepted among naturalists4 ,note #ajjag3 ,rgne ,a4 #fa4 #bnd ,ed4 ,the question of the ,classification of ,animals is discussed in the first of ,prof4 ,owen's ,lectures on the ,invertebrate #dhj ,animals 7#ahdc74 ,mr4 ,owen observes that the arrangement of animals into ,vertebrate and ,invertebrate which prevailed before ,cuvier1 was necessarily bad1 inasmuch as no negative character in ,zoology gives true natural groups4 ,hence the establishment of the sub-kingdoms1 ,mollusca1 ,articulata1 ,radiata1 as co-ordinate with ,vertebrata1 according to the arrangement of the nervous system1 was a most important advance4 ,but ,mr4 ,owen has seen reason to separate the ,radiata of ,cuvier into two divisions2 the ,nematoneura1 in which the nervous system can be traced in a filamentary form 7including ,echinoderma1 ,ciliobrachiata1 ,clelmintha1 ,rotifera17 and the ,acrita or lowest division of the animal kingdom1 including ,acalepha1 ,nudibrachiata1 ,sterelmintha1 ,polygastria4 ,sect4 #c4--;,attempts to establish the ,identity of the ,types of ,animal ,forms4 ,,supposing this great step in ,zoology1 of which we have given an account1--the reduction of all animals to four types or plans1--to be quite secure1 we are then led to ask whether any further advance is possible2--whether several of these types can be referred to one common form by any wider effort of generalization4 ,on this question there has been a considerable difference of opinion4 ,geoffroy ,saint-,hilaire1#ajaag who had previously endeavored to show that all vertebrate animals were constructed so exactly upon the same plan as to preserve the strictest analogy of parts in respect to their osteology1 thought to extend this unity of plan by demonstrating1 that the hard parts of crustaceans and insects are still only modifications of the skeleton of higher animals1 and that therefore the type of vertebrata must be made to include them also3--the segments of the articulata are held to be strictly analogous to the vertebras of the higher animals1 and thus the former live within their vertebral column in the same manner as the latter live without it4 ,attempts have even been made to reduce molluscous and vertebrate animals to a community of type1 as we shall see shortly4 ,note #ajaag3 ,mr4 ,jenyns1 ,brit4 ,assoc4 ,rep4 iv4 #aej4 ,another application of the principle1 according to which creatures the most different are developments of the same original type1 may be discerned#ajbag in the doctrine1 that the embryo of the higher forms of animal life passes by gradations through those forms which are #dha permanent in inferior animals4 ,thus1 according to this view1 the human ftus assumes successively the plan of the zoophyte1 the worm1 the fish1 the turtle1 the bird1 the beast4 ,but it has been well observed1 that in these analogies we look in vain for the precision which can alone support the inference that has been deduced2#ajcag and that at each step1 the higher embryo and the lower animal which it is supposed to resemble1 differ in having each different organs suited to their respective destinations4 ,note #ajbag3 ,dr4 ,clark1 ,report1 ,ib4 iv4 #aac4 ,note #ajcag3 ,dr4 ,clark1 p4 #aad4 ,cuvier#ajdag never assented to this view1 nor to the attempts to refer the different divisions of his system to a common type4 ,he could not admit1 says his biographer1 that the lungs or gills of the vertebrates are in the same connexion as the branchi of molluscs and crustaceans1 which in the one are situated at the base of the feet1 or fixed on the feet themselves1 and in the other often on the back or about the arms4 ,he did not admit the analogy between the skeleton of the vertebrates and the skin of the articulates2 he could not believe that the tnia and the sepia were constructed on the same plan2 that there was a similarity of composition between the bird and the echinus1 the whale and the snail2 in spite of the skill with which some persons sought gradually to efface their discrepancies4 ,note #ajdag3 ,laurillard1 ,elog4 de ,cuvier1 p4 #ff4 ,whether it may be possible to establish1 among the four great divisions of the ,animal ,kingdom1 some analogies of a higher order than those which prevail within each division1 ,i do not pretend to conjecture4 ,if this can be done1 it is clear that it must be by comparing the types of these divisions under their most general forms3 and thus ,cuvier's arrangement1 so far as it is itself rightly founded on the unity of composition of each branch1 is the surest step to the discovery of a unity pervading and uniting these branches4 ,but those who generalize surely1 and those who generalize rapidly1 may travel in the same direction1 they soon separate so widely1 that they appear to move from each other4 ,the partisans of a universal unity of composition of animals1 accused ,cuvier of being too inert in following the progress of physiological and zoological science4 ,borrowing their illustration from the political parties of the times1 they asserted that he belonged to the science of resistance1 not to the science of the movement4 ,such a charge was highly honorable to him2 for no one acquainted with the history of zoology can doubt that he had a great share in the impulse by which the movement was occasioned2 or that he #dhb himself made a large advance with it2 and it was because he was so poised by the vast mass of his knowledge1 so temperate in his love of doubtful generalizations1 that he was not swept on in the wilder part of the stream4 ,to such a charge1 moderate reformers1 who appreciate the value of the good which exists1 though they try to make it better1 and who know the knowledge1 thoughtfulness1 and caution1 which are needful in such a task1 are naturally exposed4 ,for us1 who can only decide on such a subject by the general analogies of the history of science1 it may suffice to say1 that it appears doubtful whether the fundamental conceptions of affinity1 analogy1 transition1 and developement1 have yet been fixed in the minds of physiologists with sufficient firmness and clearness1 or unfolded with sufficient consistency and generality1 to make it likely that any great additional step of this kind can for some time be made4 ,we have here considered the doctrine of the identity of the seemingly various types of animal structure1 as an attempt to extend the correspondencies which were the basis of ,cuvier's division of the animal kingdom4 ,but this doctrine has been put forward in another point of view1 as the antithesis to the doctrine of final causes4 ,this question is so important a one1 that we cannot help attempting to give some view of its state and bearings4 ,,chapter ,,viii4 ,,the ,,doctrine ,,of ,,final ,,causes ,,in ,,physiology4 ,sect4 #a4--;,assertion of the ,principle of ,unity of ,plan4 ,,we have repeatedly seen1 in the course of our historical view of ,physiology1 that those who have studied the structure of animals and plants1 have had a conviction forced upon them1 that the organs are constructed and combined in subservience to the life and functions of the whole4 ,the parts have a purpose1 as well as a law2--we can trace ,final ,causes1 as well as ,laws of ,causation4 ,this principle is peculiar to physiology2 and it might naturally be expected that1 in the progress of the science1 it would come under special consideration4 ,this accordingly has happened2 and the principle has been drawn #dhc into a prominent position by the struggle of two antagonistic schools of physiologists4 ,on the one hand1 it has been maintained that this doctrine of final causes is altogether unphilosophical1 and requires to be replaced by a more comprehensive and profound principle3 on the other hand1 it is asserted that the doctrine is not only true1 but that1 in our own time1 it has been fixed and developed so as to become the instrument of some of the most important discoveries which have been made4 ,of the views of these two schools we must endeavor to give some account4 ,the disciples of the former of the two schools express their tenets by the phrases unity of plan1 unity of composition2 and the more detailed developement of these doctrines has been termed the ,theory of ,analogies1 by ,geoffroy ,saint-,hilaire1 who claims this theory as his own creation4 ,according to this theory1 the structure and functions of animals are to be studied by the guidance of their analogy only2 our attention is to be turned1 not to the fitness of the organization for any end of life or action1 but to its resemblance to other organizations by which it is gradually derived from the original type4 ,according to the rival view of this subject1 we must not assume1 and cannot establish1 that the plan of all animals is the same1 or their composition similar4 ,the existence of a single and universal system of analogies in the construction of all animals is entirely unproved1 and therefore cannot be made our guide in the study of their properties4 ,on the other hand1 the plan of the animal1 the purpose of its organization in the support of its life1 the necessity of the functions to its existence1 are truths which are irresistibly apparent1 and which may therefore be safely taken as the bases of our reasonings4 ,this view has been put forward as the doctrine of the conditions of existence3 it may also be described as the principle of a purpose in organization2 the structure being considered as having the function for its end4 ,we must say a few words on each of these views4 ,it had been pointed out by ,cuvier1 as we have seen in the last chapter1 that the animal kingdom may be divided into four great branches2 in each of which the plan of the animal is different1 namely1 vertebrata1 articulata1 mollusca1 radiata4 ,now the question naturally occurs1 is there really no resemblance of construction in these different classes8 ,it was maintained by some1 that there is such a resemblance4 ,in #ahbj1ajeag ,m4 ,audouin1 a young naturalist of ,paris1 #dhd endeavored to fill up the chasm which separates insects from other animals2 and by examining carefully the portions which compose the solid frame-work of insects1 and following them through their various transformations in different classes1 he conceived that he found relations of position and function1 and often of number and form1 which might be compared with the relations of the parts of the skeleton in vertebrate animals4 ,he thought that the first segment of an insect1 the head1#ajfag represents one of the three vertebr which1 according to ,spix and others1 compose the vertebrate head3 the second segment of the insects1 7the prothorax of ,audouin17 is1 according to ,m4 ,geoffroy1 the second vertebra of the head of the vertebrata1 and so on4 ,upon this speculation ,cuvier#ajgag does not give any decided opinion2 observing only1 that even if false1 it leads to active thought and useful research4 ,note #ajeag3 ,cuv4 ,hist4 ,sc4 ,nat4 iii4 #dbb4 ,note #ajfag3 ,ib4 #dcg4 ,note #ajgag3 ,cuv4 ,hist4 ,sc4 ,nat4 iii4 #dda4 ,but when an attempt was further made to identify the plan of another branch of the animal world1 the mollusca1 with that of the vertebrata1 the radical opposition between such views and those of ,cuvier1 broke out into an animated controversy4 ,two ,french anatomists1 ,,mm4 ,laurencet and ,meyranx1 presented to the ,academy of ,sciences1 in #ahcj1 a ,memoir containing their views on the organization of molluscous animals2 and on the sepia or cuttle-fish in particular1 as one of the most complete examples of such animals4 ,these creatures1 indeed1 though thus placed in the same division with shell-fish of the most defective organization and obscure structure1 are far from being scantily organized4 ,they have a brain1#ajhag often eyes1 and these1 in the animals of this class1 7cephalopoda7 are more complicated than in any vertebrates2#ajiag they have sometimes ears1 salivary glands1 multiple stomachs1 a considerable liver1 a bile1 a complete double circulation1 provided with auricles and ventricles2 in short1 their vital activity is vigorous1 and their senses are distinct4 ,note #ajhag3 ,geoffroy ,saint-,hilaire denies this4 ,principes de ,phil4 ,zoologique discuts en #ahcj1 p4 #fh4 ,note #ajiag3 ,geoffroy ,saint-,hilaire1 ,principes de ,phil4 ,zoologique discuts en #ahcj1 p4 #ee4 ,but still1 though this organization1 in the abundance and diversity of its parts1 approaches that of vertebrate animals1 it had not been considered as composed in the same manner1 or arranged in the same order1 ,cuvier had always maintained that the plan of molluscs is not a continuation of the plan of vertebrates4 #dhe ,,mm4 ,laurencet and ,meyranx1 on the contrary1 conceived that the sepia might be reduced to the type of a vertebrate creature1 by considering the back-bone of the latter bent double backwards1 so as to bring the root of the tail to the nape of the neck2 the parts thus brought into contact being supposed to coalesce4 ,by this mode of conception1 these anatomists held that the viscera were placed in the same connexion as in the vertebrate type1 and the functions exercised in an analogous manner4 ,to decide on the reality of the analogy thus asserted1 clearly belonged to the jurisdiction of the most eminent anatomists and physiologists4 ,the ,memoir was committed to ,geoffroy ,saint-,hilaire and ,latreille1 two eminent zoologists1 in order to be reported on4 ,their report was extremely favorable2 and went almost to the length of adopting the views of the authors4 ,cuvier expressed some dissatisfaction with this report on its being read2#aajag and a short time afterwards1#aaaag represented ,geoffroy ,saint-,hilaire as having asserted that the new views of ,laurencet and ,meyranx refuted completely the notion of the great interval which exists between molluscous and vertebrate animals4 ,geoffroy protested against such an interpretation of his expressions2 but it soon appeared1 by the controversial character which the discussions on this and several other subjects assumed1 that a real opposition of opinions was in action4 ,note #aajag3 ,princ4 de ,phil4 ,zool4 discuts en #ahcj1 p4 #cf4 ,note #aaaag3 p4 #ej4 ,without attempting to explain the exact views of ,geoffroy1 7we may1 perhaps1 venture to say that they are hardly yet generally understood with sufficient distinctness to justify the mere historian of science in attempting such an explanation17 their general tendency may be sufficiently collected from what has been said2 and from the phrases in which his views are conveyed4#aabag ,the principle of connexions1 the elective affinities of organic elements1 the equilibrization of organs2--such are the designations of the leading doctrines which are unfolded in the preliminary discourse of his ,anatomical ,philosophy4 ,elective affinities of organic elements are the forces by which the vital structures and varied forms of living things are produced2 and the principles of connexion and equilibrium of these forces in the various parts of the organization prescribe limits and conditions to the variety and developement of such forms4 ,note #aabag3 ,phil4 ,zool4 #ae4 ,the character and tendency of this philosophy will be1 ,i think1 #dhf much more clear1 if we consider what it excludes and denies4 ,it rejects altogether all conception of a plan and purpose in the organs of animals1 as a principle which has determined their forms1 or can be of use in directing our reasonings4 ,i take care1 says ,geoffroy1 not to ascribe to ,god any intention4#aacag ,and when ,cuvier speaks of the combination of organs in such order that they may be in consistence with the part which the animal has to play in nature2 his rival rejoins1#aadag ,i know nothing of animals which have to play a part in nature4 ,such a notion is1 he holds1 unphilosophical and dangerous4 ,it is an abuse of final causes which makes the cause to be engendered by the effect4 ,and to illustrate still further his own view1 he says1 ,i have read concerning fishes1 that because they live in a medium which resists more than air1 their motive forces are calculated so as to give them the power of progression under those circumstances4 ,by this mode of reasoning1 you would say of a man who makes use of crutches1 that he was originally destined to the misfortune of having a leg paralysed or amputated4 ,note #aacag3 ,je me garde de prter ,dieu aucune intention4 ,phil4 ,zool4 #aj4 ,note #aadag3 ,je ne connais point d'animal qui ,,doive jouer un rle dans la nature4 p4 #fe4 ,how far this doctrine of unity in the plan in animals1 is admissible or probable in physiology when kept within proper limits1 that is1 when not put in opposition to the doctrine of a purpose involved in the plan of animals1 ,i do not pretend even to conjecture4 ,the question is one which appears to be at present deeply occupying the minds of the most learned and profound physiologists2 and such persons alone1 adding to their knowledge and zeal1 judicial sagacity and impartiality1 can tell us what is the general tendency of the best researches on this subject4#aaeag ,but when the anatomist expresses such opinions1 and defends them by such illustrations as those which ,i have just quoted1#aafag we perceive that he quits the entrenchments of his superior science1 in which he might #dhg have remained unassailable so long as the question was a professional one2 and the discussion is open to those who possess no peculiar knowledge of anatomy4 ,we shall1 therefore1 venture to say a few words upon it4 ,note #aaeag3 ,so far as this doctrine is generally accepted among the best physiologists1 we cannot doubt the propriety of ,meckel's remark1 7,comparative ,anatomy1 #ahba1 ,pref4 p4 xi47 that it cannot be truly asserted either to be new1 or to be peculiarly due to ,geoffroy ,saint-,hilaire4 ,note #aafag3 ,it is hardly worth while answering such illustrations1 but ,i may remark1 that the one quoted above1 irrelevant and unbecoming as it is1 tells altogether against its author4 ,the fact that the wooden leg is of the same length as the other1 proves1 and would satisfy the most incredulous man1 that it was intended for walking4 ,sect4 #b4--;,estimate of the ,doctrine of ,unity of ,plan4 ,,it has been so often repeated1 and so generally allowed in modern times1 that ,final ,causes ought not to be made our guides in natural philosophy1 that a prejudice has been established against the introduction of any views to which this designation can be applied1 into physical speculations4 ,yet1 in fact1 the assumption of an end or purpose in the structure of organized beings1 appears to be an intellectual habit which no efforts can cast off4 ,it has prevailed from the earliest to the latest ages of zoological research2 appears to be fastened upon us alike by our ignorance and our knowledge2 and has been formally accepted by so many great anatomists1 that we cannot feel any scruple in believing the rejection of it to be the superstition of a false philosophy1 and a result of the exaggeration of other principles which are supposed capable of superseding its use4 ,and the doctrine of unity of plan of all animals1 and the other principles associated with this doctrine1 so far as they exclude the conviction of an intelligible scheme and a discoverable end1 in the organization of animals1 appear to be utterly erroneous4 ,i will offer a few reasons for an opinion which may appear presumptuous in a writer who has only a general knowledge of the subject4 #a4 ,in the first place1 it appears to me that the argumentation on the case in question1 the ,sepia1 does by no means turn out to the advantage of the new hypothesis4 ,the arguments in support of the hypothetical view of the structure of this mollusc were1 that by this view the relative position of the parts was explained1 and confirmations which had appeared altogether anomalous1 were reduced to rule2 for example1 the beak1 which had been supposed to be in a position the reverse of all other beaks1 was shown1 by the assumed posture1 to have its upper mandible longer than the lower1 and thus to be regularly placed4 ,but1 says ,cuvier1#aagag supposing the posture1 in order that the side on which the funnel of the sepia is folded should be the back of the animal1 considered as similar to a vertebrate1 the brain with #dhh regard to the beak1 and the sophagus with regard to the liver1 should have positions corresponding to those in vertebrates2 but the positions of these organs are exactly contrary to the hypothesis4 ,how1 then1 can you say1 he asks1 that the cephalopods and vertebrates have identity of composition1 unity of composition1 without using words in a sense entirely different from their common meaning8 ,note #aagag3 ,g4 ,s4 ,h4 ,phil4 ,zool4 p4 #gj4 ,this argument appears to be exactly of the kind on which the value of the hypothesis must depend4#aahag ,it is1 therefore1 interesting to see the reply made to it by the theorist4 ,it is this3 ,i admit the facts here stated1 but ,i deny that they lead to the notion of a different sort of animal composition4 ,molluscous animals had been placed too high in the zoological scale2 but if they are only the embryos of its lower stages1 if they are only beings in which far fewer organs come into play1 it does not follow that the organs are destitute of the relations which the power of successive generations may demand4 ,the organ ,a will be in an unusual relation with the organ ,c1 if ,b has not been produced2--if a stoppage of the developement has fallen upon this latter organ1 and has thus prevented its production4 ,and thus1 he says1 we see how we may have different arrangements1 and divers constructions as they appear to the eye4 ,note #aahag3 ,i do not dwell on other arguments which were employed4 ,it was given as a circumstance suggesting the supposed posture of the type1 that in this way the back was colored1 and the belly was white4 ,on this ,cuvier observes 7,phil4 ,zool4 pp4 #ic1 #fh71 ,i must say1 that ,i do not know any naturalist so ignorant as to suppose that the back is determined by its dark color1 or even by its position when the animal is in motion2 they all know that the badger has a black belly and a white back2 that an infinity of other animals1 especially among insects1 are in the same case2 and that many fishes swim on their side1 or with their belly upwards4 ,it seems to me that such a concession as this entirely destroys the theory which it attempts to defend2 for what arrangement does the principle of unity of composition exclude1 if it admits unusual1 that is1 various arrangements of some organs1 accompanied by the total absence of others8 ,or how does this differ from ,cuvier's mode of stating the conclusion1 except in the introduction of certain arbitrary hypotheses of developement and stoppage8 ,i reduce the facts1 ,cuvier says1 to their true expression1 by saying that ,cephalopods have several organs which are common to them and vertebrates1 and which discharge the same offices2 but that these organs are in them differently distributed1 and often constructed in a different manner2 #dhi and they are accompanied by several other organs which vertebrates have not2 while these on the other hand have several which are wanting in cephalopods4 ,we shall see afterwards the general principles which ,cuvier himself considered as the best guides in these reasonings4 ,but ,i will first add a few words on the disposition of the school now under consideration1 to reject all assumption of an end4 #b4 ,that the parts of the bodies of animals are made in order to discharge their respective offices1 is a conviction which we cannot believe to be otherwise than an irremovable principle of the philosophy of organization1 when we see the manner in which it has constantly forced itself upon the minds of zoologists and anatomists in all ages2 not only as an inference1 but as a guide whose indications they could not help following4 ,i have already noticed expressions of this conviction in some of the principal persons who occur in the history of physiology1 as ,galen and ,harvey4 ,i might add many more1 but ,i will content myself with adducing a contemporary of ,geoffroy's whose testimony is the more remarkable1 because he obviously shares with his countryman in the common prejudice against the use of final causes4 ,i consider1 he says1 in speaking of the provisions for the reproduction of animals1#aaiag with the great ,bacon1 the philosophy of final causes as sterile2 but ,i have elsewhere acknowledged that it was very difficult for the most cautious man never to have recourse to them in his explanations4 ,after the survey which we have had to take of the history of physiology1 we cannot but see that the assumption of final causes in this branch of science is so far from being sterile1 that it has had a large share in every discovery which is included in the existing mass of real knowledge4 ,the use of every organ has been discovered by starting from the assumption that it must have some use4 ,the doctrine of the circulation of the blood was1 as we have seen1 clearly and professedly due to the persuasion of a purpose in the circulatory apparatus4 ,the study of comparative anatomy is the study of the adaption of animal structures to their purposes4 ,and we shall soon have to show that this conception of final causes has1 in our own times1 been so far from barren1 that it has1 in the hands of ,cuvier and others1 enabled us to become intimately acquainted with vast departments of zoology to which we have no other mode of access4 ,it has placed before us in a complete state1 #dij animals1 of which1 for thousands of years1 only a few fragments have existed1 and which differ widely from all existing animals2 and it has given birth1 or at least has given the greatest part of its importance and interest1 to a science which forms one of the brightest parts of the modern progress of knowledge4 ,it is1 therefore1 very far from being a vague and empty assertion1 when we say that final causes are a real and indestructible element in zoological philosophy2 and that the exclusion of them1 as attempted by the school of which we speak1 is a fundamental and most mischievous error4 ,note #aaiag3 ,cabanis1 ,rapports du ,physique et du ,morale de l',homme1 i4 9999#bii4 #c4 ,thus1 though the physiologist may persuade himself that he ought not to refer to final causes1 we find that1 practically1 he cannot help doing this2 and that the event shows that his practical habit is right and well-founded4 ,but he may still cling to the speculative difficulties and doubts in which such subjects may be involved by priori considerations4 ,he may say1 as ,saint-,hilaire does say1#abjag ,i ascribe no intention to ,god1 for ,i mistrust the feeble powers of my reason4 ,i observe facts merely1 and go no further4 ,i only pretend to the character of the historian of what is4 ,i cannot make ,nature an intelligent being who does nothing in vain1 who acts by the shortest mode1 who does all for the best4 ,note #abjag3 ,phil4 ,zool4 p4 #aj4 ,i am not going to enter at any length into this subject1 which1 thus considered1 is metaphysical and theological1 rather than physiological4 ,if any one maintain1 as some have maintained1 that no manifestation of means apparently used for ends in nature1 can prove the existence of design in the ,author of nature1 this is not the place to refute such an opinion in its general form4 ,but ,i think it may be worth while to show1 that even those who incline to such an opinion1 still cannot resist the necessity which compels men to assume1 in organized beings1 the existence of an end4 ,among the philosophers who have referred our conviction of the being of ,god to our moral nature1 and have denied the possibility of demonstration on mere physical grounds1 ,kant is perhaps the most eminent4 ,yet he has asserted the reality of such a principle of physiology as we are now maintaining in the most emphatic manner4 ,indeed1 this assumption of an end makes his very definition of an organized being4 ,an organized product of nature is that in which all the parts are mutually ends and means4#abaag ,and this1 he says1 is a universal and necessary maxim4 ,he adds1 ,it is well known that the #dia anatomizers of plants and animals1 in order to investigate their structure1 and to obtain an insight into the grounds why and to what end such parts1 why such a situation and connexion of the parts1 and exactly such an internal form1 come before them1 assume1 as indispensably necessary1 this maxim1 that in such a creature nothing is in vain1 and proceed upon it in the same way in which in general natural philosophy we proceed upon the principle that nothing happens by chance4 ,in fact1 they can as little free themselves from this teleological principle as from the general physical one2 for as1 on omitting the latter1 no experience would be possible1 so on omitting the former principle1 no clue could exist for the observation of a kind of natural objects which can be considered teleologically under the conception of natural ends4 ,note #abaag3 ,urtheilskraft1 p4 #bif4 ,even if the reader should not follow the reasoning of this celebrated philosopher1 he will still have no difficulty in seeing that he asserts1 in the most distinct manner1 that which is denied by the author whom we have before quoted1 the propriety and necessity of assuming the existence of an end as our guide in the study of animal organization4 #d4 ,it appears to me1 therefore1 that whether we judge from the arguments1 the results1 the practice of physiologists1 their speculative opinions1 or those of the philosophers of a wider field1 we are led to the same conviction1 that in the organized world we may and must adopt the belief that organization exists for its purpose1 and that the apprehension of the purpose may guide us in seeing the meaning of the organization4 ,and ,i now proceed to show how this principle has been brought into additional clearness and use by ,cuvier4 ,in doing this1 ,i may1 perhaps1 be allowed to make a reflection of a kind somewhat different from the preceding remarks1 though suggested by them4 ,in another work1#abbag ,i endeavored to show that those who have been discoverers in science have generally had minds1 the disposition of which was to believe in an intelligent ,maker of the universe2 and that the scientific speculations which produced an opposite tendency1 were generally those which1 though they might deal familiarly with known physical truths1 and conjecture boldly with regard to the unknown1 did not add to the number of solid generalizations4 ,in order to judge whether this remark is distinctly applicable in the case now considered1 ,i should have to estimate ,cuvier in comparison with other physiologists of his time1 which ,i do not presume to do4 ,but ,i may #dib observe1 that he is allowed by all to have established1 on an indestructible basis1 many of the most important generalizations which zoology now contains2 and the principal defect which his critics have pointed out1 has been1 that he did not generalize still more widely and boldly4 ,it appears1 therefore1 that he cannot but be placed among the great discoverers in the studies which he pursued2 and this being the case1 those who look with pleasure on the tendency of the thoughts of the greatest men to an ,intelligence far higher than their own1 most be gratified to find that he was an example of this tendency2 and that the acknowledgement of a creative purpose1 as well as a creative power1 not only entered into his belief but made an indispensable and prominent part of his philosophy4 ,note #abbag3 ,bridgewater ,treatise1 ,b4 iii4 c4 vii4 and viii4 ,on ,inductive ,habits of ,thought1 and on ,deductive ,habits of ,thought4 ,sect4 #c4--;,establishment and ,application of the ,principle of the ,conditions of ,existence of ,animals4--,cuvier4 ,,we have now to describe more in detail the doctrine which ,cuvier maintained in opposition to such opinions as we have been speaking of2 and which1 in his way of applying it1 we look upon as a material advance in physiological knowledge1 and therefore give to it a distinct place in our history4 ,zoology has1 he says1#abcag in the outset of his ,rgne ,animal1 a principle of reasoning which is peculiar to it1 and which it employs with advantage on many occasions3 this is the principle of the ,conditions of ,existence1 vulgarly the principle of ,final ,causes4 ,as nothing can exist if it do not combine all the conditions which render its existence possible1 the different parts of each being must be co-ordinated in such a manner as to render the total being possible1 not only in itself1 but in its relations to those which surround it2 and the analysis of these conditions often leads to general laws1 as clearly demonstrated as those which result from calculation or from experience4 ,note #abcag3 ,rgne ,an4 p4 #f4 ,this is the enunciation of his leading principle in general terms4 ,to our ascribing it to him1 some may object on the ground of its being self-evident in its nature1#abdag and having been very anciently applied4 ,but to this we reply1 that the principle must be considered as a real discovery in the hands of him who first shows how to make it an instrument of other discoveries4 ,it is true1 in other cases as well as in this1 that some vague apprehension1 of true general principles1 such as #dic priori considerations can supply1 has long preceded the knowledge of them as real and verified laws4 ,in such a way it was seen1 before ,newton1 that the motions of the planets must result from attraction2 and so1 before ,dufay and ,franklin1 it was held that electrical actions must result from a fluid4 ,cuvier's merit consisted1 not in seeing that an animal cannot exist without combining all the conditions of its existence2 but in perceiving that this truth may be taken as a guide in our researches concerning animals2--that the mode of their existence may be collected from one part of their structure1 and then applied to interpret or detect another part4 ,he went on the supposition not only that animal forms have some plan1 some purpose1 but that they have an intelligible plan1 a discoverable purpose4 ,he proceeded in his investigations like the decipherer of a manuscript1 who makes out his alphabet from one part of the context1 and then applies it to read the rest4 ,the proof that his principle was something very different from an identical proposition1 is to be found in the fact1 that it enabled him to understand and arrange the structures of animals with unprecedented clearness and completeness of order2 and to restore the forms of the extinct animals which are found in the rocks of the earth1 in a manner which has been universally assented to as irresistibly convincing4 ,these results cannot flow from a trifling or barren principle2 and they show us that if we are disposed to form such a judgment of ,cuvier's doctrine1 it must be because we do not fully apprehend its import4 ,note #abdag3 ,swainson4 ,study of ,nat4 ,hist4 p4 #he4 ,to illustrate this1 we need only quote the statement which he makes1 and the uses to which he applies it4 ,thus in the ,introduction to his great work on ,fossil ,remains he says1 ,every organized being forms an entire system of its own1 all the parts of which mutually correspond1 and concur to produce a certain definite purpose by reciprocal reaction1 or by combining to the same end4 ,hence none of these separate parts can change their forms without a corresponding change in the other parts of the same animal2 and consequently each of these parts1 taken separately1 indicates all the other parts to which it has belonged4 ,thus1 if the viscera of an animal are so organized as only to be fitted for the digestion of recent flesh1 it is also requisite that the jaws should be so constructed as to fit them for devouring prey2 the claws must be constructed for seizing it and tearing it to pieces2 the teeth for cutting and dividing its flesh2 the entire system of the limbs or organs of motion for pursuing and overtaking it2 and the organs of sense for discovering it at a distance4 ,nature must also have endowed the brain of the animal with instincts sufficient for concealing itself and for laying plans to #did catch its necessary victims4#abeag ,by such considerations he has been able to reconstruct the whole of many animals of which parts only were given2--a positive result1 which shows both the reality and the value of the truth on which he wrought4 ,note #abeag3 ,theory of the ,earth1 p4 #ij4 ,another great example1 equally showing the immense importance of this principle in ,cuvier's hands1 is the reform which1 by means of it1 he introduced into the classification of animals4 ,here again we may quote the view he himself has given#abfag of the character of his own improvements4 ,in studying the physiology of the natural classes of vertebrate animals1 he found1 he says1 in the respective quantity of their respiration1 the reason of the quantity of their motion1 and consequently of the kind of locomotion4 ,this1 again1 furnishes the reason for the forms of their skeletons and muscles2 and the energy of their senses1 and the force of their digestion1 are in a necessary proportion to the same quantity4 ,thus a division which had till then been established1 like that of vegetables1 only upon observation1 was found to rest upon causes appreciable1 and applicable to other cases4 ,accordingly1 he applied this view to invertebrates2--examined the modifications which take place in their organs of circulation1 respiration1 and sensation2 and having calculated the necessary results of these modifications1 he deduced from it a new division of those animals1 in which they are arranged according to their true relations4 ,note #abfag3 ,hist4 ,sc4 ,nat4 i4 #bic4 ,such have been some of the results of the principle of the ,conditions of ,existence1 as applied by its great assertor4 ,it is clear1 indeed1 that such a principle could acquire its practical value only in the hands of a person intimately acquainted with anatomical details1 with the functions of the organs1 and with their variety in different animals4 ,it is only by means of such nutriment that the embryo truth could be developed into a vast tree of science4 ,but it is not the less clear1 that ,cuvier's immense knowledge and great powers of thought led to their results1 only by being employed under the guidance of this master-principle3 and1 therefore1 we may justly consider it as the distinctive feature of his speculations1 and follow it with a gratified eye1 as the thread of gold which runs through1 connects1 and enriches his zoological researches3--gives them a deeper interest and a higher value than can belong to any view of the organical sciences1 in which the very essence of organization is kept out of sight4 #die ,the real philosopher1 who knows that all the kinds of truth are intimately connected1 and that all the best hopes and encouragements which are granted to our nature must be consistent with truth1 will be satisfied and confirmed1 rather than surprised and disturbed1 thus to find the ,natural ,sciences leading him to the borders of a higher region4 ,to him it will appear natural and reasonable1 that after journeying so long among the beautiful and orderly laws by which the universe is governed1 we find ourselves at last approaching to a ,source of order and law1 and intellectual beauty3--that1 after venturing into the region of life and feeling and will1 we are led to believe the ,fountain of life and will not to be itself unintelligent and dead1 but to be a living ,mind1 a ,power which aims as well as acts4 ,to us this doctrine appears like the natural cadence of the tones to which we have so long been listening2 and without such a final strain our ears would have been left craving and unsatisfied4 ,we have been lingering long amid the harmonies of law and symmetry1 constancy and development2 and these notes1 though their music was sweet and deep1 must too often have sounded to the ear of our moral nature1 as vague and unmeaning melodies1 floating in the air around us1 but conveying no definite thought1 moulded into no intelligible announcement4 ,but one passage which we have again and again caught by snatches1 though sometimes interrupted and lost1 at last swells in our ears full1 clear1 and decided2 and the religious ,hymn in honor of the ,creator1 to which ,galen so gladly lent his voice1 and in which the best physiologists of succeeding times have ever joined1 is filled into a richer and deeper harmony by the greatest philosophers of these later days1 and will roll on hereafter the perpetual song of the temple of science4 #dig ,,book ,,xviii4 ,,the ,,pal,,tiological ,,sciences4 ,,history ,,of ,,geology4 ,di quibus imperium est animarum1 ,umbrque silentes1 ,et ,chaos1 et ,phlegethon1 loca nocte silentia late1 ,sit mihi fas audita loqui2 sit1 numine vestro ,pandere res alta terr et caligine mersas4 ,,virgil4 n4 vi4 #bfd4 ,ye ,mighty ,ones1 who sway the ,souls that go ,amid the marvels of the world below6 ,ye1 silent ,shades1 who sit and hear around6 ,chaos6 and ,streams that burn beneath the ground6 ,all1 all forgive1 if by your converse stirred1 ,my lips shall utter what my ears have heard2 ,if ,i shall speak of things of doubtful birth1 ,deep sunk in darkness1 as deep sunk in earth4 #dii ,,introduction4 ,of the ,paltiological ,sciences4 ,,we now approach the last ,class of ,sciences which enter into the design of the present work2 and of these1 ,geology is the representative1 whose history we shall therefore briefly follow4 ,by the ,class of ,sciences to which ,i have referred it1 ,i mean to point out those researches in which the object is1 to ascend from the present state of things to a more ancient condition1 from which the present is derived by intelligible causes4 ,the sciences which treat of causes have sometimes been termed tiological1 from 1 a cause3 but this term would not sufficiently describe the speculations of which we now speak2 since it might include sciences which treat of ,permanent ,causality1 like ,mechanics1 as well as inquiries concerning ,progressive ,causation4 ,the investigations which ,i now wish to group together1 deal1 not only with the possible1 but with the actual past2 and a portion of that science on which we are about to enter1 ,geology1 has properly been termed ,palontology1 since it treats of beings which formerly existed4#aah ,hence1 combining these two notions1#bah ,paltiology appears to be a term not inappropriate1 to describe those speculations which thus refer to actual past events1 and attempt to explain them by laws of causation4 ,note #aah3 1 ,note #bah3 1 ,such speculations are not confined to the world of inert matter2 we have examples of them in inquiries concerning the monuments of the art and labor of distant ages2 in examinations into the origin and early progress of states and cities1 customs and languages2 as well as in researches concerning the causes and formations of mountains and rocks1 the imbedding of fossils in strata1 and their elevation from the bottom of the ocean4 ,all these speculations are connected by this bond1--that they endeavor to ascend to a past state of things1 by the aid of the evidence of the present4 ,in asserting1 with ,cuvier1 that #ejj ,the geologist is an antiquary of a new order1 we do not mark a fanciful and superficial resemblance of employment merely1 but a real and philosophical connexion of the principles of investigation4 ,the organic fossils which occur in the rock1 and the medals which we find in the ruins of ancient cities1 are to be studied in a similar spirit and for a similar purpose4 ,indeed1 it is not always easy to know where the task of the geologist ends1 and that of the antiquary begins4 ,the study of ancient geography may involve us in the examination of the causes by which the forms of coasts and plains are changed2 the ancient mound or scarped rock may force upon us the problem1 whether its form is the work of nature or of man2 the ruined temple may exhibit the traces of time in its changed level1 and sea-worn columns2 and thus the antiquarian of the earth may be brought into the very middle of the domain belonging to the antiquarian of art4 ,such a union of these different kinds of archological investigations has1 in fact1 repeatedly occurred4 ,the changes which have taken place in the temple of ,jupiter ,serapis1 near ,puzzuoli1 are of the sort which have just been described2 and this is only one example of a large class of objects2--the monuments of art converted into records of natural events4 ,and on a wider scale1 we find ,cuvier1 in his inquiries into geological changes1 bringing together historical and physical evidence4 ,dr4 ,prichard1 in his ,researches into the ,physical ,history of ,man1 has shown that to execute such a design as his1 we must combine the knowledge of the physiological laws of nature with the traditions of history and the philosophical comparison of languages4 ,and even if we refuse to admit1 as part of the business of geology1 inquiries concerning the origin and physical history of the present population of the globe2 still the geologist is compelled to take an interest in such inquiries1 in order to understand matters which rigorously belong to his proper domain2 for the ascertained history of the present state of things offers the best means of throwing light upon the causes of past changes4 ,mr4 ,lyell quotes ,dr4 ,prichard's book more frequently than any geological work of the same extent4 ,again1 we may notice another common circumstance in the studies which we are grouping together as paltiological1 diverse as they are in their subjects4 ,in all of them we have the same kind of manifestations of a number of successive changes1 each springing out of a preceding state2 and in all1 the phenomena at each step become more and more complicated1 by involving the results of all that has preceded1 modified by supervening agencies4 ,the general aspect of all these #eja trains of change is similar1 and offers the same features for description4 ,the relics and ruins of the earlier states are preserved1 mutilated and dead1 in the products of later times4 ,the analogical figures by which we are tempted to express this relation are philosophically true4 ,it is more than a mere fanciful description1 to say that in languages1 customs1 forms of ,society1 political institutions1 we see a number of formations super-imposed upon one another1 each of which is1 for the most part1 an assemblage of fragments and results of the preceding condition4 ,though our comparison might be bold1 it would be just1 if we were to assert1 that the ,english language is a conglomerate of ,latin words1 bound together in a ,saxon cement2 the fragments of the ,latin being partly portions introduced directly from the parent quarry1 with all their sharp edges1 and partly pebbles of the same material1 obscured and shaped by long rolling in a ,norman or some other channel4 ,thus the study of paltiology in the materials of the earth1 is only a type of similar studies with respect to all the elements1 which1 in the history of the earth's inhabitants1 have been constantly undergoing a series of connected changes4 ,but1 wide as is the view which such considerations give us of the class of sciences to which geology belongs1 they extend still further4 ,the science of the changes which have taken place in the organic kingdoms of nature1 7such is the description which has been given of ,geology1#cah7 may1 by following another set of connexions1 be extended beyond the modifications of the surface of our own planet4 ,for we cannot doubt that some resemblance of a closer or looser kind1 has obtained between the changes and causes of change1 on other bodies of the universe1 and on our own4 ,the appearances of something of the kind of volcanic action on the surface of the moon1 are not to be mistaken4 ,and the inquiries concerning the origin of our planet and of our solar system1 inquiries to which ,geology irresistibly impels her students1 direct us to ask what information the rest of the universe can supply1 bearing upon this subject4 ,it has been thought by some1 that we can trace systems1 more or less like our solar system1 in the process of formation2 the nebulous matter1 which is at first expansive and attenuated1 condensing gradually into suns and planets4 ,whether this ,nebular ,hypothesis be tenable or not1 ,i shall not here inquire2 but the discussion of such a question would be closely connected with #ejb geology1 both in its interests and in its methods4 ,if men are ever able to frame a science of the past changes by which the universe has been brought into its present condition1 this science will be properly described as ,cosmical ,paltiology4 ,note #cah3 ,lyell1 ,principles of ,geology1 p4 #a4 ,these paltiological sciences might properly be called historical1 if that term were sufficiently precise3 for they are all of the nature of history1 being concerned with the succession of events3 and the part of history which deals with the past causes of events1 is1 in fact1 a moral paltiology4 ,but the phrase ,natural ,history has so accustomed us to a use of the word history in which we have nothing to do with time1 that1 if we were to employ the word historical to describe the paltiological sciences1 it would be in constant danger of being misunderstood4 ,the fact is1 as ,mohs has said1 that ,natural ,history1 when systematically treated1 rigorously excludes all that is historical2 for it classes objects by their permanent and universal properties1 and has nothing to do with the narration of particular and casual facts4 ,and this is an inconsistency which we shall not attempt to rectify4 ,all paltiological sciences1 since they undertake to refer changes to their causes1 assume a certain classification of the phenomena which change brings forth1 and a knowledge of the operation of the causes of change4 ,these phenomena1 these causes1 are very different1 in the branches of knowledge which ,i have thus classed together4 ,the natural features of the earth's surface1 the works of art1 the institutions of society1 the forms of language1 taken together1 are undoubtedly a very wide collection of subjects of speculation2 and the kinds of causation which apply to them are no less varied4 ,of the causes of change in the inorganic and organic world1--the peculiar principles of ,geology--we shall hereafter have to speak4 ,as these must be studied by the geologist1 so1 in like manner1 the tendencies1 instincts1 faculties1 principles1 which direct man to architecture and sculpture1 to civil government1 to rational and grammatical speech1 and which have determined the circumstances of his progress in these paths1 must be in a great degree known to the ,paltiologist of ,art1 of ,society1 and of ,language1 respectively1 in order that he may speculate soundly upon his peculiar subject4 ,with these matters we shall not here meddle1 confining ourselves1 in our exemplification of the conditions and progress of such sciences1 to the case of ,geology4 ,the journey of survey which we have attempted to perform over the field of human knowledge1 although carefully directed according to the paths and divisions of the physical sciences1 has already #ejc conducted us to the boundaries of physical science1 and gives us a glimpse of the region beyond4 ,in following the history of ,life1 we found ourselves led to notice the perceptive and active faculties of man2 it appeared that there was a ready passage from physiology to psychology1 from physics to metaphysics4 ,in the class of sciences now under notice1 we are1 at a different point1 carried from the world of matter to the world of thought and feeling1--from things to men4 ,for1 as we have already said1 the science of the causes of change includes the productions of ,man as well as of ,nature4 ,the history of the earth1 and the history of the earth's inhabitants1 as collected from phenomena1 are governed by the same principles4 ,thus the portions of knowledge which seek to travel back towards the origin1 whether of inert things or of the works of man1 resemble each other4 ,both of them treat of events as connected by the thread of time and causation4 ,in both we endeavor to learn accurately what the present is1 and hence what the past has been4 ,both are historical sciences in the same sense4 ,it must be recollected that ,i am now speaking of history as tiological2--as it investigates causes1 and as it does this in a scientific1 that is1 in a rigorous and systematic1 manner4 ,and ,i may observe here1 though ,i cannot now dwell on the subject1 that all tiological sciences will consist of three portions2 the ,description of the facts and phenomena2--the general ,theory of the causes of change appropriate to the case2--and the ,application of the theory to the facts4 ,thus1 taking ,geology for our example1 we must have1 first ,descriptive or ,phenomenal ,geology2 next1 the exposition of the general principles by which such phenomena can be produced1 which we may term ,geological ,dynamics2 and1 lastly1 doctrines hence derived1 as to what have been the causes of the existing state of things1 which we may call ,physical ,geology4 ,these three branches of geology may be found frequently or constantly combined in the works of writers on the subject1 and it may not always be easy to discriminate exactly what belongs to each subject4#dah ,but the analogy of this science with others1 its present #ejd condition and future fortunes1 will derive great illustration from such a distribution of its history2 and in this point of view1 therefore1 we shall briefly treat of it2 dividing the history of ,geological ,dynamics1 for the sake of convenience1 into two ,chapters1 one referring to inorganic1 and one to organic1 phenomena4 ,note #dah3 ,the ,wernerians1 in distinguishing their study from ,geology1 and designating it as ,geognosy1 the knowledge of the earth1 appear to have intended to select ,descriptive ,geology for their peculiar field4 ,in like manner1 the original aim of the ,geological ,society of ,london1 which was formed 7#ahjg7 with a view to record and multiply observations1 recognized the possibility of a ,descriptive ,geology separate from the other portions of the science4 #eje ,,descriptive ,,geology4 ,,chapter ,i4 ,,prelude ,,to ,,systematic ,,descriptive ,,geology4 ,sect4 #a4--;,ancient ,notices of ,geological ,facts4 ,,the recent history of ,geology1 as to its most important points1 is bound up with what is doing at present from day to day2 and that portion of the history of the science which belongs to the past1 has been amply treated by other writers4#eah ,i shall1 therefore1 pass rapidly over the series of events of which this history consists2 and shall only attempt to mention what may seem to illustrate and confirm my own view of its state and principles4 ,note #eah3 ,as ,,mm4 ,lyell1 ,fitton1 ,conybeare1 in our own country4 ,agreeably to the order already pointed out1 ,i shall notice1 in the first place1 ,phenomenal ,geology1 or the description of the facts1 as distinct from the inquiry into their causes4 ,it is manifest that such a merely descriptive kind of knowledge may exist2 and it probably will not be contested1 that such knowledge ought to be collected1 before we attempt to frame theories concerning the causes of the phenomena4 ,but it must be observed1 that we are here speaking of the formation of a science2 and that it is not a collection of miscellaneous1 unconnected1 unarranged knowledge that can be considered as constituting science2 but a methodical1 coherent1 and1 as far as possible1 complete body of facts1 exhibiting fully the condition of the earth as regards those circumstances which are the subject matter of geological speculation4 ,such a ,descriptive ,geology is a pre-requisite to ,physical ,geology1 just as ,phenomenal ,astronomy necessarily preceded ,physical ,astronomy1 or as ,classificatory ,botany is a necessary accompaniment to ,botanical ,physiology4 ,we may observe also that ,descriptive ,geology1 such as we now speak of1 is one of the classificatory sciences1 like #ejf ,mineralogy or ,botany3 and will be found to exhibit some of the features of that class of sciences4 ,since1 then1 our ,history of ,descriptive ,geology is to include only systematic and scientific descriptions of the earth or portions of it1 we pass over1 at once1 all the casual and insulated statements of facts1 though they may be geological facts1 which occur in early writers2 such1 for instance1 as the remark of ,herodotus1#fah that there are shells in the mountains of ,egypt2 or the general statements which ,ovid puts in the mouth of ,pythagoras3#gah ,vidi ego quod fuerat solidissima tellus1 ,esse fretum2 vidi factas ex quore terras1 ,et procul a pelago conch jacuere marin4 ,note #fah3 ii4 #ab4 ,note #gah3 ,met4 xv4 #bfb4 ,we may remark here already how generally there are mingled with descriptive notices of such geological facts1 speculations concerning their causes4 ,herodotus refers to the circumstance just quoted1 for the purpose of showing that ,egypt was formerly a gulf of the sea2 and the passage of the ,roman poet is part of a series of exemplifications which he gives of the philosophical tenet1 that nothing perishes but everything changes4 ,it will be only by constant attention that we shall be able to keep our provinces of geology distinct4 ,sect4 #b4--;,early ,descriptions and ,collections of ,fossils4 ,,if we look1 as we have proposed to do1 for systematic and exact knowledge of geological facts1 we find nothing which we can properly adduce till we come to modern times4 ,but when facts such as those already mentioned1 7that sea-shells and other marine objects are found imbedded in rocks17 and other circumstances in the structure of the ,earth1 had attracted considerable attention1 the exact examination1 collection1 and record of these circumstances began to be attempted4 ,among such steps in ,descriptive ,geology1 we may notice descriptions and pictures of fossils1 descriptions of veins and mines1 collections of organic and inorganic fossils1 maps of the mineral structure of countries1 and finally1 the discoveries concerning the superposition of strata1 the constancy of their organic contents1 their correspondence in different countries1 and such great general relations of the materials and features of the earth as have been discovered up to the present time4 #ejg ,without attempting to assign to every important advance its author1 ,i shall briefly exemplify each of the modes of contributing to descriptive geology which ,i have just enumerated4 ,the study of organic fossils was first pursued with connexion and system in ,italy4 ,the hills which on each side skirt the mountain-range of the ,apennines are singularly rich in remains of marine animals4 ,when these remarkable objects drew the attention of thoughtful men1 controversies soon arose whether they really were the remains of living creatures1 or the productions of some capricious or mysterious power by which the forms of such creatures were mimicked2 and again1 if the shells were really the spoils of the sea1 whether they had been carried to the hills by the deluge of which the ,scripture speaks1 or whether they indicated revolutions of the earth of a different kind4 ,the earlier works which contain the descriptions of the phenomena have1 in almost all instances1 by far the greater part of their pages occupied with these speculations2 indeed1 the facts could not be studied without leading to such inferences1 and would not have been collected but for the interest which such reasonings possessed4 ,as one of the first persons who applied a sound and vigorous intellect to these subjects1 we may notice the celebrated painter ,leonardo da ,vinci1 whom we have already had to refer to as one of the founders of the modern mechanical sciences4 ,he strenuously asserts the contents of the rocks to be real shells1 and maintains the reality of the changes of the domain of land and sea which these spoils of the ocean imply4 ,you will tell me1 he says1 that nature and the influence of the stars have formed these shelly forms in the mountains2 then show me a place in the mountains where the stars at the present day make shelly forms of different ages1 and of different species in the same place4 ,and how1 with that1 will you explain the gravel which is hardened in stages at different heights in the mountains8 ,he then mentions several other particulars respecting these evidences that the existing mountains were formerly in the bed of the sea4 ,leonardo died in #aeai4 ,at present we refer to geological essays like his1 only so far as they are descriptive4 ,going onwards with this view1 we may notice ,fracastoro1 who wrote concerning the petrifactions which were brought to light in the mountains of ,verona1 when1 in #aeag1 they were excavated for the purpose of repairing the city4 ,little was done in the way of collection of facts for some time after this4 ,in #affi1 ,steno1 a ,dane resident in ,italy1 put forth his treatise1 ,de ,solido intra ,solidum naturaliter contento2 and the #ejh following year1 ,augustino ,scilla1 a ,sicilian painter1 published a ,latin epistle1 ,de ,corporibus ,marinis ,lapidescentibus1 illustrated by good engravings of fossil-shells1 teeth1 and corals4#hah ,after another interval of speculative controversy1 we come to ,antonio ,vallisneri1 whose letters1 ,de' ,corpi ,marini che su' ,monti si trovano1 appeared at ,venice in #agba4 ,in these letters he describes the fossils of ,monte ,bolca1 and attempts to trace the extent of the marine deposits of ,italy1#iah and to distinguish the most important of the fossils4 ,similar descriptions and figures were published with reference to our own country at a later period4 ,in #agff1 ,brander's ,fossilia ,hantoniensia1 or ,hampshire ,fossils1 appeared2 containing excellent figures of fossil shells from a part of the south coast of ,england2 and similar works came forth in other parts of ,europe4 ,note #hah3 ,augustine ,scilla's original drawings of fossil shells1 teeth1 and corals1 from which the engravings mentioned in the text were executed1 as well as the natural objects from which the drawings were made1 were bought by ,woodward1 and are now in the ,woodwardian ,museum at ,cambridge4 ,note #iah3 p4 #bj4 ,however exact might be the descriptions and figures thus produced1 they could not give such complete information as the objects themselves1 collected and permanently preserved in museums4 ,vallisneri says1#ajah that having begun to collect fossils for the purpose of forming a grotto1 he selected the best1 and preserved them as a noble diversion for the more curious4 ,the museum of ,calceolarius at ,verona contained a celebrated collection of such remains4 ,a copious description of it appeared in #afbb4 ,such collections had been made from an earlier period1 and catalogues of them published4 ,thus ,gessner's work1 ,de ,rerum ,fossilium1 ,lapidum et ,gemmarum ,figuris 7#aefe71 contains a catalogue of the cabinet of petrifactions collected by ,john ,kentman2 many catalogues of the same kind appeared in the seventeenth century4#aaah ,lhwyd's 9999,lythophylacii ,britannici ,iconographia1 published at ,oxford in #affi1 and exhibiting a very ample catalogue of ,english ,fossils contained in the ,ashmolean ,museum1 may be noticed as one of these4 ,note #ajah3 p4 #a4 ,note #aaah3 ,parkinson1 ,organic ,remains1 vol4 i4 p4 #bj4 ,one of the most remarkable occurrences in the progress of descriptive geology in ,england1 was the formation of a geological museum by ,william ,woodward as early as #afie4 ,this collection1 formed with great labor1 systematically arranged1 and carefully catalogued1 he bequeathed to the ,university of ,cambridge2 founding and endowing #eji at the same time a professorship of the study of geology4 ,the ,woodwardian ,museum still subsists1 a monument of the sagacity with which its author so early saw the importance of such a collection4 ,collections and descriptions of fossils1 including in the term specimens of minerals of all kinds1 as well as organic remains1 were frequently made1 and especially in places where mining was cultivated2 but under such circumstances1 they scarcely tended at all to that general and complete knowledge of the earth of which we are now tracing the progress4 ,in more modern times1 collections may be said to be the most important books of the geologist1 at least next to the strata themselves4 ,the identifications and arrangements of our best geologists1 the immense studies of fossil anatomy by ,cuvier and others1 have been conducted mainly by means of collections of specimens4 ,they are more important in this study than in botany1 because specimens which contain important geological information are both more rare and more permanent4 ,plants1 though each individual is perishable1 perpetuate and diffuse their kind2 while the organic impression on a stone1 if lost1 may never occur in a second instance2 but1 on the other hand1 if it be preserved in the museum1 the individual is almost as permanent in this case1 as the species in the other4 ,i shall proceed to notice another mode in which such information was conveyed4 ,sect4 #c4--;,first ,construction of ,geological ,maps4 ,,dr4 ,,lister1 a learned physician1 sent to the ,royal ,society1 in #afhc1 a proposal for maps of soils or minerals2 in which he suggested that in the map of ,england1 for example1 each soil and its boundaries might be distinguished by color1 or in some other way4 ,such a mode of expressing and connecting our knowledge of the materials of the earth was1 perhaps1 obvious1 when the mass of knowledge became considerable4 ,in #agbj1 ,fontenelle1 in his observations on a paper of ,de ,reaumur's1 which contained an account of a deposit of fossil-shells in ,touraine1 says1 that in order to reason on such cases1 we must have a kind of geographical charts1 constructed according to the collection of shells found in the earth4 ,but he justly adds1 ,what a quantity of observations1 and what time would it not require to form such maps6 ,the execution of such projects required1 not merely great labor1 but #eaj several steps in generalization and classification1 before it could take place4 ,still such attempts were made4 ,in #agdc1 was published1 ,a new ,philosophico-chorographical ,chart of ,east ,kent1 invented and delineated by ,christopher ,packe1 ,m4,d42 in which1 however1 the main object is rather to express the course of the valleys than the materials of the country4 ,guettard formed the project of a mineralogical map of ,france1 and ,monnet carried this scheme into effect in #aghj1abah by order of the king4 ,in these maps1 however1 the country is not considered as divided into soils1 still less strata2 but each part is marked with its predominant mineral only4 ,the spirit of generalization which constitutes the main value of such a work is wanting4 ,note #abah3 ,atlas et ,description ,minralogique de la ,france1 entrepris par ordre du ,roi1 par ,,mm4 ,guettard et ,monnet1 ,paris1 #aghj1 pp4 #bab1 with #ca maps4 ,geological maps belong strictly to ,descriptive ,geology2 they are free from those wide and doubtful speculations which form so large a portion of the earlier geological books4 ,yet even geological maps cannot be usefully or consistently constructed without considerable steps of classification and generalization4 ,when1 in our own time1 geologists were become weary of controversies respecting theory1 they applied themselves with extraordinary zeal to the construction of stratigraphical maps of various countries2 flattering themselves that in this way they were merely recording incontestable facts and differences4 ,nor do ,i mean to intimate that their facts were doubtful1 or their distinctions arbitrary4 ,but still they were facts interpreted1 associated1 and represented1 by means of the classifications and general laws which earlier geologists had established2 and thus even ,descriptive ,geology has been brought into existence as a science by the formation of systems and the discovery of principles4 ,at this we cannot be surprized1 when we recollect the many steps which the formation of ,classificatory ,botany required4 ,we must now notice some of the discoveries which tended to the formation of ,systematic ,descriptive ,geology4 #eaa ,,chapter ,,ii4 ,,formation ,,of ,,systematic ,,descriptive ,,geology4 ,sect4 #a4--;,discovery of the ,order and ,stratification of the ,materials of the ,earth4 ,,that the substances of which the earth is framed are not scattered and mixed at random1 but possess identity and continuity to a considerable extent1 ,lister was aware1 when he proposed his map4 ,but there is1 in his suggestions1 nothing relating to stratification2 nor any order of position1 still less of time1 assigned to these materials4 ,woodward1 however1 appears to have been fully aware of the general law of stratification4 ,on collecting information from all parts1 the result was1 he says1 that in time ,i was abundantly assured that the circumstances of these things in remoter countries were much the same with those of ours here3 that the stone1 and other terrestrial matter in ,france1 ,flanders1 ,holland1 ,spain1 ,italy1 ,germany1 ,denmark1 and ,sweden1 was distinguished into strata or layers1 as it is in ,england2 that these strata were divided by parallel fissures2 that there were enclosed in the stone and all the other denser kinds of terrestrial matter1 great numbers of the shells1 and other productions of the sea1 in the same manner as in that of this island4#acah ,so remarkable a truth1 thus collected from a copious collection of particulars by a patient induction1 was an important step in the science4 ,note #acah3 ,natural ,history of the ,earth1 #agbc4 ,these general facts now began to be commonly recognized1 and followed into detail4 9999,stukeley the antiquary#adah 7#agbd71 remarked an important feature in the strata of ,england1 that their escarpments1 or steepest sides1 are turned towards the west and north-west2 and ,strachey#aeah 7#agai71 gave a stratigraphical description of certain coal-mines near ,bath4#afah ,michell1 appointed ,woodwardian ,professor at ,cambridge #eab in #agfb1 described this stratified structure of the earth far more distinctly than his predecessors1 and pointed out1 as the consequence of it1 that the same kinds of earths1 stones1 and minerals1 will appear at the surface of the earth in long parallel slips1 parallel to the long ridges of mountains2 and so1 in fact1 we find them4#agah ,note #adah3 ,itinerarium ,curiosum1 #agbd4 ,note #aeah3 ,phil4 ,trans4 #agai1 and ,observations on ,strata1 c4 #agbi4 ,note #afah3 ,fitton1 ,annals of ,philosophy1 ,n4 ,s4 vol4 i4 and ii4 7#ahcb1 '#c71 p4 #aeg4 ,note #agah3 ,phil4 ,trans4 #agfj4 ,michell 7as appeared by papers of his which were examined after his death7 had made himself acquainted with the series of ,english strata which thus occur from ,cambridge to ,york2--that is1 from the chalk to the coal4 ,these relations of position required that geological maps1 to complete the information they conveyed1 should be accompanied by geological ,sections1 or imaginary representations of the order and mode of superpositions1 as well as of the superficial extent of the strata1 as in more recent times has usually been done4 ,the strata1 as we travel from the higher to the lower1 come from under each other into view2 and this out-cropping1 basseting1 or by whatever other term it is described1 is an important feature in their description4 ,it was further noticed that these relations of position were combined with other important facts1 which irresistibly suggested the notion of a relation in time4 ,this1 indeed1 was implied in all theories of the earth2 but observations of the facts most require our notice4 ,steno is asserted by ,humboldt#ahah to be the first who 7in #affi7 distinguished between rocks anterior to the existence of plants and animals upon the globe1 containing therefore no organic remains2 and rocks super-imposed on these1 and full of such remains2 turbidi maris sedimenta sibi invicem imposita4 ,note #ahah3 ,essai 9999,gognostique4 ,rouelle is stated1 by his pupil ,desmarest1 to have made some additional and important observations4 ,he saw1 it is said1 that the shells which occur in rocks were not the same in all countries2 that certain species occur together1 while others do not occur in the same beds2 that there is a constant order in the arrangement of these shells1 certain species lying in distinct bands4#aiah ,note #aiah3 ,encycl4 ,mthod4 ,geogr4 ,phys4 tom4 i4 p4 #daf1 as quoted by ,fitton as above1 p4 #aei4 ,such divisions as these required to be marked by technical names4 ,a distinction was made of l'ancienne terre and la nouvelle terre1 to which ,rouelle added a travaille intermdiaire4 ,rouelle died in #aggj1 having been known by lectures1 not by books4 ,lehman1 in #agef1 claims for himself the credit of being the first to observe and describe correctly the structure of stratified countries2 being ignorant1 #eac probably1 of the labors of ,strachey in ,england4 ,he divided mountains into three classes2#bjah primitive1 which were formed with the world2--those which resulted from a partial destruction of the primitive rocks2--and a third class resulting from local or universal deluges4 ,in #agei1 also1 ,arduine1#baah in his ,memoirs on the mountains of ,padua1 ,vicenza1 and ,verona1 deduced1 from original observations1 the distinction of rocks into primary1 secondary1 and tertiary4 ,note #bjah3 ,lyell1 i4 #gj4 ,note #baah3 ,ib4 #gb4 ,the relations of position and fossils were1 from this period1 inseparably connected with opinions concerning succession in time4 ,odoardi remarked1#bbah that the strata of the 9999,sub-,apennine hills are unconformable to those of the ,apennine1 7as ,strachey had observed1 that the strata above the coal were unconformable to the coal2#bcah7 and his work contained a clear argument respecting the different ages of these two classes of hills4 ,fuchsel was1 in #agfb1 aware of the distinctness of strata of different ages in ,germany4 ,pallas and ,saussure were guided by general views of the same kind in observing the countries which they visited3 but1 perhaps1 the general circulation of such notions was most due to ,werner4 ,note #bbah3 ,ib4 #gd4 ,note #bcah3 ,fitton1 p4 #aeg4 ,sect4 #b4--,systematic form given to ,descriptive ,geology4--,werner4 ,,werner expressed the general relations of the strata of the earth by means of classifications which1 so far as general applicability is concerned1 are extremely imperfect and arbitrary2 he promulgated a theory which almost entirely neglected all the facts previously discovered respecting the grouping of fossils1--which was founded upon observations made in a very limited district of ,germany1--and which was contradicted even by the facts of this district4 ,yet the acuteness of his discrimination in the subjects which he studied1 the generality of the tenets he asserted1 and the charm which he threw about his speculations1 gave to ,geology1 or1 as he termed it1 ,geognosy1 a popularity and reputation which it had never before possessed4 ,his system had asserted certain universal formations1 which followed each other in a constant order2--granite the lowest1--then mica-slate and clay-slate2--upon these primitive rocks1 generally highly inclined1 rest other transition strata2--upon these1 lie secondary ones1 which being more nearly horizontal1 are called fltz or flat4 ,the term formation1 #ead which we have thus introduced1 indicating groups which1 by evidence of all kinds1--of their materials1 their position1 and their organic contents1--are judged to belong to the same period1 implies no small amount of theory3 yet this term1 from this time forth1 is to be looked upon as a term of classification solely1 so far as classification can be separately attended to4 ,werner's distinctions of strata were for the most part drawn from mineralogical constitution4 ,doubtless1 he could not fail to perceive the great importance of organic fossils4 ,i was witness1 says ,m4 de ,humboldt1 one of his most philosophical followers1 of the lively satisfaction which he felt when1 in #agib1 ,m4 de 9999,schlottheim1 one of the most distinguished geologists of the school of ,freiberg1 began to make the relations of fossils to strata the principal object of his studies4 ,but ,werner and the disciples of his school1 even the most enlightened of them1 never employed the characters derived from organic remains with the same boldness and perseverance as those who had from the first considered them as the leading phenomena3 thus ,m4 de ,humboldt expresses doubts which perhaps many other geologists do not feel when1 in #ahbc1 he says1 ,are we justified in concluding that all formations are characterized by particular species8 that the fossil-shells of the chalk1 the muschelkalk1 the ,jura limestone1 and the ,alpine limestone1 are all different8 ,i think this would be pushing the induction much too far4#bdah ,in ,prof4 ,jamieson's ,geognosy1 which may be taken as a representation of the ,wernerian doctrines1 organic fossils are in no instance referred to as characters of formations or strata4 ,after the curious and important evidence1 contained in organic fossils1 which had been brought into view by the labors of ,italian1 ,english1 and ,german writers1 the promulgation of a system of ,descriptive ,geology1 in which all this evidence was neglected1 cannot be considered otherwise than as a retrograde step in science4 ,note #bdah3 ,gissement des ,roches1 p4 #da4 ,werner maintained the aqueous deposition of all strata above the primitive rocks2 even of those trap rocks1 to which1 from their resemblance to lava and other phenomena1 ,raspe1 ,arduino1 and others1 had already assigned a volcanic origin4 ,the fierce and long controversy between the ,vulcanists and ,neptunists1 which this dogma excited1 does not belong to this part of our history2 but the discovery of veins of granite penetrating the superincumbent slate1 to which the controversy led1 was an important event in descriptive geology4 ,hutton1 the #eae author of the theory of igneous causation which was in this country opposed to that of ,werner1 sought and found this phenomenon in the ,grampian hills1 in #aghe4 ,this supposed verification of his system filled him with delight1 and called forth such marks of joy and exultation1 that the guides who accompanied him were persuaded1 says his biographer1#beah that he must have discovered a vein of silver or gold4#bfah ,note #beah3 ,playfair's ,works1 vol4 iv4 p4 #ge4 ,note #bfah3 ,lyell1 i4 #ij4 ,desmarest's examination of ,auvergne 7#agfh7 showed that there was there an instance of a country which could not even be described without terms implying that the basalt1 which covered so large a portion of it1 had flowed from the craters of extinct volcanoes4 ,his map of ,auvergne was an excellent example of a survey of such a country1 thus exhibiting features quite different from those of common stratified countries4#bgah ,note #bgah3 ,lyell1 i4 #hf4 ,the facts connected with metalliferous veins were also objects of ,werner's attention4 ,a knowledge of such facts is valuable to the geologist as well as to the miner1 although even yet much difficulty attends all attempts to theorize concerning them4 ,the facts of this nature have been collected in great abundance in all mining districts2 and form a prominent part of the descriptive geology of such districts2 as1 for example1 the ,hartz1 and ,cornwall4 ,without further pursuing the history of the knowledge of the inorganic phenomena of the earth1 ,i turn to a still richer department of geology1 which is concerned with organic fossils4 ,sect4 #c4--;,application of ,organic ,remains as a ,geological ,character4--,smith4 ,,rouelle and ,odoardi had perceived1 as we have seen1 that fossils were grouped in bands3 but from this general observation to the execution of a survey of a large kingdom1 founded upon this principle1 would have been a vast stride1 even if the author of it had been aware of the doctrines thus asserted by these writers4 ,in fact1 however1 ,william ,smith executed such a survey of ,england1 with no other guide or help than his own sagacity and perseverance4 ,in his employments as a civil engineer1 he noticed the remarkable continuity and constant order of the strata in the neighborhood of ,bath1 as discriminated by their fossils2 and about the year #agic1 he#bhah drew up a ,tabular ,view of the #eaf strata of that district1 which contained the germ of his subsequent discoveries4 ,finding in the north of ,england the same strata and associations of strata with which he had become acquainted in the west1 he was led to name them and to represent them by means of maps1 according to their occurrence over the whole face of ,england4 ,these maps appeared#biah in #ahae2 and a work by the same author1 entitled ,the ,english ,strata identified by ,organic ,remains1 came forth later4 ,but the views on which this identification of strata rests1 belong to a considerably earlier date2 and had not only been acted upon1 but freely imparted in conversation many years before4 ,note #bhah3 ,fitton1 p4 #adh4 ,note #biah3 ,brit4 ,assoc4 #ahcb4 ,conybeare1 p4 #cgc4 ,in the meantime the study of fossils was pursued with zeal in various countries4 ,lamarck and ,defrance employed themselves in determining the fossil shells of the neighborhood of ,paris2#cjah and the interest inspired by this subject was strongly nourished and stimulated by the memorable work of ,cuvier and ,brongniart1 ,on the ,environs of ,paris1 published in #ahaa1 and by ,cuvier's subsequent researches on the subjects thus brought under notice4 ,for now1 not only the distinction1 succession1 and arrangement1 but many other relations among fossil strata1 irresistibly arrested the attention of the philosopher4 ,brongniart#caah showed that very striking resemblances occurred in their fossil remains1 between certain strata of ,europe and of ,north ,america2 and proved that a rock may be so much disguised1 that the identity of the stratum can only be recognized by geological characters4#cbah ,note #cjah3 ,humboldt1 ,giss4 d4 ,r4 p4 #ce4 ,note #caah3 ,hist4 ,nat4 des ,crustacs ,fossiles1 pp4 #eg1 #fb4 ,note #cbah3 ,humboldt1 ,giss4 d4 ,r4 p4 #de4 ,the ,italian geologists had found in their hills1 for the most part1 the same species of shells which existed in their seas2 but the ,german and ,english writers1 as ,gesner1#ccah ,raspe1#cdah and ,brander1#ceah had perceived that the fossil-shells were either of unknown species1 or of such as lived in distant latitudes4 ,to decide that the animals and plants1 of which we find the remains in a fossil state1 were of species now extinct1 obviously required an exact and extensive knowledge of natural history4 ,and if this were so1 to assign the relations of the past to the existing tribes of beings1 and the peculiarities of their vital processes and habits1 were tasks which could not be performed without the most consummate physiological skill and talent4 ,such tasks1 however1 have been the familiar employments of geologists1 and naturalists incited and #eag appealed to by geologists1 ever since ,cuvier published his examination of the fossil inhabitants of the ,paris basin4 ,without attempting a history of such labors1 ,i may notice a few circumstances connected with them4 ,note #ccah3 ,lyell1 i4 #gj4 ,note #cdah3 ,ib4 #gd4 ,note #ceah3 ,ib4 #gf4 ,sect4 #d4--;,advances in ,palontology4--,cuvier4 ,,so long as the organic fossils which were found in the strata of the earth were the remains of marine animals1 it was very difficult for geologists to be assured that the animals were such as did not exist in any part or clime of the existing ocean4 ,but when large land and river animals were discovered1 different from any known species1 the persuasion that they were of extinct races was forced upon the naturalist4 ,yet this opinion was not taken up slightly1 nor acquiesced in without many struggles4 ,bones supposed to belong to fossil elephants1 were some of the first with regard to which this conclusion was established4 ,such remains occur in vast numbers in the soil and gravel of almost every part of the world2 especially in ,siberia1 where they are called the bones of the mammoth4 ,they had been noticed by the ancients1 as we learn from ,pliny2#cfah and had been ascribed to human giants1 to elephants imported by the ,romans1 and to many other origins4 ,but in #agif1 ,cuvier had examined these opinions with a more profound knowledge than his predecessors2 and he thus stated the result of his researches4#cgah ,with regard to what have been called the fossil remains of elephants1 from ,tentzelius to ,pallas1 ,i believe that ,i am in the condition to prove1 that they belong to animals which were very clearly different in species from our existing elephants1 although they resembled them sufficiently to be considered as belonging to the same genera4 ,he had founded this conclusion principally on the structure of the teeth1 which he found to differ in the ,asiatic and ,african elephant2 while1 in the fossil animal1 it was different from both4 ,but he also reasoned in part on the form of the skull1 of which the best-known example had been described in the ,philosophical ,transactions as early as #agcg4chah ,as soon1 says ,cuvier1 at a later period1 as ,i became acquainted with ,messerschmidt's drawing1 and joined to the differences which it presented1 those which ,i had myself observed in the inferior jaw and the #eah molar teeth1 ,i no longer doubted that the fossil elephants were of a species different from the ,indian elephant4 ,this idea1 which ,i announced to the ,institute in the month of ,january1 #agif1 opened to me views entirely new respecting the theory of the earth2 and determined me to devote myself to the long researches and to the assiduous labors which have now occupied me for twenty-five years4#ciah ,note #cfah3 ,hist4 ,nat4 lib4 xxxvi4 #ah4 ,note #cgah3 ,mm4 ,inst4 ,math4 et ,phys4 tom4 ii4 p4 #d4 ,note #chah3 ,described by ,breyne from a specimen found in ,siberia by ,messerschmidt in #agbb4 ,phil4 ,trans4 xl4 #ddf4 ,note #ciah3 ,ossemens ,fossiles1 second edit4 i4 #agh4 ,we have here1 then1 the starting-point of those researches concerning extinct animals1 which1 ever since that time1 have attracted so large a share of notice from geologists and from the world4 ,cuvier could hardly have anticipated the vast storehouse of materials which lay under his feet1 ready to supply him occupation of the most intense interest in the career on which he had thus entered4 ,the examination of the strata on which ,paris stands1 and of which its buildings consist1 supplied him with animals1 not only different from existing ones1 but some of them of great size and curious peculiarities4 ,a careful examination of the remains which these strata contain was undertaken soon after the period we have referred to4 ,in #ahjb1 ,defrance had collected several hundreds of undescribed species of shells2 and ,lamarck#djah began a series of ,memoirs upon them2 remodelling the whole of ,conchology1 in order that they might be included in its classifications4 ,and two years afterwards 7#ahjd7 appears the first of ,cuvier's grand series of ,memoirs containing the restoration of the vertebrate animals of these strata4 ,in this vast natural museum1 and in contributions from other parts of the globe1 he discovered the most extraordinary creatures3--the ,palotherium1#daah which is intermediate between the horse and the pig2 the ,anoplotherium1 which stands nearest to the rhinoceros and the tapir2 the ,megalonix and ,megatherium1 animals of the sloth tribe1 but of the size of the ox and the rhinoceros4 ,the ,memoirs which contained these and many other discoveries1 set the naturalists to work in every part of ,europe4 ,note #djah3 ,annales du ,musum d',hist4 ,nat4 tom4 i4 p4 #cjh1 and the following volumes4 ,note #daah3 ,daubuisson1 ii4 #daa4 ,another very curious class of animals was brought to light principally by the geologists of ,england2 animals of which the bones1 found in the lias stratum1 were at first supposed to be those of crocodiles4 ,but in #ahaf1dbah ,sir ,everard ,home says1 ,in truth1 on a consideration of this skeleton1 we cannot but be inclined to believe1 that among the animals destroyed by the catastrophes of remote antiquity1 there had #eai been some at least that differ so entirely in their structure from any which now exist as to make it impossible to arrange their fossil remains with any known class of animals4 ,the animal thus referred to1 being clearly intermediate between fishes and lizards1 was named by ,mr4 ,knig1 ,ichthyosaurus2 and its structure and constitution were more precisely determined by ,mr4 ,conybeare in #ahba1 when he had occasion to compare with it another extinct animal of which he and ,mr4 de la ,beche had collected the remains4 ,this animal1 still more nearly approaching the lizard tribe1 was by ,mr4 ,conybeare called ,plesiosaurus4#dcah ,of each of these two genera several species were afterwards found4 ,note #dbah3 ,phil4 ,trans4 #ahaf1 p4 #bj4 ,note #dcah3 ,geol4 ,trans4 vol4 v4 ,before this time1 the differences of the races of animals and plants belonging to the past and the present periods of the earth's history1 had become a leading subject of speculation among geological naturalists4 ,the science produced by this study of the natural history of former states of the earth has been termed ,palontology2 and there is no branch of human knowledge more fitted to stir men's wonder1 or to excite them to the widest physiological speculations4 ,but in the present part of our history this science requires our notice1 only so far as it aims at the restoration of the types of ancient animals1 on clear and undoubted principles of comparative anatomy4 ,to show how extensive and how conclusive is the science when thus directed1 we need only refer to ,cuvier's ,ossemens ,fossiles2#ddah a work of vast labor and profound knowledge1 which has opened wide the doors of this part of geology4 ,i do not here attempt even to mention the labors of the many other eminent contributors to ,palontology2 as ,brocchi1 ,des ,hayes1 ,sowerby1 ,goldfuss1 ,agassiz1 who have employed themselves on animals1 and ,schlottheim1 ,brongniart1 ,hutton1 ,lindley1 on plants4 ,note #ddah3 ,the first edition appeared in #ahab1 consisting principally of the ,memoirs to which reference has already been made4 #bnd ,ed4 ,among the many valuable contributions to ,palontology in more recent times1 ,i may especially mention ,mr4 ,owen's ,reports on ,british ,fossil ,reptiles1 on ,british ,fossil ,mammalia1 and on the ,extinct ,animals of ,australia1 with descriptions of certain ,fossils indicative of large ,marsupial ,pachydermata3 and ,m4 ,agassiz's ,report on the ,fossil ,fishes of the ,devonian ,system1 his ,synoptical ,table of ,british ,fossil ,fishes1 and his ,report on the ,fishes of the ,london ,clay4 ,all these are contained in the volumes produced by the ,british ,association from #ahci to #ahde4 #ebj ,a new and most important instrument of palontological investigation has been put in the geologist's hand by ,prof4 ,owen's discovery1 that the internal structure of teeth1 as disclosed by the microscope1 is a means of determining the kind of the animal4 ,he has carried into every part of the animal kingdom an examination founded upon this discovery1 and has published the results of this in his ,odontography4 ,as an example of the application of this character of animals1 ,i may mention that a tooth brought from ,riga by ,sir ,r4 ,murchison was in this way ascertained by ,mr4 ,owen to belong to a fish of the genus ,dendrodus4 7,geology of ,russia1 i4 #fg47 ,when it had thus been established1 that the strata of the earth are characterized by innumerable remains of the organized beings which formerly inhabited it1 and that anatomical and physiological considerations must be carefully and skilfully applied in order rightly to interpret these characters1 the geologist and the palontologist obviously had1 brought before them1 many very wide and striking questions4 ,of these we may give some instances2 but1 in the first place1 we may add a few words concerning those eminent philosophers to whom the science owed the basis on which succeeding speculations were to be built4 ,sect4 #e4--;,intellectual ,characters of the ,founders of ,systematic ,descriptive ,geology4 ,,it would be in accordance with the course we have pursued in treating of other subjects1 that we should attempt to point out in the founders of the science now under consideration1 those intellectual qualities and habits to which we ascribe their success4 ,the very recent date of the generalizations of geology1 which has hardly allowed us time to distinguish the calm expression of the opinion of the wisest judges1 might1 in this instance1 relieve us from such a duty2 but since our plan appears to suggest it1 we will1 at least1 endeavor to mark the characters of the founders of geology1 by a few of their prominent lines4 ,the three persons who must be looked upon as the main authors of geological classification are1 ,werner1 ,smith1 and ,cuvier4 ,these three men were of very different mental constitution2 and it will1 perhaps1 not be difficult to compare them1 in reference to those qualities which we have all along represented as the main features of the discoverer's genius1 clearness of ideas1 the possession of numerous facts1 and the power of bringing these two elements into contact4 #eba ,in the ,german1 considering him as a geologist1 the ideal element predominated4 ,that ,werner's powers of external discrimination were extremely acute1 we have seen in speaking of him as a mineralogist2 and his talent and tendency for classifying were1 in his mineralogical studies1 fully fed by an abundant store of observation2 but when he came to apply this methodizing power to geology1 the love of system1 so fostered1 appears to have been too strong for the collection of facts he had to deal with4 ,as we have already said1 he promulgated1 as representing the world1 a scheme collected from a province1 and even too hastily gathered from that narrow field4 ,yet his intense spirit of method in some measure compensated for other deficiencies1 and enabled him to give the character of a science to what had been before a collection of miscellaneous phenomena4 ,the ardor of system-making produced a sort of fusion1 which1 however superficial1 served to bind together the mass of incoherent and mixed materials1 and thus to form1 though by strange and anomalous means1 a structure of no small strength and durability1 like the ancient vitrified structures which we find in some of our mountain regions4 ,of a very different temper and character was ,william ,smith4 ,no literary cultivation of his youth awoke in him the speculative love of symmetry and system2 but a singular clearness and precision of the classifying power1 which he possessed as a native talent1 was exercised and developed by exactly those geological facts among which his philosophical task lay4 ,some of the advances which he made1 had1 as we have seen1 been at least entered upon by others who preceded him3 but of all this he was ignorant2 and1 perhaps1 went on more steadily and eagerly to work out his own ideas1 from the persuasion that they were entirely his own4 ,at a later period of his life1 he himself published an account of the views which had animated him in his earlier progress4 ,in this account#deah he dates his attempts to discriminate and connect strata from the year #agij1 at which time he was twenty years old4 ,in #agib1 he had considered how he could best represent the order of superposition--continuity of course--and general eastern declination of the strata4 ,soon after1 doubts which had arisen were removed by the discovery of a mode of identifying the strata by the organized fossils respectively imbedded therein4 ,and thus stored with ideas1 as he expresses himself1 he began to communicate them to his friends4 ,in all this1 we see great vividness #ebb of thought and activity of mind1 unfolding itself exactly in proportion to the facts with which it had to deal4 ,we are reminded of that cyclopean architecture in which each stone1 as it occurs1 is1 with wonderful ingenuity1 and with the least possible alteration of its form1 shaped so as to fit its place in a solid and lasting edifice4 ,note #deah3 ,phil4 ,mag4 #ahcc1 vol4 i4 p4 #ch4 ,different yet again was the character 7as a geological discoverer7 of the great naturalist of the beginning of the nineteenth century4 ,in that part of his labors of which we have now to speak1 ,cuvier's dominant ideas were rather physiological than geological4 ,in his views of past physical changes1 he did not seek to include any ranges of facts which lay much beyond the narrow field of the ,paris basin4 ,but his sagacity in applying his own great principle of the ,conditions of ,existence1 gave him a peculiar and unparalleled power in interpreting the most imperfect fossil records of extinct anatomy4 ,in the constitution of his mind1 all philosophical endowments were so admirably developed and disciplined1 that it was difficult to say1 whether more of his power was due to genius or to culture4 ,the talent of classifying which he exercised in geology1 was the result of the most complete knowledge and skill in zoology2 while his views concerning the revolutions which had taken place in the organic and inorganic world1 were in no small degree aided by an extraordinary command of historical and other literature4 ,his guiding ideas had been formed1 his facts had been studied1 by the assistance of all the sciences which could be made to bear upon them4 ,in his geological labors we seem to see some beautiful temple1 not only firm and fair in itself1 but decorated with sculpture and painting1 and rich in all that art and labor1 memory and imagination1 can contribute to its beauty4 #bnd ,ed4 ,sir ,charles ,lyell 7,b4 i4 c4 iv47 has quoted with approval what ,i have elsewhere said1 that the advancement of three of the main divisions of geology in the beginning of the present century was promoted principally by the three great nations of ,europe1--the ,german1 the ,english1 and the ,french3--,mineralogical ,geology by the ,german school of ,werner3--,secondary ,geology by ,smith and his ,english successors2--,tertiary ,geology by ,cuvier and his fellow-laborers in ,france4 #ebc ,,chapter ,,iii4 ,,sequel ,,to ,,the ,,formation ,,of ,,systematic ,,descriptive ,,geology4 ,sect4 #a4--,reception and ,diffusion of ,systematic ,geology4 ,,if our nearness to the time of the discoveries to which we have just referred1 embarrasses us in speaking of their authors1 it makes it still more difficult to narrate the reception with which these discoveries met4 ,yet here we may notice a few facts which may not be without their interest4 ,the impression which ,werner made upon his hearers was very strong2 and1 as we have already said1 disciples were gathered to his school from every country1 and then went forward into all parts of the world1 animated by the views which they had caught from him4 ,we may say of him1 as has been so wisely said of a philosopher of a very different kind1#dfah ,he owed his influence to various causes2 at the head of which may be placed that genius for system1 which1 though it cramps the growth of knowledge1 perhaps finally atones for that mischief by the zeal and activity which it rouses among followers and opponents1 who discover truth by accident1 when in pursuit of weapons for their warfare4 ,the list of ,werner's pupils for a considerable period included most of the principal geologists of ,europe2 ,freisleben1 ,mohs1 ,esmark1 d',andrada1 ,raumer1 ,engelhart1 ,charpentier1 ,brocchi4 ,alexander von ,humboldt and ,leopold von ,buch went forth from his school to observe ,america and ,siberia1 the ,isles of the ,atlantic1 and the coast of ,norway4 ,professor ,jameson established at ,edinburgh a ,wernerian ,society2 and his lecture-room became a second centre of ,wernerian doctrines1 whence proceeded many zealous geological observers2 among these we may mention as one of the most distinguished1 ,m4 ,ami ,bou1 though1 like several others1 he soon cast away the peculiar opinions of the ,wernerian school4 ,the classifications of this school were1 however1 diffused over the civilized world with #ebd extraordinary success2 and were looked upon with great respect1 till the study of organic fossils threw them into the shade4 ,note #dfah3 ,mackintosh on ,hobbes1 ,dissert4 p4 #agg4 ,smith1 on the other hand1 long pursued his own thoughts without aid and without sympathy4 ,about #agii he became acquainted with a few gentlemen 7,dr4 ,anderson1 ,mr4 ,richardson1 ,mr4 ,townsend1 and ,mr4 ,davies71 who had already given some attention to organic fossils1 and who were astonished to find his knowledge so much more exact and extensive than their own4 ,from this time he conceived the intention of publishing his discoveries2 but the want of literary leisure and habits long prevented him4 ,his knowledge was orally communicated without reserve to many persons2 and thus gradually and insensibly became part of the public stock4 ,when this diffusion of his views had gone on for some time1 his friends began to complain that the author of them was deprived of his well-merited share of fame4 ,his delay in publication made it difficult to remedy this wrong2 for soon after he published his ,geological ,map of ,england1 another appeared1 founded upon separate observations2 and though1 perhaps1 not quite independent of his1 yet in many respects much more detailed and correct4 ,thus1 though his general ideas obtained universal currency1 he did not assume his due prominence as a geologist4 ,in #ahah1 a generous attempt was made to direct a proper degree of public gratitude to him1 in an article in the ,edinburgh ,review1 the production of ,dr4 ,fitton1 a distinguished ,english geologist4 ,and when the eminent philosopher1 ,wollaston1 had bequeathed to the ,geological ,society of ,london a fund from which a gold medal was to be awarded to geological services1 the first of such medals was1 in #ahca1 given to ,mr4 ,william ,smith1 in consideration of his being a great original discoverer in ,english geology2 and especially for his having been the first in this country to discover and to teach the identification of strata1 and to determine their succession by means of their imbedded fossils4 ,cuvier's discoveries1 on the other hand1 both from the high philosophic fame of their author1 and from their intrinsic importance1 arrested at once the attention of scientific ,europe2 and1 notwithstanding the undoubted priority of ,smith's labors1 for a long time were looked upon as the starting-point of our knowledge of organic fossils4 ,and1 in reality1 although ,cuvier's memoirs derived the greatest part of their value from his zoological conclusions1 they reflected back no small portion of interest on the classifications of strata which were involved in his inferences4 ,and the views which he presented gave to geology an attractive and striking character1 and a connexion with #ebe large physiological as well as physical principles1 which added incomparably to its dignity and charm4 ,in tracing the reception and diffusion of doctrines such as those of ,smith and ,cuvier1 we ought not to omit to notice more especially the formation and history of the ,geological ,society of ,london1 just mentioned4 ,it was established in #ahjg1 with a view to multiply and record observations1 and patiently to await the result of some future period2 that is1 its founders resolved to apply themselves to ,descriptive ,geology1 thinking the time not come for that theoretical geology which had then long fired the controversial ardor of ,neptunists and ,plutonists4 ,the first volume of the ,transactions of this society was published in #ahaa4 ,the greater part of the contents of this volume#dgah savor of the notions of the ,wernerian school2 and there are papers on some of the districts in ,england most rich in fossils1 which ,mr4 ,conybeare says1 well exhibit the low state of secondary geology at that period4 ,but a paper by ,mr4 ,parkinson refers to the discoveries both of ,smith and of ,cuvier2 and in the next volume1 ,mr4 ,webster gives an account of the ,isle of ,wight1 following the admirable model of ,cuvier and ,brongniart's account of the ,paris basin4 ,if we compare this memoir of ,mr4 ,webster with the preceding one of ,dr4 ,berger 7also of the ,isle of ,wight71 they at once show themselves to belong to two very distinct eras of science2 and it is difficult to believe that the interval which elapsed between their respective publication was only three or four years4#dhah ,note #dgah3 ,conybeare1 ,report4 ,brit4 ,assoc4 p4 #cgb4 ,note #dhah3 ,conybeare1 ,report1 p4 #cgb4 ,among the events belonging to the diffusion of sound geological views in this country1 we may notice the publication of a little volume entitled1 ,the ,geology of ,england and ,wales1 by ,mr4 ,conybeare and ,mr4 ,phillips1 in #ahba2 an event far more important than1 from the modest form and character of the work1 it might at first sight appear4 ,by describing in detail the geological structure and circumstances of ,england 7at least as far downwards as the coal71 it enabled a very wide class of readers to understand and verify the classifications which geology had then very recently established2 while the extensive knowledge and philosophical spirit of ,mr4 ,conybeare rendered it1 under the guise of a topographical enumeration1 in reality a profound and instructive scientific treatise4 ,the vast impulse which it gave to the study of sound descriptive geology was felt and acknowledged in other countries1 as well as in ,britain4 #ebf ,since that period1 ,descriptive ,geology in ,england has constantly advanced4 ,the advance has been due mainly to the labors of the members of the ,geological ,society2 on whose merits as cultivators of their science1 none but those who are themselves masters of the subject1 have a right to dwell4 ,yet some parts of the scientific character of these men may be appreciated by the general speculator2 for they have shown that there are no talents and no endowments which may not find their fitting employment in this science4 ,besides that they have united laborious research and comprehensive views1 acuteness and learning1 zeal and knowledge2 the philosophical eloquence with which they have conducted their discussions has had a most beneficial influence on the tone of their speculations2 and their researches in the field1 which have carried them into every country and every class of society1 have given them that prompt and liberal spirit1 and that open and cordial bearing1 which results from intercourse with the world on a large and unfettered scale4 ,it is not too much to say1 that in our time1 ,practical ,geology has been one of the best schools of philosophical and general culture of mind4 ,sect4 #b4--;,application of ,systematic ,geology4 ,geological ,surveys and ,maps4 ,,such surveys as that which ,conybeare and ,phillips's book presented with respect to ,england1 were not only a means of disseminating the knowledge implied in the classifications of such a work1 but they were also an essential part of the ,application and ,extension of the principles established by the founders of ,systematic ,geology4 ,as soon as the truth of such a system was generally acknowledged1 the persuasion of the propriety of geological surveys and maps of each country could not but impress itself on men's minds4 ,when the earlier writers1 as ,lister and ,fontenelle1 spoke of mineralogical and fossilological maps1 they could hardly be said to know the meaning of the terms which they thus used4 ,but when subsequent classifications had shown how such a suggestion might be carried into effect1 and to what important consequences it might lead1 the task was undertaken in various countries in a vigorous and consistent manner4 ,in ,england1 besides ,smith's map1 another1 drawn up by ,mr4 ,greenough1 was published by the ,geological ,society in #ahai2 and1 being founded on very numerous observations of the author and his friends1 made with great labor and cost1 was not only an important #ebg correction and confirmation of ,smith's labors1 but a valuable storehouse and standard of what had then been done in ,english geology4 ,leopold von ,buch had constructed a geological map of a large portion of ,germany1 about the same period2 but1 aware of the difficulty of the task he had thus attempted1 he still forbore to publish it4 ,at a later period1 and as materials accumulated1 more detailed maps of parts of ,germany were produced by ,hoffmann and others4 ,the ,french government entrusted to a distinguished ,professor of the ,school of ,mines 7,m4 ,brochant de ,villiers71 the task of constructing a map of ,france on the model of ,mr4 ,greenough's2 associating with him two younger persons1 selected for their energy and talents1 ,,mm4 ,beaumont and ,dufrnoy4 ,we shall have occasion hereafter to speak of the execution of this survey4 ,by various persons1 geological maps of almost every country and province of ,europe1 and of many parts of ,asia and ,america1 have been published4 ,i need not enumerate these1 but ,i may refer to the account given of them by ,mr4 ,conybeare1 in the ,reports of the ,british ,association for #ahcb1 p4 #chd4 ,these various essays may be considered as contributions1 though hitherto undoubtedly very imperfect ones1 to that at which ,descriptive ,geology ought to aim1 and which is requisite as a foundation for sound theory2--a complete geological survey of the whole earth4 ,but we must say a few words respecting the language in which such a survey must be written4 ,as we have already said1 that condition which made such maps and the accompanying descriptions possible1 was that the strata and their contents had previously undergone classification and arrangement at the hands of the fathers of geology4 ,classification1 in this as in other cases1 implied names which should give to the classes distinctness and permanence2 and when the series of strata belonging to one country were referred to in the description of another1 in which they appeared1 as was usually the case1 under an aspect at least somewhat different1 the supposed identification required a peculiar study of each case2 and thus ,geology had arrived at the point1 which we have before had to notice as one of the stages of the progress of ,classificatory ,botany1 at which a technical nomenclature and a well-understood synonymy were essential parts of the science4 ,sect4 #c4--;,geological ,nomenclature4 ,,by ,nomenclature we mean a system of names2 and hence we can #ebh not speak of a ,geological ,nomenclature till we come to ,werner and ,smith4 ,the earlier mineralogists had employed names1 often artificial and arbitrary1 for special minerals1 but no technical and constant names for strata4 ,the elements of ,werner's names for the members of his geological series were words in use among miners1 as ,gneiss1 ,grauwacke1 ,thonschiefer1 ,rothe todte liegende1 ,zechstein2 or arbitrary names of the mineralogists1 as ,syenite1 ,serpentine1 ,porphyry1 ,granite4 ,but the more technical part of his phraseology was taken from that which is the worst kind of name1 arbitrary numeration4 ,thus he had his first sandstone formation1 second sandstone1 third sandstone2 first fltz limestone1 second fltz limestone1 third fltz limestone4 ,such names are1 beyond all others1 liable to mistake in their application1 and likely to be expelled by the progress of knowledge2 and accordingly1 though the ,wernerian names for rocks mineralogically distinguished1 have still some currency1 his sandstones and limestones1 after creating endless confusion while his authority had any sway1 have utterly disappeared from good geological works4 ,the nomenclature of ,smith was founded upon ,english provincial terms of very barbarous aspect1 as ,cornbrash1 ,lias1 ,gault1 ,clunch ,clay1 ,coral ,rag4 ,yet these terms were widely diffused when his classification was generally accepted2 they kept their place1 precisely because they had no systematic signification2 and many of them are at present part of the geological language of the whole civilized world4 ,another kind of names which has been very prevalent among geologists are those borrowed from places4 ,thus the ,wernerians spoke of ,alpine ,limestone and ,jura ,limestone2 the ,english1 of ,kimmeridge ,clay and ,oxford ,clay1 ,purbeck ,marble1 and ,portland ,rock4 ,these names1 referring to the stratum of a known locality as a type1 were good1 as far as an identity with that type had been traced2 but when this had been incompletely done1 they were liable to great ambiguity4 ,if the ,alps or the ,jura contain several formations of limestone1 such terms as we have noticed1 borrowed from those mountains1 cease to be necessarily definite1 and may give rise to much confusion4 ,descriptive names1 although they might be supposed to be the best1 have1 in fact1 rarely been fortunate4 ,the reason of this is obvious2--the mark which has been selected for description may easily fail to be essential2 and the obvious connexions of natural facts may overleap the arbitrary definition4 ,as we have already stated in the history of botany1 the establishment of descriptive marks of real classes presupposes the important but difficult step1 of the discovery of such marks4 #ebi ,hence those descriptive names only have been really useful in geology which had been used without any scrupulous regard to the appropriateness of the description4 ,the ,green ,sand may be white1 brown1 or red2 the ,mountain ,limestone may occur only in valleys2 the ,oolite may have no roe-like structure2 and yet these may be excellent geological names1 if they be applied to formations geologically identical with those which the phrases originally designated4 ,the signification may assist the memory1 but must not be allowed to subjugate the faculty of natural classification4 ,the terms which have been formed by geologists in recent times have been drawn from sources similar to those of the older ones1 and will have their fortune determined by the same conditions4 ,thus ,mr4 ,lyell has given to the divisions of the tertiary strata the appellations ,pleiocene1 ,meiocene1 ,eocene1 accordingly as they contain a majority of recent species of shells1 a minority of such species1 or a small proportion of living species1 which may be looked upon as indicating the dawn of the existing state of the animate creation4 ,but in this case1 he wisely treats his distinctions1 not as definitions1 but as the marks of natural groups4 ,the plurality of species indicated by the name pleiocene must not1 he says1#diah be understood to imply an absolute majority of recent fossil shells in all cases1 but a comparative preponderance wherever the pleiocene are contrasted with strata of the period immediately preceding4 ,note #diah3 ,geol4 iii4 #cib4 ,mr4 ,lyell might have added1 that no precise percentage of recent species1 nor any numerical criterion whatever1 can be allowed to overbear the closer natural relations of strata1 proved by evidence of a superior kind1 if such can be found4 ,and this would be the proper answer to the objection made by ,de la ,beche to these names2 namely1 that it may happen that the meiocene rocks of one country may be of the same date as the pleiocene of another2 the same formation having in one place a majority1 in another a minority1 of existing species4 ,we are not to run into this incongruity1 for we are not so to apply the names4 ,the formation which has been called pleiocene1 must continue to be so called1 even where the majority of recent species fails2 and all rocks that agree with that in date1 without further reference to the numerical relations of their fossils1 must also share in the name4 ,to invent good names for these large divisions of the series of strata is indeed extremely difficult4 ,the term ,oolite is an instance in which #ecj a descriptive word has become permanent in a case of this kind2 and1 in imitation of it1 ,pcilite 7from 1 various199997 has been proposed by ,mr4 ,conybeare#ejah as a name for the group of strata inferior to the oolites1 of which the ,variegated ,sandstone 7,bunter ,sandstein1 ,grs ,bigarr17 is a conspicuous member4 ,for the series of formations which lies immediately over the rocks in which no organic remains are found1 the term ,transition was long used1 but with extreme ambiguity and vagueness4 ,when this series1 or rather the upper part of it1 was well examined in ,south ,wales1 where it consists of many well-marked members1 and may be probably taken as a type for a large portion of the rest of the world1 it became necessary to give to the group thus explored a name not necessarily leading to assumption or controversy4 ,mr4 ,murchison selected the term ,silurian1 borrowed from the former inhabitants of the country in which his types were found2 and this is a term excellent in many respects2 but one which will probably not quite supersede ,transition1 because1 in other places1 transition rocks occur which correspond to none of the members of the ,silurian region4 ,note #ejah3 ,report1 p4 #cgi4 ,though new names are inevitable accompaniments of new views of classification1 and though1 therefore1 the geological discoverer must be allowed a right to coin them1 this is a privilege which1 for the sake of his own credit1 and the circulation of his tokens1 he must exercise with great temperance and judgment4 ,m4 ,brongniart may be taken as an example of the neglect of this caution4 ,acting upon the principle1 in itself a sound one1 that inconveniences arise from geological terms which have a mineralogical signification1 he has given an entirely new list of names of the members of the geological series4 ,thus the primitive unstratified rocks are terrains agalysiens2 the transition semi-compact are hemilysiens2 the sedimentary strata are yzemiens2 the diluvial deposits are clysmiens2 and these divisions are subdivided by designations equally novel2 thus of the terrains yzemiens1 members are--the terrains clastiques1 tritoniens1 protques1 palotheriens1 epilymniques1 thalassiques4#eaah ,such a nomenclature appears to labor under great inconveniences1 since the terms are descriptive in their derivation1 yet are not generally intelligible1 and refer to theoretical views yet have not the recommendation of systematic connexion4 #eca ,note #eaah3 ,brongniart1 ,tableau des ,terrains1 #ahbi4 ,sect4 #d4--;,geological ,synonymy1 or ,determination of ,geological ,equivalents4 ,,it will easily be supposed that with so many different sources of names as we have mentioned1 the same stratum may be called by different designations2 and thus a synonymy may be necessary for geology2 as it was for botany in the time of ,bauhin1 when the same plants had been spoken of by so many different appellations in different authors4 ,but in reality1 the synonymy of geology is a still more important part of the subject than the analogy of botany would lead us to suppose4 ,for in plants1 the species are really fixed1 and easily known when seen2 and the ambiguity is only in the imperfect communication or confused ideas of the observers4 ,but in geology1 the identity of a stratum or formation in different places1 though not an arbitrary1 may be a very doubtful matter1 even to him who has seen and examined4 ,to assign its right character and place to a stratum in a new country1 is1 in a great degree1 to establish the whole geological history of the country4 ,to assume that the same names may rightly be applied to the strata of different countries1 is to take for granted1 not indeed the ,wernerian dogma of universal formations1 but a considerable degree of generality and uniformity in the known formations4 ,and how far this generality and uniformity prevail1 observation alone can teach4 ,the search for geological synonyms in different countries brings before us two questions2--first1 are there such synonyms8 and only in the second place1 and as far as they occur1 what are they8 ,in fact1 it is found that although formations which must be considered as geologically identical 7because otherwise no classification is possible17 do extend over large regions1 and pass from country to country1 their identity includes certain modifications2 and the determination of the identity and of the modifications are inseparably involved with each other1 and almost necessarily entangled with theoretical considerations4 ,and in two countries1 in which we find this modified coincidence1 instead of saying that the strata are identical1 and that their designations are synonyms1 we may1 with more propriety1 consider them as two corresponding series2 of which the members of the one may be treated as the ,representatives or ,equivalents of the members of the other4 ,this doctrine of ,representatives or ,equivalents supposes that the geological phenomena in the two countries have been the results of #ecb similar series of events1 which have1 in some measure1 coincided in time and order2 and thus1 as we have said1 refers us to a theory4 ,but yet1 considered merely as a step in classification1 the comparison of the geological series of strata in different countries is1 in the highest degree1 important and interesting4 ,indeed in the same manner in which the separation of ,classificatory from ,chemical ,mineralogy is necessary for the completion of mineralogical science1 the comparative ,classification of the strata of different countries according to their resemblances and differences alone1 is requisite as a basis for a ,theory of their causes4 ,but1 as will easily be imagined from its nature1 this part of descriptive geology deals with the most difficult and the most elevated problems2 and requires a rare union of laborious observation with a comprehensive spirit of philosophical classification4 ,in order to give instances of this process 7for of the vast labor and great talents which have been thus employed in ,england1 ,france1 and ,germany1 it is only instances that we can give17 ,i may refer to the geological survey of ,france1 which was executed1 as we have already stated1 by order of the government4 ,in this undertaking it was intended to obtain a knowledge of the whole mineral structure of ,france2 but no small portion of this knowledge was brought into view1 when a synonymy had been established between the ,secondary ,rocks of ,france and the corresponding members of the ,english and ,german series1 which had been so well studied as to have become classical points of standard reference4 ,for the purpose of doing this1 the principal directors of the survey1 ,,mm4 ,brochant de ,villiers1 ,de ,beaumont1 and ,dufrnoy1 came to ,england in #ahbb1 and following the steps of the best ,english geologists1 in a few months made themselves acquainted with the ,english series4 ,they then returned to ,france1 and1 starting from the chalk of ,paris in various directions1 travelled on the lines which carried them over the edges of the strata which emerge from beneath the chalk1 identifying1 as they could1 the strata with their foreign analogues4 ,they thus recognized almost all of the principal beds of the oolitic series of ,england4#ebah ,at the same time they found differences as well as resemblances4 ,thus the ,portland and ,kimmeridge beds of ,france were found to contain in abundance a certain shell1 the grypha virgula1 which had not before been much remarked in those beds in ,england4 ,with regard to the synonyms in ,germany1 on the other hand1 a difference of opinion #ech arose between ,m4 ,elie de ,beaumont and ,m4 ,voltz1#ecah the former considering the ,grs de ,vosges as the equivalent of the ,rothe todte liegende1 which occurs beneath the ,zechstein1 while ,m4 ,voltz held that it was the lower portion of the ,red or ,variegated ,sandstone which rests on the ,zechstein4 ,note #ebah3 ,de la ,beche1 ,manual1 #cje4 ,note #ecah3 ,de la ,beche1 ,manual1 #cha4 ,in the same manner1 from the first promulgation of the ,wernerian system1 attempts were made to identify the ,english with the ,german members of the geological alphabet2 but it was long before this alphabet was rightly read4 ,thus the ,english geologists who first tried to apply the ,wernerian series to this country1 conceived the ,old and ,new ,red ,sandstone of ,england to be the same with the ,old and ,new ,red ,sandstone of ,werner2 whereas ,werner's ,old ,red1 the ,rothe todte liegende1 is above the coal1 while the ,english ,old ,red is below it4 ,this mistake led to a further erroneous identification of our ,mountain ,limestone with ,werner's ,first ,fltz ,limestone2 and caused an almost inextricable confusion1 which1 even at a recent period1 has perplexed the views of ,german geologists respecting this country4 ,again1 the ,lias of ,england was1 at first1 supposed to be the equivalent of the ,muschelkalk of ,germany4 ,but the error of this identification was brought into view by examinations and discussions in which ,,mm4 yenhausen and ,dechen took the lead2 and at a later period1 ,professor ,sedgwick1 by a laborious examination of the strata of ,england1 was enabled to show the true relation of this part of the geology of the two countries4 ,according to him1 the ,new ,red ,sandstone of ,england1 considered as one great complex formation1 may be divided into seven members1 composed of sandstones1 limestones1 and marls2 five of which represent respectively the ,rothe todte liegende2 the ,kupfer schiefer2 the ,zechstein1 7with the ,rauchwack1 ,asche1 and ,stinkstein of the ,thuringenwald27 the ,bunter sandstein2 and the ,keuper3 while the ,muschelkalk1 which lies between the two last members of the ,german list1 has not yet been discovered in our geological series4 ,such a coincidence1 he observes1#edah in the subdivisions of two distant mechanical deposits1 even upon the supposition of their being strictly contemporaneous1 is truly astonishing4 ,it has not been assumed hypothetically1 but is the fair result of the facts which are recorded in this paper4 ,note #edah3 ,geol4 ,trans4 ,second ,series1 iii4 #aba4 ,as an example in which the study of geological equivalents becomes still more difficult1 we may notice the attempts to refer the strata of #ecd the ,alps to those of the north-west of ,europe4 ,the dark-colored marbles and schists resembling mica slate#eeah were1 during the prevalence of the ,wernerian theory1 referred1 as was natural1 to the transition class4 ,the striking physical characters of this mountain region1 and its long-standing celebrity as a subject of mineralogical examination1 made a complete subversion of the received opinion respecting its place in the geological series1 an event of great importance in the history of the science4 ,yet this was what occurred when ,dr4 ,buckland1 in #ahbj1 threw his piercing glance upon this district4 ,he immediately pointed out that these masses1 by their fossils1 approach to the ,oolitic ,series of this country4 ,from this view it followed1 that the geological equivalents of that series were to be found among rocks in which the mineralogical characters were altogether different1 and that the loose limestones of ,england represent some of the highly-compact and crystalline marbles of ,italy and ,greece4 ,this view was confirmed by subsequent investigations2 and the correspondence was traced1 not only in the general body of the formations1 but in the occurrence of the ,red ,marl at its bottom1 and the ,green ,sand and ,chalk at its top4 ,note #eeah3 ,de la ,beche1 ,manual1 #cac4 ,the talents and the knowledge which such tasks require are of no ordinary kind2 nor1 even with a consummate acquaintance with the well-ascertained formations1 can the place of problematical strata be decided without immense labor4 ,thus the examination and delineation of hundreds of shells by the most skilful conchologists1 has been thought necessary in order to determine whether the calcareous beds of ,maestricht and of ,gosau are or are not intermediate1 as to their organic contents1 between the chalk and the tertiary formations4 ,and scarcely any point of geological classification can be settled without a similar union of the accomplished naturalist with the laborious geological collector4 ,it follows from the views already presented1 of this part of geology1 that no attempt to apply to distant countries the names by which the well-known ,european strata have been described1 can be of any value1 if not accompanied by a corresponding attempt to show how far the ,european series is really applicable4 ,this must be borne in mind in estimating the import of the geological accounts which have been given of various parts of ,asia1 ,africa1 and ,america4 ,for instance1 when the carboniferous group and the new red sandstone are stated to #ece be found in ,india1 we require to be assured that these formations are1 in some way1 the equivalents of their synonyms in countries better explored4 ,till this is done1 the results of observation in such places would be better conveyed by a nomenclature implying only those facts of resemblance1 difference1 and order1 which have been ascertained in the country so described4 ,we know that serious errors were incurred by the attempts made to identify the ,tertiary strata of other countries with those first studied in the ,paris basin4 ,fancied points of resemblance1 ,mr4 ,lyell observes1 were magnified into undue importance1 and essential differences in mineral character and organic contents were slurred over4 #bnd ,ed4 ,the extension of geological surveys1 the construction of geological maps1 and the determination of the geological equivalents which replace each other in various countries1 have been carried on in continuation of the labors mentioned above1 with enlarged activity1 range1 and means4 ,it is estimated that one-third of the land of each hemisphere has been geologically explored2 and that thus ,descriptive ,geology has now been prosecuted so far1 that it is not likely that even the extension of it to the whole globe would give any material novelty of aspect to ,theoretical ,geology4 ,the recent literature of the subject is so voluminous that it is impossible for me to give any account of it here2 very imperfectly acquainted1 as ,i am1 even with the ,english portion1 and still more1 with what has been produced in other countries4 ,while ,i admire the energetic and enlightened labors by which the philosophers of ,france1 ,belgium1 ,germany1 ,italy1 ,russia1 and ,america1 have promoted scientific geology1 ,i may be allowed to rejoice to see in the very phraseology of the subject1 the evidence that ,english geologists have not failed to contribute their share to the latest advances in the science4 ,the following order of strata proceeding upwards is now1 ,i think1 recognized throughout ,europe4 ,the ,silurian2 the ,devonian 7,old ,red ,sandstone27 the ,carboniferous2 the ,permian1 7,lower part of the new ,red ,sandstone series27 the ,trias1 7,upper three members of the ,new ,red ,sandstone series27 the ,lias2 the ,oolite1 7in which are reckoned by ,m4 ,d',orbigny the ,etages ,bathonien1 ,oxonien1 ,kimmeridgien1 and ,portlandien27 the ,neocomien1 7,lower ,green ,sand17 the ,chalk2 and above these1 ,tertiary and ,supra-,tertiary beds4 ,of these1 the ,silurian1 described by ,sir ,r4 ,murchison from its types in ,south ,wales1 has been traced by ,european ,geologists through the ,ardennes1 ,servia1 ,turkey1 the shores of the ,gulf of ,finland1 the valley #ecf of the ,mississippi1 the west coast of ,north ,america1 and the mountains of ,south ,america4 ,again1 the labors of ,prof4 ,sedgwick and ,sir ,r4 ,murchison1 in #ahcf1 '#g1 and '#h1 aided by the sagacity of ,mr4 ,lonsdale1 led to their placing certain rocks of ,devon and ,cornwall as a formation intermediate between the ,silurian and ,carboniferous ,series2 and the ,devonian ,system thus established has been accepted by geologists in general1 and has been traced1 not only in various parts of ,europe1 but in ,australia and ,tasmania1 and in the neighborhood of the ,alleganies4 ,above the ,carboniferous ,series1 ,sir ,r4 ,murchison and his fellow laborers1 ,m4 de ,verneuil and ,count ,keyserling1 have found in ,russia a well-developed series of rocks occupying the ancient kingdom of ,permia1 which they have hence called the ,permian formation2 and this term also has found general acceptance4 ,the next group1 the ,keuper1 ,muschelkalk1 and ,bunter ,sandstein of ,germany1 has been termed ,trias by the continental geologists4 ,the ,neocomien is called from ,neuchatel1 where it is largely developed4 ,below all these rocks come1 in ,england1 the ,cambrian on which ,prof4 ,sedgwick has expended so many years of valuable labor4 ,the comparison of the ,protozoic and ,hypozoic rocks of different countries is probably still incomplete4 ,the geologists of ,north ,america have made great progress in decyphering and describing the structure of their own country2 and they have wisely gone1 in a great measure1 upon the plan which ,i have commended at the end of the third ,chapter2--they have compared the rocks of their own country with each other1 and given to the different beds and formations names borrowed from their own localities4 ,this course will facilitate rather than impede the redaction of their classification to its synonyms and equivalents in the old world4 ,of course it is not to be expected nor desired that books belonging to ,descriptive ,geology shall exclude the other two branches of the subject1 ,geological ,dynamics and ,physical ,geology4 ,on the contrary1 among the most valuable contributions to both these departments have been speculations appended to descriptive works4 ,and this is naturally and rightly more and more the case as the description embraces a wider field4 ,the noble work ,on the ,geology of ,russia and the ,urals1 by ,sir ,roderick ,murchison and his companions1 is a great example of this1 as of other merits in a geological book4 ,the author introduces into his pages the various portions of geological dynamics of which ,i shall have to speak afterwards2 and thus endeavors to make out the #ecg physical history of the region1 the boundaries of its raised sea bottoms1 the shores of the great continent on which the mammoths lived1 the period when the gold ore was formed1 and when the watershed of the ,ural chain was elevated4 ,,chapter ,,iv4 ,,attempts ,,to ,,discover ,,general ,,laws ,,in ,,geology4 ,sect4 #a4--;,general ,geological ,phenomena4 ,,besides thus noticing such features in the rocks of each country as were necessary to the identification of the strata1 geologists have had many other phenomena of the earth's surface and materials presented to their notice2 and these they have1 to a certain extent1 attempted to generalize1 so as to obtain on this subject what we have elsewhere termed the ,laws of ,phenomena1 which are the best materials for physical theory4 ,without dwelling long upon these1 we may briefly note some of the most obvious4 ,thus it has been observed that mountain ranges often consist of a ridge of subjacent rock1 on which lie1 on each side1 strata sloping from the ridge4 ,such a ridge is an ,anticlinal ,line1 a ,mineralogical ,axis4 ,the sloping strata present their ,escarpements1 or steep edges1 to this axis4 ,again1 in mining countries1 the ,veins which contain the ore are usually a system of parallel and nearly vertical partitions in the rock2 and these are1 in very many cases1 intersected by another system of veins parallel to each other and nearly perpendicular to the former4 ,rocky regions are often intersected by ,faults1 or fissures interrupting the strata1 in which the rock on one side the fissure appears to have been at first continuous with that on the other1 and shoved aside or up or down after the fracture4 ,again1 besides these larger fractures1 rocks have ,joints1--separations1 or tendencies to separate in some directions rather than in others2 and a slaty ,cleavage1 in which the parallel subdivisions may be carried on1 so as to produce lamin of indefinite thinness4 ,as an example of those laws of phenomena of which we have spoken1 we may instance the general law asserted by ,prof4 #ech ,sedgwick 7not1 however1 as free from exception71 that in one particular class of rocks the slaty ,cleavage never coincides with the ,direction of the strata4 ,the phenomena of metalliferous veins may be referred to1 as another large class of facts which demand the notice of the geologist4 ,it would be difficult to point out briefly any general laws which prevail in such cases2 but in order to show the curious and complex nature of the facts1 it may be sufficient to refer to the description of the metallic veins of ,cornwall by ,mr4 ,carne2#efah in which the author maintains that their various contents1 and the manner in which they cut across1 and stop1 or shift1 each other1 leads naturally to the assumption of veins of no less than six or eight different ages in one kind of rock4 ,note #efah3 ,transactions of the ,geol4 ,soc4 of ,cornwall1 vol4 ii4 ,again1 as important characters belonging to the physical history of the earth1 and therefore to geology1 we may notice all the general laws which refer to its temperature2--both the laws of climate1 as determined by the isothermal lines1 which ,humboldt has drawn1 by the aid of very numerous observations made in all parts of the world2 and also those still more curious facts1 of the increase of temperature which takes place as we descend in the solid mass4 ,the latter circumstance1 after being for a while rejected as a fable1 or explained away as an accident1 is now generally acknowledged to be the true state of things in many distant parts of the globe1 and probably in all4 ,again1 to turn to cases of another kind3 some writers have endeavored to state in a general manner laws according to which the members of the geological series succeed each other2 and to reduce apparent anomalies to order of a wider kind4 ,among those who have written with such views1 we may notice ,alexander von ,humboldt1 always1 and in all sciences1 foremost in the race of generalization4 ,in his attempt to extend the doctrine of geological equivalents from the rocks of ,europe#egah to those of the ,andes1 he has marked by appropriate terms the general modes of geological succession4 ,i have insisted1 he says#ehah principally upon the phenomena of alternation1 oscillation1 and local suppression1 and on those presented by the passages of formations from one to another1 by the effect of an interior developement4 ,note #egah3 ,gissement des ,roches dans les deux ,hemisphres1 #ahbc4 ,note #ehah3 ,pref4 p4 vi4 ,the phenomena of alternation to which ,m4 de ,humboldt here refers are1 in fact1 very curious3 as exhibiting a mode in which the transitions from one formation to another may become gradual and insensible1 #eci instead of sudden and abrupt4 ,thus the coal measures in the south of ,england are above the mountain limestone2 and the distinction of the formations is of the most marked kind4 ,but as we advance northward into the coal-field of ,yorkshire and ,durham1 the subjacent limestone begins to be subdivided by thick masses of sandstone and carbonaceous strata1 and passes into a complex deposit1 not distinguishable from the overlying coal measures2 and in this manner the transition from the limestone to the coal is made by alternation4 ,thus1 to use another expression of ,m4 de ,humboldt's in ascending from the limestone1 the coal1 before we quit the subjacent stratum1 preludes to its fuller exhibition in the superior beds4 ,again1 as to another point3 geologists have gone on up to the present time endeavoring to discover general laws and facts1 with regard to the position of mountain and mineral masses upon the surface of the earth4 ,thus ,m4 ,von ,buch1 in his physical description of the ,canaries1 has given a masterly description of the lines of volcanic action and volcanic products1 all over the globe4 ,and1 more recently1 ,m4 ,elie de ,beaumont has offered some generalizations of a still wider kind4 ,in this new doctrine1 those mountain ranges1 even in distant parts of the world1 which are of the same age1 according to the classifications already spoken of1 are asserted to be parallel#eiah to each other1 while those ranges which are of different ages lie in different directions4 ,this very wide and striking proposition may be considered as being at present upon its trial among the geologists of ,europe4#fjah ,note #eiah3 ,we may observe that the notion of parallelism1 when applied to lines drawn on remote portions of a globular surface1 requires to be interpreted in so arbitrary a manner1 that we can hardly imagine it to express a physical law4 ,note #fjah3 ,mr4 ,lyell1 in the sixth edition of his ,principles1 ,b4 i4 c4 xii41 has combated the hypothesis of ,m4 ,elie de ,beaumont1 stated in the text4 ,he has argued both against the catastrophic character of the elevation of mountain chains1 and the parallelism of the contemporaneous ridges4 ,it is evident that the former doctrine may be true1 though the latter be shown to be false4 ,among the organic phenomena1 also1 which have been the subject of geological study1 general laws of a very wide and comprehensive kind have been suggested1 and in a greater or less degree confirmed by adequate assemblages of facts4 ,thus ,m4 ,adolphe ,brongniart has not only1 in his ,fossil ,flora1 represented and skilfully restored a vast number of the plants of the ancient world2 but he has also1 in the ,prodromus of the work1 presented various important and striking views of the general character of the vegetation of former periods1 as #edj insular or continental1 tropical or temperate4 ,and ,m4 ,agassiz1 by the examination of an incredible number of specimens and collections of fossil fish1 has been led to results which1 expressed in terms of his own ichthyological classification1 form remarkable general laws4 ,thus1 according to him1#faah when we go below the lias1 we lose all traces of two of the four orders under which he comprehends all known kinds of fish2 namely1 the ,cyclodean and the ,ctenodean2 while the other two orders1 the ,ganodean and ,placodean1 rare in our days1 suddenly appear in great numbers1 together with large sauroid and carnivorous fishes4 ,cuvier1 in constructing his great work on ichthyology1 transferred to ,m4 ,agassiz the whole subject of fossil fishes1 thus showing how highly he esteemed his talents as a naturalist4 ,and ,m4 ,agassiz has shown himself worthy of his great predecessor in geological natural history1 not only by his acuteness and activity1 but by the comprehensive character of his zoological philosophy1 and by the courage with which he has addressed himself to the vast labors which lie before him4 ,in his ,report on the ,fossil ,fish discovered in ,england1 published in #ahce1 he briefly sketches some of the large questions which his researches have suggested2 and then adds1#fbah ,such is the meagre outline of a history of the highest interest1 full of curious episodes1 but most difficult to relate4 ,to unfold the details which it contains will be the business of my life4 ,note #faah3 ,greenough1 ,address to ,geol4 ,soc4 #ahce1 p4 #ai4 ,note #fbah3 ,brit4 ,assoc4 ,report1 p4 #gb4 #bnd ,ed4 ,in proceeding downwards through the series of formations into which geologists have distributed the rocks of the earth1 one class of organic forms after another is found to disappear4 ,in the ,tertiary ,period we find all the classes of the present world3 ,mammals1 ,birds1 ,reptiles1 ,fishes1 ,crustaceans1 ,mollusks1 ,zoophytes4 ,in the ,secondary ,period1 from the ,chalk down to the ,new ,red ,sandstone1 ,mammals are not found1 with the minute exception of the marsupial amphitherium and phascolotherium in the ,stonesfield slate4 ,in the ,carboniferous and ,devonian period we have no large ,reptiles1 with1 again1 a minute amount of exception4 ,in the lower part of the ,silurian rocks1 ,fishes vanish1 and we have no animal forms but ,mollusks1 ,crustaceans and ,zoophytes4 ,the ,carboniferous1 ,devonian and ,silurian formations1 thus containing the oldest forms of life1 have been termed palozoic4 ,the boundaries of the life-bearing series have not yet been determined2 but the series in which vertebrated animals do not appear has been #eda provisionally termed protozoic1 and the lower ,silurian rocks may probably be looked upon as its upper members4 ,below this1 geologists place a hypozoic or azoic series of rocks4 ,geologists differ as to the question whether these changes in the inhabitants of the globe were made by determinate steps or by insensible gradations4 ,m4 ,agassiz has been led to the conviction that the organized population of the globe was renewed in the interval of each principal member of its formations4#fcah ,mr4 ,lyell1 on the other hand1 conceives that the change in the collection of organized beings was gradual1 and has proposed on this subject an hypothesis which ,i shall hereafter consider4 ,note #fcah3 ,brit4 ,assoc4 ,report #ahdb1 p4 #hc4 ,sect4 #b4--,transition to ,geological ,dynamics4 ,,while we have been giving this account of the objects with which ,descriptive ,geology is occupied1 it must have been felt how difficult it is1 in contemplating such facts1 to confine ourselves to description and classification4 ,conjectures and reasonings respecting the causes of the phenomena force themselves upon us at every step2 and even influence our classification and nomenclature4 ,our ,descriptive ,geology impels us to endeavor to construct a ,physical ,geology4 ,this close connexion of the two branches of the subject by no means invalidates the necessity of distinguishing them3 as in ,botany1 although the formation of a ,natural ,system necessarily brings us to physiological relations1 we still distinguish ,systematic from ,physiological ,botany4 ,supposing1 however1 our ,descriptive ,geology to be completed1 as far as can be done without considering closely the causes by which the strata have been produced1 we have now to enter upon the other province of the science1 which treats of those causes1 and of which we have already spoken1 as ,physical ,geology4 ,but before we can treat this department of speculation in a manner suitable to the conditions of science1 and to the analogy of other parts of our knowledge1 a certain intermediate and preparatory science must be formed1 of which we shall now consider the origin and progress4 #edb ,,geological ,,dynamics4 ,,chapter ,v4 ,,inorganic ,,geological ,,dynamics4 ,sect4 #a4--,necessity and ,object of a ,science of ,geological ,dynamics4 ,,when the structure and arrangement which men observed in the materials of the earth instigated them to speculate concerning the past changes and revolutions by which such results had been produced1 they at first supposed themselves sufficiently able to judge what would be the effects of any of the obvious agents of change1 as water or volcanic fire4 ,it did not at once occur to them to suspect1 that their common and extemporaneous judgment on such points was far from sufficient for sound knowledge2--they did not foresee that they must create a special science1 whose object should be to estimate the general laws and effects of assumed causes1 before they could pronounce whether such causes had actually produced the particular facts which their survey of the earth had disclosed to them4 ,yet the analogy of the progress of knowledge on other subjects points out very clearly the necessity of such a science4 ,when phenomenal astronomy had arrived at a high point of completeness1 by the labors of ages1 and especially by the discovery of ,kepler's laws1 astronomers were vehemently desirous of knowing the causes of these motions2 and sanguine men1 such as ,kepler1 readily conjectured that the motions were the effects of certain virtues and influences1 by which the heavenly bodies acted upon each other4 ,but it did not at first occur to him and his fellow-speculators1 that they had not ascertained what motions the influences of one body upon another could produce3 and that1 therefore1 they were not prepared to judge whether such causes as they spoke of1 did really regulate the motions of the planets4 ,yet such was found to be the necessary course of sound inference4 ,men needed a science of motion1 in order to arrive at a science of the #edc heavenly motions3 they could not advance in the study of the ,mechanics of the heavens1 till they had learned the ,mechanics of terrestrial bodies4 ,and thus they were1 in such speculations1 at a stand for nearly a century1 from the time of ,kepler to the time of ,newton1 while the science of ,mechanics was formed by ,galileo and his successors4 ,till that task was executed1 all the attempts to assign the causes of cosmical phenomena were fanciful guesses and vague assertions2 after that was done1 they became demonstrations4 ,the science of ,dynamics enabled philosophers to pass securely and completely from ,phenomenal ,astronomy to ,physical ,astronomy4 ,in like manner1 in order that we may advance from ,phenomenal ,geology to ,physical ,geology1 we need a science of ,geological ,dynamics2--that is1 a science which shall investigate and determine the laws and consequences of the known causes of changes such as those which ,geology considers3--and which shall do this1 not in an occasional1 imperfect1 and unconnected manner1 but by systematic1 complete1 and conclusive methods2--shall1 in short1 be a ,science1 and not a promiscuous assemblage of desultory essays4 ,the necessity of such a study1 as a distinct branch of geology1 is perhaps hardly yet formally recognized1 although the researches which belong to it have1 of late years1 assumed a much more methodical and scientific character than they before possessed4 ,mr4 ,lyell's work 7,principles of ,geology71 in particular1 has eminently contributed to place ,geological ,dynamics in its proper prominent position4 ,of the four books of his ,treatise1 the second and third are upon this division of the subject2 the second book treating of aqueous and igneous causes of change1 and the third1 of changes in the organic world4 ,there is no difficulty in separating this auxiliary geological science from theoretical ,geology itself1 in which we apply our principles to the explanation of the actual facts of the earth's surface4 ,the former1 if perfected1 would be a demonstrative science dealing with general cases2 the latter is an tiological view having reference to special facts2 the one attempts to determine what always must be under given conditions2 the other is satisfied with knowing what is and has been1 and why it has been2 the first study has a strong resemblance to ,mechanics1 the other to philosophical ,archology4 ,since this portion of science is still so new1 it is scarcely possible to give any historical account of its progress1 or any complete survey of its shape and component parts4 ,i can only attempt a few notices1 #edd which may enable us in some measure to judge to what point this division of our subject is tending4 ,we may remark1 in this as in former cases1 that since we have here to consider the formation and progress of a science1 we must treat as unimportant preludes to its history1 the detached and casual observations of the effects of causes of change which we find in older writers4 ,it is only when we come to systematic collections of information1 such as may afford the means of drawing general conclusions2 or to rigorous deductions from known laws of nature2--that we can recognise the separate existence of geological dynamics1 as a path of scientific research4 ,the following may perhaps suffice1 for the present1 as a sketch of the subjects of which this science treats3--the aqueous causes of change1 or those in which water adds to1 takes from1 or transfers1 the materials of the land3--the igneous causes2 volcanoes1 and1 closely connected with them1 earthquakes1 and the forces by which they are produced2--the calculations which determine1 on physical principles1 the effects of assumed mechanical causes acting upon large portions of the crust of the earth2--the effect of the forces1 whatever they be1 which produce the crystalline texture of rocks1 their fissile structure1 and the separation of materials1 of which we see the results in metalliferous veins4 ,again1 the estimation of the results of changes of temperature in the earth1 whether operating by pressure1 expansion1 or in any other way2--the effects of assumed changes in the superficial condition1 extent1 and elevation1 of terrestrial continents upon the climates of the earth2--the effect of assumed cosmical changes upon the temperature of this planet2--and researches of the same nature as these4 ,these researches are concerned with the causes of change in the inorganic world2 but the subject requires no less that we should investigate the causes which may modify the forms and conditions of organic things2 and in the large sense in which we have to use the phrase1 we may include researches on such subjects also as parts of ,geological ,dynamics2 although1 in truth1 this department of physiology has been cultivated1 as it well deserves to be1 independently of its bearing upon geological theories4 ,the great problem which offers itself here1 in reference to ,geology1 is1 to examine the value of any hypotheses by which it may be attempted to explain the succession of different races of animals and plants in different strata2 and though it may be difficult1 in this inquiry1 to arrive at any positive result1 we #ede may at least be able to show the improbability of some conjectures which have been propounded4 ,i shall now give a very brief account of some of the attempts made in these various departments of this province of our knowledge2 and in the present chapter1 of ,inorganic ,changes4 ,sect4 #b4--;,aqueous ,causes of ,change4 ,,the controversies to which the various theories of geologists gave rise1 proceeding in various ways upon the effects of the existing causes of change1 led men to observe1 with some attention and perseverance1 the actual operation of such causes4 ,in this way1 the known effect of the ,rhine1 in filling up the ,lake of ,geneva at its upper extremity1 was referred to by ,de ,luc1 ,kirwan1 and others1 in their dispute with the ,huttonians2 and attempts were even made to calculate how distant the period was1 when this alluvial deposit first began4 ,other modern observers have attended to similar facts in the natural history of rivers and seas4 ,but the subject may be considered as having first assumed its proper form1 when taken up by ,mr4 ,von ,hoff2 of whose ,history of the ,natural ,changes of the ,earth's surface which are proved by ,tradition1 the first part1 treating of aqueous changes1 appeared in #ahbb4 ,this work was occasioned by a ,prize ,question of the ,royal ,society of ,gttingen1 promulgated in #ahah2 in which these changes were proposed as the subject of inquiry1 with a special reference to geology4 ,although ,von ,hoff does not attempt to establish any general inductions upon the facts which his book contains1 the collection of such a body of facts gave almost a new aspect to the subject1 by showing that changes in the relative extent of land and water were going on at every time1 and almost at every place2 and that mutability and fluctuation in the form of the solid parts of the earth1 which had been supposed by most persons to be a rare exception to the common course of events1 was1 in fact1 the universal rule4 ,but it was ,mr4 ,lyell's ,principles of ,geology1 being an attempt to explain the former ,changes of the ,earth's ,surface by the ,causes now in action 7of which the first volume was published in #ahcj71 which disclosed the full effect of such researches on geology2 and which attempted to present such assemblages of special facts1 as examples of general laws4 ,thus this work may1 as we have said1 be looked upon as the beginning of ,geological ,dynamics1 at least among us4 ,such generalizations and applications as it contains give the most lively #edf interest to a thousand observations respecting rivers and floods1 mountains and morasses1 which otherwise appear without aim or meaning2 and thus this department of science cannot fail to be constantly augmented by contributions from every side4 ,at the same time it is clear1 that these contributions1 voluminous as they must become1 must1 from time to time1 be resolved into laws of greater and greater generality2 and that thus alone the progress of this1 as of all other sciences1 can be furthered4 ,i need not attempt any detailed enumeration of the modes of aqueous action which are here to be considered4 ,some are destructive1 as when the rivers erode the channels in which they flow2 or when the waves1 by their perpetual assault1 shatter the shores1 and carry the ruins of them into the abyss of the ocean4 ,some operations of the water1 on the other hand1 add to the land2 as when deltas are formed at the mouths of rivers or when calcareous springs form deposits of travertin4 ,even when bound in icy fetters1 water is by no mean deprived of its active power2 the glacier carries into the valley masses of its native mountain1 and often1 becoming ice-bergs1 float with a lading of such materials far into the seas of the temperate zone4 ,it is indisputable that vast beds of worn down fragments of the existing land are now forming into strata at the bottom of the ocean2 and that many other effects are constantly produced by existing aqueous causes1 which resemble some1 at least1 of the facts which geology has to explain4 #bnd ,ed4 ,the effects of glaciers above mentioned are obvious2 but the mechanism of these bodies1--the mechanical cause of their motions1--was an unsolved problem till within a very few years4 ,that they slide as rigid masses2--that they advance by the expansion of their mass2--that they advance as a collection of rigid fragments2 were doctrines which were held by eminent physicists2 though a very slight attention to the subject shows these opinions to be untenable4 ,in ,professor ,james ,forbes's theory on the subject 7published in his ,travels through the ,alps1 #ahdc17 we find a solution of the problem1 so simple1 and yet so exact1 as to produce the most entire conviction4 ,in this theory1 the ice of a glacier is1 on a great scale1 supposed to be a plastic or viscous mass1 though small portions of it are sensibly rigid4 ,it advances down the slope of the valley in which it lies as a plastic mass would do1 accommodating itself to the varying shape and size of its bed1 and showing by its crevasses its mixed character between fluid and rigid4 ,it shows this character still more curiously by a ribboned #edg structure on a small scale1 which is common in the solid ice of the glacier4 ,the planes of these ribbons are1 for the most part1 at right angles to the crevasses1 near the sides of the glacier1 while1 near its central line1 they dip towards the upper part of the glacier4 ,this structure appears to arise from the difference of velocities of contiguous moving filaments of the icy mass1 as the crevasses themselves arise from the tension of larger portions4 ,mr4 ,forbes has1 in successive publications1 removed the objections which have been urged against this theory4 ,in the last of them1 a ,memoir in the ,phil4 ,trans41 #ahdf1 7,illustrations of the ,viscous ,theory of ,glacier ,motion17 he very naturally expresses astonishment at the opposition which has been made to the theory on the ground of the rigidity of small pieces of ice4 ,he has himself shown that the ice of glaciers has a plastic flexibility1 by marking forty-five points in a transverse straight line upon the ,mer de ,glace1 and observing them for several days4 ,the straight line in that time not only became oblique to the side1 but also became visibly curved4 ,both ,mr4 ,forbes and other philosophers have made it in the highest degree probable that glaciers have existed in many places in which they now exist no longer1 and have exercised great powers in transporting large blocks of rock1 furrowing and polishing the rocks along which they slide1 and leaving lines and masses of detritus or moraine which they had carried along with them or pushed before them4 ,it cannot be doubted that extinct glaciers have produced some of the effects which the geologist has to endeavor to explain4 ,but this part of the machinery of nature has been worked by some theorists into an exaggerated form1 in which it cannot1 as ,i conceive1 have any place in an account of ,geological ,dynamics which aims at being permanent4 ,the great problem of the diffusion of drift and erratic blocks from their parent rocks to great distances1 has driven geologists to the consideration of other hypothetical machinery by which the effects may be accounted for3 especially the great northern drift and boulders1--the rocks from the ,scandinavian chain which cover the north of ,europe on a vast area1 having a length of #bjjj and breadth of from #djj to #hjj miles4 ,the diffusion of these blocks has been accounted for by supposing them to be imbedded in icebergs1 detached from the shore1 and floated into oceanic spaces1 where they have grounded and been deposited by the melting of the ice4 ,and this mode of action may to some extent be safely admitted into geological speculation4 ,for it is a matter of fact1 that our navigators in arctic and antarctic regions have #edh repeatedly seen icebergs and icefloes sailing along laden with such materials4 ,the above explanation of the phenomena of drift supposes the land on which the travelled materials are found to have been the bottom of a sea where they were deposited4 ,but it does not1 even granting the conditions1 account for some of the facts observed2--that the drift and the boulders are deposited in traines or streaks1 which1 in direction1 diverge from the parent rock2--and that the boulders are of smaller and smaller size1 as they are found more remote from that centre4 ,these phenomena rather suggest the notion of currents of water as the cause of the distribution of the materials into their present situations4 ,and though the supposition that the whole area occupied by drift and boulders was a sea-bottom when they were scattered over it much reduces the amount of violence which it is necessary to assume in order to distribute the loose masses1 yet still the work appears to be beyond the possible effect of ordinary marine currents1 or any movements which would be occasioned by a slow and gradual rising of the centre of distribution4 ,it has been suggested that a sudden rise of the centre of distribution would cause a motion in the surrounding ocean sufficient to produce such an effect3 and in confirmation of this reference has been made to ,mr4 ,scott ,russell's investigations with respect to waves1 already referred to4 7,book ,,viii47 ,the wave in this case would be the wave of translation1 in which the motion of the water is as great at the bottom as at the top2 and it has hence been asserted that by paroxysmal elevations of #ajj or #bjj feet1 a current of #be or #cj miles an hour might be accounted for4 ,but ,i think it has not been sufficiently noted that at each point this current is transient3 it lasts only while the wave is passing over the point1 and therefore it would only either carry a single mass the whole way with its own velocity1 or move through a short distance a series of masses over which it successively passed4 ,it does not appear1 therefore1 that we have here a complete account of the transport of a collection of materials1 in which each part is transferred through great distances3--except1 indeed1 we were to suppose a numerous succession of paroxysmal elevations4 ,such a battery might1 by successive shocks1 transmitting their force through the water1 diffuse the fragments of the central mass over any area1 however wide4 ,the fact that the erratic blocks are found to rest on the lower drift1 is well explained by supposing the latter to have been spread on the #edi sea bottom while rock-bearing ice-masses floated on the surface till they deposited their lading4 ,sir ,r4 ,murchison has pointed out another operation of ice in producing mounds of rocky masses2 namely1 the effects of rivers and lakes1 in climates where1 as in ,russia1 the waters carry rocky fragments entangled in the winter ice1 and leave them in heaps at the highest level which the waters attain4 ,the extent to which the effects of glaciers1 now vanished1 are apparent in many places1 especially in ,switzerland and in ,england1 and other phenomena of the like tendency1 have led some of the most eminent geologists to the conviction that1 interior to the period of our present temperature1 there was a ,glacial ,period1 at which the temperature of ,europe was lower than it now is4 ,although the study of the common operations of water may give the geologist such an acquaintance with the laws of his subject as may much aid his judgment respecting the extent to which such effects may proceed1 a long course of observation and thought must be requisite before such operations can be analysed into their fundamental principles1 and become the subjects of calculation1 or of rigorous reasoning in any manner which is as precise and certain as calculation4 ,various portions of ,hydraulics have an important bearing upon these subjects1 including some researches which have been pursued with no small labor by engineers and mathematicians2 as the effects of currents and waves1 the laws of tides and of rivers1 and many similar problems4 ,in truth1 however1 such subjects have not hitherto been treated by mathematicians with much success2 and probably several generations must elapse before this portion of geological dynamics can become an exact science4 ,sect4 #c4--;,igneous ,causes of ,change4--,motions of the ,earth's ,surface4 ,,the effects of volcanoes have long been noted as important and striking features in the physical history of our globe2 and the probability of their connexion with many geological phenomena1 had not escaped notice at an early period4 ,but it was not till more recent times1 that the full import of these phenomena was apprehended4 ,the person who first looked at such operations with that commanding general view which showed their extensive connexion with physical geology1 was ,alexander von ,humboldt1 who explored the volcanic phenomena #eej of the ,new ,world1 from #agii to #ahjd4 ,he remarked#fdah the linear distribution of volcanic domes1 considering them as vents placed along the edge of vast fissures communicating with reservoirs of igneous matter1 and extending across whole continents4 ,he observed1 also1 the frequent sympathy of volcanic and terremotive action in remote districts of the earth's surface1 thus showing how deeply seated must be the cause of these convulsions4 ,these views strongly excited and influenced the speculations of geologists2 and since then1 phenomena of this kind have been collected into a general view as parts of a natural-historical science4 ,von ,hoff1 in the second volume of the work already mentioned1 was one of the first who did this2 ,at least1 he himself says1#feah 7#ahbd17 it was not known to him that any one before him had endeavored to combine so large a mass of facts with the general ideas of the natural philosopher1 so as to form a whole4 ,other attempts were1 however1 soon made4 ,in #ahbe1 ,m4 von ,ungern-,sternberg published his book ,on the ,nature and ,origin of ,volcanoes1#ffah in which1 he says1 his object is1 to give an empirical representation of these phenomena4 ,in the same year1 ,mr4 ,poulett ,scrope published a work in which he described the known facts of volcanic action2 not1 however1 confining himself to description2 his purpose being1 as his title states1 to consider the probable causes of their phenomena1 the laws which determine their march1 the disposition of their products1 and their connexion with the present state and past history of the globe2 leading to the establishment of a new theory of the earth4 ,and in #ahbf1 ,dr4 ,daubeny1 of ,oxford1 produced ,a ,description of ,active and ,extinct ,volcanoes1 including in the latter phrase the volcanic rocks of central ,france1 of the ,rhine1 of northern and central ,italy1 and many other countries4 ,indeed1 the near connexion between the volcanic effects now going on1 and those by which the basaltic rocks of ,auvergne and many other places had been produced1 was1 by this time1 no longer doubted by any2 and therefore the line which here separates the study of existing causes from that of past effects may seem to melt away4 ,but yet it is manifest that the assumption of an identity of scale and mechanism between volcanoes now active1 and the igneous catastrophes of which the products have #eea survived great revolutions on the earth's surface1 is hypothetical2 and all which depends on this assumption belongs to theoretical geology4 ,note #fdah3 ,humboldt1 ,relation ,historique2 and his other works4 ,note #feah3 ,vol4 ii4 ,prop4 #e4 ,note #ffah3 ,werden und ,seyn des ,vulkanischen ,gebirges4 ,carlsruhe1 #ahbe4 ,confining ourselves1 then1 to volcanic effects1 which have been produced1 certainly or probably1 since the earth's surface assumed its present form1 we have still an ample exhibition of powerful causes of change1 in the streams of lava and other materials emitted in eruptions2 and still more in the earthquakes which1 as men easily satisfied themselves1 are produced by the same causes as the eruptions of volcanic fire4 ,mr4 ,lyell's work was important in this as in other portions of this subject4 ,he extended the conceptions previously entertained of the effects which such causes may produce1 not only by showing how great these operations are historically known to have been1 and how constantly they are going on1 if we take into our survey the whole surface of the earth2 but still more1 by urging the consequences which would follow in a long course of time from the constant repetition of operations in themselves of no extraordinary amount4 ,a lava-stream many miles long and wide1 and several yards deep1 a subsidence or elevation of a portion of the earth's surface of a few feet1 are by no means extraordinary facts4 ,let these operations1 said ,mr4 ,lyell1 be repeated thousands of times2 and we have results of the same order with the changes which geology discloses4 ,the most mitigated earthquakes have1 however1 a character of violence4 ,but it has been thought by many philosophers that there is evidence of a change of level of the land in cases where none of these violent operations are going on4 ,the most celebrated of these cases is ,sweden2 the whole of the land from ,gottenburg to the north of the ,gulf of ,bothnia has been supposed in the act of rising1 slowly and insensibly1 from the surrounding waters4 ,the opinion of such a change of level has long been the belief of the inhabitants2 and was maintained by ,celsius in the beginning of the eighteenth century4 ,it has since been conceived to be confirmed by various observations of marks cut on the face of the rock2 beds of shells1 such as now live in the neighboring seas1 raised to a considerable height2 and other indications4 ,some of these proofs appear doubtful2 but ,mr4 ,lyell1 after examining the facts upon the spot in #ahcd1 says1 ,in regard to the proposition that the land1 in certain parts of ,sweden1 is gradually rising1 ,i have no hesitation in assenting to it1 after my visit to the districts above alluded to4#fgah ,if this conclusion be generally accepted by #eeb geologists1 we have here a daily example of the operation of some powerful agent which belongs to geological dynamics2 and which1 for the purposes of the geological theorist1 does the work of the earthquake upon a very large scale1 without assuming its terrors4 ,note #fgah3 ,phil4 ,trans4 #ahce1 p4 #cb4 #bnd ,ed4 ,examples of changes of level of large districts occurring at periods when the country has been agitated by earthquakes are well ascertained1 as the rising of the coast of ,chili in #ahbb1 and the subsidence of the district of ,cutch1 in the delta of the ,indus1 in #ahai4 7,lyell1 ,b4 ,,ii4 c4 xv47 ,but the cases of more slow and tranquil movement seem also to be established4 ,the gradual secular rise of the shore of the ,baltic1 mentioned in the text1 has been confirmed by subsequent investigation4 ,it appears that the rate of elevation increases from ,stockholm1 where it is only a few inches in a century1 to the ,north ,cape1 where it is several feet4 ,it appears also that several other regions are in a like state of secular change4 ,the coast of ,greenland is sinking4 7,lyell1 ,b4 ,,ii4 c4 xviii47 ,and the existence of raised beaches along various coasts is now generally accepted among geologists4 ,such beaches1 anciently forming the margin of the sea1 but now far above it1 exist in many places2 for instance1 along a great part of the ,scotch coast2 and among the raised beaches of that country we ought probably1 with ,mr4 ,darwin1 to include the parallel roads of ,glenroy1 the subject1 in former days1 of so much controversy among geologists and antiquaries4 ,connected with the secular rise and fall of large portions of the earth's surface1 another agency which plays an important part in ,geological dynamics has been the subject of some bold yet singularly persuasive speculations by ,mr4 ,darwin4 ,i speak of the formation of ,coral1 and ,coral ,reefs4 ,he says that the coral-building animal works only at small and definite distances below the surface4 ,how then are we to account for the vast number of coral islands1 rings1 and reefs1 which are scattered over the ,pacific and ,indian ,oceans6 ,can we suppose that there are so many mountains1 craters1 and ridges1 all exactly within a few feet of the same height through this vast portion of the globe's surface8 ,this is incredible4 ,how then are we to explain the facts8 ,mr4 ,darwin replies1 that if we suppose the land to subside slowly beneath the sea1 and at the same time suppose the coralline zoophytes to go on building1 so that their structure constantly rises nearly to the surface of the water1 we shall have the facts explained4 ,a submerged island will produce a ring2 a long coast1 a barrier reef2 and so on4 ,mr4 ,darwin also notes other phenomena1 as #eec elevated beds of coral1 which1 occurring in other places1 indicate a recent rising of the land2 and on such grounds as these he divides the surface of those parts of the ocean into regions of elevation and of depression4 ,the labors of coralline zoophytes1 as thus observed1 form masses of coral1 such as are found fossilized in the strata of the earth4 ,but our knowledge of the laws of life which have probably affected the distribution of marine remains in strata1 has received other very striking accessions by the labors of ,prof4 ,edward ,forbes in observing the marine animals of the gean ,sea4 ,he found that1 even in their living state1 the mollusks and zoophytes are already distributed into strata4 ,dividing the depth into eight regions1 from #b to #bcj fathoms1 he found that each region had its peculiar inhabitants1 which disappeared speedily either in ascending or in descending4 ,the zero of animal life appeared to occur at about #cjj fathoms4 ,this curious result bears in various ways upon geology4 ,mr4 ,forbes himself has given an example of the mode in which it may be applied1 by determining the depth at which the submarine eruption took place which produced the volcanic isle of ,neokaimeni in #agjg4 ,by an examination of the fossils embedded in the pumice1 he showed that it came from the fourth region4#fhah ,note #fhah3 ,british ,assoc4 ,reports1 #ahdc1 p4 #agg4 ,to the modes in which organized beings operate in producing the materials of the earth1 we must add those pointed out by the extraordinary microscopic discoveries of ,professor ,ehrenberg4 ,it appears that whole beds of earthy matter consist of the cases of certain infusoria1 the remains of these creatures being accumulated in numbers which it confounds our thoughts to contemplate4 ,speculations concerning the causes of volcanoes and earthquakes1 and of the rising and sinking of land1 are a highly important portion of this science1 at least as far as the calculation of the possible results of definite causes is concerned4 ,but the various hypotheses which have been propounded on this subject can hardly be considered as sufficiently matured for such calculation4 ,a mass of matter in a state of igneous fusion1 extending to the centre of the earth1 even if we make such an hypothesis1 requires some additional cause to produce eruption4 ,the supposition that this fire may be produced by intense chemical action between combining elements1 requires further1 not only some agency to bring together such elements1 but some reason why #eed they should be originally separate4 ,and if any other causes have been suggested1 as electricity or magnetism1 this has been done so vaguely as to elude all possibility of rigorous deduction from the hypothesis4 ,the doctrine of a ,central ,heat1 however1 has occupied so considerable a place in theoretical geology1 that it ought undoubtedly to form an article in geological dynamics4 ,sect4 #d4--,the ,doctrine of ,central ,heat4 ,,the early geological theorists who1 like ,leibnitz and ,buffon1 assumed that the earth was originally a mass in a state of igneous fusion1 naturally went on to deduce from this hypothesis1 that the crust consolidated and cooled before the interior1 and that there might still remain a central heat1 capable of producing many important effects4 ,but it is in more recent times that we have measures of such effects1 and calculations which we can compare with measures4 ,it was found1 as we have said1 that in descending below the surface of the earth1 the temperature of its materials increased4 ,now it followed from ,fourier's mathematical investigations of the distribution of heat in the earth1 that if there be no primitive heat 7chaleur d'origine71 the temperature1 when we descend below the crust1 will be constant in each vertical line4 ,hence an observed increase of temperature in descending1 appeared to point out a central heat resulting from some cause now no longer in action4 ,the doctrine of a central heat has usually been combined with the supposition of a central igneous fluidity2 for the heat in the neighborhood of the centre must be very intense1 according to any law of its increase in descending which is consistent with known principles4 ,but to this central fluidity it has been objected that such a fluid must be in constant circulation by the cooling of its exterior4 ,mr4 ,daniell found this to be the case in all fused metals4 ,it has also been objected that there must be1 in such a central fluid1 tides produced by the moon and sun2 but this inference would require several additional suppositions and calculations to give it a precise form4 ,again1 the supposition of a central heat of the earth1 considered as the effect of a more ancient state of its mass1 appeared to indicate that its cooling must still be going on4 ,but if this were so1 the earth might contract1 as most bodies do when they cool2 and this contraction might lead to mechanical results1 as the shortening of the day4 ,laplace satisfied himself1 by reference to ancient astronomical records1 that no such #eee alteration in the length of the day had taken place1 even to the amount of one two-hundredth of a second2 and thus1 there was here no confirmation of the hypothesis of a primitive heat of the earth4 ,though we find no evidence of the secular contraction of the earth in the observations with which astronomy deals1 there are some geological facts which at first appear to point to the reality of a refrigeration within geological periods2 as the existence of the remains of plants and shells of tropical climates1 in the strata of countries which are now near to or within the frigid zones4 ,these facts1 however1 have given rise to theories of the changes of climate1 which we must consider separately4 ,but we may notice1 as connected with the doctrine of central heat1 the manner in which this hypothesis has been applied to explain volcanic and geological phenomena4 ,it does not enter into my plan1 to consider explanations in which this central heat is supposed to give rise to an expansive force1#fiah without any distinct reference to known physical laws4 ,but we may notice2 as more likely to become useful materials of the science now before us1 such speculations as those of ,mr4 ,babbage2 in which he combines the doctrine of central heat with other physical laws2#gjah as1 that solid rocks expand by being heated1 but that clay contracts2 that different rocks and strata conduct heat differently2 that the earth radiates heat differently1 or at different parts of its surface1 according as it is covered with forests1 with mountains1 with deserts1 or with water4 ,these principles1 applied to large masses1 such as those which constitute the crust of the earth1 might give rise to changes as great as any which geology discloses4 ,for example3 when the bed of a sea is covered by a thick deposit of new matter worn from the shores1 the strata below the bed1 being protected by a bad conductor of heat1 will be heated1 and1 being heated1 maybe expanded2 or1 as ,sir ,j4 ,herschel has observed1 may produce explosion by the conversion of their moisture into steam4 ,such speculations1 when founded on real data and sound calculations1 may hereafter be of material use in geology4 ,note #fiah3 ,scrope ,on ,volcanoes1 p4 #aib4 ,note #gjah3 ,on the ,temple of ,serapis1 #ahcd4 ,see also ,journal of the ,royal ,inst4 vol4 ii41 quoted in ,conyb4 and ,ph4 p4 xv4 ,lyell1 ,b4 ii4 c4 xix4 p4 #chc1 7#dth ed47 on ,expansion of ,stone4 ,the doctrine of central heat and fluidity has been rejected by some eminent philosophers4 ,mr4 ,lyell's reasons for this rejection belong #eef rather to ,theoretical ,geology2 but ,i may here notice ,m4 9999,poisson's opinion4 ,he does not assent to the conclusion of ,fourier1 that once the temperature increases in descending1 there must be some primitive central heat4 ,on the contrary1 he considers that such an increase may arise from this2--that the earth1 at some former period1 passed 7by the motion of the solar system in the universe17 9999through a portion of space which was warmer than the space in which it now revolves 7by reason1 it may be1 of the heat of other stars to which it was then nearer74 ,he supposes that1 since such a period1 the surface has cooled down by the influence of the surrounding circumstances2 while the interior1 for a certain unknown depth1 retains the trace of the former elevation of temperature4 ,but this assumption is not likely to expel the belief is the terrestrial origin of the subterraneous heat4 ,for the supposition of such an inequality in the temperature of the different regions in which the solar system is placed at different times1 is altogether arbitrary2 and1 if pushed to the amount to which it must be carried1 in order to account for the phenomenon1 is highly improbable4#gaah ,the doctrine of central heat1 on the other hand1 7which need not be conceived as implying the universal fluidity of the mass17 is not only naturally suggested by the subterraneous increase of temperatures1 but explains the spheroidal figure of the earth2 and falls in with almost any theory which can be devised1 of volcanoes1 earthquakes1 and great geological changes4 ,note #gaah3 ,for this hypothesis would make it necessary to suppose that the earth has1 at some former period1 derived from some other star or stars more heat than she now derives from the sun4 ,but this would imply1 as highly probable1 that at some period some other star or stars must have produced also a mechanical effect upon the solar system1 greater than the effect of the sun4 ,now such a past operation of forces1 fitted to obliterate all order and symmetry1 is quite inconsistent with the simple1 regular1 and symmetrical relation which the whole solar system1 as far as ,uranus1 bears to the present central body4 ,sect4 #e4--,problems respecting ,elevations and ,crystalline ,forces4 ,,other problems respecting the forces by which great masses of the earth's crust have been displaced1 have also been solved by various mathematicians4 ,it has been maintained by ,von ,buch that there occur1 in various places1 craters of elevation2 that is1 mountain-masses resembling the craters of volcanoes1 but really produced by an expansive force from below1 bursting an aperture through horizontal strata1 #eeg and elevating them in a conical form4 ,against this doctrine1 as exemplified in the most noted instances1 strong arguments have been adduced by other geologists4 ,yet the protrusion of fused rock by subterraneous forces upon a large scale is not denied3 and how far the examples of such operations may1 in any cases1 be termed craters of elevation1 must be considered as a question not yet decided4 ,on the supposition of the truth of ,von ,buch's doctrine1 ,m4 de ,beaumont has calculated the relations of position1 the fissures1 c41 which would arise4 ,and ,mr4 ,hopkins1#gbah of ,cambridge1 has investigated in a much more general manner1 upon mechanical principles1 the laws of the elevations1 fissures1 faults1 veins1 and other phenomena which would result from an elevatory force1 acting simultaneously at every point beneath extensive portions of the crust of the earth4 ,an application of mathematical reasoning to the illustration of the phenomena of veins had before been made in ,germany by ,schmidt and ,zimmerman4#gcah ,the conclusion which ,mr4 ,hopkins has obtained1 respecting the two sets of fissures1 at right angles to each other1 which would in general be produced by such forces as he supposes1 may suggest interesting points of examination respecting the geological phenomena of fissured districts4 ,note #gbah3 ,trans4 ,camb4 ,phil4 ,soc4 vol4 vi4 #ahcf4 ,note #gcah3 ,phil4 ,mag4 ,july1 #ahcf1 p4 #b4 #bnd ,ed4 ,the theory of craters of elevation probably errs rather by making the elevation of a point into a particular class of volcanic agency1 than by giving volcanic agency too great a power of elevation4 ,a mature consideration of the subject will make us hesitate to ascribe much value to the labors of those writers who have applied mathematical reasoning to geological questions4 ,such reasoning1 when it is carried to the extent which requires symbolical processes1 has always been1 ,i conceive1 a source1 not of knowledge1 but of error1 and confusion2 for in such applications the real questions are slurred over in the hypothetical assumptions of the mathematician1 while the calculation misleads its followers by a false aspect of demonstration4 ,all symbolical reasonings concerning the fissures of a semi-rigid mass produced by elevatory or other forces1 appear to me to have turned out valueless4 ,at the same time it cannot be too strongly borne in mind1 that mathematical and mechanical habits of thought are requisite to all clear thinking on such subjects4 ,other forces1 still more secure in their nature and laws1 have played a very important part in the formation of the earth's crust4 ,i speak of the forces by which the crystalline1 slaty1 and jointed structure of #eeh mineral masses has been produced4 ,these forces are probably identical1 on the one hand1 with the cohesive forces from which rocks derive their solidity and their physical properties2 while1 on the other hand1 they are closely connected with the forces of chemical attraction4 ,no attempts1 of any lucid and hopeful kind1 have yet been made to bring such forces under definite mechanical conceptions3 and perhaps mineralogy1 to which science1 as the point of junction of chemistry and crystallography1 such attempts would belong1 is hardly yet ripe for such speculations4 ,but when we look at the universal prevalence of crystalline forms and cleavages1 at the extent of the phenomena of slaty cleavage1 and at the segregation of special minerals into veins and nodules1 which has taken place in some unknown manner1 we cannot doubt that the forces of which we now speak have acted very widely and energetically4 ,any elucidation of their nature would be an important step in ,geological ,dynamics4 #bnd ,ed4 ,a point of ,geological ,dynamics of great importance is1 the change which rocks undergo in structure after they are deposited1 either by the action of subterraneous heat1 or by the influence of crystalline or other corpuscular forces4 ,by such agencies1 sedimentary rocks may be converted into crystalline1 the traces of organic fossils may be obliterated1 a slaty cleavage may be produced1 and other like effects4 ,the possibility of such changes was urged by ,dr4 ,hutton in his ,theory2 and ,sir ,james ,hall's very instructive and striking experiments were made for the purpose of illustrating this theory4 ,in these experiments1 powdered chalk was1 by the application of heat under pressure1 converted into crystalline calcspar4 ,afterwards ,dr4 ,mc,culloch's labors had an important influence in satisfying geologists of the reality of corresponding changes in nature4 ,dr4 ,mc,culloch1 by his very lively and copious descriptions of volcanic regions1 by his representations of them1 by his classification of igneous rocks1 and his comprehensive views of the phenomena which they exhibit1 probably was the means of converting many geologists from the ,wernerian opinions4 ,rocks which have undergone changes since they were deposited are termed by ,mr4 ,lyell metamorphic4 ,the great extent of metamorphic rock changed by heat is now uncontested4 ,the internal changes which are produced by the crystalline forces of mountain masses have been the subjects of important and comprehensive speculations by ,professor ,sedgwick4 #eei ,sect4 #f4--,theories of ,changes of ,climate4 ,,as we have already stated1 ,geology offers to us strong evidence that the climate of the ancient periods of the earth's history was hotter than that which now exists in the same countries4 ,this1 and other circumstances1 have led geologists to the investigation of the effects of any hypothetical causes of such changes of condition in respect of heat4 ,the love of the contemplation of geometrical symmetry1 as well as other reasons1 suggested the hypothesis that the earth's axis had originally no obliquity1 but was perpendicular to the equator4 ,such a construction of the world had been thought of before the time of ,milton1#gdah as what might be supposed to have existed when man was expelled from ,paradise2 and ,burnet1 in his ,sacred ,theory of the ,earth 7#afij71 adopted this notion of the paradisiacal condition of the globe3 ,the spring ,perpetual smiled on earth with verdant flowers1 ,equal in days and nights4 ,note #gdah3 ,some said he bade his angels turn askance ,the poles of earth twice ten degrees and more ,from the sun's axle1 c4--,paradise ,lost1 x4 #bad4 ,in modern times1 too1 some persons have been disposed to adopt this hypothesis1 because they have conceived that the present polar distribution of light is inconsistent with the production of the fossil plants which are found in those regions1#geah even if we could1 in some other way1 account for the change of temperature4 ,but this alteration in the axes of a revolution could not take place without a subversion of the equilibrium of the surface1 such as does not appear to have occurred2 and the change has of late been generally declared impossible by physical astronomers4 ,note #geah3 ,lyell1 i4 #aee4 ,lindley1 ,fossil ,flora4 ,the effects of other astronomical changes have been calculated by ,sir ,john ,herschel4 ,he has examined1 for instance1 the thermotical consequences of the diminution of the eccentricity of the earth's orbit1 which has been going on for ages beyond the records of history4 ,he finds#gfah that1 on this account1 the annual effect of solar radiation would increase as we go back to remoter periods of the past2 but 7probably at least7 not in a degree sufficient to account for the apparent past #efj changes of climate4 ,he finds1 however1 that though the effect of this change on the mean temperature of the year may be small1 the effect on the extreme temperature of the seasons will be much more considerable2 so as to produce alternately1 in the same latitude of either hemisphere1 a perpetual spring1 or the extreme vicissitudes of a burning summer and a rigorous winter4#ggah ,note #gfah3 ,geol4 ,trans4 vol4 iii4 p4 #bie4 ,note #ggah3 ,geol4 ,trans4 vol4 iii4 p4 #bih4 ,mr4 ,lyell has traced the consequences of another hypothesis on this subject1 which appears at first sight to promise no very striking results1 but which yet is found1 upon examination1 to involve adequate causes of very great changes3 ,i refer to the supposed various distribution of land and water at different periods of the earth's history4 ,if the land were all gathered into the neighborhood of the poles1 it would become the seat of constant ice and snow1 and would thus very greatly reduce the temperature of the whole surface of the globe4 ,if1 on the other hand1 the polar regions were principally water1 while the tropics were occupied with a belt of land1 there would be no part of the earth's surface on which the frost could fasten a firm hold1 while the torrid zone would act like a furnace to heat the whole4 ,and1 supposing a cycle of terrestrial changes in which these conditions should succeed each other1 the winter and summer of this great year might differ much more than the elevated temperature which we are led to ascribe to former periods of the globe1 can be judged to have differed from the present state of things4 ,the ingenuity and plausibility of this theory cannot be doubted3 and perhaps its results may hereafter be found not quite out of the reach of calculation4 ,some progress has already been made in calculating the movement of heat into1 through1 and out of the earth2 but when we add to this the effects of the currents of the ocean and the atmosphere1 the problem1 thus involving so many thermotical and atmological laws1 operating under complex conditions1 is undoubtedly one of extreme difficulty4 ,still1 it is something1 in this as in all cases1 to have the problem even stated2 and none of the elements of the solution appears to be of such a nature that we need allow ourselves to yield to despair1 respecting the possibility of dealing with it in a useful manner1 as our knowledge becomes more complete and definite4 #efa ,,chapter ,,vi4 ,,progress ,,of ,,the ,,geological ,,dynamics ,,of ,,organized ,,beings4 ,sect4 #a4--,objects of this ,science4 ,,perhaps in extending the term ,geological ,dynamics to the causes of changes in organized beings1 ,i shall be thought to be employing a forced and inconvenient phraseology4 ,but it will be found that1 in order to treat geology in a truly scientific manner1 we must bring together all the classes of speculations concerning known causes of change2 and the ,organic ,dynamics of ,geology1 or of ,geography1 if the reader prefers the word1 appears not an inappropriate phrase for one part of this body of researches4 ,as has already been said1 the species of plants and animals which are found embedded in the strata of the earth1 are not only different from those which now live in the same regions1 but1 for the most part1 different from any now existing on the face of the earth4 ,the remains which we discover imply a past state of things different from that which now prevails2 they imply also that the whole organic creation has been renewed1 and that this renewal has taken place several times4 ,such extraordinary general facts have naturally put in activity very bold speculations4 ,but it has already been said1 we cannot speculate upon such facts in the past history of the globe1 without taking a large survey of its present condition4 ,does the present animal and vegetable population differ from the past1 in the same way in which the products of one region of the existing earth differ from those of another8 ,can the creation and diffusion of the fossil species be explained in the same manner as the creation and diffusion of the creatures among which we live8 ,and these questions lead us onwards another step1 to ask1--,what are the laws by which the plants and animals of different parts of the earth differ8 ,what was the manner in which they were originally diffused8--,thus we have to include1 as portions of our subject1 #efb the ,geography of ,plants1 and of ,animals1 and the ,history of their change and diffusion2 intending by the latter subject1 of course1 paltiological history1--the examination of the causes of what has occurred1 and the inference of past events1 from what we know of causes4 ,it is unnecessary for me to give at any length a statement of the problems which are included in these branches of science1 or of the progress which has been made in them2 since ,mr4 ,lyell1 in his ,principles of ,geology1 has treated these subjects in a very able manner1 and in the same point of view in which ,i am thus led to consider them4 ,i will only briefly refer to some points1 availing myself of his labors and his ideas4 ,sect4 #b4--;,geography of ,plants and ,animals4 ,,with regard both to plants and animals1 it appears1#ghah that besides such differences in the products of different regions as we may naturally suppose to be occasioned by climate and other external causes2 an examination of the whole organic population of the globe leads us to consider the earth as divided into provinces1 each province being occupied by its own group of species1 and these groups not being mixed or interfused among each other to any great extent4 ,and thus1 as the earth is occupied by various nations of men1 each appearing at first sight to be of a different stock1 so each other tribe of living things is scattered over the ground in a similar manner1 and distributed into its separate nations in distant countries4 ,the places where species are thus peculiarly found1 are1 in the case of plants1 called their stations4 ,yet each species in its own region loves and selects some peculiar conditions of shade or exposure1 soil or moisture3 its place1 defined by the general description of such conditions1 is called its habitation4 ,note #ghah3 ,lyell1 ,principles1 ,b4 iii4 c4 v4 ,not only each species thus placed in its own province1 has its position further fixed by its own habits1 but more general groups and assemblages are found to be determined in their situation by more general conditions4 ,thus it is the character of the flora of a collection of islands1 scattered through a wide ocean in a tropical and humid climate1 to contain an immense preponderance of tree-ferns4 ,in the same way1 the situation and depth at which certain genera of shells are found have been tabulated#giah by ,mr4 ,broderip4 ,such general inferences1 if #efc they can be securely made1 are of extreme interest in their bearing on geological speculations4 ,note #giah3 ,greenough1 ,add4 #ahce1 p4 #bj4 ,the means by which plants and animals are now diffused from one place to another1 have been well described by ,mr4 ,lyell4#hjah ,and he has considered also1 with due attention1 the manner in which they become imbedded in mineral deposits of various kinds4#haah ,he has thus followed the history of organized bodies1 from the germ to the tomb1 and thence to the cabinet of the geologist4 ,note #hjah3 ,lyell1 ,b4 iii4 c4 v4 vi4 vii4 ,note #haah3 ,b4 iii4 c4 xiii4 xiv4 xv4 xvi4 ,but1 besides the fortunes of individual plants and animals1 there is another class of questions1 of great interest1 but of great difficulty2--the fortunes of each species4 ,in what manner do species which were not1 begin to be8 as geology teaches us that they many times have done2 and1 as even our own reasonings convince us they must have done1 at least in the case of the species among which we live4 ,we here obviously place before us1 as a subject of research1 the ,creation of ,living ,things2--a subject shrouded in mystery1 and not to be approached without reverence4 ,but though we may conceive1 that1 on this subject1 we are not to seek our belief from science alone1 we shall find1 it is asserted1 within the limits of allowable and unavoidable speculation1 many curious and important problems which may well employ our physiological skill4 ,for example1 we may ask3--how we are to recognize the species which were originally created distinct8--whether the population of the earth at one geological epoch could pass to the form which it has at a succeeding period1 by the agency of natural causes alone8--and if not1 what other account we can give of the succession which we find to have taken place8 ,the most remarkable point in the attempts to answer these and the like questions1 is the controversy between the advocates and the opponents of the doctrine of the transmutation of species4 ,this question is1 even from its mere physiological import1 one of great interest2 and the interest is much enhanced by our geological researches1 which again bring the question before us in a striking form1 and on a gigantic scale4 ,we shall1 therefore1 briefly state the point at issue4 ,sect4 #c4--,question of the ,transmutation of ,species4 ,,we see that animals and plants may1 by the influence of breeding1 and of external agents operating upon their constitution1 be greatly #efd modified1 so as to give rise to varieties and races different from what before existed4 ,how different1 for instance1 is one kind and breed of dog from another6 ,the question1 then1 is1 whether organized beings can1 by the mere working of natural causes1 pass from the type of one species to that of another8 whether the wolf may1 by domestication1 become the dog8 whether the ourang-outang may1 by the power of external circumstances1 be brought within the circle of the human species8 ,and the dilemma in which we are placed is this2--that if species are not thus interchangeable1 we must suppose the fluctuations of which each species is capable1 and which are apparently indefinite1 to be bounded by rigorous limits2 whereas1 if we allow such a transmutation of species1 we abandon that belief in the adaptation of the structure of every creature to its destined mode of being1 which not only most persons would give up with repugnance1 but which1 as we have seen1 has constantly and irresistibly impressed itself on the minds of the best naturalists1 as the true view of the order of the world4 ,but the study of ,geology opens to us the spectacle of many groups of species which have1 in the course of the earth's history1 succeeded each other at vast intervals of time2 one set of animals and plants disappearing1 as it would seem1 from the face of our planet1 and others1 which did not before exist1 becoming the only occupants of the globe4 ,and the dilemma then presents itself to us anew3--either we must accept the doctrine of the transmutation of species1 and must suppose that the organized species of one geological epoch were transmuted into those of another by some long-continued agency of natural causes2 or else1 we must believe in many successive acts of creation and extinction of species1 out of the common course of nature2 acts which1 therefore1 we may properly call miraculous4 ,this latter dilemma1 however1 is a question concerning the facts which have happened in the history of the world2 the deliberation respecting it belongs to physical geology itself1 and not to that subsidiary science which we are now describing1 and which is concerned only with such causes as we know to be in constant and orderly action4 ,the former question1 of the limited or unlimited extent of the modifications of animals and plants1 has received full and careful consideration from eminent physiologists2 and in their opinions we find1 ,i think1 an indisputable preponderance to that decision which rejects the transmutation of species1 and which accepts the former side of the dilemma2 namely1 that the changes of which each species is #efe susceptible1 though difficult to define in words1 are limited in fact4 ,it is extremely interesting and satisfactory thus to receive an answer in which we can confide1 to inquiries seemingly so wide and bold as those which this subject involves4 ,i refer to ,mr4 ,lyell1 ,dr4 ,prichard1 ,mr4 ,lawrence1 and others1 for the history of the discussion1 and for the grounds of the decision2 and ,i shall quote very briefly the main points and conclusions to which the inquiry has led4#hbah ,note #hbah3 ,lyell1 ,b4 iii4 c4 iv4 ,it may be considered1 then1 as determined by the over-balance of physiological authority1 that there is a capacity in all species to accommodate themselves1 to a certain extent1 to a change of external circumstances2 this extent varying greatly according to the species4 ,there may thus arise changes of appearance or structure1 and some of these changes are transmissible to the offspring3 but the mutations thus superinduced are governed by constant laws1 and confined within certain limits4 ,indefinite divergence from the original type is not possible2 and the extreme limit of possible variation may usually be reached in a brief period of time3 in short1 species have a real existence in nature1 and a transmutation from one to another does not exist4 ,thus1 for example1 ,cuvier remarks1 that notwithstanding all the differences of size1 appearance1 and habits1 which we find in the dogs of various races and countries1 and though we have 7in the ,egyptian mummies7 skeletons of this animal as it existed three thousand years ago1 the relation of the bones to each other remains essentially the same2 and1 with all the varieties of their shape#hcah and size1 there are characters which resist all the influences both of external nature1 of human intercourse1 and of time4 ,note #hcah3 ,ossem4 ,foss4 ,disc4 ,prl4 p4 #fa4 ,sect4 #d4--;,hypothesis of ,progressive ,tendencies4 ,,within certain limits1 however1 as we have said1 external circumstances produce changes in the forms of organized beings4 ,the causes of change1 and the laws and limits of their effects1 as they obtain in the existing state of the organic creation1 are in the highest degree interesting4 ,and1 as has been already intimated1 the knowledge thus obtained1 has been applied with a view to explain the origin of the existing population of the world1 and the succession of its past conditions4 ,but those who have attempted such an explanation1 have found it necessary to assume certain additional laws1 in order to enable themselves to #eff deduce1 from the tenet of the transmutability of the species of organized beings1 such a state of things as we see about us1 and such a succession of states as is evidenced by geological researches4 ,and here1 again1 we are brought to questions of which we must seek the answers from the most profound physiologists4 ,now referring1 as before1 to those which appear to be the best authorities1 it is found that these additional positive laws are still more inadmissible than the primary assumption of indefinite capacity of change4 ,for example1 in order to account1 on this hypothesis1 for the seeming adaptation of the endowments of animals to their wants1 it is held that the endowments are the result of the wants2 that the swiftness of the antelope1 the claws and teeth of the lion1 the trunk of the elephant1 the long neck of the giraffe have been produced by a certain plastic character in the constitution of animals1 operated upon1 for a long course of ages1 by the attempts which these animals made to attain objects which their previous organization did not place within their reach4 ,in this way1 it is maintained that the most striking attributes of animals1 those which apparently imply most clearly the providing skill of their ,creator1 have been brought forth by the long-repeated efforts of the creatures to attain the object of their desire2 thus animals with the highest endowments have been gradually developed from ancestral forms of the most limited organization2 thus fish1 bird1 and beast1 have grown from small gelatinous bodies1 petits corps gelatineux1 possessing some obscure principle of life1 and the capacity of development2 and thus man himself with all his intellectual and moral1 as well as physical privileges1 has been derived from some creature of the ape or baboon tribe1 urged by a constant tendency to improve1 or at least to alter his condition4 ,as we have said1 in order to arrive even hypothetically at this result1 it is necessary to assume besides a mere capacity for change1 other positive and active principles1 some of which we may notice4 ,thus1 we must have as the direct productions of nature on this hypothesis1 certain monads or rough draughts1 the primary rudiments of plants and animals4 ,we must have1 in these1 a constant tendency to progressive improvement1 to the attainment of higher powers and faculties than they possess2 which tendency is again perpetually modified and controlled by the force of external circumstances4 ,and in order to account for the simultaneous existence of animals in every stage of this imaginary progress1 we must suppose that nature is compelled to be constantly producing those elementary beings1 from which all animals are successively developed4 #efg ,i need not stay to point out how extremely arbitrary every part of this scheme is2 and how complex its machinery would be1 even if it did account for the facts4 ,it may be sufficient to observe1 as others have done1#hdah that the capacity of change1 and of being influenced by external circumstances1 such as we really find it in nature1 and therefore such as in science we must represent it1 is a tendency1 not to improve1 but to deteriorate4 ,when species are modified by external causes1 they usually degenerate1 and do not advance4 ,and there is no instance of a species acquiring an entirely new sense1 faculty1 or organ1 in addition to1 or in the place of1 what it had before4 ,note #hdah3 ,lyell1 ,b4 ,,iii4 c4 iv4 ,not only1 then1 is the doctrine of the transmutation of species in itself disproved by the best physiological reasonings1 but the additional assumptions which are requisite1 to enable its advocates to apply it to the explanation of the geological and other phenomena of the earth1 are altogether gratuitous and fantastical4 ,such is the judgment to which we are led by the examination of the discussions which have taken place on this subject4 ,yet in certain speculations1 occasioned by the discovery of the ,sivatherium1 a new fossil animal from the ,sub-,himalaya mountains of ,india1 ,m4 ,geoffroy ,saint-,hilaire speaks of the belief in the immutability of species as a conviction which is fading away from men's minds4 ,he speaks too of the termination of the age of ,cuvier1 la clture du sicle de ,cuvier1 and of the commencement of a better zoological philosophy4#heah ,but though he expresses himself with great animation1 ,i do not perceive that he adduces1 in support of his peculiar opinions1 any arguments in addition to those which he urged during the lifetime of ,cuvier4 ,and the reader#hfah may recollect that the consideration of that controversy led us to very different anticipations from his1 respecting the probable future progress of physiology4 ,the discovery of the ,sivatherium supplies no particle of proof to the hypothesis1 that the existing species of animals are descended from extinct creatures which are specifically distinct3 and we cannot act more wisely than in listening to the advice of that eminent naturalist1 ,m4 de ,blainville4#hgah ,against this hypothesis1 which1 up to the present time1 ,i regard as purely gratuitous1 and likely to turn geologists out of the sound and excellent road in which they now are1 ,i willingly raise my voice1 with the most absolute conviction of being in the right4 #efh ,note #heah3 ,compte ,rendu de l',acad4 des ,sc4 #ahcg1 ,no4 #c1 p4 #ha4 ,note #hfah3 ,see ,b4 ,,xvii4 c4 vii4 ,note #hgah3 ,compte ,rendu1 #ahcg1 ,no4 #e1 p4 #afh4 #bnd ,ed4 ,the hypothesis of the progressive developement of species has been urged recently1 in connexion with the physiological tenet of ,tiedemann and ,de ,serres1 noticed in ,b4 ,,xvii4 c4 vii4 sect4 #c2--namely1 that the embryo of the higher forms of animals passes by gradations through those forms which are permanent in inferior animals4 ,assuming this tenet as exact1 it has been maintained that the higher animals which are found in the more recent strata may have been produced by an ulterior development of the lower forms in the embryo state2 the circumstances being such as to favor such a developement4 ,but all the best physiologists agree in declaring that such an extraordinary developement of the embryo is inconsistent with physiological possibility4 ,even if the progression of the embryo in time have a general correspondence with the order of animal forms as more or less perfectly organized 7which is true in an extremely incomplete and inexact degree71 this correspondence must be considered1 not as any indication of causality1 but as one of those marks of universal analogy and symmetry which are stamped upon every part of the creation4 ,mr4 ,lyell#hhah notices this doctrine of ,tiedemann and ,de ,serres2 and observes1 that though nature presents us with cases of animal forms degraded by incomplete developement1 she offers none of forms exalted by extraordinary developement4 ,mr4 ,lyell's own hypothesis of the introduction of new species upon the earth1 not having any physiological basis1 hardly belongs to this chapter4 ,note #hhah3 ,principles1 ,b4 ,,iii4 c4 iv4 ,sect4 #e4--,question of ,creation as related to ,science4 ,,but since we reject the production of new species by means of external influence1 do we then1 it may be asked1 accept the other side of the dilemma which we have stated2 and admit a series of creations of species1 by some power beyond that which we trace in the ordinary course of nature8 ,to this question1 the history and analogy of science1 ,i conceive1 teach us to reply as follows3--,all paltiological sciences1 all speculations which attempt to ascend from the present to the remote past1 by the chain of causation1 do also1 by an inevitable consequence1 urge us to look for the beginning of the state of things which we thus contemplate2 but in none of these cases have men been able1 by the aid of science1 to arrive at a beginning which is homogeneous with the #efi known course of events4 ,the first origin of language1 of civilization1 of law and government1 cannot be clearly made out by reasoning and research2 just as little1 we may expect1 will a knowledge of the origin of the existing and extinct species of plants and animals1 be the result of physiological and geological investigation4 ,but1 though philosophers have never yet demonstrated1 and perhaps never will be able to demonstrate1 what was that primitive state of things in the social and material worlds1 from which the progressive state took its first departure2 they can still1 in all the lines of research to which we have referred1 go very far back2--determine many of the remote circumstances of the past sequence of events2--ascend to a point which1 from our position at least1 seems to be near the origin2--and exclude many suppositions respecting the origin itself4 ,whether1 by the light of reason alone1 men will ever be able to do more than this1 it is difficult to say4 ,it is1 ,i think1 no irrational opinion1 even on grounds of philosophical analogy alone1 that in all those sciences which look back and seek a beginning of things1 we may be unable to arrive at a consistent and definite belief1 without having recourse to other grounds of truth1 as well as to historical research and scientific reasoning4 ,when our thoughts would apprehend steadily the creation of things1 we find that we are obliged to summon up other ideas than those which regulate the pursuit of scientific truths2--to call in other powers than those to which we refer natural events3 it cannot1 then1 be considered as very surprizing1 if1 in this part of our inquiry1 we are compelled to look for other than the ordinary evidence of science4 ,geology1 forming one of the paltiological class of sciences1 which trace back the history of the earth and its inhabitants on philosophical grounds1 is thus associated with a number of other kinds of research1 which are concerned about language1 law1 art1 and consequently about the internal faculties of man1 his thoughts1 his social habits1 his conception of right1 his love of beauty4 ,geology being thus brought into the atmosphere of moral and mental speculations1 it may be expected that her investigations of the probable past will share an influence common to them2 and that she will not be allowed to point to an origin of her own1 a merely physical beginning of things2 but that1 as she approaches towards such a goal1 she will be led to see that it is the origin of many trains of events1 the point of convergence of many lines4 ,it may be1 that instead of being allowed to travel up to this focus of being1 we are only able to estimate its place and nature1 and #egj to form of it such a judgment as this2--that it is not only the source of mere vegetable and animal life1 but also of rational and social life1 language and arts1 law and order2 in short1 of all the progressive tendencies by which the highest principles of the intellectual and moral world have been and are developed1 as well as of the succession of organic forms1 which we find scattered1 dead or living1 over the earth4 ,this reflection concerning the natural scientific view of creation1 it will be observed1 has not been sought for1 from a wish to arrive at such conclusions2 but it has flowed spontaneously from the manner in which we have had to introduce geology into our classification of the sciences2 and this classification was framed from an unbiassed consideration of the general analogies and guiding ideas of the various portions of our knowledge4 ,such remarks as we have made may on this account be considered more worthy of attention4 ,but such a train of thought must be pursued with caution4 ,although it may not be possible to arrive at a right conviction respecting the origin of the world1 without having recourse to other than physical considerations1 and to other than geological evidence3 yet extraneous considerations1 and extraneous evidence1 respecting the nature of the beginning of things1 must never be allowed to influence our physics or our geology4 ,our geological dynamics1 like our astronomical dynamics1 may be inadequate to carry us back to an origin of that state of things1 of which it explains the progress3 but this deficiency must be supplied1 not by adding supernatural to natural geological dynamics1 but by accepting1 in their proper place1 the views supplied by a portion of knowledge of a different character and order4 ,if we include in our ,theology the speculations to which we have recourse for this purpose1 we must exclude from them our ,geology4 ,the two sciences may conspire1 not by having any part in common3 but because1 though widely diverse in their lines1 both point to a mysterious and invisible origin of the world4 ,all that which claims our assent on those higher grounds of which theology takes cognizance1 must claim such assent as is consistent with those grounds2 that is1 it must require belief in respect of all that bears upon the highest relations of our being1 those on which depend our duties and our hopes4 ,doctrines of this kind may and must be conveyed and maintained1 by means of information concerning the past history of man1 and his social and material1 as well as moral and spiritual fortunes4 ,he who believes that a ,providence has #ega ruled the affairs of mankind1 will also believe that a ,providence has governed the material world4 ,but any language in which the narrative of this government of the material world can be conveyed1 must necessarily be very imperfect and inappropriate2 being expressed in terms of those ideas which have been selected by men1 in order to describe appearances and relations of created things as they affect one another4 ,in all cases1 therefore1 where we have to attempt to interpret such a narrative1 we must feel that we are extremely liable to err2 and most of all1 when our interpretation refers to those material objects and operations which are most foreign to the main purpose of a history of providence4 ,if we have to consider a communication containing a view of such a government of the world1 imparted to us1 as we may suppose1 in order to point out the right direction for our feelings of trust1 and reverence1 and hope1 towards the ,governor of the world1 we may expect that we shall be in no danger of collecting from our authority erroneous notions with regard to the power1 and wisdom1 and goodness of ,his government2 or with respect to our own place1 duties1 and prospects1 and the history of our race so far as our duties and prospects are concerned4 ,but that we shall rightly understand the detail of all events in the history of man1 or of the skies1 or of the earth1 which are narrated for the purpose of thus giving a right direction to our minds1 is by no means equally certain2 and ,i do not think it would be too much to say1 that an immunity from perplexity and error1 in such matters1 is1 on general grounds1 very improbable4 ,it cannot then surprise us to find1 that parts of such narrations which seem to refer to occurrences like those of which astronomers and geologists have attempted to determine the laws1 have given rise to many interpretations1 all inconsistent with one another1 and most of them at variance with the best established principles of astronomy and geology4 ,it may be urged1 that all truths must be consistent with all other truths1 and that therefore the results of true geology or astronomy cannot be irreconcileable with the statements of true theology4 ,and this universal consistency of truth with itself must be assented to2 but it by no means follows that we must be able to obtain a full insight into the nature and manner of such a consistency4 ,such an insight would only be possible if we could obtain a clear view of that central body of truth1 the source of the principles which appear in the separate lines of speculation4 ,to expect that we should see clearly how the providential government of the world is consistent with the unvarying laws #egb by which its motions and developements are regulated1 is to expect to understand thoroughly the laws of motion1 of developement1 and of providence2 it is to expect that we may ascend from geology and astronomy to the creative and legislative centre1 from which proceeded earth and stars2 and then descend again into the moral and spiritual world1 because its source and centre are the same as those of the material creation4 ,it is to say that reason1 whether finite or infinite1 must be consistent with itself2 and that1 therefore1 the finite must be able to comprehend the infinite1 to travel from any one province of the moral and material universe to any other1 to trace their bearing1 and to connect their boundaries4 ,one of the advantages of the study of the history and nature of science in which we are now engaged is1 that it warns us of the hopeless and presumptuous character of such attempts to understand the government of the world by the aid of science1 without throwing any discredit upon the reality of our knowledge2--that while it shows how solid and certain each science is1 so long as it refers its own facts to its own ideas1 it confines each science within its own limits1 and condemns it as empty and helpless1 when it pronounces upon those subjects which are extraneous to it4 ,the error of persons who should seek a geological narrative in theological records1 would be rather in the search itself than in their interpretation of what they might find2 and in like manner the error of those who would conclude against a supernatural beginning1 or a providential direction of the world1 upon geological or physiological reasonings1 would be1 that they had expected those sciences alone to place the origin or the government of the world in its proper light4 ,though these observations apply generally to all the paltiological sciences1 they may be permitted here1 because they have an especial bearing upon some of the difficulties which have embarrassed the progress of geological speculation2 and though such difficulties are1 ,i trust1 nearly gone by1 it is important for us to see them in their true bearing4 ,from what has been said1 it follows that geology and astronomy are1 of themselves1 incapable of giving us any distinct and satisfactory account of the origin of the universe1 or of its parts4 ,we need not wonder1 then1 at any particular instance of this incapacity2 as1 for example1 that of which we have been speaking1 the impossibility of accounting by any natural means for the production of all the successive tribes of plants and animals which have peopled the world in the #egc various stages of its progress1 as geology teaches us4 ,that they were1 like our own animal and vegetable contemporaries1 profoundly adapted to the condition in which they were placed1 we have ample reason to believe2 but when we inquire whence they came into this our world1 geology is silent4 ,the mystery of creation is not within the range of her legitimate territory2 she says nothing1 but she points upwards4 ,sect4 #f4--,the ,hypothesis of the regular ,creation and ,extinction of ,species4 #a4 ,creation of ,species4--,we have already seen1 how untenable1 as a physiological doctrine1 is the principle of the transmutability and progressive tendency of species2 and therefore1 when we come to apply to theoretical geology the principles of the present chapter1 this portion of the subject will easily be disposed of4 ,i hardly know whether ,i can state that there is any other principle which has been applied to the solution of the geological problem1 and which1 therefore1 as a general truth1 ought to be considered here4 ,mr4 ,lyell1 indeed1 has spoken#hiah of an hypothesis that the successive creation of species may constitute a regular part of the economy of nature3 but he has nowhere1 ,i think1 so described this process as to make it appear in what department of science we are to place the hypothesis4 ,are these new species created by the production1 at long intervals1 of an offspring different in species from the parents8 ,or are the species so created produced without parents8 ,are they gradually evolved from some embryo substance8 or do they suddenly start from the ground1 as in the creation of the poet8 4 4 4 4 4 4 4 ,perfect forms ,limbed and full-grown3 out of the ground up rose ,as from his lair1 the wild beast where he wons ,in forest wild1 in thicket1 brake1 or den2 4 4 4 ,the grassy clods now calved2 now half appeared ,the tawny lion1 pawing to get free ,his hinder parts2 then springs as broke from bounds1 ,and rampant shakes his brinded mane2 c4 c4 ,paradise ,lost1 ,b4 vii4 ,note #hiah3 ,b4 ,,iii4 c4 xi4 p4 #bcd4 ,some selection of one of these forms of the hypothesis1 rather than the others1 with evidence for the selection1 is requisite to entitle us to #egd place it among the known causes of change which in this chapter we are considering4 ,the bare conviction that a creation of species has taken place1 whether once or many times1 so long as it is unconnected with our organical sciences1 is a tenet of ,natural ,theology rather than of ,physical ,philosophy4 #bnd ,ed4 ,mr4 ,lyell has explained his theory#ijah by supposing man to people a great desert1 introducing into it living plants and animals3 and he has traced1 in a very interesting manner1 the results of such a hypothesis on the distribution of vegetable and animal species4 ,but he supposes the agents who do this1 before they import species into particular localities1 to study attentively the climate and other physical conditions of each spot1 and to use various precautions4 ,it is on account of the notion of design thus introduced that ,i have1 above1 described this opinion as rather a tenet of ,natural ,theology than of ,physical ,philosophy4 ,note #ijah3 ,b4 ,,iii4 c4 viii4 p4 #aff4 ,mr4 ,edward ,forbes has published some highly interesting speculations on the distribution of existing species of animals and plants4 ,it appears that the manner in which animal and vegetable forms are now diffused requires us to assume centres from which the diffusion took place by no means limited by the present divisions of continents and islands4 ,the changes of land and water which have thus occurred since the existing species were placed on the earth must have been very extensive1 and perhaps reach into the glacial period of which ,i have spoken above4#iaah ,note #iaah3 ,see1 in ,memoirs of the ,geological ,survey of ,great ,britain1 vol4 i4 p4 #ccf1 ,professor ,forbes's ,memoir ,on the ,connection between the ,distribution of the existing ,fauna and ,flora of the ,british ,isles1 and the ,geological ,changes which have affected their area1 especially during the epoch of the ,northern ,drift4 ,according to ,mr4 ,forbes's views1 for which he has offered a great body of very striking and converging reasons1 the present vegetable and animal population of the ,british ,isles is to be accounted for by the following series of events4 ,the marine deposits of the meiocine formation were elevated into a great ,atlantic continent1 yet separate from what is now ,america1 and having its western shore where now the great semi-circular belt of gulf-weed ranges from the #aeth to the #deth parallel of latitude4 ,this continent then became stocked with life1 and of its vegetable population1 the flora of the west of ,ireland1 which has many points in common with the flora of ,spain and the #ege ,atlantic islands 7the ,asturian flora71 is the record4 ,the region between ,spain and ,ireland1 and the rest of this meiocene continent1 was destroyed by some geological movement1 but there were left traces of the connexion which still remain4 ,eastwards of the flora just mentioned1 there is a flora common to ,devon and ,cornwall1 to the south-east part of ,ireland1 the ,channel ,isles1 and the adjacent provinces of ,france2--a flora passing to a southern character2 and having its course marked by the remains of a great rocky barrier1 the destruction of which probably took place anterior to the formation of the narrower part of the channel4 ,eastward from this ,devon or ,norman flora1 again1 we have the ,kentish flora1 which is an extension of the flora of ,north-western ,france1 insulated by the breach which formed the straits of ,dover4 ,then came the ,glacial period1 when the east of ,england and the north of ,europe were submerged1 the northern drift was distributed1 and ,england was reduced to a chain of islands or ridges1 formed by the mountains of ,wales1 ,cumberland1 and ,scotland1 which were connected with the land of ,scandinavia4 ,this was the period of glaciers1 of the dispersion of boulders1 of the grooving and scratching of rocks as they are now found4 ,the climate being then much colder than it now is1 the flora1 even down to the water's edge1 consisted of what are now ,alpine plants2 and this ,alpine flora is common to ,scandinavia and to our mountain-summits4 ,and these plants kept their places1 when1 by the elevation of the land1 the whole of the present ,german ,ocean became a continent connecting ,britain with central ,europe4 ,for the increased elevation of their stations counterbalanced the diminished cold of the succeeding period4 ,along the dry bed of the ,german ,sea1 thus elevated1 the principal part of the existing flora of ,england1 the ,germanic flora1 migrated4 ,a large portion of our existing animal population also came over through the same region2 and along with those1 came hyenas1 tigers1 rhinoceros1 aurochs1 elk1 wolves1 beavers1 which are extinct in ,britain1 and other animals which are extinct altogether1 as the primigenian elephant or mammoth4 ,but then1 again1 the ,german ,ocean and the ,irish ,channel were scooped out2 and the climate again changed4 ,in our islands1 so detached1 many of the larger beasts perished1 and their bones were covered up in peat-mosses and caves1 where we find them4 ,this distinguished naturalist has further shown that the population of the sea lends itself to the same view4 ,mr4 ,forbes says that the writings of ,mr4 ,smith1 of ,jordan-hill1 ,on the last ,changes in the relative ,levels of the ,land and ,sea in the ,british ,islands1 published in the ,memoirs of the #egf ,wernerian ,society for #ahcg-h1 must be esteemed the foundation of a critical investigation of this subject in ,britain4 #b4 ,extinction of ,species4--,with regard to the extinction of species ,mr4 ,lyell has propounded a doctrine which is deserving of great attention here4 ,brocchi1 when he had satisfied himself1 by examination of the ,sub-,apennines1 that about half the species which had lived at the period of their deposition1 had since become extinct1 suggested as a possible cause for this occurrence1 that the vital energies of a species1 like that of an individual1 might gradually decay in the progress of time and of generations1 till at last the prolific power might fail1 and the species wither away4 ,such a property would be conceivable as a physiological fact2 for we see something of the kind in fruit-trees propagated by cuttings3 after some time1 the stock appears to wear out1 and loses its peculiar qualities4 ,but we have no sufficient evidence that this is the case in generations of creatures continued by the reproductive powers4 ,mr4 ,lyell conceives1 that1 without admitting any inherent constitutional tendency to deteriorate1 the misfortunes to which plants and animals are exposed by the change of the physical circumstances of the earth1 by the alteration of land and water1 and by the changes of climate1 must very frequently occasion the loss of several species4 ,we have historical evidence of the extinction of one conspicuous species1 the ,dodo1 a bird of large size and singular form1 which inhabited the ,isle of ,france when that island was first discovered1 and which now no longer exists4 ,several other species of animals and plants seem to be in the course of vanishing from the face of the earth1 even under our own observation4 ,and taking into account the greater changes of the surface of the globe which geology compels us to assume1 we may imagine many or all the existing species of living things to be extirpated4 ,if1 for instance1 that reduction of the climate of the earth which appears1 from geological evidence1 to have taken place already1 be supposed to go on much further1 the advancing snow and cold of the polar regions may destroy the greater part of our plants and animals1 and drive the remainder1 or those of them which possess the requisite faculties of migration and accommodation1 to seek an asylum near the equator4 ,and if we suppose the temperature of the earth to be still further reduced1 this zone of now-existing life1 having no further place of refuge1 will perish1 and the whole earth will be tenanted1 if at all1 by a new creation4 ,other causes might produce the same effect as a change of climate2 and1 without supposing such causes to affect the whole globe1 it is easy to #egg imagine circumstances such as might entirely disturb the equilibrium which the powers of diffusion of different species have produced2--might give to some the opportunity of invading and conquering the domain of others2 and in the end1 the means of entirely suppressing them1 and establishing themselves in their place4 ,that this extirpation of certain species1 which1 as we have seen1 happens in a few cases under common circumstances1 might happen upon a greater scale1 if the range of external changes were to be much enlarged1 cannot be doubted4 ,the extent1 therefore1 to which natural causes may account for the extinction of species1 will depend upon the amount of change which we suppose in the physical conditions of the earth4 ,it must be a task of extreme difficulty to estimate the effect upon the organic world1 even if the physical circumstances were given4 ,to determine the physical condition to which a given state of the earth would give rise1 ,i have already noted as another very difficult problem4 ,yet these two problems must be solved1 in order to enable us to judge of the sufficiency of any hypothesis of the extinction of species2 and in the mean time1 for the mode in which new species come into the places of those which are extinguished1 we have 7as we have seen7 no hypothesis which physiology can1 for a moment1 sanction4 ,sect4 #g4--,the ,imbedding of ,organic ,remains4 ,,there is still one portion of the ,dynamics of ,geology1 a branch of great and manifest importance1 which ,i have to notice1 but upon which ,i need only speak very briefly4 ,the mode in which the spoils of existing plants and animals are imbedded in the deposits now forming1 is a subject which has naturally attracted the attention of geologists4 ,during the controversy which took place in ,italy respecting the fossils of the ,sub-,apennine hills1 ,vitaliano ,donati1#ibah in #agej1 undertook an examination of the ,adriatic1 and found that deposits containing shells and corals1 extremely resembling the strata of the hills1 were there in the act of formation4 ,but without dwelling on other observations of like kind1 ,i may state that ,mr4 ,lyell has treated this subject1 and all the topics connected with it1 in a very full and satisfactory manner4 ,he has explained1#icah by an excellent collection of illustrative facts1 how deposits of various substance and contents are formed2 how plants and animals become fossil in peat1 in blown sand1 in volcanic matter1 in #egh alluvial soil1 in caves1 and in the beds of lakes and seas4 ,this exposition is of the most instructive character1 as a means of obtaining right conclusions concerning the causes of geological phenomena4 ,indeed1 in many cases1 the similarity of past effects with operations now going on1 is so complete1 that they may be considered as identical2 and the discussion of such cases belongs1 at the same time1 to ,geological ,dynamics and to ,physical ,geology2 just as the problem of the fall of meteorolites may be considered as belonging alike to mechanics and to physical astronomy4 ,the growth of modern peat-mosses1 for example1 fully explains the formation of the most ancient3 objects are buried in the same manner in the ejections of active and of extinct volcanoes2 within the limits of history1 many estuaries have been filled up2 and in the deposits which have occupied these places1 are strata containing shells1#idah as in the older formations4 ,note #ibah3 ,lyell1 ,b4 ,i4 c4 iii4 p4 #fg4 7#dth ed47 ,note #icah3 ,b4 ,,iii4 c4 xiii4 xiv4 xv4 xvi4 xvii4 ,note #idah3 ,lyell1 ,b4 ,,iii4 c4 xvii4 p4 #bhf4 ,see also his ,address to the ,geological ,society in #ahcg1 for an account of the ,researches of ,mr4 ,stokes and of ,professor ,gppert1 on the lapidification of vegetables4 #egi ,,physical ,,geology4 ,,chapter ,,vii4 ,,progress ,,of ,,physical ,,geology4 ,sect4 #a4--,object and ,distinctions of ,physical ,geology4 ,,being1 in consequence of the steps which we have attempted to describe1 in possession of two sciences1 one of which traces the laws of action of known causes1 and the other describes the phenomena which the earth's surface presents1 we are now prepared to examine how far the attempts to refer the facts to their causes have been successful3 we are ready to enter upon the consideration of ,theoretical or ,physical ,geology1 as1 by analogy with ,physical ,astronomy1 we may term this branch of speculation4 ,the distinction of this from other portions of our knowledge is sufficiently evident4 ,in former times1 ,geology was always associated with ,mineralogy1 and sometimes confounded with it2 but the mistake of such an arrangement must be clear1 from what has been said4 ,geology is connected with ,mineralogy1 only so far as the latter science classifies a large portion of the objects which ,geology employs as evidence of its statements4 ,to confound the two is the same error as it would be to treat philosophical history as identical with the knowledge of medals4 ,geology procures evidence of her conclusions wherever she can2 from minerals or from seas2 from inorganic or from organic bodies2 from the ground or from the skies4 ,the geologist's business is to learn the past history of the earth2 and he is no more limited to one or a few kinds of documents1 as his sources of information1 than is the historian of man1 in the execution of a similar task4 ,physical ,geology1 of which ,i now speak1 may not be always easily separable from ,descriptive ,geology3 in fact1 they have generally been combined1 for few have been content to describe1 without attempting in some measure to explain4 ,indeed1 if they had done so1 it is #ehj probable that their labors would have been far less zealous1 and their expositions far less impressive4 ,we by no means regret1 therefore1 the mixture of these two kinds of knowledge1 which has so often occurred2 but still1 it is our business to separate them4 ,the works of astronomers before the rise of sound physical astronomy1 were full of theories1 but these were advantageous1 not prejudicial1 to the progress of the science4 ,geological theories have been abundant and various2 but yet our history of them must be brief4 ,for our object is1 as must be borne in mind1 to exhibit these1 only so far as they are steps discoverably tending to the true theory of the earth3 and in most of them we do not trace this character4 ,or rather1 the portions of the labors of geologists which do merit this praise1 belong to the two preceding divisions of the subject1 and have been treated of there4 ,the history of ,physical ,geology1 considered as the advance towards a science as real and stable as those which we have already treated of 7and this is the form in which we ought to trace it71 hitherto consists of few steps4 ,we hardly know whether the progress is begun4 ,the history of ,physical ,astronomy almost commences with ,newton1 and few persons will venture to assert that the ,newton of ,geology has yet appeared4 ,still1 some examination of the attempts which have been made is requisite1 in order to explain and justify the view which the analogy of scientific history leads us to take1 of the state of the subject4 ,though far from intending to give even a sketch of all past geological speculations1 ,i must notice some of the forms such speculations have at different times assumed4 ,sect4 #b4--,of ,fanciful ,geological ,opinions4 ,,real and permanent geological knowledge1 like all other physical knowledge1 can be obtained only by inductions of classification and law from many clearly seen phenomena4 ,the labor of the most active1 the talent of the most intelligent1 are requisite for such a purpose4 ,but far less than this is sufficient to put in busy operation the inventive and capricious fancy4 ,a few appearances hastily seen1 and arbitrarily interpreted1 are enough to give rise to a wondrous tale of the past1 full of strange events and supernatural agencies4 ,the mythology and early poetry of nations afford sufficient evidence of man's love of the wonderful1 and of his inventive powers1 in early stages of intellectual development4 ,the scientific faculty1 on the other hand1 #eha and especially that part of it which is requisite for the induction of laws from facts1 emerges slowly and with difficulty from the crowd of adverse influences1 even under the most favorable circumstances4 ,we have seen that in the ancient world1 the ,greeks alone showed themselves to possess this talent2 and what they thus attained to1 amounted only to a few sound doctrines in astronomy1 and one or two extremely imperfect truths in mechanics1 optics1 and music1 which their successors were unable to retain4 ,no other nation1 till we come to the dawn of a better day in modern ,europe1 made any positive step at all in sound physical speculation4 ,empty dreams or useless exhibitions of ingenuity1 formed the whole of their essays at such knowledge4 ,it must1 therefore1 independently of positive evidence1 be considered as extremely improbable1 that any of these nations should1 at an early period1 have arrived1 by observation and induction1 at wide general truths1 such as the philosophers of modern times have only satisfied themselves of by long and patient labor and thought4 ,if resemblances should be discovered between the assertions of ancient writers and the discoveries of modern science1 the probability in all cases1 the certainty in most1 is that these are accidental coincidences2--that the ancient opinion is no anticipation of the modern discovery1 but is one guess among many1 not a whit the more valuable because its expression agrees with a truth4 ,the author of the guess could not intend the truth1 because his mind was not prepared to comprehend it4 ,those of the ancients who spoke of the harmony which binds all things together1 could not mean the ,newtonian gravitation1 because they had never been led to conceive an attractive force1 governed by definite mathematical laws in its quantity and operation4 ,in agreement with these views1 we must1 ,i conceive1 estimate the opinions which we find among the ancients1 respecting the changes which the earth's surface has undergone4 ,these opinions1 when they are at all of a general kind1 are arbitrary fictions of the fancy1 showing man's love of generality indeed1 but indulging it without that expense of labor and thought which alone can render it legitimate4 ,we might1 therefore1 pass by all the traditions and speculations of ,oriental1 ,egyptian1 and ,greek cosmogony1 as extraneous to our subject4 ,but since these have recently been spoken of1 as conclusions collected1 however vaguely1 from observed facts1#ieah we may make a remark or two upon them4 #ehb ,note #ieah3 ,lyell1 ,b4 i4 c4 ii4 p4 #h4 7#dth ed47 ,the notion of a series of creations and destructions of worlds1 which appears in the sacred volume of the ,hindoos1 which formed part of the traditionary lore of ,egypt1 and which was afterwards adopted into the poetry and philosophy of ,greece1 must be considered as a mythological1 not a physical1 doctrine4 ,when this doctrine was dwelt upon1 men's thoughts were directed1 not to the terrestrial facts which it seemed to explain1 but to the attributes of the deities which it illustrated4 ,the conception of a ,supreme power1 impelling and guiding the progress of events1 which is permanent among all perpetual change1 and regular among all seeming chance1 was readily entertained by contemplative and enthusiastic minds2 and when natural phenomena were referred to this doctrine1 it was rather for the purpose of fastening its impressiveness upon the senses1 than in the way of giving to it authority and support4 ,hence we perceive that in the exposition of this doctrine1 an attempt was always made to fill and elevate the mind with the notions of marvellous events1 and of infinite times1 in which vast cycles of order recurred4 ,the great year1 in which all celestial phenomena come round1 offered itself as capable of being calculated2 and a similar great year was readily assumed for terrestrial and human events4 ,hence there were to be brought round by great cycles1 not only deluges and conflagrations which were to destroy and renovate the earth1 but also the series of historical occurrences4 ,not only the sea and land were to recommence their alternations1 but there was to be another ,argo1 which should carry warriors on the first sea-foray1#ifah and another succession of heroic wars4 ,looking at the passages of ancient authors which refer to terrestrial changes in this view1 we shall see that they are addressed almost entirely to the love of the marvellous and the infinite1 and cannot with propriety be taken as indications of a spirit of physical philosophy4 ,for example1 if we turn to the celebrated passage in ,ovid1#igah where ,pythagoras is represented as asserting that land becomes sea1 and sea land1 and many other changes which geologists have verified1 we find that these observations are associated with many fables1 as being matter of exactly the same kind2--the fountain of ,ammon which was cold by day and warm by night2#ihah--the waters of ,salmacis which effeminate men2--the ,clitorian spring which makes them loathe wine2--the ,simplegades islands which were once moveable2--the ,tritonian lake which covered men's bodies with feathers2--and many similar marvels4 ,and the general purport of #ehc the whole is1 to countenance the doctrine of the metempsychosis1 and the ,pythagorean injunction of not eating animal food4 ,it is clear1 ,i think1 that facts so introduced must be considered as having been contemplated rather in the spirit of poetry than of science4 ,note #ifah3 ,virg4 ,eclog4 #d4 ,note #igah3 ,met4 ,lib4 xv4 ,note #ihah3 ,v4 #cji1 c4 ,we must estimate in the same manner1 the very remarkable passage brought to light by ,m4 ,elie de ,beaumont1#iiah from the ,arabian writer1 ,kazwiri2 in which we have a representation of the same spot of ground1 as being1 at successive intervals of five hundred years1 a city1 a sea1 a desert1 and again a city4 ,this invention is adduced1 ,i conceive1 rather to feed the appetite of wonder1 than to fix it upon any reality3 as the title of his book1 ,the ,marvels of ,nature obviously intimates4 ,note #iiah3 ,ann4 des ,sc4 ,nat4 xxv4 #chj4 ,the speculations of ,aristotle1 concerning the exchanges of land and sea which take place in long periods1 are not formed in exactly the same spirit1 but they are hardly more substantial2 and seem to be quite as arbitrary1 since they are not confirmed by any examples and proofs4 ,after stating1#ajjah that the same spots of the earth are not always land and always water1 he gives the reason4 ,the principle and cause of this is1 he says1 that the inner parts of the earth1 like the bodies of plants and animals1 have their ages of vigor and of decline2 but in plants and animals all the parts are in vigor1 and all grow old1 at once3 in the earth different parts arrive at maturity at different times by the operation of cold and heat3 they grow and decay on account of the sun and the revolution of the stars1 and thus the parts of the earth acquire different power1 so that for a certain time they remain moist1 and then become dry and old3 and then other places are revivified1 and become partially watery4 ,we are1 ,i conceive1 doing no injustice to such speculations by classing them among fanciful geological opinions4 ,note #ajjah3 ,meteorol4 i4 #ad4 ,we must also1 ,i conceive1 range in the same division another class of writers of much more modern times2--,i mean those who have trained their geology by interpretations of ,scripture4 ,i have already endeavored to show that such an attempt is a perversion of the purpose of a divine communication1 and cannot lead to any physical truth4 ,i do not here speak of geological speculations in which the ,mosaic account of the deluge has been referred to2 for whatever errors may have been committed on that subject1 it would be as absurd to disregard the most ancient historical record1 in attempting to trace back the history of the earth1 as it would be1 gratuitously to reject any other #ehd source of information4 ,but the interpretations of the account of the creation have gone further beyond the limits of sound philosophy3 and when we look at the arbitrary and fantastical inventions by which a few phrases of the writings of ,moses have been moulded into complete systems1 we cannot doubt that these interpretations belong to the present ,section4 ,i shall not attempt to criticize1 nor even to enumerate1 these ,scriptural ,geologies1--,sacred ,theories of the ,earth1 as ,burnet termed his4 ,ray1 ,woodward1 ,whiston1 and many other persons to whom science has considerable obligations1 were involved1 by the speculative habits of their times1 in these essays2 and they have been resumed by persons of considerable talent and some knowledge1 on various occasions up to the present day2 but the more geology has been studied on its own proper evidence1 the more have geologists seen the unprofitable character of such labors4 ,i proceed now to the next step in the progress of ,theoretical ,geology4 ,sect4 #c4--,of ,premature ,geological ,theories4 ,,while we were giving our account of ,descriptive ,geology1 the attentive reader would perceive that we did1 in fact1 state several steps in the advance towards general knowledge2 but when1 in those cases1 the theoretical aspect of such discoveries softened into an appearance of mere classification1 the occurrence was assigned to the history of ,descriptive rather than of ,theoretical ,geology4 ,of such a kind was the establishment1 by a long and vehement controversy1 of the fact1 that the impressions in rocks are really the traces of ancient living things2 such1 again1 were the division of rocks into ,primitive1 ,secondary1 ,tertiary2 the ascertainment of the orderly succession of organic remains3 the consequent fixation of a standard series of formations and strata2 the establishment of the igneous nature of trap rocks2 and the like4 ,these are geological truths which are assumed and implied in the very language which geology uses2 thus showing how in this1 as in all other sciences1 the succeeding steps involve the preceding4 ,but in the history of geological theory1 we have to consider the wider attempts to combine the facts1 and to assign them to their causes4 ,the close of the last century produced two antagonist theories of this kind1 which long maintained a fierce and doubtful struggle2--that of ,werner and that of ,hutton3 the one termed ,neptunian1 from its #ehe ascribing the phenomena of the earth's surface mainly to aqueous agency2 the other ,plutonian or ,vulcanian1 because it employed the force of subterraneous fire as its principal machinery4 ,the circumstance which is most worthy of notice in these remarkable essays is1 the endeavor to give1 by means of such materials as the authors possessed1 a complete and simple account of all the facts of the earth's history4 ,the ,saxon professor1 proceeding on the examination of a small district in ,germany1 maintained the existence of a chaotic fluid1 from which a series of universal formations had been precipitated1 the position of the strata being broken up by the falling in of subterraneous cavities1 in the intervals between these depositions4 ,the ,scotch philosopher1 who had observed in ,england and ,scotland1 thought himself justified in declaring that the existing causes were sufficient to spread new strata on the bottom of the ocean1 and that they are consolidated1 elevated1 and fractured by volcanic heat1 so as to give rise to new continents4 ,it will hardly be now denied that all that is to remain as permanent science in each of these systems must be proved by the examination of many cases and limited by many conditions and circumstances4 ,theories so wide and simple1 were consistent only with a comparatively scanty collection of facts1 and belong to the early stage of geological knowledge4 ,in the progress of the science1 the theory of each part of the earth must come out of the examination of that part1 combined with all that is well established1 concerning all the rest2 and a general theory must result from the comparison of all such partial theoretical views4 ,any attempt to snatch it before its time must fail2 and therefore we may venture at present to designate general theories1 like those of ,hutton and ,werner1 as premature4 ,this1 indeed1 is the sentiment of most of the good geologists of the present day4 ,the time for such general systems1 and for the fierce wars to which the opposition of such generalities gives rise1 is probably now past for ever2 and geology will not again witness such a controversy as that of the ,wernerian and ,huttonian schools4 4 4 4 4 4 4 ,as when two black clouds ,with heaven's artillery fraught1 come rattling on ,over the ,caspian3 then stand front to front1 ,hovering a space1 till winds the signal blow ,to join their dark encounter in mid-air4 ,so frowned the mighty combatants1 that hell ,grew darker at their frown2 so matched they stood3 ,for never but once more was either like ,to meet so great a foe4 #ehf ,the main points really affecting the progress of sound theoretical geology1 will find a place in one of the two next ,sections4 #bnd ,ed4 ,i think ,i do no injustice to ,dr4 ,hutton in describing his theory of the earth as premature4 ,prof4 ,playfair's elegant work1 ,illustrations of the ,huttonian ,theory 7#ahjb17 so justly admired1 contains many doctrines which the more mature geology of modern times rejects2 such as the igneous origin of chalk-flints1 siliceous pudding stone1 and the like2 the universal formation of river-beds by the rivers themselves2 and other points4 ,with regard to this last-mentioned question1 ,i think all who have read ,deluc's ,geologie 7#ahaj7 will deem his refutation of ,playfair complete4 ,but though ,hutton's theory was premature1 as well as ,werner's1 the former had a far greater value as an important step on the road to truth4 ,many of its boldest hypotheses and generalizations have become a part of the general creed of geologists2 and its publication is perhaps the greatest event which has yet occurred in the progress of ,physical ,geology4 ,,chapter ,,viii4 ,,the ,,two ,,antagonist ,,doctrines ,,of ,,geology4 ,sect4 #a4--,of the ,doctrine of ,geological ,catastrophes4 ,,that great changes1 of a kind and intensity quite different from the common course of events1 and which may therefore properly be called catastrophes1 have taken place upon the earth's surface1 was an opinion which appeared to be forced upon men by obvious facts4 ,rejecting1 as a mere play of fancy1 the notions of the destruction of the earth by cataclysms or conflagrations1 of which we have already spoken1 we find that the first really scientific examination of the materials of the earth1 that of the ,sub-,apennine hills1 led men to draw this inference4 ,leonardo da ,vinci1 whom we have already noticed for his early and strenuous assertion of the real marine origin of fossil impressions of shells1 also maintained that the bottom of the sea had become the top of the mountain2 yet his mode of explaining this may perhaps be claimed by the modern advocates of uniform causes as more allied to their #ehg opinion1 than to the doctrine of catastrophes4#ajaah ,but ,steno1 in #affi1 approached nearer to this doctrine2 for he asserted that ,tuscany must have changed its face at intervals1 so as to acquire six different configurations1 by the successive breaking down of the older strata into inclined positions1 and the horizontal deposit of new ones upon them4 ,strabo1 indeed1 at an earlier period had recourse to earthquakes1 to explain the occurrence of shells in mountains2 and ,hooke published the same opinion later4 ,but the ,italian geologists prosecuted their researches under the advantage of having1 close at hand1 large collections of conspicuous and consistent phenomena4 ,lazzaro ,moro1 in #agdj1 attempted to apply the theory of earthquakes to the ,italian strata2 but both he and his expositor1 ,cirillo ,generelli1 inclined rather to reduce the violence of these operations within the ordinary course of nature1#ajbah and thus leant to the doctrine of uniformity1 of which we have afterwards to speak4 ,moro was encouraged in this line of speculation by the extraordinary occurrence1 as it was deemed by most persons1 of the rise of a new volcanic island from a deep part of the ,mediterranean1 near ,santorino1 in #agjg4ajcah ,but in other countries1 as the geological facts were studied1 the doctrine of catastrophes appeared to gain ground4 ,thus in ,england1 where1 through a large part of the country1 the coal-measures are extremely inclined and contorted1 and covered over by more horizontal fragmentary beds1 the opinion that some violent catastrophe had occurred to dislocate them1 before the superincumbent strata were deposited1 was strongly held4 ,it was conceived that a period of violent and destructive action must have succeeded to one of repose2 and that1 for a time1 some unusual and paroxysmal forces must have been employed in elevating and breaking the pre-existing strata1 and wearing their fragments into smooth pebbles1 before nature subsided into a new age of tranquillity and vitality4 ,in like manner ,cuvier1 from the alternations of fresh-water and salt-water species in the strata of ,paris1 collected the opinion of a series of great revolutions1 in which the thread of induction was broken4 ,deluc and others1 to whom we owe the first steps in geological dynamics1 attempted carefully to distinguish between causes now in action1 and those which have ceased to act2 in which latter class they reckoned the causes which have #ehh elevated the existing continents4 ,this distinction was assented to by many succeeding geologists4 ,the forces which have raised into the clouds the vast chains of the ,pyrenees1 the ,alps1 the ,andes1 must have been1 it was deemed1 something very different from any agencies now operating4 ,note #ajaah3 ,here is a part of the earth which has become more light1 and which rises1 while the opposite part approaches nearer to the centre1 and what was the bottom of the sea is become the top of the mountain4--,venturi's ,lonardo da ,vinci4 ,note #ajbah3 ,lyell1 i4 #c4 p4 #fd4 7#dth ed47 ,note #ajcah3 ,ib4 p4 #fj4 ,this opinion was further confirmed by the appearance of a complete change in the forms of animal and vegetable life1 in passing from one formation to another4 ,the species of which the remains occurred1 were entirely different1 it was said1 in two successive epochs3 a new creation appears to have intervened2 and it was readily believed that a transition1 so entirely out of the common course of the world1 might be accompanied by paroxysms of mechanical energy4 ,such views prevail extensively among geologists up to the present time3 for instance1 in the comprehensive theoretical generalizations of ,elie de ,beaumont and others1 respecting mountain-chains1 it is supposed that1 at certain vast intervals1 systems of mountains1 which may be recognized by the parallelism of course of their inclined beds1 have been disturbed and elevated1 lifting up with them the aqueous strata which had been deposited among them in the intervening periods of tranquillity1 and which are recognized and identified by means of their organic remains3 and according to the adherents of this hypothesis1 these sudden elevations of mountain-chains have been followed1 again and again1 by mighty waves1 desolating whole regions of the earth4 ,the peculiar bearing of such opinions upon the progress of physical geology will be better understood by attending to the doctrine of uniformity1 which is opposed to them1 and with the consideration of which we shall close our survey of this science1 the last branch of our present task4 ,sect4 #b4--,of the ,doctrine of ,geological ,uniformity4 ,,the opinion that the history of the earth had involved a serious of catastrophes1 confirmed by the two great classes of facts1 the symptoms of mechanical violence on a very large scale1 and of complete changes in the living things by which the earth had been tenanted1 took strong hold of the geologists of ,england1 ,france1 and ,germany4 ,hutton1 though he denied that there was evidence of a beginning of the present state of things1 and referred many processes in the formation of strata to existing causes1 did not assert that the elevatory forces which raise continents from the bottom of the ocean1 were of the same order1 #ehi as well as of the same kind1 with the volcanoes and earthquakes which now shake the surface4 ,his doctrine of uniformity was founded rather on the supposed analogy of other lines of speculation1 than on the examination of the amount of changes now going on4 ,the ,author of nature1 it was said1 has not permitted in ,his works any symptom of infancy or of old age1 or any sign by which we may estimate either their future or their past duration3 and the example of the planetary system was referred to in illustration of this4#ajdah ,and a general persuasion that the champions of this theory were not disposed to accept the usual opinions on the subject of creation1 was allowed1 perhaps very unjustly1 to weigh strongly against them in the public opinion4 ,note #ajdah3 ,lyell1 i4 #d1 p4 #id4 ,while the rest of ,europe had a decided bias towards the doctrine of geological catastrophes1 the phenomena of ,italy1 which1 as we have seen1 had already tended to soften the rigor of that doctrine1 in the progress of speculation from ,steno to ,generelli1 were destined to mitigate it still more1 by converting to the belief of uniformity transalpine geologists who had been bred up in the catastrophist creed4 ,this effect was1 indeed1 gradual4 ,for a time the distinction of the recent and the tertiary period was held to be marked and strong4 ,brocchi asserted that a large portion of the ,sub-,apennine fossil shells belonged to a living species of the ,mediterranean ,sea3 but the geologists of the rest of ,europe turned an incredulous ear to this ,italian tenet2 and the persuasion of the distinction of the tertiary and the recent period was deeply impressed on most geologists by the memorable labors of ,cuvier and ,brongniart on the ,paris basin4 ,still1 as other tertiary deposits were examined1 it was found that they could by no means be considered as contemporaneous1 but that they formed a chain of posts1 advancing nearer and nearer to the recent period4 ,above the strata of the basins of ,london and ,paris1#ajeah lie the newer strata of ,touraine1 of ,bourdeaux1 of the valley of the ,bormida and the ,superga near ,turin1 and of the basin of ,vienna1 explored by ,m4 ,constant ,prevost4 ,newer and higher still than these1 are found the ,sub-,apennine formations of ,northern ,italy1 and probably of the same period1 the ,english crag of ,norfolk and ,suffolk4 ,and most of these marine formations are associated with volcanic products and fresh-water deposits1 so as to imply apparently a long train of alternations of corresponding processes4 ,it may easily be supposed that1 when the subject had assumed this form1 the boundary of the present and past condition of the earth #eij was in some measure obscured4 ,but it was not long before a very able attempt was made to obliterate it altogether4 ,in #ahbh1 ,mr4 ,lyell set out on a geological tour through ,france and ,italy4#ajfah ,he had already conceived the idea of classing the tertiary groups by reference to the number of recent species which were found in a fossil state4 ,but as he passed from the north to the south of ,italy1 he found1 by communication with the best fossil conchologists1 ,borelli at ,turin1 ,guidotti at ,parma1 ,costa at ,naples1 that the number of extinct species decreased2 so that the last-mentioned naturalist1 from an examination of the fossil shells of ,otranto and ,calabria1 and of the neighboring seas1 was of opinion that few of the tertiary shells were of extinct species4 ,to complete the series of proof1 ,mr4 ,lyell himself explored the strata of ,ischia1 and found1 #bjjj feet above the level of the sea1 shells1 which were all pronounced to be of species now inhabiting the ,mediterranean2 and soon after1 he made collections of a similar description on the flanks of ,etna1 in the ,val di ,noto1 and in other places4 ,note #ajeah3 ,lyell1 #ast ed4 vol4 iii4 p4 #fa4 ,note #ajfah3 #ast ed4 vol4 iii4 ,pref4 ,the impression produced by these researches is described by himself4#ajgah ,in the course of my tour ,i had been frequently led to reflect on the precept of ,descartes1 that a philosopher should once in his life doubt everything he had been taught2 but ,i still retained so much faith in my early geological creed as to feel the most lively surprize on visiting ,sortino1 ,pentalica1 ,syracuse1 and other parts of the ,val di ,noto1 at beholding a limestone of enormous thickness1 filled with recent shells1 or sometimes with mere casts of shells1 resting on marl in which shells of ,mediterranean species were imbedded in a high state of preservation4 ,all idea of necessarily attaching a high antiquity to a regularly-stratified limestone1 in which the casts and impressions of shells alone were visible1 vanished at once from my mind4 ,at the same time1 ,i was struck with the identity of the associated igneous rocks of the ,val di ,noto with well-known varieties of 'trap' in ,scotland and other parts of ,europe2 varieties which ,i had also seen entering largely into the structure of ,etna4 ,note #ajgah3 ,lyell1 #ast ed4 ,pref4 x4 ,i occasionally amused myself1 ,mr4 ,lyell adds1 with speculating on the different rate of progress which geology might have made1 had it been first cultivated with success at ,catania1 where the phenomena above alluded to1 and the great elevation of the modern tertiary beds in the ,val di ,noto1 and the changes produced in the historical era by the ,calabrian earthquakes1 would have been familiarly known4 #eia ,before ,mr4 ,lyell entered upon his journey1 he had put into the hands of the printer the first volume of his ,principles of ,geology1 being an attempt to explain the former ,changes of the ,earth's ,surface by reference to the ,causes now in ,operation4 ,and after viewing such phenomena as we have spoken of1 he1 no doubt1 judged that the doctrine of catastrophes of a kind entirely different from the existing course of events1 would never have been generally received1 if geologists had at first formed their opinions upon the ,sicilian strata4 ,the boundary separating the present from the anterior state of things crumbled away2 the difference of fossil and recent species had disappeared1 and1 at the same time1 the changes of position which marine strata had undergone1 although not inferior to those of earlier geological periods1 might be ascribed1 it was thought1 to the same kind of earthquakes as those which still agitate that region4 ,both the supposed proofs of catastrophic transition1 the organical and the mechanical changes1 failed at the same time2 the one by the removal of the fact1 the other by the exhibition of the cause4 ,the powers of earthquakes1 even such as they now exist1 were1 it was supposed1 if allowed to operate for an illimitable time1 adequate to produce all the mechanical effects which the strata of all ages display4 ,and it was declared that all evidence of a beginning of the present state of the earth1 or of any material alteration in the energy of the forces by which it has been modified at various epochs1 was entirely wanting4 ,other circumstances in the progress of geology tended the same way4 ,thus1 in cases where there had appeared in one country a sudden and violent transition from one stratum to the next1 it was found1 that by tracing the formations into other countries1 the chasm between them was filled up by intermediate strata2 so that the passage became as gradual and gentle as any other step in the series4 ,for example1 though the conglomerates1 which in some parts of ,england overlie the coal-measures1 appear to have been produced by a complete discontinuity in the series of changes2 yet in the coal-fields of ,yorkshire1 ,durham1 and ,cumberland1 the transition is smoothed down in such a way that the two formations pass into each other4 ,a similar passage is observed in ,central-,germany1 and in ,thuringia is so complete1 that the coal-measures have sometimes been considered as subordinate to the todtliegendes4#ajhah ,note #ajhah3 ,de la ,beche1 p4 #dad1 ,manual4 ,upon such evidence and such arguments1 the doctrine of #eib catastrophes was rejected with some contempt and ridicule2 and it was maintained1 that the operation of the causes of geological change may properly and philosophically be held to have been uniform through all ages and periods4 ,on this opinion1 and the grounds on which it he been urged1 we shall make a few concluding remarks4 ,it must be granted at once1 to the advocates of this geological uniformity1 that we are not arbitrarily to assume the existence of catastrophes4 ,the degree of uniformity and continuity with which terremotive forces have acted1 must be collected1 not from any gratuitous hypothesis1 but from the facts of the case4 ,we must suppose the causes which have produced geological phenomena1 to have been as similar to existing causes1 and as dissimilar1 as the effects teach us4 ,we are to avoid all bias in favor of powers deviating in kind and degree from those which act at present2 a bias which1 ,mr4 ,lyell asserts1 has extensively prevailed among geologists4 ,but when ,mr4 ,lyell goes further1 and considers it a merit in a course of geological speculation that it rejects any difference between the intensity of existing and of past causes1 we conceive that he errs no less than those whom he censures4 ,an earnest and patient endeavor to reconcile the former indication of change1#ajiah with any restricted class of causes1--a habit which he enjoins1--is not1 we may suggest1 the temper in which science ought to be pursued4 ,the effects must themselves teach us the nature and intensity of the causes which have operated2 and we are in danger of error1 if we seek for slow and shun violent agencies further than the facts naturally direct us1 no less than if we were parsimonious of time and prodigal of violence4 ,time1 inexhaustible and ever accumulating his efficacy1 can undoubtedly do much for the theorist in geology2 but ,force1 whose limits we cannot measure1 and whose nature we cannot fathom1 is also a power never to be slighted3 and to call in the one to protect us from the other1 is equally presumptuous1 to whichever of the two our superstition leans4 ,to invoke ,time1 with ten thousand earthquakes1 to overturn and set on edge a mountain-chain1 should the phenomena indicate the change to have been sudden and not successive1 would be ill excused by pleading the obligation of first appealing to known causes4#aajah #eic ,note #ajiah3 ,lyell1 ,b4 iv4 c4 i4 p4 #cbh1 #dth ed4 ,note #aajah3 #bnd ,ed4 ,i have1 in the text1 quoted the fourth edition of ,mr4 ,lyell's ,principles1 in which he recommends an earnest and patient endeavor to reconcile the former indications of change with the evidence of gradual mutation now in progress4 ,in the sixth edition1 in that which is1 ,i presume1 the corresponding passage1 although it is transferred from the fourth to the first ,book 7,b4 i4 c4 xiii4 p4 #cbe7 he recommends1 instead1 an earnest and patient inquiry how far geological appearances are reconcileable with the effect of changes now in progress4 ,but while ,mr4 ,lyell has thus softened the advocate's character in his language in this passage1 the transposition which ,i have noticed appears to me to have an opposite tendency4 ,for in the former edition1 the causes now in action were first described in the second and third ,books1 and the great problem of ,geology1 stated in the first ,book1 was attempted to be solved in the fourth4 ,but by incorporating this fourth ,book with the first1 and thus prefixing to the study of existing causes arguments against the belief of their geological insufficiency1 there is an appearance as if the author wished his reader to be prepared by a previous pleading against the doctrine of catastrophes1 before he went to the study of existing causes4 ,the ,doctrines of ,catastrophes and of ,uniformity1 and the other leading questions of the ,paltiological ,sciences1 are further discussed in the ,philosophy of the ,inductive ,sciences1 ,book x4 ,in truth1 we know causes only by their effects2 and in order to learn the nature of the causes which modify the earth1 we must study them through all ages of their action1 and not select arbitrarily the period in which we live as the standard for all other epochs4 ,the forces which have produced the ,alps and ,andes are known to us by experience1 no less than the forces which have raised ,etna to its present height2 for we learn their amount in both cases by their results4 ,why1 then1 do we make a merit of using the latter case as a measure for the former8 ,or how can we know the true scale of such force1 except by comprehending in our view all the facts which we can bring together8 ,in reality when we speak of the uniformity of nature1 are we not obliged to use the term in a very large sense1 in order to make the doctrine at all tenable8 ,it includes catastrophes and convulsions of a very extensive and intense kind2 what is the limit to the violence which we must allow to these changes8 ,in order to enable ourselves to represent geological causes as operating with uniform energy through all time1 we must measure our time by long cycles1 in which repose and violence alternate2 how long may we extend this cycle of change1 the repetition of which we express by the word uniformity8 ,and why must we suppose that all our experience1 geological as well as historical1 includes more than one such cycle8 ,why must we insist upon it1 that man has been long enough an observer to obtain the average of forces which are changing through immeasurable time8 #eid ,the analogy of other sciences has been referred to1 as sanctioning this attempt to refer the whole train of facts to known causes4 ,to have done this1 it has been said1 is the glory of ,astronomy3 she seeks no hidden virtues1 but explains all by the force of gravitation1 which we witness operating at every moment4 ,but let us ask1 whether it would really have been a merit in the founders of ,physical ,astronomy1 to assume that the celestial revolutions resulted from any selected class of known causes8 ,when ,newton first attempted to explain the motions of the moon by the force of gravity1 and failed because the measures to which he referred were erroneous1 would it have been philosophical in him1 to insist that the difference which he found ought to be overlooked1 since otherwise we should be compelled to go to causes other than those which we usually witness in action8 ,or was there any praise due to those who assumed the celestial forces to be the same with gravity1 rather than to those who assimilated them with any other known force1 as magnetism1 till the calculation of the laws and amount of these forces1 from the celestial phenomena1 had clearly sanctioned such an identification8 ,we are not to select a conclusion now well proved1 to persuade ourselves that it would have been wise to assume it anterior to proof1 and to attempt to philosophize in the method thus recommended4 ,again1 the analogy of ,astronomy has been referred to1 as confirming the assumption of perpetual uniformity4 ,the analysis of the heavenly motions1 it has been said1 supplies no trace of a beginning1 no promise of an end4 ,but here1 also1 this analogy is erroneously applied4 ,astronomy1 as the science of cyclical motions1 has nothing in common with ,geology4 ,but look at ,astronomy where she has an analogy with ,geology2 consider our knowledge of the heavens as a paltiological science2--as the study of a past condition1 from which the present is derived by causes acting in time4 ,is there then no evidence of a beginning1 or of a progress8 ,what is the import of the ,nebular ,hypothesis8 ,a luminous matter is condensing1 solid bodies are forming1 are arranging themselves into systems of cyclical motion2 in short1 we have exactly what we are told1 on this analogy1 we ought not to have2--the beginning of a world4 ,i will not1 to justify this argument1 maintain the truth of the nebular hypothesis2 but if geologists wish to borrow maxims of philosophizing from astronomy1 such speculations as have led to that hypothesis must be their model4 ,or1 let them look at any of the other provinces of paltiological speculation2 at the history of states1 of civilization1 of languages4 ,we #eie may assume some resemblance or connexion between the principles which determined the progress of government1 or of society1 or of literature1 in the earliest ages1 and those which now operate2 but who has speculated successfully1 assuming an identity of such causes8 ,where do we now find a language in the process of formation1 unfolding itself in inflexions1 terminations1 changes of vowels by grammatical relations1 such as characterize the oldest known languages8 ,where do we see a nation1 by its natural faculties1 inventing writing1 or the arts of life1 as we find them in the most ancient civilized nations8 ,we may assume hypothetically1 that man's faculties develop themselves in these ways2 but we see no such effects produced by these faculties1 in our own time1 and now in progress1 without the influence of foreigners4 ,is it not clear1 in all these cases1 that history does not exhibit a series of cycles1 the aggregate of which may be represented as a uniform state1 without indication of origin or termination8 ,does it not rather seem evident that1 in reality1 the whole course of the world1 from the earliest to the present times1 is but one cycle1 yet unfinished2--offering1 indeed1 no clear evidence of the mode of its beginning2 but still less entitling us to consider it as a repetition or series of repetitions of what had gone before8 ,thus we find1 in the analogy of the sciences1 no confirmation of the doctrine of uniformity1 as it has been maintained in ,geology4 ,yet we discern1 in this analogy1 no ground for resigning our hope1 that future researches1 both in ,geology and in other paltiological sciences1 may throw much additional light on the question of the uniform or catastrophic progress of things1 and on the earliest history of the earth and of man4 ,but when we see how wide and complex is the range of speculation to which our analogy has referred us1 we may well be disposed to pause in our review of science2--to survey from our present position the ground that we have passed over2--and thus to collect1 so far as we may1 guidance and encouragement to enable us to advance in the track which lies before us4 ,before we quit the subject now under consideration1 we may1 however1 observe1 that what the analogy of science really teaches us1 as the most promising means of promoting this science1 is the strenuous cultivation of the two subordinate sciences1 ,geological ,knowledge of ,facts1 and ,geological ,dynamics4 ,these are the two provinces of knowledge--corresponding to ,phenomenal ,astronomy1 and ,mathematical ,mechanics--which may lead on to the epoch of the ,newton of #eif geology4 ,we may1 indeed1 readily believe that we have much to do in both these departments4 ,while so large a portion of the globe is geologically unexplored2--while all the general views which are to extend our classifications satisfactorily from one hemisphere to another1 from one zone to another1 are still unformed2 while the organic fossils of the tropics are almost unknown1 and their general relation to the existing state of things has not even been conjectured2--how can we expect to speculate rightly and securely1 respecting the history of the whole of our globe8 ,and if ,geological ,classification and ,description are thus imperfect1 the knowledge of ,geological ,causes is still more so4 ,as we have seen1 the necessity and the method of constructing a science of such causes1 are only just beginning to be perceived4 ,here1 then1 is the point where the labors of geologists may be usefully applied2 and not in premature attempts to decide the widest and abstrusest questions which the human mind can propose to itself4 ,it has been stated1#aaaah that when the ,geological ,society of ,london was formed1 their professed object was to multiply and record observations1 and patiently to await the result at some future time2 and their favorite maxim was1 it is added1 that the time was not yet come for a ,general ,system of ,geology4 ,this was a wise and philosophical temper1 and a due appreciation of their position4 ,and even now1 their task is not yet finished2 their mission is not yet accomplished4 ,they have still much to do1 in the way of collecting ,facts2 and in entering upon the exact estimation of ,causes1 they have only just thrown open the door of a vast ,labyrinth1 which it may employ many generations to traverse1 but which they must needs explore1 before they can penetrate to the ,oracular ,chamber of ,truth4 ,note #aaaah3 ,lyell1 ,b4 i4 c4 iv4 p4 #ajc4 ,i ,,rejoice1 on many accounts1 to find myself arriving at the termination of the task which ,i have attempted4 ,one reason why ,i am glad to close my history is1 that in it ,i have been compelled1 especially in the latter part of my labors1 to speak as a judge respecting eminent philosophers whom ,i reverence as my ,teachers in those very sciences on which ,i have had to pronounce a judgment2--if1 indeed1 even the appellation of ,pupil be not too presumptuous4 ,but ,i doubt not that such men are as full of candor and tolerance1 as they are of knowledge and thought4 ,and if they deem1 as ,i did1 that such a history of #eig science ought to be attempted1 they will know that it was not only the historian's privilege1 but his duty1 to estimate the import and amount of the advances which he had to narrate2 and if they judge1 as ,i trust they will1 that the attempt has been made with full integrity of intention and no want of labor1 they will look upon the inevitable imperfections of the execution of my work with indulgence and hope4 ,there is another source of satisfaction in arriving at this point of my labors4 ,if1 after our long wandering through the region of physical science1 we were left with minds unsatisfied and unraised1 to ask1 ,whether this be all8--our employment might well be deemed weary and idle4 ,if it appeared that all the vast labor and intense thought which has passed under our review had produced nothing but a barren ,knowledge of the external world1 or a few ,arts ministering merely to our gratification2 or if it seemed that the methods of arriving at truth1 so successfully applied in these cases1 aid us not when we come to the higher aims and prospects of our being2--this ,history might well be estimated as no less melancholy and unprofitable than those which narrate the wars of states and the wiles of statesmen4 ,but such1 ,i trust1 is not the impression which our survey has tended to produce4 ,at various points1 the researches which we have followed out1 have offered to lead us from matter to mind1 from the external to the internal world2 and it was not because the thread of investigation snapped in our hands1 but rather because we were resolved to confine ourselves1 for the present1 to the material sciences1 that we did not proceed onwards to subjects of a closer interest4 ,it will appear1 also1 ,i trust1 that the most perfect method of obtaining speculative truth1--that of which ,i have had to relate the result1--is by no means confined to the least worthy subjects2 but that the ,methods of learning what is really true1 though they must assume different aspects in cases where a mere contemplation of external objects is concerned1 and where our own internal world of thought1 feeling1 and will1 supplies the matter of our speculations1 have yet a unity and harmony throughout all the possible employments of our minds4 ,to be able to trace such connexions as this1 is the proper sequel1 and would be the high reward1 of the labor which has been bestowed on the present work4 ,and if a persuasion of the reality of such connexions1 and a preparation for studying them1 have been conveyed to the reader's mind while he has been accompanying me through our long survey1 his time may not have been employed on #eih these pages in vain4 ,however vague and hesitating and obscure may be such a persuasion1 it belongs1 ,i doubt not1 to the dawning of a better ,philosophy1 which it may be my lot1 perhaps1 to develop more fully hereafter1 if permitted by that ,superior ,power to whom all sound philosophy directs our thoughts4 #eii ,,additions ,,to ,,the ,,third ,,edition4 ,,book ,,viii4 ,,acoustics4 ,,chapter ,,iii4 ,,sound4 ,the ,velocity of ,sound in ,water4 ,,the ,science of which the history is narrated in this ,book has for its objects1 the minute ,vibrations of the parts of bodies such as those by which ,sounds are produced1 and the properties of ,sounds4 ,the ,vibrations of bodies are the result of a certain tension of their structure which we term ,elasticity4 ,the ,elasticity determines the rate of ,vibration3 the rate of ,vibration determines the audible note3 the ,elasticity determines also the velocity with which the vibration travels through the substance4 ,these points of the subject1 ,elasticity1 ,rate of ,vibration1 ,velocity of ,propagation1 ,audible ,note1 are connected in each substance1 and are different in different substances4 ,in the history of this ,science1 considered as tending to a satisfactory general theory1 the ,problems which have obviously offered themselves were1 to explain the properties of ,sounds by the relations of their constituent vibrations2 and to explain the existence of vibrations by the elasticity of the substances in which they occurred3 as in ,optics1 philosophers have explained the phenomenon of light and colors by the ,undulatory ,theory1 and are still engaged in explaining the requisite modulations by means of the elasticity of the ,ether4 ,but the ,undulatory ,theory of ,sound was seen to be true at an early period of the ,science3 and the explanation1 in a general way at least1 of all kinds of such undulations by means of the elasticity of the vibrating substances has been performed by a series of mathematicians of whom ,i have given an account in this ,book4 ,hence the points of the subject already mentioned 7,elasticity1 ,vibrations and their ,propagations1 #fjj and ,note71 have a known material dependence1 and each may be employed in determining the other3 for instance1 the ,note may be employed in determining the velocity of sound and the elasticity of the vibrating substance4 ,chladni1#a;,b and the ,webers1#b;,b had made valuable experimental inquiries on such subjects4 ,but more complete investigations of this kind have been conducted with care and skill by ,m4 ,wertheim4#c;,b ,for instance1 he has determined the velocity with which sound travels in water1 by making an organ-pipe to sound by the passage of water through it4 ,this is a matter of some difficulty2 for the mouthpiece of an organ-pipe1 if it be not properly and carefully constructed1 produces sounds of its own1 which are not the genuine musical note of the pipe4 ,and though the note depends mainly upon the length of the pipe1 it depends also1 in a small degree1 on the breadth of the pipe and the size of the mouthpiece4 ,note #a;,b3 ,trait d',acoustique1 #ahji4 ,note #b;,b3 ,wellenlehre1 #aheb4 ,note #c;,b3 ,mmoires de ,physique ,mcanique4 ,paris1 #ahdh4 ,if the pipe were a mere line1 the time of a vibration would be the time in which a vibration travels from one end of the pipe to the other2 and thus the note for a given length 7which is determined by the time of vibration71 is connected with the velocity of vibration4 ,he thus found that the velocity of a vibration along the pipe in sea-water is #aaeg mtres per second4 ,but ,m4 ,wertheim conceived that he had previously shown1 by general mathematical reasoning1 that the velocity with which sound travels in an unlimited expanse of any substance1 is to the velocity with which it travels along a pipe or linear strip of the same substance as the square root of #c to the square root of #b4 ,hence the velocity of sound in sea-water would be #aded mtres a second4 ,the velocity of sound in air is #ccb mtres4 ,m4 ,wertheim also employed the vibrations of rods of steel and other metals in order to determine their modulus of elasticity--that is1 the quantity which determines for each substance1 the extent to which1 in virtue of its elasticity1 it is compressed and expanded by given pressures or tensions4 ,for this purpose he caused the rod to vibrate near to a tuning-fork of given pitch1 so that both the rod and the tuning-fork by their vibrations traced undulating curves on a revolving disk4 ,the curves traced by the two could be compared so as to give their relative rate1 and thus to determine the elasticity of the substance4 #fja ,,book ,,ix4 ,,physical ,,optics4 ,photography4 ,i ,,have1 at the end of ,chapter xi41 stated that the theory of which ,i have endeavored to sketch the history professes to explain only the phenomena of radiant visible light2 and that though we know that light has other properties--for instance1 that it produces chemical effects--these are not contemplated as included within the domain of the theory4 ,the chemical effects of light cannot as yet be included in exact and general truths1 such as those which constitute the undulatory theory of radiant visible light4 ,but though the present age has not yet attained to a ,science of the chemistry of ,light1 it has been enriched with a most exquisite ,art1 which involves the principles of such a science1 and may hereafter be made the instrument of bringing them into the view of the philosopher4 ,i speak of the ,art of ,photography1 in which chemistry has discovered the means of producing surfaces almost as sensitive to the modifications of light as the most sensitive of organic textures1 the retina of the eye3 and has given permanence to images which in the eye are only momentary impressions4 ,hereafter1 when the laws shall have been theoretically established1 which connect the chemical constitution of bodies with the action of light upon them1 the prominent names in the ,prelude to such an ,epoch must be those who by their insight1 invention1 and perseverance1 discovered and carried to their present marvellous perfection the processes of photographic ,art3--,niepce and ,daguerre in ,france1 and our own accomplished countryman1 ,mr4 ,fox ,talbot4 ,fluorescence4 ,as already remarked1 it is not within the province of the undulatory theory to explain the phenomena of the absorption of light which take place in various ways when the light is transmitted through various #fjb mediums4 ,i have1 at the end of ,chapter iii41 given the reasons which prevent my assenting to the assertion of a special analysis of light by absorption4 ,in the same manner1 with regard to other effects produced by media upon light1 it is sufficient for the defence of the theory that it should be consistent with the possibility of the laws of phenomena which are observed1 not that it should explain those laws2 for they belong1 apparently1 to another province of philosophy4 ,some of the optical properties of bodies which have recently attracted notice appear to be of this kind4 ,it was noticed by ,sir ,john ,herschel1#d;,b that a certain liquid1 sulphate of quinine1 which is under common circumstances colorless1 exhibits in certain aspects and under certain incidences of light1 a beautiful celestial blue color4 ,it appeared that this color proceeded from the surface on which the light first fell2 and color thus produced ,sir ,j4 ,herschel called epipolic colors1 and spoke of the light as epipolized4 ,sir ,david ,brewster had previously noted effects of color in transparent bodies which he ascribed to internal dispersion3#e;,b and he conceived that the colors observed by ,sir ,j4 ,herschel were of the same class4 ,professor ,stokes#f;,b of ,cambridge applied himself to the examination of these phenomena1 and was led to the conviction that they arise from a power which certain bodies possess1 of changing the color1 and with it1 the refrangibility of the rays of light which fall upon them3 and he traced this property in various substances1 into various remarkable consequences4 ,as this change of refrangibility always makes the rays less refrangible1 it was proposed to call it a degradation of the light2 or again1 dependent emission1 because the light is emitted in the manner of self-luminous bodies1 but only in dependence upon the active rays1 and so long as the body is under their influence4 ,in this respect it differs from phosphorescence1 in which light is emitted without such dependence4 ,the phenomenon occurs in a conspicuous and beautiful manner in certain kinds of fluor spar3 and the term fluorescence1 suggested by ,professor ,stokes1 has the advantage of inserting no hypothesis1 and will probably be found the most generally acceptable4#g;,b ,note #d;,b3 ,phil4 ,trans4 #ahde4 ,note #e;,b3 ,edinb4 ,trans4 #ahcc4 ,note #f;,b3 ,phil4 ,trans4 #aheb and #ahed4 ,note #g;,b3 ,phil4 ,trans4 #aheb4 ,it may be remarked that ,professor ,stokes rejects altogether the doctrine that light of definite refrangibility may still be compound1 and maybe analysed by absorption4 ,he says1 ,i have not overlooked the remarkable effect of absorbing media in causing apparent changes #fjc of color in a pure spectrum2 but this ,i believe to be a subjective phenomenon depending upon contrast4 ,,chapter ,,xiii4 ,,undulatory ,,theory4 ,direction of the ,transverse ,vibrations in ,polarization4 ,,in the conclusion of ,chapter xiii4 ,i have stated that there is a point in the undulatory theory which was regarded as left undecided by ,young and ,fresnel1 and on which the two different opinions have been maintained by different mathematicians2 namely1 whether the vibrations of polarized light are perpendicular to the plane of polarization or in that plane4 ,professor ,stokes of ,cambridge has attempted to solve this question in a manner which is1 theoretically1 exceedingly ingenious1 though it is difficult to make the requisite experiments in a decisive manner4 ,the method may be briefly described4 ,if polarized light be diffracted 7see ,chap4 xi4 sect4 #b71 each ray will be bent from its position1 but will still be polarized4 ,the original ray and the diffracted ray1 thus forming a broken line1 may be supposed to be connected at the angle by a universal joint 7called a ,hooke's ,joint71 such that when the original ray turns about its axis1 the diffracted ray also turns about its axis2 as in the case of the long handle of a telescope and the screw which is turned by it4 ,now if the motion of the original ray round its axis be uniform1 the motion of the diffracted ray round its axis is not uniform3 and hence if1 in a series of cases1 the planes of polarization of the original ray differ by equal angles1 in the diffracted ray the planes of polarization will differ by unequal angles4 ,then if vibrations be perpendicular to the plane of polarization1 the planes of polarization in the diffracted rays will be crowded together in the neighborhood of the plane in which the diffraction takes place1 and will be more rarely distributed in the neighborhood of the plane perpendicular to this1 in which is the diffracting thread or groove4 ,on making the experiment1 ,prof4 ,stokes conceived that he found1 in his experiments1 such a crowding of the planes of diffracted polarization towards the plane of diffraction2 and thus he held that the #fjd hypothesis that the transverse vibrations which constitute polarization are perpendicularly transverse to the plane of polarization was confirmed4#h;,b ,note #h;,b3 ,camb4 ,trans41 vol4 ix4 part i4 #ahdi4 ,but ,mr4 ,holtzmann1#i;,b who1 assenting to the reasoning1 has made the experiment in a somewhat different manner1 has obtained an opposite result2 so that the point may be regarded as still doubtful4 ,note #i;,b3 ,phil4 ,mag41 ,feb4 #aheg4 ,final ,disproof of the ,emission ,theory4 ,as ,i have stated in the ,history1 we cannot properly say that there ever was an ,emission ,theory of ,light which was the rival of the ,undulatory ,theory3 for while the undulatory theory provided explanations of new classes of phenomena as fast as they arose1 and exhibited a consilience of theories in these explanations1 the hypothesis of emitted particles required new machinery for every new set of facts1 and soon ceased to be capable even of expressing the facts4 ,the simple cases of the ordinary reflexion and refraction of light were explained by ,newton on the supposition that the transmission of light is the motion of particles3 and though his explanation includes a somewhat harsh assumption 7that a refracting surface exercises an attractive force through a fixed finite space71 the authority of his great name gave it a sort of permanent notoriety1 and made it to be regarded as a standard point of comparison between a supposed ,emission ,theory and the undulation theory4 ,and the way in which the theories were to be tested in this case was obvious3 in the ,newtonian theory1 the velocity of light is increased by the refracting medium2 in the undulatory theory1 it is diminished4 ,on the former hypothesis the velocity of light in air and in water is as #c to #d2 in the latter1 as #d to #c4 ,but the immense velocity of light made it appear impossible to measure it1 within the limits of any finite space which we can occupy with refracting matter4 ,the velocity of light is known from astronomical phenomena2--from the eclipses of ,jupiter's satellites1 by which it appears that light occupies #h minutes in coming from the sun to the earth2 and from the aberration of light1 by which its velocity is shown to be #aj1jjj times the velocity of the earth in its orbit4 ,is it1 then1 possible to make apparent so small a difference as that between its passing through a few yards of air and of water8 ,mr4 ,wheatstone1 in #ahca1 invented a machine by which this could #fje be done4 ,his object was to determine the velocity of the electric shock4 ,his apparatus consisted in a small mirror1 turning with great velocity about an axis which is in its own plane1 like a coin spinning on its edge4 ,the velocity of spinning may be made so great1 that an object reflected shall change its place perceptibly after an almost inconceivably small fraction of a second4 ,the application of this contrivance to measure the velocity of light1 was1 at the suggestion of ,arago1 who had seen the times of the rival theories of light1 undertaken by younger men at ,paris1 his eyesight not allowing him to prosecute such a task himself4 ,it was necessary that the mirrors should turn more than #ajjj times in a second1 in order that the two images1 produced1 one by light coming through air1 and the other by light coming through an equal length of water1 should have places perceptibly different4 ,the mechanical difficulties of the experiment consisted in keeping up this great velocity by the machinery without destroying the machinery1 and in transmitting the light without too much enfeebling it4 ,these difficulties were overcome in #ahej1 by ,m4 ,fizeau and ,m4 ,lon ,foucault separately3 and the result was1 that the velocity of light was found to be less in water than in air4 ,and thus the ,newtonian explanation of refraction1 the last remnant of the ,emission ,theory1 was proved to be false4 #fjf ,,book ,x4 ,,thermotics4--,,atmology4 ,,chapter ,,iii4 ,,the ,,relation ,,of ,,vapour ,,and ,,air4 ,sect4 #d4--;,force of ,steam4 ,,the experiments on the elastic force of steam made by the ,french ,academy are fitted in an especial manner to decide the question between rival formul1 in consequence of the great amount of force to which they extend2 namely1 #fj feet of mercury1 or #bd atmospheres3 for formul which give results almost indistinguishable in the lower part of the scale diverge widely at those elevated points4 ,mr4 ,waterston#aj;,b has reduced both these and other experiments to a rule in the following manner3--,he takes the zero of gaseous tension1 determined by other experimenters 7,rudberg1 ,magnus1 and ,regnault17 to be #dfa below the zero of ,fahrenheit1 or #bgd below the zero of the centigrade scale3 and temperatures reckoned from this zero he calls ,g temperatures4 ,the square root of the ,g temperatures is the element to which the elastic force is referred 7for certain theoretical reasons71 and it is found that the density of steam is as the sixth power of this element4 ,the agreement of this rule with the special results is strikingly close4 ,a like rule was found by him to apply generally to many other gases in contact with their liquids4 ,note #aj;,b3 ,phil4 ,trans4 #aheb4 ,but ,m4 ,regnault has recently investigated the subject in the most complete and ample manner1 and has obtained results somewhat different4#aa;,b ,he is led to the conclusion that no formula proceeding by #fjg a power of the temperature can represent the experiments4 ,he also finds that the rule of ,dalton 7that as the temperatures increase in arithmetical progression1 the elastic force increases in geometric progression7 deviates from the observations1 especially at high temperatures4 ,dalton's rule would be expressed by saying that the variable part of the elastic force is as at1 where t is the temperature4 ,this failing1 ,m4 ,regnault makes trial of a formula suggested by ,m4 ,biot1 consisting of a sum of two terms1 one of which is as at1 and the other is bt3 and in this way satisfies the experiments very closely4 ,but this can only be considered as a formula of interpolation1 and has no theoretical basis4 ,m4 ,roche had proposed a formula in which the force is as az1 z depending upon the temperature by an equation#ab;,b to which he had been led by theoretical considerations4 ,this agrees better with observation than any other formula which includes only the same number of coefficients4 ,note #aa;,b3 ,mm4 de l',institut1 vol4 xxi4 7#ahdg74 ,m4 ,regnault's ,memoir occupies #gfg pages4 ,note #ab;,b3 ,the equation z t 7#a mt74 ,among the experimental thermotical laws referred to by ,m4 ,regnault are1 the ,law of ,watt1#ac;,b that the quantity of heat which is required to convert a pint of water at a temperature of zero into steam1 is the same whatever be the pressure4 ,also1 the ,law of ,southern1 that the latent heat of vaporization1 that is the heat absorbed in the passage from the liquid to the gaseous consistence1 is constant for all purposes3 and that we obtain the total heat in adding to the constant latent heat the number which represents the latent heat of steam4 ,southern found the latent heat of the steam of water to be represented by about #iej degrees of ,fahrenheit4#ad;,b ,note #ac;,b3 ,see ,robison's ,mechanical ,philosophy1 vol4 ii4 p4 #h4 ,note #ad;,b3 ,ib4 p4 #afj4 ,sect4 #e4--,temperature of the ,atmosphere4 ,i ,,may notice1 as important additions to our knowledge on this subject1 the results of four balloon ascents made in #aheb1ae;,b by the ,committee of the ,meteorological ,observatory established at ,kew by the ,british ,association for the ,advancement of ,science4 ,in these ascents the observers mounted to more than #ac1jjj1 #ah1jjj1 and #ai1jjj feet1 and in the last to #bb1cgj2 by which ascent the temperature fell from #di degrees to nearly #aj degrees below zero2 and the dew-point fell from #cg to #ab4 ,perhaps the most marked result of these observations is the #fjh following3--,the temperature of the air decreases uniformly as we ascend above the earth's surface2 but this decrease does not go on continuously4 ,at a certain elevation1 varying on different days1 the decrease is arrested3 and for a depth of two or three thousand feet of air1 the temperature decreases little1 or even increases in ascending4 ,above this1 the diminution again takes place at nearly the same rate as in the lower regions4 ,this intermediate region of undecreasing temperature extended in the various ascents1 from about altitude #djjj to #fjjj feet1 #fejj to #aj1jjj1 #bjjj to #dejj1 and #djjj to #hjjj4 ,this interruption in the decrease of temperature is accompanied by a large and abrupt fall in the temperature of the dew-point1 or by an actual condensation of vapor4 ,thus1 this region is the region of the clouds1 and the increase of heat appears to arise from the latent heat liberated when aqueous vapor is formed into clouds4 ,note #ae;,b3 ,phil4 ,trans4 #ahec4 ,,chapter ,,iv4 ,,theories ,,of ,,heat4 ,the ,dynamical ,theory of ,heat4 ,,that the transmission of radiant ,heat takes place by means of the vibrations of a medium1 as the transmission of ,sound certainly does1 and the transmission of ,light most probably1 is a theory which1 as ,i have endeavored to explain1 has strong arguments and analogies in its favor4 ,but that ,heat itself1 in its essence and quantity1 is ,motion is a hypothesis of quite another kind4 ,this hypothesis has been recently asserted and maintained with great ability4 ,the doctrine thus asserted is1 that ,motion may be converted into ,heat1 and ,heat into ,motion2 that ,heat and ,motion may produce each other1 as we see in the rarefaction and condensation of air1 in steam-engines1 and the like3 and that in all such cases the ,motion produced and the ,heat expended exactly measure each other4 ,the foundation of this theory is conceived to have been laid by ,mr4 ,joule of ,manchester1 in #ahdd3 and it has since been prosecuted by him and by ,professor ,thomson of ,glasgow1 by experimental investigations of various kinds4 ,it is difficult to make these experiments so as to be quite satisfactory2 for it is #fji difficult to measure all the heat gained or lost in any of the changes here contemplated4 ,that friction1 agitation of fluids1 condensation of gases1 conversion of gases into fluids and liquids into solids1 produce heat1 is undoubted3 and that the quantity of such heat may be measured by the mechanical force which produces it1 or which it produces1 is a generalization which will very likely be found a fertile source of new propositions1 and probably of important consequences4 ,as an example of the conclusions which ,professor ,thomson draws from this doctrine of the mutual conversion of motion and heat1 ,i may mention his speculations concerning the cause which produces and sustains the heat of the sun4#af;,b ,he conceives that the support of the solar heat must be meteoric matter which is perpetually falling towards the globe of the sun1 and has its motion converted into heat4 ,he inclines to think that the meteors containing the stores of energy for future ,sun-light must be principally within the earth's orbit2 and that we actually see them there as the ,zodiacal ,light1 an illuminated shower1 or rather tornado1 of stones4 ,the inner parts of this tornado are always getting caught in the ,sun's atmosphere1 and drawn to his mass by gravitation4 ,note #af;,b3 ,on the ,mechanical ,energies of the ,solar ,system4 ,edinb4 ,trans4 vol4 ,,xxi4 part i4 7#ahed71 p4 #fg4 #faj ,,book ,,xi4 ,,electricity4 ,,general ,,remarks4 ,,electricity in the form in which it was originally studied--,franklinic1 frictional1 or statical electricity--has been so completely identified with electricity in its more comprehensive form--,voltaic1 chemical1 or dynamical electricity--that any additions we might have to make to the history of the earlier form of the subject are included in the later science4 ,there are1 however1 several subjects which may still be regarded rather as branches of ,electricity than of the ,cognate ,sciences4 ,such are1 for instance1 ,atmospheric ,electricity1 with all that belongs to ,thunderstorms and ,lightning ,conductors4 ,the observation of ,atmospheric ,electricity has been prosecuted with great zeal at various meteorological observatories2 and especially at the ,observatory established by the ,british ,association at ,kew4 ,the ,aurora ,borealis1 again1 is plainly an electrical phenomenon2 but probably belonging rather to dynamical than to statical electricity4 ,for it strongly affects the magnetic needle1 and its position has reference to the direction of magnetism2 but it has not been observed to affect the electroscope4 ,the general features of this phenomenon have been described by ,m4 de ,humboldt1 and more recently by ,m4 de ,bravais2 and theories of the mode of its production have been propounded by ,,mm4 ,biot1 ,de la ,rive1 ,kaemtz1 and others4 ,again1 there are several fishes which have the power of giving an electrical shock3--the torpedo1 the gymnotus1 and the silurus4 ,the agency of these creatures has been identified with electricity in the most general sense4 ,the peculiar energy of the animal has been made to produce the effects which are produced by an electrical discharge or a voltaic current3--not only to destroy life in small animals1 but to #faa deflect a magnet1 to make a magnet1 to decompose water1 and to produce a spark4 ,dr4 ,faraday's ,views of ,statical ,electric ,induction4 ,according to the theories of electricity of pinus and ,coulomb1 which in this ,book of our ,history are regarded as constituting a main part of the progress of this portion of science1 the particles of the electric fluid or fluids exert forces1 attractive and repulsive1 upon each other in straight lines at a distance1 in the same way in which1 in the ,newtonian theory of the universe1 the particles of matter are conceived as exerting attractive forces upon each other4 ,an electrized body presented a conducting body of any form1 determines a new arrangement of the electric fluids in the conductor1 attracting the like fluid to its own side1 and repelling the opposite fluid to the opposite side4 ,this is ,electrical ,induction4 ,and as1 by the theory1 the attraction is greater at the smaller distances1 the distribution of the fluid upon the conductor in virtue of this ,induction will not be symmetrical1 but will be governed by laws which it will require a complex and difficult calculation to determine--as we have seen was the case in the investigations of ,coulomb1 ,poisson1 and others4 ,instead of this action at a distance4 ,dr4 ,faraday has been led to conceive ,electrical ,induction to be the result of an action taking place between the electrized body and the conductor through lines of contiguous particles in the mass of the intermediate body1 which he calls the ,dielectric4 ,and the irregularities of the distribution of the electricity in these cases of ,induction1 and indeed the existence of an action in points protected from direct action by the protuberant sides of the conductor1 are the causes1 ,i conceive1 which lead him to the conclusion that ,induction takes place in curved lines#ag;,b of such contiguous particles4 ,note #ag;,b3 ,researches1 #aafe1 c4 ,with reference to this1 ,i may remark that1 as ,i have said1 the distribution of electricity on a conductor in the presence of an electrized body is so complex a mathematical problem that ,i do not conceive any merely popular way of regarding the result can entitle us to say1 that the distribution which we find cannot be explained by the ,coulombian theory1 and must force us upon the assumption of an action in curved lines3--which is1 indeed1 itself a theory1 and so vague a one #fab that it requires to be made much more precise before we can say what consequences it does or does not lead to4 ,professor ,w4 ,thomson has arrived at a mathematical proof that the effect of induction on the view of ,coulomb and of ,faraday must1 under certain conditions1 be necessarily and universally the same4 ,with regard to the influence of different ,dielectrics upon ,induction1 the inquiry appears to be of the highest importance2 and may certainly necessitate some addition to the theory4 #fac ,,book ,,xii4 ,,magnetism4 ,recent ,progress of ,terrestrial ,magnetism4 ,,in ,chapter ,,ii41 ,i have noticed the history of ,terrestrial ,magnetism2 ,hansteen's map published in #ahai2 the discovery of magnetic storms about #ahbe2 the chain of associated magnetic observations1 suggested by ,m4 de ,humboldt1 and promoted by the ,british ,association and the ,royal ,society2 the demand for the continuation of these till #ahdh2 the magnetic observations made in several voyages2 the magnetic surveys of various countries4 ,and ,i have spoken also of ,gauss's theory of ,terrestrial ,magnetism1 and his directions and requirements concerning the observations to be made4 ,i may add a few words with regard to the more recent progress of the subject4 ,the magnetic observations made over large portions of the ,earth's surface by various persons1 and on the ,ocean by ,british officers1 have been transmitted to ,woolwich1 where they have been employed by ,general ,sabine in constructing magnetic maps of the ,earth for the year #ahdj4ah;,b ,following the course of inquiry described in the part of the history referred to1 these maps exhibit the declination1 inclination1 and intensity of the magnetic force at every point of the earth's surface4 ,the curves which mark equal amounts of each of these three elements 7the lines of equal declination1 inclination1 and force3--the isogonal1 the isoclinal1 and the isodynamic lines17 are1 in their general form1 complex and irregular2 and it has been made a matter of question 7the facts being agreed upon7 whether it be more proper to say that they indicate four poles1 as ,halley and as ,hansteen said1 or only two poles1 as ,gauss asserts4 ,the matter appears to become more clear if we draw magnetic meridians2 that is1 lines obtained by following the directions1 or pointings1 of the magnetic needle to the north or to #fad the south1 till we arrive at the points of convergence of all their directions2 for there are only two such poles1 one in the ,arctic and one in the ,antarctic region4 ,but in consequence of the irregularity of the magnetic constitution of the earth1 if we follow the inclination of the magnetic force round the earth on any parallel of latitude1 we find that it has two maxima and two minima1 as if there were four magnetic poles4 ,the isodynamic map is a new presentation of the facts of this subject2 the first having been constructed by ,colonel ,sabine in #ahcg4 ,note #ah;,b3 ,these maps are published in ,mr4 ,keith ,johnstone's ,physical ,atlas4 ,i have stated also that the magnetic elements at each place are to be observed in such a manner as to bring into view both their periodical1 their secular1 and their irregular or occasional changes4 ,the observations made at ,toronto in ,canada1 and at ,hobart ,town in ,van ,diemen's ,land1 two stations at equal distances from the two poles of the earth1 and also at ,st ,helena1 a station within the tropics1 have been discussed by ,general ,sabine with great care1 and with an amount of labor approaching to that employed upon reductions of astronomical observations4 ,and the results have been curious and unexpected4 ,the declination was first examined4#ai;,b ,this magnetical element is1 as we have already seen 7p4 #bcb71 liable both to a diurnal and to an annual inequality2 and also to irregular perturbations which have been termed magnetic storms4 ,now it was found that all these inequalities went on increasing gradually and steadily from #ahdc to #ahdh1 so as to become1 at the end of that time1 above twice as large as they were at the beginning of it4 ,a new periodical change in all these elements appeared to be clearly established by this examination4 ,m4 ,lamont1 of ,munich1 had already remarked indications of a decennial period in the diurnal variation of the declination of the needle4 ,the duration of the period from minimum to maximum being about five years1 and therefore the whole period about ten years4 ,the same conclusion was found to follow still more decidedly from the observations of the dip and intensity4 ,note #ai;,b3 ,phil4 ,trans4 #aheb and #ahef4 ,this period of ten years had no familiar meaning in astronomy2 and if none such had been found for it1 its occurrence as a magnetic period must have been regarded1 as ,general ,sabine says1#bj;,b in the light of a fragmentary fact4 ,but it happened about this time that the scientific world was made aware of the existence of a like period in a #fae phenomenon which no one would have guessed to be connected with terrestrial magnetism1 namely1 the spots in the ,sun4 ,m4 ,schwabe1 of ,dessau1 had observed the ,sun's disk with immense perseverance for #bd years3--often examining it more than #cjj days in the year2 and had found that the spots had1 as to their quantity and frequency1 a periodical character4 ,the years of maximum are #ahbh1 #ahch1 #ahdh1 in which there were respectively #bbe1ba;,b #bhb1 #ccj groups of spots4 ,the minimum years1 #ahcc1 #ahdc1 had only #cc and #cd such groups4 ,this curious fact#bb;,b was first made public by ,m4 de ,humboldt1 in the third volume of his ,kosmos 7#ahej74 ,the coincidence of the periods and epochs of these two classes of facts was pointed out by ,general ,sabine in a ,memoir presented to the ,royal ,society in ,march1 #aheb4 ,note #bj;,b3 ,phil4 ,trans4 #ahef1 p4 #chb4 ,note #ba;,b3 ,in #ahcg there were #ccc4 ,note #bb;,b3 ,the observations up to #ahdd were published in ,poggendorf's ,annalen4 ,of course it was natural to suppose1 even before this discovery1 that the diurnal and annual inequalities of the magnetic element at each place depend upon the action of the sun1 in some way or other4 ,dr4 ,faraday had endeavored to point out how the effect of the solar heat upon the atmosphere would1 according to the known relations of heat and magnetism1 explain many of the phenomena4 ,but this new feature of the phenomena1 their quinquennial increase and decrease1 makes us doubt whether such an explanation can really be the true one4 ,of the secular changes in the magnetic elements1 not much more is known than was known some years ago4 ,these changes go on1 but their laws are imperfectly known1 and their causes not even conjectured4 ,m4 ,hansteen1 in a recent memoir1#bc;,b says that the decrease of the inclination goes on progressively diminishing4 ,with us this rate of decrease appears to be at present nearly uniform4 ,we cannot help conjecturing that the sun1 which has so plain a connexion with the diurnal1 annual1 and occasional movements of the needle1 must also have some connexion with its secular movements4 ,note #bc;,b3 ,see ,k4 ,johnstone's ,physical ,atlas4 ,in #ahdj the observations made at various places had to a great extent enabled ,gauss1 in connexion with ,w4 ,weber1 to apply his ,theory to the actual condition of the ,earth2#bd;,b and he calculated the ,declination1 ,inclination1 and ,intensity at above #ajj places1 and found #faf the agreement1 as he says1 far beyond his hopes4 ,they show1 he says1 that the ,theory comes near to the ,truth4 ,note #bd;,b3 ,atlas des ,erdmagnetismus nach den ,elementen der ,theorie ,entworfen4 ,see ,preface4 ,correction of ,ship's ,compasses4 ,the magnetic needle had become of importance when it was found that it always pointed to the ,north4 ,since that time the history of magnetism has had its events reflected in the history of navigation4 ,the change of the declination arising from a change of place terrified the companions of ,columbus4 ,the determination of the laws of this change was the object of the voyage of ,halley2 and has been pursued with the utmost energy in the ,arctic and ,antarctic regions by navigators up to the present time4 ,probably the dependence of the magnetic declination upon place is now known well enough for the purposes of navigation4 ,but a new source of difficulty has in the meantime come into view2 the effect of the iron in the ship upon the ,compass4 ,and this has gone on increasing as guns1 cables1 stays1 knees1 have been made of iron2 then steam-engines with funnels1 wheels1 and screws1 have been added2 and finally the whole ship has been made of iron4 ,how can the compass be trusted in such cases8 ,i have already said in the history that ,mr4 ,barlow proposed to correct the error of the compass by placing near to the compass an iron plate1 which from its proximity to the compass might counterbalance magnetically the whole effect of the ship's iron upon the compass4 ,this correction was not effectual1 because the magnetic forces of the plate and of the ship do not change their direction and value according to the same law1 with the change of position4 ,i have further stated that ,mr4 ,airy devised other means of correcting the error4 ,i may add a few words on the subject2 for the subject has been further examined by ,mr4 ,airy#be;,b and by others4 ,note #be;,b3 ,phil4 ,trans4 #ahef4 ,it appears1 by mathematical reasoning1 that the magnetic effect of the iron in a ship may be regarded as producing two kinds of deviation which are added together2--a polar-magnet deviation1 which changes from positive to negative as the direction of the ship's keel1 in a horizontal revolution1 passes from semicircle to semicircle2 and a quadrantal deviation1 which changes from positive to negative as the keel turns from quadrant to quadrant4 ,the latter deviation may be remedied completely by a mass of unmagnetized iron placed on a level #fag with the compass1 either in the athwartship line or in the fore-and-aft line1 according to circumstances4 ,the polar-magnet-deviation may be corrected at any given place by a magnet or magnets1 but the magnets thus applied at one place will not always correct the deviation in another magnetic latitude4 ,for it appears that this deviation arises partly from a magnetism inherent in the materials of the ship1 not changing with the change of magnetic position1 and partly from the effect of terrestrial magnetism upon the ship's iron4 ,but the errors arising from both sources may be remedied by adjusting1 at a new locality1 the positions of the corrective magnets4 ,the inherent magnetism of the ship1 of which ,i have spoken1 may be much affected by the position in which the ship was built2 and may change from time to time2 for instance1 by the effect of the battering of the waves1 and other causes4 ,hence it is called by ,mr4 ,airy sub-permanent magnetism4 ,another method of correcting the errors of a ship's compass has been proposed1 and is used to some extent2 namely1 by swinging the ship round 7in harbor7 to all points of azimuth1 and thus constructing a ,table of ,compass ,errors for that particular ship4 ,but to this method it is objected that the ,table loses its value in a new magnetic latitude much more than the correction by magnets does2 besides the inconveniences of steering a ship by a ,table4 #fah ,,book ,,xiii4 ,,voltaic ,,electricity4 ,,chapter ,,vii4 ,,magneto-,,electric ,,induction4 ,,faraday',s discovery that1 in combinations like those in which a voltaic current was known to produce motion1 motion would produce a voltaic current1 naturally excited great attention among the scientific men of ,europe4 ,the general nature of his discovery was communicated by letter#bf;,b to ,m4 ,hachette at ,paris1 in ,december1 #ahca2 and experiments having the like results were forthwith made by ,,mm4 ,becquerel and ,ampre at ,paris1 and ,,mm4 ,nobili and ,antinori at ,florence4 ,note #bf;,b3 ,ann4 de ,chimie1 vol4 xlviii4 7#ahca71 p4 #djb4 ,it was natural also that in a case in which the relations of space which determine the results are so complicated1 different philosophers should look at them in different ways4 ,there had been1 from the first discovery by ,oersted of the effect of a voltaic current upon a magnet1 two rival methods of regarding the facts4 ,electric and magnetic lines exert an effort to place themselves transverse to each other 7see chapter iv4 of this ,book71 and 7as ,i have already said7 two ways offered themselves of simplifying this general truth3--to suppose an electric current made up of transverse magnetic lines2 or to suppose magnetic lines made up of transverse electric currents4 ,on either of these assumptions1 the result was expressed by saying that like currents or lines 7electric or magnetic7 tend to place themselves parallel2 which is a law more generally intelligible than the law of transverse position4 ,faraday had adopted the former view2 had taken the lines of magnetic force for the fundamental lines of his system1 and defined the direction of the magneto-electric current of induction by the relation #fai of the motion to these lines4 ,ampre1 on the other hand1 supposed the magnet to be made up of transverse electric currents 7chap4 vi472 and had deduced all the facts of electro-dynamical action1 with great felicity1 from this conception4 ,the question naturally arose1 in what manner1 on this view1 were the new facts of magneto-electric induction by motion to be explained1 or even expressed8 ,various philosophers attempted to answer this question4 ,perhaps the form in which the answer has obtained most general acceptance is that in which it was put by ,lenz1 who discoursed on the subject to the ,academy of ,st4 ,petersburg in #ahcc4bg;,b ,his general rule is to this effect3 when a wire moves in the neighborhood of an electric current or a magnet1 a current takes place in it1 such as1 existing independently1 would have produced a motion opposite to the actual motion4 ,thus two parallel forward currents move towards each other3--hence if a current move towards a parallel wire1 it produces in it a backward current4 ,a moveable wire conducting a current downwards will move round the north pole of a magnet in the direction ,n41 ,w41 ,s41 ,e43--hence if1 when the wire have in it no current1 we move it in the direction ,n41 ,w41 ,s41 ,e41 we produce in the wire an upward current4 ,and thus1 as ,m4 de la ,rive remarks1#bh;,b in cases in which the mutual action of two currents produces a limited motion1 as attraction or repulsion1 or a deviation right or left1 the corresponding magneto-electric induction produces an instantaneous current only2 but when the electrodynamic action produces a continued motion1 the corresponding motion produces1 by induction1 a continued current4 ,note #bg;,b3 ,acad4 ,petrop4 ,nov4 #bi1 #ahcc4 ,pogg4 ,ann4 vol4 xxxi4 p4 #dhc4 ,note #bh;,b3 ,trait de l',electricit1 vol4 i4 p4 #dda 7#ahed74 ,looking at this mode of stating the law1 it is impossible not to regard this effect as a sort of reaction2 and accordingly1 this view was at once taken of it4 ,professor ,ritchie said1 in #ahcc1 ,the law is founded on the universal principle that action and reaction are equal4 ,thus1 if voltaic electricity induce magnetism under certain arrangements1 magnetism will1 by similar arrangements1 react on a conductor and induce voltaic electricity4#bi;,b ,note #bi;,b3 ,on the ,reduction of ,mr4 ,faraday's discoveries in ,magneto-electric ,induction to a ,general ,law4 ,trans4 of ,r4 ,s4 in ,phil4 ,mag4 ,n4,s4 vol4 iii4 #cg1 and vol4 iv4 p4 #aa4 ,in the second edition of this history ,i used the like expressions4 ,there are still other ways of looking at this matter4 ,i have elsewhere pointed out that where polar properties co-exist1 they are #fbj generally found to be connected1#cj;,b and have illustrated this law in the case of electrical1 magnetical1 and chemical polarities4 ,if we regard motion backwards and forwards1 to the right and the left1 and the like1 as polar relations1 we see that magneto-electric induction gives us a new manifestation of connected polarities4 ,note #cj;,b3 ,phil4 ,ind4 ,sc4 ,b4 v4 c4 ii4 ,diamagnetic ,polarity4 ,but the manifestation of co-existent polarities which are brought into view in this most curious department of nature is not yet exhausted by those which we have described4 ,i have already spoken 7chap4 9999vii47 of ,dr4 ,faraday's discovery that there are diamagnetic as well as magnetic bodies2 bodies which are repelled by the pole of a magnet1 as well as bodies which are attracted4 ,here is a new opposition of properties4 ,what is the exact definition of this opposition in connexion with other polarities8 ,to this1 at present1 different philosophers give different answers4 ,some say that diamagnetism is completely the opposite of ordinary magnetism1 or1 as ,dr4 ,faraday has termed it for the sake of distinction1 of paramagnetism4 ,they say that as a north pole of a magnet gives to the neighboring extremity of a piece of soft iron a south pole1 so it gives to the neighboring extremity of a piece of bismuth a north pole1 and that the bismuth becomes for a time an inverted magnet2 and hence1 arranges itself across the line of magnetised force1 instead of along it4 ,dr4 ,faraday himself at first adopted this view2#ca;,b but he now conceives that the bismuth is not made polar1 but is simply repelled by the magnet2 and that the transverse position which it assumes1 arises merely from its elongated form1 each end trying to recede as far as possible from the repulsive pole of the magnet4 ,note #ca;,b3 ,faraday's ,researches1 ,art4 #bdbi1 #bdcj4 ,several philosophers of great eminence1 however1 who have examined the subject with great care1 adhere to ,dr4 ,faraday's first view of the nature of ,diamagnetism--as ,w4 ,weber1#cb;,b ,plcker1 and ,mr4 ,tyndall among ourselves4 ,if we translate this view into the language of ,ampre's theory1 it comes to this3--that as currents are induced in iron and magnetics parallel to those existing in the inducing magnet or battery wire2 so in bismuth1 heavy glass1 and other diamagnetic bodies1 the currents induced are in the contrary #fba directions3--these hypothetical currents being in non-conducting diamagnetic1 as in magnetic bodies1 not in the mass1 but round the particles of the matter4 ,note #cb;,b3 ,poggendorf's ,ann4 ,jou4 #ahdh4 ,magneto-optic ,effects and ,magnecrystallic ,polarity4 ,not even yet have we terminated the enumeration of the co-existent polarities which in this province of nature have been brought into view4 ,light has polar properties2 the very term polarization is the record of the discovery of these4 ,the forces which determine the crystalline forms of bodies are of a polar nature3 crystalline forms1 when complete1 may be defined as those forms which have a certain degree of symmetry in reference to opposite poles4 ,now has this optical and crystalline polarity any relation to the electrical polarity of which we have been speaking8 ,however much we might be disposed beforehand to conjecture that there is some relation between these two groups of polar properties1 yet in this as in the other parts of this history of discoveries respecting polarities1 no conjecture hits the nature of the relation1 such as experiment showed it to be4 ,in ,november1 #ahdf1 ,faraday announced the discovery of what he then called the action of magnets on light4 ,but this action was manifested1 not on light directly1 but on light passing through certain kinds of glass4#cc;,b ,when this glass1 subjected to the action of the powerful magnets which he used1 transmitted a ray of light parallel to the line of magnetic force1 an effect was produced upon the light4 ,but of what nature was this effect8 ,when light was ordinary light1 no change in its condition was discoverable4 ,but if the light were light polarized in any plane1 the plane of polarization was turned round through a certain angle while the ray passed through the glass3--a greater angle1 in proportion as the magnetic force was greater1 and the thickness of the glass greater4 ,note #cc;,b3 ,silicated borate of lead4 ,see ,researches1 #baea1 c4 ,also flint glass1 rock salt1 water 7#bbae74 ,a power in some respects of this kind1 namely1 a power to rotate the plane of polarization of a ray passing through them1 is possessed by some bodies in their natural state2 for instance1 quartz crystals1 and oil of turpentine4 ,but yet1 as ,dr4 ,faraday remarks1#cd;,b there is a great difference in the two cases4 ,when polarized rays pass through oil of turpentine1 in whatever direction they pass1 they all of them have their #fbb plane of polarization rotated in the same direction2 that is1 all to the right or all to the left2 but when a ray passes through the heavy glass1 the power of rotation exists only in a plane perpendicular to the magnetic line1 and its direction as right or left-handed is reversed by reversing the magnetic polarity4 ,note #cd;,b3 ,researches1 ,art4 #bbca4 ,in this case1 we have optical properties1 which do not depend on crystalline form1 affected by the magnetic force4 ,but it has also been found that crystalline form1 which is so fertile a source of optical properties1 affords indications of magnetic forces4 ,in #ahdg1 ,m4 ,plcker1#ce;,b of the ,university of ,bonn1 using a powerful magnetic apparatus1 similar to ,faraday's1 found that crystals in general are magnetic1 in this sense1 that the axes of crystalline form tend to assume a certain position with reference to the magnetic lines of force4 ,the possession of one optic axis or of two is one of the broad distinctions of the different crystalline forms3 and using this distinction1 ,m4 ,plcker found that a crystal having a single optic axis tends to place itself with this axis transverse to the magnetic line of force1 as if its optic axis were repelled by each magnetic pole2 and crystals with two axes act as if each of these axes were repelled by the magnetic poles4 ,this force is independent of the magnetic or diamagnetic character of the crystal2 and is a directive1 more properly than an attractive or repulsive force4 ,note #ce;,b3 ,taylor's ,scientific ,memoirs1 vol4 v4 ,soon afterwards 7in #ahdh7 ,faraday also discovered#cf;,b an effect of magnetism depending on crystalline form1 which at first sight appeared to be different from the effects observed by ,m4 ,plcker4 ,he found that a crystal of bismuth1 of which the form is nearly a cube1 but more truly a rhombohedron with one diagonal a little longer than the others1 tends to place itself with this diagonal in the direction of the lines of magnetic force4 ,at first he conceived#cg;,b the properties thus detected to be different from those observed by ,m4 ,plcker2 since in this case the force of a crystalline axis is axial1 whereas in those1 it was equatorial4 ,but a further consideration of the subject1 led him#ch;,b to a conviction that these forces must be fundamentally identical3 for it was easy to conceive a combination of bismuth crystals which would behave in the magnetic field as a crystal of calcspar does2 or a combination of calcspar crystals which would behave as a crystal of bismuth does4 ,note #cf;,b3 ,researches1 ,art4 #bded1 c4 ,note #cg;,b3 ,art4 #bdfi4 ,note #ch;,b3 ,art #beic1 #bfja4 ,and thus we have fresh examples to show that the ,connexion of coexistent ,polarities is a thought deeply seated in the minds of the #fbc profoundest and most sagacious philosophers1 and perpetually verified and illustrated1 by unforeseen discoveries in unguessed forms1 through the labors of the most skilful experimenters4 ,magneto-electric ,machines4 ,the discovery that a voltaic wire moved in presence of a magnet1 has a current generated in it1 was employed as the ground of the construction of machines to produce electrical effects4 ,in ,saxton's machine two coils of wire including a core of soft iron revolved opposite to the ends of a horseshoe magnet1 and thus1 as the two coils came opposite to the ,n4 and ,s4 and to the ,s4 and ,n4 poles of the magnet1 currents were generated alternately in the wires in opposite directions4 ,but by arranging the connexions of the ends of the wires1 the successive currents might be made to pass in corresponding directions4 ,the alternations or successions of currents in such machines are governed by a contrivance which alternately interrupts and permits the action2 this contrivance has been called a rheotome4 ,clarke gave a new form to a machine of the same nature as ,saxton's4 ,but the like effect may be produced by using an electro-magnet instead of a common magnet4 ,when this is done1 a current is produced which by induction produces a current in another wire1 and the action is alternately excited and interrupted4 ,when the inducing current is interrupted1 a momentary current in an opposite direction is produced in the induced wire2 and when this current stops1 it produces in the inducing wire a current in the original direction1 which may be adjusted so as to reinforce the resumed action of the original current4 ,this was pointed out by ,m4 ,de la ,rive in #ahdc4ci;,b ,machines have been constructed on such principles by him and others4 ,of such machines the most powerful hitherto known is that constructed by ,m4 ,ruhmkorff4 ,the effects of this instrument are exceedingly energetic4 ,note #ci;,b3 ,trait de l',elect4 i4 #cia4 ,applications of ,electrodynamic ,discoveries4 ,the great series of discoveries of which ,i have had to speak have been applied in many important ways to the uses of life4 ,the ,electric ,telegraph is one of the most remarkable of these4 ,by wires extended to the most distant places1 the electric current is transmitted #fbd thither in an imperceptible time2 and by means of well-devised systems of operation1 is made to convey from man to man words1 which are now most emphatically winged words4 ,in the most civilised states such wires now form a net-work across the land1 which is familiar to our thoughts as the highway is to our feet2 and wide seas have such pathways of human thought buried deep in their waves from shore to shore4 ,again1 by using the chemical effects of electrodynamic action1 of which we shall have to speak in the next ,book1 a new means has been obtained of copying1 with an exactness unattainable before1 any forms which art or nature has produced1 and of covering them with a surface of metal4 ,the ,electrotype ,process is now one of the great powers which manufacturing art employs4 ,but these discoveries have also been employed in explaining natural phenomena1 the causes of which had before been altogether inscrutable4 ,this is the case with regard to the diurnal variation of the magnetic needle2 a fact which as to its existence is universal in all places1 and which yet is so curiously diverse in its course at different places4 ,dr4 ,faraday has shown that some of the most remarkable of these diversities1 and probably all1 seem to be accounted for by the different magnetic effects of air at different temperatures3 although1 as ,i have already said1 99997,book xii47 the discovery of a decennial period in the diurnal changes of magnetic declination shows that any explanation of those changes which refers them to causes existing in the atmosphere must be very incomplete4#dj;,b ,note #dj;,b3 ,researches1 ,art4 #bhib4 #fbe ,,book ,,xiv4 ,,chemistry4 ,,chapter ,,ix4 ,,the ,,electro-,,chemical ,,theory4 ,,among the consequences of the ,electro-chemical ,theory1 must be ranged the various improvements which have been made in the voltaic battery4 ,daniel introduced between the two metals a partition permeable by chemical action1 but such as to allow of two different acid solutions being in contact with the two metals4 ,mr4 ,grove's battery1 in which the partition is of porous porcelain1 and the metals are platinum and amalgamated zinc1 is one of the most powerful hitherto known4 ,another has been constructed by ,dr4 ,callan1 in which the negative or conducting plate is a cylinder of cast iron1 and the positive element a cylinder of amalgamated zinc placed in a porous cell4 ,this also has great energy4 ,the ,number of ,elementary ,substances4 ,there have not been1 ,i believe1 any well-established additions to the list of the simple substances recognized by chemists4 ,indeed the tendency at present appears to be rather to deny the separate elementary character of some already announced as such substances4 ,pelopium and ,niobium were1 as ,i have said1 two of the new metals4 ,but ,naumann1 in his ,elemente der ,mineralogie 7#dth ed4 #ahee71 says1 in a foot note 7page #be73 ,pelopium is happily again got rid of2 for ,pelopic ,acid and ,niobic ,acid possess the same ,radical4 ,donarium had a still shorter existence4 ,in the same way1 when ,hermann imagined that he had discovered a new simple metallic substance in the mineral ,samarskite from ,miask1 the discovery was disproved by ,h4 ,rose 7,pogg4 ,ann4 ,b4 #gc1 s4 #ddi74 #fbf ,in general the insulation of the new simple substances1 the metallic bases of the earths1 and the like1--their separation from their combinations1 and the exhibition of them in a metallic form--has been a difficult chemical process1 and has rarely been executed on any considerable scale4 ,but in the case of ,aluminium1 the basis of the earth ,alumina1 the process of its extraction has recently been so much facilitated1 that the metal can be produced in abundance4 ,this being the case1 it will probably soon be applied to special economical uses1 for which it is fitted by possessing special properties4 #fbf ,,book ,,xv4 ,,mineralogy4 ,,by the kindness of ,w4 ,h4 ,miller1 ,esq41 ,professor of ,mineralogy in the ,university of ,cambridge1 ,i am able to add to this part the following notices of books and memoirs4 #a4 ,crystallography4 ,elemente der ,krystallographie1 nebst einer tabellarischen ,uebersicht der ,mineralien nach der ,krystallformen1 von ,gustav ,rose4 #b4 ,auflage4 ,berlin1 #ahch4 ,the crystallographic method here adopted is1 for the most part1 that of ,weiss4 ,the method of this work has been followed in ,a ,system of ,crystallography1 with its ,applications to ,mineralogy4 ,by ,john ,joseph ,griffin4 ,glasgow1 #ahda4 ,mr4 ,griffin has1 however1 modified the notation of ,rose4 ,he has constructed a series of models of crystalline forms4 ,frankenheim's ,system der ,krystalle4 #ahdb4 ,this work adopts nearly the ,mohsian systems of crystallization4 ,it contains ,tables of the chemical constitution1 inclinations of the axis1 and magnitude of the axes of all the crystals of which a description was to be found1 including those formed in the laboratory1 as well as those usually called minerals2 #gac in all4 ,fr4 ,aug4 ,quenstedt1 ,methode der ,krystallographie1 #ahdj1 employs a fanciful method of representing a crystal by projecting upon one face of the crystal all the other faces4 ,this invention appears to be more curious than useful4 ,dr4 ,karl ,naumann1 who is spoken of in ,chap4 ix4 of this ,book1 as the author of the best of the ,mixed ,systems of ,classification1 published also ,grundriss der ,krystallographie1 ,leipzig1 #ahbf4 ,in this and other works he modifies the notation of ,mohs in a very advantageous manner4 #fbh ,professor ,dana1 in his ,system of ,mineralogy1 ,new ,haven 7,u4,s471 #ahcg1 follows ,naumann for the most part1 both in crystallography and in mineral classification4 ,in the latter part of the subject1 he has made the attempt1 which in all cases is a source of confusion and of failure1 to introduce a whole system of new names of the members of his classification4 ,the geometry of crystallography has been investigated in a very original manner by ,m4 ,bravais1 in papers published in the ,journal of the ,ecole ,polytechnique1 entitled ,mmoires sur les ,systmes forms par des ,points4 #ahej4 ,etudes ,crystallographiques4 #ahea4 ,hermann ,kopp 7,einleitung in die ,krystallographie1 ,braunschweig4 #ahdi7 has given the description and measurement of the angles of a large number of laboratory crystals4 ,rammelsberg 7,krystallographische ,chemie1 ,berlin1 #ahee7 has collected an account of the systems1 simple forms and angles of all the laboratory crystals of which he could obtain descriptions4 ,schabus of ,vienna 7,bestimmung der ,krystallgestalten 9999in ,chemischen ,laboratorien erzeugten ,producte1 ,wien1 #ahee2 a successful ,prize ,essay7 has given a description1 accompanied by measurements1 of #ij crystalline species from his own observations4 ,to these attempts made in other countries to simplify and improve crystallography1 ,i may add a remarkable ,essay very recently made here by ,mr4 ,brooke1 and suggested to him by his exact and familiar knowledge of ,mineralogy4 ,it is to this effect4 ,all the crystalline forms of any given mineral species are derived from the primitive form of that species2 and the degree of symmetry1 and the parameters1 of this form determine the angles of all derivative forms4 ,but how is this primitive form selected and its parameters determined8 ,the selection of the kind of the primitive form depends upon the degree of symmetry which appears in all the derivative forms2 according to which they belong to the rhombohedral1 prismatic1 square pyramidal1 or some other system3 and this determination is commonly clear4 ,but the parameters1 or the angles1 of the primitive form1 are commonly determined by the cleavage of the mineral4 ,is this a sufficient and necessary ground of such determination8 ,may not a simplification be effected1 in some cases1 by taking some other parameters8 by taking a primitive form which belongs to the proper system1 but which has some other angles than those given by cleavage8 ,mr4 ,brooke has tried whether1 for instance1 crystals of the rhombohedral system may not be referred with advantage to primitive rhombohedrons which have1 in all #fbi the species1 nearly the same angles4 ,the advantage to be obtained by such a change would be the simplification of the laws of derivation in the derivative forms3 and therefore we have to ask1 whether the indices of derivation are smaller numbers in this way or with the hitherto accepted fundamental angles4 ,it appears to me1 from the examples given1 that the advantage of simplicity in the indices is on the side of the old system3 but whether this be so or not1 it was a great benefit to crystallography to have the two methods compared4 ,mr4 ,brooke's ,essay is a ,memoir presented to the ,royal ,society in #ahef4 #b4 ,optical ,properties of ,minerals4 ,the ,handbuch der ,optik1 von ,f4 ,w4 ,g4 ,radicke1 ,berlin1 #ahci1 contains a chapter on the optical properties of crystals4 ,the author's chief authority is ,sir ,d4 ,brewster1 as might be expected4 ,m4 ,haidinger has devoted much attention to experiments on the pleochroism of minerals4 ,he has invented an instrument which makes the dichroism of minerals more evident by exhibiting the two colors side by side4 ,the pleochroism of minerals1 and especially the remarkable clouds that in the cases of ,iolite1 ,andalusite1 ,augite1 ,epidote1 and ,axinite1 border the positions of either optical axis1 have been most successfully imitated by ,m4 de ,senarmont by means of artificial crystallizations4 7,ann4 de ,chim4 #c ,ser4 xli4 p4 #cai47 ,m4 ,pasteur has found that ,racemic ,acid consists of two different acids1 having the same density and composition4 ,the salts of these acids1 with bases of ,ammonia and of ,potassa1 are hemihedral1 the hemihedral faces which occur in the one being wanting in the other4 ,the acids of these different crystals have circular polarization of opposite kinds4 7,ann4 de ,chim4 #c ,ser4 xxviii4 #ef1 #ii47 ,this discovery was marked by the assignation of the ,rumford ,medal to ,m4 ,pasteur in #ahef4 ,m4 ,marbach has discovered that crystals of chlorate of soda1 which apparently belongs to the cubic or tessular system1 exhibit hemihedral faces of a peculiar character2 and that the crystals have circular polarization of opposite kinds in accordance with the differences of the plagihedral faces4 7,poggendorf's ,annalen1 xci4 #dhb47 ,m4 ,seybolt of ,vienna has found a means of detecting plagihedral faces in quartz crystals which do not reveal them externally4 7,akad4 d4 ,wissenschaft zu ,wien1 ,b4 xv4 s4 #ei47 #fcj #c4 ,classification of ,minerals4 ,in the ,philosophy of the ,inductive ,sciences1 ,b4 ,,viii4 ,c4 iii41 ,i have treated of the ,application of the ,natural-history ,method of ,classification to ,mineralogy1 and have spoken of the ,systems of this kind which have been proposed4 ,i have there especially discussed the system proposed in the treatise of ,m4 ,necker1 ,le ,rgne ,minral ramen aux ,mthodes d',histoire ,naturelle 7,paris1 #ahce74 ,more recently have been published ,m4 ,beudant's ,cours lmentaire d',histoire ,naturelle1 ,minralogie 7,paris1 #ahda72 and ,m4 ,a4 ,dufresnoy's ,trait de ,minralogie 7,paris1 #ahde74 ,both these works are so far governed by mere chemical views that they lapse into the inconveniences and defects which are avoided in the best systems of ,german mineralogists4 ,the last mineral system of ,berzelius has been developed by ,m4 ,rammelsberg 7,nrnberg1 #ahdg74 ,it is in principle such as we have described it in the history4 ,m4 9999,nordenskild's system 7#crd ,ed4 #ahdi17 has been criticised by ,g4 ,rose1 who observes that it removes the defects of the system of ,berzelius only in part4 ,he himself proposes what he calls a ,krystallo-,chemisches ,system1 in which the crystalline form determines the genus and the chemical composition the species4 ,his classes are-- #a4 ,simple ,substances4 #b4 ,combinations of ,sulphur1 ,selenium1 ,titanium1 ,arsenic1 ,antimony4 #c4 ,chlorides1 ,fluorides1 ,bromides1 ,iodides4 #d4 ,combinations with ,oxygen4 ,we have already said that for us1 all chemical compounds are minerals1 in so far that they are included in our classifications4 ,the propriety of this mode of dealing with the subject is confirmed by our finding that there is really no tenable distinction between native minerals and the products of the laboratory4 ,a great number of eminent chemists have been employed in producing1 by artificial means1 crystals which had before been known only as native products4 #fca ,,book ,,xvi4 ,,classificatory ,,sciences4 ,,botany4 ,,for the purpose of giving to my reader some indication of the present tendency of ,botanical ,science1 ,i conceive that ,i cannot do better than direct his attention to the reflections1 procedure1 and reasonings which have been suggested by the most recent extensions of man's knowledge of the vegetable world4 ,and as a specimen of these1 ,i may take the labors of ,dr4 ,joseph ,hooker1 on the ,flora of the ,antarctic ,regions1#da;,b and especially of ,new ,zealand4 ,dr4 ,hooker was the ,botanist to an expedition commanded by ,sir ,james ,ross1 sent out mainly for the purpose of investigating the phenomena of ,terrestrial ,magnetism near the ,south ,pole2 but directed also to the improvement of ,natural ,history4 ,the extension of botanical descriptions and classifications to a large mass of new objects necessarily suggests wider views of the value of classes 7genera1 species1 c417 and the conclusions to be drawn from their constancy or inconstancy4 ,a few of ,dr4 ,hooker's remarks may show the nature of the views taken under such circumstances4 ,note #da;,b3 ,the ,botany of the ,antarctic ,voyage of ,h4 ,m4 ,discovery ,ships ,erebus and ,terror1 in the years #ahci-dj4 ,published #ahdg4 ,flora ,nov ,zelandi4 #ahec4 ,i may notice1 in the first place1 7since this work is intended for general rather than for scientific readers17 ,dr4 ,hooker's testimony to the value of a technical descriptive language for a classificatory science--a ,terminology1 as it is called4 ,he says1 ,it is impossible to write ,botanical descriptions which a person ignorant of ,botany can understand1 although it is supposed by many unacquainted with science that this can and should be done4 ,and hence1 he says1 the state of botanical science demands ,latin descriptions of the plants2 and this is a lesson which he especially urges upon the ,colonists who study the indigenous plants4 #fcb ,dr4 ,hooker's remarks on the limits of species1 their dispersion and variation1 are striking and instructive4 ,he is of opinion that species vary more1 and are more widely diffused1 than is usually supposed4 ,hence he conceives that the number of species has been needlessly and erroneously multiplied1 by distinguishing the specimens which occur in different places1 and vary in unessential features4 ,he says that though1 according to the lowest estimate of compilers1 #ajj1jjj is the commonly received number of known plants1 he thinks that half that number is much nearer the truth4 ,this1 he says1 may be well conceived1 when it is notorious that nineteen species have been made of the ,common ,potatoe1 and many more of ,solanum nigrum alone4 ,pteris aquilina has given rise to numerous book species2 ,vernonia cinerea of ,india to fifteen at least4 4 4 4 4 4 4 ,many more plants are common to most countries than is supposed2 ,i have found #fj ,new ,zealand flowering plants and #i ,ferns to be ,european ones1 besides inhabiting numerous intermediate countries4 4 4 4 4 4 ,so long ago as #ahad1 ,mr4 ,brown drew attention to the importance of such considerations1 and gave a list of #aej ,european plants common to ,australia4 ,as an example of the extent to which unessential differences may go1 he says 7p4 xvii417 ,the few remaining native ,cedars of ,lebanon may be abnormal states of the tree which was once spread over the whole of the ,lebanon2 for there are now growing in ,england varieties of it which have no existence in a wild state4 ,some of them closely resemble the ,cedars of ,atlas and of the ,himalayas 7,deodar27 and the absence of any valid botanical differences tends to prove that all1 though generally supposed to be different species1 are one4 ,still the great majority of the species of plants in those ,southern regions are peculiar4 ,there are upwards of #ajj genera1 subgenera1 or other well marked groups of plants1 entirely or nearly confined to ,new ,zealand1 ,australia1 and extra-tropical ,south ,america4 ,they are represented by one or more species in two or more of those countries1 and thus effect a botanical relationship or affinity between them all which every botanist appreciates4 ,in reference to the ,history of ,botany1 ,i have received corrections and remarks from ,dr4 ,hooker1 with which ,i am allowed to enrich my pages4 ,p4 #cei4 ,note #c4 ,note #caf ,nelumbium speciosum1 the ,lotus of ,india4 ,the ,nelumbium does not float1 but raises both leaf and flower several feet above the water3 the ,nympha ,lotus has floating leaves4 ,both enter largely into the symbolism of the ,hindoos1 and are often confounded4 #fcc ,p4 #cfb4 ,note #e4 ,note #acaf ,for ,arachnis read ,arachis4 ,the ,arachidna of ,theophrastus cannot1 however1 be the ,arachis or ground-nut4 ,pp4 #chh and #cid4 ,for ,harlecamp read ,hartecamp4 ,p4 #cid4 ,for ,kerlen read ,kalm4 ,p4 #cid4 ,for ,asbech read ,osbeck4 ,p4 #chf4 ,john ,ray4 ,ray was further the author of the present ,natural ,system in its most comprehensive sense4 ,he first divided plants into ,flowerless and ,flowering2 and the latter into ,monocotyledonous and ,dicotyledonous3--',floriferas dividemus in ,,dicotyledones1 quarum semina sata binis foliis1 seminalibus dictis1 qu cotyledonorum usum prstant1 e terra exeunt1 vel in binos saltem lobos dividuntur1 quamvis eos supra terram foliorum specie non efferant2 et ,,monocotyledones1 qu nec folia bina seminalia efferunt nec lobos binos condunt4 ,hc divisio ad arbores etiam extendi potest2 siquidem ,palm et congeneres hoc respectu eodem modo a reliquis arboribus differunt quo ,monocotyledones a reliquis herbis4' ,p4 #djh4 ,endogenous and ,exogenous ,growth4 ,the exact course of the wood fibres which traverse the stems of both ,monocotyledonous and ,dicotyledonous plants has been only lately discovered4 ,in the ,monocotyledons1 those fibres are collected in bundles1 which follow a very peculiar course3--from the base of each leaf they may be followed downwards and inwards1 towards the axis of the trunk1 when they form an arch with the convexity to the centre2 and curving outwards again reach the circumference1 where they are lost amongst the previously deposited fibres4 ,the intrusion of the bases of these bundles amongst those already deposited1 causes the circumference of the stem to be harder than the centre2 and as all these arcs have a short course 7their chords being nearly equal71 the trunk does not increase in girth1 and grows at the apex only4 ,the wood-bundles are here definite4 ,in the ,dicotyledonous trunks1 the layers of wood run in parallel courses from the base to the top of the trunk1 each externally to that last formed1 and the trunk increases both in height and girth2 the wood-bundles are here indefinite4 ,with regard to the ,cotyledons1 though it is often difficult to distinguish a ,monocotyledonous ,embryo from a ,dicotyledonous1 they may always be discriminated when germinating4 ,the ,cotyledons1 when two or more1 and primordial leaves 7when no ,cotyledons are visible7 of a ,monocotyledon1 are alternate2 those of a ,dicotyledon are opposite4 ,a further physiological distinction between ,monocotyledons and #fcd ,dicotyledons is observed in germination1 when the ,dicotyledonous radicle elongates and forms the root of the young plant2 the ,monocotyledonous radicle does not elongate1 but pushes out rootlets from itself at once4 ,hence the not very good terms1 exorhizal for ,dicotyledonous1 and endorhizal for ,monocotyledonous4 ,the highest physiological generalization in the vegetable kingdom is between ,phnogama and ,cryptogama4 ,in the former1 fertilization is effected by a pollen-tube touching the nucleus of an ovule2 in ,cryptogams1 the same process is effected by the contact of a sperm-cell1 usually ciliated 7antherozoid71 upon another kind of cell called a germ-cell4 ,in ,phnogams1 further1 the organs of fructification are all modified leaves2 those of ,cryptogams are not homologous4 7,j4 ,d4 ,h47 ,,zoology4 ,i have exemplified the considerations which govern zoological classification by quoting the reflexions which ,cuvier gives us1 as having led him to his own classification of ,fishes4 ,since the varieties of ,quadrupeds1 or ,mammals 7omitting whales1 c471 are more familiar to the common reader than those of ,fishes1 ,i may notice some of the steps in their classification2 the more so as some curious questions have recently arisen thereupon4 ,linnus first divides ,mammals into two groups1 as they have ,claws1 or ,hoofs 7unguiculata1 ungulata47 ,but he then again divides them into six orders 7omitting whales1 c471 according to their number of incisor1 laniary1 and molar teeth2 namely3-- ,primates4 7,man1 ,monkey1 c47 ,bruta4 7,rhinoceros1 ,elephant1 c47 ,fer4 7,dog1 ,cat1 ,bear1 ,mole1 c47 ,glires4 7,mouse1 ,squirrel1 ,hare1 c47 ,pecora4 7,camel1 ,giraffe1 ,stag1 ,goat1 ,sheep1 ,ox1 c47 ,bellu4 7,horse1 ,hippopotamus1 ,tapir1 ,sow1 c47 ,in the place of these1 ,cuvier1 as ,i have stated in the ,philosophy 7,on the ,language of ,sciences1 ,aphorism xvi471 introduced the following orders3 ,bimanes1 ,quadrumanes1 ,carnassiers1 ,rongeurs1 ,edents1 ,pachyderms1 ,ruminans4 ,of these1 the ,carnassiers correspond to the ,fer of ,linnus2 the ,rongeurs to his ,glires2 the ,edents are a new order1 taking the ,sloths1 ,ant-eaters1 c41 from the ,bruta of ,linnus1 the ,megatherium from extinct animals1 and the ,ornithorhynchus1 c41 from the new animals of ,australia2 the ,ruminans agree with the #fce ,pecora2 the ,pachyderms include some of the ,bruta and the ,bellu1 comprehending also extinct animals1 as ,anoplotherium and ,palotherium4 ,but the two orders of ,hoofed ,animals1 the ,pachyderms and the ,ruminants1 form a group which is held by ,mr4 ,owen to admit of a better separation1 on the ground of a character already pointed out by ,cuvier2 namely1 as to whether they are two-toed or three-toed4 ,according to this view1 the ,horse is connected with the ,tapir1 the ,palotherium1 and the ,rhinoceros1 not only by his teeth1 but by his feet1 for he has really three digits4 ,and ,cuvier notices that in the two-toed or even-toed ,pachyderms1 the astragalus bone has its face divided into two equal parts by a ridge2 while in the uneven-toed pachyderms it has a narrow cuboid face4 ,mr4 ,owen has adopted this division of ,pachyderms and ,ruminants1 giving the names artiodactyla and perissodactyla to the two groups2 the former including the ,ox1 ,hog1 ,peccary1 ,hippopotamus1 c42 the latter comprehending the ,horse1 ,tapir1 ,rhinoceros1 ,hyrax1 c4 ,and thus the ,ruminants take their place as a subordinate group of the great natural even-toed ,division of the ,hoofed ,section of ,mammals2 and the ,horse is widely separated from them1 inasmuch as he belongs to the odd-toed division4#db;,b ,note #db;,b3 ,owen1 ,odontography4 ,as we have seen1 these modern classifications are so constructed as to include extinct as well as living species of animals2 and indeed the species which have been discovered in a fossil state have tended to fill up the gaps in the series of zoological forms which had marred the systems of modern zoologists4 ,this has been the case with the division of which we are speaking4 ,mr4 ,owen had established two genera of extinct ,herbivorous ,animals1 on the strength of fossil remains brought from ,south ,america3--,toxodon1 and ,nesodon4 ,in a recent communication to the ,royal ,society#dc;,b he has considered the bearing of these genera upon the divisions of odd-toed and even-toed animals4 ,he had already been led to the opinion that the three sections1 ,proboscidea1 ,perissodactyla1 and ,artiodactyla1 formed a natural division of ,ungulata2 and he is now led to think that this division implies another group1 a distinct division of the ,ungulata1 of equal value1 if not with the ,perissodactyla and ,artiodactyla at least with the ,proboscidea4 ,this group he proposes to call ,toxodonta4 ,note #dc;,b3 ,phil4 ,trans41 #ahec4 #fcf ,,book ,,xvii4 ,,physiology ,,and ,,comparative ,,anatomy4 ,,vegetable ,,morphology4 ,morphology in ,linnus4 ,i ,,have stated that ,linnus had some views on this subject4 ,dr4 ,hooker conceives these views to be more complete and correct than is generally allowed1 though unhappily clothed in metaphorical language and mixed with speculative matter4 ,by his permission ,i insert some remarks which ,i have received from him4 ,the fundamental passage on this subject is in the ,systema ,natur2 in the ,introduction to which work the following passage occurs3-- ,prolepsis 7,anticipation7 exhibits the mystery of the metamorphosis of plants1 by which the herb1 which is the larva or imperfect condition1 is changed into the declared fructification3 for the plant is capable of producing either a leafy herb or a fructification4 4 4 4 4 4 ,when a tree produces a flower1 nature anticipates the produce of five years where these come out all at once2 forming of the bud-leaves of the next year bracts2 of those of the following year1 the calyx2 of the following1 the corolla2 of the next1 the stamina2 of the subsequent1 the pistils1 filled with the granulated marrow of the seed1 the terminus of the life of a vegetable4 ,dr4 ,hooker says1 ,i derive my idea of his having a better knowledge of the subject than most ,botanists admit1 not only from the ,prolepsis1 but from his paper called ,reformatio ,botanices 7,amn4 ,acad4 vol4 vi472 a remarkable work1 in respect of his candor in speaking of his predecessors' labors1 and the sagacity he shows in indicating researches to be undertaken or completed4 ,amongst the latter is ,v4 ',prolepsis plantarum1 ulterius extendenda per earum metamorphoses4' ,the last word occurs rarely in his ,prolepsis2 but when it does it seems to me that he uses it as indicating a normal change and not an accidental one4 #fcg ,in the ,prolepsis the speculative matter1 which ,linnus himself carefully distinguishes as such1 must be separated from the rest1 and this may ,i think be done in most of the sections4 ,he starts with explaining clearly and well the origin and position of buds1 and their constant presence1 whether developed or not1 in the axil of the leaf3 adding abundance of acute observations and experiments to prove his statements4 ,the leaf he declares to be the first effort of the plant in spring3 he proceeds to show1 successively1 that bracts1 calyx1 corolla1 stamens1 and pistil are each of them metamorphosed leaves1 in every case giving ,,many ,,examples1 both from monsters and from characters presented by those organs in their normal condition4 ,the 7to me7 obscure and critical part of the ,prolepsis was that relating to the change of the style of ,carduus into two leaves4 ,mr4 ,brown has explained this4 ,he says it was a puzzle to him1 till he went to ,upsala and consulted ,fries and ,wahlenberg1 who informed him that such monstrous ,cardui grew in the neighborhood1 and procured him some4 ,considering how minute and masked the organs of ,composit are1 it shows no little skill in ,linnus1 and a very clear view of the whole matter1 to have traced the metamorphosis of all their floral organs into leaves1 except their stamens1 of which he says1 ',sexti anni folia e staminibus me non in compositis vidisse fateor1 sed illorum loco folia pistillacea1 qu in compositis aut plenis sunt frequentissima4' ,i must say that nothing could well be clearer to my mind than the full and accurate appreciation which ,linnus shows of the whole series of phenomena1 and their rationale4 ,he over and over again asserts that these organs are leaves1 every one of them1--,i do not understand him to say that the prolepsis is an accidental change of leaves into bracts1 of bracts into calyx1 and so forth4 ,even were the language more obscure1 much might be inferred from the wide range and accuracy of the observations he details so scientifically4 ,it is inconceivable that a man should have traced the sequence of the phenomena under so many varied aspects1 and shown such skill1 knowledge1 ingenuity1 and accuracy in his methods of observing and describing1 and yet missed the rationale of the whole4 ,eliminate the speculative parts and there is not a single error of observation or judgment2 whilst his history of the developement of buds1 leaves1 and floral organs1 and of various other obscure matters of equal interest and importance1 are of a very high order of merit1 are1 in fact1 for the time profound4 ,there is nothing in all this that detracts from the merit of ,goethe's #fch re-discovery4 ,with ,goethe it was1 ,i think1 a deductive process1--with ,linnus an inductive4 ,analyse ,linnus's observations and method1 and ,i think it will prove a good example of inductive reasoning4 ,p4 #dgc4 ,perhaps ,professor ,auguste ,st ,hilaire of ,montpellier should share with ,de ,candolle the honor of contributing largely to establish the metamorphic doctrine2--their labors were cotemporaneous4 ,p4 9999#dgd4 ,linnus pointed out that the pappus was calyx3 ',et pappum gigni ex quarti anni foliis1 in jam nominatis ,carduis4'--,prol4 ,plant4 #cch4 7,j4 ,d4 ,h47 ,,chapter ,,vii4 ,,animal ,,morphology4 ,,the subject of ,animal ,morphology has recently been expanded into a form strikingly comprehensive and systematic by ,mr4 ,owen2 and supplied by him with a copious and carefully-chosen language2 which in his hands facilitates vastly the comparison and appreciation of the previous labors of physiologists1 and opens the way to new truths and philosophical generalizations4 ,though the steps which have been made had been prepared by previous anatomists1 ,i will borrow my view of them mainly from him2 with the less scruple1 inasmuch as he has brought into full view the labors of his predecessors4 ,i have stated in the ,history that the skeletons of all vertebrate animals are conceived to be reducible to a single ,type1 and the skull reducible to a series of vertebr4 ,but inasmuch as this reduction includes not only a detailed correspondence of the bones of man with those of beasts1 but also with those of birds1 fishes1 and reptiles1 it may easily be conceived that the similarities and connexions are of a various and often remote kind4 ,the views of such relations1 held by previous ,comparative ,anatomists1 have led to the designations of the bones of animals which have been employed in anatomical descriptions2 and these designations having been framed and adopted by anatomists looking at the subject from different sides1 and having different views of analogies and relations1 have been very various and unstable2 besides being often of cumbrous length and inconvenient form4 ,the corresponding parts in different animals are called homologues1 #fci a term first applied to anatomy by the philosophers of ,germany2 and this term ,mr4 ,owen adopts1 to the exclusion of terms more loosely denoting identity or similarity4 ,and the ,homology of the various bones of vertebrates having been in a great degree determined by the labors of previous anatomists1 ,mr4 ,owen has proposed names for each of the bones3 the condition of such names being1 that the homologues in all vertebrates shall be called by the same name1 and that these names shall be founded upon the terms and phrases in which the great anatomists of the #afth1 #agth1 and #ahth centuries expressed the results of their researches respecting the human skeleton4 ,these names1 thus selected1 so far as concerned the bones of the ,head of ,fishes1 one of the most difficult cases of this ,special ,homology1 he published in a ,table1#dd;,b in which they were compared1 in parallel columns1 with the names or phrases used for the like purpose by ,cuvier1 ,agassiz1 ,geoffroy1 ,hallman1 ,smmering1 ,meckel1 and ,wagner4 ,as an example of the considerations by which this selection of names was determined1 ,i may quote what he says with regard to one of these bones of the skull4 ,note #dd;,b3 ,lectures on ,vertebrates4 #ahdf1 p4 #aeh4 ,and ,on the ,archetype and ,homologies of the ,vertebrate ,skeleton4 #ahdh1 p4 #agb4 ,with regard to the 'squamosal' 7squamosum4 ,lat4 pars squamosa ossis temporis4--,smmering71 it might be asked why the term 'temporal' might not be retained for this bone4 ,i reply1 because that term has long been1 and is now universally1 understood in human anatomy to signify a peculiarly anthropotomical coalesced congeries of bones1 which includes the 'squamosal' together with the 'petrosal1' the 'tympanic1' the 'mastoid1' and the 'stylohyal4' ,it seems preferable1 therefore1 to restrict the signification of the term 'temporal' to the whole 7in ,man7 of which the 'squamosal' is a part4 ,to this part ,cuvier has unfortunately applied the term 'temporal' in one class1 and 'jugal' in another2 and he has also transferred the term 'temporal' to a third equally distinct bone in fishes2 while to increase the confusion ,m4 ,agassiz has shifted the name to a fourth different bone in the skull of fishes4 ,whatever1 therefore1 may be the value assigned to the arguments which will be presently set forth1 as to the special homologies of the 'pars squamosa ossis temporis1' ,i have felt compelled to express the conclusion by a definite term1 and in the present instance1 have selected that which recalls the best accepted anthropomorphical designation of the part2 although 'squamosal' must be understood and applied in an arbitrary sense2 and not as descriptive of a scale-like #fdj form2 which in reference to the bone so called1 is rather its exceptional than normal figure in the vertebrate series4 ,the principles which ,mr4 ,owen here adopts in the selection of names for the parts of the skeleton are wise and temperate4 ,they agree with the aphorisms concerning the language of science which ,i published in the ,philosophy of the ,inductive ,sciences2 and ,mr4 ,owen does me the great honor of quoting with approval some of those ,aphorisms4 ,i may perhaps take the liberty of remarking that the system of terms which he has constructed1 may1 according to our principles1 be called rather a ,terminology 9999than a ,nomenclature3 that is1 they are analogous more nearly to the terms by which botanists describe the parts and organs of plants1 than to the names by which they denote genera and species4 ,as we have seen in the ,history1 plants as well as animals are subject to morphological laws2 and the names which are given to organs in consequence of those laws are a part of the ,terminology of the science4 ,nor is this distinction between ,terminology and ,nomenclature without its use2 for the rules of prudence and propriety in the selection of words in the two cases are different4 ,the ,nomenclature of genera and species may be arbitrary and casual1 as is the case to a great extent in ,botany and in ,zoology1 especially of fossil remains2 names being given1 for instance1 simply as marks of honor to individuals4 ,but in a ,terminology1 such a mode of derivation is not admissible3 some significant analogy or idea must be adopted1 at least as the origin of the name1 though not necessarily true in all its applications1 as we have seen in the case of the squamosal just quoted4 ,this difference in the rules respecting two classes of scientific words is stated in the ,aphorisms xiii4 and xiv4 concerning the ,language of ,science4 ,such a ,terminology of the bones of the skeletons of all vertebrates as ,mr4 ,owen has thus propounded1 cannot be otherwise than an immense acquisition to science1 and a means of ascending from what we know already to wider truths and new morphological doctrines4 ,with regard to one of these doctrines1 the resolution of the human head into vertebr1 ,mr4 ,owen now regards it as a great truth1 and replies to the objections of ,cuvier and ,m4 ,agassiz1 in detail4#de;,b ,he gives a ,table in which the ,bones of the ,head are resolved into four vertebr1 which he terms the ,occipital1 ,parietal1 ,frontal1 and ,nasal ,vertebra1 respectively4 ,these four vertebr agree in general with what ,oken called the ,ear-vertebra1 the ,jaw-vertebra1 the ,eye-vertebra1 and #fda the ,nose-vertebra1 in his work ,on the ,signification of the ,bones of the ,skull1 published in #ahjg3 and in various degrees1 with similar views promulgated by ,spix 7#ahae71 ,bojanus 7#ahah71 ,geoffroy 7#ahbd71 ,carus 99997#ahbh74 ,and ,i believe that these views1 bold and fanciful as they at first appeared1 have now been accepted by most of the principal physiologists of our time4 ,note #de;,b3 ,archetype and ,homologies of the ,vertebrate ,skeleton4 #ahdh1 p4 #ada4 ,but another aspect of this generalization has been propounded among physiologists2 and has1 like the others1 been extended1 systematized1 and provided with a convenient language by ,mr4 ,owen4 ,since animal skeletons are thus made up of vertebr and their parts are to be understood as developements of the parts of vertebr1 ,geoffroy 7#ahbb71 ,carus 7#ahbh71 ,mller 7#ahcd71 ,cuvier 7#ahcf71 had employed certain terms while speaking of such developements2 ,mr4 ,owen in the ,geological ,transactions in #ahch1 while discussing the osteology of certain fossil ,saurians1 used terms of this kind1 which are more systematic than those of his predecessors1 and to which he has given currency by the quantity of valuable knowledge and thought which he has embodied in them4 ,according to his ,terminology1#df;,b a vertebra1 in its typical completeness1 consists of a central part or centrum2 at the back of this1 two plates 7the neural apophyses7 and a third outward projecting piece 7the neural spine71 which three1 with the centrum1 form a canal for the spinal marrow2 at the front of the centrum two other plates 7the hmal apophyses7 and a projecting piece1 forming a canal for a vascular trunk4 ,further lateral elements 7pleuro-apophyses7 and other projections1 are in a certain sense dependent on these principal bones2 besides which the vertebra may support diverging appendages4 ,these parts of the vertebra are fixed together1 so that a vertebra is by some anatomists described as a single bone2 but the parts now mentioned are usually developed from distinct and independent centres1 and are therefore called by ,mr4 ,owen autogenous elements4 ,note #df;,b3 ,archetype and ,homologies of the ,vertebrate ,skeleton4 #ahdh1 p4 #ha4 ,the ,general ,homology of the vertebral skeleton is the reference of all the parts of a skeleton to their true types in a series of vertebr3 and thus1 as special homology refers all the parts of skeletons to a given type of skeleton1 say that of ,man1 general homology refers all the parts of every skeleton1 say that of ,man1 to the parts of a series of ,vertebr4 ,and thus as ,oken propounded his views of the ,head as a resolution of the ,problem of the ,signification of the ,bones of the ,head1 #fdb so have we in like manner1 for the purposes of ,general ,homology1 to solve the ,problem of the ,signification of ,limbs4 ,the whole of the animal being a string of vertebr1 what are arms and legs1 hands and paws1 claws and fingers1 wings and fins1 and the like8 ,this inquiry ,mr4 ,owen has pursued as a necessary part of his inquiries4 ,in giving a public lecture upon the subject in #ahdi1dg;,b he conceived that the phrase which ,i have just employed would not be clearly apprehended by an ,english ,audience1 and entitled his ,discourse ,on the ,nature of ,limbs3 and in this discourse he explained the modifications by which the various kinds of limbs are derived from their rudiments in an archetypal skeleton1 that is1 a mere series of vertebr without head1 arms1 legs1 wings1 or fins4 ,note #dg;,b3 ,on the ,nature of ,limbs1 a discourse delivered at a ,meeting of the ,royal ,institution1 #ahdi4 ,final ,causes ,it has been mentioned in the ,history that in the discussions which took place concerning the ,unity of ,plan of animal structure1 this principle was in some measure put in opposition to the principle of ,final ,causes3 ,morphology was opposed to ,teleology4 ,it is natural to ask whether the recent study of ,morphology has affected this antithesis4 ,if there be advocates of ,final ,causes in ,physiology who would push their doctrines so far as to assert that every feature and every relation in the structure of animals have a purpose discoverable by man1 such reasoners are liable to be perpetually thwarted and embarrassed by the progress of anatomical knowledge2 for this progress often shows that an arrangement which had been explained and admired with reference to some purpose1 exists also in cases where the purpose disappears2 and again1 that what had been noted as a special teleological arrangement is the result of a general morphological law4 ,thus to take an example given by ,mr4 ,owen3 that the ossification of the head originates in several centres1 and thus in its early stages admits of compression1 has been pointed out as a provision to facilitate the birth of viviparous animals2 but our view of this provision is disturbed1 when we find that the same mode of the formation of the bony framework takes place in animals which are born from an egg4 ,and the number of points from which ossification begins1 depends in a wider sense on the general homology of the animal frame1 according to which each part is composed of a certain number of autogenous vertebral elements4 ,in this #fdc way1 the admission of a new view as to ,unity of ,plan will almost necessarily displace or modify some of the old views respecting ,final ,causes4 ,but though the view of ,final ,causes is displaced1 it is not obliterated2 and especially if the advocate of ,purpose is also ready to admit visible correspondences which have not a discoverable object1 as well as contrivances which have4 ,and in truth1 how is it possible for the student of anatomy to shut his eyes to either of these two evident aspects of nature8 ,the arm and hand of man are made for taking and holding1 the wing of the sparrow is made for flying2 and each is adapted to its end with subtle and manifest contrivance4 ,there is plainly ,design4 ,but the arm of man and the wing of the sparrow correspond to each other in the most exact manner1 bone for bone4 ,where is the ,use or the ,purpose of this correspondence8 ,if it be said that there may be a purpose though we do not see it1 that is granted4 ,but ,final ,causes for us are contrivances of which we see the end2 and nothing is added to the evidence of ,design by the perception of a unity of plan which in no way tends to promote the design4 ,it may be said that the design appears in the modification of the plan in special ways for special purposes2--that the vertebral plan of an animal being given1 the fore limbs are modified in ,man and in ,sparrow1 as the nature and life of each require4 ,and this is truly said2 and is indeed the truth which we are endeavoring to bring into view3--that there are in such speculations1 two elements2 one given1 the other to be worked out from our examination of the case2 the datum and the problem2 the homology and the teleology4 ,mr4 ,owen1 who has done so much for the former of these portions of our knowledge1 has also been constantly at the same time contributing to the other4 ,while he has been aiding our advances towards the ,unity of ,nature1 he has been ever alive to the perception of an ,intelligence which pervades ,nature4 ,while his morphological doctrines have moved the point of view from which he sees ,design1 they have never obscured his view of it1 but1 on the contrary1 have led him to present it to his readers in new and striking aspects4 ,thus he has pointed out the final purposes in the different centres of ossification of the long bones of the limbs of mammals1 and shown how and why they differ in this respect from reptiles 7,archetype1 p4 #ajd74 ,and in this way he has been able to point out the insufficiency of the rule laid down both by ,geoffroy ,st4 ,hilaire and ,cuvier1 for ascertaining the true number of bones in each species4 #fdd ,final ,causes1 or ,evidences of ,design1 appear1 as we have said1 not merely as contrivances for evident purposes1 but as modifications of a given general ,plan for special given ends4 ,if the general ,plan be discovered after the contrivance has been noticed1 the discovery may at first seem to obscure our perception of ,purpose2 but it will soon be found that it merely transfers us to a higher point of view4 ,the adaptation of the ,means to the ,end remains1 though the ,means are parts of a more general scheme than we were aware of4 ,no generalization of the ,means can or ought permanently to shake our conviction of the ,end2 because we must needs suppose that the ,intelligence which contemplates the ,end is an intelligence which can see at a glance along a vista of ,means1 however long and complex4 ,and on the other hand1 no special contrivance1 however clear be its arrangement1 can be unconnected with the general correspondences and harmonies by which all parts of nature are pervaded and bound together4 ,and thus no luminous teleological point can be extinguished by homology2 nor1 on the other hand1 can it be detached from the general expanse of homological light4 ,the reference to ,final ,causes is sometimes spoken of as unphilosophical1 in consequence of ,francis ,bacon's comparison of ,final ,causes in ,physics to ,vestal ,virgins devoted to ,god1 and barren4 ,i have repeatedly shown that1 in ,physiology1 almost all the great discoveries which have been made1 have been made by the assumption of a purpose in animal structures4 ,with reference to ,bacon's simile1 ,i have elsewhere said that if he had had occasion to develope its bearings1 full of latent meaning as his similes so often are1 he would probably have said that to those ,final ,causes barrenness was no reproach1 seeing they ought to be not the ,mothers but the ,daughters of our ,natural ,sciences2 and that they were barren1 not by imperfection of their nature1 but in order that they might be kept pure and undefiled1 and so fit ministers in the temple of ,god4 ,i might add that in ,physiology1 if they are not ,mothers1 they are admirable ,nurses2 skilful and sagacious in perceiving the signs of pregnancy1 and helpful in bringing the ,infant ,truth into the light of day4 ,there is another aspect of the doctrine of the ,archetypal ,unity of ,composition of ,animals1 by which it points to an ,intelligence from which the frame of nature proceeds2 namely this3--that the ,archetype of the ,animal ,structure being of the nature of an ,idea1 implies a mind in which this ,idea existed2 and that thus ,homology itself points the way to the ,divine ,mind4 ,but while we acknowledge the full #fde value of this view of theological bearing of physiology1 we may venture to say that it is a view quite different from that which is described by speaking of ,final ,causes1 and one much more difficult to present in a lucid manner to ordinary minds4 #fdf ,,book ,,xviii4 ,,geology4 ,,with regard to ,geology1 as a ,paltiological ,science1 ,i do not know that any new light of an important kind has been thrown upon the general doctrines of the science4 ,surveys and examinations of special phenomena and special districts have been carried on with activity and intelligence2 and the animals of which the remains people the strata1 have been reconstructed by the skill and knowledge of zoologists3--of such reconstructions we have1 for instance1 a fine assemblage in the publications of the ,palontological ,society4 ,but the great questions of the manner of the creation and succession of animal and vegetable species upon the earth remain1 ,i think1 at the point at which they were when ,i published the last edition of the ,history4 ,i may notice the views propounded by some chemists of certain bearings of ,mineralogy upon ,geology4 ,as we have1 in mineral masses1 organic remains of former organized beings1 so have we crystalline remains of former crystals2 namely1 what are commonly called pseudomorphoses--the shape of one crystal in the substance of another4 ,m4 ,g4 ,bischoff#dh;,b considers the study of pseudomorphs as important in geology1 and as frequently the only means of tracing processes which have taken place and are still going on in the mineral kingdom4 ,note #dh;,b3 ,chemical and ,physical ,geology4 ,i may notice also ,professor ,breithaupt's researches on the order of succession of different minerals1 by observing the mode in which they occur and the order in which different crystals have been deposited1 promise to be of great use in following out the geological changes which the crust of the globe has undergone4 7,die ,paragenesis der ,mineralien4 ,freiberg4 #ahdi47 ,in conjunction with these may be taken ,m4 de ,senarmont's experiments on the formation of minerals in veins2 and besides ,bischoff's #fdg ,chemical ,geology1 ,sartorius von ,walterhausen's ,observations on the occurrence of minerals in ,amygdaloid4 ,as a recent example of speculations concerning ,botanical ,paltiology1 ,i may give ,dr4 ,hooker's views of the probable history of the ,flora of the ,pacific4 ,in speculating upon this question1 ,dr4 ,hooker is led to the discussion of geological doctrines concerning the former continuity of tracts of land which are now separate1 the elevation of low lands into mountain ranges in the course of ages1 and the like4 ,we have already seen1 in the speculations of the late lamented ,edward ,forbes1 7see ,book xviii4 chap4 vi4 of this ,history17 an example of a hypothesis propounded to account for the existing ,flora of ,england3 a hypothesis1 namely1 of a former ,connexion of the ,west of the ,british ,isles with ,portugal1 of the ,alps of ,scotland with those of ,scandinavia1 and of the plains of ,east ,anglia with those of ,holland4 ,in like manner ,dr4 ,hooker says 7p4 xxi47 that he was led to speculate on the possibility of the plants of the ,southern ,ocean being the remains of a ,flora that had once spread over a larger and more continuous tract of land than now exists in the ocean2 and that the peculiar ,antarctic genera and species may be the vestiges of a ,flora characterized by the predominance of plants which are now scattered throughout the ,southern islands4 ,he conceives this hypothesis to be greatly supported by the observations and reasonings of ,mr4 ,darwin1 tending to show that such risings and sinkings are in active progress over large portions of the continents and islands of the ,southern hemisphere3 and by the speculations of ,sir ,c4 ,lyell respecting the influence of climate on the migrations of plants and animals1 and the influence of geological changes upon climate4 ,in ,zoology ,i may notice 7following ,mr4 ,owen7#di;,b recent discoveries of the remains of the animals which come nearest to man in their structure4 ,at the time of ,cuvier's death1 in #ahcb1 no evidence had been obtained of fossil ,quadrumana2 and he supposed that these1 as well as ,bimana1 were of very recent introduction4 ,soon after1 in the oldest 7eocene7 tertiary deposits of ,suffolk1 remains were found proving the existence of a monkey of the genus ,macacus4 ,in the ,himalayan tertiaries were found petrified bones of a ,semnopithecus2 in ,brazil1 remains of an extinct platyrhine monkey of great size2 and lastly1 in the middle tertiary series of the ,south of ,france1 was discovered a fragment of the jaw of the long-armed ape 7,hylobates74 ,but no fossil human #fdh remains have been discovered in the regularly deposited layers of any divisions 7not even the pleiocene7 of the tertiary series2 and thus we have evidence that the placing of man on the earth was the last and peculiar act of ,creation4 ,note #di;,b3 ,brit4 ,asso4 #ahed1 p4 #aab4 ,,the ,,end4 ,transcriber's ,notes ,whewell's book was originally published in #c volumes in ,london in #ahcg4 ,a second edition appeared in #ahdg1 and a third in #aheg4 ,a #b-volume version of the #crd edition was published in ,new ,york in #aheh1 reprinted #ahge4 ,this ,project ,gutenberg text1 combining both volumes in sequence1 was derived from the #ahge version1 relying upon resources kindly provided by the ,internet ,archive4 ,three items have been added to the ,contents of the ,first ,volume2 they are marked off by 1 as are any other additions to the text4 ,printed page numbers have been transcribed in 2 pages without a printed number have been indicated by 4 ,where words were hyphenated across pages1 the number has been placed before the word4 ,fractions have been transcribed as numerator_/denominator1 occasionally using parentheses to disambiguate4 ,the original sometimes has numerator over a line with denominator below1 at other times numerator hyphen denominator4 ,superscripted characters are marked by a before the character4 ,footnotes in the original text were numbered by chapter2 here they have been numbered by ,book 7the number of which is given after a 1 for the two appendices to the #crd edition ,a has been used for volume #a1 ,b for volume #b74 ,they are placed after the paragraph in which they occur1 and are transcribed ,note mn3 4444 ,footnote anchors are transcribed mn4 ,all other square brackets are in the original text4 ,one difficult item is the use of numbers within a ring as names of asteroids2 here the numbers are in 7 74 ,corrections to the text have been marked with 99994 ,they are listed below1 and were usually confirmed by reference to ,english printings of the text4 ,inconsistencies1 especially with respect to accents and formatting1 are numerous and have in general not been adjusted1 though ,greek quotations have been checked against other versions where available4 ,nor have ,whewell's unbalanced quotation marks been modernised4 ,the ,english versions have been used to restore ,whewell's gesperrt emphases in some ,greek passages4 ,location #ahge ,text ,correction ,vol4 #a p4 #be ,cruikshanks ,cruickshank p4 #cj #ai #fe p4 #cj 3 2 p4 #cc 7thrice7 #ahd #ahb p4 #cf #ahd #ahb p4 #ga ,arisotelians ,aristotelians p4 #ge p4 #gi p4 #aja note #ab #f #g p4 #age ecliptical elliptical note #ad iv4 vi4 note #ged ,summ ,summa note #aje iii4 iv4 p4 #bga 7twice7 ,mastlin ,mstlin p4 #bhb ,dialogo ,dialogo p4 #bhd semil semel p4 #bhg endeaver endeavor note #gf #a4 i4 note #hf ,dial4 i4 p4 #dj4 p4 #ada4 note #if ,speculutionum ,speculationum p4 #cbe ,gualtier ,gualter p4 #cda and #cdb ,marsenne ,mersenne p4 #cgd of p4 #cgg prependicularity perpendicularity p4 #djc note #cjg ,cosmotheros ,cosmotheoros p4 #dae casual causal p4 #daf 7 p4 #dai p4 #dca a a note #fig #adec #agec note #hdg ,ast4 ,ass4 p4 #dfc ,philosphical ,philosophical p4 #dga p4 #efd prevalance prevalence ,vol4 #b p4 #ej p4 #hd p4 #he viii4 vii4 p4 #aae #ahec #ahbc p4 #adi 1 4 p4 #afb ,footnote number missing in text p4 #bja stream steam p4 #bac and note #ciaa same number as the preceding note p4 #bdj ,cruikshanks ,cruickshank note #ahac ,mass-bestimmengen ,mass-bestimmungen p4 #bfd in is note #aaad ,stahl ,stahl p4 #bie the the note #ghad the entire text of this note is missing p4 #cja lecture lectures note #hgad #if4 #ifc4 note #ibad #aec #hec p4 #ccj ,angels ,angles p4 #ccf given giving p4 #cdc p4 #cid ,surien ,surian p4 #daa ,cours ,elmentaire ,cours ,elmentaire note #acfaf p4 #dej dependance dependence p4 #deg sucking-beasts suckling-beasts note #hjag hlich hnlich note #hiag #bbi #abi p4 #dgg osseuze osseuse note #aaiag #bbi #bii99 p4 #ejh ,lythophylaccii ,lythophylacii p4 #eaa ,stukely ,stukeley note #ahah ,gognastique ,gognostique p4 #eac ,sabapennine ,sub-,apennine p4 #ead ,schlotheim ,schlottheim p4 #ecj 1 7 17 p4 #eef ,poissons ,poisson's p4 #fbj iv4 vii4 p4 #fbd 7 p4 #fbh in 7not italicised in text7 p4 #fcj ,nordenskiold's ,nordenskild's p4 #fch #cij #dgd p4 #fdj then than p4 #fda #ahbh 7#ahbh7 99 ,this is the page number given in the ,english edition4 ,in the only version of the text referred to that ,i have found1 the quotation is in a footnote on page #ceb of the second edition 7#ahje72 the note was not in the first edition4