,,novum ,,organon ,,renovatum4 ,,by ,,william ,,whewell1 ,d4,d41 ,,master ,,of ,,trinity ,,college1 ,,cambridge1 ,,and ,,corresponding ,,member ,,of ,,the ,,institute ,,of ,,france4 ,,being ,,the ,,second ,,part ,,of ,,the ,,philosophy ,,of ,,the ,,inductive ,,sciences4 ,,the ,,third ,,edition1 ,,with ,,large ,,additions4 ,i ,i,i ,i ,,london3 ,,john ,w4 ,,parker ,,and ,,son1 ,,west ,,strand4 #aheh4 ,,it is to our immortal countryman2 ,bacon1 that we owe the broad announcement of this grand and fertile principle2 and the developement of the idea1 that the whole of natural philosophy consists entirely of a series of inductive generalizations1 commencing with the most circumstantially stated particulars1 and carried up to universal laws1 or axioms1 which comprehend in their statements every subordinate degree of generality2 and of a corresponding series of inverted reasoning from generals to particulars1 by which these axioms are traced back into their remotest consequences1 and all particular propositions deduced from them2 as well those by whose immediate considerations we rose to their discovery1 as those of which we had no previous knowledge4 ,,herschel1 ,discourse on ,natural ,philosophy1 ,art4 #if4 ,,cambridge3 ,,printed ,,by ,c4 ,j4 ,,clay1 ,m4,a4 ,,at ,,the ,,university ,,press4 iii ,,preface4 ,,even if ,bacon's ,novum ,organon had possessed the character to which it aspired as completely as was possible in its own day1 it would at present need renovation3 and even if no such book had ever been written1 it would be a worthy undertaking to determine the machinery1 intellectual1 social and material1 by which human knowledge can best be augmented4 ,bacon could only divine how sciences might be constructed2 we can trace1 in their history1 how their construction has taken place4 ,however sagacious were his conjectures1 the facts which have really occurred must give additional instruction3 however large were his anticipations1 the actual progress of science since his time has illustrated them in all their extent4 ,and as to the structure and operation of the ,organ by which truth is to be collected from nature1--that is1 the ,methods by which science is to be promoted--we know that1 though ,bacon's general maxims are sagacious and animating1 his particular precepts failed in his hands1 and are now practically useless4 ,this1 perhaps1 was not wonderful1 seeing that they were1 as ,i have said1 mainly derived from conjectures respecting knowledge and the progress of knowledge2 but at iv the present day1 when1 in several provinces of knowledge1 we have a large actual progress of solid truth to look back upon1 we may make the like attempt with the prospect of better success1 at least on that ground4 ,it may be a task1 not hopeless1 to extract from the past progress of science the elements of an effectual and substantial method of ,scientific ,discovery4 ,the advances which have1 during the last three centuries1 been made in the physical sciences2--in ,astronomy1 in ,physics1 in ,chemistry1 in ,natural ,history1 in ,physiology2--these are allowed by all to be real1 to be great1 to be striking2 may it not be that the steps of progress in these different cases have in them something alike8 ,may it not be that in each advancing movement of such knowledge there is some common principle1 some common process8 ,may it not be that discoveries are made by an ,organ which has something uniform in its working8 ,if we can shew that this is so1 we shall have the ,new ,organ1 which ,bacon aspired to construct1 renovated according to our advanced intellectual position and office4 ,it was with the view of opening the way to such an attempt that ,i undertook that survey of the past progress of physical knowledge1 of which ,i have given the results in the ,history of the ,sciences1 and the ,history of ,scientific ,ideas#a,p2 the former containing the history of the sciences1 so far as it depends on v observed ,facts2 the latter containing the history of those ,ideas by which such ,facts are bound into ,theories4 ,note #a,p3 ,published in two former editions as part of the ,philosophy of the ,inductive ,sciences 7b4 i--x474 ,it can hardly happen that a work which treats of ,methods of ,scientific ,discovery1 shall not seem to fail in the positive results which it offers4 ,for an ,art of ,discovery is not possible4 ,at each step of the investigation are needed ,invention1 ,sagacity1 ,genius1--elements which no art can give4 ,we may hope in vain1 as ,bacon hoped1 for an ,organ which shall enable all men to construct ,scientific ,truths1 as a pair of compasses enables all men to construct exact circles#b,p4 ,this cannot be4 ,the practical results of the ,philosophy of ,science must be rather classification and analysis of what has been done1 than precept and method for future doing4 ,yet ,i think that the methods of discovery which ,i have to recommend1 though gathered from a wider survey of scientific history1 both as to subjects and as to time1 than 7so far as ,i am aware7 has been elsewhere attempted1 are quite as definite and practical as any others which have been proposed2 with the great additional advantage of being the methods by which all great discoveries in science have really been made4 ,this may be said1 for instance1 of the ,method of ,gradation and the ,method of ,natural ,classification1 spoken of b4 iii4 c4 viii2 and in a narrower sense1 of the ,method of ,curves1 the ,method of vi ,means1 the ,method of ,least ,squares and the ,method of ,residues1 spoken of in chap4 vii4 of the same ,book4 ,also the ,remarks on the ,use of ,hypotheses and on the ,tests of ,hypotheses 7b4 ii4 c4 v47 point out features which mark the usual course of discovery4 ,note #b,p3 ,nov4 ,org4 lib4 i4 aph4 #fa4 ,but one of the principal lessons resulting from our views is undoubtedly this3--that different sciences may be expected to advance by different modes of procedure1 according to their present condition2 and that in many of these sciences1 an ,induction performed by any of the methods which have just been referred to is not the next step which we may expect to see made4 ,several of the sciences may not be in a condition which fits them for such a ,colligation of ,facts2 7to use the phraseology to which the succeeding analysis has led me74 ,the ,facts may1 at the present time1 require to be more fully observed1 or the ,idea by which they are to be colligated may require to be more fully unfolded4 ,but in this point also1 our speculations are far from being barren of practical results4 ,the examination to which we have subjected each science1 gives us the means of discerning whether what is needed for the further progress of the science1 has its place in the ,observations1 or in the ,ideas1 or in the union of the two4 ,if observations be wanted1 the ,methods of ,observation1 given in b4 iii4 c4 ii4 may be referred to4 ,if those who are to make the next discoveries need1 for that purpose1 a developement of their ,ideas1 the modes in which such a developement has usually taken vii place are treated of in ,chapters iii4 and iv4 of that ,book4 ,no one who has well studied the history of science can fail to see how important a part of that history is the explication1 or as ,i might call it1 the clarification of men's ,ideas4 ,this1 the metaphysical aspect of each of the physical sciences1 is very far from being1 as some have tried to teach1 an aspect which it passes through at an early period of progress1 and previously to the stage of positive knowledge4 ,on the contrary1 the metaphysical movement is a necessary part of the inductive movement4 ,this1 which is evidently so by the nature of the case1 was proved by a copious collection of historical evidences1 in the ,history of ,scientific ,ideas4 ,the ten ,books of that ,history contain an account of the principal philosophical controversies which have taken place in all the physical sciences1 from ,mathematics to ,physiology4 ,these controversies1 which must be called metaphysical if anything be so called1 have been conducted by the greatest discoverers in each science1 and have been an essential part of the discoveries made4 ,physical discoverers have differed from barren speculators1 not by having no metaphysics in their heads1 but by having good metaphysics in their heads while their adversaries had bad2 and by binding their metaphysics to their physics1 instead of keeping the two asunder4 ,i trust that the ,history of ,scientific ,ideas is of some value1 even as a record of a number of remarkable controversies2 but ,i conceive that it also contains an indisputable proof that there viii is1 in progressive science1 a metaphysical as well as a physical element2--ideas as well as facts2--thoughts as well as things4 ,metaphysics is the process of ascertaining that thought is consistent with itself3 and if it be not so1 our supposed knowledge is not knowledge4 ,in ,chapter vi4 of the ,second ,book1 ,i have spoken of the ,logic of ,induction4 ,several writers#c,p have quoted very emphatically my assertion that the ,logic of ,induction does not exist in previous writers3 using it as an introduction to ,logical ,schemes of their own4 ,they seem to have overlooked the fact that at the same time that ,i noted the deficiency1 ,i offered a scheme which ,i think fitted to supply this want4 ,and ,i am obliged to say that ,i do not regard the schemes proposed by any of those gentlemen as at all satisfactory for the purpose4 ,but ,i must defer to a future occasion any criticism of authors who have written on the subjects here treated4 ,a critical notice of such authors formed the ,twelfth ,book of the former edition of the ,philosophy of the ,sciences4 ,i have there examined the opinions concerning the ,nature of ,real ,knowledge and the mode of acquiring it1 which have been promulgated in all ages1 from ,plato and ,aristotle1 to ,roger ,bacon1 to ,francis ,bacon1 to ,newton1 to ,herschel4 ,such a survey1 with the additions which ,i should now have to make to it1 may hereafter be put forth as a separate book3 but ,i ix have endeavoured to confine the present volume to such positive teaching regarding ,knowledge and ,science as results from the investigations pursued in the other works of this series4 ,but with regard to this matter1 of the ,logic of ,induction1 ,i may venture to say1 that we shall not find anything deserving the name explained in the common writers on ,logic1 or exhibited under the ordinary ,logical ,forms4 ,that in previous writers which comes the nearest to the notice of such a ,logic as the history of science has suggested and verified1 is the striking declaration of ,bacon in two of his ,aphorisms 7b4 i4 aph4 civ4 cv474 ,note #c,p3 ,apelt ,die ,theorie der ,induction3 ,gratry ,logique4 ,there will be good hopes for the ,sciences then1 and not till then1 when by a true ,,scale or ,ladder1 and by successive steps1 following continuously without gaps or breaks1 men shall ascend from particulars to the narrower ,propositions1 from those to intermediate ones1 rising in order one above another1 and at last to the most general4 ,but in establishing such propositions1 we must devise some other ,,form ,,of ,,induction than has hitherto been in use2 and this must be one which serves not only to prove and discover ,principles1 7as very general ,propositions are called17 but also the narrower and the intermediate1 and in short1 all true ,propositions4 ,and he elsewhere speaks of successive ,,floors of ,induction4 ,all the truths of an extensive science form a ,series of such ,floors1 connected by such ,scales or ,ladders2 and a part of the ,logic of ,induction consists1 as ,i x conceive1 in the construction of a ,scheme of such ,floors4 ,converging from a wide basis of various classes of particulars1 at last to one or a few general truths1 these schemes necessarily take the shape of a ,pyramid4 ,i have constructed such ,pyramids for ,astronomy and for ,optics#d,p2 and the illustrious ,von ,humboldt in speaking of the former subject1 does me the honour to say that my attempt in that department is perfectly successful#e,p4 ,the ,logic of ,induction contains other portions1 which may be seen in the following work1 b4 ii4 c4 vi4 ,note #d,p3 ,see the ,tables at the end of book ii4 ,note #e,p3 ,cosmos1 vol4 ii4 n4 #ce4 ,i have made large additions to the present edition1 especially in what regards the ,application of ,science1 7b4 iii4 c4 ix47 and the ,language of ,science4 ,the former subject ,i am aware that ,i have treated very imperfectly4 ,it would indeed1 of itself1 furnish material for a large work2 and would require an acquaintance with practical arts and manufactures of the most exact and extensive kind4 ,but even a general observer may see how much more close the union of ,art with ,science is now than it ever was before2 and what large and animating hopes this union inspires1 both for the progress of ,art and of ,science4 ,on another subject also ,i might have dilated to a great extent1--what ,i may call 7as ,i have just now called it7 the social machinery for the advancement of science4 ,there can be no doubt that at certain stages of sciences1 xi ,societies and ,associations may do much to promote their further progress2 by combining their observations1 comparing their views1 contributing to provide material means of observation and calculation1 and dividing the offices of observer and generalizer4 ,we have had in ,europe in general1 and especially in this country1 very encouraging examples of what may be done by such ,associations4 ,for the present ,i have only ventured to propound one ,aphorism on the subject1 namely this2 7,aph4 ,,lv47 ,that it is worth considering whether a continued and connected system of observation and calculation1 like that of ,astronomy1 might not be employed in improving our knowledge of other subjects2 as ,tides1 ,currents1 ,winds1 ,clouds1 ,rain1 ,terrestrial ,magnetism1 ,aurora ,borealis1 composition of crystals1 and the like4 ,in saying this1 ,i have mentioned those subjects which are1 as appears to me1 most likely to profit by continued and connected observations4 ,i have thrown the substance of my results into ,aphorisms1 as ,bacon had done in his ,novum ,organum4 ,this ,i have done1 not in the way of delivering dogmatic assertions or oracular sentences2 for the ,aphorisms are all supported by reasoning1 and were1 in fact1 written after the reasoning1 and extracted from it4 ,i have adopted this mode of gathering results into compact sentences1 because it seems to convey lessons with additional clearness and emphasis4 ,i have only to repeat what ,i have already said2 that this task of adapting the ,novum ,organum to the xii present state of ,physical ,science1 and of constructing a ,newer ,organ which may answer the purposes at which ,bacon aimed1 seems to belong to the present generation2 and being here founded upon a survey of the past history and present condition of the ,physical ,sciences1 will ,i hope1 not be deemed presumptuous4 ,,trinity ,,lodge1 #a ,november1 #aheh4 xiii ,,table ,,of ,,contents4 ,,page ,,preface 9999iii ,,book ,i4 ,,aphorisms ,,concerning ,,ideas4 ,,aphorisms ,i4--,,xviii4 ,ideas in general #e--g ,,xix4--,,xliv4 ,ideas in the ,pure ,sciences #h--ab ,,xlv4--,,lv4 ,ideas in the ,mechanical ,sciences #ac--ae ,,lvi4--,,lxxi4 ,ideas in the ,secondary ,mechanical ,sciences4 #ae--ah ,,lxxii4--9999,,lxxiii4 ,ideas in the ,mechanico-chemical ,sciences #ah ,,lxxiv4--,,lxxix4 ,ideas in ,chemistry #ah ,,lxxx4--,,lxxxi4 ,ideas in ,morphology #ai 9999,,lxxxii4--,c4 ,ideas in ,classificatory ,science #bj--bc ,,ci4--,,cvi4 ,ideas in ,biology #bc--bd ,,cvii4--,,cxvii4 ,ideas in ,palontology #bd--bf ,,book ,,ii4 ,,of ,,knowledge4 ,,chap4 ,i4 ,,of ,,two ,,principal ,,processes ,,by ,,which ,,science ,,is ,,constructed #bg ,,chap4 ,,ii4 ,,of ,,the ,,explication ,,of ,,conceptions #cj ,sect4 ,i4 ,the ,historical ,progress4 ,art4 #a4 ,the ,explication of ,conceptions1 #b4 ,has taken place historically by discussions4 xiv ,art4 #c4 ,false ,doctrines when exposed appear impossible3 #d4 ,but were plausible before #e4 ,men's ,minds gradually cleared4 ,sect4 ,,ii4 ,use of definitions4 ,art4 #f4 ,controversies about ,definitions4 #g4 ,not arbitrary ,definitions4 #h4 ,attention to ,facts requisite4 #i4 ,definition is not essential4 #aj4 ,the omission of ,definition not always blameable4 ,sect4 ,,iii4 ,use of ,axioms4 ,art4 #aa4 ,axioms serve to express ,ideas4 ,sect4 ,,iv4 ,clear and appropriate ,ideas4 ,art4 #ab4 ,we must see the ,axioms clearly4 #ac4 ,inappropriate ,ideas cannot lead to ,truth4 #ad4 ,the fault is in the ,conceptions4 #ae4 ,rules cannot teach ,discovery2 #af4 ,but are not useless4 #ag4 ,discussion as well as ,facts needed4 ,sect4 ,v4 ,accidental ,discoveries4 ,art4 #ah4 ,no ,scientific ,discovery is accidental4 #ai4 ,such accidents do not happen to common ,men4 #bj4 ,examples4 #ba4 ,so far ,explication of ,conceptions4 ,,chap4 ,,iii4 ,,of ,,facts ,,as ,,the ,,materials ,,of ,,science #ej ,art4 #a4 ,facts must be true4 #b4 ,facts not separable from ,ideas4 #c4 ,the ,ideas must be distinct4 #d4 ,conceptions of the ,intellect only to be admitted4 #e4 ,facts are to be observed with reference to ,space and ,time3 #f4 ,and also to other ,ideas4 #g4 ,the ,decomposition of ,facts4 xv ,art4 #h4 ,this step is not sufficient4 #i4 ,it introduces ,technical ,terms1 #aj4 ,and ,classification4 #aa4 ,the materials of ,science4 ,,chap4 ,,iv4 ,,of ,,the ,,colligation ,,of ,,facts #ei ,art4 #a4 ,facts are colligated by ,conceptions4 #b4 ,science begins with common ,observation4 #c4 ,facts must be decomposed4 #d4 ,what ,ideas first give ,sciences4 #e4 ,facts must be referred to ,ideas4 #f4 ,sagacity needed4 #g4 ,discovery made by ,guesses4 #h4 ,false ,hypotheses preluding to true ones4 #i4 ,new ,hypotheses not mere modifications of old ones4 #aj4 ,hypotheses may have superfluous parts4 #aa4 ,hypotheses to be compared with ,facts4 #ab4 ,secondary ,steps4 ,,chap4 ,v4 ,,of ,,certain ,,characteristics ,,of ,,scientific ,,induction #gj ,sect4 ,i4 ,invention a part of ,induction4 ,art4 #a4 ,induction the source of ,knowledge4 #b4 ,induction involves a ,new ,element4 #c4 ,meaning of ,induction4 #d4 ,the ,new ,element is soon forgotten4 #e4 ,induction includes a ,definition and a ,proposition4 ,sect4 ,,ii4 ,use of ,hypotheses4 ,art4 #f4 ,discoveries made by ,guesses1 #g4 ,which must be compared with ,facts4 #h4 ,hypotheses are suspected4 #i4 ,hypotheses may be useful though inaccurate4 ,sect4 ,,iii4 ,tests of ,hypotheses4 ,art4 #aj4 ,true ,hypotheses foretel ,phenomena1 #aa4 ,even of different kinds4--,consilience of ,inductions4 xvi ,art4 #ab4 ,true ,theories tend to ,simplicity4 #ac4 ,connexion of the last ,tests4 ,,chap4 ,,vi4 ,,of ,,the ,,logic ,,of ,,induction #ig ,art4 #a4 ,steps of ,generalization1 #b4 ,may be expressed by ,tables4 #c4 ,which exhibit ,inductive ,steps2 #d4 ,and the ,consilience of ,inductions2 #e4 ,and the tendency to ,simplicity2 #f4 ,and the names of ,discoverers2 #g4 ,and the ,verifications of ,theory2 #h4 ,by means of several easy steps4 #i4 ,this resembles ,book-keeping4 #aj4 ,the ,logic of ,induction4 #aa4 ,attention at each step required4 #ab4 ,general ,truths are not mere additions of particulars3 #ac4 ,but a new view is introduced4 #ad4 ,formula of ,inductive ,logic3 #ae4 ,may refer to ,definition4 #af4 ,formula inadequate4 #ag4 ,deductive ,connexion of ,steps4 #ah4 ,relation of ,deductive and ,inductive ,reasoning4 #ai4 ,the ,criterion of ,truth4 #bj4 ,theory and ,fact4 #ba4 ,higher and ,lower ,generalizations4 ,,chap4 ,,vii4 ,,of ,,laws ,,of ,,phenomena ,,and ,,of ,,causes #aah ,art4 #a4 ,knowledge of ,laws of ,phenomena4 #b4 ,formal and ,physical ,sciences4 #c4 ,causes in ,astronomy4 #d4 ,different ,mechanical ,causes in other ,sciences4 #e4 ,chemical and ,vital ,forces as ,causes4 #f4 ,difference of these kinds of ,force4 #g4 ,difficulty of conceiving new ,causes4 #h4 ,men willingly take old ,causes4 #i4 ,is the ,magnetic ,fluid real8 #aj4 ,are ,causes to be sought8 7,comte's ,doctrine47 #aa4 ,both ,laws and ,causes to be studied4 xvii ,,chap4 ,,viii4 ,,of ,,art ,,and ,,science #abi ,art4 #a4 ,art precedes ,science4 #b4 ,contrast of ,art and ,science4 #c4 ,instinct and ,insight4 #d4 ,difference of ,art and ,instinct4 #e4 ,does ,art involve ,science8 #f4 ,science unfolds ,principles4 #g4 ,science may improve ,art4 #h4 ,arts not classified with ,sciences4 ,,chap4 ,,ix4 ,,of ,,the ,,classification ,,of ,,sciences #acf ,art4 #a4 ,use and ,limits of such ,classification4 #b4 ,classification depends on the ,ideas4 #c4 ,this points out ,transitions4 #d4 ,the ,classification4 ,,inductive ,,table ,,of ,,astronomy #adj ,,inductive ,,table ,,of ,,optics #adj ,,book ,,iii4 ,,of ,,methods ,,employed ,,in ,,the ,,formation ,,of ,,science4 ,,chap4 ,i4 ,,introduction #ada ,art4 #a4 ,object of this ,book4 #b4 ,an ,art of ,discovery not possible4 #c4 ,use of ,methods4 #d4 ,series of ,six ,processes4 #e4 ,methods of ,observation and ,induction4 ,,chap4 ,,ii4 ,,of ,,methods ,,of ,,observation #ade ,art4 #a4 ,referring to ,number1 ,space1 and ,time4 #b4 ,observations are never perfect4 #c4 7,i47 ,number is naturally exact4 #d4 7,,ii47 ,measurement of ,space4 #e4 ,instruments ,invented in ,astronomy1 #f4 ,and improved4 xviii ,art4 #g4 ,goniometer4 #h4 ,standard of ,length4 #aj4 7,,iii47 ,measurement of ,time4 #aa4 ,unit of ,time4 #ab4 ,transit ,instrument4 #ac4 ,chronometers4 #ad4 7,,iv47 ,conversion of ,space and ,time4 #ae4 ,space may ,measure ,time4 #af4 ,time may ,measure ,space4 #ag4 7,v47 ,the ,method of ,repetition4 #ah4 ,the ,method of ,coincidences4 #ai4 ,applied to ,pendulums4 #bj4 7,,vi47 ,measurement of ,weight4 #ba4 ,standard of ,weight4 #bb4 7,,vii47 ,measurement of ,secondary ,qualities4 #bc4 ,the ,howl in ,harmonics4 #bd4 7,,viii47 ,manipulation4 #be4 ,examples in ,optics4 #bf4 7,,ix47 ,the ,education of the ,senses1 #bg4 ,by the ,study of ,natural ,history4 #bh4 ,preparation for ,ideas4 ,,chap4 ,,iii4 ,,of ,,methods ,,of ,,acquiring ,,clear ,,scientific ,,ideas2 and first ,,of ,,intellectual ,,education #afd ,art4 #a4 7,i47 ,idea of ,space4 #b4 ,education by ,geometry4 #c4 7,,ii47 ,idea of ,number4 #d4 ,effect of the usual ,education4 #e4 7,,iii47 ,idea of ,force4 #f4 ,study of ,mechanics needed1 #g4 ,to make ,newton intelligible4 #h4 ,no ,popular ,road4 #i4 7,,iv47 ,chemical ,ideas4 #aj4 7,v47 ,natural ,history ,ideas4 #aa4 ,natural ,classes to be taught4 #ab4 ,mathematical ,prejudices1 #ac4 ,to be corrected by ,natural ,history4 #ad4 ,method of ,natural ,history1 #ae4 ,resembles common language4 xix ,art4 #af4 ,its ,lessons4 #ag4 7,,vi47 ,well-established ,ideas alone to be used4 #ah4 ,how are ,ideas cleared8 ,,chap4 ,,iv4 ,,of ,,methods ,,of ,,acquiring ,,clear ,,scientific ,,ideas1 continued4--,,of ,,the ,,discussion ,,of ,,ideas #ahj ,art4 #a4 ,successive ,clearness1 #b4 ,produced by ,discussion4 #c4 ,examples4 #d4 ,disputes not useless1 #e4 ,although metaphysical4 #f4 ,connected with ,facts4 ,,chap4 ,v4 ,,analysis ,,of ,,the ,,process ,,of ,,induction #ahf ,sect4 ,i4 ,the ,three ,steps of ,induction4 ,art4 #a4 ,methods may be useful4 #b4 ,the three ,steps4 #c4 ,examples4 #d4 ,mathematical names of the ,steps4 ,sect4 ,,ii4 ,of the ,selection of the ,fundamental ,idea4 ,art4 #e4 ,examples4 #f4 ,the ,idea to be found by trying1 #g4 ,till the ,discovery is made2 #h4 ,preluded by ,guesses4 #i4 ,idea and ,facts homogeneous4 #aj4 ,idea tested by the ,facts4 ,,chap4 ,,vi4 ,,general ,,rules ,,for ,,the ,,construction ,,of ,,the ,,conception #aie ,art4 #a4 ,first3 for ,quantity4 #b4 ,formula and ,coefficients found together4 #c4 ,example4 ,law of ,cooling4 #d4 ,determined by ,experiment4 #e4 ,progressive ,series of ,numbers4 #f4 ,recurrent ,series4 #g4 ,use of ,hypotheses4 #h4 ,even with this there are difficulties4 xv ,,chap4 ,,vii4 ,,special ,,methods ,,of ,,induction ,,applicable ,,to ,,quantity #bjb ,sect4 ,i4 ,the ,method of ,curves4 ,art4 #a4 ,its ,process4 #b4 ,its ,use4 #c4 ,with imperfect ,observations4 #d4 ,it corrects ,observations4 #e4 ,obstacles4 7,i47 ,ignorance of the argument4 #f4 7,,ii47 ,combination of ,laws4 ,sect4 ,,ii4 ,the ,method of ,means4 ,art4 #g4 ,its ,relation to the ,method of ,curves4 #h4 ,its process4 #i4 ,argument required to be known4 #aj4 ,use of the ,method4 #aa4 ,large masses of ,observations used4 #ab4 ,proof of the ,use of the ,method4 ,sect4 ,,iii4 ,the ,method of ,least ,squares4 ,art4 #ac4 ,is a ,method of ,means4 #ad4 ,example4 ,sect4 ,,iv4 ,the ,method of ,residues4 ,art4 #ae4 ,occasion for its ,use4 #af4 ,its ,process4 #ag4 ,examples4 #ah4 ,its ,relation to the ,method of ,means4 #ai4 ,example4 #bj4 ,residual ,phenomena4 ,,chap4 ,,viii4 ,,methods ,,of ,,induction ,,depending ,,on ,,resemblance #bbj ,sect4 ,i4 ,the ,law of ,continuity4 ,art4 #a4 ,its ,nature and ,application1 #b4 ,to ,falling ,bodies1 #c4 ,to ,hard ,bodies1 #d4 ,to ,gravitation4 #e4 ,the ,evidence4 xxi ,sect4 ,,ii4 ,the ,method of ,gradation4 ,art4 #f4 ,occasions of its ,use4 #g4 ,examples4 #h4 ,not enjoined by ,bacon4 #i4 ,other ,examples4 #aj4 ,its ,value in ,geology4 #aa4 ,limited ,results4 ,sect4 ,,iii4 ,the ,method of ,natural ,classification4 ,art4 #ab4 ,examples of its ,use4 #ac4 ,its ,process4 #ad4 ,negative ,results4 #ae4 ,is opposed to ,arbitrary ,definitions4 #af4 ,propositions and ,definitions correlative4 #ag4 ,definitions only provisional4 ,,chap4 ,,ix4 ,,of ,,the ,,application ,,of ,,inductive ,,truths #bcc ,art4 #a4 ,this forms the ,sequel of ,discovery4 #b4 ,systematic ,verification of ,discoveries4 #c4 ,correction of ,coefficients4 #d4 ,astronomy a ,model4 #e4 ,verification by new cases4 #f4 ,often requires fresh calculation4 #g4 ,cause of ,dew4 #h4 ,useful ,applications4 ,,chap4 ,x4 ,,of ,,the ,,induction ,,of ,,causes #bdg ,art4 #a4 ,is to be pursued4 #b4 ,induction of ,substance4 #c4 ,induction of ,force4 #d4 ,induction of ,polarity4 #e4 ,is ,gravity ,polar8 #f4 ,induction of ,ulterior ,causes4 #g4 ,of the ,supreme ,cause4 xxii ,,book ,,iv1 ,,of ,,the ,,language ,,of ,,science4 ,,introduction #beg ,,aphorisms ,,concerning ,,the ,,language ,,of ,,science4 ,aphorism ,i4 ,relative to the ,ancient ,period #beh ,art4 #a4 ,common ,words4 #b4 ,descriptive ,terms4 #c4 ,theoretical ,terms4 ,aphorism ,,ii4 ,relative to the ,modern ,period #bfi ,art4 #a4 ,systematic ,nomenclature4 #b4 ,systematic ,terminology4 #c4 ,systematic ,modification4 ,aphorisms 7,,iii4 ,,iv4 ,v4 ,,vi4 ,,vii7 relative to the ,application of ,common ,words #bgh ,aphorisms 7,,viii4 ,,ix4 ,x4 ,,xi4 ,,xii4 ,,xiii47 relative to the ,construction of ,new ,terms #bhe ,aphorism ,,xiv4 ,binary ,nomenclature #cjg ,,xv4 ,linnan ,maxims #cjh ,,xvi4 ,numerical ,names #cji ,,xvii4 ,names of more than two ,steps #caj ,,xviii4 ,no arbitrary ,terms #caa ,,xix4 ,forms fixed by ,convention #cad ,,xx4 ,form of ,terms #cah ,art4 #a4 ,terms derived from ,latin and ,greek4 #b4 ,german ,terms4 #c4 ,descriptive ,terms4 #d4 ,nomenclature4 ,zoology4 #e4 ------------- ,mineralogy4 #f4 ------------- ,botany4 #g4 ------------- ,chemistry4 #h4 ------------- ,crystallography4 xxiii ,aphorism ,,xxi4 ,philological ,rules #cbh ,art4 #a4 ,hybrids4 #b4 ,terminations of ,substantives4 #c4 ,formations of ,substantives 7names of things74 #d4 ,abstract ,substantives4 #e4 ,rules of derivation from ,greek and ,latin4 #f4 ,modification of ,terminations4 ,aphorism ,,xxii4 ,introduction of ,changes #cda ,,further ,,illustrations ,,of ,,the ,,aphorisms ,,on ,,scientific ,,language1 ,,from ,,the ,,recent ,,course ,,of ,,sciences4 #a4 ,,botany4 ,aphorism ,,xxiii4 ,multiplication of ,genera #cdf #b4 ,,comparative ,,anatomy4 ,aphorism ,,xxiv4 ,single ,names to be used #cec ,,xxv4 ,the ,history of ,science is the ,history of its ,language #cee ,,xxvi4 ,algebraical ,symbols #ceg ,,xxvii4 ,algebraical ,analogies #cfd ,,xxviii4 ,capricious ,derivations #cfe ,,xxix4 ,inductions are our ,definitions #cfh #a ,,novum ,,organon ,,renovatum4 ,,de ,scientiis tum demum bene sperandum est1 quando per ,,scalam veram et per gradus continuos1 et non intermissos aut hiulcos1 a particularibus ascendetur ad ,axiomata minora1 et deinde ad media1 alia aliis superiora1 et postremo demum ad generalissima4 ,in constituendo autem ,axiomate1 ,forma ,,inductionis alia quam adhuc in usu fuit1 excogitanda est2 et qu non ad ,principia tantum 7qu vocant7 probanda et invenienda1 sed etiam ad ,axiomata minora1 et media1 denique omnia4 ,,bacon1 ,nov4 ,org41 ,aph4 civ4 cv4 #c ,,novum ,,organon ,,renovatum4 ,,the name ,organon was applied to the works of ,aristotle which treated of ,logic1 that is1 of the method of establishing and proving knowledge1 and of refuting errour1 by means of ,syllogisms4 ,francis ,bacon1 holding that this method was insufficient and futile for the augmentation of real and useful knowledge1 published his ,novum ,organon1 in which he proposed for that purpose methods from which he promised a better success4 ,since his time real and useful knowledge has made great progress1 and many ,sciences have been greatly extended or newly constructed2 so that even if ,bacon's method had been the right one1 and had been complete as far as the progress of ,science up to his time could direct it1 there would be room for the revision and improvement of the methods of arriving at scientific knowledge4 ,inasmuch as we have gone through the ,histories of the principal ,sciences1 from the earliest up to the present time1 in a previous work1 and have also traced the ,history of ,scientific ,ideas in another work1 it may perhaps be regarded as not too presumptuous if we attempt this revision and improvement of the methods by which ,sciences must rise and grow4 ,this #d is our task in the present volume2 and to mark the reference of this undertaking to the work of ,bacon1 we name our book ,novum ,organon ,renovatum4 ,bacon has delivered his precepts in ,aphorisms1 some of them stated nakedly1 others expanded into dissertations4 ,the general results at which we have arrived by tracing the history of ,scientific ,ideas are the groundwork of such ,precepts as we have to give3 and ,i shall therefore begin by summing up these results in ,aphorisms1 referring to the former work for the historical proof that these ,aphorisms are true4 #e ,,novum ,,organon ,,renovatum4 ,,book ,i4 ,,aphorisms ,,concerning ,,ideas ,,derived ,,from ,,the ,,history ,,of ,,ideas4 ,i4 ,,man is the ,interpreter of ,nature1 ,science the right interpretation4 7,history of ,scientific ,ideas3 ,book ,i4 ,chapter #a47 ,,ii4 ,the ,senses place before us the ,characters of the ,book of ,nature2 but these convey no knowledge to us1 till we have discovered the ,alphabet by which they are to be read4 7,ibid4 ,i4 #b47 ,,iii4 ,the ,alphabet1 by means of which we interpret ,phenomena1 consists of the ,ideas existing in our own minds2 for these give to the phenomena that coherence and significance which is not an object of sense4 7,i4 #b47 ,,iv4 ,the antithesis of ,sense and ,ideas is the foundation of the ,philosophy of ,science4 ,no knowledge can exist without the union1 no philosophy without the separation1 of these two elements4 7,i4 #b47 #f ,v4 ,fact and ,theory correspond to ,sense on the one hand1 and to ,ideas on the other1 so far as we are conscious of our ,ideas3 but all facts involve ideas unconsciously2 and thus the distinction of ,facts and ,theories is not tenable1 as that of ,sense and ,ideas is4 7,i4 #b47 ,,vi4 ,sensations and ,ideas in our knowledge are like ,matter and ,form in bodies4 ,matter cannot exist without ,form1 nor ,form without ,matter3 yet the two are altogether distinct and opposite4 ,there is no possibility either of separating1 or of confounding them4 ,the same is the case with ,sensations and ,ideas4 7,i4 #b47 ,,vii4 ,ideas are not transformed1 but informed ,sensations2 for without ideas1 sensations have no form4 7,i4 #b47 ,,viii4 ,the ,sensations are the ,objective1 the ,ideas the ,subjective part of every act of perception or knowledge4 7,i4 #b47 ,,ix4 ,general ,terms denote ,ideal ,conceptions1 as a circle1 an orbit1 a rose4 ,these are not ,images of real things1 as was held by the ,realists1 but ,conceptions3 yet they are conceptions1 not bound together by mere ,name1 as the ,nominalists held1 but by an ,idea4 7,i4 #b47 ,x4 ,it has been said by some1 that all ,conceptions are merely states or feelings of the mind1 but this assertion only tends to confound what it is our business to distinguish4 7,i4 #b47 ,,xi4 ,observed ,facts are connected so as to produce new truths1 by superinducing upon them an ,idea3 and such truths are obtained by ,induction4 7,i4 #b47 #g ,,xii4 ,truths once obtained by legitimate ,induction are ,facts3 these ,facts may be again connected1 so as to produce higher truths3 and thus we advance to ,successive ,generalizations4 7,i4 #b47 ,,xiii4 ,truths obtained by ,induction are made compact and permanent by being expressed in ,technical ,terms4 7,i4 #c47 ,,xiv4 ,experience cannot conduct us to universal and necessary truths3--,not to universal1 because she has not tried all cases3--,not to necessary1 because necessity is not a matter to which experience can testify4 7,i4 #e47 ,,xv4 ,necessary truths derive their necessity from the ,ideas which they involve2 and the existence of necessary truths proves the existence of ,ideas not generated by experience4 7,i4 #e47 ,,xvi4 ,in ,deductive ,reasoning1 we cannot have any truth in the conclusion which is not virtually contained in the premises4 7,i4 #f47 ,,xvii4 ,in order to acquire any exact and solid knowledge1 the student must possess with perfect precision the ideas appropriate to that part of knowledge3 and this precision is tested by the student's perceiving the axiomatic evidence of the axioms belonging to each ,fundamental ,idea4 7,i4 #f47 ,,xviii4 ,the ,fundamental ,ideas which it is most important to consider1 as being the ,bases of the ,material ,sciences1 are the ,ideas of ,space1 ,time 7including ,number71 ,cause 7including ,force and ,matter71 ,outness of ,objects1 and ,media of ,perception of ,secondary ,qualities1 ,polarity 7,contrariety71 #h ,chemical ,composition and ,affinity1 ,substance1 ,likeness and ,natural ,affinity1 ,means and ,ends 7whence the ,notion of ,organization71 ,symmetry1 and the ,ideas of ,vital ,powers4 7,i4 #h47 ,,xix4 ,the ,sciences which depend upon the ,ideas of ,space and ,number are ,pure ,sciences1 not ,inductive ,sciences3 they do not infer special ,theories from ,facts1 but deduce the conditions of all theory from ,ideas4 ,the ,elementary ,pure ,sciences1 or ,elementary ,mathematics1 are ,geometry1 ,theoretical ,arithmetic and ,algebra4 7,,ii4 #a47 ,,xx4 ,the ,ideas on which the ,pure ,sciences depend1 are those of ,space and ,number2 but ,number is a modification of the conception of ,repetition1 which belongs to the ,idea of ,time4 7,,ii4 #a47 ,,xxi4 ,the ,idea of ,space is not derived from experience1 for experience of external objects presupposes bodies to exist in ,space1 ,space is a condition under which the mind receives the impressions of sense1 and therefore the relations of space are necessarily and universally true of all perceived objects4 ,space is a form of our perceptions1 and regulates them1 whatever the matter of them may be4 7,,ii4 #b47 ,,xxii4 ,space is not a ,general ,notion collected by abstraction from particular cases2 for we do not speak of ,spaces in general1 but of universal or absolute ,space4 ,absolute ,space is infinite4 ,all special spaces are in absolute space1 and are parts of it4 7,,ii4 #c47 ,,xxiii4 ,space is not a real object or thing1 distinct from the objects which exist in it2 but it is a real condition of the existence of external objects4 7,,ii4 #c47 #i ,,xxiv4 ,we have an ,intuition of objects in space2 that is1 we contemplate objects as made up of spatial parts1 and apprehend their spatial relations by the same act by which we apprehend the objects themselves4 7,,ii4 #c47 ,,xxv4 ,form or ,figure is space limited by boundaries4 ,space has necessarily three dimensions1 length1 breadth1 depth2 and no others which cannot be resolved into these4 7,,ii4 #c47 ,,xxvi4 ,the ,idea of ,space is exhibited for scientific purposes1 by the ,definitions and ,axioms of ,geometry2 such1 for instance1 as these3--the ,definition of a ,right ,angle1 and of a ,circle2--the ,definition of ,parallel ,lines1 and the ,axiom concerning them2--the ,axiom that two straight lines cannot inclose a space4 ,these ,definitions are necessary1 not arbitrary2 and the ,axioms are needed as well as the ,definitions1 in order to express the necessary conditions which the ,idea of ,space imposes4 7,,ii4 #d47 ,,xxvii4 ,the ,definitions and ,axioms of ,elementary ,geometry do not completely exhibit the ,idea of ,space4 ,in proceeding to the ,higher ,geometry1 we may introduce other additional and independent ,axioms2 such as that of ,archimedes1 that a curve line which joins two points is less than any broken line joining the same points and including the curve line4 7,,ii4 #d47 ,,xxviii4 ,the perception of a solid object by sight requires that act of mind by which1 from figure and shade1 we infer distance and position in space4 ,the perception of figure by sight requires that act of mind by which we give an outline to each object4 7,,ii4 #f47 #aj ,,xxix4 ,the perception of ,form by touch is not an impression on the passive sense1 but requires an act of our muscular frame by which we become aware of the position of our own limbs4 ,the perceptive faculty involved in this act has been called the muscular sense4 7,,ii4 #f47 ,,xxx4 ,the ,idea of ,time is not derived from experience1 for experience of changes presupposes occurrences to take place in ,time4 ,time is a condition under which the mind receives the impressions of sense1 and therefore the relations of time are necessarily and universally true of all perceived occurrences4 ,time is a form of our perceptions1 and regulates them1 whatever the matter of them may be4 7,,ii4 #g47 ,,xxxi4 ,time is not a ,general ,notion collected by abstraction from particular cases4 ,for we do not speak of particular ,times as examples of time in general1 but as parts of a single and infinite ,time4 7,,ii4 #h47 ,,xxxii4 ,time1 like ,space1 is a form1 not only of perception1 but of ,intuition4 ,we consider the whole of any time as equal to the sum of the parts2 and an occurrence as coinciding with the portion of time which it occupies4 7,,ii4 #h47 ,,xxxiii4 ,time is analogous to ,space of one dimension3 portions of both have a beginning and an end1 are long or short4 ,there is nothing in ,time which is analogous to ,space of two1 or of three1 dimensions1 and thus nothing which corresponds to ,figure4 7,,ii4 #h47 ,,xxxiv4 ,the ,repetition of a set of occurrences1 as1 for example1 strong and weak1 or long and short sounds1 according to a #aa steadfast order1 produces ,rhythm1 which is a conception peculiar to ,time1 as ,figure is to ,space4 7,,ii4 #h47 ,,xxxv4 ,the simplest form of ,repetition is that in which there is no variety1 and thus gives rise to the conception of ,number4 7,,ii4 #h47 ,,xxxvi4 ,the simplest numerical truths are seen by ,intuition2 when we endeavour to deduce the more complex from these simplest1 we employ such maxims as these3--,if equals be added to equals the wholes are equal3--,if equals be subtracted from equals the remainders are equal3--,the whole is equal to the sum of all its parts4 7,,ii4 #i47 ,,xxxvii4 ,the ,perception of ,time involves a constant and latent kind of memory1 which may be termed a ,sense of ,succession4 ,the ,perception of ,number also involves this ,sense of ,succession1 although in small numbers we appear to apprehend the units simultaneously and not successively4 7,,ii4 #aj47 ,,xxxviii4 ,the ,perception of ,rhythm is not an impression on the passive sense1 but requires an act of thought by which we connect and group the strokes which form the ,rhythm4 7,,ii4 #aj47 ,,xxxix4 ,intuitive is opposed to ,discursive reason4 ,in intuition1 we obtain our conclusions by dwelling upon one aspect of the fundamental ,idea2 in discursive reasoning1 we combine several aspects of the ,idea1 7that is1 several axioms17 and reason from the combination4 7,,ii4 #aa47 ,,xl4 ,geometrical deduction 7and deduction in general7 is called ,synthesis1 because we introduce1 at successive steps1 the #ab results of new principles4 ,but in reasoning on the relations of space1 we sometimes go on separating truths into their component truths1 and these into other component truths2 and so on3 and this is geometrical ,analysis4 7,,ii4 #aa47 ,,xli4 ,among the foundations of the ,higher ,mathematics1 is the ,idea of ,symbols considered as general ,signs of ,quantity4 ,this idea of a ,sign is distinct from1 and independent of other ideas4 ,the ,axiom to which we refer in reasoning by means of ,symbols of quantity is this3--,the interpretation of such symbols must be perfectly general4 ,this ,idea 9999and ,axiom are the bases of ,algebra in its most general form4 7,,ii4 #ab47 ,,xlii4 ,among the foundations of the ,higher ,mathematics is also the ,idea of a ,limit4 ,the ,idea of a ,limit cannot be superseded by any other definitions or ,hypotheses1 ,the ,axiom which we employ in introducing this ,idea into our reasoning is this3--,what is true up to the ,limit is true at the ,limit4 ,this ,idea and ,axiom are the bases of all ,methods of ,limits1 ,fluxions1 ,differentials1 ,variations1 and the like4 7,,ii4 #ab47 ,,xliii4 ,there is a pure ,science of ,motion1 which does not depend upon observed facts1 but upon the ,idea of motion4 ,it may also be termed ,pure ,mechanism1 in opposition to ,mechanics ,proper1 or ,machinery1 which involves the mechanical conceptions of force and matter4 ,it has been proposed to name this ,pure ,science of ,motion1 ,kinematics4 7,,ii4 #ac47 ,,xliv4 ,the pure ,mathematical ,sciences must be successfully cultivated1 in order that the progress of the principal ,inductive ,sciences may take place4 ,this appears in the case of ,astronomy1 in which ,science1 both in ancient and in modern times1 each advance of the theory has depended upon the #ac previous solution of problems in pure mathematics4 ,it appears also inversely in the ,science of the ,tides1 in which1 at present1 we cannot advance in the theory1 because we cannot solve the requisite problems in the ,integral ,calculus4 7,,ii4 #ad47 ,,xlv4 ,the ,idea of ,cause1 modified into the conceptions of mechanical cause1 or ,force1 and resistance to force1 or ,matter1 is the foundation of the ,mechanical ,sciences2 that is1 ,mechanics1 7including ,statics and ,dynamics17 ,hydrostatics1 and ,physical ,astronomy4 7,,iii4 #a47 ,,xlvi4 ,the ,idea of ,cause is not derived from experience2 for in judging of occurrences which we contemplate1 we consider them as being1 universally and necessarily1 ,causes and ,effects1 which a finite experience could not authorize us to do4 ,the ,axiom1 that every event must have a cause1 is true independently of experience1 and beyond the limits of experience4 7,,iii4 #b47 ,,xlvii4 ,the ,idea of ,cause is expressed for purposes of science by these three ,axioms3--,every ,event must have a ,cause3--,causes are measured by their ,effects3--,reaction is equal and opposite to ,action4 7,,iii4 #d47 ,,xlviii4 ,the ,conception of ,force involves the ,idea of ,cause1 as applied to the motion and rest of bodies4 ,the conception of force is suggested by muscular action exerted3 the conception of matter arises from muscular action resisted4 ,we necessarily ascribe to all bodies solidity and inertia1 since we conceive ,matter as that which cannot be compressed or moved without resistance4 7,,iii4 #e47 ,,xlix4 ,mechanical ,science depends on the ,conception of ,force2 and is divided into ,statics1 the doctrine of ,force preventing #ad motion1 and ,dynamics1 the doctrine of ,force producing motion4 7,,iii4 #f47 ,l4 ,the ,science of ,statics depends upon the ,axiom1 that ,action and ,reaction are equal1 which in ,statics assumes this form3--,when two equal weights are supported on the middle point between them1 the pressure on the fulcrum is equal to the sum of the weights4 7,,iii4 #f47 ,,li4 ,the ,science of ,hydrostatics depends upon the ,fundamental ,principle that fluids press equally in all directions4 ,this principle necessarily results from the conception of a ,fluid1 as a body of which the parts are perfectly moveable in all directions4 ,for since the ,fluid is a body1 it can transmit pressure2 and the transmitted pressure is equal to the original pressure1 in virtue of the ,axiom that ,reaction is equal to ,action4 ,that the ,fundamental ,principle is not derived from experience1 is plain both from its evidence and from its history4 7,,iii4 #f47 ,,lii4 ,the ,science of ,dynamics depends upon the three ,axioms above stated respecting ,cause4 ,the ,first ,axiom1--that every change must have a ,cause1--gives rise to the ,first ,law of ,motion1--that a body not acted upon by a force will move with a uniform velocity in a straight line4 ,the ,second ,axiom1--that ,causes are measured by their ,effects1--gives rise to the ,second ,law of ,motion1--that when a force acts upon a body in motion1 the effect of the force is compounded with the previously existing motion4 ,the ,third ,axiom1--that ,reaction is equal and opposite to ,action1--gives rise to the ,third ,law of ,motion1 which is expressed in the same terms as the ,axiom2 ,action and ,reaction being understood to signify momentum gained and lost4 7,,iii4 #g47 #ae ,,liii4 ,the above ,laws of ,motion1 historically speaking1 were established by means of experiment3 but since they have been discovered and reduced to their simplest form1 they have been considered by many philosophers as self-evident4 ,this result is principally due to the introduction and establishment of terms and definitions1 which enable us to express the ,laws in a very simple manner4 7,,iii4 #g47 ,,liv4 ,in the establishment of the ,laws of ,motion1 it happened1 in several instances1 that ,principles were assumed as self-evident which do not now appear evident1 but which have since been demonstrated from the simplest and most evident principles4 ,thus it was assumed that a perpetual motion is impossible2--that the velocities of bodies acquired by falling down planes or curves of the same vertical height are equal2--that the actual descent of the center of gravity is equal to its potential ascent4 ,but we are not hence to suppose that these assumptions were made without ground3 for since they really follow from the laws of motion1 they were probably1 in the minds of the discoverers1 the results of undeveloped demonstrations which their sagacity led them to divine4 7,,iii4 #g47 ,,lv4 ,it is a ,paradox that ,experience should lead us to truths confessedly universal1 and apparently necessary1 such as the ,laws of ,motion are4 ,the ,solution of this paradox is1 that these laws are interpretations of the ,axioms of ,causation4 ,the axioms are universally and necessarily true1 but the right interpretation of the terms which they involve1 is learnt by experience4 ,our ,idea of ,cause supplies the ,form1 ,experience1 the ,matter1 of these ,laws4 7,,iii4 #h47 ,,lvi4 ,primary ,qualities of ,bodies are those which we can conceive as directly perceived2 ,secondary ,qualities are those #af which we conceive as perceived by means of a ,medium4 7,,iv4 #a47 ,,lvii4 ,we necessarily perceive bodies as without us2 the ,idea of ,externality is one of the conditions of perception4 7,,iv4 #a47 ,,lviii4 ,we necessarily assume a ,medium for the perceptions of ,light1 ,colour1 ,sound1 ,heat1 ,odours1 ,tastes2 and this ,medium must convey impressions by means of its mechanical attributes4 7,,iv4 #a47 ,,lix4 ,secondary ,qualities are not extended but intensive3 their effects are not augmented by addition of parts1 but by increased operation of the medium4 ,hence they are not measured directly1 but by scales2 not by units1 but by degrees4 7,,iv4 #d47 ,,lx4 ,in the ,scales of ,secondary ,qualities1 it is a condition 7in order that the scale may be complete17 that every example of the quality must either agree with one of the degrees of the ,scale1 or lie between two contiguous degrees4 7,,iv4 #d47 ,,lxi4 ,we perceive by means of a medium and by means of impressions on the nerves3 but we do not 7by our senses7 perceive either the medium or the impressions on the nerves4 7,,iv4 #a47 ,,lxii4 ,the ,prerogatives of the ,sight are1 that by this sense we necessarily and immediately apprehend the position of its objects3 and that from visible circumstances1 we infer the distance of objects from us1 so readily that we seem to perceive and not to infer4 7,,iv4 #b47 #ag ,,lxiii4 ,the ,prerogatives of the ,hearing are1 that by this sense we perceive relations perfectly precise and definite between two notes1 namely1 ,musical ,intervals 7as an ,octave1 a ,fifth72 and that when two notes are perceived together1 they are comprehended as distinct1 7a ,chord17 and as having a certain relation1 7,concord or ,discord47 7,,iv4 #b47 ,,lxiv4 ,the ,sight cannot decompose a compound colour into simple colours1 or distinguish a compound from a simple colour4 ,the ,hearing cannot directly perceive the place1 still less the distance1 of its objects3 we infer these obscurely and vaguely from audible circumstances4 7,,iv4 #b47 ,,lxv4 ,the ,first ,paradox of ,vision is1 that we see objects upright1 though the images on the retina are inverted4 ,the solution is1 that we do not see the image on the retina at all1 we only see by means of it4 7,,iv4 #b47 ,,lxvi4 ,the ,second ,paradox of ,vision is1 that we see objects single1 though there are two images on the retinas1 one in each eye4 ,the explanation is1 that it is a ,law of ,vision that we see 7small or distant7 objects single1 when their images fall on corresponding points of the two retinas4 7,,iv4 #b47 ,,lxvii4 ,the law of single vision for near objects is this3--,when the two images in the two eyes are situated1 part for part1 nearly but not exactly1 upon corresponding points1 the object is apprehended as single and solid if the two objects are such as would be produced by a single solid object seen by the eyes separately4 7,,iv4 #b47 ,,lxviii4 ,the ultimate object of each of the ,secondary ,mechanical ,sciences is1 to determine the nature and laws of the processes #ah by which the impression of the ,secondary ,quality treated of is conveyed3 but before we discover the cause1 it may be necessary to determine the laws of the phenomena2 and for this purpose a ,measure or ,scale of each quality is necessary4 7,,iv4 #d47 ,,lxix4 ,secondary qualities are measured by means of such effects as can be estimated in number or space4 7,,iv4 #d47 ,,lxx4 ,the ,measure of ,sounds1 as high or low1 is the ,musical ,scale1 or ,harmonic ,canon4 7,,iv4 #d47 ,,lxxi4 ,the ,measures of ,pure ,colours are the ,prismatic ,scale2 the same1 including ,fraunhofer's ,lines2 and ,newton's ,scale of ,colours4 ,the principal ,scales of ,impure ,colours are ,werner's ,nomenclature of ,colours1 and ,merime's ,nomenclature of ,colours4 7,,iv4 #d47 ,,lxxii4 ,the ,idea of ,polarity involves the conception of contrary properties in contrary directions3--the properties being1 for example1 attraction and repulsion1 darkness and light1 synthesis and analysis2 and the contrary directions being those which are directly opposite1 or1 in some cases1 those which are at right angles4 7,v4 #a47 ,,lxxiii4 7,doubtful47 ,coexistent polarities are fundamentally identical4 7,v4 #b47 ,,lxxiv4 ,the ,idea of ,chemical ,affinity1 as implied in ,elementary ,composition1 involves peculiar conceptions4 ,it is not properly expressed by assuming the qualities of bodies to resemble those of the elements1 or to depend on the figure of the elements1 or on their attractions4 7,,vi4 #a47 #ai ,,lxxv4 ,attractions take place between bodies1 ,affinities between the particles of a body4 ,the former may be compared to the alliances of states1 the latter to the ties of family4 7,,vi4 #b47 ,,lxxvi4 ,the governing principles of ,chemical ,affinity are1 that it is elective2 that it is definite2 that it determines the properties of the compound2 and that analysis is possible4 7,,vi4 #b47 ,,lxxvii4 ,we have an idea of ,substance3 and an axiom involved in this ,idea is1 that the weight of a body is the sum of the weights of all its elements4 7,,vi4 #c47 ,,lxxviii4 ,hence ,imponderable ,fluids are not to be admitted as chemical elements4 7,,vi4 #d47 ,,lxxix4 ,the ,doctrine of ,atoms is admissible as a mode of expressing and calculating laws of nature2 but is not proved by any fact1 chemical or physical1 as a philosophical truth4 7,,vi4 #e47 ,,lxxx4 ,we have an ,idea of ,symmetry2 and an axiom involved in this ,idea is1 that in a symmetrical natural body1 if there be a tendency to modify any member in any manner1 there is a tendency to modify all the corresponding members in the same manner4 7,,vii4 #a47 ,,lxxxi4 ,all hypotheses respecting the manner in which the elements of inorganic bodies are arranged in space1 must be constructed with regard to the general facts of crystallization4 7,,vii4 #c47 #bj ,,lxxxii4 ,when we consider any object as ,one1 we give unity to it by an act of thought4 ,the condition which determines what this unity shall include1 and what it shall exclude1 is this2--that assertions concerning the one thing shall be possible4 7,,viii4 #a47 ,,lxxxiii4 ,we collect individuals into ,kinds by applying to them the ,idea of ,likeness4 ,kinds of things are not determined by definitions1 but by this condition3--that general assertions concerning such kinds of things shall be possible4 7,,viii4 #a47 ,,lxxxiv4 ,the ,names of kinds of things are governed by their use2 and that may be a right name in one use which is not so in another4 ,a whale is not a fish in natural history1 but it is a fish in commerce and law4 7,,viii4 #a47 ,,lxxxv4 ,we take for granted that each kind of things has a special character which may be expressed by a ,definition4 ,the ground of our assumption is this2--that reasoning must be possible4 7,,viii4 #a47 ,,lxxxvi4 ,the ,five ,words1 ,genus1 ,species1 ,difference1 ,property1 ,accident1 were used by the ,aristotelians1 in order to express the subordination of ,kinds1 and to describe the nature of ,definitions and ,propositions4 ,in modern times1 these technical expressions have been more referred to by ,natural ,historians than by ,metaphysicians4 7,,viii4 #a47 ,,lxxxvii4 ,the construction of a ,classificatory ,science includes ,terminology1 the formation of a descriptive language2--,diataxis1 the ,plan of the ,system of ,classification1 called #ba also the ,systematick2--,diagnosis1 the ,scheme of the ,characters by which the different ,classes are known1 called also the ,characteristick4 ,physiography is the knowledge which the ,system is employed to convey4 ,diataxis includes ,nomenclature4 7,,viii4 #b47 ,,lxxxviii4 ,terminology must be conventional1 precise1 constant2 copious in words1 and minute in distinctions1 according to the needs of the science4 ,the student must understand the terms1 directly according to the convention1 not through the medium of explanation or comparison4 7,,viii4 #b47 ,,lxxxix4 ,the ,diataxis1 or ,plan of the ,system1 may aim at a ,natural or at an ,artificial ,system4 ,but no classes can be absolutely artificial1 for if they were1 no assertions could be made concerning them4 7,,viii4 #b47 ,,xc4 ,an ,artificial ,system is one in which the smaller groups 7the ,genera7 are natural2 and in which the wider divisions 7,classes1 ,orders7 are constructed by the peremptory application of selected ,characters2 7selected1 however1 so as not to break up the smaller groups47 7,,viii4 #b47 ,,xci4 ,a ,natural ,system is one which attempts to make all the divisions natural1 the widest as well as the narrowest2 and therefore applies no characters peremptorily4 7,,viii4 #b47 ,,xcii4 ,natural ,groups are best described1 not by any ,definition which marks their boundaries1 but by a ,type which marks their center4 ,the ,type of any natural group is an example which possesses in a marked degree all the leading characters of the class4 7,,viii4 #b47 #bb ,,xciii4 ,a ,natural ,group is steadily fixed1 though not precisely limited2 it is given in position1 though not circumscribed2 it is determined1 not by a boundary without1 but by a central point within2--not by what it strictly excludes1 but by what it eminently includes2--by a ,type1 not by a ,definition4 7,,viii4 #b47 ,,xciv4 ,the prevalence of ,mathematics as an element of education has made us think ,definition the philosophical mode of fixing the meaning of a word3 if 7,scientific7 ,natural ,history were introduced into education1 men might become familiar with the fixation of the signification of words by ,types2 and this process agrees more nearly with the common processes by which words acquire their significations4 7,,viii4 #b47 ,,xcv4 ,the attempts at ,natural ,classification are of three sorts2 according as they are made by the process of blind trial1 of general comparison1 or of subordination of characters4 ,the process of ,blind ,trial professes to make its classes by attention to all the characters1 but without proceeding methodically4 ,the process of ,general ,comparison professes to enumerate all the characters1 and forms its classes by the majority4 ,neither of these methods can really be carried into effect4 ,the method of ,subordination of ,characters considers some characters as more important than others2 and this method gives more consistent results than the others4 ,this method1 however1 does not depend upon the ,idea of ,likeness only1 but introduces the ,idea of ,organization or ,function4 7,,viii4 #b47 ,,xcvi4 ,a ,species is a collection of individuals1 which are descended from a common stock1 or which resemble such a collection as much as these resemble each other3 the resemblance being opposed to a definite difference4 7,,viii4 #b47 #bc ,,xcvii4 ,a ,genus is a collection of species which resemble each other more than they resemble other species3 the resemblance being opposed to a definite difference4 7,,viii4 #b47 ,,xcviii4 ,the ,nomenclature of a ,classificatory ,science is the collection of the names of the ,species1 ,genera1 and other divisions4 ,the binary nomenclature1 which denotes a species by the generic and specific name1 is now commonly adopted in ,natural ,history4 7,,viii4 #b47 ,,xcix4 ,the ,diagnosis1 or ,scheme of the ,characters1 comes1 in the order of philosophy1 after the ,classification4 ,the characters do not make the classes1 they only enable us to recognize them4 ,the ,diagnosis is an ,artificial ,key to a ,natural ,system4 7,,viii4 #b47 ,c4 ,the basis of all ,natural ,systems of ,classification is the ,idea of ,natural ,affinity4 ,the ,principle which this ,idea involves is this3--,natural arrangements1 obtained from different sets of characters1 must coincide with each other4 7,,viii4 #d47 ,,ci4 ,in order to obtain a ,science of ,biology1 we must analyse the ,idea of ,life4 ,it has been proved by the biological speculations of past time1 that ,organic ,life cannot rightly be solved into ,mechanical or ,chemical ,forces1 or the operation of a ,vital ,fluid1 or of a ,soul4 7,,ix4 #b47 ,,cii4 ,life is a ,system of ,vital ,forces2 and the conception of such ,forces involves a peculiar ,fundamental ,idea4 7,,ix4 #c47 #bd ,,ciii4 ,mechanical1 chemical1 and vital ,forces form an ascending progression1 each including the preceding4 ,chemical ,affinity includes in its nature ,mechanical ,force1 and may often be practically resolved into ,mechanical ,force4 7,thus the ingredients of gunpowder1 liberated from their chemical union1 exert great mechanical ,force3 a galvanic battery acting by chemical process does the like47 ,vital ,forces include in their nature both chemical ,affinities and mechanical ,forces3 for ,vital ,powers produce both chemical changes1 7as digestion17 and motions which imply considerable mechanical force1 7as the motion of the sap and of the blood47 7,,ix4 #d47 ,,civ4 ,in voluntary motions1 ,sensations produce ,actions1 and the connexion is made by means of ,ideas3 in reflected motions1 the connexion neither seems to be nor is made by means of ,ideas3 in instinctive motions1 the connexion is such as requires ,ideas1 but we cannot believe the ,ideas to exist4 7,,ix4 #e47 ,,cv4 ,the ,assumption of a ,final ,cause in the structure of each part of animals and plants is as inevitable as the assumption of an ,efficient ,cause for every event4 ,the maxim that in organized bodies nothing is in vain1 is as necessarily true as the maxim that nothing happens by chance4 7,,ix4 #f47 ,,cvi4 ,the ,idea of living beings as subject to disease includes a recognition of a ,final ,cause in organization2 for disease is a state in which the vital forces do not attain their proper ends4 7,,ix4 #g47 ,,cvii4 ,the ,paltiological ,sciences depend upon the ,idea of ,cause3 but the leading conception which they involve is that of historical cause1 not mechanical cause4 7,x4 #a47 #be ,,cviii4 ,each ,paltiological ,science1 when complete1 must possess three members3 the ,phenomenology1 the tiology1 and the ,theory4 7,x4 #b47 ,,cix4 ,there are1 in the ,paltiological ,sciences1 two antagonist doctrines3 ,catastrophes and ,uniformity4 ,the doctrine of a uniform course of nature is tenable only when we extend the nation of ,uniformity so far that it shall include ,catastrophes4 7,x4 #c47 ,,cx4 ,the ,catastrophist constructs ,theories1 the ,uniformitarian demolishes them4 ,the former adduces evidence of an ,origin1 the latter explains the evidence away4 ,the ,catastrophist's dogmatism is undermined by the ,uniformitarian's skeptical hypotheses4 ,but when these hypotheses are asserted dogmatically they cease to be consistent with the doctrine of ,uniformity4 7,x4 #c47 ,,cxi4 ,in each of the ,paltiological ,sciences1 we can ascend to remote periods by a chain of causes1 but in none can we ascend to a beginning of the chain4 7,x4 #c47 ,,cxii4 ,since the ,paltiological sciences deal with the conceptions of historical cause1 ,history1 including ,tradition1 is an important source of materials for such sciences4 7,x4 #d47 ,,cxiii4 ,the history and tradition which present to us the providential course of the world form a ,sacred ,narrative2 and in reconciling the ,sacred ,narrative with the results of science1 arise inevitable difficulties which disturb the minds of those who reverence the ,sacred ,narrative4 7,x4 #d47 #bf ,,cxiv4 ,the disturbance of reverent minds1 arising from scientific views1 ceases when such views become familiar1 the ,sacred ,narrative being then interpreted anew in accordance with such views4 7,x4 #d47 ,,cxv4 ,a new interpretation of the ,sacred ,narrative1 made for the purpose of reconciling it with doctrines of science1 should not be insisted on till such doctrines are clearly proved2 and when they are so proved1 should be frankly accepted1 in the confidence that a reverence for the ,sacred ,narrative is consistent with a reverence for the ,truth4 7,x4 #d47 ,,cxvi4 ,in contemplating the series of causes and effects which constitutes the world1 we necessarily assume a ,first ,cause of the whole series4 7,x4 #e47 ,,cxvii4 ,the ,paltiological ,sciences point backwards with lines which are broken1 but which all converge to the same invisible point3 and this point is the ,origin of the ,moral and ,spiritual1 as well as of the ,natural ,world4 7,x4 #e47 ,,novum ,,organon ,,renovatum4 #bg ,,book ,,ii4 ,,of ,,the ,,construction ,,of ,,science4 ,,chapter ,i4 ,,of ,,two ,,principal ,,processes ,,by ,,which ,,science ,,is ,,constructed4 ,,aphorism ,i4 ,,the two processes by which ,science is constructed are the ,explication of ,conceptions1 and the ,colligation of ,facts4 ,,to the subject of the present and next ,book all that has preceded is subordinate and preparatory4 ,in former works we have treated of the ,history of ,scientific ,discoveries and of the ,history of ,scientific ,ideas4 ,we have now to attempt to describe the manner in which discoveries are made1 and in which ,ideas give rise to knowledge4 ,it has already been stated that ,knowledge requires us to possess both ,facts and ,ideas2--that every step in our knowledge consists in applying the ,ideas and ,conceptions furnished by our minds to the ,facts which observation and experiment offer to us4 ,when our ,conceptions are clear and distinct1 when our ,facts are certain and sufficiently numerous1 and when the ,conceptions1 being suited to the nature of the #bh ,facts1 are applied to them so as to produce an exact and universal accordance1 we attain knowledge of a precise and comprehensive kind1 which we may term ,science4 ,and we apply this term to our knowledge still more decidedly when1 ,facts being thus included in exact and general ,propositions1 such ,propositions are1 in the same manner1 included with equal rigour in ,propositions of a higher degree of ,generality2 and these again in others of a still wider nature1 so as to form a large and systematic whole4 ,but after thus stating1 in a general way1 the nature of science1 and the elements of which it consists1 we have been examining with a more close and extensive scrutiny1 some of those elements2 and we must now return to our main subject1 and apply to it the results of our long investigation4 ,we have been exploring the realm of ,ideas2 we have been passing in review the difficulties in which the workings of our own minds involve us when we would make our conceptions consistent with themselves3 and we have endeavoured to get a sight of the true solutions of these difficulties4 ,we have now to inquire how the results of these long and laborious efforts of thought find their due place in the formation of our ,knowledge4 ,what do we gain by these attempts to make our notions distinct and consistent2 and in what manner is the gain of which we thus become possessed1 carried to the general treasure-house of our permanent and indestructible knowledge8 ,after all this battling in the world of ideas1 all this struggling with the shadowy and changing forms of intellectual perplexity1 how do we secure to ourselves the fruits of our warfare1 and assure ourselves that we have really pushed forwards the frontier of the empire of ,science8 ,it is by such an appropriation1 that the task which we have had in our hands during the two previous works1 7the ,history of the ,inductive ,sciences and the ,history of ,scientific ,ideas17 must acquire its real value and true place in our design4 ,in order to do this1 we must reconsider1 in a more definite and precise shape1 the doctrine which has already been laid down2--that our ,knowledge consists #bi in applying ,ideas to ,facts2 and that the conditions of real knowledge are that the ideas be distinct and appropriate1 and exactly applied to clear and certain facts4 ,the steps by which our knowledge is advanced are those by which one or the other of these two processes is rendered more complete2--by which ,conceptions are made more clear in themselves1 or by which the ,conceptions more strictly bind together the ,facts4 ,these two processes may be considered as together constituting the whole formation of our knowledge2 and the principles which have been established in the ,history of ,scientific ,ideas bear principally upon the former of these two operations2--upon the business of elevating our conceptions to the highest possible point of precision and generality4 ,but these two portions of the progress of knowledge are so clearly connected with each other1 that we shall deal with them in immediate succession4 ,and having now to consider these operations in a more exact and formal manner than it was before possible to do1 we shall designate them by certain constant and technical phrases4 ,we shall speak of the two processes by which we arrive at science1 as the ,explication of ,conceptions and the ,colligation of ,facts3 we shall show how the discussions in which we have been engaged have been necessary in order to promote the former of these offices2 and we shall endeavour to point out modes1 maxims1 and principles by which the second of the two tasks may also be furthered4 #cj ,,chapter ,,ii4 ,,of ,,the ,,explication ,,of ,,conceptions4 ,,aphorism ,,ii4 ,the ,explication of ,conceptions1 as requisite for the progress of science1 has been effected by means of discussions and controversies among scientists2 often by debates concerning definitions2 these controversies have frequently led to the establishment of a ,definition2 but along with the ,definition1 a corresponding ,proposition has always been expressed or implied4 ,the essential requisite for the advance of science is the clearness of the ,conception1 not the establishment of a ,definition4 ,the construction of an exact ,definition is often very difficult4 ,the requisite conditions of clear ,conceptions may often be expressed by ,axioms as well as by ,definitions4 ,,aphorism ,,iii4 ,conceptions1 for purposes of science1 must be appropriate as well as clear3 that is1 they must be modifications of that ,fundamental ,idea1 by which the phenomena can really be interpreted4 ,this maxim may warn us from errour1 though it may not lead to discovery4 ,discovery depends upon the previous cultivation or natural clearness of the appropriate ,idea1 and therefore no discovery is the work of accident4 ,,sect4 ,i4--,historical ,progress of the ,explication of ,conceptions4 #a4 ,,we have given the appellation of ,ideas to certain comprehensive forms of thought1--as space1 number1 cause1 composition1 resemblance1--which we apply to the phenomena which we contemplate4 ,but the special modifications of these ideas which are #ca exemplified in particular facts1 we have termed ,conceptions2 as a circle1 a square number1 an accelerating force1 a neutral combination of elements1 a genus4 ,such ,conceptions involve in themselves certain necessary and universal relations derived from the ,ideas just enumerated2 and these relations are an indispensable portion of the texture of our knowledge4 ,but to determine the contents and limits of this portion of our knowledge1 requires an examination of the ,ideas and ,conceptions from which it proceeds4 ,the ,conceptions must be1 as it were1 carefully unfolded1 so as to bring into clear view the elements of truth with which they are marked from their ideal origin4 ,this is one of the processes by which our knowledge is extended and made more exact2 and this ,i shall describe as the ,explication of ,conceptions4 ,in the several ,books of the ,history of ,ideas we have discussed a great many of the ,fundamental ,ideas of the most important existing sciences4 ,we have1 in those ,books1 abundant exemplifications of the process now under our consideration4 ,we shall here add a few general remarks1 suggested by the survey which we have thus made4 #b4 ,such discussions as those in which we have been engaged concerning our fundamental ,ideas1 have been the course by which1 historically speaking1 those ,conceptions which the existing sciences involve have been rendered so clear as to be fit elements of exact knowledge4 ,thus1 the disputes concerning the various kinds and measures of ,force were an important part of the progress of the science of ,mechanics4 ,the struggles by which philosophers attained a right general conception of plane1 of circular1 of elliptical ,polarization1 were some of the most difficult steps in the modern discoveries of ,optics4 ,a ,conception of the ,atomic ,constitution of bodies1 such as shall include what we know1 and assume nothing more1 is even now a matter of conflict among ,chemists4 ,the debates by which1 in recent times1 the ,conceptions of ,species and ,genera have been rendered more exact1 have improved the science of ,botany3 the imperfection of the science of #cb ,mineralogy arises in a great measure from the circumstance1 that in that subject1 the ,conception of a ,species is not yet fixed4 ,in ,physiology1 what a vast advance would that philosopher make1 who should establish a precise1 tenable1 and consistent ,conception of ,life6 ,thus discussions and speculations concerning the import of very abstract and general terms and notions1 may be1 and in reality have been1 far from useless and barren4 ,such discussions arose from the desire of men to impress their opinions on others1 but they had the effect of making the opinions much more clear and distinct4 ,in trying to make others understand them1 they learnt to understand themselves4 ,their speculations were begun in twilight1 and ended in the full brilliance of day4 ,it was not easily and at once1 without expenditure of labour or time1 that men arrived at those notions which now form the elements of our knowledge2 on the contrary1 we have1 in the history of science1 seen how hard1 discoverers1 and the forerunners of discoverers1 have had to struggle with the indistinctness and obscurity of the intellect1 before they could advance to the critical point at which truth became clearly visible4 ,and so long as1 in this advance1 some speculators were more forward than others1 there was a natural and inevitable ground of difference of opinion1 of argumentation1 of wrangling4 ,but the tendency of all such controversy is to diffuse truth and to dispel errour4 ,truth is consistent1 and can bear the tug of war2 ,errour is incoherent1 and falls to pieces in the struggle4 ,true ,conceptions can endure the sun1 and become clearer as a fuller light is obtained2 confused and inconsistent notions vanish like visionary spectres at the break of a brighter day4 ,and thus all the controversies concerning such ,conceptions as science involves1 have ever ended in the establishment of the side on which the truth was found4 #c4 ,indeed1 so complete has been the victory of truth in most of these instances1 that at present we can hardly imagine the struggle to have been necessary4 ,the very essence of these triumphs is that they lead us to regard the views we reject as not only false1 #cc but inconceivable4 ,and hence we are led rather to look back upon the vanquished with contempt than upon the victors with gratitude4 ,we now despise those who1 in the ,copernican controversy1 could not conceive the apparent motion of the sun on the heliocentric hypothesis2--or those who1 in opposition to ,galileo1 thought that a uniform force might be that which generated a velocity proportional to the space2--or those who held there was something absurd in ,newton's doctrine of the different refrangibility of differently coloured rays2--or those who imagined that when elements combine1 their sensible qualities must be manifest in the compound2--or those who were reluctant to give up the distinction of vegetables into herbs1 shrubs1 and trees4 ,we cannot help thinking that men must have been singularly dull of comprehension1 to find a difficulty in admitting what is to us so plain and simple4 ,we have a latent persuasion that we in their place should have been wiser and more clear-sighted2--that we should have taken the right side1 and given our assent at once to the truth4 #d4 ,yet in reality1 such a persuasion is a mere delusion4 ,the persons who1 in such instances as the above1 were on the losing side1 were very far1 in most cases1 from being persons more prejudiced1 or stupid1 or narrow-minded1 than the greater part of mankind now are2 and the cause for which they fought was far from being a manifestly bad one1 till it had been so decided by the result of the war4 ,it is the peculiar character of scientific contests1 that what is only an epigram with regard to other warfare is a truth in this2--,they who are defeated are really in the wrong4 ,but they may1 nevertheless1 be men of great subtilty1 sagacity1 and genius2 and we nourish a very foolish self-complacency when we suppose that we are their superiors4 ,that this is so1 is proved by recollecting that many of those who have made very great discoveries have laboured under the imperfection of thought which was the obstacle to the next step in knowledge4 ,though ,kepler detected with great acuteness the ,numerical ,laws of the solar system1 he laboured in #cd vain to conceive the very simplest of the ,laws of ,motion by which the paths of the planets are governed4 ,though ,priestley made some important steps in chemistry1 he could not bring his mind to admit the doctrine of a general ,principle of ,oxidation4 ,how many ingenious men in the last century rejected the ,newtonian ,attraction as an impossible chimera6 ,how many more1 equally intelligent1 have1 in the same manner1 in our own time1 rejected1 ,i do not now mean as false1 but as inconceivable1 the doctrine of ,luminiferous ,undulations6 ,to err in this way is the lot1 not only of men in general1 but of men of great endowments1 and very sincere love of truth4 #e4 ,and those who liberate themselves from such perplexities1 and who thus go on in advance of their age in such matters1 owe their superiority in no small degree to such discussions and controversies as those to which we now refer4 ,in such controversies1 the ,conceptions in question are turned in all directions1 examined on all sides2 the strength and the weakness of the maxims which men apply to them are fully tested2 the light of the brightest minds is diffused to other minds4 ,inconsistency is unfolded into self-contradiction2 axioms are built up into a system of necessary truths2 and ready exemplifications are accumulated of that which is to be proved or disproved1 concerning the ideas which are the basis of the controversy4 ,the ,history of ,mechanics from the time of ,kepler to that of ,lagrange1 is perhaps the best exemplification of the mode in which the progress of a science depends upon such disputes and speculations as give clearness and generality to its elementary conceptions4 ,this1 it is to be recollected1 is the kind of progress of which we are now speaking2 and this is the principal feature in the portion of scientific history which we have mentioned4 ,for almost all that was to be done by reference to observation1 was executed by ,galileo and his disciples4 ,what remained was the task of generalization and simplification4 ,and this was promoted in no small degree by the various controversies which took place within that period concerning #ce mechanical conceptions3--as1 for example1 the question concerning the measure of the ,force of ,percussion2--the war of the ,vis ,viva2--the controversy of the ,center of ,oscillation2--of the independence of ,statics and ,dynamics2--of the principle of ,least ,action2--of the evidence of the ,laws of ,motion2--and of the number of ,laws really distinct4 ,none of these discussions was without its influence in giving generality and clearness to the mechanical ideas of mathematicians3 and therefore1 though remote from general apprehension1 and dealing with very abstract notions1 they were of eminent use in the perfecting the science of ,mechanics4 ,similar controversies concerning fundamental notions1 those1 for example1 which ,galileo himself had to maintain1 were no less useful in the formation of the science of ,hydrostatics4 ,and the like struggles and conflicts1 whether they take the form of controversies between several persons1 or only operate in the efforts and fluctuations of the discoverer's mind1 are always requisite1 before the conceptions acquire that clearness which makes them flt to appear in the enunciation of scientific truth4 ,this1 then1 was one object of the ,history of ,ideas2--to bring under the reader's notice the main elements of the controversies which have thus had so important a share in the formation of the existing body of science1 and the decisions on the controverted points to which the mature examination of the subject has led2 and thus to give an abundant exhibition of that step which we term the ,explication of ,conceptions4 ,,sect4 ,,ii4--,use of ,definitions4 #f4 ,the result of such controversies as we have been speaking of1 often appears to be summed up in a ,definition2 and the controversy itself has often assumed the form of a battle of definitions4 ,for example1 the inquiry concerning the ,laws of ,falling ,bodies led to the question whether the proper ,definition of a uniform force is1 that it generates a velocity proportional to the space from rest1 or to the time4 ,the controversy of the ,vis ,viva was1 what was the #cf proper ,definition of the measure of force4 ,a principal question in the classification of minerals is1 what is the ,definition of a mineral species4 ,physiologists have endeavoured to throw light on their subject1 by ,defining organization1 or some similar term4 #g4 ,it is very important for us to observe1 that these controversies have never been questions of insulated and arbitrary ,definitions1 as men seem often tempted to suppose them to have been4 ,in all cases there is a tacit assumption of some ,proposition which is to be expressed by means of the ,definition1 and which gives it its importance4 ,the dispute concerning the ,definition thus acquires a real value1 and becomes a question concerning true and false4 ,thus in the discussion of the question1 ,what is a ,uniform ,force8 it was taken for granted that 'gravity is a uniform force3'--in the debate of the ,vis ,viva1 it was assumed that 'in the mutual action of bodies the whole effect of the force is unchanged3'--in the zoological definition of ,species1 7that it consists of individuals which have1 or may have1 sprung from the same parents17 it is presumed that 'individuals so related resemble each other more than those which are excluded by such a definition2' or perhaps1 that 'species so defined have permanent and definite differences4' ,a definition of ,organization1 or of any other term1 which was not employed to express some principle1 would be of no value4 ,the establishment1 therefore1 of a right ,definition of a ,term may be a useful step in the ,explication of our ,conceptions2 but this will be the case then only when we have under our consideration some ,proposition in which the ,term is employed4 ,for then the question really is1 how the ,conception shall be understood and defined in order that the ,proposition may be true4 #h4 ,the establishment of a ,proposition requires an attention to observed ,facts1 and can never be rightly derived from our ,conceptions alone4 ,we must hereafter consider the necessity which exists that the ,facts should be rightly bound together1 as well as that our ,conceptions should be clearly employed1 in order to #cg lead us to real knowledge4 ,but we may observe here that1 in such cases at least as we are now considering1 the two processes are co-ordinate4 ,to unfold our ,conceptions by the means of ,definitions1 has never been serviceable to science1 except when it has been associated with an immediate use of the ,definitions4 ,the endeavour to define a uniform ,force was combined with the assertion that 'gravity is a uniform force3' the attempt to define ,accelerating ,force was immediately followed by the doctrine that 'accelerating forces may be compounded3' the process of defining ,momentum was connected with the principle that 'momenta gained and lost are equal3' naturalists would have given in vain the ,definition of ,species which we have quoted1 if they had not also given the 'characters' of species so separated4 ,definition and ,proposition are the two handles of the instrument by which we apprehend truth2 the former is of no use without the latter4 ,definition may be the best mode of explaining our ,conception1 but that which alone makes it worth while to explain it in any mode1 is the opportunity of using it in the expression of ,truth4 ,when a ,definition is propounded to us as a useful step in knowledge1 we are always entitled to ask what ,principle it serves to enunciate4 ,if there be no answer to this inquiry1 we define and give clearness to our conceptions in vain4 ,while we labour at such a task1 we do but light up a vacant room2--we sharpen a knife with which we have nothing to cut2--we take exact aim1 while we load our artillery with blank cartridge2--we apply strict rules of grammar to sentences which have no meaning4 ,if1 on the other hand1 we have under our consideration a proposition probably established1 every step which we can make in giving distinctness and exactness to the ,terms which this proposition involves1 is an important step towards scientific truth4 ,in such cases1 any improvement in our ,definition is a real advance in the explication of our ,conception4 ,the clearness of our impressions casts a light upon the ,ideas which we contemplate and convey to others4 #ch #i4 ,but though ,definition may be subservient to a right explication of our conceptions1 it is not essential to that process4 ,it is absolutely necessary to every advance in our knowledge1 that those by whom such advances are made should possess clearly the conceptions which they employ3 but it is by no means necessary that they should unfold these conceptions in the words of a formal ,definition4 ,it is easily seen1 by examining the course of ,galileo's discoveries1 that he had a distinct conception of the ,moving ,force which urges bodies downwards upon an inclined plane1 while he still hesitated whether to call it ,momentum1 ,energy1 ,impetus1 or ,force1 and did not venture to offer a ,definition of the thing which was the subject of his thoughts4 ,the ,conception of ,polarization was clear in the minds of many optical speculators1 from the time of ,huyghens and ,newton to that of ,young and ,fresnel4 ,this ,conception we have defined to be ',opposite properties depending upon opposite positions2' but this notion was1 by the discoverers1 though constantly assumed and expressed by means of superfluous hypotheses1 never clothed in definite language4 ,and in the mean time1 it was the custom1 among subordinate writers on the same subjects1 to say1 that the term ,polarization had no definite meaning1 and was merely an expression of our ignorance4 ,the ,definition which was offered by ,hay and others of a ,mineralogical ,species2--',the same elements combined in the same proportions1 with the same fundamental form2'--was false1 inasmuch as it was incapable of being rigorously applied to any one case2 but this defect did not prevent the philosophers who propounded such a ,definition from making many valuable additions to mineralogical knowledge1 in the way of identifying some species and distinguishing others4 ,the right ,conception which they possessed in their minds prevented their being misled by their own very erroneous ,definition4 ,the want of any precise ,definitions of ,strata1 and ,formations1 and ,epochs1 among geologists1 has not prevented the discussions which they have carried on upon such subjects from being highly serviceable #ci in the promotion of geological knowledge4 ,for however much the apparent vagueness of these terms might leave their arguments open to cavil1 there was a general understanding prevalent among the most intelligent cultivators of the science1 as to what was meant in such expressions2 and this common understanding sufficed to determine what evidence should be considered conclusive and what inconclusive1 in these inquiries4 ,and thus the distinctness of ,conception1 which is a real requisite of scientific progress1 existed in the minds of the inquirers1 although ,definitions1 which are a partial and accidental evidence of this distinctness1 had not yet been hit upon4 ,the ,idea had been developed in men's minds1 although a clothing of words had not been contrived for it1 nor1 perhaps1 the necessity of such a vehicle felt3 and thus that essential condition of the progress of knowledge1 of which we are here speaking1 existed2 while it was left to the succeeding speculators to put this unwritten ,rule in the form of a verbal ,statute4 #aj4 ,men are often prone to consider it as a thoughtless omission of an essential circumstance1 and as a neglect which involves some blame1 when knowledge thus assumes a form in which ,definitions1 or rather ,conceptions1 are implied but are not expressed4 ,but in such a judgment1 they assume that to be a matter of choice requiring attention only1 which is in fact as difficult and precarious as any other portion of the task of discovery4 ,to define1 so that our ,definition shall have any scientific value1 requires no small portion of that sagacity by which truth is detected4 ,as we have already said1 ,definitions and ,propositions are co-ordinate in their use and in their origin4 ,in many cases1 perhaps in most1 the ,proposition which contains a scientific truth1 is apprehended with confidence1 but with some vagueness and vacillation1 before it is put in a positive1 distinct1 and definite form4--,it is thus known to be true1 before it can be enunciated in terms each of which is rigorously defined4 ,the business of ,definition is part of the business of discovery4 ,when it has been clearly seen what ought to be our ,definition1 it #dj must be pretty well known what truth we have to state4 ,the ,definition1 as well as the discovery1 supposes a decided step in our knowledge to have been made4 ,the writers on ,logic in the middle ages1 made ,definition the last stage in the progress of knowledge2 and in this arrangement at least1 the history of science1 and the philosophy derived from the history1 confirm their speculative views4 ,if the ,explication of our ,conceptions ever assume the form of a ,definition1 this will come to pass1 not as an arbitrary process1 or as a matter of course1 but as the mark of one of those happy efforts of sagacity to which all the successive advances of our knowledge are owing4 ,,sect4 ,,iii4--,use of ,axioms4 #aa4 ,our ,conceptions1 then1 even when they become so clear as the progress of knowledge requires1 are not adequately expressed1 or necessarily expressed at all1 by means of ,definitions4 ,we may ask1 then1 whether there is any other mode of expression in which we may look for the evidence and exposition of that peculiar exactness of thought which the formation of ,science demands4 ,and in answer to this inquiry1 we may refer to the discussions respecting many of the ,fundamental ,ideas of the sciences contained in our ,history of such ,ideas4 ,it has there been seen that these ,ideas involve many elementary truths which enter into the texture of our knowledge1 introducing into it connexions and relations of the most important kind1 although these elementary truths cannot be deduced from any verbal definition of the idea4 ,it has been seen that these elementary truths may often be enunciated by means of ,axioms1 stated in addition to1 or in preference to1 ,definitions4 ,for example1 the ,idea of ,cause1 which forms the basis of the science of ,mechanics1 makes its appearance in our elementary mechanical reasonings1 not as a ,definition1 but by means of the ,axioms that ',causes are measured by their effects1' and that ',reaction is equal and opposite to action4' ,such axioms1 tacitly assumed or #da occasionally stated1 as maxims of acknowledged validity1 belong to all the ,ideas which form the foundations of the sciences1 and are constantly employed in the reasoning and speculations of those who think clearly on such subjects4 ,it may often be a task of some difficulty to detect and enunciate in words the ,principles which are thus1 perhaps silently and unconsciously1 taken for granted by those who have a share in the establishment of scientific truth3 but inasmuch as these ,principles are an essential element in our knowledge1 it is very important to our present purpose to separate them from the associated materials1 and to trace them to their origin4 ,this accordingly ,i attempted to do1 with regard to a considerable number of the most prominent of such ,ideas1 in the ,history4 ,the reader will there find many of these ,ideas resolved into ,axioms and ,principles by means of which their effect upon the elementary reasonings of the various sciences may be expressed4 ,that ,work is intended to form1 in some measure1 a representation of the ,ideal ,side of our physical knowledge2--a ,table of those contents of our ,conceptions which are not received directly from facts2--an exhibition of ,rules to which we know that truth must conform4 ,,sect4 ,,iv4--,clear and appropriate ,ideas4 #ab4 ,in order1 however1 that we may see the necessary cogency of these rules1 we must possess1 clearly and steadily1 the ,ideas from which the rules flow4 ,in order to perceive the necessary relations of the ,circles of the ,sphere1 we must possess clearly the ,idea of ,solid ,space3--in order that we may see the demonstration of the composition of forces1 we must have the ,idea of ,cause moulded into a distinct ,conception of ,statical ,force4 ,this is that ,clearness of ,ideas which we stipulate for in any one's mind1 as the first essential condition of his making any new step in the discovery of truth4 ,and we now see what answer we are able to give1 if we are asked for a ,criterion of this ,clearness of #db ,idea4 ,the ,criterion is1 that the person shall see the necessity of the ,axioms belonging to each ,idea2--shall accept them in such a manner as to perceive the cogency of the reasonings founded upon them4 ,thus1 a person has a clear ,idea of ,space who follows the reasonings of geometry and fully apprehends their conclusiveness4 ,the ,explication of ,conceptions1 which we are speaking of as an essential part of real knowledge1 is the process by which we bring the ,clearness of our ,ideas to bear upon the ,formation of our knowledge4 ,and this is done1 as we have now seen1 not always1 nor generally1 nor principally1 by laying down a ,definition of the ,conception2 but by acquiring such a possession of it in our minds as enables1 indeed compels us1 to admit1 along with the ,conception1 all the ,axioms and ,principles which it necessarily implies1 and by which it produces its effect upon our reasonings4 #ac4 ,but in order that we may make any real advance in the discovery of truth1 our ,ideas must not only be clear1 they must also be appropriate4 ,each science has for its basis a different class of ,ideas2 and the steps which constitute the progress of one science can never be made by employing the ,ideas of another kind of science4 ,no genuine advance could ever be obtained in ,mechanics by applying to the subject the ,ideas of ,space and ,time merely3--no advance in ,chemistry1 by the use of mere ,mechanical ,conceptions3--no discovery in ,physiology1 by referring facts to mere ,chemical and ,mechanical ,principles4 ,mechanics must involve the ,conception of ,force2--,chemistry1 the ,conception of ,elementary ,composition2--,physiology1 the ,conception of ,vital ,powers4 ,each science must advance by means of its appropriate ,conceptions4 ,each has its own field1 which extends as far as its principles can be applied4 ,i have already noted the separation of several of these fields by the divisions of the ,books of the ,history of ,ideas4 ,the ,mechanical1 the ,secondary ,mechanical1 the ,chemical1 the ,classificatory1 the ,biological ,sciences form so many great ,provinces in the ,kingdom of knowledge1 each in a great measure possessing its own peculiar fundamental principles4 ,every attempt to build up a #dc new science by the application of principles which belong to an old one1 will lead to frivolous and barren speculations4 ,this truth has been exemplified in all the instances in which subtle speculative men have failed in their attempts to frame new sciences1 and especially in the essays of the ancient schools of philosophy in ,greece1 as has already been stated in the ,history of ,science4 ,aristotle and his followers endeavoured in vain to account for the mechanical relation of forces in the lever by applying the inappropriate geometrical conceptions of the properties of the circle3--they speculated to no purpose about the elementary composition of bodies1 because they assumed the inappropriate conception of likeness between the elements and the compound1 instead of the genuine notion of elements merely determining the qualities of the compound4 ,and in like manner1 in modern times1 we have seen1 in the history of the fundamental ideas of the physiological sciences1 how all the inappropriate mechanical and chemical and other ideas which were applied in succession to the subject failed in bringing into view any genuine physiological truth4 #ad4 ,that the real cause of the failure in the instances above mentioned lay in the ,conceptions1 is plain4 ,it was not ignorance of the facts which in these cases prevented the discovery of the truth4 ,aristotle was as well acquainted with the fact of the proportion of the weights which balance on a ,lever as ,archimedes was1 although ,archimedes alone gave the true mechanical reason for the proportion4 ,with regard to the doctrine of the ,four ,elements indeed1 the inapplicability of the conception of composition of qualities1 required1 perhaps1 to be proved by some reference to facts4 ,but this conception was devised at first1 and accepted by succeeding times1 in a blind and gratuitous manner1 which could hardly have happened if men had been awake to the necessary condition of our knowledge2--that the conceptions which we introduce into our doctrines are not arbitrary or accidental notions1 but certain peculiar modes of #dd apprehension strictly determined by the subject of our speculations4 #ae4 ,it may1 however1 be said that this injunction that we are to employ appropriate ,conceptions only in the formation of our knowledge1 cannot be of practical use1 because we can only determine what ,ideas are appropriate1 by finding that they truly combine the facts4 ,and this is to a certain extent true4 ,scientific discovery must ever depend upon some happy thought1 of which we cannot trace the origin2--some fortunate cast of intellect1 rising above all rules4 ,no maxims can be given which inevitably lead to discovery4 ,no precepts will elevate a man of ordinary endowments to the level of a man of genius3 nor will an inquirer of truly inventive mind need to come to the teacher of inductive philosophy to learn how to exercise the faculties which nature has given him4 ,such persons as ,kepler or ,fresnel1 or ,brewster1 will have their powers of discovering truth little augmented by any injunctions respecting ,distinct and ,appropriate ,ideas2 and such men may very naturally question the utility of rules altogether4 #af4 ,but yet the opinions which such persons may entertain1 will not lead us to doubt concerning the value of the attempts to analyse and methodize the process of discovery4 ,who would attend to ,kepler if he had maintained that the speculations of ,francis ,bacon were worthless8 ,notwithstanding what has been said1 we may venture to assert that the ,maxim which points out the necessity of ,ideas appropriate as well as clear1 for the purpose of discovering truth1 is not without its use4 ,it may1 at least1 have a value as a caution or prohibition1 and may thus turn us away from labours certain to be fruitless4 ,we have already seen1 in the ,history of ,ideas1 that this maxim1 if duly attended to1 would have at once condemned1 as wrongly directed1 the speculations of physiologists of the mathematical1 mechanical1 chemical1 and vital-fluid schools2 since the ,ideas which the teachers of these schools introduce1 cannot suffice for the purposes of physiology1 which seeks truths respecting the vital powers4 ,again1 #de it is clear from similar considerations that no definition of a mineralogical species by chemical characters alone can answer the end of science1 since we seek to make mineralogy1 not an analytical but a classificatory science#ab4 ,even before the appropriate conception is matured in men's minds so that they see clearly what it is1 they may still have light enough to see what it is not4 ,note #ab3 ,this agrees with what ,m4 ,necker has well observed in his ,rgne ,mineral1 that those who have treated mineralogy as a merely chemical science1 have substituted the analysis of substances for the classification of individuals4 ,see ,history of ,ideas1 b4 viii4 chap4 iii4 #ag4 ,another result of this view of the necessity of appropriate ,ideas1 combined with a survey of the history of science is1 that though for the most part1 as we shall see1 the progress of science consists in accumulating and combining ,facts rather than in debating concerning ,definitions2 there are still certain periods when the discussion of ,definitions may be the most useful mode of cultivating some special branch of science4 ,this discussion is of course always to be conducted by the light of facts2 and1 as has already been said1 along with the settlement of every good ,definition will occur the corresponding establishment of some ,proposition4 ,but still at particular periods1 the want of a ,definition1 or of the clear conceptions which ,definition supposes1 may be peculiarly felt4 ,a good and tenable ,definition of ,species in ,mineralogy would at present be perhaps the most important step which the science could make4 ,a just conception of the nature of ,life1 7and if expressed by means of a ,definition1 so much the better17 can hardly fail to give its possessor an immense advantage in the speculations which now come under the considerations of physiologists4 ,and controversies respecting ,definitions1 in these cases1 and such as these1 may be very far from idle and unprofitable4 ,thus the knowledge that ,clear and ,appropriate ,ideas are requisite for discovery1 although it does not lead to any very precise precepts1 or supersede the value of natural sagacity and inventiveness1 may still #df be of use to us in our pursuit after truth4 ,it may show us what course of research is1 in each stage of science1 recommended by the general analogy of the history of knowledge2 and it may both save us from hopeless and barren paths of speculation1 and make us advance with more courage and confidence1 to know that we are looking for discoveries in the manner in which they have always hitherto been made4 ,,sect4 ,v4--,accidental ,discoveries4 #ah4 ,another consequence follows from the views presented in this ,chapter1 and it is the last ,i shall at present mention4 ,no scientific discovery can1 with any justice1 be considered due to accident4 ,in whatever manner facts may be presented to the notice of a discoverer1 they can never become the materials of exact knowledge1 except they find his mind already provided with precise and suitable conceptions by which they may be analysed and connected4 ,indeed1 as we have already seen1 facts cannot be observed as ,facts1 except in virtue of the ,conceptions which the observer#bb himself unconsciously supplies2 and they are not ,facts of ,observation for any purpose of ,discovery1 except these familiar and unconscious acts of thought be themselves of a just and precise kind4 ,but supposing the ,facts to be adequately observed1 they can never be combined into any new ,truth1 except by means of some new ,conceptions1 clear and appropriate1 such as ,i have endeavoured to characterize4 ,when the observer's mind is prepared with such instruments1 a very few facts1 or it may be a single one1 may bring the process of discovery into action4 ,but in such cases1 this previous condition of the intellect1 and not the single fact1 is really the main and peculiar cause of the success4 ,the fact is merely the occasion by which the engine of discovery is brought into play sooner or later4 ,it is1 as ,i have elsewhere said1 only the spark which discharges a gun already loaded and pointed2 and there #dg is little propriety in speaking of such an accident as the cause why the bullet hits the mark4 ,if it were true that the fall of an apple was the occasion of ,newton's pursuing the train of thought which led to the doctrine of universal gravitation1 the habits and constitution of ,newton's intellect1 and not the apple1 were the real source of this great event in the progress of knowledge4 ,the common love of the marvellous1 and the vulgar desire to bring down the greatest achievements of genius to our own level1 may lead men to ascribe such results to any casual circumstances which accompany them2 but no one who fairly considers the real nature of great discoveries1 and the intellectual processes which they involve1 can seriously hold the opinion of their being the effect of accident4 ,note #bb3 ,b4 i4 of this vol4 ,aphorism ,,iii4 #ai4 ,such accidents never happen to common men4 ,thousands of men1 even of the most inquiring and speculative men1 had seen bodies fall2 but who1 except ,newton1 ever followed the accident to such consequences8 ,and in fact1 how little of his train of thought was contained in1 or even directly suggested by1 the fall of the apple6 ,if the apple fall1 said the discoverer1 'why should not the moon1 the planets1 the satellites1 fall8' ,but how much previous thought1--what a steady conception of the universality of the laws of motion gathered from other sources1--were requisite1 that the inquirer should see any connexion in these cases6 ,was it by accident that he saw in the apple an image of the moon1 and of every body in the solar system8 #bj4 ,the same observations may be made with regard to the other cases which are sometimes adduced as examples of accidental discovery4 ,it has been said1 ',by the accidental placing of a rhomb of calcareous spar upon a book or line ,bartholinus discovered the property of the ,double ,refraction of light4' ,but ,bartholinus could have seen no such consequence in the accident if he had not previously had a clear conception of single refraction4 ,a lady1 in describing an optical experiment which had been shown her1 said of her teacher1 ',he told me to increase and diminish #dh the angle of refraction1 and at last ,i found that he only meant me to move my head up and down4' ,at any rate1 till the lady had acquired the notions which the technical terms convey1 she could not have made ,bartholinus's discovery by means of his accident4 ',by accidentally combining two rhombs in different positions1' it is added1 ',huyghens discovered the ,polarization of ,light4' ,supposing that this experiment had been made without design1 what ,huyghens really observed was1 that the images appeared and disappeared alternately as he turned one of the rhombs round4 ,but was it an easy or an obvious business to analyze this curious alternation into the circumstances of the rays of light having sides1 as ,newton expressed it1 and into the additional hypotheses which are implied in the term 'polarization'8 ,those will be able to answer this question1 who have found how far from easy it is to understand clearly what is meant by 'polarization' in this case1 now that the property is fully established4 ,huyghens's success depended on his clearness of thought1 for this enabled him to perform the intellectual analysis1 which never would have occurred to most men1 however often they had 'accidentally combined two rhombs in different positions4' ',by accidentally looking through a prism of the same substance1 and turning it round1 ,malus discovered the polarization of light by reflection4' ,malus saw that1 in some positions of the prism1 the light reflected from the windows of the ,louvre thus seen through the prism1 became dim4 ,a common man would have supposed this dimness the result of accident2 but ,malus's mind was differently constituted and disciplined4 ,he considered the position of the window1 and of the prism2 repeated the experiment over and over2 and in virtue of the eminently distinct conceptions of space which he possessed1 resolved the phenomena into its geometrical conditions4 ,a believer in accident would not have sought them2 a person of less clear ideas would not have found them4 ,a person must have a strange confidence in the virtue of chance1 and the worthlessness of intellect1 who can say that #di 'in all these fundamental discoveries appropriate ideas had no share1' and that the discoveries 'might have been made by the most ordinary observers4' #ba4 ,i have now1 ,i trust1 shown in various ways1 how the ,explication of ,conceptions1 including in this term their clear development from ,fundamental ,ideas in the discoverer's mind1 as well as their precise expression in the form of ,definitions or ,axioms1 when that can be done1 is an essential part in the establishment of all exact and general physical truths4 ,in doing this1 ,i have endeavoured to explain in what sense the possession of clear and appropriate ideas is a main requisite for every step in scientific discovery4 ,that it is far from being the only step1 ,i shall soon have to show2 and if any obscurity remain on the subject treated of in the present chapter1 it will1 ,i hope1 be removed when we have examined the other elements which enter into the constitution of our knowledge4 #ej ,,chapter ,,iii4 ,,of ,,facts ,,as ,,the ,,materials ,,of ,,science4 ,,aphorism ,,iv4 ,facts are the materials of science1 but all ,facts involve ,ideas4 ,since in observing ,facts1 we cannot exclude ,ideas1 we must1 for the purposes of science1 take care that the ,ideas are clear and rigorously applied4 ,,aphorism ,v4 ,the last ,aphorism leads to such ,rules as the following3--,that ,facts1 for the purposes of material science1 must involve ,conceptions of the ,intellect only1 and not ,emotions3--,that ,facts must be observed with reference to our most exact conceptions1 ,number1 ,place1 ,figure1 ,motion3--,that they must also be observed with reference to any other exact conceptions which the phenomena suggest1 as ,force1 in mechanical phenomena1 ,concord1 in musical4 ,,aphorism ,,vi4 ,the resolution of complex ,facts into precise and measured partial ,facts1 we call the ,decomposition of ,facts4 ,this process is requisite for the progress of science1 but does not necessarily lead to progress4 #a4 ,,we have now to examine how ,science is built up by the combination of ,facts4 ,in doing this1 we suppose that we have already attained a supply of definite and certain ,facts1 free from obscurity and doubt4 ,we must1 therefore1 first consider under what conditions ,facts can assume this character4 ,when we inquire what ,facts are to be made the materials of ,science1 perhaps the answer which we #ea should most commonly receive would be1 that they must be ,true ,facts1 as distinguished from any mere inferences or opinions of our own4 ,we should probably be told that we must be careful in such a case to consider as ,facts1 only what we really observe2--that we must assert only what we see2 and believe nothing except upon the testimony of our senses4 ,but such maxims are far from being easy to apply1 as a little examination will convince us4 #b4 ,it has been explained1 in preceding works1 that all perception of external objects and occurrences involves an active as well as a passive process of the mind2--includes not only ,sensations1 but also ,ideas by which ,sensations are bound together1 and have a unity given to them4 ,from this it follows1 that there is a difficulty in separating in our perceptions what we receive from without1 and what we ourselves contribute from within2--what we perceive1 and what we infer4 ,in many cases1 this difficulty is obvious to all3 as1 for example1 when we witness the performances of a juggler or a ventriloquist4 ,in these instances1 we imagine ourselves to see and to hear what certainly we do not see and hear4 ,the performer takes advantage of the habits by which our minds supply interruptions and infer connexions2 and by giving us fallacious indications1 he leads us to perceive as an actual fact1 what does not happen at all4 ,in these cases1 it is evident that we ourselves assist in making the fact2 for we make one which does not really exist4 ,in other cases1 though the fact which we perceive be true1 we can easily see that a large portion of the perception is our own act2 as when1 from the sight of a bird of prey we infer a carcase1 or when we read a half-obliterated inscription4 ,in the latter case1 the mind supplies the meaning1 and perhaps half the letters2 yet we do not hesitate to say that we actually read the inscription4 ,thus1 in many cases1 our own inferences and interpretations enter into our facts4 ,but this happens in many instances in which it is at first sight less obvious4 ,when any one has seen an oak-tree blown down by a strong gust of wind1 he does not think of the occurrence #eb any otherwise than as a ,fact of which he is assured by his senses4 ,yet by what sense does he perceive the ,force which he thus supposes the wind to exert8 ,by what sense does he distinguish an ,oak-tree from all other trees8 ,it is clear upon reflexion1 that in such a case1 his own mind supplies the conception of extraneous impulse and pressure1 by which he thus interprets the motions observed1 and the distinction of different kinds of trees1 according to which he thus names the one under his notice4 ,the ,idea of ,force1 and the idea of definite ,resemblances and ,differences1 are thus combined with the impressions on our senses1 and form an undistinguished portion of that which we consider as the ,fact4 ,and it is evident that we can in no other way perceive ,force1 than by seeing motion2 and cannot give a ,name to any object1 without not only seeing a difference of single objects1 but supposing a difference of classes of objects4 ,when we speak as if we saw impulse and attraction1 things and classes1 we really see only objects of various forms and colours1 more or less numerous1 variously combined4 ,but do we really perceive so much as this8 ,when we see the form1 the size1 the number1 the motion of objects1 are these really mere impressions on our senses1 unmodified by any contribution or operation of the mind itself8 ,a very little attention will suffice to convince us that this is not the case4 ,when we see a windmill turning1 it may happen1 as we have elsewhere noticed#cb1 that we mistake the direction in which the sails turn3 when we look at certain diagrams1 they may appear either convex or concave3 when we see the moon first in the horizon and afterwards high up in the sky1 we judge her to be much larger in the former than in the latter position1 although to the eye she subtends the same angle4 ,and in these cases and the like1 it has been seen that the errour and confusion which we thus incur arise from the mixture of acts of the mind itself with impressions on the senses4 ,but such acts are1 as we have also seen1 inseparable portions of the process #ec of perception4 ,a certain activity of the mind is involved1 not only in seeing objects erroneously1 but in seeing them at all4 ,with regard to solid objects1 this is generally acknowledged4 ,when we seem to see an edifice occupying space in all dimensions1 we really see only a representation of it as it appears referred by perspective to a surface4 ,the inference of the solid form is an operation of our own1 alike when we look at a reality and when we look at a picture4 ,but we may go further4 ,is plane ,figure really a mere ,sensation8 ,if we look at a decagon1 do we see at once that it has ten sides1 or is it not necessary for us to count them3 and is not counting an act of the mind8 ,all objects are seen in space2 all objects are seen as one or many3 but are not the ,idea of ,space and the ,idea of ,number requisite in order that we may thus apprehend what we see8 ,that these ,ideas of ,space and ,number involve a connexion derived from the mind1 and not from the senses1 appears1 as we have already seen1 from this1 that those ,ideas afford us the materials of universal and necessary truths3--such truths as the senses cannot possibly supply4 ,and thus1 even the perception of such facts as the size1 shape1 and number of objects1 cannot be said to be impressions of sense1 distinct from all acts of mind1 and cannot be expected to be free from errour on the ground of their being mere observed ,facts4 ,note #cb3 ,history of ,ideas1 ,b4 ii4 c4 vi4 s4 #f4 ,thus the difficulty which we have been illustrating1 of distinguishing ,facts from inferences and from interpretations of facts1 is not only great1 but amounts to an impossibility4 ,the separation at which we aimed in the outset of this discussion1 and which was supposed to be necessary in order to obtain a firm groundwork for science1 is found to be unattainable4 ,we cannot obtain a sure basis of ,facts1 by rejecting all inferences and judgments of our own1 for such inferences and judgments form an unavoidable element in all ,facts4 ,we cannot exclude our ,ideas from our ,perceptions1 for our ,perceptions involve our ,ideas4 #c4 ,but still1 it cannot be doubted that in selecting the ,facts which are to form the foundation of ,science1 #ed we must reduce them to their most simple and certain form2 and must reject everything from which doubt or errour may arise4 ,now since this1 it appears1 cannot be done1 by rejecting the ,ideas which all ,facts involve1 in what manner are we to conform to the obvious maxim1 that the ,facts which form the basis of ,science must be perfectly definite and certain8 ,the analysis of facts into ,ideas and ,sensations1 which we have so often referred to1 suggests the answer to this inquiry4 ,we are not able1 nor need we endeavour1 to exclude ,ideas from our ,facts2 but we may be able to discern1 with perfect distinctness1 the ,ideas which we include4 ,we cannot observe any phenomena without applying to them such ,ideas as ,space and ,number1 ,cause and ,resemblance1 and usually1 several others2 but we may avoid applying these ,ideas in a wavering or obscure manner1 and confounding ,ideas with one another4 ,we cannot read any of the inscriptions which nature presents to us1 without interpreting them by means of some language which we ourselves are accustomed to speak2 but we may make it our business to acquaint ourselves perfectly with the language which we thus employ1 and to interpret it according to the rigorous rules of grammar and analogy4 ,this maxim1 that when ,facts are employed as the basis of ,science1 we must distinguish clearly the ,ideas which they involve1 and must apply these in a distinct and rigorous manner1 will be found to be a more precise guide than we might perhaps at first expect4 ,we may notice one or two ,rules which flow from it4 #d4 ,in the first place4 ,facts1 when used as the materials of physical ,science1 must be referred to ,conceptions of the ,intellect only1 all emotions of fear1 admiration1 and the like1 being rejected or subdued4 ,thus1 the observations of phenomena which are related as portents and prodigies1 striking terrour and boding evil1 are of no value for purposes of science4 ,the tales of armies seen warring in the sky1 the sound of arms heard from the clouds1 fiery dragons1 chariots1 swords seen in the air1 may refer to meteorological phenomena2 but the records of phenomena observed in the #ee state of mind which these descriptions imply can be of no scientific value4 ,we cannot make the poets our observers4 ,armorum sonitum toto ,germania clo ,audiit2 insolitis tremuerunt motibus ,alpes4 ,vox quoque per lucos vulgo exaudita silentes ,ingens2 et simulacra modis pallentia miris ,visa sub obscurum noctis3 pecudesque locut4 ,the mixture of fancy and emotion with the observation of facts has often disfigured them to an extent which is too familiar to all to need illustration4 ,we have an example of this result1 in the manner in which ,comets are described in the treatises of the middle ages4 ,in such works1 these bodies are regularly distributed into several classes1 accordingly as they assume the form of a sword1 of a spear1 of a cross1 and so on4 ,when such resemblances had become matters of interest1 the impressions of the senses were governed1 not by the rigorous conceptions of form and colour1 but by these assumed images2 and under these circumstances1 we can attach little value to the statement of what was seen4 ,in all such phenomena1 the reference of the objects to the exact ,ideas of ,space1 ,number1 ,position1 ,motion1 and the like1 is the first step of ,science3 and accordingly1 this reference was established at an early period in those sciences which made an early progress1 as1 for instance1 ,astronomy4 ,yet even in astronomy there appears to have been a period when the predominant conceptions of men in regarding the heavens and the stars pointed to mythical story and supernatural influence1 rather than to mere relations of space1 time1 and motion3 and of this primeval condition of those who gazed at the stars1 we seem to have remnants in the ,constellations1 in the mythological ,names of the ,planets1 and in the early prevalence of ,astrology4 ,it was only at a later period1 when men had begun to measure the places1 or at least to count the revolutions of the stars1 that ,astronomy had its birth4 #e4 ,and thus we are led to another ,rule3--that in collecting ,facts which are to be made the basis of #ef ,science1 the ,facts are to be observed1 as far as possible1 with reference to place1 figure1 number1 motion1 and the like ,conceptions2 which1 depending upon the ,ideas of ,space and ,time1 are the most universal1 exact1 and simple of our conceptions4 ,it was by early attention to these relations in the case of the heavenly bodies1 that the ancients formed the science of ,astronomy3 it was by not making precise observations of this kind in the case of terrestrial bodies1 that they failed in framing a science of the ,mechanics of ,motion4 ,they succeeded in ,optics as far as they made observations of this nature2 but when they ceased to trace the geometrical paths of rays in the actual experiment1 they ceased to go forwards in the knowledge of this subject4 #f4 ,but we may state a further ,rule3--that though these relations of ,time and ,space are highly important in almost all ,facts1 we are not to confine ourselves to these3 but are to consider the phenomena with reference to other ,conceptions also3 it being always understood that these conceptions are to be made as exact and rigorous as those of geometry and number4 ,thus the science of ,harmonics arose from considering sounds with reference to ,concords and ,discords2 the science of ,mechanics arose from not only observing motions as they take place in ,time and ,space1 but further1 referring them to ,force as their ,cause4 ,and in like manner1 other sciences depend upon other ,ideas1 which1 as ,i have endeavoured to show1 are not less fundamental than those of ,time and ,space2 and like them1 capable of leading to rigorous consequences4 #g4 ,thus the ,facts which we assume as the basis of ,science are to be freed from all the mists which imagination and passion throw round them2 and to be separated into those elementary ,facts which exhibit simple and evident relations of ,time1 or ,space1 or ,cause1 or some other ,ideas equally clear4 ,we resolve the complex appearances which nature offers to us1 and the mixed and manifold modes of looking at these appearances which rise in our thoughts1 into limited1 definite1 and clearly-understood portions4 ,this process we may term the ,decomposition of ,facts4 ,it is the #eg beginning of exact knowledge1--the first step in the formation of all ,science4 ,this ,decomposition of ,facts into ,elementary ,facts1 clearly understood and surely ascertained1 must precede all discovery of the laws of nature4 #h4 ,but though this step is necessary1 it is not infallibly sufficient4 ,it by no means follows that when we have thus decomposed ,facts into ,elementary ,truths of observation1 we shall soon be able to combine these1 so as to obtain ,truths of a higher and more speculative kind4 ,we have examples which show us how far this is from being a necessary consequence of the former step4 ,observations of the weather1 made and recorded for many years1 have not led to any general truths1 forming a science of ,meteorology3 and although great numerical precision has been given to such observations by means of barometers1 thermometers1 and other instruments1 still1 no general laws regulating the cycles of change of such phenomena have yet been discovered4 ,in like manner the faces of crystals1 and the sides of the polygons which these crystals form1 were counted1 and thus numerical facts were obtained1 perfectly true and definite1 but still of no value for purposes of science4 ,and when it was discovered what ,element of the form of crystals it was important to observe and measure1 namely1 the ,angle made by two faces with each other1 this discovery was a step of a higher order1 and did not belong to that department1 of mere exact observation of manifest ,facts1 with which we are here concerned4 #i4 ,when the ,complex ,facts which nature offers to us are thus decomposed into ,simple ,facts1 the decomposition1 in general1 leads to the introduction of ,terms and ,phrases1 more or less technical1 by which these ,simple ,facts are described4 ,when ,astronomy was thus made a science of measurement1 the things measured were soon described as ,hours1 and ,days1 and ,cycles1 ,altitude and ,declination1 ,phases and ,aspects4 ,in the same manner1 in ,music1 the concords had names assigned them1 as ,diapente1 ,diatessaron1 ,diapason2 in studying ,optics1 the ,rays of light were spoken of as #eh having their course altered by ,reflexion and ,refraction2 and when useful observations began to be made in ,mechanics1 the observers spoke of ,force1 ,pressure1 ,momentum1 ,inertia1 and the like4 #aj4 ,when we take phenomena in which the leading ,idea is ,resemblance1 and resolve them into precise component ,facts1 we obtain some kind of ,classification2 as1 for instance1 when we lay down certain ,rules by which particular trees1 or particular animals are to be known4 ,this is the earliest form of ,natural ,history2 and the ,classification which it involves is that which corresponds1 nearly or exactly1 with the usual ,names of the objects thus classified4 #aa4 ,thus the first attempts to render observation certain and exact1 lead to a decomposition of the obvious facts into ,elementary ,facts1 connected by the ,ideas of ,space1 ,time1 ,number1 ,cause1 ,likeness1 and others3 and into a ,classification of the ,simple ,facts2 a classification more or less just1 and marked by ,names either common or technical4 ,elementary ,facts1 and ,individual ,objects1 thus observed and classified1 form the materials of ,science2 and any improvement in ,classification or ,nomenclature1 or any discovery of a ,connexion among the materials thus accumulated1 leads us fairly within the precincts of ,science4 ,we must now1 therefore1 consider the manner in which ,science is built up of such materials2--the process by which they are brought into their places1 and the texture of the bond which unites and cements them4 #ei ,,chapter ,,iv4 ,,of ,,the ,,colligation ,,of ,,facts4 ,,aphorism ,,vii4 ,science begins with common observation of facts2 but even at this stage1 requires that the observations be precise4 ,hence the sciences which depend upon space and number were the earliest formed4 ,after common observation1 come ,scientific ,observation and ,experiment4 ,,aphorism ,,viii4 ,the ,conceptions by which ,facts are bound together1 are suggested by the sagacity of discoverers4 ,this sagacity cannot be taught4 ,it commonly succeeds by guessing2 and this success seems to consist in framing several tentative hypotheses and selecting the right one4 ,but a supply of appropriate hypotheses cannot be constructed by rule1 nor without inventive talent4 ,,aphorism ,,ix4 ,the truth of tentative hypotheses must be tested by their application to facts4 ,the discoverer must be ready1 carefully to try his hypotheses in this manner1 and to reject them if they will not bear the test1 in spite of indolence and vanity4 #a4 ,,facts such as the last ,chapter speaks of are1 by means of such ,conceptions as are described in the preceding ,chapter1 bound together so as to give rise to those general ,propositions of which ,science consists4 ,thus the ,facts that the planets revolve #fj about the sun in certain periodic times and at certain distances1 are included and connected in ,kepler's ,law1 by means of such ,conceptions as the squares of numbers1 the cubes of distances1 and the proportionality of these quantities4 ,again the existence of this proportion in the motions of any two planets1 forms a set of ,facts which may all be combined by means of the ,conception of a certain central accelerating force1 as was proved by ,newton4 ,the whole of our physical knowledge consists in the establishment of such propositions2 and in all such cases1 ,facts are bound together by the aid of suitable ,conceptions4 ,this part of the formation of our knowledge ,i have called the ,colligation of ,facts3 and we may apply this term to every case in which1 by an act of the intellect1 we establish a precise connexion among the phenomena which are presented to our senses4 ,the knowledge of such connexions1 accumulated and systematized1 is ,science4 ,on the steps by which science is thus collected from phenomena we shall proceed now to make a few remarks4 #b4 ,science begins with ,common ,observation of facts1 in which we are not conscious of any peculiar discipline or habit of thought exercised in observing4 ,thus the common perceptions of the appearances and recurrences of the celestial luminaries1 were the first steps of ,astronomy3 the obvious cases in which bodies fall or are supported1 were the beginning of ,mechanics2 the familiar aspects of visible things1 were the origin of ,optics2 the usual distinctions of well-known plants1 first gave rise to ,botany4 ,facts belonging to such parts of our knowledge are noticed by us1 and accumulated in our memories1 in the common course of our habits1 almost without our being aware that we are observing and collecting facts4 ,yet such facts may lead to many scientific truths2 for instance1 in the first stages of ,astronomy 7as we have shown in the ,history7 such facts led to ,methods of ,intercalation and ,rules of the ,recurrence of ,eclipses4 ,in succeeding stages of science1 more especial attention and preparation on the part of the observer1 and a selection of certain #fa kinds of facts1 becomes necessary2 but there is an early period in the progress of knowledge at which man is a physical philosopher1 without seeking to be so1 or being aware that he is so4 #c4 ,but in all stages of the progress1 even in that early one of which we have just spoken1 it is necessary1 in order that the facts may be fit materials of any knowledge1 that they should be decomposed into ,elementary ,facts1 and that these should be observed with precision4 ,thus1 in the first infancy of astronomy1 the recurrence of phases of the moon1 of places of the sun's rising and setting1 of planets1 of eclipses1 was observed to take place at intervals of certain definite numbers of days1 and in a certain exact order2 and thus it was1 that the observations became portions of astronomical science4 ,in other cases1 although the facts were equally numerous1 and their general aspect equally familiar1 they led to no science1 because their exact circumstances were not apprehended4 ,a vague and loose mode of looking at facts very easily observable1 left men for a long time under the belief that a body1 ten times as heavy as another1 falls ten times as fast2--that objects immersed in water are always magnified1 without regard to the form of the surface2--that the magnet exerts an irresistible force2--that crystal is always found associated with ice2--and the like4 ,these and many others are examples how blind and careless men can be1 even in observation of the plainest and commonest appearances2 and they show us that the mere faculties of perception1 although constantly exercised upon innumerable objects1 may long fail in leading to any exact knowledge4 #d4 ,if we further inquire what was the favourable condition through which some special classes of facts were1 from the first1 fitted to become portions of science1 we shall find it to have been principally this2--that these facts were considered with reference to the ,ideas of ,time1 ,number1 and ,space1 which are ,ideas possessing peculiar definiteness and precision2 so that with regard to them1 confusion and indistinctness are hardly possible4 ,the interval from new moon to new #fb moon was always a particular number of days3 the sun in his yearly course rose and set near to a known succession of distant objects3 the moon's path passed among the stars in a certain order3--these are observations in which mistake and obscurity are not likely to occur1 if the smallest degree of attention is bestowed upon the task4 ,to count a number is1 from the first opening of man's mental faculties1 an operation which no science can render more precise4 ,the relations of space are nearest to those of number in obvious and universal evidence4 ,sciences depending upon these ,ideas arise with the first dawn of intellectual civilization4 ,but few of the other ,ideas which man employs in the acquisition of knowledge possess this clearness in their common use4 ,the ,idea of ,resemblance may be noticed1 as coming next to those of ,space and ,number in original precision2 and the ,idea of ,cause1 in a certain vague and general mode of application1 sufficient for the purposes of common life1 but not for the ends of science1 exercises a very extensive influence over men's thoughts4 ,but the other ,ideas on which science depends1 with the ,conceptions which arise out of them1 are not unfolded till a much later period of intellectual progress2 and therefore1 except in such limited cases as ,i have noticed1 the observations of common spectators and uncultivated nations1 however numerous or varied1 are of little or no effect in giving rise to ,science4 #e4 ,let us now suppose that1 besides common everyday perception of facts1 we turn our attention to some other occurrences and appearances1 with a design of obtaining from them speculative knowledge4 ,this process is more peculiarly called ,observation1 or1 when we ourselves occasion the facts1 ,experiment4 ,but the same remark which we have already made1 still holds good here4 ,these facts can be of no value1 except they are resolved into those exact ,conceptions which contain the essential circumstances of the case4 ,they must be determined1 not indeed necessarily1 as has sometimes been said1 'according to ,number1 ,weight1 and ,measure2' for1 as we have endeavoured to show #fc in the preceding ,books#db1 there are many other ,conceptions to which phenomena may be subordinated1 quite different from these1 and yet not at all less definite and precise4 ,but in order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge1 they must be apprehended and analysed according to some ,conceptions which1 applied for this purpose1 give distinct and definite results1 such as can be steadily taken hold of and reasoned from2 that is1 the facts must be referred to ,clear and ,appropriate ,ideas1 according to the manner in which we have already explained this condition of the derivation of our knowledge4 ,the phenomena of light1 when they are such as to indicate sides in the ray1 must be referred to the ,conception of polarization2 the phenomena of mixture1 when there is an alteration of qualities as well as quantities1 must be combined by a ,conception of elementary composition4 ,and thus1 when mere position1 and number1 and resemblance1 will no longer answer the purpose of enabling us to connect the facts1 we call in other ,ideas1 in such cases more efficacious1 though less obvious4 ,note #db3 ,hist4 of ,sci4 ,id4 ,bs4 v4 vi4 vii4 viii4 ix4 x4 #f4 ,but how are we1 in these cases1 to discover such ,ideas1 and to judge which will be efficacious1 in leading to a scientific combination of our experimental data8 ,to this question1 we must in the first place answer1 that the first and great instrument by which facts1 so observed with a view to the formation of exact knowledge1 are combined into important and permanent truths1 is that peculiar ,sagacity which belongs to the genius of a ,discoverer2 and which1 while it supplies those distinct and appropriate ,conceptions which lead to its success1 cannot be limited by rules1 or expressed in definitions4 ,it would be difficult or impossible to describe in words the habits of thought which led ,archimedes to refer the conditions of equilibrium on the ,lever to the ,conception of pressure1 while ,aristotle could not see in them anything more than the results #fd of the strangeness of the properties of the circle2--or which impelled ,pascal to explain by means of the ,conception of the weight of air1 the facts which his predecessors had connected by the notion of nature's horrour of a vacuum2--or which caused ,vitello and ,roger ,bacon to refer the magnifying power of a convex lens to the bending of the rays of light towards the perpendicular by refraction1 while others conceived the effect to result from the matter of medium1 with no consideration of its form4 ,these are what are commonly spoken of as felicitous and inexplicable strokes of inventive talent2 and such1 no doubt1 they are4 ,no rules can ensure to us similar success in new cases2 or can enable men who do not possess similar endowments1 to make like advances in knowledge4 #g4 ,yet still1 we may do something in tracing the process by which such discoveries are made2 and this it is here our business to do4 ,we may observe that these1 and the like discoveries1 are not improperly described as happy ,guesses2 and that ,guesses1 in these as in other instances1 imply various suppositions made1 of which some one turns out to be the right one4 ,we may1 in such cases1 conceive the discoverer as inventing and trying many conjectures1 till he finds one which answers the purpose of combining the scattered facts into a single rule4 ,the discovery of general truths from special facts is performed1 commonly at least1 and more commonly than at first appears1 by the use of a series of ,suppositions1 or ,hypotheses1 which are looked at in quick succession1 and of which the one which really leads to truth is rapidly detected1 and when caught sight of1 firmly held1 verified1 and followed to its consequences4 ,in the minds of most discoverers1 this process of invention1 trial1 and acceptance or rejection of the hypothesis1 goes on so rapidly that we cannot trace it in its successive steps4 ,but in some instances1 we can do so2 and we can also see that the other examples of discovery do not differ essentially from these4 ,the same intellectual operations take place in other cases1 although this often happens so instantaneously that we lose the trace of the #fe progression4 ,in the discoveries made by ,kepler1 we have a curious and memorable exhibition of this process in its details4 ,thanks to his communicative disposition1 we know that he made nineteen hypotheses with regard to the motion of ,mars1 and calculated the results of each1 before he established the true doctrine1 that the planet's path is an ellipse4 ,we know1 in like manner1 that ,galileo made wrong suppositions respecting the laws of falling bodies1 and ,mariotte1 concerning the motion of water in a siphon1 before they hit upon the correct view of these cases4 #h4 ,but it has very often happened in the history of science1 that the erroneous hypotheses which preceded the discovery of the truth have been made1 not by the discoverer himself1 but by his precursors2 to whom he thus owed the service1 often an important one in such cases1 of exhausting the most tempting forms of errour4 ,thus the various fruitless suppositions by which ,kepler endeavoured to discover the law of reflection1 led the way to its real detection by ,snell2 ,kepler's numerous imaginations concerning the forces by which the celestial motions are produced1--his 'physical reasonings' as he termed them1--were a natural prelude to the truer physical reasonings of ,newton4 ,the various hypotheses by which the suspension of vapour in air had been explained1 and their failure1 left the field open for ,dalton with his doctrine of the mechanical mixture of gases4 ,in most cases1 if we could truly analyze the operation of the thoughts of those who make1 or who endeavour to make discoveries in science1 we should find that many more suppositions pass through their minds than those which are expressed in words2 many a possible combination of conceptions is formed and soon rejected4 ,there is a constant invention and activity1 a perpetual creating and selecting power at work1 of which the last results only are exhibited to us4 ,trains of hypotheses are called up and pass rapidly in review2 and the judgment makes its choice from the varied group4 #i4 ,it would1 however1 be a great mistake to suppose that the hypotheses1 among which our choice thus #ff lies1 are constructed by an enumeration of obvious cases1 or by a wanton alteration of relations which occur in some first hypothesis4 ,it may1 indeed1 sometimes happen that the proposition which is finally established is such as may be formed1 by some slight alteration1 from those which are justly rejected4 ,thus ,kepler's elliptical theory of ,mars's motions1 involved relations of lines and angles much of the same nature as his previous false suppositions3 and the true law of refraction so much resembles those erroneous ones which ,kepler tried1 that we cannot help wondering how he chanced to miss it4 ,but it more frequently happens that new truths are brought into view by the application of new ,ideas1 not by new modifications of old ones4 ,the cause of the properties of the ,lever was learnt1 not by introducing any new geometrical combination of lines and circles1 but by referring the properties to genuine mechanical ,conceptions4 ,when the ,motions of the ,planets were to be explained1 this was done1 not by merely improving the previous notions1 of cycles of time1 but by introducing the new conception of epicycles in space4 ,the doctrine of the ,four ,simple ,elements was expelled1 not by forming any new scheme of elements which should impart1 according to new rules1 their sensible qualities to their compounds1 but by considering the elements of bodies as neutralizing each other4 ,the ,fringes of ,shadows could not be explained by ascribing new properties to the single rays of light1 but were reduced to law by referring them to the interference of several rays4 ,since the true supposition is thus very frequently something altogether diverse from all the obvious conjectures and combinations1 we see here how far we are from being able to reduce discovery to rule1 or to give any precepts by which the want of real invention and sagacity shall be supplied4 ,we may warn and encourage these faculties when they exist1 but we cannot create them1 or make great discoveries when they are absent4 #aj4 ,the ,conceptions which a true theory requires are very often clothed in a ,hypothesis which connects #fg with them several superfluous and irrelevant circumstances4 ,thus the ,conception of the ,polarization of ,light was originally represented under the image of particles of light having their poles all turned in the same direction4 ,the ,laws of ,heat may be made out perhaps most conveniently by conceiving ,heat to be a ,fluid4 ,the ,attraction of ,gravitation might have been successfully applied to the explanation of facts1 if ,newton had throughout treated ,attraction as the result of an ,ether diffused through space2 a supposition which he has noticed as a possibility4 ,the doctrine of ,definite and ,multiple ,proportions may be conveniently expressed by the hypothesis of ,atoms4 ,in such cases1 the ,hypothesis may serve at first to facilitate the introduction of a new ,conception4 ,thus a pervading ,ether might for a time remove a difficulty1 which some persons find considerable1 of imagining a body to exert force at a distance4 ,a ,particle with ,poles is more easily conceived than ,polarization in the abstract4 ,and if hypotheses thus employed will really explain the facts by means of a few simple assumptions1 the laws so obtained may afterwards be reduced to a simpler form than that in which they were first suggested4 ,the general laws of ,heat1 of ,attraction1 of ,polarization1 of ,multiple ,proportions1 are now certain1 whatever image we may form to ourselves of their ultimate causes4 #aa4 ,in order1 then1 to discover scientific truths1 suppositions consisting either of new ,conceptions1 or of new ,combinations of old ones1 are to be made1 till we find one supposition which succeeds in binding together the ,facts4 ,but how are we to find this8 ,how is the trial to be made8 ,what is meant by 'success' in these cases8 ,to this we reply1 that our inquiry must be1 whether the ,facts have the same relation in the ,hypothesis which they have in reality2--whether the results of our suppositions agree with the phenomena which nature presents to us4 ,for this purpose1 we must both carefully observe the phenomena1 and steadily trace the consequences of our assumptions1 till we can #fh bring the two into comparison4 ,the ,conceptions which our hypotheses involve1 being derived from certain ,fundamental ,ideas1 afford a basis of rigorous reasoning1 as we have shown in the ,books of the ,history of those ,ideas4 ,and the results to which this reasoning leads1 will be susceptible of being verified or contradicted by observation of the facts4 ,thus the ,epicyclical ,theory of the ,moon1 once assumed1 determined what the moon's place among the stars ought to be at any given time1 and could therefore be tested by actually observing the moon's places4 ,the doctrine that musical strings of the same length1 stretched with weights of #a1 #d1 #i1 #af1 would give the musical intervals of an octave1 a fifth1 a fourth1 in succession1 could be put to the trial by any one whose ear was capable of appreciating those intervals3 and the inference which follows from this doctrine by numerical reasoning1--that there must be certain imperfections in the concords of every musical scale1--could in like manner be confirmed by trying various modes of ,temperament4 ,in like manner all received theories in science1 up to the present time1 have been established by taking up some supposition1 and comparing it1 directly or by means of its remoter consequences1 with the facts it was intended to embrace4 ,its agreement1 under certain cautions and conditions1 of which we may hereafter speak1 is held to be the evidence of its truth4 ,it answers its genuine purpose1 the ,colligation of ,facts4 #ab4 ,when we have1 in any subject1 succeeded in one attempt of this kind1 and obtained some true ,bond of ,unity by which the phenomena are held together1 the subject is open to further prosecution2 which ulterior process may1 for the most part1 be conducted in a more formal and technical manner4 ,the first great outline of the subject is drawn2 and the finishing of the resemblance of nature demands a more minute pencilling1 but perhaps requires less of genius in the master4 ,in the pursuance of this task1 rules and precepts may be given1 and features and leading circumstances pointed out1 of which it may often be useful to the inquirer to be aware4 #fi ,before proceeding further1 ,i shall speak of some characteristic marks which belong to such scientific processes as are now the subject of our consideration1 and which may sometimes aid us in determining when the task has been rightly executed4 #gj ,,chapter ,v4 ,,of ,,certain ,,characteristics ,,of ,,scientific ,,induction4 ,,aphorism ,x4 ,the process of scientific discovery is cautious and rigorous1 not by abstaining from hypotheses1 but by rigorously comparing hypotheses with facts1 and by resolutely rejecting all which the comparison does not confirm4 ,,aphorism ,,xi4 ,hypotheses may be useful1 though involving much that is superfluous1 and even erroneous3 for they may supply the true bond of connexion of the facts2 and the superfluity and errour may afterwards be pared away4 ,,aphorism ,,xii4 ,it is a test of true theories not only to account for1 but to predict phenomena4 ,,aphorism ,,xiii4 ,induction is a term applied to describe the process of a true ,colligation of ,facts by means of an exact and appropriate ,conception4 ,an ,induction is also employed to denote the proposition which results from this process4 ,,aphorism ,,xiv4 ,the ,consilience of ,inductions takes place when an ,induction1 obtained from one class of facts1 coincides with an ,induction1 obtained from another different class4 ,this #ga ,consilience is a test of the truth of the ,theory in which it occurs4 ,,aphorism ,,xv4 ,an ,induction is not the mere sum of the ,facts which are colligated4 ,the ,facts are not only brought together1 but seen in a new point of view4 ,a new mental ,element is superinduced2 and a peculiar constitution and discipline of mind are requisite in order to make this ,induction4 ,,aphorism ,,xvi4 ,although in ,every ,induction a new conception is superinduced upon the ,facts2 yet this once effectually done1 the novelty of the conception is overlooked1 and the conception is considered as a part of the fact4 ,,sect4 ,i4--,invention a part of ,induction4 #a4 ,,the two operations spoken of in the preceding chapters1--the ,explication of the ,conceptions of our own minds1 and the ,colligation of observed ,facts by the aid of such ,conceptions1--are1 as we have just said1 inseparably connected with each other4 ,when united1 and employed in collecting knowledge from the phenomena which the world presents to us1 they constitute the mental process of ,induction2 which is usually and justly spoken of as the genuine source of all our real general knowledge respecting the external world4 ,and we see1 from the preceding analysis of this process into its two constituents1 from what origin it derives each of its characters4 ,it is real1 because it arises from the combination of ,real ,facts1 but it is general1 because it implies the possession of ,general ,ideas4 ,without the former1 it would not be knowledge of the ,external ,world2 without the latter1 it would not be ,knowledge at all4 ,when ,ideas and ,facts are separated from each other1 the neglect of ,facts gives rise to empty speculations1 idle subtleties1 visionary inventions1 false opinions concerning the laws of phenomena1 disregard of the true aspect of nature3 #gb while the want of ,ideas leaves the mind overwhelmed1 bewildered1 and stupified by particular sensations1 with no means of connecting the past with the future1 the absent with the present1 the example with the rule2 open to the impression of all appearances1 but capable of appropriating none4 ,ideas are the ,form1 facts the ,material1 of our structure4 ,knowledge does not consist in the empty mould1 or in the brute mass of matter1 but in the rightly-moulded substance4 ,induction gathers general truths from particular facts2--and in her harvest1 the corn and the reaper1 the solid ears and the binding band1 are alike requisite4 ,all our knowledge of nature is obtained by ,induction2 the term being understood according to the explanation we have now given4 ,and our knowledge is then most complete1 then most truly deserves the name of ,science1 when both its elements are most perfect2--when the ,ideas which have been concerned in its formation have1 at every step1 been clear and consistent2 and when they have1 at every step also1 been employed in binding together real and certain ,facts4 ,of such ,induction1 ,i have already given so many examples and illustrations in the two preceding chapters1 that ,i need not now dwell further upon the subject4 #b4 ,induction is familiarly spoken of as the process by which we collect a ,general ,proposition from a number of ,particular ,cases3 and it appears to be frequently imagined that the general proposition results from a mere juxta-position of the cases1 or at most1 from merely conjoining and extending them4 ,but if we consider the process more closely1 as exhibited in the cases lately spoken of1 we shall perceive that this is an inadequate account of the matter4 ,the particular facts are not merely brought together1 but there is a ,new ,element added to the combination by the very act of thought by which they are combined4 ,there is a ,conception of the mind introduced in the general proposition1 which did not exist in any of the observed facts4 ,when the ,greeks1 after long observing the motions of the planets1 saw that these motions might be rightly considered as produced by the motion of one #gc wheel revolving in the inside of another wheel1 these ,wheels were ,creations of their minds1 added to the ,facts which they perceived by sense4 ,and even if the wheels were no longer supposed to be material1 but were reduced to mere geometrical spheres or circles1 they were not the less products of the mind alone1--something additional to the facts observed4 ,the same is the case in all other discoveries4 ,the facts are known1 but they are insulated and unconnected1 till the discoverer supplies from his own stores a ,principle of ,connexion4 ,the pearls are there1 but they will not hang together till some one provides the ,string4 ,the distances and periods of the planets were all so many separate facts2 by ,kepler's ,third ,law they are connected into a single truth3 but the ,conceptions which this law involves were supplied by ,kepler's mind1 and without these1 the facts were of no avail4 ,the planets described ellipses round the sun1 in the contemplation of others as well as of ,newton2 but ,newton conceived the deflection from the tangent in these elliptical motions in a new light1--as the effect of a ,central ,force following a certain law2 and then it was1 that such a force was discovered truly to exist4 ,thus#eb in each inference made by ,induction1 there is introduced some ,general ,conception1 which is given1 not by the phenomena1 but by the mind4 ,the conclusion is not contained in the premises1 but includes them by the introduction of a ,new ,generality4 ,in order to obtain our inference1 we travel beyond the cases which we have before us2 we consider them as mere exemplifications of some ,ideal ,case in which the relations are complete and intelligible4 ,we take a ,standard1 and measure the facts by it2 and this ,standard is constructed by us1 not offered by ,nature4 ,we assert1 for example1 that a body left to itself will move on with unaltered velocity2 not because our senses ever disclosed to us a body doing this1 but because 7taking this as our ,ideal ,case7 we find that all #gd actual cases are intelligible and explicable by means of the ,conception of ,forces1 causing change and motion1 and exerted by surrounding bodies4 ,in like manner1 we see bodies striking each other1 and thus moving and stopping1 accelerating and retarding each other3 but in all this1 we do not perceive by our senses that abstract quantity1 ,momentum1 which is always lost by one body as it is gained by another4 ,this ,momentum is a creation of the mind1 brought in among the facts1 in order to convert their apparent confusion into order1 their seeming chance into certainty1 their perplexing variety into simplicity4 ,this the ,conception of ,momentum gained and lost does3 and in like manner1 in any other case in which a truth is established by ,induction1 some ,conception is introduced1 some ,idea is applied1 as the means of binding together the facts1 and thus producing the truth4 ,note #eb3 ,i repeat here remarks made at the end of the ,mechanical ,euclid1 p4 #agh4 #c4 ,hence in every inference by ,induction1 there is some ,conception superinduced upon the ,facts3 and we may henceforth conceive this to be the peculiar import of the term ,induction4 ,i am not to be understood as asserting that the term was originally or anciently employed with this notion of its meaning2 for the peculiar feature just pointed out in ,induction has generally been overlooked4 ,this appears by the accounts generally given of ,induction4 ',induction1' says ,aristotle#fb1 'is when by means of one extreme term#gb we infer the other extreme term to be true of the middle term4' ,thus1 7to take such exemplifications as belong to our subject17 from knowing that ,mercury1 ,venus1 ,mars1 describe ellipses about the ,sun1 we infer that all ,planets describe ellipses about the ,sun4 ,in making this inference syllogistically1 we assume that the evident proposition1 ',mercury1 ,venus1 ,mars1 do what all ,planets do1' may be taken conversely1 ',all #ge ,planets do what ,mercury1 ,venus1 ,mars1 do4' ,but we may remark that1 in this passage1 ,aristotle 7as was natural in his line of discussion7 turns his attention entirely to the evidence of the inference2 and overlooks a step which is of far more importance to our knowledge1 namely1 the invention of the second extreme term4 ,in the above instance1 the particular luminaries1 ,mercury1 ,venus1 ,mars1 are one logical ,extreme2 the general designation ,planets is the ,middle ,term2 but having these before us1 how do we come to think of description of ellipses1 which is the other ,extreme of the syllogism8 ,when we have once invented this 'second ,extreme ,term1' we may1 or may not1 be satisfied with the evidence of the syllogism2 we may1 or may not1 be convinced that1 so far as this property goes1 the extremes are co-extensive with the middle term#hb2 but the statement of the syllogism is the important step in science4 ,we know how long ,kepler laboured1 how hard he fought1 how many devices he tried1 before he hit upon this ,term1 the ,elliptical ,motion4 ,he rejected1 as we know1 many other 'second extreme ,terms1' for example1 various combinations of epicyclical constructions1 because they did not represent with sufficient accuracy the special facts of observation4 ,when he had established his premiss1 that ',mars does describe an ,ellipse about the ,sun1' he does not hesitate to guess at least that1 in this respect1 he might convert the other premiss1 and assert that ',all the ,planets do what ,mars does4' ,but the main business was1 the inventing and verifying the proposition respecting the ,ellipse4 ,the ,invention of the ,conception was the great step in the discovery2 the ,verification of the ,proposition was the great step in the proof of the discovery4 ,if ,logic consists in pointing out the conditions of proof1 the ,logic of ,induction must consist in showing what are the conditions of proof1 in such inferences as this3 but this subject must be pursued in the next chapter2 ,i now speak principally of the act of #gf ,invention1 which is requisite in every inductive inference4 ,note #fb3 ,analyt4 ,prior4 lib4 ii4 c4 xxiii4 4 ,note #gb3 ,the syllogism here alluded to would be this3-- ,mercury1 ,venus1 ,mars1 describe ellipses about the ,sun2 ,all ,planets do what ,mercury1 ,venus1 ,mars1 do2 ,therefore all ,planets describe ellipses about the ,sun4 ,note #hb3 4--,aristot4 ,ibid4 #d4 ,although in every inductive inference1 an act of invention is requisite1 the act soon slips out of notice4 ,although we bind together facts by superinducing upon them a new ,conception1 this ,conception1 once introduced and applied1 is looked upon as inseparably connected with the facts1 and necessarily implied in them4 ,having once had the phenomena bound together in their minds in virtue of the ,conception1 men can no longer easily restore them back to the detached and incoherent condition in which they were before they were thus combined4 ,the pearls once strung1 they seem to form a chain by their nature4 ,induction has given them a unity which it is so far from costing us an effort to preserve1 that it requires an effort to imagine it dissolved4 ,for instance1 we usually represent to ourselves the ,earth as round1 the ,earth and the ,planets as revolving about the ,sun1 and as drawn to the ,sun by a ,central ,force2 we can hardly understand how it could cost the ,greeks1 and ,copernicus1 and ,newton1 so much pains and trouble to arrive at a view which to us is so familiar4 ,these are no longer to us ,conceptions caught hold of and kept hold of by a severe struggle2 they are the simplest modes of conceiving the facts3 they are really ,facts4 ,we are willing to own our obligation to those discoverers1 but we hardly feel it3 for in what other manner 7we ask in our thoughts7 could we represent the facts to ourselves8 ,thus we see why it is that this step of which we now speak1 the ,invention of a new ,conception in every inductive inference1 is so generally overlooked that it has hardly been noticed by preceding philosophers4 ,when once performed by the discoverer1 it takes a fixed and permanent place in the understanding of every one4 ,it is a thought which1 once breathed forth1 permeates all men's minds4 ,all fancy they nearly or quite knew it before4 ,it oft was thought1 or almost thought1 though never till now expressed4 ,men accept it and retain it1 and know it cannot be taken #gg from them1 and look upon it as their own4 ,they will not and cannot part with it1 even though they may deem it trivial and obvious4 ,it is a secret1 which once uttered1 cannot be recalled1 even though it be despised by those to whom it is imparted4 ,as soon as the leading term of a new theory has been pronounced and understood1 all the phenomena change their aspect4 ,there is a standard to which we cannot help referring them4 ,we cannot fall back into the helpless and bewildered state in which we gazed at them when we possessed no principle which gave them unity4 ,eclipses arrive in mysterious confusion3 the notion of a ,cycle dispels the mystery4 ,the ,planets perform a tangled and mazy dance2 but ,epicycles reduce the maze to order4 ,the ,epicycles themselves run into confusion2 the conception of an ,ellipse makes all clear and simple4 ,and thus from stage to stage1 new elements of intelligible order are introduced4 ,but this intelligible order is so completely adopted by the human understanding1 as to seem part of its texture4 ,men ask ,whether ,eclipses follow a ,cycle2 ,whether the ,planets describe ,ellipses2 and they imagine that so long as they do not answer such questions rashly1 they take nothing for granted4 ,they do not recollect how much they assume in asking the question3--how far the conceptions of ,cycles and of ,ellipses are beyond the visible surface of the celestial phenomena3--how many ages elapsed1 how much thought1 how much observation1 were needed1 before men's thoughts were fashioned into the words which they now so familiarly use4 ,and thus they treat the subject1 as we have seen ,aristotle treating it2 as if it were a question1 not of invention1 but of proof2 not of substance1 but of form3 as if the main thing were not what we assert1 but how we assert it4 ,but for our purpose1 it is requisite to bear in mind the feature which we have thus attempted to mark2 and to recollect that1 in every inference by induction1 there is a ,conception supplied by the mind and superinduced upon the ,facts4 #e4 ,in collecting scientific truths by ,induction1 we often find 7as has already been observed7 a ,definition #gh and a ,proposition established at the same time1--introduced together1 and mutually dependent on each other4 ,the combination of the two constitutes the ,inductive act2 and we may consider the ,definition as representing the superinduced ,conception1 and the ,proposition as exhibiting the ,colligation of ,facts4 ,,sect4 ,,ii4--,use of ,hypotheses4 #f4 ,to discover a ,conception of the mind which will justly represent a train of observed facts is1 in some measure1 a process of conjecture1 as ,i have stated already2 and as ,i then observed1 the business of conjecture is commonly conducted by calling up before our minds several suppositions1 and selecting that one which most agrees with what we know of the observed facts4 ,hence he who has to discover the laws of nature may have to invent many suppositions before he hits upon the right one2 and among the endowments which lead to his success1 we must reckon that fertility of invention which ministers to him such imaginary schemes1 till at last he finds the one which conforms to the true order of nature4 ,a facility in devising hypotheses1 therefore1 is so far from being a fault in the intellectual character of a discoverer1 that it is1 in truth1 a faculty indispensable to his task4 ,it is1 for his purposes1 much better that he should be too ready in contriving1 too eager in pursuing systems which promise to introduce law and order among a mass of unarranged facts1 than that he should be barren of such inventions and hopeless of such success4 ,accordingly1 as we have already noticed1 great discoverers have often invented hypotheses which would not answer to all the facts1 as well as those which would2 and have fancied themselves to have discovered laws1 which a more careful examination of the facts overturned4 ,the tendencies of our speculative nature#ib1 carrying #gi us onwards in pursuit of symmetry and rule1 and thus producing all true theories1 perpetually show their vigour by overshooting the mark4 ,they obtain something1 by aiming at much more4 ,they detect the order and connexion which exist1 by conceiving imaginary relations of order and connexion 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 discoverers as we read the books of ,kepler4 ,to try wrong guesses is1 with most persons1 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 conceived1 and brought into rigid contact with facts4 ,he sees and compares distinctly the ,ideas and the ,things2--the relations of his notions to each other and to phenomena4 ,under these conditions1 it is not only excusable1 but necessary for him1 to snatch at every semblance of general rule1--to try all promising forms of simplicity and symmetry4 ,note #ib3 ,i here take the liberty of characterizing inventive minds in general in the same phraseology which1 in the ,history of ,science1 ,i have employed in reference to particular examples4 ,these expressions are what ,i have used in speaking of the discoveries of ,copernicus4--,hist4 ,ind4 ,sc4 b4 v4 c4 ii4 ,hence advances in knowledge#ajb 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 the many possibilities1 and selecting the appropriate one8 ,it is true1 that when we have rejected all the inadmissible suppositions1 they are often quickly forgotten2 and few think it necessary to dwell on these discarded hypotheses1 and on the process by which they were condemned4 ,but all who discover truths1 must have reasoned upon many errours to obtain each truth2 #hj every accepted doctrine must have been one chosen out of many candidates4 ,if many of the guesses of philosophers of bygone times now appear fanciful and absurd1 because time and observation have refuted them1 others1 which were at the time equally gratuitous1 have been conformed in a manner which makes them appear marvellously sagacious4 ,to form hypotheses1 and then to employ much labour and skill in refuting them1 if they do not succeed in establishing them1 is a part of the usual process of inventive minds4 ,such a proceeding belongs to the rule of the genius of discovery1 rather than 7as has often been taught in modern times7 to the exception4 ,note #ajb3 ,these observations are made on occasion of ,kepler's speculations1 and are illustrated by reference to his discoveries4--,hist4 ,ind4 ,sc4 b4 v4 c4 iv4 sect4 #a4 #g4 ,but if it be an advantage for the discoverer of truth that he be ingenious and fertile in inventing hypotheses which may connect the phenomena of nature1 it is indispensably requisite that he be diligent and careful in comparing his hypotheses with the facts1 and ready to abandon his invention as soon as it appears that it does not agree with the course of actual occurrences4 ,this constant comparison of his own conceptions and supposition with observed facts under all aspects1 forms the leading employment of the discoverer3 this candid and simple love of truth1 which makes him willing to suppress the most favourite production of his own ingenuity as soon as it appears to be at variance with realities1 constitutes the first characteristic of his temper4 ,he must have neither the blindness which cannot1 nor the obstinacy which will not1 perceive the discrepancy of his fancies and his facts4 ,he must allow no indolence1 or partial views1 or self-complacency1 or delight in seeming demonstration1 to make him tenacious of the schemes which he devises1 any further than they are confirmed by their accordance with nature4 ,the framing of hypotheses is1 for the inquirer after truth1 not the end1 but the beginning of his work4 ,each of his systems is invented1 not that he may admire it and follow it into all its consistent consequences1 but that he may make it the occasion of a course of active experiment and observation4 ,and if the results of this process #ha contradict his fundamental assumptions1 however ingenious1 however symmetrical1 however elegant his system may be1 he rejects it without hesitation4 ,he allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign1 ,truth3 to her he not only gives his affections and his wishes1 but strenuous labour and scrupulous minuteness of attention4 ,we may refer to what we have said of ,kepler1 ,newton1 and other eminent philosophers1 for illustrations of this character4 ,in ,kepler we have remarked#aab the courage and perseverance with which he undertook and executed the task of computing his own hypotheses3 and1 as a still more admirable characteristic1 that he never allowed the labour he had spent upon any conjecture to produce any reluctance in abandoning the hypothesis1 as soon as he had evidence of its inaccuracy4 ,and in the history of ,newton's discovery that the moon is retained in her orbit by the force of gravity1 we have noticed the same moderation in maintaining the hypothesis1 after it had once occurred to the author's mind4 ,the hypothesis required that the moon should fall from the tangent of her orbit every second through a space of sixteen feet2 but according to his first calculations it appeared that in fact she only fell through a space of thirteen feet in that time4 ,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 the difference4 ,but ,newton acquiesced in it as a disproof of his conjecture1 and 'laid aside at that time any further thoughts of this matter#abb4' ,note #aab3 ,hist4 ,ind4 ,sc4 b4 v4 c4 iv4 sect4 #a4 ,note #abb3 ,hist4 ,ind4 ,sc4 b4 vii4 c4 ii4 sect4 #c4 #h4 ,it has often happened that those who have undertaken to instruct mankind have not possessed this pure love of truth and comparative indifference to the maintenance of their own inventions4 ,men have frequently adhered with great tenacity and vehemence to the hypotheses which they have once framed2 and in their #hb affection for these1 have been prone to overlook1 to distort1 and to misinterpret facts4 ,in this manner1 ,hypotheses have so often been prejudicial to the genuine pursuit of truth1 that they have fallen into a kind of obloquy2 and have been considered as dangerous temptations and fallacious guides4 ,many warnings have been uttered against the fabrication of hypotheses1 by those who profess to teach philosophy2 many disclaimers of such a course by those who cultivate science4 ,thus we shall find ,bacon frequently discommending this habit1 under the name of 'anticipation of the mind1' and ,newton thinks it necessary to say emphatically 'hypotheses non fingo4' ,it has been constantly urged that the inductions by which sciences are formed must be cautious and rigorous2 and the various imaginations which passed through ,kepler's brain1 and to which he has given utterance1 have been blamed or pitied1 as lamentable instances of an unphilosophical frame of mind4 ,yet it has appeared in the preceding remarks that hypotheses rightly used are among the helps1 far more than the dangers1 of science2--that scientific induction is not a 'cautious' or a 'rigorous' process in the sense of abstaining from such suppositions1 but in not adhering to them till they are confirmed by fact1 and in carefully seeking from facts confirmation or refutation4 ,kepler's distinctive character was1 not that he was peculiarly given to the construction of hypotheses1 but that he narrated with extraordinary copiousness and candour the course of his thoughts1 his labours1 and his feelings4 ,in the minds of most persons1 as we have said1 the inadmissible suppositions1 when rejected1 are soon forgotten3 and thus the trace of them vanishes from the thoughts1 and the successful hypothesis alone holds its place in our memory4 ,but in reality1 many other transient suppositions must have been made by all discoverers2--hypotheses which are not afterwards asserted as true systems1 but entertained for an instant2--'tentative hypotheses1' as they have been called4 ,each of these hypotheses is followed by its corresponding train of observations1 from which it derives its power of leading to truth4 ,the hypothesis is #hc like the captain1 and the observations like the soldiers of an army3 while he appears to command them1 and in this way to work his own will1 he does in fact derive all his power of conquest from their obedience1 and becomes helpless and useless if they mutiny4 ,since the discoverer has thus constantly to work his way onwards by means of hypotheses1 false and true1 it is highly important for him to possess talents and means for rapidly testing each supposition as it offers itself4 ,in this as in other parts of the work of discovery1 success has in general been mainly owing to the native ingenuity and sagacity of the discoverer's mind4 ,yet some ,rules tending to further this object have been delivered by eminent philosophers1 and some others may perhaps be suggested4 ,of these we shall here notice only some of the most general1 leaving for a future chapter the consideration of some more limited and detailed processes by which1 in certain cases1 the discovery of the laws of nature may be materially assisted4 ,,sect4 ,,iii4--,tests of ,hypotheses4 #i4 ,a maxim which it may be useful to recollect is this2--that hypotheses may often be of service to science1 when they involve a certain portion of incompleteness1 and even of errour4 ,the object of such inventions is to bind together facts which without them are loose and detached2 and if they do this1 they may lead the way to a perception of the true rule by which the phenomena are associated together1 even if they themselves somewhat misstate the matter4 ,the imagined arrangement enables us to contemplate1 as a whole1 a collection of special cases which perplex and overload our minds when they are considered in succession2 and if our scheme has so much of truth in it as to conjoin what is really connected1 we may afterwards duly correct or limit the mechanism of this connexion4 ,if our hypothesis renders a reason for the agreement of cases really similar1 we may afterwards find this reason to be #hd false1 but we shall be able to translate it into the language of truth4 ,a conspicuous example of such an hypothesis1--one which was of the highest value to science1 though very incomplete1 and as a representation of nature altogether false1--is seen in the ,doctrine of epicycles by which the ancient astronomers explained the motions of the sun1 moon1 and planets4 ,this doctrine connected the places and velocities of these bodies at particular times in a manner which was1 in its general features1 agreeable to nature4 ,yet this doctrine was erroneous in its assertion of the circular nature of all the celestial motions1 and in making the heavenly bodies revolve round the earth4 ,it was1 however1 of immense value to the progress of astronomical science2 for it enabled men to express and reason upon many important truths which they discovered respecting the motion of the stars1 up to the time of ,kepler4 ,indeed we can hardly imagine that astronomy could1 in its outset1 have made so great a progress under any other form1 as it did in consequence of being cultivated in this shape of the incomplete and false epicyclical hypothesis4 ,we may notice another instance of an exploded hypothesis1 which is generally mentioned only to be ridiculed1 and which undoubtedly is both false in the extent of its assertion1 and unphilosophical in its expression2 but which still1 in its day1 was not without merit4 ,i mean the doctrine of ,nature's horrour of a vacuum 7fuga vacui71 by which the action of siphons and pumps and many other phenomena were explained1 till ,mersenne and ,pascal taught a truer doctrine4 ,this hypothesis was of real service2 for it brought together many facts which really belong to the same class1 although they are very different in their first aspect4 ,a scientific writer of modern times#acb appears to wonder that men did not at once divine the weight of the air1 from which the phenomena formerly ascribed to the fuga vacui really result4 ',loaded1 #he compressed by the atmosphere1' he says1 'they did not recognize its action4 ,in vain all nature testified that air was elastic and heavy2 they shut their eyes to her testimony4 ,the water rose in pumps and flowed in siphons at that time1 as it does at this day4 ,they could not separate the boards of a pair of bellows of which the holes were stopped2 and they could not bring together the same boards without difficulty1 if they were at first separated4 ,infants sucked the milk of their mothers2 air entered rapidly into the lungs of animals at every inspiration2 cupping-glasses produced tumours on the skin2 and in spite of all these striking proofs of the weight and elasticity of the air1 the ancient philosophers maintained resolutely that air was light1 and explained all these phenomena by the horrour which they said nature had for a vacuum4' ,it is curious that it should not have occurred to the author while writing this1 that if these facts1 so numerous and various1 can all be accounted for by one principle1 there is a strong presumption that the principle is not altogether baseless4 ,and in reality is it not true that nature does abhor a vacuum1 and does all she can to avoid it8 ,no doubt this power is not unlimited2 and moreover we can trace it to a mechanical cause1 the pressure of the circumambient air4 ,but the tendency1 arising from this pressure1 which the bodies surrounding a space void of air have to rush into it1 may be expressed1 in no extravagant or unintelligible manner1 by saying that nature has a repugnance to a vacuum4 ,note #acb3 ,deluc1 ,modifications de l',atmosphre1 ,partie #a4 ,that imperfect and false hypotheses1 though they may thus explain some phenomena1 and may be useful in the progress of science1 cannot explain all phenomena2--and that we are never to rest in our labours or acquiesce in our results1 till we have found some view of the subject which is consistent with all the observed facts2--will of course be understood4 ,we shall afterwards have to speak of the other steps of such a progress4 #aj4 ,thus the hypotheses which we accept ought to explain phenomena which we have observed4 ,but they #hf ought to do more than this3 our hypotheses ought to foretel phenomena which have not yet been observed2 at least all phenomena of the same kind as those which the hypothesis was invented to explain4 ,for our assent to the hypothesis implies that it is held to be true of all particular instances4 ,that these cases belong to past or to future times1 that they have or have not already occurred1 makes no difference in the applicability of the rule to them4 ,because the rule prevails1 it includes all cases2 and will determine them all1 if we can only calculate its real consequences4 ,hence it will predict the results of new combinations1 as well as explain the appearances which have occurred in old ones4 ,and that it does this with certainty and correctness1 is one mode in which the hypothesis is to be verified as right and useful4 ,the scientific doctrines which have at various periods been established have been verified in this manner4 ,for example1 the ,epicyclical ,theory of the heavens was confirmed by its predicting truly eclipses of the sun and moon1 configurations of the planets1 and other celestial phenomena2 and by its leading to the construction of ,tables by which the places of the heavenly bodies were given at every moment of time4 ,the truth and accuracy of these predictions were a proof that the hypothesis was valuable1 and1 at least to a great extent1 true2 although1 as was afterwards found1 it involved a false representation of the structure of the heavens4 ,in like manner1 the discovery of the ,laws of ,refraction enabled mathematicians to predict1 by calculation1 what would be the effect of any new form or combination of transparent lenses4 ,newton's hypothesis of ,fits of ,easy ,transmission and ,easy ,reflection in the particles of light1 although not confirmed by other kinds of facts1 involved a true statement of the law of the phenomena which it was framed to include1 and served to predict the forms and colours of thin plates for a wide range of given cases4 ,the hypothesis that ,light operates by ,undulations and ,interferences1 afforded the means of predicting results under a still larger extent of conditions4 ,in like manner in the #hg progress of chemical knowledge1 the doctrine of ,phlogiston supplied the means of foreseeing the consequence of many combinations of elements1 even before they were tried2 but the ,oxygen ,theory1 besides affording predictions1 at least equally exact1 with regard to the general results of chemical operations1 included all the facts concerning the relations of weight of the elements and their compounds1 and enabled chemists to foresee such facts in untried cases4 ,and the ,theory of ,electromagnetic ,forces1 as soon as it was rightly understood1 enabled those who had mastered it to predict motions such as had not been before observed1 which were accordingly found to take place4 ,men cannot help believing that the laws laid down by discoverers must be in a great measure identical with the real laws of nature1 when the discoverers thus determine effects beforehand in the same manner in which nature herself determines them when the occasion occurs4 ,those who can do this1 must1 to a considerable extent1 have detected nature's secret2--must have fixed upon the conditions to which she attends1 and must have seized the rules by which she applies them4 ,such a coincidence of untried facts with speculative assertions cannot be the work of chance1 but implies some large portion of truth in the principles on which the reasoning is founded4 ,to trace order and law in that which has been observed1 may be considered as interpreting what nature has written down for us1 and will commonly prove that we understand her alphabet4 ,but to predict what has not been observed1 is to attempt ourselves to use the legislative phrases of nature2 and when she responds plainly and precisely to that which we thus utter1 we cannot but suppose that we have in a great measure made ourselves masters of the meaning and structure of her language4 ,the prediction of results1 even of the same kind as those which have been observed1 in new cases1 is a proof of real success in our inductive processes4 #aa4 ,we have here spoken of the prediction of facts of the same kind as those from which our rule was collected4 ,but the evidence in favour of our #hh induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis4 ,the instances in which this has occurred1 indeed1 impress us with a conviction that the truth of our hypothesis is certain4 ,no accident could give rise to such an extraordinary coincidence4 ,no false supposition could1 after being adjusted to one class of phenomena1 exactly represent a different class1 where the agreement was unforeseen and uncontemplated4 ,that rules springing from remote and unconnected quarters should thus leap to the same point1 can only arise from that being the point where truth resides4 ,accordingly the cases in which inductions from classes of facts altogether different have thus jumped together1 belong only to the best established theories which the history of science contains4 ,and as ,i shall have occasion to refer to this peculiar feature in their evidence1 ,i will take the liberty of describing it by a particular phrase2 and will term it the ,consilience of ,inductions4 ,it is exemplified principally in some of the greatest discoveries4 ,thus it was found by ,newton that the doctrine of the ,attraction of the ,sun varying according to the ,inverse ,square of this distance1 which explained ,kepler's ,third ,law1 of the proportionality of the cubes of the distances to the squares of the periodic times of the planets1 explained also his ,first and ,second ,laws1 of the elliptical motion of each planet2 although no connexion of these laws had been visible before4 ,again1 it appeared that the force of universal ,gravitation1 which had been inferred from the ,perturbations of the moon and planets by the sun and by each other1 also accounted for the fact1 apparently altogether dissimilar and remote1 of the ,precession of the equinoxes4 ,here was a most striking and surprising coincidence1 which gave to the theory a stamp of truth beyond the power of ingenuity to counterfeit4 ,in like manner in ,optics2 the hypothesis of alternate ,fits of easy ,transmission and ,reflection would explain #hi the colours of thin plates1 and indeed was devised and adjusted for that very purpose2 but it could give no account of the phenomena of the fringes of shadows4 ,but the doctrine of ,interferences1 constructed at first with reference to phenomena of the nature of the ,fringes1 explained also the ,colours of thin plates better than the supposition of the ,fits invented for that very purpose4 ,and we have in ,physical ,optics another example of the same kind1 which is quite as striking as the explanation of ,precession by inferences from the facts of ,perturbation4 ,the doctrine of ,undulations propagated in a ,spheroidal ,form was contrived at first by ,huyghens1 with a view to explain the laws of ,double ,refraction in calc-spar2 and was pursued with the same view by ,fresnel4 ,but in the course of the investigation it appeared1 in a most unexpected and wonderful manner1 that this same doctrine of spheroidal undulations1 when it was so modified as to account for the directions of the two refracted rays1 accounted also for the positions of their ,planes of ,polarization#adb1 a phenomenon which1 taken by itself1 it had perplexed previous mathematicians1 even to represent4 ,note #adb3 ,hist4 ,ind4 ,sc4 b4 ix4 c4 xi4 sect4 #d4 ,the ,theory of ,universal ,gravitation1 and of the ,undulatory ,theory of ,light1 are1 indeed1 full of examples of this ,consilience of ,inductions4 ,with regard to the latter1 it has been justly asserted by ,herschel1 that the history of the undulatory theory was a succession of felicities#aeb4 ,and it is precisely the unexpected coincidences of results drawn from distant parts of the subject which are properly thus described4 ,thus the ,laws of the ,modification of polarization to which ,fresnel was led by his general views1 accounted for the ,rule respecting the ,angle at which light is polarized1 discovered by ,sir ,d4 ,brewster#afb4 ,the conceptions of the theory pointed out peculiar ,modifications of the phenomena when ,newton's rings were produced by polarised light1 which modifications were #ij ascertained to take place in fact1 by ,arago and ,airy#agb4 ,when the beautiful phenomena of ,dipolarized light were discovered by ,arago and ,biot1 ,young was able to declare that they were reducible to the general laws of ,interference which he had already established#ahb4 ,and what was no less striking a confirmation of the truth of the theory1 ,measures of the same element deduced from various classes of facts were found to coincide4 ,thus the ,length of a luminiferous undulation1 calculated by ,young from the measurement of ,fringes of shadows1 was found to agree very nearly with the previous calculation from the colours of ,thin plates#aib4 ,note #aeb3 ,see ,hist4 ,ind4 ,sc4 b4 ix4 c4 xii4 ,note #afb3 ,ib4 c4 xi4 sect4 #d4 ,note #agb3 ,see ,hist4 ,ind4 ,sc4 b4 ix4 c4 xiii4 sect4 #f4 ,note #ahb3 ,ib4 c4 xi4 sect4 #e4 ,note #aib3 ,ib4 c4 xi4 sect4 #b4 ,no example can be pointed out1 in the whole history of science1 so far as ,i am aware1 in which this ,consilience of ,inductions has given testimony in favour of an hypothesis afterwards discovered to be false4 ,if we take one class of facts only1 knowing the law which they follow1 we may construct an hypothesis1 or perhaps several1 which may represent them3 and as new circumstances are discovered1 we may often adjust the hypothesis so as to correspond to these also4 ,but when the hypothesis1 of itself and without adjustment for the purpose1 gives us the rule and reason of a class of facts not contemplated in its construction1 we have a criterion of its reality1 which has never yet been produced in favour of falsehood4 #ab4 ,in the preceding ,article ,i have spoken of the hypothesis with which we compare our facts as being framed all at once1 each of its parts being included in the original scheme4 ,in reality1 however1 it often happens that the various suppositions which our system contains are added upon occasion of different researches4 ,thus in the ,ptolemaic doctrine of the heavens1 new epicycles and eccentrics were added as new inequalities of the motions of the heavenly bodies were discovered2 and in the ,newtonian doctrine of material rays of light1 the supposition that these rays had #ia 'fits1' was added to explain the colours of thin plates2 and the supposition that they had 'sides' was introduced on occasion of the phenomena of polarization4 ,in like manner other theories have been built up of parts devised at different times4 ,this being the mode in which theories are often framed1 we have to notice a distinction which is found to prevail in the progress of true and false theories4 ,in the former class all the additional suppositions tend to simplicity and harmony2 the new suppositions resolve themselves into the old ones1 or at least require only some easy modification of the hypothesis first assumed3 the system becomes more coherent as it is further extended4 ,the elements which we require for explaining a new class of facts are already contained in our system4 ,different members of the theory run together1 and we have thus a constant convergence to unity4 ,in false theories1 the contrary is the case4 ,the new suppositions are something altogether additional2--not suggested by the original scheme2 perhaps difficult to reconcile with it4 ,every such addition adds to the complexity of the hypothetical system1 which at last becomes unmanageable1 and is compelled to surrender its place to some simpler explanation4 ,such a false theory1 for example1 was the ancient doctrine of eccentrics and epicycles4 ,it explained the general succession of the ,places of the ,sun1 ,moon1 and ,planets2 it would not have explained the proportion of their ,magnitudes at different times1 if these could have been accurately observed2 but this the ancient astronomers were unable to do4 ,when1 however1 ,tycho and other astronomers came to be able to observe the planets accurately in all positions1 it was found that no combination of equable circular motions would exactly represent all the observations4 ,we may see1 in ,kepler's works1 the many new modifications of the epicyclical hypothesis which offered themselves to him2 some of which would have agreed with the phenomena with a certain degree of accuracy1 but not with so great a degree as ,kepler1 fortunately for the progress of science1 insisted upon obtaining4 ,after these #ib epicycles had been thus accumulated1 they all disappeared and gave way to the simpler conception of an elliptical motion4 ,in like manner1 the discovery of new inequalities in the ,moon's motions encumbered her system more and more with new machinery1 which was at last rejected all at once in favour of the elliptical theory4 ,astronomers could not but suppose themselves in a wrong path1 when the prospect grew darker and more entangled at every step4 ,again2 the ,cartesian system of ,vortices might be said to explain the primary phenomena of the revolutions of planets about the sun1 and satellites about planets4 ,but the elliptical form of the orbits required new suppositions4 ,bernoulli ascribed this curve to the shape of the planet1 operating on the stream of the vortex in a manner similar to the rudder of a boat4 ,but then the motions of the aphelia1 and of the nodes1--the perturbations1--even the action of gravity towards the earth1--could not be accounted for without new and independent suppositions4 ,here was none of the simplicity of truth4 ,the theory of ,gravitation1 on the other hand1 became more simple as the facts to be explained became more numerous4 ,the attraction of the sun accounted for the motions of the planets2 the attraction of the planets was the cause of the motion of the satellites4 ,but this being assumed1 the perturbations1 and the motions of the nodes and aphelia1 only made it requisite to extend the attraction of the sun to the satellites1 and that of the planets to each other3--the tides1 the spheroidal form of the earth1 the precession1 still required nothing more than that the moon and sun should attract the parts of the earth1 and that these should attract each other2--so that all the suppositions resolved themselves into the single one1 of the universal gravitation of all matter4 ,it is difficult to imagine a more convincing manifestation of simplicity and unity4 ,again1 to take an example from another science2--the doctrine of ,phlogiston brought together many facts in a very plausible manner1--combustion1 acidification1 and others1--and very naturally prevailed for a while4 #ic ,but the balance came to be used in chemical operations1 and the facts of weight as well as of combination were to be accounted for4 ,on the phlogistic theory1 it appeared that this could not be done without a new supposition1 and that1 a very strange one2--that phlogiston was an element not only not heavy1 but absolutely light1 so that it diminished the weight of the compounds into which it entered4 ,some chemists for a time adopted this extravagant view1 but the wiser of them saw1 in the necessity of such a supposition to the defence of the theory1 an evidence that the hypothesis of an element phlogiston was erroneous4 ,and the opposite hypothesis1 which taught that oxygen was subtracted1 and not phlogiston added1 was accepted because it required no such novel and inadmissible assumption4 ,again1 we find the same evidence of truth in the progress of the ,undulatory ,theory of light1 in the course of its application from one class of facts to another4 ,thus 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 undulation3 the phenomena of ,diffraction also require such intervals2 and the intervals thus required agree exactly with the others in magnitude1 so that no new property is needed4 ,polarization for a moment appears to require some new hypothesis2 yet this is hardly the case2 for the direction of our vibrations is hitherto arbitrary3--we allow polarization to decide it1 and we suppose the undulations to be transverse4 ,having done this for the sake of ,polarization1 we turn to the phenomena of ,double ,refraction1 and inquire what new hypothesis they require4 ,but the answer is1 that they require none3 the supposition of transverse vibrations1 which we have made in order to explain ,polarization1 gives us also the law of ,double ,refraction4 ,truth may give rise to such a coincidence2 falsehood cannot4 ,again1 the facts of ,dipolarization come into view4 ,but they hardly require any new assumption2 for the difference of optical elasticity of crystals in different directions1 #id which is already assumed in uniaxal crystals#bjb1 is extended to biaxal exactly according to the law of symmetry2 and this being done1 the laws of the phenomena1 curious and complex as they are1 are fully explained4 ,the phenomena of ,circular ,polarization by internal reflection1 instead of requiring a new hypothesis1 are found to be given by an interpretation of an apparently inexplicable result of an old hypothesis4 ,the ,circular ,polarization of ,quartz and the ,double ,refraction does indeed appear to require a new assumption1 but still not one which at all disturbs the form of the theory2 and in short1 the whole history of this theory is a progress1 constant and steady1 often striking and startling1 from one degree of evidence and consistence to another of a higher order4 ,note #bjb3 ,hist4 ,ind4 ,sc4 b4 ix4 c4 xi4 sect4 #e4 ,in the ,emission ,theory1 on the other hand1 as in the theory of solid epicycles1 we see 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 supposition--an addition to the machinery3 and as observation goes on1 these incoherent appendages accumulate1 till they overwhelm and upset the original frame-work4 ,such has been the hypothesis of the ,material ,emission of light4 ,in its original form1 it explained ,reflection and ,refraction3 but the colours of ,thin ,plates added to it the ,fits of easy ,transmission and ,reflection2 the phenomena of ,diffraction further invested the emitted particles with complex laws of ,attraction and ,repulsion2 ,polarization gave them ,sides3 ,double ,refraction subjected them to peculiar ,forces emanating from the axes of the crystal3 ,finally1 ,dipolarization loaded them with the complex and unconnected contrivance of ,moveable ,polarization3 and even when all this had been done1 additional mechanism was wanting4 ,there is here no unexpected success1 no happy coincidence1 no convergence of principles from remote quarters4 ,the philosopher builds #ie the machine1 but its parts do not fit4 ,they hold together only while he presses them4 ,this is not the character of truth4 ,as another example of the application of the ,maxim now under consideration1 ,i may perhaps be allowed to refer to the judgment which1 in the ,history of ,thermotics1 ,i have ventured to give respecting ,laplace's ,theory of ,gases4 ,i have stated#bab1 that we cannot help forming an unfavourable judgment of this theory1 by looking for that great characteristic of true theory2 namely1 that the hypotheses which were assumed to account for one class of facts are found to explain another class of a different nature4 ,thus ,laplace's first suppositions explain the connexion of ,compression with ,density1 7the law of ,boyle and ,mariotte17 and the connexion of ,elasticity with ,heat1 7the law of ,dalton and ,gay ,lussac74 ,but the theory requires other assumptions when we come to ,latent ,heat2 and yet these new assumptions produce no effect upon the calculations in any application of the theory4 ,when the hypothesis1 constructed with reference to the ,elasticity and ,temperature1 is applied to another class of facts1 those of ,latent ,heat1 we have no ,simplification of the ,hypothesis1 and therefore no evidence of the truth of the theory4 ,note #bab3 ,hist4 ,ind4 ,sc4 b4 x4 c4 iv4 #ac4 ,the last two sections of this chapter direct our attention to two circumstances1 which tend to prove1 in a manner which we may term irresistible1 the truth of the theories which they characterize3--the ,consilience of ,inductions from different and separate classes of facts2--and the progressive ,simplification of the ,theory as it is extended to new cases4 ,these two ,characters are1 in fact1 hardly different2 they are exemplified by the same cases4 ,for if these ,inductions1 collected from one class of facts1 supply an unexpected explanation of a new class1 which is the case first spoken of1 there will be no need for new machinery in the hypothesis to apply it to the newly-contemplated facts2 and thus1 we have a case in which the system does not become #if more complex when its application is extended to a wider field1 which was the character of true theory in its second aspect4 ,the ,consiliences of our ,inductions give rise to a constant ,convergence of our ,theory towards ,simplicity and ,unity4 ,but1 moreover1 both these cases of the extension of the theory1 without difficulty or new suppositions1 to a wider range and to new classes of phenomena1 may be conveniently considered in yet another point of view2 namely1 as successive steps by which we gradually ascend in our speculative views to a higher and higher point of generality4 ,for when the theory1 either by the concurrence of two indications1 or by an extension without complication1 has included a new range of phenomena1 we have1 in fact1 a new induction of a more general kind1 to which the inductions formerly obtained are subordinate1 as particular cases to a general proposition4 ,we have in such examples1 in short1 an instance of successive generalization4 ,this is a subject of great importance1 and deserving of being well illustrated2 it will come under our notice in the next chapter4 #ig ,,chapter ,,vi4 ,,of ,,the ,,logic ,,of ,,induction4 ,,aphorism ,,xvii4 ,the ,logic of ,induction consists in stating the ,facts and the ,inference in such a manner1 that the ,evidence of the ,inference is manifest3 just as the ,logic of ,deduction consists in stating the ,premises and the ,conclusion in such a manner that the ,evidence of the ,conclusion is manifest4 ,,aphorism ,,xviii4 ,the ,logic of ,deduction is exhibited by means of a certain ,formula2 namely1 a ,syllogism2 and every train of deductive reasoning1 to be demonstrative1 must be capable of resolution into a series of such ,formul legitimately constructed4 ,in like manner1 the ,logic of ,induction may be exhibited by means of certain ,formul2 and every train of inductive inference to be sound1 must be capable of resolution into a scheme of such ,formul1 legitimately constructed4 ,,aphorism ,,xix4 ,the inductive act of thought by which several ,facts are colligated into one ,proposition1 may be expressed by saying3 ,the several ,facts are exactly expressed as one ,fact1 if1 and only if1 we adopt the ,conceptions and the ,assertion of the ,proposition4 ,,aphorism ,,xx4 ,the ,one ,fact1 thus inductively obtained from several ,facts1 may be combined with other ,facts1 and colligated with them by a new act of ,induction4 ,this process may be #ih indefinitely repeated3 and these successive processes are the ,steps of ,induction1 or of ,generalization1 from the lowest to the highest4 ,,aphorism ,,xxi4 ,the relation of the successive ,steps of ,induction may be exhibited by means of an ,inductive ,table1 in which the several ,facts are indicated1 and tied together by a ,bracket1 and the ,inductive ,inference placed on the other side of the ,bracket2 and this arrangement repeated1 so as to form a genealogical ,table of each ,induction1 from the lowest to the highest4 ,,aphorism ,,xxii4 ,the ,logic of ,induction is the ,criterion of ,truth inferred from ,facts1 as the ,logic of ,deduction is the ,criterion of ,truth deduced from necessary ,principles4 ,the ,inductive ,table enables us to apply such a ,criterion2 for we can determine whether each ,induction is verified and justified by the ,facts which its ,bracket includes2 and if each induction in particular be sound1 the highest1 which merely combines them all1 must necessarily be sound also4 ,,aphorism ,,xxiii4 ,the distinction of ,fact and ,theory is only relative4 ,events and phenomena1 considered as ,particulars which may be colligated by ,induction1 are ,facts2 considered as ,generalities already obtained by colligation of other ,facts1 they are ,theories4 ,the same event or phenomenon is a ,fact or a ,theory1 according as it is considered as standing on one side or the other of the ,inductive ,bracket4 #a4 ,,the subject to which the present chapter refers is described by phrases which are at the present day familiarly used in speaking of the progress of knowledge4 ,we hear very frequent mention of ascending from particular to general propositions1 and from these to propositions still more general2--of #ii truths included in other truths of a higher degree of generality2--of different stages of generalization2--and of the highest step of the process of discovery1 to which all others are subordinate and preparatory4 ,as these expressions1 so familiar to our ears1 especially since the time of ,francis ,bacon1 denote1 very significantly1 processes and relations which are of great importance in the formation of science1 it is necessary for us to give a clear account of them1 illustrated with general exemplifications2 and this we shall endeavour to do4 ,we have1 indeed1 already explained that science consists of ,propositions which include the ,facts from which they were collected2 and other wider ,propositions1 collected in like manner from the former1 and including them4 ,thus1 that the stars1 the moon1 the sun1 rise1 culminate1 and set1 are facts included in the proposition that the heavens1 carrying with them all the celestial bodies1 have a diurnal revolution about the axis of the earth4 ,again1 the observed monthly motions of the moon1 and the annual motions of the sun1 are included in certain propositions concerning the movements of those luminaries with respect to the stars4 ,but all these propositions are really included in the doctrine that the earth1 revolving on its axis1 moves round the sun1 and the moon round the earth4 ,these movements1 again1 considered as facts1 are explained and included in the statement of the forces which the earth exerts upon the moon1 and the sun upon the earth4 ,again1 this doctrine of the forces of these three bodies is included in the assertion1 that all the bodies of the solar system1 and all parts of matter1 exert forces1 each upon each4 ,and we might easily show that all the leading facts in astronomy are comprehended in the same generalization4 ,in like manner with regard to any other science1 so far as its truths have been well established and fully developed1 we might show that it consists of a gradation of propositions1 proceeding from the most special facts to the most general theoretical assertions4 ,we shall exhibit this gradation in some of the principal branches of science4 #ajj #b4 ,this gradation of truths1 successively included in other truths1 may be conveniently represented by ,tables resembling the genealogical tables by which the derivation of descendants from a common ancestor is exhibited2 except that it is proper in this case to invert the form of the ,table1 and to make it converge to unity downwards instead of upwards1 since it has for its purpose to express1 not the derivation of many from one1 but the collection of one truth from many things4 ,two or more co-ordinate facts or propositions may be ranged side by side1 and joined by some mark of connexion1 7a bracket1 as or 17 beneath which may be placed the more general proposition which is collected by induction from the former4 ,again1 propositions co-ordinate with this more general one may be placed on a level with it2 and the combination of these1 and the result of the combination1 may be indicated by brackets in the same manner2 and so on1 through any number of gradations4 ,by this means the streams of knowledge from various classes of facts will constantly run together into a smaller and smaller number of channels2 like the confluent rivulets of a great river1 coming together from many sources1 uniting their ramifications so as to form larger branches1 these again uniting in a single trunk4 ,the genealogical tree of each great portion of science1 thus formed1 will contain all the leading truths of the science arranged in their due co-ordination and subordination4 ,such ,tables1 constructed for the sciences of ,astronomy and of ,optics1 will be given at the end of this chapter4 #c4 ,the union of co-ordinate propositions into a proposition of a higher order1 which occurs in this ,tree of ,science wherever two twigs unite in one branch1 is1 in each case1 an example of ,induction4 ,the single proposition is collected by the process of induction from its several members4 ,but here we may observe1 that the image of a mere union of the parts at each of these points1 which the figure of a tree or a river presents1 is very inadequate to convey the true state of the case2 for in ,induction1 as we have seen1 besides mere collection of particulars1 there is always a new conception1 a #aja principle of connexion and unity1 supplied by the mind1 and superinduced upon the particulars4 ,there is not merely a juxta-position of materials1 by which the new proposition contains all that its component parts contained2 but also a formative act exerted by the understanding1 so that these materials are contained in a new shape4 ,we must remember1 therefore1 that our ,inductive ,tables1 although they represent the elements and the order of these inductive steps1 do not fully represent the whole signification of the process in each case4 #d4 ,the principal features of the progress of science spoken of in the last chapter are clearly exhibited in these ,tables2 namely1 the ,consilience of ,inductions and the constant ,tendency to ,simplicity observable in true theories4 ,indeed in all cases in which1 from propositions of considerable generality1 propositions of a still higher degree are obtained1 there is a convergence of inductions2 and if in one of the lines which thus converge1 the steps be rapidly and suddenly made in order to meet the other line1 we may consider that we have an example of ,consilience4 ,thus when ,newton had collected1 from ,kepler's ,laws1 the ,central ,force of the sun1 and from these1 combined with other facts1 the ,universal ,force of all the heavenly bodies1 he suddenly turned round to include in his generalization the ,precession of the ,equinoxes1 which he declared to arise from the attraction of the sun and moon upon the protuberant part of the terrestrial spheroid4 ,the apparent remoteness of this fact1 in its nature1 from the other facts with which he thus associated it1 causes this part of his reasoning to strike us as a remarkable example of ,consilience4 ,accordingly1 in the ,table of ,astronomy we find that the columns which contain the facts and theories relative to the sun and planets1 after exhibiting several stages of induction within themselves1 are at length suddenly connected with a column till then quite distinct1 containing the precession of the equinoxes4 ,in like manner1 in the ,table of ,optics1 the columns which contain the facts and theories relative to double refraction1 and those which #ajb include polarization by crystals1 each go separately through several stages of induction2 and then these two sets of columns are suddenly connected by ,fresnel's mathematical induction1 that double refraction and polarization arise from the same cause3 thus exhibiting a remarkable ,consilience4 #e4 ,the constant ,tendency to ,simplicity in the sciences of which the progress is thus represented1 appears from the form of the ,table itself2 for the single trunk into which all the branches converge1 contains in itself the substance of all the propositions by means of which this last generalization was arrived at4 ,it is true1 that this ultimate result is sometimes not so simple as in the ,table it appears3 for instance1 the ultimate generalization of the ,table exhibiting the progress of ,physical ,optics1--namely1 that ,light consists in ,undulations1--must be understood as including some other hypotheses2 as1 that the undulations are transverse1 that the ether through which they are propagated has its elasticity in crystals and other transparent bodies regulated by certain laws2 and the like4 ,yet still1 even acknowledging all the complication thus implied1 the ,table in question evidences clearly enough the constant advance towards unity1 consistency1 and simplicity1 which have marked the progress of this ,theory4 ,the same is the case in the ,inductive ,table of ,astronomy in a still greater degree4 #f4 ,these ,tables naturally afford the opportunity of assigning to each of the distinct steps of which the progress of science consists1 the name of the ,discoverer to whom it is due4 ,every one of the inductive processes which the brackets of our ,tables mark1 directs our attention to some person by whom the induction was first distinctly made4 ,these names ,i have endeavoured to put in their due places in the ,tables2 and the ,inductive ,tree of our knowledge in each science becomes1 in this way1 an exhibition of the claims of each discoverer to distinction1 and1 as it were1 a ,genealogical ,tree of scientific nobility4 ,it is by no means pretended that such a tree includes the #ajc names of all the meritorious labourers in each department of science4 ,many persons are most usefully employed in collecting and verifying truths1 who do not advance to any new truths4 ,the labours of a number of such are included in each stage of our ascent4 ,but such ,tables as we have now before us will present to us the names of all the most eminent discoverers3 for the main steps of which the progress of science consists1 are transitions from more particular to more general truths1 and must therefore be rightly given by these ,tables2 and those must be the greatest names in science to whom the principal events of its advance are thus due4 #g4 ,the ,tables1 as we have presented them1 exhibit the course by which we pass from ,particular to ,general through various gradations1 and so to the most general4 ,they display the order of discovery4 ,but by reading them in an inverted manner1 beginning at the single comprehensive truths with which the ,tables end1 and tracing these back into the more partial truths1 and these again into special facts1 they answer another purpose2--they exhibit the process of verification of discoveries once made4 ,for each of our general propositions is true in virtue of the truth of the narrower propositions which it involves2 and we cannot satisfy ourselves of its truth in any other way than by ascertaining that these its constituent elements are true4 ,to assure ourselves that the sun attracts the planets with forces varying inversely as the square of the distance1 we must analyse by geometry the motion of a body in an ellipse about the focus1 so as to see that such a motion does imply such a force4 ,we must also verify those calculations by which the observed places of each planet are stated to be included in an ellipse4 ,these calculations involve assumptions respecting the path which the earth describes about the sun1 which assumptions must again be verified by reference to observation4 ,and thus1 proceeding from step to step1 we resolve the most general truths into their constituent parts2 and these again into their parts2 and by testing1 at each step1 both the reality of the asserted ingredients and the propriety #ajd of the conjunction1 we establish the whole system of truths1 however wide and various it may be4 #h4 ,it is a very great advantage1 in such a mode of exhibiting scientific truths1 that it resolves the verification of the most complex and comprehensive theories1 into a number of small steps1 of which almost any one falls within the reach of common talents and industry4 ,that if the particulars of any one step be true1 the generalization also is true1 any person with a mind properly disciplined may satisfy himself by a little study4 ,that each of these particular propositions is true1 may be ascertained1 by the same kind of attention1 when this proposition is resolved into its constituent and more special propositions4 ,and thus we may proceed1 till the most general truth is broken up into small and manageable portions4 ,of these portions1 each may appear by itself narrow and easy2 and yet they are so woven together1 by hypothesis and conjunction1 that the truth of the parts necessarily assures us of the truth of the whole4 ,the verification is of the same nature as the verification of a large and complex statement of great sums received by a mercantile office on various accounts from many quarters4 ,the statement is separated into certain comprehensive heads1 and these into others less extensive2 and these again into smaller collections of separate articles1 each of which can be inquired into and reported on by separate persons4 ,and thus at last1 the mere addition of numbers performed by these various persons1 and the summation of the results which they obtain1 executed by other accountants1 is a complete and entire security that there is no errour in the whole of the process4 #i4 ,this comparison of the process by which we verify scientific truth to the process of ,book-keeping in a large commercial establishment1 may appear to some persons not sufficiently dignified for the subject4 ,but1 in fact1 the possibility of giving this formal and business-like aspect to the evidence of science1 as involved in the process of successive generalization1 is an inestimable advantage4 ,for if no one could pronounce concerning a wide and profound theory except he who #aje could at once embrace in his mind the whole range of inference1 extending from the special facts up to the most general principles1 none but the greatest geniuses would be entitled to judge concerning the truth or errour of scientific discoveries4 ,but1 in reality1 we seldom need to verify more than one or two steps of such discoveries at one time2 and this may commonly be done 7when the discoveries have been fully established and developed17 by any one who brings to the task clear conceptions and steady attention4 ,the progress of science is gradual3 the discoveries which are successively made1 are also verified successively4 ,we have never any very large collections of them on our hands at once4 ,the doubts and uncertainties of any one who has studied science with care and perseverance are generally confined to a few points4 ,if he can satisfy himself upon these1 he has no misgivings respecting the rest of the structure2 which has indeed been repeatedly verified by other persons in like manner4 ,the fact that science is capable of being resolved into separate processes of verification1 is that which renders it possible to form a great body of scientific truth1 by adding together a vast number of truths1 of which many men1 at various times and by multiplied efforts1 have satisfied themselves4 ,the treasury of ,science is constantly rich and abundant1 because it accumulates the wealth which is thus gathered by so many1 and reckoned over by so many more3 and the dignity of ,knowledge is no more lowered by the multiplicity of the tasks on which her servants are employed1 and the narrow field of labour to which some confine themselves1 than the rich merchant is degraded by the number of offices which it is necessary for him to maintain1 and the minute articles of which he requires an exact statement from his accountants4 #aj4 ,the analysis of doctrines inductively obtained1 into their constituent facts1 and the arrangement of them in such a form that the conclusiveness of the induction may be distinctly seen1 may be termed the ,logic of ,induction4 ,by ,logic has generally been meant a system which teaches us so to arrange our #ajf reasonings that their truth or falsehood shall be evident in their form4 ,in deductive reasonings1 in which the general principles are assumed1 and the question is concerning their application and combination in particular cases1 the device which thus enables us to judge whether our reasonings are conclusive is the ,syllogism2 and this form1 along with the rules which belong to it1 does in fact supply us with a criterion of deductive or demonstrative reasoning4 ,the ,inductive ,table1 such as it is presented in the present chapter1 in like manner supplies the means of ascertaining the truth of our inductive inferences1 so far as the form in which our reasoning may be stated can afford such a criterion4 ,of course some care is requisite in order to reduce a train of demonstration into the form of a series of syllogisms2 and certainly not less thought and attention are required for resolving all the main doctrines of any great department of science into a graduated table of co-ordinate and subordinate inductions4 ,but in each case1 when this task is once executed1 the evidence or want of evidence of our conclusions appears immediately in a most luminous manner4 ,in each step of induction1 our ,table enumerates the particular facts1 and states the general theoretical truth which includes these and which these constitute4 ,the special act of attention by which we satisfy ourselves that the facts are so included1--that the general truth is so constituted1--then affords little room for errour1 with moderate attention and clearness of thought4 #aa4 ,we may find an example of this act of attention thus required1 at any one of the steps of induction in our ,tables2 for instance1 at the step in the early progress of astronomy at which it was inferred1 that the earth is a globe1 and that the sphere of the heavens 7relatively7 performs a diurnal revolution round this globe of the earth4 ,how was this established in the belief of the ,greeks1 and how is it fixed in our conviction8 ,as to the globular form1 we find that as we travel to the north1 the apparent pole of the heavenly motions1 and the constellations which are near it1 seem to mount higher1 and as we proceed southwards they descend4 #ajg ,again1 if we proceed from two different points considerably to the east and west of each other1 and travel directly northwards from each1 as from the south of ,spain to the north of ,scotland1 and from ,greece to ,scandinavia1 these two north and south lines will be much nearer to each other in their northern than in their southern parts4 ,these and similar facts1 as soon as they are clearly estimated and connected in the mind1 are seen to be consistent with a convex surface of the earth1 and with no other3 and this notion is further confirmed by observing that the boundary of the earth's shadow upon the moon is always circular2 it being supposed to be already established that the moon receives her light from the sun1 and that lunar eclipses are caused by the interposition of the earth4 ,as for the assertion of the 7relative7 diurnal revolution of the starry sphere1 it is merely putting the visible phenomena in an exact geometrical form3 and thus we establish and verify the doctrine of the revolution of the sphere of the heavens about the globe of the earth1 by contemplating it so as to see that it does really and exactly include the particular facts from which it is collected4 ,we may1 in like manner1 illustrate this mode of verification by any of the other steps of the same ,table4 ,thus if we take the great ,induction of ,copernicus1 the heliocentric scheme of the solar system1 we find it in the ,table exhibited as including and explaining1 first1 the diurnal revolution just spoken of2 second1 the motions of the moon among the fixed stars2 third1 the motions of the planets with reference to the fixed stars and the sun2 fourth1 the motion of the sun in the ecliptic4 ,and the scheme being clearly conceived1 we see that all the particular facts are faithfully represented by it2 and this agreement1 along with the simplicity of the scheme1 in which respect it is so far superior to any other conception of the solar system1 persuade us that it is really the plan of nature4 ,in exactly the same way1 if we attend to any of the several remarkable discoveries of ,newton1 which form the principal steps in the latter part of the ,table1 as for instance1 the proposition that the sun attracts all #ajh the planets with a force which varies inversely as the square of the distance1 we find it proved by its including three other propositions previously established2--first1 that the sun's mean force on different planets follows the specified variation 7which is proved from ,kepler's third law72 second1 that the force by which each planet is acted upon in different parts of its orbit tends to the sun 7which is proved by the equable description of areas72 third1 that this force in different parts of the same orbit is also inversely as the square of the distance 7which is proved from the elliptical form of the orbit74 ,and the ,newtonian generalization1 when its consequences are mathematically traced1 is seen to agree with each of these particular propositions1 and thus is fully established4 #ab4 ,but when we say that the more general proposition includes the several more particular ones1 we must recollect what has before been said1 that these particulars form the general truth1 not by being merely enumerated and added together1 but by being seen in a new light4 ,no mere verbal recitation of the particulars can decide whether the general proposition is true2 a special act of thought is requisite in order to determine how truly each is included in the supposed induction4 ,in this respect the ,inductive ,table is not like a mere schedule of accounts1 where the rightness of each part of the reckoning is tested by mere addition of the particulars4 ,on the contrary1 the ,inductive truth is never the mere sum of the facts4 ,it is made into something more by the introduction of a new mental element2 and the mind1 in order to be able to supply this element1 must have peculiar endowments and discipline4 ,thus looking back at the instances noticed in the last article1 how are we to see that a convex surface of the earth is necessarily implied by the convergence of meridians towards the north1 or by the visible descent of the north pole of the heavens as we travel south8 ,manifestly the student1 in order to see this1 must have clear conceptions of the relations of space1 either naturally inherent in his mind1 or established there by geometrical cultivation1--by #aji studying the properties of circles and spheres4 ,when he is so prepared1 he will feel the force of the expressions we have used1 that the facts just mentioned are seen to be consistent with a globular form of the earth2 but without such aptitude he will not see this consistency3 and if this be so1 the mere assertion of it in words will not avail him in satisfying himself of the truth of the proposition4 ,in like manner1 in order to perceive the force of the ,copernican induction1 the student must have his mind so disciplined by geometrical studies1 or otherwise1 that he sees clearly how absolute motion and relative motion would alike produce apparent motion4 ,he must have learnt to cast away all prejudices arising from the seeming fixity of the earth2 and then he will see that there is nothing which stands in the way of the induction1 while there is much which is on its side4 ,and in the same manner the ,newtonian induction of the law of the sun's force from the elliptical form of the orbit1 will be evidently satisfactory to him only who has such an insight into ,mechanics as to see that a curvilinear path must arise from a constantly deflecting force2 and who is able to follow the steps of geometrical reasoning by which1 from the properties of the ellipse1 ,newton proves this deflection to be in the proportion in which he asserts the force to be4 ,and thus in all cases the inductive truth must indeed be verified by comparing it with the particular facts2 but then this comparison is possible for him only whose mind is properly disciplined and prepared in the use of those conceptions1 which1 in addition to the facts1 the act of induction requires4 #ac4 ,in the ,tables some indication is given1 at several of the steps1 of the act which the mind must thus perform1 besides the mere conjunction of facts1 in order to attain to the inductive truth4 ,thus in the cases of the ,newtonian inductions just spoken of1 the inferences are stated to be made ',by ,mechanics2' and in the case of the ,copernican induction1 it is said that1 ',by the nature of motion1 the apparent motion is the same1 whether the heavens or the earth have a #aaj diurnal motion2 and the latter is more simple4' ,but these verbal statements are to be understood as mere hints#bbb3 they cannot supersede the necessity of the student's contemplating for himself the mechanical principles and the nature of motion thus referred to4 ,note #bbb3 ,in the ,inductive ,tables they are marked by an asterisk4 #ad4 ,in the common or ,syllogistic ,logic1 a certain ,formula of language is used in stating the reasoning1 and is useful in enabling us more readily to apply the ,criterion of ,form to alleged demonstrations4 ,this formula is the usual ,syllogism2 with its members1 ,major ,premiss1 ,minor ,premiss1 and ,conclusion4 ,it may naturally be asked whether in ,inductive ,logic there is any such ,formula8 whether there is any standard form of words in which we may most properly express the inference of a general truth from particular facts8 ,at first it might be supposed that the formula of ,inductive ,logic need only be of this kind3 ',these particulars1 and all known particulars of the same kind1 are exactly included in the following general proposition4' ,but a moment's reflection on what has just been said will show us that this is not sufficient3 for the particulars are not merely included in the general proposition4 ,it is not enough that they appertain to it by enumeration4 ,it is1 for instance1 no adequate example of ,induction to say1 ',mercury describes an elliptical path1 so does ,venus1 so do the ,earth1 ,mars1 ,jupiter1 ,saturn1 ,uranus2 therefore all the ,planets describe elliptical paths4' ,this is1 as we have seen1 the mode of stating the evidence when the proposition is once suggested2 but the ,inductive step consists in the suggestion of a conception not before apparent4 ,when ,kepler1 after trying to connect the observed places of the planet ,mars in many other ways1 found at last that the conception of an ellipse would include them all1 he obtained a truth by induction3 for this conclusion was not obviously included in the phenomena1 and had not been applied to these #aaa facts previously4 ,thus in our ,formula1 besides stating that the particulars are included in the general proposition1 we must also imply that the generality is constituted by a new ,conception1--new at least in its application4 ,hence our ,inductive ,formula might be something like the following3 ',these particulars1 and all known particulars of the same kind1 are exactly expressed by adopting the ,conceptions and ,statement of the following ,proposition4' ,it is of course requisite that the ,conceptions should be perfectly clear1 and should precisely embrace the facts1 according to the explanation we have already given of those conditions4 #ae4 ,it may happen1 as we have already stated1 that the ,explication of a ,conception1 by which it acquires its due distinctness1 leads to a ,definition1 which ,definition may be taken as the summary and total result of the intellectual efforts to which this distinctness is due4 ,in such cases1 the ,formula of ,induction may be modified according to this condition2 and we may state the inference by saying1 after an enumeration and analysis of the appropriate facts1 ',these facts are completely and distinctly expressed by adopting the following ,definition and ,proposition4' ,this ,formula has been adopted in stating the ,inductive ,propositions which constitute the basis of the science of ,mechanics1 in a work intitled ,the ,mechanical ,euclid4 ,the fundamental truths of the subject are expressed in ,inductive ,pairs of ,assertions1 consisting each of a ,definition and a ,proposition1 such as the following3 ,,def4--,a ,uniform ,force is that which acting in the direction of the body's motion1 adds or subtracts equal velocities in equal times4 ,,prop4--,gravity is a ,uniform ,force4 ,again1 ,,def4--,two ,motions are compounded when each produces its separate effect in a direction parallel to itself4 ,,prop4--,when any ,force acts upon a body in motion1 the motion which the ,force would produce in the #aab body at rest is compounded with the previous motion of the body4 ,and in like manner in other cases4 ,in these cases the proposition is1 of course1 established1 and the definition realized1 by an enumeration of the facts4 ,and in the case of inferences made in such a form1 the ,definition of the ,conception and the ,assertion of the ,truth are both requisite and are correlative to one another4 ,each of the two steps contains the verification and justification of the other4 ,the ,proposition derives its meaning from the ,definition2 the ,definition derives its reality from the ,proposition4 ,if they are separated1 the ,definition is arbitrary or empty1 the ,proposition vague or ambiguous4 #af4 ,but it must be observed that neither of the preceding ,formul expresses the full cogency of the inductive proof4 ,they declare only that the results can be clearly explained and rigorously deduced by the employment of a certain ,definition and a certain ,proposition4 ,but in order to make the conclusion demonstrative1 which in perfect examples of ,induction it is1 we ought to be able to declare that the results can be clearly explained and rigorously declared only by the ,definition and ,proposition which we adopt4 ,and in reality1 the conviction of the sound inductive reasoner does reach to this point4 ,the ,mathematician asserts the ,laws of ,motion1 seeing clearly that they 7or laws equivalent to them7 afford the only means of clearly expressing and deducing the actual facts4 ,but this conviction1 that the inductive inference is not only consistent with the facts1 but necessary1 finds its place in the mind gradually1 as the contemplation of the consequences of the proposition1 and the various relations of the facts1 becomes steady and familiar4 ,it is scarcely possible for the student at once to satisfy himself that the inference is thus inevitable4 ,and when he arrives at this conviction1 he sees also1 in many cases at least1 that there may be other ways of expressing the substance of the truth established1 besides that special ,proposition which he has under his notice4 #aac ,we may1 therefore1 without impropriety1 renounce the undertaking of conveying in our formula this final conviction of the necessary truth of our inference4 ,we may leave it to be thought1 without insisting upon saying it1 that in such cases what can be true1 is true4 ,but if we wish to express the ultimate significance of the ,inductive ,act of thought1 we may take as our ,formula for the ,colligation of ,facts by ,induction1 this3--',the several ,facts are exactly expressed as one ,fact if1 and only if1 we adopt the ,conception and the ,assertion' of the inductive inference4 #ag4 ,i have said that the mind must be properly disciplined in order that it may see the necessary connexion between the facts and the general proposition in which they are included4 ,and the perception of this connexion1 though treated as one step in our inductive inference1 may imply many steps of demonstrative proof4 ,the connexion is this1 that the particular case is included in the general one1 that is1 may be deduced from it3 but this deduction may often require many links of reasoning4 ,thus in the case of the inference of the law of the force from the elliptical form of the orbit by ,newton1 the proof that in the ellipse the deflection from the tangent is inversely as the square of the distance from the focus of the ellipse1 is a ratiocination consisting of several steps1 and involving several properties of ,conic ,sections2 these properties being supposed to be previously established by a geometrical system of demonstration on the special subject of the ,conic ,sections4 ,in this and similar cases the ,induction involves many steps of ,deduction4 ,and in such cases1 although the ,inductive ,step1 the ,invention of the ,conception1 is really the most important1 yet since1 when once made1 it occupies a familiar place in men's minds2 and since the ,deductive ,demonstration is of considerable length and requires intellectual effort to follow it at every step2 men often admire the deductive part of the proposition1 the geometrical or algebraical demonstration1 far more than that part in which the philosophical merit really resides4 #aad #ah4 ,deductive reasoning is virtually a collection of syllogisms1 as has already been stated3 and in such reasoning1 the general principles1 the ,definitions and ,axioms1 necessarily stand at the beginning of the demonstration4 ,in an inductive inference1 the ,definitions and ,principles are the final result of the reasoning1 the ultimate effect of the proof4 ,hence when an ,inductive ,proposition is to be established by a proof involving several steps of demonstrative reasoning1 the enunciation of the ,proposition will contain1 explicitly or implicitly1 principles which the demonstration proceeds upon as axioms1 but which are really inductive inferences4 ,thus in order to prove that the force which retains a planet in an ellipse varies inversely as the square of the distance1 it is taken for granted that the ,laws of ,motion are true1 and that they apply to the planets4 ,yet the doctrine that this is so1 as well as the law of the force1 were established only by this and the like demonstrations4 ,the doctrine which is the hypothesis of the deductive reasoning1 is the inference of the inductive process4 ,the special facts which are the basis of the inductive inference1 are the conclusion of the train of deduction4 ,and in this manner the deduction establishes the induction4 ,the principle which we gather from the facts is true1 because the facts can be derived from it by rigorous demonstration4 ,induction moves upwards1 and deduction downwards1 on the same stair4 ,but still there is a great difference in the character of their movements4 ,deduction descends steadily and methodically1 step by step3 ,induction mounts by a leap which is out of the reach of method4 ,she bounds to the top of the stair at once2 and then it is the business of ,deduction1 by trying each step in order1 to establish the solidity of her companion's footing4 ,yet these must be processes of the same mind4 ,the ,inductive ,intellect makes an assertion which is subsequently justified by demonstration2 and it shows its sagacity1 its peculiar character1 by enunciating the proposition when as yet the demonstration does not #aae exist3 but then it shows that it is sagacity1 by also producing the demonstration4 ,it has been said that inductive and deductive reasoning are contrary in their scheme2 that in ,deduction we infer particular from general truths2 while in ,induction we infer general from particular3 that ,deduction consists of many steps1 in each of which we apply known general propositions in particular cases2 while in ,induction we have a single step1 in which we pass from many particular truths to one general proposition4 ,and this is truly said2 but though contrary in their motions1 the two are the operation of the same mind travelling over the same ground4 ,deduction is a necessary part of ,induction4 ,deduction justifies by calculation what ,induction had happily guessed4 ,induction recognizes the ore of truth by its weight2 ,deduction confirms the recognition by chemical analysis4 ,every step of ,induction must be confirmed by rigorous deductive reasoning1 followed into such detail as the nature and complexity of the relations 7whether of quantity or any other7 render requisite4 ,if not so justified by the supposed discoverer1 it is not ,induction4 #ai4 ,such ,tabular arrangements of propositions as we have constructed may be considered as the ,criterion of ,truth for the doctrines which they include4 ,they are the ,criterion of ,inductive ,truth1 in the same sense in which ,syllogistic ,demonstration is the ,criterion of ,necessary ,truth1--of the certainty of conclusions1 depending upon evident ,first ,principles4 ,and that such ,tables are really a ,criterion of the truth of the propositions which they contain1 will be plain by examining their structure4 ,for if the connexion which the inductive process assumes be ascertained to be in each case real and true1 the assertion of the general proposition merely collects together ascertained truths2 and in like manner each of those more particular propositions is true1 because it merely expresses collectively more special facts3 so that the most general theory is only the assertion of a great body of facts1 duly classified and subordinated4 ,when we #aaf assert the truth of the ,copernican theory of the motions of the solar system1 or of the ,newtonian theory of the forces by which they are caused1 we merely assert the groups of propositions which1 in the ,table of ,astronomical ,induction1 are included in these doctrines2 and ultimately1 we may consider ourselves as merely asserting at once so many ,facts1 and therefore1 of course1 expressing an indisputable truth4 #bj4 ,at any one of these steps of ,induction in the ,table1 the inductive proposition is a ,theory with regard to the ,facts which it includes1 while it is to be looked upon as a ,fact with respect to the higher generalizations in which it is included4 ,in any other sense1 as was formerly shown1 the opposition of ,fact and ,theory is untenable1 and leads to endless perplexity and debate4 ,is it a ,fact or a ,theory that the planet ,mars revolves in an ,ellipse about the ,sun8 ,to ,kepler1 employed in endeavouring to combine the separate observations by the ,conception of an ,ellipse1 it is a ,theory2 to ,newton1 engaged in inferring the law of force from a knowledge of the elliptical motion1 it is a ,fact4 ,there are1 as we have already seen1 no special attributes of ,theory and ,fact which distinguish them from one another4 ,facts are phenomena apprehended by the aid of conceptions and mental acts1 as ,theories also are4 ,we commonly call our observations ,facts1 when we apply1 without effort or consciousness1 conceptions perfectly familiar to us3 while we speak of ,theories1 when we have previously contemplated the ,facts and the connecting ,conception separately1 and have made the connexion by a conscious mental act4 ,the real difference is a difference of relation2 as the same proposition in a demonstration is the premiss of one syllogism and the conclusion in another2--as the same person is a father and a son4 ,propositions are ,facts and ,theories1 according as they stand above or below the ,inductive ,brackets of our ,tables4 #ba4 ,to obviate mistakes ,i may remark that the terms higher and lower1 when used of generalizations1 are unavoidably represented by their opposites in our ,inductive ,tables4 ,the highest generalization is that #aag which includes all others2 and this stands the lowest on our page1 because1 reading downwards1 that is the place which we last reach4 ,there is a distinction of the knowledge acquired by ,scientific ,induction into two kinds1 which is so important that we shall consider it in the succeeding chapter4 #aah ,,chapter ,,vii4 ,,of ,,laws ,,of ,,phenomena ,,and ,,of ,,causes4 ,,aphorism ,,xxiv4 ,inductive truths are of two kinds1 ,laws of ,phenomena1 and ,theories of ,causes4 ,it is necessary to begin in every science with the ,laws of ,phenomena2 but it is impossible that we should be satisfied to stop short of a ,theory of ,causes4 ,in ,physical ,astronomy1 ,physical ,optics1 ,geology1 and other sciences1 we have instances showing that we can make a great advance in inquiries after true ,theories of ,causes4 #a4 ,,in the first attempts at acquiring an exact and connected knowledge of the appearances and operations which nature presents1 men went no further than to learn what takes place1 not why it occurs4 ,they discovered an ,order which the phenomena follow1 ,rules which they obey2 but they did not come in sight of the ,powers by which these rules are determined1 the ,causes of which this order is the effect4 ,thus1 for example1 they found that many of the celestial motions took place as if the sun and stars were carried round by the revolutions of certain celestial spheres2 but what causes kept these spheres in constant motion1 they were never able to explain4 ,in like manner in modern times1 ,kepler discovered that the planets describe ellipses1 before ,newton explained why they select this particular curve1 and describe it in a particular manner4 ,the laws of reflection1 refraction1 dispersion1 and other properties of light have long been known2 the causes of these laws are at present under discussion4 ,and the same might be #aai said of many other sciences4 ,the discovery of the ,laws of ,phenomena is1 in all cases1 the first step in exact knowledge2 these ,laws may often for a long period constitute the whole of our science2 and it is always a matter requiring great talents and great efforts1 to advance to a knowledge of the ,causes of the phenomena4 ,hence the larger part of our knowledge of nature1 at least of the certain portion of it1 consists of the knowledge of the ,laws of ,phenomena4 ,in ,astronomy indeed1 besides knowing the rules which guide the appearances1 and resolving them into the real motions from which they arise1 we can refer these motions to the forces which produce them4 ,in ,optics1 we have become acquainted with a vast number of laws by which varied and beautiful phenomena are governed2 and perhaps we may assume1 since the evidence of the ,undulatory ,theory has been so fully developed1 that we know also the ,causes of the ,phenomena4 ,but in a large class of sciences1 while we have learnt many ,laws of ,phenomena1 the causes by which these are produced are still unknown or disputed4 ,are we to ascribe to the operation of a fluid or fluids1 and if so1 in what manner1 the facts of heat1 magnetism1 electricity1 galvanism8 ,what are the forces by which the elements of chemical compounds are held together8 ,what are the forces1 of a higher order1 as we cannot help believing1 by which the course of vital action in organized bodies is kept up8 ,in these and other cases1 we have extensive departments of science2 but we are as yet unable to trace the effects to their causes2 and our science1 so far as it is positive and certain1 consists entirely of the laws of phenomena4 #b4 ,in those cases in which we have a division of the science which teaches us the doctrine of the causes1 as well as one which states the rules which the effects follow1 ,i have1 in the ,history1 distinguished the two portions of the science by certain terms4 ,i have thus spoken of ,formal ,astronomy and ,physical ,astronomy4 ,the latter phrase has long been commonly employed to describe that department of ,astronomy which deals with #abj those forces by which the heavenly bodies are guided in their motions2 the former adjective appears well suited to describe a collection of rules depending on those ideas of space1 time1 position1 number1 which are1 as we have already said1 the forms of our apprehension of phenomena4 ,the laws of phenomena may be considered as formul1 expressing results in terms of those ideas4 ,in like manner1 ,i have spoken of ,formal ,optics and ,physical ,optics2 the latter division including all speculations concerning the machinery by which the effects are produced4 ,formal ,acoustics and ,physical ,acoustics may be distinguished in like manner1 although these two portions of science have been a good deal mixed together by most of those who have treated of them4 ,formal ,thermotics1 the knowledge of the laws of the phenomena of heat1 ought in like manner to lead to ,physical ,thermotics1 or the ,theory of ,heat with reference to the cause by which its effects are produced2--a branch of science which as yet can hardly be said to exist4 #c4 ,what kinds of cause are we to admit in science8 ,this is an important1 and by no means an easy question4 ,in order to answer it1 we must consider in what manner our progress in the knowledge of causes has hitherto been made4 ,by far the most conspicuous instance of success in such researches1 is the discovery of the causes of the motions of the heavenly bodies4 ,in this case1 after the formal laws of the motions1--their conditions as to space and time1--had become known1 men were enabled to go a step further2 to reduce them to the familiar and general cause of motion--mechanical force2 and to determine the laws which this force follows4 ,that this was a step in addition to the knowledge previously possessed1 and that it was a real and peculiar truth1 will not be contested4 ,and a step in any other subject which should be analogous to this in astronomy2--a discovery of causes and forces as certain and clear as the discovery of universal gravitation2--would undoubtedly be a vast advance upon a body of science consisting only of the laws of phenomena4 #aba #d4 ,but although physical astronomy may well be taken as a standard in estimating the value and magnitude of the advance from the knowledge of phenomena to the knowledge of causes2 the peculiar features of the transition from formal to physical science in that subject must not be allowed to limit too narrowly our views of the nature of this transition in other cases4 ,we are not1 for example1 to consider that the step which leads us to the knowledge of causes in any province of nature must necessarily consist in the discovery of centers of forces1 and collections of such centers1 by which the effects are produced4 ,the discovery of the causes of phenomena may imply the detection of a fluid by whose undulations1 or other operations1 the results are occasioned4 ,the phenomena of acoustics are1 we know1 produced in this manner by the air2 and in the cases of light1 heat1 magnetism1 and others1 even if we reject all the theories of such fluids which have hitherto been proposed1 we still cannot deny that such theories are intelligible and possible1 as the discussions concerning them have shown4 ,nor can it be doubted that if the assumption of such a fluid1 in any case1 were as well evidenced as the doctrine of universal gravitation is1 it must be considered as a highly valuable theory4 #e4 ,but again2 not only must we1 in aiming at the formation of a ,causal ,section in each ,science of ,phenomena1 consider ,fluids and their various modes of operation admissible1 as well as centers of mechanical force2 but we must be prepared1 if it be necessary1 to consider the forces1 or powers to which we refer the phenomena1 under still more general aspects1 and invested with characters different from mere mechanical force4 ,for example2 the forces by which the chemical elements of bodies are bound together1 and from which arise1 both their sensible texture1 their crystalline form1 and their chemical composition1 are certainly forces of a very different nature from the mere attraction of matter according to its mass4 ,the powers of assimilation and reproduction in plants and animals are obviously still more removed from mere mechanism2 yet #abb these powers are not on that account less real1 nor a less fit and worthy subject of scientific inquiry4 #f4 ,in fact1 these forces--mechanical1 chemical and vital1--as we advance from one to the other1 each bring into our consideration new characters2 and what these characters are1 has appeared in the historical survey which we made of the ,fundamental ,ideas of the various sciences4 ,it was then shown that the forces by which chemical effects are produced necessarily involve the ,idea of ,polarity1--they are polar forces2 the particles tend together in virtue of opposite properties which in the combination neutralize each other4 ,hence1 in attempting to advance to a theory of ,causes in chemistry1 our task is by no means to invent laws of mechanical force1 and collections of forces1 by which the effects may be produced4 ,we know beforehand that no such attempt can succeed4 ,our aim must be to conceive such new kinds of force1 including ,polarity among their characters1 as may best render the results intelligible4 #g4 ,thus in advancing to a ,science of ,cause in any subject1 the labour and the struggle is1 not to analyse the phenomena according to any preconceived and already familiar ideas1 but to form distinctly new conceptions1 such as do really carry us to a more intimate view of the processes of nature4 ,thus in the case of astronomy1 the obstacle which deferred the discovery of the true causes from the time of ,kepler to that of ,newton1 was the difficulty of taking hold of mechanical conceptions and axioms with sufficient clearness and steadiness2 which1 during the whole of that interval1 mathematicians were learning to do4 ,in the question of causation which now lies most immediately in the path of science1 that of the causes of electrical and chemical phenomena1 the business of rightly fixing and limiting the conception of polarity1 is the proper object of the efforts of discoverers4 ,accordingly a large portion of ,mr ,faraday's recent labours#bcb is directed1 not to #abc the attempt at discovering new laws of phenomena1 but to the task of throwing light upon the conception of polarity1 and of showing how it must be understood1 so that it shall include electrical induction and other phenomena1 which have commonly been ascribed to forces acting mechanically at a distance4 ,he is by no means content1 nor would it answer the ends of science that he should be1 with stating the results of his experiments2 he is constantly1 in every page1 pointing out the interpretation of his experiments1 and showing how the conception of ,polar ,forces enters into this interpretation4 ',i shall1' he says#bdb1 'use every opportunity which presents itself of returning to that strong test of truth1 experiment2 but1' he adds1 ',i shall necessarily have occasion to speak theoretically1 and even hypothetically4' ,his hypothesis that electrical inductive action always takes place by means of a continuous line of polarized particles1 and not by attraction and repulsion at a distance1 if established1 cannot fail to be a great step on our way towards a knowledge of causes1 as well as phenomena1 in the subjects under his consideration4 ,note #bcb3 ,eleventh1 ,twelfth1 and ,thirteenth ,series of ,researches1 ,phil4 ,trans4 #ahcg and #h4 ,note #bdb3 ,art4 #acah4 #h4 ,the process of obtaining new conceptions is1 to most minds1 far more unwelcome than any labour in employing old ideas4 ,the effort is indeed painful and oppressive2 it is feeling in the dark for an object which we cannot find4 ,hence it is not surprising that we should far more willingly proceed to seek for new causes by applying conceptions borrowed from old ones4 ,men were familiar with solid frames1 and with whirlpools of fluid1 when they had not learnt to form any clear conception of attraction at a distance4 ,hence they at first imagined the heavenly motions to be caused by ,crystalline ,spheres1 and by ,vortices4 ,at length they were taught to conceive ,central ,forces1 and then they reduced the solar system to these4 ,but having done this1 they fancied that all the rest of the machinery of nature must be central forces4 ,we find ,newton #abd expressing this conviction#beb1 and the mathematicians of the last century acted upon it very extensively4 ,we may especially remark ,laplace's labours in this field4 ,having explained1 by such forces1 the phenomena of capillary attraction1 he attempted to apply the same kind of explanation to the reflection1 refraction1 and double refraction of light2--to the constitution of gases2--to the operation of heat4 ,it was soon seen that the explanation of refraction was arbitrary1 and that of double refraction illusory2 while polarization entirely eluded the grasp of this machinery4 ,centers of force would no longer represent the modes of causation which belonged to the phenomena4 ,polarization required some other contrivance1 such as the undulatory theory supplied4 ,no theory of light can be of any avail in which the fundamental idea of ,polarity is not clearly exhibited4 ,note #beb3 ,multa me movent1 c41--,pref4 to the ,principia1 already quoted in the ,history4 #i4 ,the sciences of magnetism and electricity have given rise to theories in which this relation of polarity is exhibited by means of two opposite fluids#bfb2--;a positive and a negative fluid1 or a vitreous and a resinous1 for electricity1 and a boreal and an austral fluid for magnetism4 ,the hypothesis of such fluids gives results agreeing in a remarkable manner with the facts and their measures1 as ,coulomb and others have shown4 ,it may be asked how far we may1 in such a case1 suppose that we have discovered the true cause of the phenomena1 and whether it is sufficiently proved that these fluids really exist4 ,the right answer seems to be1 that the hypothesis certainly represents the truth so far as regards the polar relation of the two energies1 and the laws of the attractive and repulsive forces of the particles in which these energies reside2 but that we are not entitled to assume that the vehicles of these energies possess other attributes of material fluids1 or that the forces thus ascribed to the particles are the primary elementary forces from which #abe the action originates4 ,we are the more bound to place this cautious limit to our acceptance of the ,coulombian theory1 since in electricity ,faraday has in vain endeavoured to bring into view one of the polar fluids without the other3 whereas such a result ought to be possible if there were two separable fluids4 ,the impossibility of this separate exhibition of one fluid appears to show that the fluids are real only so far as they are polar4 ,and ,faraday's view above mentioned1 according to which the attractions at a distance are resolved into the action of lines of polarized particles of air1 appears still further to show that the conceptions hitherto entertained of electrical forces1 according to the ,coulombian theory1 do not penetrate to the real and intimate nature of the causation belonging to this case4 ,note #bfb3 ,hist4 ,ind4 ,sc4 b4 xi4 c4 ii4 #aj4 ,since it is thus difficult to know when we have seized the true cause of the phenomena in any department of science1 it may appear to some persons that physical inquirers are imprudent and unphilosophical in undertaking this ,research of ,causes2 and that it would be safer and wiser to confine ourselves to the investigation of the laws of phenomena1 in which field the knowledge which we obtain is definite and certain4 ,hence there have not been wanting those who have laid it down as a maxim that 'science must study only the laws of phenomena1 and never the mode of production#bgb4' ,but it is easy to see that such a maxim would confine the breadth and depth of scientific inquiries to a most scanty and miserable limit4 ,indeed1 such a rule would defeat its own object2 for the laws of phenomena1 in many cases1 cannot be even expressed or understood without some hypothesis respecting their mode of production4 ,how could the phenomena of polarization have been conceived or reasoned upon1 except by imagining a polar arrangement of particles1 or transverse vibrations1 or some equivalent hypothesis8 ,the doctrines of fits of easy transmission1 the doctrine of moveable polarization1 and the like1 even when #abf erroneous as representing the whole of the phenomena1 were still useful in combining some of them into laws2 and without some such hypotheses the facts could not have been followed out4 ,the doctrine of a fluid caloric may be false2 but without imagining such a fluid1 how could the movement of heat from one part of a body to another be conceived8 ,it may be replied that ,fourier1 ,laplace1 ,poisson1 who have principally cultivated the ,theory of ,heat1 have not conceived it as a fluid1 but have referred conduction to the radiation of the molecules of bodies1 which they suppose to be separate points4 ,but this molecular constitution of bodies is itself an assumption of the mode in which the phenomena are produced2 and the radiation of heat suggests inquiries concerning a fluid emanation1 no less than its conduction does4 ,in like manner1 the attempts to connect the laws of phenomena of heat and of gases1 have led to hypotheses respecting the constitution of gases1 and the combination of their particles with those of caloric1 which hypotheses may be false1 but are probably the best means of discovering the truth4 ,note #bgb3 ,comte1 ,philosophie ,positive4 ,to debar science from inquiries like these1 on the ground that it is her business to inquire into facts1 and not to speculate about causes1 is a curious example of that barren caution which hopes for truth without daring to venture upon the quest of it4 ,this temper would have stopped with ,kepler's discoveries1 and would have refused to go on with ,newton to inquire into the mode in which the phenomena are produced4 ,it would have stopped with ,newton's optical facts1 and would have refused to go on with him and his successors to inquire into the mode in which these phenomena are produced4 ,and1 as we have abundantly shown1 it would1 on that very account1 have failed in seeing what the phenomena really are4 ,in many subjects the attempt to study the laws of phenomena1 independently of any speculations respecting the causes which have produced them1 is neither possible for human intelligence nor for human temper4 ,men cannot contemplate the phenomena without clothing them in terms of some hypothesis1 and will #abg not be schooled to suppress the questionings which at every moment rise up within them concerning the causes of the phenomena4 ,who can attend to the appearances which come under the notice of the geologist2--strata regularly bedded1 full of the remains of animals such as now live in the depths of the ocean1 raised to the tops of mountains1 broken1 contorted1 mixed with rocks such as still flow from the mouths of volcanos1--who can see phenomena like these1 and imagine that he best promotes the progress of our knowledge of the earth's history1 by noting down the facts1 and abstaining from all inquiry whether these are really proof of past states of the earth and of subterraneous forces1 or merely an accidental imitation of the effects of such causes8 ,in this and similar cases1 to proscribe the inquiry into causes would be to annihilate the science4 ,finally1 this caution does not even gain its own single end1 the escape from hypotheses4 ,for1 as we have said1 those who will not seek for new and appropriate causes of newly-studied phenomena1 are almost inevitably led to ascribe the facts to modifications of causes already familiar4 ,they may declare that they will not hear of such causes as vital powers1 elective affinities1 electric1 or calorific1 or luminiferous ethers or fluids2 but they will not the less on that account assume hypotheses equally unauthorized2--for instance--universal mechanical forces2 a molecular constitution of bodies2 solid1 hard1 inert matter2--and will apply these hypotheses in a manner which is arbitrary in itself as well as quite insufficient for its purpose4 #aa4 ,it appears1 then1 to be required1 both by the analogy of the most successful efforts of science in past times and by the irrepressible speculative powers of the human mind1 that we should attempt to discover both the laws of phenomena1 and their causes4 ,in every department of science1 when prosecuted far enough1 these two great steps of investigation must succeed each other4 ,the laws of phenomena must be known before we can speculate concerning causes2 the causes must be inquired into when the phenomena have been #abh reduced to rule4 ,in both these speculations the suppositions and conceptions which occur must be constantly tested by reference to observation and experiment4 ,in both we must1 as far as possible1 devise hypotheses which1 when we thus test them1 display those characters of truth of which we have already spoken2--an agreement with facts such as will stand the most patient and rigid inquiry2 a provision for predicting truly the results of untried cases2 a consilience of inductions from various classes of facts2 and a progressive tendency of the scheme to simplicity and unity4 ,we shall attempt hereafter to give several rules of a more precise and detailed kind for the discovery of the causes1 and still more1 of the laws of phenomena4 ,but it will be useful in the first place to point out the ,classification of the ,sciences which results from the principles already established in this 9999work4 ,and for this purpose we must previously decide the question1 whether the practical ,arts1 as ,medicine and ,engineering1 must be included in our list of ,sciences4 #abi ,,chapter ,,viii4 ,,of ,,art ,,and ,,science4 ,,aphorism ,,xxv4 ,art and ,science differ4 ,the object of ,science is ,knowledge2 the objects of ,art1 are ,works4 ,in ,art1 truth is a means to an end2 in ,science1 it is the only end4 ,hence the ,practical ,arts are not to be classed among the ,sciences4 ,,aphorism ,,xxvi4 ,practical ,knowledge1 such as ,art implies1 is not ,knowledge such as ,science includes4 ,brute animals have a practical knowledge of relations of space and force2 but they have no knowledge of ,geometry or ,mechanics4 #a4 ,,the distinction of ,arts and ,sciences very materially affects all classifications of the departments of ,human ,knowledge4 ,it is often maintained1 expressly or tacitly1 that the ,arts are a part of our knowledge1 in the same sense in which the ,sciences are so2 and that ,art is the application of ,science to the purposes of practical life4 ,it will be found that these views require some correction1 when we understand ,science in the exact sense in which we have throughout endeavoured to contemplate it1 and in which alone our examination of its nature can instruct us in the true foundations of our knowledge4 ,when we cast our eyes upon the early stages of the histories of nations1 we cannot fail to be struck with the consideration1 that in many countries the ,arts of life already appear1 at least in some rude form or other1 when1 as yet1 nothing of science exists4 ,a #acj practical knowledge of ,astronomy1 such as enables them to reckon months and years1 is found among all nations except the mere savages4 ,a practical knowledge of ,mechanics must have existed in those nations which have left us the gigantic monuments of early architecture4 ,the pyramids and temples of ,egypt and ,nubia1 the ,cyclopean walls of ,italy and ,greece1 the temples of ,magna ,grcia and ,sicily1 the obelisks and edifices of ,india1 the cromlechs and ,druidical circles of countries formerly ,celtic1--must have demanded no small practical mechanical skill and power4 ,yet those modes of reckoning time must have preceded the rise of speculative ,astronomy2 these structures must have been erected before the theory of ,mechanics was known4 ,to suppose1 as some have done1 a great body of science1 now lost1 to have existed in the remote ages to which these remains belong1 is not only quite gratuitous1 and contrary to all analogy1 but is a supposition which cannot be extended so far as to explain all such cases4 ,for it is impossible to imagine that every art has been preceded by the science which renders a reason for its processes4 ,certainly men formed wine from the grape1 before they possessed a ,science of ,fermentation2 the first instructor of every artificer in brass and iron can hardly be supposed to have taught the ,chemistry of metals as a ,science2 the inventor of the square and the compasses had probably no more knowledge of demonstrated ,geometry than have the artisans who now use those implements2 and finally1 the use of speech1 the employment of the inflections and combinations of words1 must needs be assumed as having been prior to any general view of the nature and analogy of ,language4 ,even at this moment1 the greater part of the arts which exist in the world are not accompanied by the sciences on which they theoretically depend4 ,who shall state to us the general chemical truths to which the manufactures of glass1 and porcelain1 and iron1 and brass1 owe their existence8 ,do not almost all artisans practise many successful artifices long before science explains the ground of the process8 ,do not arts at this day exist1 in a high state #aca of perfection1 in countries in which there is no science1 as ,china and ,india8 ,these countries and many others have no theories of mechanics1 of optics1 of chemistry1 of physiology2 yet they construct and use mechanical and optical instruments1 make chemical combinations1 take advantage of physiological laws4 ,it is too evident to need further illustration that ,art may exist without ,science2--that the former has usually been anterior to the latter1 and even now commonly advances independently1 leaving science to follow as it can4 #b4 ,we here mean by ,science1 that exact1 general1 speculative knowledge1 of which we have1 throughout this work1 been endeavouring to exhibit the nature and rules4 ,between such ,science and the practical ,arts of life1 the points of difference are sufficiently manifest4 ,the object of ,science is ,knowledge2 the object of ,art are ,works4 ,the latter is satisfied with producing its material results2 to the former1 the operations of matter1 whether natural or artificial1 are interesting only so far as they can be embraced by intelligible principles4 ,the ,end of ,art is the ,beginning of ,science2 for when it is seen what is done1 then comes the question why it is done4 ,art may have fixed general rules1 stated in words2 but she has these merely as means to an end3 to ,science1 the propositions which she obtains are each1 in itself1 a sufficient end of the effort by which it is acquired4 ,when ,art has brought forth her product1 her task is finished2 ,science is constantly led by one step of her path to another3 each proposition which she obtains impels her to go onwards to other propositions more general1 more profound1 more simple4 ,art puts elements together1 without caring to know what they are1 or why they coalesce4 ,science analyses the compound1 and at every such step strives not only to perform1 but to understand the analysis4 ,art advances in proportion as she becomes able to bring forth products more multiplied1 more complex1 more various2 but ,science1 straining her eyes to penetrate more and more deeply into the nature of things1 reckons her success in proportion as she sees1 in all the phenomena1 however #acb multiplied2 complex1 and varied1 the results of one or two simple and general laws4 #c4 ,there are many acts which man1 as well as animals1 performs by the guidance of nature1 without seeing or seeking the reason why he does so2 as1 the acts by which he balances himself in standing or moving1 and those by which he judges of the form and position of the objects around him4 ,these actions have their reason in the principles of geometry and mechanics2 but of such reasons he who thus acts is unaware3 he works blindly1 under the impulse of an unknown principle which we call ,instinct4 ,when man's speculative nature seeks and finds the reasons why he should act thus or thus2--why he should stretch out his arm to prevent his falling1 or assign a certain position to an object in consequence of the angles under which it is seen2--he may perform the same actions as before1 but they are then done by the aid of a different faculty1 which1 for the sake of distinction1 we may call ,insight4 ,instinct is a purely active principle2 it is seen in deeds alone2 it has no power of looking inwards2 it asks no questions2 it has no tendency to discover reasons or rules2 it is the opposite of ,insight4 #d4 ,art is not identical with ,instinct3 on the contrary1 there are broad differences4 ,instinct is stationary2 ,art is progressive4 ,instinct is mute2 it acts1 but gives no rules for acting3 ,art can speak2 she can lay down rules4 ,but though ,art is thus separate from ,instinct1 she is not essentially combined with ,insight4 ,she can see what to do1 but she needs not to see why it is done4 ,she may lay down ,rules1 but it is not her business to give ,reasons4 ,when man makes that his employment1 he enters upon the domain of ,science4 ,art takes the phenomena and laws of nature as she finds them3 that they are multiplied1 complex1 capricious1 incoherent1 disturbs her not4 ,she is content that the rules of nature's operations should be perfectly arbitrary and unintelligible1 provided they are constant1 so that she can depend upon their effects4 ,but ,science is impatient of all appearance of caprice1 #acc inconsistency1 irregularity1 in nature4 ,she will not believe in the existence of such characters4 ,she resolves one apparent anomaly after another2 her task is not ended till every thing is so plain and simple1 that she is tempted to believe that she sees that it could by no possibility have been otherwise than it is4 #e4 ,it may be said that1 after all1 ,art does really involve the knowledge which ,science delivers2--that the artisan who raises large weights1 practically knows the properties of the mechanical powers2--that he who manufactures chemical compounds is virtually acquainted with the laws of chemical combination4 ,to this we reply1 that it might on the same grounds be asserted1 that he who acts upon the principle that two sides of a triangle are greater than the third is really acquainted with geometry2 and that he who balances himself on one foot knows the properties of the center of gravity4 ,but this is an acquaintance with geometry and mechanics which even brute animals possess4 ,it is evident that it is not of such knowledge as this that we have here to treat4 ,it is plain that this mode of possessing principles is altogether different from that contemplation of them on which science is founded4 ,we neglect the most essential and manifest differences1 if we confound our unconscious assumptions with our demonstrative reasonings4 #f4 ,the real state of the case is1 that the principles which ,art involves1 ,science alone evolves4 ,the truths on which the success of ,art depends1 lurk in the artist's mind in an undeveloped state2 guiding his hand1 stimulating his invention1 balancing his judgment2 but not appearing in the form of enunciated ,propositions4 ,principles are not to him direct objects of meditation3 they are secret ,powers of ,nature1 to which the forms which tenant the world owe their constancy1 their movements1 their changes1 their luxuriant and varied growth1 but which he can nowhere directly contemplate4 ,that the creative and directive ,principles which have their lodgment in the artist's mind1 when unfolded by our speculative powers into #acd systematic shape1 become ,science1 is true2 but it is precisely this process of development which gives to them their character of ,science4 ,in practical ,art1 principles are unseen guides1 leading us by invisible strings through paths where the end alone is looked at3 it is for ,science to direct and purge our vision so that these airy ties1 these principles and laws1 generalizations and theories1 become distinct objects of vision4 ,many may feel the intellectual monitor1 but it is only to her favourite heroes that the ,goddess of ,wisdom visibly reveals herself4 #g4 ,thus ,art1 in its earlier stages at least1 is widely different from ,science1 is independent of it1 and is anterior to it4 ,at a later period1 no doubt1 ,art may borrow aid from ,science2 and the discoveries of the philosopher may be of great value to the manufacturer and the artist4 ,but even then1 this application forms no essential part of the science3 the interest which belongs to it is not an intellectual interest4 ,the augmentation of human power and convenience may impel or reward the physical philosopher2 but the processes by which man's repasts are rendered more delicious1 his journeys more rapid1 his weapons more terrible1 are not1 therefore1 ,science4 ,they may involve principles which are of the highest interest to science2 but as the advantage is not practically more precious because it results from a beautiful theory1 so the theoretical principle has no more conspicuous place in science because it leads to convenient practical consequences4 ,the nature of ,science is purely intellectual2 ,knowledge alone1--exact general ,truth1--is her object2 and we cannot mix with such material1 as matters of the same kind1 the merely ,empirical maxims of ,art1 without introducing endless confusion into the subject1 and making it impossible to attain any solid footing in our philosophy4 #h4 ,i shall therefore not place1 in our ,classification of the ,sciences1 the ,arts1 as has generally been done2 nor shall ,i notice the applications of sciences to art1 as forming any separate portion of each science4 ,the sciences1 considered as bodies of general speculative #ace truths1 are what we are here concerned with2 and applications of such truths1 whether useful or useless1 are important to us only as illustrations and examples4 ,whatever place in human knowledge the ,practical ,arts may hold1 they are not ,sciences4 ,and it is only by this rigorous separation of the ,practical from the ,theoretical1 that we can arrive at any solid conclusions respecting the nature of ,truth1 and the mode of arriving at it1 such as it is our object to attain4 #acf ,,chapter ,,ix4 ,,of ,,the ,,classification ,,of ,,sciences4 #a4 ,,the ,classification of ,sciences has its chief use in pointing out to us the extent of our powers of arriving at truth1 and the analogies which may obtain between those certain and lucid portions of knowledge with which we are here concerned1 and those other portions1 of a very different interest and evidence1 which we here purposely abstain to touch upon4 ,the classification of human knowledge will1 therefore1 have a more peculiar importance when we can include in it the moral1 political1 and metaphysical1 as well as the physical portions of our knowledge4 ,but such a survey does not belong to our present undertaking3 and a general view of the connexion and order of the branches of sciences which our review has hitherto included1 will even now possess some interest2 and may serve hereafter as an introduction to a more complete scheme of the general body of human knowledge4 #b4 ,in this1 as in any other case1 a sound classification must be the result1 not of any assumed principles imperatively applied to the subject1 but of an examination of the objects to be classified2--of an analysis of them into the principles in which they agree and differ4 ,the ,classification of ,sciences must result from the consideration of their nature and contents4 ,accordingly1 that review of the ,sciences in which the ,history of the ,sciences engaged us1 led to a ,classification1 of which the main features are indicated in that work4 ,the ,classification thus obtained1 depends neither upon the faculties of the mind to which the separate parts of our knowledge owe their origin1 nor upon the objects which each science contemplates2 but upon a more #acg natural and fundamental element2--namely1 the ,ideas which each science involves4 ,the ,ideas regulate and connect the facts1 and are the foundations of the reasoning1 in each science3 and having in another work more fully examined these ,ideas1 we are now prepared to state here the classification to which they lead4 ,if we have rightly traced each science to the ,conceptions which are really fundamental with regard to it1 and which give rise to the first principles on which it depends1 it is not necessary for our purpose that we should decide whether these ,conceptions are absolutely ultimate principles of thought1 or whether1 on the contrary1 they can be further resolved into other ,fundamental ,ideas4 ,we need not now suppose it determined whether or not ,number is a mere modification of the ,idea of ,time1 and ,force a mere modification of the ,idea of ,cause3 for however this may be1 our ,conception of ,number is the foundation of ,arithmetic1 and our ,conception of ,force is the foundation of ,mechanics4 ,it is to be observed also that in our classification1 each ,science may involve1 not only the ,ideas or ,conceptions which are placed opposite to it in the list1 but also all which precede it4 ,thus ,formal ,astronomy involves not only the ,conception of ,motion1 but also those which are the foundation of ,arithmetic and ,geometry4 ,in like manner4 ,physical ,astronomy employs the ,sciences of ,statics and ,dynamics1 and thus1 rests on their foundations2 and they1 in turn1 depend upon the ,ideas of ,space and of ,time1 as well as of ,cause4 #c4 ,we may further observe1 that this arrangement of ,sciences according to the ,fundamental ,ideas which they involve1 points out the transition from those parts of human knowledge which have been included in our ,history and ,philosophy1 to other regions of speculation into which we have not entered4 ,we have repeatedly found ourselves upon the borders of inquiries of a psychological1 or moral1 or theological nature4 ,thus the ,history of ,physiology#bhb led us to the consideration #ach of ,life1 ,sensation1 and ,volition2 and at these ,ideas we stopped1 that we might not transgress the boundaries of our subject as then predetermined4 ,it is plain that the pursuit of such conceptions and their consequences1 would lead us to the sciences 7if we are allowed to call them sciences7 which contemplate not only animal1 but human principles of action1 to ,anthropology1 and ,psychology4 ,in other ways1 too1 the ,ideas which we hare examined1 although manifestly the foundations of sciences such as we have here treated of also plainly pointed to speculations of a different order2 thus the ,idea of a ,final ,cause is an indispensable guide in ,biology1 as we have seen2 but the conception of ,design as directing the order of nature1 once admitted1 soon carries us to higher contemplations4 ,again1 the ,class of ,paltiological ,sciences which we were in the ,history led to construct1 although we there admitted only one example of the ,class1 namely ,geology1 does in reality include many vast lines of research2 as the history and causes of the division of plants and animals1 the history of languages1 arts1 and consequently of civilization4 ,along with these researches1 comes the question how far these histories point backwards to a natural or a supernatural origin2 and the ,idea of a ,first ,cause is thus brought under our consideration4 ,finally1 it is not difficult to see that as the ,physical ,sciences have their peculiar governing ,ideas1 which support and shape them1 so the ,moral and ,political ,sciences also must similarly have their fundamental and formative ,ideas1 the source of universal and certain truths1 each of their proper kind4 ,but to follow out the traces of this analogy1 and to verify the existence of those ,fundamental ,ideas in ,morals and ,politics1 is a task quite out of the sphere of the work in which we are here engaged4 ,note #bhb3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 v4 sect4 #b4 #d4 ,we may now place before the reader our ,classification of the ,sciences4 ,i have added to the list of ,sciences1 a few not belonging to our present subject1 that the nature of the transition by which we are to extend our philosophy into a wider and higher region may be in some measure perceived4 #aci ,the ,classification of the ,sciences is given over leaf4 ,a few remarks upon it offer themselves4 ,the ,pure ,mathematical ,sciences can hardly be called ,inductive ,sciences4 ,their principles are not obtained by ,induction from ,facts1 but are necessarily assumed in reasoning upon the subject matter which those sciences involve4 ,the ,astronomy of the ,ancients aimed only at explaining the motions of the heavenly bodies1 as a mechanism4 ,modern ,astronomy1 explains these motions on the principles of ,mechanics4 ,the term ,physics1 when confined to a peculiar class of ,sciences1 is usually understood to exclude the ,mechanical ,sciences on the one side1 and ,chemistry on the other2 and thus embraces the ,secondary ,mechanical and ,analytico-,mechanical ,sciences4 ,but the adjective ,physical applied to any science and opposed to ,formal1 as in ,astronomy and ,optics1 implies those speculations in which we consider not only the ,laws of ,phenomena but their ,causes2 and generally1 as in those cases1 their ,mechanical ,causes4 ,the term ,metaphysics is applied to subjects in which the ,facts examined are emotions1 thoughts and mental conditions2 subjects not included in our present survey4 #adj ,fundamental ,ideas or ,sciences4 ,classification4 ,conceptions4 ,space ,geometry 7 ,time 7 ,pure ,mathematical ,number ,arithmetic ,sign ,algebra 7 ,sciences4 ,limit ,differentials 7 ,motion ,pure ,mechanism ,pure ,motional ,formal ,astronomy ,sciences4 ,cause ,force ,statics 7 ,matter ,dynamics 7 ,mechanical ,inertia ,hydrostatics ,fluid ,pressure ,hydrodynamics 7 ,sciences4 ,physical ,astronomy 7 ,outness ,medium of ,sensation ,acoustics 7 ,intensity of ,qualities ,formal ,optics 7 ,secondary ,scales of ,qualities ,physical ,optics ,mechanical ,thermotics 7 ,sciences4 ,atmology 7 7,physics47 ,polarity ,electricity 7 ,analytico-,mecha- ,magnetism nical ,sciences4 ,galvanism 7 7,physics47 ,element 7,composition7 ,chemical ,affinity ,substance 7,atoms7 ,chemistry ,analytical ,science4 ,symmetry ,crystallography ,analytico-,classifi- ,likeness ,systematic ,mineralogy catory ,sciences4 ,degrees of ,likeness ,systematic ,botany 7 ,systematic ,zoology ,classificatory ,natural ,affinity ,comparative ,anatomy 7 ,sciences4 7,vital ,powers7 ,assimilation ,irritability 7,organization7 ,biology ,organical ,sciences4 ,final ,cause ,instinct ,emotion ,psychology 7,metaphysics47 ,thought ,historical ,causation ,geology 7 ,distribution of 7 ,paltiological ,plants and ,animals ,sciences4 ,glossology 7 ,ethnography 7 ,first ,cause ,natural ,theology4 99,transcriber's ,note3 ,the two following tables were inserted on separate sheets at this point4 ,they were structured as trees1 but have here been converted into a diagram to be read from left to right1 and an associated key4 ,arrows have replaced the brackets ,whewell used4 ,in the original1 the names of discoverers and comments about inadequate explanations were printed in red4 ,,inductive ,,table ,,of ,,astronomy a r 7 7 7 7 b j s 7 ,j 7 7 z 7 c k 7 7 7 7 d l t 7 7 7 e m 7 7 b#a c#a m#a 7 u 7 ,a ,e ,h 7 ,m ,n ,q ,w 7 f n 7 7 b#a d#a n#a 7 7 7 7 7 7 ,r ,x b#a e#a 7 7 7 g o v ,b ,f ,i ,k 7 7 7 7 7 ,o ,s ,y b#a f#a 7 o#a 7 7 7 7 7 7 7 ,s ,z b#a g#a 7 7 7 u#a h p w ,c ,g ,l 7 7 t#a 7 ,p ,t b#a h#a p#a 7 7 7 7 q x ,d b#a i#a q#a 7 7 7 7 i y b#a j#a r#a 7 7 7 7 ,u a#a b#a k#a s#a 7 7 7 7 ,v b#a l#a 7 7 a ,,the ,,earth appears to be immovable4 b ,,the ,,stars keep their relative places in the vault of the sky1 and with the ,sun and ,moon1 rise1 move1 and set4 c ,,the ,,moon',s bright part is of the shape of a ball enlightened by the ,sun4 d ,,the ,,moon',s ,,eclipses occur when she is full4 e ,,eclipses ,,of ,,the ,,sun ,,and ,,moon often occur4 f ,,the ,,moon rises and sets at different times and places4 ,her course among the ,stars varies4 g ,,the ,,planets are morning and evening ,stars3 are direct1 stationary1 and retrograde4 h ,,the ,,sun rises1 culminates1 and sets in different times and places at different seasons3 different ,,constellations are visible at night4 i ,,the ,,tides ebb and flow4 j ,chaldns4 ,the ,sphere of the ,heavens appears to make a ,diurnal ,revolution4 k ,greeks4 ,the ,moon receives her light from the ,sun4 l ,greeks4 ,the ,moon's ,eclipses are caused by the ,earth's shadow4 m ,chaldns4 ,the ,moon's ,eclipses follow certain cycles4 n ,greeks4 ,the ,moon appears to revolve monthly in an oblique orbit1 which has ,nodes and an ,apogee4 o ,chaldeans4 ,the ,planets have proper motions and certain ,cycles4 p ,pythagoras4 ,the ,sun appears to move annually in an ,ecliptic oblique to the diurnal motion4 q ,the places of ,stars are determined by their ,longitude measured from the ,equinox4 r ,the forms and dists of known parts of the earth are such as fit a convex surface4 s ,the visible ,pole of the ,heavens rises or drops as we travel ,n4 or ,s4 t ,the boundary of the ,earth's shadow is always circular4 u ,by observations of ,eclipses1 the ,moon's ,nodes and ,apogee revolve1 and her motion is unequal according to certain laws4 v ,by observations of the ,planets1 their progressions1 stations1 and retrogradations4 w ,by observations of the ,sun1 his motion is unequal according to certain laws4 x ,by observations1 ,longitudes of ,stars increase4 y ,by observations1 the ,tides depend on the ,moon and ,sun4 z ,aristotle8 ,the ,earth is a ,globe1 about which the ,sphere of the ,heavens performs a ,diurnal ,revolution4 ,a ,hipparchus4 ,the ,moon appears to move in an ,epicycle carried by a ,deferent3 the ,velocity of ,apogee and ,nodes determined4 ,b ,eudoxus4 ,the ,planets appear to move in ,epicycles carried by ,deferents4 ,c ,hipparchus4 ,the ,sun appears to move in an ,eccentric1 his ,apogee being fixed4 ,d ,hippar4 ,there is a ,precession of the ,equinoxes4 ,e ,by additional observations1 the ,moon's motion has another inequality4 ,evection4 ,f ,by additional observations1 the ,planets' motions in their ,epicycles are unequal according to certain laws4 ,g ,by additional observations1 the ,sun's ,apogee moves4 ,albategnius4 ,h ,ptolemy4 ,the ,moon appears to move in an ,epicycle carried by an ,eccentric4 ,i ,ptolemy4 ,the ,planets appear to move in ,epicycles carried by ,eccentrics4 ,j 99 ,by the nature of motion1 the apparent motion is the same whether the ,heavens or the ,earth have a diurnal revolution3 the latter is simpler4 ,k 99 ,by the nature of motion1 the apparent motion is the same if the ,planets revolve about the ,sun3 this is simpler4 ,l 99 ,by the nature of motion1 the apparent motion of the ,sun is the same if the ,earth revolve round the ,sun3 this is simpler4 ,m 99 ,copernicus4 ,the ,earth and ,planets revolve about the ,sun as a center in ,orbits nearly circular4 ,the ,earth revolves about its axis inclined to the ,ecliptic in a constant position1 and the ,moon revolves about the ,earth4 ,the ,heliocentric ,theory governs subsequent speculations4 ,n ,retaining ,moon's ,eccentric and ,epicycle2 ,by additional observations1 the ,moon's motion has other inequalities4 ,o ,retaining but referring to the ,sun as center the ,planets' ,epicycles and ,eccentrics and the annual ,orbit2 ,p ,retaining obsns4 ,earth's ,aphelion revolves4 ,q ,tycho4 ,moon's ,variation2 ,unequal ,motion of ,node2 ,change of ,inclination4 ,r ,by calcns4 of the periodic times and distances4 ,s ,by additional observations and calculations4 ,t ,planets' ,aphelia revolve4 ,jupiter and ,saturn's motions have an inequality depg4 on their mutual positions4 ,u ,,the ,,weight of bodies dimins in going towards the ,equator4 ,v ,,the ,,satellites of ,jupiter and ,saturn revolve according to ,kepler's ,laws4 ,w ,horrox4 ,halley4 ,the ,moon moves in an ,ellipse with variable axis and eccentricity4 ,x ,kepler4 ,distances cubed are as times squared4 ,y ,kepler4 ,areas as described by ,planets are as times4 ,z ,kepler4 ,curves described by ,planets are as ellipses4 a#a ,newton4 ,earth is oblate4 b#a 99 ,by ,mechanics4 c#a 99 ,newton4 ,moon is attracted by the ,earth4 ,fall of heavy bodies4 d#a 99 ,newton4 ,moon's inequalities produced by attraction of ,sun4 e#a 99 ,newton4 ,wren4 ,hooke4 ,sun's force on different ,planets is invers4 as square of distance4 f#a 99 ,newton4 ,planets are attracted by the ,sun4 g#a 99 ,newton4 ,sun attracts ,planets invers4 as square of distance4 h#a 99 ,newton4 ,these inequalities are produced by mutual attraction of the ,planets4 i#a ,precession of ,equinoxes is produced by attraction of ,moon and ,sun on oblate ,earth4 j#a ,tides are produced by attraction of ,moon and ,sun on ,sea4 ,explanation imperfect4 k#a ,diminution of gravity and oblateness of ,earth arise from attractions of parts4 l#a 99 ,newton4 ,jupiter and ,saturn attract their ,satellites inversely as the square of the distance1 and the ,sun attracts ,planets and ,satellites alike4 m#a ,newton4 ,earth attracts ,moon invers4 as square of distance4 n#a ,newton4 ,sun attracts ,moon4 o#a ,newton4 ,sun attracts ,planets inversely as the square of the distance4 p#a ,newton4 ,planets attract each other4 q#a 99 ,newton4 ,moon and ,sun attract parts of the ,earth4 r#a 99 ,newton4 ,moon and ,sun attract the ,ocean4 s#a 99 ,newton4 ,parts of the ,earth attract each other4 t#a ,newton4 ,all parts of the ,earth1 ,sun1 ,moon4 and ,planets attract each other with ,forces inversely as the square of the distance4 u#a ,newton4 ,,the ,,theory ,,of ,,universal ,,gravitation4 7,all bodies attract each other with a ,force of ,gravity which is inversely as the squares of the distances47 ,,inductive ,,table ,,of ,,optics ,first ,facts4 ,the common and obvious ,phnomena of ,light and ,vision4 ,by the ,idea of a ,medium ,light and ,vision take place by means of something intermediate4 ,first ,law of ,phnomena4 ,the effects take place in straight lines denoted by the ,term ,rays4 ,facts of a m h#a 7 7 7 7 7 7 7 7 b n 7 7 i#a 7 7 7 7 7 r 7 7 7 ,c#a 7 7 c o 7 7 ,k 7 7 7 7 ,f#a 7 7 7 j#a 7 x#a 7 7 7 d p 7 ,l ,s 7 7 7 7 7 7 7 7 e s ,m 7 ,t h#a 7 ,d#a 7 7 7 ,h#a 7 7 7 7 7 7 f t 7 ,u k#a 7 7 7 ,g#a 7 7 7 ,e#a 7 7 7 g 7 7 u ,w l#a 7 7 7 7 7 7 7 7 7 7 7 7 v ,x l#a 7 y#a 7 7 7 q 7 7 7 7 7 7 w ,y j#a 7 7 7 7 7 7 7 7 x ,z 7 7 7 7 7 7 m#a 7 7 7 7 y a#a 7 7 7 7 7 7 7 ,i#a 7 7 z n#a 7 z#a 7 7 7 7 7 7 ,k#a 7 ,a ,n b#a o#a 7 7 7 q 7 7 7 7 7 ,b ,o p#a 7 7 7 7 7 7 ,c 7 c#a q#a 7 7 7 7 7 ,v 7 7 7 7 ,d 7 d#a q#a 7 7 7 7 7 7 7 7 ,e j#a 7 ,a#a 7 7 7 7 7 7 7 ,f ,p e#a 7 7 7 7 7 7 r#a 7 7 7 7 ,g f#a 7 7 7 7 7 7 ,j#a 7 7 ,h ,q s#a 7 7 h 7 ,r g#a t#a 7 7 7 7 7 i 7 ,i u#a 7 7 7 7 7 j 7 v#a 7 ,b#a 7 7 7 k 7 w#a 7 7 7 ,j 7 7 l 7 w#a 7 7 a ,rays falling on water1 specula1 c4 b ,rays passing through water1 glass1 c4 ,measures4 ,ptolemy4 c ,colours seen by prisms1 in rainbow1 c4 d ,colours in diff4 transp4 ,substances4 ,optical instrumts4 e ,two ,images in ,rhomb4 of ,calcspar4 f ,two ,images in other crystals4 g ,two ,rhombs of ,calcspar make #d images alternately appear and disappear4 h ,fringes of shadows4 ,grimaldi4 ,hook4 ,newton4 i ,spectra of gratings4 ,fraunhofer4 j ,colours of striated surfaces4 ,coventry's ,micrometr4 ,barton's ,buttons4 ,young4 k ,colours of thick ,plates4 ,newton4 l ,colours of thin ,plates4 ,hook4 ,newton4 m ,euclid4 ,ang4 ,inc4 equals ,ang4 ,reflection4 n ,snell4 ,sin4 ,refr4 to ,sin4 ,inc4 in giv4 ,ratio in same med4 o ,by measures of ,refraction4 p ,dispersion of colours is same when ,refr4 is diff4 ,measures4 ,dollond4 q ,huyghens4 ,rays of light have four ,sides with regard to which their properties alternate4 ,newton4 ,idea of ,polarization introduced1 which governs subsequent observations4 ,dipolarization with ,colours4 r ,newt4 ,refr4 ,ro4 is diff4 for diff4 colours1 but in same med4 is const4 for each colour4 s ,measures4 ,huyghens4 t ,double ,refr4 in biaxal crystals4 ,brewster4 u ,rays are polarized by ,calcspar1 ,quartz1 c4 v ,rays are polarized by biaxal crystals4 w ,rays are polarized by ,tourmaline1 ,agate1 c4 x ,rays are polarised by ,refl4 at glass4 y ,rays are polarized by transmission through glass4 z ,variable qy4 of pol4 refl4 light paral4 plane of ,refl4 ,arago4 ,a ,variable qy4 of pol4 refl4 light perp4 plane of ,refl4 ,b ,whole light reflected by internal ,refl4 ,c ,pol4 ,rays through uniaxal crystals give colours4 ,rings4 ,wollaston4 ,d ,pol4 ,rays through biaxal crystals give colours4 ,arago4 ,e ,pol4 ,rays4 through imperf4 crystallized bodies give colours4 7,glass strained1 jellies prest47 ,brewster4 ,f ,pol4 ,rays in axis of ,quartz give a peculiar set of colours4 ,plane of ,poln twisted diffly4 for diff4 colours4 ,biot4 ,arago4 ,g ,pol4 ,rays oblique in ,quartz give peculiar rings1 c4 ,h ,pol4 ,rays through certain liquids give a peculiar set of colours4 ,i ,the ,laws of these ,phnomena were never discovered till ,theory had indicated them4 ,j ,newton's ,scale of ,colours4 ,fits of ,rays4 ,newton4 ,k ,dollond4 ,l ,propn of ,ref4 ,rs is diff4 in diff4 med4 ,achromatism4 ,m ,huyghs4 ,law of ,double ,ref4 exp4 by a spheroid4 ,n ,change of plane of pol4 by ,refl4 ,arago ,o ,light is circularly pol4 by #b ,refl4 in ,fresnel's ,rhomb4 ,fresnel4 ,p in dirn of plagihedral faces4 ,j4 ,herschel4 ,q ,plane of ,poln4 twisted4 ,biot ,r ,fringes obliterated by stopping light from one edge or interposing a glass4 ,young4 ,arago4 ,s ,ratios not reconcilable4 ,irrationality4 ,blair4 ,t ,fresnel4 ,u ,law exp4 by surface of #d dims4 ,v ,optical classification of crystals4 ,brewster4 ,w ,newt4 ,malus4 ,ray pol4 in principal plane of ,rhomb42 and perp4 to it4 ,x ,brews4 ,biot4 ,ray pol4 in plane bisecting ang4 at axis2 and perp4 to it4 ,y ,brews4 ,ray pol4 paral4 to axis4 ,z ,malus4 ,ray pol4 in plane of ,refl4 for given angle4 a#a ,malus4 ,ray partially pol4 in plane perp4 to plane of ,reflection4 b#a ,none ,refld4 if tan4 ang4 equal ,refr4 ,ro4 ,brewster4 c#a ,tint is as sq4 of sin4 ,biot4 d#a ,tint is as sin4 sin4 4 ,brewster4 ,biot4 ,lemniscates4 ,j4 ,herschel4 e#a 99 ,by interf4 of resolved undulns4 of #b rays circularly pold4 in opp4 directions4 99 ,fresnel4 f#a 99 ,by interf4 of resolved undulns4 of #b rays elliptically pold4 in opp4 directions4 99 ,airy4 g#a 99 ,by interf4 of rays from edges4 ,young4 h#a 99 ,refl4 produced by spherical undulns4 i#a 99 ,refr4 produced by spherical undulns4 of diff4 vel4 for diff4 colour4 j#a ,explanation imperfect4 k#a 99 ,refr4 produced by curved surf4 undulns4 l#a 99 ,poln4 being prod4 by resolution of transve undulns4 m#a 99 ,polarization being produced by resolution of transverse undulations4 n#a 99 ,undulns4 being comd4 acc4 to laws of elastic bodies4 o#a 99 ,undulns4 being comd4 acc4 to a certain hypothesis4 p#a 99 ,impossible formul being interpreted by analogy4 q#a 99 ,by interf4 of resolved parts of transverse undulns4 r#a 99 ,same hypothesis explains separation of rays in axis and oblique4 ,explanation imperfect4 99 ,maccullagh4 s#a ,explan4 wanting4 t#a 99 ,by interf4 of rays from all parts4 99 ,young4 99 ,fresnel4 u#a 99 ,by interf4 of undulns4 from all parts4 99 ,fraunhofer4 v#a 99 ,by interf4 of rays from stri4 99 ,young4 w#a 99 ,by interf4 of undulns4 from two surfaces4 99 ,young4 x#a 99 ,huyghens4 ,reflection and ,refraction are propagation of undulations4 y#a 99 ,young4 99 ,fresnel4 ,polarization in crystals is transverse undulations4 z#a 99 ,fresnel4 ,polarization in ,reflection and ,refraction is transverse undulations4 ,a#a 99 ,fresnel4 99 ,arago4 ,dipolarized ,colours are produced by interference of ,rays polarized in same plane2 length of undulation being different for different colours4 ,b#a 99 ,young4 99 ,fresnel4 ,colours of ,fringes1 ,gratings1 ,stri1 thick ,plates1 thin ,plates c4 are produced by interference of undulations2 length of undulation being different for different colours4 ,c#a 99 ,undulations being propagated by the uniform elasticity of each medium4 ,d#a 99 ,undulns4 prop4 by ely4 of medium diff4 in #b diff4 dirns1 7axis of crystal47 ,e#a 99 ,undulns4 being prop4 by elasticity of med4 diff4 in #c diff4 directions 7axes74 ,f#a ,young4 ,reflection and double ,refraction are propagation of undulations by crystalline elasticity4 ,g#a 99 ,fresnel4 ,double ,refr4 and ,pol4 arise from same cause4 ,h#a ,young4 ,fresnel4 ,light is transverse undulations propagated in media by elasticity dependent on axis1 when crystalline4 ,i#a ,fresnel4 ,light is transverse undulns4 transmitted from one med4 to another according to probable hypotheses4 ,j#a ,young4 ,fresnel4 ,colours result from interferences1 the lengths of undulation being different for different colours4 ,k#a ,,the ,,undulatory ,,theory ,,of ,,light4 #ada ,,novum ,,organon ,,renovatum4 ,,book ,,iii4 ,,of ,,methods ,,employed ,,in ,,the ,,formation ,,of ,,science4 ,,chapter ,i4 ,,introduction4 ,,aphorism ,,xxvii4 ,the ,methods by which the construction of ,science is promoted are1 ,methods of ,observation1 ,methods of obtaining clear ,ideas1 and ,methods of ,induction4 #a4 ,,in the preceding ,book1 we pointed out certain general ,characters of scientific knowledge which may often serve to distinguish it from opinions of a looser or vaguer kind4 ,in the course of the progress of knowledge from the earliest to the present time1 men have been led to a perception1 more or less clear1 of these characteristics4 ,various philosophers1 from ,plato and ,aristotle in the ancient world1 to ,richard de ,saint ,victor and ,roger ,bacon in the middle ages1 ,galileo and ,gilbert1 ,francis ,bacon and ,isaac ,newton1 in modern times1 were led to offer precepts and maxims1 as fitted to guide us to a real and fundamental knowledge of nature4 ,it may on another occasion be our business to estimate the value of these precepts and maxims4 ,and other contributions of the same kind to the philosophy of science might be noticed1 and some which #adb contain still more valuable suggestions1 and indicate a more practical acquaintance with the subject4 ,among these1 ,i must especially distinguish ,sir ,john ,herschel's ,discourse on the ,study of ,natural ,philosophy4 ,but my object at present is not to relate the history1 but to present the really valuable results of preceding labours3 and ,i shall endeavour to collect1 both from them and from my own researches and reflections1 such views and such rules as seem best adapted to assist us in the discovery and recognition of scientific truth2 or1 at least1 such as may enable us to understand the process by which this truth is obtained4 ,i would present to the reader the ,philosophy and1 if possible1 the ,art of ,discovery4 #b4 ,but1 in truth1 we must acknowledge1 before we proceed with this subject1 that1 speaking with strictness1 an ,art of ,discovery is not possible2--that we can give no ,rules for the pursuit of truth which shall be universally and peremptorily applicable2--and that the helps which we can offer to the inquirer in such cases are limited and precarious4 ,still1 we trust it will be found that aids may be pointed out which are neither worthless nor uninstructive4 ,the mere classification of examples of successful inquiry1 to which our rules give occasion1 is full of interest for the philosophical speculator4 ,and if our maxims direct the discoverer to no operations which might not have occurred to his mind of themselves1 they may still concentrate our attention on that which is most important and characteristic in these operations1 and may direct us to the best mode of insuring their success4 ,i shall1 therefore1 attempt to resolve the ,process of ,discovery into its parts1 and to give an account as distinct as may be of ,rules and ,methods which belong to each portion of the process4 #c4 ,in ,book ,,ii4 we considered the three main parts of the process by which science is constructed3 namely1 the ,decomposition and ,observation of ,complex ,facts2 the ,explication of our ,ideal ,conceptions2 and the ,colligation of ,elementary ,facts by means of those ,conceptions4 ,the first and last of #adc these three steps are capable of receiving additional accuracy by peculiar processes4 ,they may further the advance of science in a more effectual manner1 when directed by special technical ,methods1 of which in the present ,book we must give a brief view4 ,in this more technical form1 the observation of facts involves the ,measurement of ,phenomena2 and the ,colligation of ,facts includes all arts and rules by which the process of ,induction can be assisted4 ,hence we shall have here to consider ,methods of ,observation1 and ,methods of ,induction1 using these phrases in the widest sense4 ,the second of the three steps above mentioned1 the ,explication of our ,conceptions1 does not admit of being much assisted by methods1 although something may be done by ,education and ,discussion4 #d4 ,the ,methods of ,induction1 of which we have to speak1 apply only to the first step in our ascent from phenomena to laws of nature2--the discovery of ,laws of ,phenomena4 ,a higher and ulterior step remains behind1 and follows in natural order the discovery of ,laws of ,phenomena2 namely1 the ,discovery of ,causes2 and this must be stated as a distinct and essential process in a complete view of the course of science4 ,again1 when we have thus ascended to the causes of phenomena and of their laws1 we can often reason downwards from the cause so discovered2 and we are thus led to suggestions of new phenomena1 or to new explanations of phenomena already known4 ,such proceedings may be termed ,applications of our ,discoveries2 including in the phrase1 ,verifications of our ,doctrines by such an application of them to observed facts4 ,hence we have the following series of processes concerned in the formation of science4 7#a47 ,decomposition of ,facts2 7#b47 ,measurement of ,phenomena2 7#c47 ,explication of ,conceptions2 7#d47 ,induction of ,laws of ,phenomena2 7#e47 ,induction of ,causes2 7#f47 ,application of ,inductive ,discoveries4 #e4 ,of these six processes1 the methods by which the second and fourth may be assisted are here our #add peculiar object of attention4 ,the treatment of these subjects in the present work must necessarily be scanty and imperfect1 although we may perhaps be able to add something to what has hitherto been systematically taught on these heads4 ,methods of ,observation and of ,induction might of themselves form an abundant subject for a treatise1 and hereafter probably will do so1 in the hands of future writers4 ,a few remarks1 offered as contributions to this subject1 may serve to show how extensive it is1 and how much more ready it now is than it ever before was1 for a systematic discussion4 ,of the above steps of the formation of science1 the first1 the ,decomposition of ,facts1 has already been sufficiently explained in the last ,book3 for if we pursue it into further detail and exactitude1 we find that we gradually trench upon some of the succeeding parts4 ,i1 therefore1 proceed to treat of the second step1 the ,measurement of ,phenomena2--of ,methods by which this work1 in its widest sense1 is executed1 and these ,i shall term ,methods of ,observation4 #ade ,,chapter ,,ii4 ,,of ,,methods ,,of ,,observation4 ,,aphorism ,,xxviii4 ,the ,methods of ,observation of ,quantity in general are1 ,numeration1 which is precise by the nature of ,number2 the ,measurement of ,space and of ,time1 which are easily made precise2 the ,conversion of ,space and ,time1 by which each aids the measurement of the other2 the ,method of ,repetition2 the ,method of ,coincidences or ,interferences4 ,the measurement of ,weight is made precise by the ,method of ,double-weighing4 ,secondary ,qualities are measured by means of ,scales of ,degrees2 but in order to apply these ,scales1 the student requires the ,education of the ,senses4 ,the ,education of the ,senses is forwarded by the practical study of ,descriptive ,natural ,history1 ,chemical ,manipulation1 and ,astronomical ,observation4 #a4 ,i ,,shall speak1 in this chapter1 of ,methods of exact and systematic observation1 by which such facts are collected as form the materials of precise scientific propositions4 ,these ,methods are very various1 according to the nature of the subject inquired into1 and other circumstances3 but a great portion of them agree in being processes of measurement4 ,these ,i shall peculiarly consider3 and in the first place those referring to ,number1 ,space1 and ,time1 which are at the same time objects and instruments of measurement4 #b4 ,but though we have to explain how observations may be made as perfect as possible1 we must not forget that in most cases complete perfection is unattainable4 ,observations are never perfect4 ,for we #adf observe phenomena by our senses1 and measure their relations in time and space2 but our senses and our measures are all1 from various causes1 inaccurate4 ,if we have to observe the exact place of the moon among the stars1 how much of instrumental apparatus is necessary6 ,this apparatus has been improved by many successive generations of astronomers1 yet it is still far from being perfect4 ,and the senses of man1 as well as his implements1 are limited in their exactness4 ,two different observers do not obtain precisely the same measures of the time and place of a phenomenon2 as1 for instance1 of the moment at which the moon occults a star1 and the point of her limb at which the occultation takes place4 ,here1 then1 is a source of inaccuracy and errour1 even in astronomy1 where the means of exact observation are incomparably more complete than they are in any other department of human research4 ,in other cases1 the task of obtaining accurate measures is far more difficult4 ,if we have to observe the tides of the ocean when rippled with waves1 we can see the average level of the water first rise and then fall2 but how hard is it to select the exact moment when it is at its greatest height1 or the exact highest point which it reaches6 ,it is very easy1 in such a case1 to err by many minutes in time1 and by several inches in space4 ,still1 in many cases1 good ,methods can remove very much of this inaccuracy1 and to these we now proceed4 #c4 7,i47 ,number4--,number is the first step of measurement1 since it measures itself1 and does not1 like space and time1 require an arbitrary standard4 ,hence the first exact observations1 and the first advances of rigorous knowledge1 appear to have been made by means of number2 as for example1--the number of days in a month and in a year2--the cycles according to which eclipses occur2--the number of days in the revolutions of the planets2 and the like4 ,all these discoveries1 as we have seen in the ,history of ,astronomy1 go back to the earliest period of the science1 anterior to any distinct tradition2 and these discoveries presuppose a series1 probably a very long series1 of observations1 made #adg principally by means of number4 ,nations so rude as to have no other means of exact measurement1 have still systems of numeration by which they can reckon to a considerable extent4 ,very often1 such nations have very complex systems1 which are capable of expressing numbers of great magnitude4 ,number supplies the means of measuring other quantities1 by the assumption of a unit of measure of the appropriate kind3 but where nature supplies the unit1 number is applicable directly and immediately4 ,number is an important element in the ,classificatory as well as in the ,mathematical ,sciences4 ,the ,history of those ,sciences shows how the formation of botanical systems was effected by the adoption of number as a leading element1 by ,csalpinus2 and how afterwards the ,reform of ,linnus in classification depended in a great degree on his finding1 in the pistils and stamens1 a better numerical basis than those before employed4 ,in like manner1 the number of rays in the membrane of the gills#ac1 and the number of rays in the fins of fish1 were found to be important elements in ichthyological classification by ,artedi and ,linnus4 ,there are innumerable instances1 in all parts of ,natural ,history1 of the importance of the observation of number4 ,and in this observation1 no instrument1 scale or standard is needed1 or can be applied2 except the scale of natural numbers1 expressed either in words or in figures1 can be considered as an instrument4 ,note #ac3 ,hist4 ,ind4 ,sc4 b4 xvi4 c4 vii4 #d4 7,,ii47 ,measurement of ,space4--,of quantities admitting of continuous increase and decrease1 7for number is discontinuous17 space is the most simple in its mode of measurement1 and requires most frequently to be measured4 ,the obvious mode of measuring space is by the repeated application of a material measure1 as when we take a foot-rule and measure the length of a room4 ,and in this case the foot-rule is the unit of space1 and the length of the room is expressed by the number of such units which it contains3 or1 as it may not contain an exact number1 by a number with a fraction4 ,but besides this measurement of linear space1 #adh there is another kind of space which1 for purposes of science1 it is still more important to measure1 namely1 angular space4 ,the visible heavens being considered as a sphere1 the portions and paths of the heavenly bodies are determined by drawing circles on the surface of this sphere1 and are expressed by means of the parts of these circles thus intercepted3 by such measures the doctrines of astronomy were obtained in the very beginning of the science4 ,the arcs of circles thus measured1 are not like linear spaces1 reckoned by means of an arbitrary unit1 for there is a natural unit1 the total circumference1 to which all arcs may be referred4 ,for the sake of convenience1 the whole circumference is divided into #cfj parts or degrees2 and by means of these degrees and their parts1 all arcs are expressed4 ,the arcs are the measures of the angles at the center1 and the degrees may be considered indifferently as measuring the one or the other of these quantities4 #e4 ,in the ,history of ,astronomy#bc1 ,i have described the method of observation of celestial angles employed by the ,greeks4 ,they determined the lines in which the heavenly bodies were seen1 by means either of ,shadows1 or of ,sights2 and measured the angles between such lines by arcs or rules properly applied to them4 ,the ,armill1 ,astrolabe1 ,dioptra1 and ,parallactic ,instrument of the ancients1 were some of the instruments thus constructed4 ,tycho ,brahe greatly improved the methods of astronomical observation by giving steadiness to the frame of his instruments1 7which were large quadrants17 and accuracy to the divisions of the limb#cc4 ,but the application of the telescope to the astronomical quadrant and the fixation of the center of the field by a cross of fine wires placed in the focus1 was an immense improvement of the instrument1 since it substituted a precise visual ray1 pointing to the star1 instead of the coarse coincidence of ,sights4 ,the accuracy of observation was still further increased #adi by applying to the telescope a micrometer which might subdivide the smaller divisions of the arc4 ,note #bc3 ,hist4 ,ind4 ,sc4 b4 iii4 c4 iv4 sect4 #c4 ,note #cc3 ,ib4 b4 vii4 c4 vi4 sect4 #a4 #f4 ,by this means1 the precision of astronomical observation was made so great1 that very minute angular spaces could be measured3 and it then became a question whether discrepancies which appeared at first as defects in the theory1 might not arise sometimes from a bending or shaking of the instrument1 and from the degrees marked on the limb being really somewhat unequal1 instead of being rigorously equal4 ,accordingly1 the framing and balancing of the instrument1 so as to avoid all possible tremor or flexure1 and the exact division of an arc into equal parts1 became great objects of those who wished to improve astronomical observations4 ,the observer no longer gazed at the stars from a lofty tower1 but placed his telescope on the solid ground1--and braced and balanced it with various contrivances4 ,instead of a quadrant1 an entire circle was introduced 7by ,ramsden27 and various processes were invented for the dividing of instruments4 ,among these we may notice ,troughton's method of dividing2 in which the visual ray of a microscope was substituted for the points of a pair of compasses1 and1 by stepping round the circle1 the partial arcs were made to bear their exact relation to the whole circumference4 #g4 ,astronomy is not the only science which depends on the measurement of angles4 ,crystallography also requires exact measures of this kind2 and the goniometer1 especially that devised by ,wollaston1 supplies the means of obtaining such measures4 ,the science of ,optics also1 in many cases1 requires the measurement of angles4 #h4 ,in the measurement of linear space1 there is no natural standard which offers itself4 ,most of the common measures appear to be taken from some part of the human body2 as a foot1 a cubit1 a fathom2 but such measures cannot possess any precision1 and are altered by convention3 thus there were in ancient times many kinds of cubits2 and in modern ,europe1 there are a great number of different standards of the foot1 as the ,rhenish foot1 the ,paris foot1 the ,english foot4 ,it is #aej very desirable that1 if possible1 some permanent standard1 founded in nature1 should be adopted2 for the conventional measures are lost in the course of ages2 and thus1 dimensions expressed by means of them become unintelligible4 ,two different natural standards have been employed in modern times3 the ,french have referred their measures of length to the total circumference of a meridian of the earth2 a quadrant of this meridian consists of ten million units or metres4 ,the ,english have fixed their linear measure by reference to the length of a pendulum which employs an exact second of time in its small oscillation4 ,both these methods occasion considerable difficulties in carrying them into effect2 and are to be considered mainly as means of recovering the standard if it should ever be lost4 ,for common purposes1 some material standard is adopted as authority for the time3 for example1 the standard which in ,england possessed legal authority up to the year #ahce was preserved in the ,house of ,parliament2 and was lost in the conflagration which destroyed that edifice4 ,the standard of length now generally referred to by men of science in ,england is that which is in the possession of the ,astronomical ,society of ,london4 #i4 ,a standard of length being established1 the artifices for applying it1 and for subdividing it in the most accurate manner1 are nearly the same as in the case of measures of arcs3 as for instance1 the employment of the visual rays of microscopes instead of the legs of compasses and the edges of rules2 the use of micrometers for minute measurements2 and the like4 ,many different modes of avoiding errour in such measurements have been devised by various observers1 according to the nature of the cases with which they had to deal#dc4 ,note #dc3 ,on the precautions employed in astronomical instruments for the measure of space1 see ,sir ,j4 ,herschel's ,astronomy 7in the ,cabinet ,cyclopdia17 ,arts4 #ajc-aaj4 #aj4 7,,iii47 ,measurement of ,time4--,the methods of measuring ,time are not so obvious as the methods of #aea measuring space2 for we cannot apply one portion of time to another1 so as to test their equality4 ,we are obliged to begin by assuming some change as the measure of time4 ,thus the motion of the sun in the sky1 or the length and position of the shadows of objects1 were the first modes of measuring the parts of the day4 ,but what assurance had men1 or what assurance could they have1 that the motion of the sun or of the shadow was uniform8 ,they could have no such assurance1 till they had adopted some measure of smaller times2 which smaller times1 making up larger times by repetition1 they took as the standard of uniformity2--for example1 an hour-glass1 or a clepsydra which answered the same purpose among the ancients4 ,there is no apparent reason why the successive periods measured by the emptying of the hour-glass should be unequal2 they are implicitly accepted as equal2 and by reference to these1 the uniformity of the sun's motion may be verified4 ,but the great improvement in the measurement of time was the use of a pendulum for the purpose by ,galileo1 and the application of this device to clocks by ,huyghens in #afef4 ,for the successive oscillations of a pendulum are rigorously equal1 and a clock is only a train of machinery employed for the purpose of counting these oscillations4 ,by means of this invention1 the measure of time in astronomical observations became as accurate as the measure of space4 #aa4 ,what is the natural unit of time8 ,it was assumed from the first by the ,greek astronomers1 that the sidereal days1 measured by the revolution of a star from any meridian to the same meridian again1 are exactly equal2 and all improvements in the measure of time tended to confirm this assumption4 ,the sidereal day is therefore the natural standard of time4 ,but the solar day1 determined by the diurnal revolution of the sun1 although not rigorously invariable1 as the sidereal day is1 undergoes scarcely any perceptible variation2 and since the course of daily occurrences is regulated by the sun1 it is far more convenient to seek the basis of our unit of time in his motions4 ,accordingly the solar day 7the mean solar day7 is divided into #bd hours1 #aeb and these1 into minutes and seconds2 and this is our scale of time4 ,of such time1 the sidereal day has #bc hours #ef minutes #dji seconds4 ,and it is plain that by such a statement the length of the hour is fixed1 with reference to a sidereal day4 ,the standard of time 7and the standard of space in like manner7 equally answers its purpose1 whether or not it coincides with any whole number of units4 #ab4 ,since the sidereal day is thus the standard of our measures of time1 it becomes desirable to refer to it1 constantly and exactly1 the instruments by which time is measured1 in order that we may secure ourselves against errour4 ,for this purpose1 in astronomical observatories1 observations are constantly made of the transit of stars across the meridian2 the transit instrument with which this is done being adjusted with all imaginable regard to accuracy#ec4 ,note #ec3 ,on the precautions employed in the measure of time by astronomers1 see ,herschel's ,astronomy1 ,art4 #aae-abg4 #ac4 ,when exact measures of time are required in other than astronomical observations1 the same instruments are still used1 namely1 clocks and chronometers4 ,in chronometers1 the regulating part is an oscillating body2 not1 as in clocks1 a pendulum oscillating by the force of gravity1 but a wheel swinging to and fro on its center1 in consequence of the vibrations of a slender coil of elastic wire4 ,to divide time into still smaller portions than these vibrations1 other artifices are used2 some of which will be mentioned under the next head4 #ad4 7,,iv47 ,conversion of ,space and ,time4--,space and time agree in being extended quantities1 which are made up and measured by the repetition of homogeneous parts4 ,if a body move uniformly1 whether in the way of revolving or otherwise1 the space which any point describes1 is proportional to the time of its motion2 and the space and the time may each be taken as a measure of the other4 ,hence in such cases1 by taking space instead of time1 or time instead of #aec space1 we may often obtain more convenient and precise measures1 than we can by measuring directly the element with which we are concerned4 ,the most prominent example of such a conversion1 is the measurement of the ,right ,ascension of stars1 7that is1 their angular distance from a standard meridian#fc on the celestial sphere17 by means of the time employed in their coming to the meridian of the place of observation4 ,since1 as we have already stated1 the visible celestial sphere1 carrying the fixed stars1 revolves with perfect uniformity about the pole2 if we observe the stars as they come in succession to a fixed circle passing through the poles1 the intervals of time between these observations will be proportional to the angles which the meridian circles passing through these stars make at the poles where they meet2 and hence1 if we have the means of measuring time with great accuracy1 we can1 by watching the times of the transits of successive stars across some visible mark in our own meridian1 determine the angular distances of the meridian circles of all the stars from one another4 ,note #fc3 ,a meridian is a circle passing through the poles about which the celestial sphere revolves4 ,the meridian of any place on the earth is that meridian which is exactly over the place4 ,accordingly1 now that the pendulum clock affords astronomers the means of determining time exactly1 a measurement of the ,right ,ascensions of heavenly bodies by means of a clock and a transit instrument1 is a part of the regular business of an observatory4 ,if the sidereal clock be so adjusted that it marks the beginning of its scale of time when the first point of ,right ,ascension is upon the visible meridian of our observatory1 the point of the scale at which the clock points when any other star is in our meridian1 will truly represent the ,right ,ascension of the star4 ,thus as the motion of the stars is our measure of time1 we employ time1 conversely1 as our measure of the places of the stars4 ,the celestial machine and our terrestrial machines correspond to each other in their movements2 and the star steals silently and steadily #aed across our meridian line1 just as the pointer of the clock steals past the mark of the hour4 ,we may judge of the scale of this motion by considering that the full moon employs about two minutes of time in sailing across any fixed line seen against the sky1 transverse to her path3 and all the celestial bodies1 carried along by the revolving sphere1 travel at the same rate4 #ae4 ,in this case1 up to a certain degree1 we render our measures of astronomical angles more exact and convenient by substituting time for space2 but when1 in the very same kind of observation1 we wish to proceed to a greater degree of accuracy1 we find that it is best done by substituting space for time4 ,in observing the transit of a star across the meridian1 if we have the clock within hearing1 we can count the beats of the pendulum by the noise which they make1 and tell exactly at which second of time the passage of the star across the visible thread takes place2 and thus we measure ,right ,ascension by means of time4 ,but our perception of time does not allow us to divide a second into ten parts1 and to pronounce whether the transit takes place three-tenths1 six-tenths1 or seven-tenths of a second after the preceding beat of the clock4 ,this1 however1 can be done by the usual mode of observing the transit of a star4 ,the observer1 listening to the beat of his clock1 fastens his attention upon the star at each beat1 and especially at the one immediately before and the one immediately after the passage of the thread3 and by this means he has these two positions and the position of the thread so far present to his intuition at once1 that he can judge in what proportion the thread is nearer to one position than the other1 and can thus divide the intervening second in its due proportion4 ,thus if he observe that at the beginning of the second the star is on one side of the thread1 and at the end of the second on the other side2 and that the two distances from the thread are as two to three1 he knows that the transit took place at two-fifths 7or four-tenths7 of a second after the former beat4 ,in this way a second of time in astronomical observations may1 by a skilful observer1 be divided into ten equal #aee parts2 although when time is observed as time1 a tenth of a second appears almost to escape our senses4 ,from the above explanation1 it will be seen that the reason why the subdivision is possible in the way thus described1 is this3--that the moment of time thus to be divided is so small1 that the eye and the mind can retain1 to the end of this moment1 the impression of position which it received at the beginning4 ,though the two positions of the star1 and the intermediate thread1 are seen successively1 they can be contemplated by the mind as if they were seen simultaneously3 and thus it is precisely the smallness of this portion of time which enables us to subdivide it by means of space4 #af4 ,there is another case1 of somewhat a different kind1 in which time is employed in measuring space2 namely1 when space1 or the standard of space1 is defined by the length of a pendulum oscillating in a given time4 ,we might in this way define any space by the time which a pendulum of such a length would take in oscillating2 and thus we might speak1 as was observed by those who suggested this device1 of five minutes of cloth1 or a rope half an hour long4 ,we may observe1 however1 that in this case1 the space is not proportional to the time4 ,and we may add1 that though we thus appear to avoid the arbitrary standard of space 7for as we have seen1 the standard of measures of time is a natural one17 we do not do so in fact3 for we assume the invariableness of gravity1 which really varies 7though very slightly17 from place to place4 #ag4 7,v47 ,the ,method of ,repetition in ,measurement4--,in many cases we can give great additional accuracy to our measurements by repeatedly adding to itself the quantity which we wish to measure4 ,thus if we wished to ascertain the exact breadth of a thread1 it might not be easy to determine whether it was one-ninetieth1 or one-ninety-fifth1 or one-hundredth part of an inch2 but if we find that ninety-six such threads placed side by side occupy exactly an inch1 we have the precise measure of the breadth of the thread4 ,in #aef the same manner1 if two clocks are going nearly at the same rate1 we may not be able to distinguish the excess of an oscillation of one of the pendulums over an oscillation of the other3 but when the two clocks have gone for an hour1 one of them may have gained ten seconds upon the other2 thus showing that the proportion of their times of oscillation is #cfaj to #cfjj4 ,in the latter of these instances1 we have the principle of repetition truly exemplified1 because 7as has been justly observed by ,sir ,j4 ,herschel#gc17 there is then 'a juxtaposition of units without errour1'--'one vibration commences exactly where the last terminates1 no part of time being lost or gained in the addition of the units so counted4' ,in space1 this juxtaposition of units without errour cannot be rigorously accomplished1 since the units must be added together by material contact 7as in the above case of the threads17 or in some equivalent manner4 ,yet the principle of repetition has been applied to angular measurement with considerable success in ,borda's ,repeating ,circle4 ,in this instrument1 the angle between two objects which we have to observe1 is repeated along the graduated limb of the circle by turning the telescope from one object to the other1 alternately fastened to the circle 7by its clamp7 and loose from it 7by unclamping74 ,in this manner the errours of graduation may 7theoretically7 be entirely got rid of3 for if an angle repeated nine times be found to go twice round the circle1 it must be exactly eighty degrees3 and where the repetition does not give an exact number of circumferences1 it may still be made to subdivide the errour to any required extent4 ,note #gc3 ,disc4 ,nat4 ,phil4 art4 #aba4 #ah4 ,connected with the principle of repetition1 is the ,method of coincidences or interferences4 ,if we have two ,scales1 on one of which an inch is divided into #aj1 and on the other into #aa equal parts2 and if1 these ,scales being placed side by side1 it appear that the beginning of the latter ,scale is between the #bnd and #crd division of the former1 it may not be apparent #aeg what fraction added to #b determines the place of beginning of the second ,scale as measured on the first4 ,but if it appear also that the #crd division of the second ,scale coincides with a certain division of the first1 7the #eth17 it is certain that #b and three-tenths is the exact place of the beginning of the second ,scale1 measured on the first ,scale4 ,the #crd division of the #aa ,scale will coincide 7or interfere with7 a division of the #aj ,scale1 when the beginning or zero of the #aa divisions is three-tenths of a division beyond the preceding line of the #aj ,scale2 as will be plain on a little consideration4 ,and if we have two ,scales of equal units1 in which each unit is divided into nearly1 but not quite1 the same number of equal parts 7as #aj and #aa1 #ai and #bj1 #bi and #cj17 and one sliding on the other1 it will always happen that some one or other of the division lines will coincide1 or very nearly coincide2 and thus the exact position of the beginning of one unit1 measured on the other scale1 is determined4 ,a sliding scale1 thus divided for the purpose of subdividing the units of that on which it slides1 is called a ,vernier1 from the name of its inventor4 #ai4 ,the same ,principle of ,coincidence or ,interference is applied to the exact measurement of the length of time occupied in the oscillation of a pendulum4 ,if a detached pendulum1 of such a length as to swing in little less than a second1 be placed before the seconds' pendulum of a clock1 and if the two pendulums begin to move together1 the former will gain upon the latter1 and in a little while their motions will be quite discordant4 ,but if we go on watching1 we shall find them1 after a time1 to agree again exactly2 namely1 when the detached pendulum has gained one complete oscillation 7back and forwards17 upon the clock pendulum1 and again coincides with it in its motion4 ,if this happen after #e minutes1 we know that the times of oscillation of the two pendulums are in the proportion of #cjj to #cjb1 and therefore the detached pendulum oscillates in #aej_/aea of a second4 ,the accuracy which can be obtained in the measure of an oscillation by this means is great2 for the clock can be compared 7by #aeh observing transits of the stars or otherwise7 with the natural standard of time1 the sidereal day4 ,and the moment of coincidence of the two pendulums may1 by proper arrangements1 be very exactly determined4 ,we have hitherto spoken of methods of measuring time and space1 but other elements also may be very precisely measured by various means4 #bj4 7,,vi47 ,measurement of ,weight4--,weight1 like space and time1 is a quantity made up by addition of parts1 and may be measured by similar methods4 ,the principle of repetition is applicable to the measurement of weight2 for if two bodies be simultaneously put in the same pan of a balance1 and if they balance pieces in the other pan1 their weights are exactly added4 ,there may be difficulties of practiced workmanship in carrying into effect the mathematical conditions of a perfect balance2 for example1 in securing an exact equality of the effective arms of the beam in all positions4 ,these difficulties are evaded by the ,method of double weighing2 according to which the standard weights1 and the body which is to be weighed1 are successively put in the same pan1 and made to balance by a third body in the opposite scale4 ,by this means the different lengths of the arms of the beam1 and other imperfections of the balance1 become of no consequence#hc4 ,note #hc3 ,for other methods of measuring weights accurately1 see ,faraday's ,chemical ,manipulation1 p4 #be4 #ba4 ,there is no natural ,standard of weight4 ,the conventional weight taken as the standard1 is the weight of a given bulk of some known substance2 for instance1 a cubic foot of water4 ,but in order that this may be definite1 the water must not contain any portion of heterogeneous substance3 hence it is required that the water be distilled water4 #bb4 7,,vii47 ,measurement of ,secondary ,qualities4--,we have already seen#ic that secondary qualities are estimated by means of conventional ,scales1 which refer #aei them to space1 number1 or some other definite expression4 ,thus the ,thermometer measures heat2 the ,musical ,scale1 with or without the aid of number1 expresses the pitch of a note2 and we may have an exact and complete ,scale of ,colours1 pure and impure4 ,we may remark1 however1 that with regard to sound and colour1 the estimates of the ear and the eye are not superseded1 but only assisted3 for if we determine what a note is1 by comparing it with an instrument known to be in tune1 we still leave the ear to decide when the note is in unison with one of the notes of the instrument4 ,and when we compare a colour with our chromatometer1 we judge by the eye which division of the chromatometer it matches4 ,colour and sound have their ,natural ,scales1 which the eye and ear habitually apply2 what science requires is1 that those scales should be systematized4 ,we have seen that several conditions are requisite in such scales of qualities3 the observer's skill and ingenuity are mainly shown in devising such scales and methods of applying them4 ,note #ic3 ,b4 iii4 c4 ii4 ,of the ,measure of ,secondary ,qualities4 #bc4 ,the ,method of ,coincidences is employed in harmonics3 for if two notes are nearly1 but not quite1 in unison1 the coincidences of the vibrations produce an audible undulation in the note1 which is called the howl2 and the exactness of the unison is known by this howl vanishing4 #bd4 7,,viii47 ,manipulation4--,the process of applying practically methods of experiment and observation1 is termed ,manipulation2 and the value of observations depends much upon the proficiency of the observer in this art4 ,this skill appears1 as we have said1 not only in devising means and modes in measuring results1 but also in inventing and executing arrangements by which elements are subjected to such conditions as the investigation requires3 in finding and using some material combination by which nature shall be asked the question which we have in our minds4 ,to do this in any subject may be considered as a peculiar ,art1 but especially in ,chemistry2 where 'many experiments1 and even whole trains of research1 are #afj essentially dependent for success on mere manipulation#ajc4' ,the changes which the chemist has to study1--compositions1 decompositions1 and mutual actions1 affecting the internal structure rather than the external form and motion of bodies1--are not familiarly recognized by common observers1 as those actions are which operate upon the total mass of a body3 and hence it is only when the chemist has become1 to a certain degree1 familiar with his science1 that he has the power of observing4 ,he must learn to interpret the effects of mixture1 heat1 and other ,chemical agencies1 so as to see in them those facts which chemistry makes the basis of her doctrines4 ,and in learning to interpret this language1 he must also learn to call it forth2--to place bodies under the requisite conditions1 by the apparatus of his own laboratory and the operations of his own fingers4 ,to do this with readiness and precision1 is1 as we have said1 an ,art1 both of the mind and of the hand1 in no small degree recondite and difficult4 ,a person may be well acquainted with all the doctrines of chemistry1 and may yet fail in the simplest experiment4 ,how many precautions and observances1 what resource and invention1 what delicacy and vigilance1 are requisite in ,chemical ,manipulation1 may be seen by reference to ,dr4 ,faraday's work on that subject4 ,note #ajc3 ,faraday's ,chemical ,manipulation1 p4 #c4 #be4 ,the same qualities in the observer are requisite in some other departments of science2 for example1 in the researches of ,optics3 for in these1 after the first broad facts have been noticed1 the remaining features of the phenomena are both very complex and very minute2 and require both ingenuity in the invention of experiments1 and a keen scrutiny of their results4 ,we have instances of the application of these qualities in most of the optical experimenters of recent times1 and certainly in no one more than ,sir ,david ,brewster4 ,omitting here all notice of his succeeding labours1 his ,treatise on ,new ,philosophical ,instruments1 published in #ahac1 is an excellent model of the kind of resource #afa and skill of which we now speak4 ,i may mention as an example of this skill1 his mode of determining the refractive power of an irregular fragment of any transparent substance4 ,at first this might appear an impossible problem2 for it would seem that a regular and smooth surface are requisite1 in order that we may have any measurable refraction4 ,but ,sir ,david ,brewster overcame the difficulty by immersing the fragment in a combination of fluids1 so mixed1 that they had the same refractive power as the specimen4 ,the question1 when they had this power1 was answered by noticing when the fragment became so transparent that its surface could hardly be seen2 for this happened when1 the refractive power within and without the fragment being the same1 there was no refraction at the surface4 ,and this condition being obtained1 the refractive power of the fluid1 and therefore of the fragment1 was easily ascertained4 #bf4 7,,ix47 ,the ,education of the ,senses4--,colour and ,musical ,tone are1 as we have seen1 determined by means of the ,senses1 whether or not ,systematical ,scales are used in expressing the observed fact4 ,systematical ,scales of sensible qualities1 however1 not only give precision to the record1 but to the observation4 ,but for this purpose such an ,education of the ,senses is requisite as may enable us to apply the scale immediately4 ,the memory must retain the sensation or perception to which the technical term or degree of the scale refers4 ,thus with regard to colour1 as we have said already#aac1 when we find such terms as tin-white or pinchbeck-brown1 the metallic colour so denoted ought to occur at once to our recollection without delay or search4 ,the observer's senses1 therefore1 must be educated1 at first by an actual exhibition of the standard1 and afterwards by a familiar use of it1 to understand readily and clearly each phrase and degree of the scales which in his observations he has to apply4 ,this is not only the best1 but in many cases the only way in which the observation can be expressed4 ,thus glassy lustre1 fatty lustre1 adamantine lustre1 denote certain kinds of #afb shining in minerals1 which appearances we should endeavour in vain to describe by periphrasis2 and which the terms1 if considered as terms in common language1 would by no means clearly discriminate3 for who1 in common language1 would say that coal has a fatty lustre8 ,but these terms1 in their conventional sense1 are perfectly definite2 and when the eye is once familiarized with this application of them1 are easily and clearly intelligible4 ,note #aac3 ,b4 viii4 c4 iii4 ,terminology4 #bg4 ,the education of the senses1 which is thus requisite in order to understand well the terminology of any science1 must be acquired by an inspection of the objects which the science deals with2 and is1 perhaps1 best promoted by the practical study of ,natural ,history4 ,in the different departments of ,natural ,history1 the descriptions of species are given by means of an extensive technical terminology3 and that education of which we now speak1 ought to produce the effect of making the observer as familiar with each of the terms of this terminology as we are with the words of our common language4 ,the technical terms have a much more precise meaning than other terms1 since they are defined by express convention1 and not learnt by common usage merely4 ,yet though they are thus defined1 not the definition1 but the perception itself1 is that which the term suggests to the proficient4 ,in order to use the terminology to any good purpose1 the student must possess it1 not as a dictionary1 but as a language4 ,the terminology of his sciences must be the natural historian's most familiar tongue4 ,he must learn to think in such language4 ,and when this is achieved1 the terminology1 as ,i have elsewhere said1 though to an uneducated eye cumbrous and pedantical1 is felt to be a useful implement1 not an oppressive burden#abc4 ,the impatient schoolboy looks upon his grammar and vocabulary as irksome and burdensome2 but the accomplished student who has learnt the language by means of them1 knows that they have given him the means of expressing what he thinks1 and #afc even of thinking more precisely4 ,and as the study of language thus gives precision to the thoughts1 the study of ,natural ,history1 and especially of the descriptive part of it1 gives precision to the senses4 ,note #abc3 ,hist4 ,ind4 ,sc4 b4 xvi4 c4 iv4 sect4 #b4 ,the ,education of the ,senses is also greatly promoted by the practical pursuit of any science of experiment and observation1 as chemistry or astronomy4 ,the methods of manipulating1 of which we have just spoken1 in chemistry1 and the methods of measuring extremely minute portions of space and time which are employed in astronomy1 and which are described in the former part of this chapter1 are among the best modes of educating the senses for purposes of scientific observation4 #bh4 ,by the various ,methods of precise observation which we have thus very briefly described1 facts are collected1 of an exact and definite kind2 they are then bound together in general laws1 by the aid of general ideas and of such methods as we have now to consider4 ,it is true1 that the ideas which enable us to combine facts into general propositions1 do commonly operate in our minds while we are still engaged in the office of observing4 ,ideas of one kind or other are requisite to connect our phenomena into facts1 and to give meaning to the terms of our descriptions3 and it frequently happens1 that long before we have collected all the facts which induction requires1 the mind catches the suggestion which some of these ideas offer1 and leaps forwards to a conjectural law while the labour of observation is yet unfinished4 ,but though this actually occurs1 it is easy to see that the process of combining and generalizing facts is1 in the order of nature1 posterior to1 and distinct from1 the process of observing facts4 ,not only is this so1 but there is an intermediate step which1 though inseparable from all successful generalization1 may be distinguished from it in our survey2 and may1 in some degree1 be assisted by peculiar methods4 ,to the consideration of such methods we now proceed4 #afd ,,chapter ,,iii4 ,,of ,,methods ,,of ,,acquiring ,,clear ,,scientific ,,ideas2 and first ,,of ,,intellectual ,,education4 ,,aphorism ,,xxix4 ,the ,methods by which the acquisition of clear ,scientific ,ideas is promoted1 are mainly two2 ,intellectual ,education and ,discussion of ,ideas4 ,,aphorism ,,xxx4 ,the ,idea of ,space becomes more clear by studying ,geometry2 the ,idea of ,force1 by studying ,mechanics2 the ,ideas of ,likeness1 of ,kind1 of ,subordination of ,classes1 by studying ,natural ,history4 ,,aphorism ,,xxxi4 ,elementary ,mechanics should now form a part of intellectual education1 in order that the student may understand the ,theory of ,universal ,gravitation3 for an intellectual education should cultivate such ideas as enable the student to understand the most complete and admirable portions of the knowledge which the human race has attained to4 ,,aphorism ,,xxxii4 ,natural ,history ought to form a part of intellectual education1 in order to correct certain prejudices which arise from cultivating the intellect by means of mathematics alone2 and in order to lead the student to see that the division of things into ,kinds1 and the attribution and use of ,names1 are processes susceptible of great precision4 #afe ,,the ways in which men become masters of those clear and yet comprehensive conceptions which the formation and reception of science require1 are mainly two2 which1 although we cannot reduce them to any exact scheme1 we may still1 in a loose use of the term1 call ,methods of acquiring clear ,ideas4 ,these two ways are ,education and ,discussion4 #a4 7,i47 ,idea of ,space4--,it is easily seen that ,education may do at least something to render our ideas distinct and precise4 ,to learn ,geometry in youth1 tends1 manifestly1 to render our idea of space clear and exact4 ,by such an education1 all the relations1 and all the consequences of this idea1 come to be readily and steadily apprehended2 and thus it becomes easy for us to understand portions of science which otherwise we should by no means be able to comprehend4 ,the conception of similar triangles was to be mastered1 before the disciples of ,thales could see the validity of his method of determining the height of lofty objects by the length of their shadows4 ,the conception of the sphere with its circles had to become familiar1 before the annual motion of the sun and its influence upon the lengths of days could be rightly traced4 ,the properties of circles1 combined with the pure#acc doctrine of motion1 were required as an introduction to the theory of ,epicycles3 the properties of conic sections were needed1 as a preparation for the discoveries of ,kepler4 ,and not only was it necessary that men should possess a knowledge of certain figures and their properties2 but it was equally necessary that they should have the habit of reasoning with perfect steadiness1 precision1 and conclusiveness concerning the relations of space4 ,no small discipline of the mind is requisite1 in most cases1 to accustom it to go1 with complete insight and security1 through the demonstrations respecting intersecting planes and lines1 dihedral and trihedral angles1 which occur in solid geometry4 ,yet how absolutely necessary is a perfect mastery of such reasonings1 to him who is to explain the motions of the moon in #aff latitude and longitude6 ,how necessary1 again1 is the same faculty to the student of crystallography6 ,without mathematical habits of conception and of thinking1 these portions of science are perfectly inaccessible4 ,but the early study of plane and solid geometry gives to all tolerably gifted persons1 the habits which are thus needed4 ,the discipline of following the reasonings of didactic works on this subject1 till we are quite familiar with them1 and of devising for ourselves reasonings of the same kind1 7as1 for instance1 the solutions of problems proposed17 soon gives the mind the power of discoursing with perfect facility concerning the most complex and multiplied relations of space1 and enables us to refer to the properties of all plane and solid figures as surely as to the visible forms of objects4 ,thus we have here a signal instance of the efficacy of education in giving to our ,conceptions that clearness1 which the formation and existence of science indispensably require4 ,note #acc3 ,see ,hist4 ,sc4 ,ideas1 b4 ii4 c4 xiii4 #b4 ,it is not my intention here to enter into the details of the form which should be given to education1 in order that it may answer the purposes now contemplated4 ,but ,i may make a remark1 which the above examples naturally suggest1 that in a mathematical education1 considered as a preparation for furthering or understanding physical science1 ,geometry is to be cultivated1 far rather than ,algebra3--the properties of space are to be studied and reasoned upon as they are in themselves1 not as they are replaced and disguised by symbolical representations4 ,it is true1 that when the student is become quite familiar with elementary geometry1 he may often enable himself to deal in a more rapid and comprehensive manner with the relations of space1 by using the language of symbols and the principles of symbolical calculation3 but this is an ulterior step1 which may be added to1 but can never be substituted for1 the direct cultivation of geometry4 ,the method of symbolical reasoning employed upon subjects of geometry and mechanics1 has certainly achieved some remarkable triumphs in the treatment of the theory of the universe4 ,these successful #afg applications of symbols in the highest problems of physical astronomy appear to have made some teachers of mathematics imagine that it is best to begin the pupil's course with such symbolical generalities4 ,but this mode of proceeding will be so far from giving the student clear ideas of mathematical relations1 that it will involve him in utter confusion1 and probably prevent his ever obtaining a firm footing in geometry4 ,to commence mathematics in such a way1 would be much as if we should begin the study of a language by reading the highest strains of its lyrical poetry4 #c4 7,,ii47 ,idea of ,number1 c4--,the study of mathematics1 as ,i need hardly observe1 developes and renders exact1 our conceptions of the relations of number1 as well as of space4 ,and although1 as we have already noticed1 even in their original form the conceptions of number are for the most part very distinct1 they may be still further improved by such discipline4 ,in complex cases1 a methodical cultivation of the mind in such subjects is needed3 for instance1 questions concerning ,cycles1 and ,intercalations1 and ,epacts1 and the like1 require very great steadiness of arithmetical apprehension in order that the reasoner may deal with them rightly4 ,in the same manner1 a mastery of problems belonging to the science of ,pure ,motion1 or1 as ,i have termed it1 ,mechanism1 requires either great natural aptitude in the student1 or a mind properly disciplined by suitable branches of mathematical study4 #d4 ,arithmetic and ,geometry have long been standard portions of the education of cultured persons throughout the civilized world2 and hence all such persons have been able to accept and comprehend those portions of science which depend upon the idea of space3 for instance1 the doctrine of the globular form of the earth1 with its consequences1 such as the measures of latitude and longitude2--the heliocentric system of the universe in modern1 or the geocentric in ancient times2--the explanation of the rainbow2 and the like4 ,in nations where there is no such education1 these portions of science cannot exist as a part of the general stock of the knowledge of society1 however intelligently they #afh may be pursued by single philosophers dispersed here and there in the community4 #e4 7,,iii47 ,idea of ,force4--,as the idea of ,space is brought out in its full evidence by the study of ,geometry1 so the idea of ,force is called up and developed by the study of the science of ,mechanics4 ,it has already been shown1 in our scrutiny of the ,ideas of the ,mechanical ,sciences1 that ,force1 the ,cause of motion or of equilibrium1 involves an independent ,fundamental ,idea1 and is quite incapable of being resolved into any mere modification of our conceptions of space1 time1 and motion4 ,and in order that the student may possess this idea in a precise and manifest shape1 he must pursue the science of ,mechanics in the mode which this view of its nature demands2--that is1 he must study it as an independent science1 resting on solid elementary principles of its own1 and not built upon some other unmechanical science as its substructure4 ,he must trace the truths of ,mechanics from their own axioms and definitions2 these axioms and definitions being considered as merely means of bringing into play the ,idea on which the science depends4 ,the conceptions of force and matter1 of action and reaction1 of momentum and inertia1 with the reasonings in which they are involved1 cannot be evaded by any substitution of lines or symbols for the conceptions4 ,any attempts at such substitution would render the study of ,mechanics useless as a preparation of the mind for physical science2 and would1 indeed1 except counteracted by great natural clearness of thought on such subjects1 fill the mind with confused and vague notions1 quite unavailing for any purposes of sound reasoning4 ,but1 on the other hand1 the study of ,mechanics1 in its genuine form1 as a branch of education1 is fitted to give a most useful and valuable precision of thought on such subjects2 and is the more to be recommended1 since1 in the general habits of most men's minds1 the mechanical conceptions are tainted with far greater obscurity and perplexity than belongs to the conceptions of number1 space1 and motion4 #f4 ,as habitually distinct conceptions of space and #afi motion were requisite for the reception of the doctrines of formal astronomy1 7the ,ptolemaic and ,copernican system17 so a clear and steady conception of force is indispensably necessary for understanding the ,newtonian system of physical astronomy4 ,it may be objected that the study of ,mechanics as a science has not commonly formed part of a liberal education in ,europe1 and yet that educated persons have commonly accepted the ,newtonian system4 ,but to this we reply1 that although most persons of good intellectual culture have professed to assent to the ,newtonian system of the universe1 yet they have1 in fact1 entertained it in so vague and perplexed a manner as to show very clearly that a better mental preparation than the usual one is necessary1 in order that such persons may really understand the doctrine of universal attraction4 ,i have elsewhere spoken of the prevalent indistinctness of mechanical conceptions#adc2 and need not here dwell upon the indications1 constantly occurring in conversation and in literature1 of the utter inaccuracy of thought on such subjects which may often be detected2 for instance1 in the mode in which many men speak of centrifugal and centripetal forces2--of projectile and central forces2--of the effect of the moon upon the waters of the ocean2 and the like4 ,the incoherence of ideas which we frequently witness on such points1 shows us clearly that1 in the minds of a great number of men1 well educated according to the present standard1 the acceptance of the doctrine of ,universal ,gravitation is a result of traditional prejudice1 not of rational conviction4 ,and those who are ,newtonians on such grounds1 are not at all more intellectually advanced by being ,newtonians in the nineteenth century1 than they would have been by being ,ptolemaics in the fifteenth4 ,note #adc3 ,hist4 ,sc4 ,ideas1 b4 iii4 c4 x4 #g4 ,it is undoubtedly in the highest degree desirable that all great advances in science should become the common property of all cultivated men4 ,and this can only be done by introducing into the course of a liberal education such studies as unfold and fix in men's minds #agj the fundamental ideas upon which the new-discovered truths rest4 ,the progress made by the ancients in geography1 astronomy1 and other sciences1 led them to assign1 wisely and well1 a place to arithmetic and geometry among the steps of an ingenuous education4 ,the discoveries of modern times have rendered these steps still more indispensable2 for we cannot consider a man as cultivated up to the standard of his times1 if he is not only ignorant of1 but incapable of comprehending1 the greatest achievements of the human intellect4 ,and as innumerable discoveries of all ages have thus secured to ,geometry her place as a part of good education1 so the great discoveries of ,newton make it proper to introduce ,elementary ,mechanics as a part of the same course4 ,if the education deserve to be called good1 the pupil will not remain ignorant of those discoveries1 the most remarkable extensions of the field of human knowledge which have ever occurred4 ,yet he cannot by possibility comprehend them1 except his mind be previously disciplined by mechanical studies4 ,the period appears now to be arrived when we may venture1 or rather when we are bound to endeavour1 to include a new class of ,fundamental ,ideas in the elementary discipline of the human intellect4 ,this is indispensable1 if we wish to educe the powers which we know that it possesses1 and to enrich it with the wealth which lies within its reach#aec4 ,note #aec3 ,the ,university of ,cambridge has1 by a recent law1 made an examination in ,elementary ,mechanics requisite for the ,degree of ,b4,a4 #h4 ,by the view which is thus presented to us of the nature and objects of intellectual education1 we are led to consider the mind of man as undergoing a progress from age to age4 ,by the discoveries which are made1 and by the clearness and evidence which1 after a time1 7not suddenly nor soon17 the truths thus discovered acquire1 one portion of knowledge after another becomes elementary2 and if we would really secure this progress1 and make men share in it1 these new portions must be treated as elementary in the constitution of a #aga liberal education4 ,even in the rudest forms of intelligence1 man is immeasurably elevated above the unprogressive brute1 for the idea of number is so far developed that he can count his flock or his arrows4 ,but when number is contemplated in a speculative form1 he has made a vast additional progress2 when he steadily apprehends the relations of space1 he has again advanced2 when in thought he carries these relations into the vault of the sky1 into the expanse of the universe1 he reaches a higher intellectual position4 ,and when he carries into these wide regions1 not only the relations of space and time1 but of cause and effect1 of force and reaction1 he has again made an intellectual advance2 which1 wide as it is at first1 is accessible to all2 and with which all should acquaint themselves1 if they really desire to prosecute with energy the ascending path of truth and knowledge which lies before them4 ,this should be an object of exertion to all ingenuous and hopeful minds4 ,for1 that exertion is necessary1--that after all possible facilities have been afforded1 it is still a matter of toil and struggle to appropriate to ourselves the acquisitions of great discoverers1 is not to be denied4 ,elementary mechanics1 like elementary geometry1 is a study accessible to all3 but like that too1 or perhaps more than that1 it is a study which requires effort and contention of mind1--a forced steadiness of thought4 ,it is long since one complained of this labour in geometry2 and was answered that in that region there is no ,royal ,road4 ,the same is true of ,mechanics1 and must be true of all branches of solid education4 ,but we should express the truth more appropriately in our days by saying that there is no ,popular ,road to these sciences4 ,in the mind1 as in the body1 strenuous exercise alone can give strength and activity4 ,the art of exact thought can be acquired only by the labour of close thinking4 #i4 7,,iv47 ,chemical ,ideas4--,we appear then to have arrived at a point of human progress in which a liberal education of the scientific intellect should include1 besides arithmetic1 elementary geometry and mechanics4 #agb ,the question then occurs to us1 whether there are any other ,fundamental ,ideas1 among those belonging to other sciences1 which ought also to be made part of such an education2--whether1 for example1 we should strive to develope in the minds of all cultured men the ideas of polarity1 mechanical and chemical1 of which we spoke in a former part of this work4 ,the views to which we have been conducted by the previous inquiry lead us to reply that it would not be well at present to make chemical ,polarities1 at any rate1 a subject of elementary instruction4 ,for even the most profound and acute philosophers who have speculated upon this subject1--they who are leading the van in the march of discovery1--do not seem yet to have reduced their thoughts on this subject to a consistency1 or to have taken hold of this idea of ,polarity in a manner quite satisfactory to their own minds4 ,this part of the subject is1 therefore1 by no means ready to be introduced into a course of general elementary education2 for1 with a view to such a purpose1 nothing less than the most thoroughly luminous and transparent condition of the idea will suffice4 ,its whole efficacy1 as a means and object of disciplinal study1 depends upon there being no obscurity1 perplexity1 or indefiniteness with regard to it1 beyond that transient deficiency which at first exists in the learner's mind1 and is to be removed by his studies4 ,the idea of chemical ,polarity is not yet in this condition2 and therefore is not yet fit for a place in education4 ,yet since this idea of ,polarity is the most general idea which enters into chemistry1 and appears to be that which includes almost all the others1 it would be unphilosophical1 and inconsistent with all sound views of science1 to introduce into education some chemical conceptions1 and to omit those which depend upon this idea3 indeed such a partial adoption of the science could hardly take place without not only omitting1 but misrepresenting1 a great part of our chemical knowledge4 ,the conclusion to which we are necessarily led1 therefore1 is this3--that at present chemistry #agc cannot with any advantage1 form a portion of the general intellectual education#afc4 ,note #afc3 ,i do not here stop to prove that an education 7if it be so called7 in which the memory only retains the verbal expression of results1 while the mind does not apprehend the principles of the subject1 and therefore cannot even understand the words in which its doctrines are expressed1 is of no value whatever to the intellect1 but rather1 is highly hurtful to the habits of thinking and reasoning4 #aj4 7,v47 ,natural-,history ,ideas4--,but there remains still another class of ,ideas1 with regard to which we may very properly ask whether they may not advantageously form a portion of a liberal education3 ,i mean the ,ideas of definite ,resemblance and ,difference1 and of one set of resemblances subordinate to another1 which form the bases of the classificatory sciences4 ,these ,ideas are developed by the study of the various branches of ,natural ,history1 as ,botany1 and ,zoology2 and beyond all doubt1 those pursuits1 if assiduously followed1 very materially affect the mental habits4 ,there is this obvious advantage to be looked for from the study of ,natural ,history1 considered as a means of intellectual discipline3--that it gives us1 in a precise and scientific form1 examples of the classing and naming of objects2 which operations the use of common language leads us constantly to perform in a loose and inexact way4 ,in the usual habits of our minds and tongues1 things are distinguished or brought together1 and names are applied1 in a manner very indefinite1 vacillating1 and seemingly capricious3 and we may naturally be led to doubt whether such defects can be avoided2--whether exact distinctions of things1 and rigorous use of words be possible4 ,now upon this point we may receive the instruction of ,natural ,history2 which proves to us1 by the actual performance of the task1 that a precise classification and nomenclature are attainable1 at least for a mass of objects all of the same kind4 ,further1 we also learn from this study1 that there may exist1 not only an exact distinction of kinds of things1 but a series of distinctions1 one set subordinate to another1 and the more general including #agd the more special1 so as to form a system of classification4 ,all these are valuable lessons4 ,if by the study of ,natural ,history we evolve1 in a clear and well defined form1 the conceptions of genus1 species1 and of higher and lower steps of classification1 we communicate precision1 clearness1 and method to the intellect1 through a great range of its operations4 #aa4 ,it must be observed1 that in order to attain the disciplinal benefit which the study of ,natural ,history is fitted to bestow1 we must teach the natural not the artificial classifications2 or at least the natural as well as the artificial4 ,for it is important for the student to perceive that there are classifications1 not merely arbitrary1 founded upon some assumed character1 but natural1 recognized by some discovered character3 he ought to see that our classes being collected according to one mark1 are confirmed by many marks not originally stated in our scheme2 and are thus found to be grouped together1 not by a single resemblance1 but by a mass of resemblances1 indicating a natural affinity4 ,that objects may be collected into such groups1 is a highly important lesson1 which ,natural ,history alone1 pursued as the science of natural classes1 can teach4 #ab4 ,natural ,history has not unfrequently been made a portion of education3 and has in some degree produced such effects as we have pointed out4 ,it would appear1 however1 that its lessons have1 for the most part1 been very imperfectly learnt or understood by persons of ordinary education3 and that there are perverse intellectual habits very commonly prevalent in the cultivated classes1 which ought ere now to have been corrected by the general teaching of ,natural ,history4 ,we may detect among speculative men many prejudices respecting the nature and rules of reasoning1 which arise from pure mathematics having been so long and so universally the instrument of intellectual cultivation4 ,pure ,mathematics reasons from definitions3 whatever term is introduced into her pages1 as a circle1 or a square1 its definition comes along with it3 and this definition is supposed to supply all that the reasoner needs to know1 respecting the term4 #age ,if there be any doubt concerning the validity of the conclusion1 the doubt is resolved by recurring to the definitions4 ,hence it has come to pass that in other subjects also1 men seek for and demand definitions as the most secure foundation of reasoning4 ,the definition and the term defined are conceived to be so far identical1 that in all cases the one may be substituted for the other2 and such a substitution is held to be the best mode of detecting fallacies4 #ac4 ,it has already been shown that even geometry is not founded upon definitions alone3 and we shall not here again analyse the fallacy of this belief in the supreme value of definitions4 ,but we may remark that the study of ,natural ,history appears to be the proper remedy for this erroneous habit of thought4 ,for in every department of ,natural ,history the object of our study is kinds of things1 not one of which kinds can be rigorously defined1 yet all of them are sufficiently definite4 ,in these cases we may indeed give a specific description of one of the kinds1 and may call it a definition2 but it is clear that such a definition does not contain the essence of the thing4 ,we say#agc that the ,rose ,tribe are ',polypetalous dicotyledons1 with lateral styles1 superior simple ovaria1 regular perigynous stamens1 exalbuminous definite seeds1 and alternate stipulate leaves4' ,but no one would say that this was our essential conception of a rose1 to be substituted for it in all cases of doubt or obscurity1 by way of making our reasonings perfectly clear4 ,not only so2 but as we have already seen#ahc1 the definition does not even apply to all the tribe4 ,for the stipul are absent in ,lowea3 the albumen is present in ,neillia3 the fruit of ,spira sorbifolia is capsular4 ,if1 then1 we can possess any certain knowledge in ,natural ,history1 7which no cultivator of the subject will doubt17 it is evident that our knowledge cannot depend on the possibility of laying down exact definitions and reasoning from them4 ,note #agc3 ,lindley's ,nat4 ,syst4 ,bot4 p4 #ha4 ,note #ahc3 ,hist4 ,sc4 ,ideas1 b4 viii4 c4 ii4 sect4 #c4 #ad4 ,but it may be asked1 if we cannot define a #agf word1 or a class of things which a word denotes1 how can we distinguish what it does mean from what it does not mean8 ,how can we say that it signifies one thing rather than another1 except we declare what is its signification8 ,the answer to this question involves the general principle of a natural method of classification1 which has already been stated#aic and need not here be again dwelt on4 ,it has been shown that names of kinds of things 7genera7 associate them according to total resemblances1 not partial characters4 ,the principle which connects a group of objects in natural history is not a definition1 but a type4 ,thus we take as the type of the ,rose family1 it may be1 the common wild rose2 all species which resemble this flower more than they resemble any other group of species are also roses1 and form one genus4 ,all genera which resemble ,roses more than they resemble any other group of genera are of the same family4 ,and thus the ,rose family is collected about some one species1 which is the type or central point of the group4 ,note #aic3 ,hist4 ,sc4 ,ideas1 b4 viii4 c4 ii4 sect4 #c4 ,in such an arrangement1 it may readily be conceived that though the nucleus of each group may cohere firmly together1 the outskirts of contiguous groups may approach1 and may even be intermingled1 so that some species may doubtfully adhere to one group or another4 ,yet this uncertainty does not at all affect the truths which we find ourselves enabled to assert with regard to the general mass of each group4 ,and thus we are taught that there may be very important differences between two groups of objects1 although we are unable to tell where the one group ends and where the other begins2 and that there may be propositions of indisputable truth1 in which it is impossible to give unexceptionable definitions of the terms employed4 #ae4 ,these lessons are of the highest value with regard to all employments of the human mind2 for the mode in which words in common use acquire their meaning1 approaches far more nearly to the ,method of #agg ,type than to the method of definition4 ,the terms which belong to our practical concerns1 or to our spontaneous and unscientific speculations1 are rarely capable of exact definition4 ,they have been devised in order to express assertions1 often very important1 yet very vaguely conceived3 and the signification of the word is extended1 as far as the assertion conveyed by it can be extended1 by apparent connexion or by analogy4 ,and thus1 in all the attempts of man to grasp at knowledge1 we have an exemplification of that which we have stated as the rule of induction1 that ,definition and ,proposition are mutually dependent1 each adjusted so as to give value and meaning to the other3 and this is so1 even when both the elements of truth are defective in precision3 the ,definition being replaced by an incomplete description or a loose reference to a ,type2 and the ,proposition being in a corresponding degree insecure4 #af4 ,thus the study of ,natural ,history1 as a corrective of the belief that definitions are essential to substantial truth1 might be of great use2 and the advantage which might thus be obtained is such as well entitles this study to a place in a liberal education4 ,we may further observe1 that in order that ,natural ,history may produce such an effect1 it must be studied by inspection of the objects themselves1 and not by the reading of books only4 ,its lesson is1 that we must in all cases of doubt or obscurity refer1 not to words or definitions1 but to things4 ,the ,book of ,nature is its dictionary3 it is there that the natural historian looks1 to find the meaning of the words which he uses#bjc4 ,so #agh long as a plant1 in its most essential parts1 is more like a rose than any thing else1 it is a rose4 ,he knows no other definition4 ,note #bjc3 ,it is a curious example of the influence of the belief in definitions1 that elementary books have been written in which ,natural ,history is taught in the way of question and answer1 and consequently by means of words alone4 ,in such a scheme1 of course all objects are defined3 and we may easily anticipate the value of the knowledge thus conveyed4 ,thus1 ',iron is a well-known hard metal1 of a darkish gray colour1 and very elastic3' ',copper is an orange-coloured metal1 more sonorous than any other1 and the most elastic of any except iron4' ,this is to pervert the meaning of education1 and to make it a business of mere words4 #ag4 7,,vi47 ,well-established ,ideas alone to be used4--,we may assert in general what we have elsewhere1 as above1 stated specially with reference to the fundamental principles of chemistry3--no ,ideas are suited to become the elements of elementary education1 till they have not only become perfectly distinct and fixed in the minds of the leading cultivators of the science to which they belong2 but till they have been so for some considerable period4 ,the entire clearness and steadiness of view which is essential to sound science1 must have time to extend itself to a wide circle of disciples4 ,the views and principles which are detected by the most profound and acute philosophers1 are soon appropriated by all the most intelligent and active minds of their own and of the following generations2 and when this has taken place1 7and not till then17 it is right1 by a proper constitution of our liberal education1 to extend a general knowledge of such principles to all cultivated persons4 ,and it follows1 from this view of the matter1 that we are by no means to be in haste to adopt1 into our course of education1 all new discoveries as soon as they are made4 ,they require some time1 in order to settle into their proper place and position in men's minds1 and to show themselves under their true aspects2 and till this is done1 we confuse and disturb1 rather than enlighten and unfold1 the ideas of learners1 by introducing the discoveries into our elementary instruction4 ,hence it was perhaps reasonable that a century should elapse from the time of ,galileo1 before the rigorous teaching of ,mechanics became a general element of intellectual training2 and the doctrine of ,universal ,gravitation was hardly ripe for such an employment till the end of the last century4 ,we must not direct the unformed youthful mind to launch its little bark upon the waters of speculation1 till all the agitation of discovery1 with its consequent fluctuation and controversy1 has well subsided4 #ah4 ,but it may be asked1 ,how is it that time #agi operates to give distinctness and evidence to scientific ideas8 ,in what way does it happen that views and principles1 obscure and wavering at first1 after a while become luminous and steady8 ,can we point out any process1 any intermediate steps1 by which this result is produced8 ,if we can1 this process must be an important portion of the subject now under our consideration4 ,to this we reply1 that the transition from the hesitation and contradiction with which true ideas are first received1 to the general assent and clear apprehension which they afterwards obtain1 takes place through the circulation of various arguments for and against them1 and various modes of presenting and testing them1 all which we may include under the term ,discussion1 which we have already mentioned as the second of the two ways by which scientific views are developed into full maturity4 #ahj ,,chapter ,,iv4 ,,of ,,methods ,,of ,,acquiring ,,clear ,,scientific ,,ideas1 continued4--,,of ,,the ,,discussion ,,of ,,ideas4 ,,aphorism ,,xxxiii4 ,the conception involved in scientific truths have attained the requisite degree of clearness by means of the ,discussions respecting ideas which have taken place among discoverers and their followers4 ,such discussions are very far from being unprofitable to science4 ,they are metaphysical1 and must be so3 the difference between discoverers and barren reasoners is1 that the former employ good1 and the latter bad metaphysics4 #a4 ,,it is easily seen that in every part of science1 the establishment of a new set of ideas has been accompanied with much of doubt and dissent4 ,and by means of discussions so occasioned1 the new conceptions1 and the opinions which involve them1 have gradually become definite and clear4 ,the authors and asserters of the new opinions1 in order to make them defensible1 have been compelled to make them consistent3 in order to recommend them to others1 they have been obliged to make them more entirely intelligible to themselves4 ,and thus the ,terms which formed the main points of the controversy1 although applied in a loose and vacillating manner at first1 have in the end become perfectly definite and exact4 ,the opinions discussed have been1 in their main features1 the same throughout the debate2 but they have at first been dimly1 and at last clearly apprehended3 like the objects of a landscape1 at which we look through a telescope ill adjusted1 till1 by sliding the tube backwards and #aha forwards1 we at last bring it into focus1 and perceive every feature of the prospect sharp and bright4 #b4 ,we have in the last ,book#bac fully exemplified this gradual progress of conceptions from obscurity to clearness by means of ,discussion4 ,we have seen1 too1 that this mode of treating the subject has never been successful1 except when it has been associated with an appeal to facts as well as to reasonings4 ,a combination of experiment with argument1 of observation with demonstration1 has always been found requisite in order that men should arrive at those distinct conceptions which give them substantial truths4 ,the arguments used led to the rejection of undefined1 ambiguous1 self-contradictory notions2 but the reference to facts led to the selection1 or at least to the retention1 of the conceptions which were both true and useful4 ,the two correlative processes1 definition and true assertion1 the formation of clear ideas and the induction of laws1 went on together4 ,note #bac3 ,b4 9999ii4 c4 ii4 ,of the ,explication of ,conceptions4 ,thus those discussions by which scientific conceptions are rendered ultimately quite distinct and fixed1 include both reasonings from ,principles and illustrations from ,facts4 ,at present we turn our attention more peculiarly to the former part of the process2 according to the distinction already drawn1 between the ,explication of ,conceptions and the ,colligation of ,facts4 ,the ,discussions of which we here speak1 are the ,method 7if they may be called a method7 by which the ,explication of ,conceptions is carried to the requisite point among philosophers4 #c4 ,in the ,history of the ,fundamental ,ideas of the ,sciences which forms the ,prelude to this work1 and in the ,history of the ,inductive ,sciences1 ,i have1 in several instances1 traced the steps by which1 historically speaking1 these ,ideas have obtained their ultimate and permanent place in the minds of speculative men4 ,i have thus exemplified the reasonings and controversies which constitute such ,discussion as we now speak of4 ,i have stated1 at considerable length1 the #ahb various attempts1 failures1 and advances1 by which the ideas which enter into the science of ,mechanics were evolved into their present evidence4 ,in like manner we have seen the conception of refracted rays of light1 obscure and confused in ,seneca1 growing clearer in ,roger ,bacon1 more definite in ,descartes1 perfectly distinct in ,newton4 ,the polarity of light1 at first contemplated with some perplexity1 became very distinct to ,malus1 ,young1 and ,fresnel2 yet the phenomena of circular polarization1 and still more1 the circular polarization of fluids1 leave us1 even at present1 some difficulty in fully mastering this conception4 ,the related polarities of electricity and magnetism are not yet fully comprehended1 even by our greatest philosophers4 ,one of ,mr4 ,faraday's late papers 7the ,fourteenth ,series of his ,researches7 is employed in an experimental discussion of this subject1 which leads to no satisfactory result4 ,the controversy between ,,mm4 ,biot and ,ampre#bbc1 on the nature of the ,elementary ,forces in electro-dynamic action1 is another evidence that the discussion of this subject has not yet reached its termination4 ,with regard to chemical polarity1 ,i have already stated that this idea is as yet very far from being brought to an ultimate condition of definiteness2 and the subject of ,chemical ,forces1 7for that whole subject must be included in this idea of polarity17 which has already occasioned much perplexity and controversy1 may easily occasion much more1 before it is settled to the satisfaction of the philosophical world4 ,the ideas of the classificatory sciences also have of late been undergoing much1 and very instructive discussion1 in the controversies respecting the relations and offices of the natural and artificial methods4 ,and with regard to physiological ideas1 it would hardly be too much to say1 that the whole history of physiology up to the present time has consisted of the discussion of the fundamental ideas of the science1 such as ,vital ,forces1 ,nutrition1 ,reproduction1 and the like4 ,we had before us at some length1 in the ,history of ,scientific ,ideas1 a review #ahc of the opposite opinions which have been advanced on this subject2 and we attempted in some degree to estimate the direction in which these ideas are permanently settling4 ,but without attaching any importance to this attempt1 the account there given may at least serve to show1 how important a share in the past progress of this subject the discussion of its ,fundamental ,ideas has hitherto had4 ,note #bbc3 ,hist4 ,ind4 ,sc4 b4 xiii4 c4 #f4 #d4 ,there is one reflexion which is very pointedly suggested by what has been said4 ,the manner in which our scientific ideas acquire their distinct and ultimate form being such as has been described1--always involving much abstract reasoning and analysis of our conceptions1 often much opposite argumentation and debate2--how unphilosophical is it to speak of abstraction and analysis1 of dispute and controversy1 as frivolous and unprofitable processes1 by which true science can never be benefitted2 and how erroneous to put such employments in antithesis with the study of facts6 ,yet some writers are accustomed to talk with contempt of all past controversies1 and to wonder at the blindness of those who did not at first take the view which was established at last4 ,such persons forget that it was precisely the controversy1 which established among speculative men that final doctrine which they themselves have quietly accepted4 ,it is true1 they have had no difficulty in thoroughly adopting the truth2 but that has occurred because all dissentient doctrines have been suppressed and forgotten2 and because systems1 and books1 and language itself1 have been accommodated peculiarly to the expression of the accepted truth4 ,to despise those who have1 by their mental struggles and conflicts1 brought the subject into a condition in which errour is almost out of our reach1 is to be ungrateful exactly in proportion to the amount of the benefit received4 ,it is as if a child1 when its teacher had with many trials and much trouble prepared a telescope so that the vision through it was distinct1 should wonder at his stupidity in pushing the tube of the eye-glass out and in so often4 #ahd #e4 ,again1 some persons condemn all that we have here spoken of as the discussion of ideas1 terming it metaphysical3 and in this spirit1 one writer#bcc has spoken of the 'metaphysical period' of each science1 as preceding the period of 'positive knowledge4' ,but as we have seen1 that process which is here termed 'metaphysical1'--the analysis of our conceptions and the exposure of their inconsistencies1--7accompanied with the study of facts17--has always gone on most actively in the most prosperous periods of each science4 ,there is1 in ,galileo1 ,kepler1 ,gassendi1 and the other fathers of mechanical philosophy1 as much of metaphysics as in their adversaries4 ,the main difference is1 that the metaphysics is of a better kind2 it is more conformable to metaphysical truth4 ,and the same is the case in other sciences4 ,nor can it be otherwise4 ,for all truth1 before it can be consistent with facts1 must be consistent with itself3 and although this rule is of undeniable authority1 its application is often far from easy4 ,the perplexities and ambiguities which arise from our having the same idea presented to us under different aspects1 are often difficult to disentangle3 and no common acuteness and steadiness of thought must be expended on the task4 ,it would be easy to adduce1 from the works of all great discoverers1 passages more profoundly metaphysical than any which are to be found in the pages of barren priori reasoners4 ,note #bcc3 ,m4 ,auguste ,comte1 ,cours de ,philosophie ,positive4 #f4 ,as we have said1 these metaphysical discussions are not to be put in opposition to the study of facts2 but are to be stimulated1 nourished and directed by a constant recourse to experiment and observation4 ,the cultivation of ideas is to be conducted as having for its object the connexion of facts2 never to be pursued as a mere exercise of the subtilty of the mind1 striving to build up a world of its own1 and neglecting that which exists about us4 ,for although man may in this way please himself1 and admire the creations of his own brain1 he can never1 by this course1 hit upon the #ahe real scheme of nature4 ,with his ideas unfolded by education1 sharpened by controversy1 rectified by metaphysics1 he may understand the natural world1 but he cannot invent it4 ,at every step1 he must try the value of the advances he has made in thought1 by applying his thoughts to things4 ,the ,explication of ,conceptions must be carried on with a perpetual reference to the ,colligation of ,facts4 ,having here treated of ,education and ,discussion as the methods by which the former of these two processes is to be promoted1 we have now to explain the methods which science employs in order most successfully to execute the latter4 ,but the ,colligation of ,facts1 as already stated1 may offer to us two steps of a very different kind1--the laws of ,phenomena1 and their ,causes4 ,we shall first describe some of the methods employed in obtaining truths of the former of these two kinds4 #ahf ,,chapter ,v4 ,,analysis ,,of ,,the ,,process ,,of ,,induction4 ,,aphorism ,,xxxiv4 ,the ,process of ,induction may be resolved into three steps2 the ,selection of the ,idea1 the ,construction of the ,conception1 and the ,determination of the ,magnitudes4 ,,aphorism ,,xxxv4 ,these three steps correspond to the determination of the ,independent ,variable1 the ,formula1 and the ,coefficients1 in mathematical investigations2 or to the ,argument1 the ,law1 and the ,numerical ,data1 in a ,table of an astronomical or other ,inequality4 ,,aphorism ,,xxxvi4 ,the ,selection of the ,idea depends mainly upon inventive sagacity3 which operates by suggesting and trying various hypotheses4 ,some inquirers try erroneous hypotheses2 and thus1 exhausting the forms of errour1 form the ,prelude to ,discovery4 ,,aphorism ,,xxxvii4 ,the following ,rules may be given1 in order to the selection of the ,idea for purposes of ,induction3--the ,idea and the ,facts must be homogeneous2 and the ,rule must be tested by the ,facts4 ,,sect4 ,i4--,the ,three ,steps of ,induction4 #a4 ,,when facts have been decomposed and phenomena measured1 the philosopher endeavours to combine them into general laws1 by the aid of #ahg ,ideas and ,conceptions2 these being illustrated and regulated by such means as we have spoken of in the last two chapters4 ,in this task1 of gathering laws of nature from observed facts1 as we have already said#bdc1 the natural sagacity of gifted minds is the power by which the greater part of the successful results have been obtained2 and this power will probably always be more efficacious than any ,method can be4 ,still there are certain methods of procedure which may1 in such investigations1 give us no inconsiderable aid1 and these ,i shall endeavour to expound4 ,note #bdc3 ,b4 ii4 c4 vi4 #b4 ,for this purpose1 ,i remark that the ,colligation of ascertained ,facts into general ,propositions may be considered as containing three steps1 which ,i shall term the ,selection of the ,idea1 the ,construction of the ,conception1 and the ,determination of the ,magnitudes4 ,it will be recollected that by the word ,idea1 7or ,fundamental ,idea17 used in a peculiar sense1 ,i mean certain wide and general fields of intelligible relation1 such as ,space1 ,number1 ,cause1 ,likeness2 while by ,conception ,i denote more special modifications of these ideas1 as a circle1 a square number1 a uniform force1 a like form of flower4 ,now in order to establish any law by reference to facts1 we must select the true ,idea and the true ,conception4 ,for example2 when ,hipparchus found#bec that the distance of the bright star ,spica ,virginis from the equinoxial point had increased by two degrees in about two hundred years1 and desired to reduce this change to a law1 he had first to assign1 if possible1 the idea on which it depended2--whether it was regulated for instance1 by space1 or by time2 whether it was determined by the positions of other stars at each moment1 or went on progressively with the lapse of ages4 ,and when there was found reason to select time as the regulative idea of this change1 it was then to be determined how the change went on with the time2--whether uniformly1 or in some other manner3 the conception1 or the rule of the progression1 was to be #ahh rightly constructed4 ,finally1 it being ascertained that the change did go on uniformly1 the question then occurred what was its amount3--whether exactly a degree in a century1 or more1 or less1 and how much3 and thus the determination of the magnitude completed the discovery of the law of phenomena respecting this star4 ,note #bec3 ,hist4 ,ind4 ,sc4 b4 iii4 c4 iv4 sect4 #c4 #c4 ,steps similar to these three may be discerned in all other discoveries of laws of nature4 ,thus1 in investigating the laws of the motions of the sun1 moon or planets1 we find that these motions may be resolved1 besides a uniform motion1 into a series of partial motions1 or ,inequalities2 and for each of these ,inequalities1 we have to learn upon what it directly depends1 whether upon the progress of time only1 or upon some configuration of the heavenly bodies in space2 then1 we have to ascertain its law2 and finally1 we have to determine what is its amount4 ,in the case of such ,inequalities1 the fundamental element on which the ,inequality depends1 is called by mathematicians the ,argument4 ,and when the ,inequality has been fully reduced to known rules1 and expressed in the form of a ,table1 the ,argument is the fundamental ,series of ,numbers which stands in the margin of the ,table1 and by means of which we refer to the other ,numbers which express the ,inequality4 ,thus1 in order to obtain from a ,solar ,table the ,inequality of the sun's annual motion1 the ,argument is the ,number which expresses the day of the year2 the ,inequalities for each day being 7in the ,table7 ranged in a line corresponding to the days4 ,moreover1 the ,argument of an ,inequality being assumed to be known1 we must1 in order to calculate the ,table1 that is1 in order to exhibit the law of nature1 know also the ,law of the ,inequality1 and its ,amount4 ,and the investigation of these three things1 the ,argument1 the ,law1 and the ,amount of the ,inequality1 represents the three steps above described1 the ,selection of the ,idea1 the ,construction of the ,conception1 and the ,determination of the ,magnitude4 #d4 ,in a great body of cases1 mathematical language and calculation are used to express the connexion #ahi between the general law and the special facts4 ,and when this is done1 the three steps above described may be spoken of as the ,selection of the ,independent ,variable1 the ,construction of the ,formula1 and the ,determination of the ,coefficients4 ,it may be worth our while to attend to an exemplification of this4 ,suppose then1 that1 in such observations as we have just spoken of1 namely1 the shifting of a star from its place in the heavens by an unknown law1 astronomers had1 at the end of three successive years1 found that the star had removed by #c1 by #h1 and by #ae minutes from its original place4 ,suppose it to be ascertained also1 by methods of which we shall hereafter treat1 that this change depends upon the time2 we must then take the time1 7which we may denote by the symbol t17 for the independent variable4 ,but though the star changes its place with the time1 the change is not proportional to the time2 for its motion which is only #c minutes in the first year1 is #e minutes in the second year1 and #g in the third4 ,but it is not difficult for a person a little versed in mathematics to perceive that the series #c1 #h1 #ae1 may be obtained by means of two terms1 one of which is proportional to the time1 and the other to the square of the time2 that is1 it is expressed by the formula at btt4 ,the question then occurs1 what are the values of the coefficients a and b2 and a little examination of the case shows us that a must be #b1 and b1 #a3 so that the formula is #bt tt4 ,indeed if we add together the series #b1 #d1 #f1 which expresses a change proportional to the time1 and #a1 #d1 #i1 which is proportional to the square of the time1 we obtain the series #c1 #h1 #ae1 which is the series of numbers given by observation4 ,and thus the three steps which give us the ,idea1 the ,conception1 and the ,magnitudes2 or the ,argument1 the ,law1 and the ,amount1 of the change2 give us the ,independent ,variable1 the ,formula1 and the ,coefficients1 respectively4 ,we now proceed to offer some suggestions of methods by which each of these steps may be in some degree promoted4 #aij ,,sect4 ,,ii4--,of the ,selection of the ,fundamental ,idea4 #e4 ,when we turn our thoughts upon any assemblage of facts1 with a view of collecting from them some connexion or law1 the most important step1 and at the same time that in which rules can least aid us1 is the ,selection of the ,idea by which they are to be collected4 ,so long as this idea has not been detected1 all seems to be hopeless confusion or insulated facts2 when the connecting idea has been caught sight of1 we constantly regard the facts with reference to their connexion1 and wonder that it should be possible for any one to consider them in any other point of view4 ,thus the different seasons1 and the various aspects of the heavenly bodies1 might at first appear to be direct manifestations from some superior power1 which man could not even understand3 but it was soon found that the ideas of time and space1 of motion and recurrence1 would give coherency to many of the phenomena4 ,yet this took place by successive steps4 ,eclipses1 for a long period1 seemed to follow no law2 and being very remarkable events1 continued to be deemed the indications of a supernatural will1 after the common motions of the heavens were seen to be governed by relations of time and space4 ,at length1 however1 the ,chaldeans discovered that1 after a period of eighteen years1 similar sets of eclipses recur2 and1 thus selecting the idea of time1 simply1 as that to which these events were to be referred1 they were able to reduce them to rule2 and from that time1 eclipses were recognized as parts of a regular order of things4 ,we may1 in the same manner1 consider any other course of events1 and may enquire by what idea they are bound together4 ,for example1 if we take the weather1 years peculiarly wet or dry1 hot and cold1 productive and unproductive1 follow each other in a manner which1 at first sight at least1 seems utterly lawless and irregular4 ,now can we in any way discover some rule and order in these occurrences8 ,is there1 for example1 in these events1 as in eclipses1 a certain cycle of years1 after which like #aia seasons come round again8 or does the weather depend upon the force of some extraneous body--for instance1 the moon--and follow in some way her aspects8 or would the most proper way of investigating this subject be to consider the effect of the moisture and heat of various tracts of the earth's surface upon the ambient air8 ,it is at our choice to try these and other modes of obtaining a science of the weather3 that is1 we may refer the phenomena to the idea of time1 introducing the conception of a cycle2--or to the idea of external force1 by the conception of the moon's action2--or to the idea of mutual action1 introducing the conceptions of thermotical and atmological agencies1 operating between different regions of earth1 water1 and air4 #f4 ,it may be asked1 ,how are we to decide in such alternatives8 ,how are we to select the one right idea out of several conceivable ones8 ,to which we can only reply1 that this must be done by trying which will succeed4 ,if there really exist a cycle of the weather1 as well as of eclipses1 this must be established by comparing the asserted cycle with a good register of the seasons1 of sufficient extent4 ,or if the moon really influence the meteorological conditions of the air1 the asserted influence must be compared with the observed facts1 and so accepted or rejected4 ,when ,hipparchus had observed the increase of longitude of the stars1 the idea of a motion of the celestial sphere suggested itself as the explanation of the change2 but this thought was verified only by observing several stars4 ,it was conceivable that each star should have an independent motion1 governed by time only1 or by other circumstances1 instead of being regulated by its place in the sphere2 and this possibility could be rejected by trial alone4 ,in like manner1 the original opinion of the composition of bodies supposed the compounds to derive their properties from the elements according to the law of likeness2 but this opinion was overturned by a thousand facts2 and thus the really applicable ,idea of ,chemical ,composition was introduced in modern times4 ,in what has already been said on the ,history of ,ideas1 we have seen how each science was in a state #aib of confusion and darkness till the right idea was introduced4 #g4 ,no general method of evolving such ideas can be given4 ,such events appear to result from a peculiar sagacity and felicity of mind2--never without labour1 never without preparation2--yet with no constant dependence upon preparation1 or upon labour1 or even entirely upon personal endowments4 ,newton explained the colours which refraction produces1 by referring each colour to a peculiar angle of refraction1 thus introducing the right idea4 ,but when the same philosopher tried to explain the colours produced by diffraction1 he erred1 by attempting to apply the same idea1 7the course of a single ray17 instead of applying the truer idea1 of the interference of two rays4 ,newton gave a wrong rule for the double refraction of ,iceland spar1 by making the refraction depend on the edges of the rhombohedron3 ,huyghens1 more happy1 introduced the idea of the axis of symmetry of the solid1 and thus was able to give the true law of the phenomena4 #h4 ,although the selected idea is proved to be the right one1 only when the true law of nature is established by means of it1 yet it often happens that there prevails a settled conviction respecting the relation which must afford the key to the phenomena1 before the selection has been confirmed by the laws to which it leads4 ,even before the empirical laws of the tides were made out1 it was not doubtful that these laws depended upon the places and motions of the sun and moon4 ,we know that the crystalline form of a body must depend upon its chemical composition1 though we are as yet unable to assign the law of this dependence4 ,indeed in most cases of great discoveries1 the right idea to which the facts were to be referred1 was selected by many philosophers1 before the decisive demonstration that it was the right idea1 was given by the discoverer4 ,thus ,newton showed that the motions of the planets might be explained by means of a central force in the sun3 but though he established1 he did not first select the idea involved in the conception of a #aic central force4 ,the idea had already been sufficiently pointed out1 dimly by ,kepler1 more clearly by ,borelli1 ,huyghens1 ,wren1 and ,hooke4 ,indeed this anticipation of the true idea is always a principal part of that which1 in the ,history of the ,sciences1 we have termed the ,prelude of a ,discovery4 ,the two steps of proposing a philosophical problem1 and of solving it1 are1 as we have elsewhere said1 both important1 and are often performed by different persons4 ,the former step is1 in fact1 the ,selection of the ,idea4 ,in explaining any change1 we have to discover first the ,argument1 and then the ,law of the change4 ,the selection of the ,argument is the step of which we here speak2 and is that in which inventiveness of mind and justness of thought are mainly shown4 #i4 ,although1 as we have said1 we can give few precise directions for this cardinal process1 the ,selection of the ,idea1 in speculating on phenomena1 yet there is one ,rule which may have its use3 it is this3--,the idea and the facts must be homogeneous3 the elementary ,conceptions1 into which the facts have been decomposed1 must be of the same nature as the ,idea by which we attempt to collect them into laws4 ,thus1 if facts have been observed and measured by reference to space1 they must be bound together by the idea of space3 if we would obtain a knowledge of mechanical forces in the solar system1 we must observe mechanical phenomena4 ,kepler erred against this rule in his attempts at obtaining physical laws of the system2 for the facts which he took were the velocities1 not the changes of velocity1 which are really the mechanical facts4 ,again1 there has been a transgression of this ,rule committed by all chemical philosophers who have attempted to assign the relative position of the elementary particles of bodies in their component molecules4 ,for their purpose has been to discover the relations of the particles in space2 and yet they have neglected the only facts in the constitution of bodies which have a reference to space--namely1 crystalline form1 and optical properties4 ,no progress can be made in the theory of the elementary structure of bodies1 #aid without making these classes of facts the main basis of our speculations4 #aj4 ,the only other ,rule which ,i have to offer on this subject1 is that which ,i have already given3--the ,idea must be tested by the facts4 ,it must be tried by applying to the facts the conceptions which are derived from the idea1 and not accepted till some of these succeed in giving the law of the phenomena4 ,the justice of the suggestion cannot be known otherwise than by making the trial4 ,if we can discover a true law by employing any conceptions1 the idea from which these conceptions are derived is the right one2 nor can there be any proof of its rightness so complete and satisfactory1 as that we are by it led to a solid and permanent truth4 ,this1 however1 can hardly be termed a ,rule2 for when we would know1 to conjecture and to try the truth of our conjecture by a comparison with the facts1 is the natural and obvious dictate of common sense4 ,supposing the ,idea which we adopt1 or which we would try1 to be now fixed upon1 we still have before us the range of many ,conceptions derived from it2 many ,formul may be devised depending on the same ,independent ,variable1 and we must now consider how our selection among these is to be made4 #aie ,,chapter ,,vi4 ,,general ,,rules ,,for ,,the ,,construction ,,of ,,the ,,conception4 ,,aphorism ,,xxxviii4 ,the ,construction of the ,conception very often includes1 in a great measure1 the ,determination of the ,magnitudes4 ,,aphorism ,,xxxix4 ,when a series of progressive numbers is given as the result of observation1 it may generally be reduced to law by combinations of arithmetical and geometrical progressions4 ,,aphorism ,,xl4 ,a true formula for a progressive series of numbers cannot commonly be obtained from a narrow range of observations4 ,,aphorism ,,xli4 ,recurrent series of numbers must1 in most cases1 be expressed by circular formul4 ,,aphorism ,,xlii4 ,the true construction of the conception is frequently suggested by some hypothesis2 and in these cases1 the hypothesis may be useful1 though containing superfluous parts4 ,i4 ,,in speaking of the discovery of laws of nature1 those which depend upon quantity1 as number1 space1 and the like1 are most prominent and most easily conceived1 and therefore in speaking of such researches1 we shall often use language which applies peculiarly to #aif the cases in which quantities numerically measurable are concerned1 leaving it for a subsequent task to extend our principles to ideas of other kinds4 ,hence we may at present consider the ,construction of a ,conception which shall include and connect the facts1 as being the construction of a ,mathematical ,formula1 coinciding with the numerical expression of the facts2 and we have to consider how this process can be facilitated1 it being supposed that we have already before us the numerical measures given by observation4 #b4 ,we may remark1 however1 that the construction of the right ,formula for any such case1 and the determination of the ,coefficients of such formula1 which we have spoken of as two separate steps1 are in practice almost necessarily simultaneous2 for the near coincidence of the results of the theoretical rule with the observed facts confirms at the same time the ,formula and its ,coefficients4 ,in this case also1 the mode of arriving at truth is to try various hypotheses2--to modify the hypotheses so as to approximate to the facts1 and to multiply the facts so as to test the hypotheses4 ,the ,independent ,variable1 and the ,formula which we would try1 being once selected1 mathematicians have devised certain special and technical processes by which the value of the coefficients may be determined4 ,these we shall treat of in the next ,chapter2 but in the mean time we may note1 in a more general manner1 the mode in which1 in physical researches1 the proper formula may be obtained4 #c4 ,a person somewhat versed in mathematics1 having before him a series of numbers1 will generally be able to devise a formula which approaches near to those numbers4 ,if1 for instance1 the series is constantly progressive1 he will be able to see whether it more nearly resembles an arithmetical or a geometrical progression4 ,for example1 ,,mm4 ,dulong and ,petit1 in their investigation of the law of cooling of bodies1 obtained the following series of measures4 ,a thermometer1 made hot1 was placed in an enclosure of which the temperature was #j degrees1 and the rapidity of #aig cooling of the thermometer was noted for many temperatures4 ,it was found that ,for the temperature #bdj the rapidity of cooling was #ajfi #bbj #hha #bjj #gdj #ahj #faj #afj #dhi #adj #chh and so on4 ,now this series of numbers manifestly increases with greater rapidity as we proceed from the lower to the higher parts of the scale4 ,the numbers do not1 however1 form a geometrical series1 as we may easily ascertain4 ,but if we were to take the differences of the successive terms we should find them to be-- #ahh1 #ada1 #acj1 #aba1 #aja1 c4 and these numbers are very nearly the terms of a geometric series4 ,for if we divide each term by the succeeding one1 we find these numbers1 #acc1 #aji1 #ajg1 #abj1 #abg1 in which there does not appear to be any constant tendency to diminish or increase4 ,and we shall find that a geometrical series in which the ratio is #aafe1 may be made to approach very near to this series1 the deviations from it being only such as may be accounted for by conceiving them as errours of observation4 ,in this manner a certain formula#bfc is obtained1 giving results #aih which very nearly coincide with the observed facts1 as may be seen in the margin4 ,note #bfc3 ,the formula is v #bjcg7;at - #a7 where v is the velocity of cooling1 t the temperature of the thermometer expressed in degrees1 and a is the quantity1 #ajjgg4 ,the degree of coincidence is as follows3-- ,excess of temperature of ,observed ,calculated the thermometer1 or values values values of t4 of v4 of v4 #bdj #ajfi #ajfh #bbj #hha #hhi #bjj #gdj #gcd #ahj #faj #fjc #afj #dhi #dhg #adj #chh #chi #abj #cjb #cje #ajj #bcj #bcc #hj #agd #agb ,the physical law expressed by the formula just spoken of is this3--that when a body is cooling in an empty inclosure which is kept at a constant temperature1 the quickness of the cooling1 for excesses of temperature in arithmetical progression1 increases as the terms of a geometrical progression1 diminished by a constant number4 #d4 ,in the actual investigation of ,dulong and ,petit1 however1 the formula was not obtained in precisely the manner just described4 ,for the quickness of cooling depends upon two elements1 the temperature of the hot body and the temperature of the inclosure2 not merely upon the excess of one of these over the other4 ,and it was found most convenient1 first1 to make such experiments as should exhibit the dependence of the velocity of cooling upon the temperature of the enclosure2 which dependence is contained in the following law3--,the quickness of cooling of a thermometer in vacuo for a constant excess of temperature1 increases in geometric progression1 when the temperature of the inclosure increases in arithmetic progression4 ,from this law the preceding one follows by necessary consequence#bgc4 ,note #bgc3 ,for if be the temperature of the inclosure1 and t the excess of temperature of the hot body1 it appears1 by this law1 that the radiation of heat is as a4 ,and hence the quickness of cooling1 which is as the excess of radiation1 is as at - a2 that is1 as a7at - #a7 which agrees with the formula given in the last note4 ,the whole of this series of researches of ,dulong and ,petit is full of the most beautiful and instructive artifices for the construction of the proper formul in physical research4 ,this example may serve to show the nature of the artifices which may be used for the construction of formul1 when we have a constantly progressive series of numbers to represent4 ,we must not only endeavour by trial to contrive a formula which will answer the conditions1 but we must vary our experiments so as to determine1 first one factor or portion of the formula1 and then the other2 and we must use the most #aii probable hypothesis as means of suggestion for our formul4 #e4 ,in a progressive series of numbers1 unless the formula which we adopt be really that which expresses the law of nature1 the deviations of the formula from the facts will generally become enormous1 when the experiments are extended into new parts of the scale4 ,true formul for a progressive series of results can hardly ever be obtained from a very limited range of experiments3 just as the attempt to guess the general course of a road or a river1 by knowing two or three points of it in the neighbourhood of one another1 would generally fail4 ,in the investigation respecting the laws of the cooling of bodies just noticed1 one great advantage of the course pursued by the experimenters was1 that their experiments included so great a range of temperatures4 ,the attempts to assign the law of elasticity of steam deduced from experiments made with moderate temperatures1 were found to be enormously wrong1 when very high temperatures were made the subject of experiment4 ,it is easy to see that this must be so3 an arithmetical and a geometrical series may nearly coincide for a few terms moderately near each other3 but if we take remote corresponding terms in the two series1 one of these will be very many times the other4 ,and hence1 from a narrow range of experiments1 we may infer one of these series when we ought to infer the other2 and thus obtain a law which is widely erroneous4 #f4 ,in ,astronomy1 the series of observations which we have to study are1 for the most part1 not progressive1 but recurrent4 ,the numbers observed do not go on constantly increasing2 but after increasing up to a certain amount they diminish2 then1 after a certain space1 increase again2 and so on1 changing constantly through certain cycles4 ,in cases in which the observed numbers are of this kind1 the formula which expresses them must be a circular function1 of some sort or other2 involving1 for instance1 sines1 tangents1 and other forms of calculation1 which have recurring values when the angle on which they depend goes on constantly #bjj increasing4 ,the main business of formal astronomy consists in resolving the celestial phenomena into a series of terms of this kind1 in detecting their arguments1 and in determining their coefficients4 #g4 ,in constructing the formul by which laws of nature are expressed1 although the first object is to assign the ,law of the ,phenomena1 philosophers have1 in almost all cases1 not proceeded in a purely empirical manner1 to connect the observed numbers by some expression of calculation1 but have been guided1 in the selection of their formula1 by some ,hypothesis respecting the mode of connexion of the facts4 ,thus the formula of ,dulong and ,petit above given was suggested by the ,theory of ,exchanges2 the first attempts at the resolution of the heavenly motions into circular functions were clothed in the hypothesis of ,epicycles4 ,and this was almost inevitable4 ',we must confess1' says ,copernicus#bhc1 'that the celestial motions are circular1 or compounded of several circles1 since their inequalities observe a fixed law1 and recur in value at certain intervals1 which could not be except they were circular3 for a circle alone can make that quantity which has occurred recur again4' ,in like manner the first publication of the ,law of the ,sines1 the true formula of optical refraction1 was accompanied by ,descartes with an hypothesis1 in which an explanation of the law was pretended4 ,in such cases1 the mere comparison of observations may long fail in suggesting the true formul4 ,the fringes of shadows and other diffracted colours were studied in vain by ,newton1 ,grimaldi1 ,comparetti1 the elder ,herschel1 and ,mr4 ,brougham1 so long as these inquirers attempted merely to trace the laws of the facts as they appeared in themselves2 while ,young1 ,fresnel1 ,fraunhofer1 ,schwerdt1 and others1 determined these laws in the most rigorous manner1 when they applied to the observations the ,hypothesis of ,interferences4 ,note #bhc3 ,de ,rev4 l4 i4 c4 iv4 #h4 ,but with all the aid that ,hypotheses and ,calculation can afford1 the construction of true formul1 in #bja those cardinal discoveries by which the progress of science has mainly been caused1 has been a matter of great labour and difficulty1 and of good fortune added to sagacity4 ,in the ,history of ,science1 we have seen how long and how hard ,kepler laboured1 before he converted the formula for the planetary motions1 from an epicyclical combination1 to a simple ellipse4 ,the same philosopher1 labouring with equal zeal and perseverance to discover the formula of optical refraction1 which now appears to us so simple1 was utterly foiled4 ,malus sought in vain the formula determining the ,angle at which a transparent surface polarizes light3 ,sir ,d4 ,brewster#bic1 with a happy sagacity1 discovered the formula to be simply this1 that the index of refraction is the tangent of the angle of polarization4 ,note #bic3 ,hist4 ,ind4 ,sc4 b4 ix4 c4 vi4 ,though we cannot give rules which will be of much service when we have thus to divine the general form of the relation by which phenomena are connected1 there are certain methods by which1 in a narrower field1 our investigations may be materially promoted2--certain special methods of obtaining laws from ,observations4 ,of these we shall now proceed to treat4 #bjb ,,chapter ,,vii4 ,,special ,,methods ,,of ,,induction ,,applicable ,,to ,,quantity4 ,,aphorism ,,xliii4 ,there are special ,methods of ,induction applicable to ,quantity2 of which the principal are1 the ,method of ,curves1 the ,method of ,means1 the ,method of ,least ,squares1 and the ,method of ,residues4 ,,aphorism ,,xliv4 ,the ,method of ,curves consists in drawing a curve of which the observed quantities are the ,ordinates1 the quantity on which the change of these quantities depends being the ,abscissa4 ,the efficacy of this ,method depends upon the faculty which the eye possesses1 of readily detecting regularity and irregularity in forms4 ,the ,method may be used to detect the ,laws which the observed quantities follow3 and also1 when the ,observations are inexact1 it may be used to correct these ,observations1 so as to obtain data more true than the observed facts themselves4 ,,aphorism ,,xlv4 ,the ,method of ,means gets rid of irregularities by taking the arithmetical mean of a great number of observed quantities4 ,its efficacy depends upon this2 that in cases in which observed quantities are affected by other inequalities1 besides that of which we wish to determine the law1 the excesses above and defects below the quantities which the law in question would produce1 will1 in a collection of many observations1 balance each other4 #bjc ,,aphorism ,,xlvi4 ,the ,method of ,least ,squares is a ,method of ,means1 in which the mean is taken according to the condition1 that the sum of the squares of the errours of observation shall be the least possible which the law of the facts allows4 ,it appears1 by the ,doctrine of ,chances1 that this is the most probable mean4 ,,aphorism ,,xlvii4 ,the ,method of ,residues consists in subtracting1 from the quantities given by ,observation1 the quantity given by any ,law already discovered2 and then examining the remainder1 or ,residue1 in order to discover the leading ,law which it follows4 ,when this second ,law has been discovered1 the quantity given by it may be subtracted from the first ,residue2 thus giving a ,second ,residue1 which may be examined in the same manner2 and so on4 ,the efficacy of this method depends principally upon the circumstance of the ,laws of variation being successively smaller and smaller in amount 7or at least in their mean effect72 so that the ulterior undiscovered ,laws do not prevent the ,law in question from being prominent in the observations4 ,,aphorism ,,xlviii4 ,the ,method of ,means and the ,method of ,least ,squares cannot be applied without our knowing the ,arguments of the ,inequalities which we seek4 ,the ,method of ,curves and the ,method of ,residues1 when the ,arguments of the principal ,inequalities are known1 often make it easy to find the others4 ,,in cases where the phenomena admit of numerical measurement and expression1 certain mathematical methods may be employed to facilitate and give accuracy to the determination of the formula by which the observations are connected into laws4 ,among the most usual and important of these ,methods are the following3--#bjd ,i4 ,the ,method of ,curves4 ,,ii4 ,the ,method of ,means4 ,,iii4 ,the ,method of ,least ,squares4 ,,iv4 ,the ,method of ,residues4 ,,sect4 ,i4--,the ,method of ,curves4 #a4 ,,the ,method of ,curves proceeds upon this basis2 that when one quantity undergoes a series of changes depending on the progress of another quantity1 7as1 for instance1 the ,deviation of the ,moon from her equable place depends upon the progress of ,time17 this dependence may be expressed by means of a curve4 ,in the language of mathematicians1 the variable quantity1 whose changes we would consider1 is made the ordinate of the curve1 and the quantity on which the changes depend is made the abscissa4 ,in this manner1 the curve will exhibit in its form a series of undulations1 rising and falling so as to correspond with the alternate ,increase and ,diminution of the quantity represented1 at intervals of ,space which correspond to the intervals of ,time1 or other quantity by which the changes are regulated4 ,thus1 to take another example1 if we set up1 at equal intervals1 a series of ordinates representing the ,height of all the successive ,high ,waters brought by the tides at a given place1 for a year1 the curve which connects the summits of all these ordinates will exhibit a series of undulations1 ascending and descending once in about each ,fortnight2 since1 in that interval1 we have1 in succession1 the high spring tides and the low neap tides4 ,the curve thus drawn offers to the eye a picture of the order and magnitude of the changes to which the quantity under contemplation1 7the height of high water17 is subject4 #b4 ,now the peculiar facility and efficacy of the ,method of ,curves depends upon this circumstance2--that order and regularity are more readily and clearly recognized1 when thus exhibited to the eye in a picture1 than they are when presented to the mind in any other manner4 ,to detect the relations of ,number considered directly as ,number1 is not easy3 and we might #bje contemplate for a long time a ,table of recorded ,numbers without perceiving the order of their increase and diminution1 even if the law were moderately simple2 as any one may satisfy himself by looking at a ,tide ,table4 ,but if these ,numbers are expressed by the magnitude of ,lines1 and if these ,lines are arranged in regular order1 the eye readily discovers the rule of their changes3 it follows the curve which runs along their extremities1 and takes note of the order in which its convexities and concavities succeed each other1 if any order be readily discoverable4 ,the separate observations are in this manner compared and generalized and reduced to rule by the eye alone4 ,and the eye1 so employed1 detects relations of order and succession with a peculiar celerity and evidence4 ,if1 for example1 we thus arrive as ordinates the prices of corn in each year for a series of years1 we shall see the order1 rapidity1 and amount of the increase and decrease of price1 far more clearly than in any other manner4 ,and if there were any recurrence of increase and decrease at stated intervals of years1 we should in this manner perceive it4 ,the eye1 constantly active and busy1 and employed in making into shapes the hints and traces of form which it contemplates1 runs along the curve thus offered to it2 and as it travels backwards and forwards1 is ever on the watch to detect some resemblance or contrast between one part and another4 ,and these resemblances and contrasts1 when discovered1 are the images of ,laws of ,phenomena2 which are made manifest at once by this artifice1 although the mind could not easily catch the indications of their existence1 if they were not thus reflected to her in the clear mirror of ,space4 ,thus when we have a series of good ,observations1 and know the argument upon which their change of magnitude depends1 the ,method of ,curves enables us to ascertain1 almost at a glance1 the law of the change2 and by further attention1 may be made to give us a formula with great accuracy4 ,the ,method enables us to perceive1 among our observations1 an order1 which without the method1 is concealed in obscurity and perplexity4 #bjf #c4 ,but the ,method of ,curves not only enables us to obtain laws of nature from good ,observations1 but also1 in a great degree1 from observations which are very imperfect4 ,for the imperfection of observations may in part be corrected by this consideration2--that though they may appear irregular1 the correct facts which they imperfectly represent1 are really regular4 ,and the ,method of ,curves enables us to remedy this apparent irregularity1 at least in part4 ,for when ,observations thus imperfect are laid down as ,ordinates1 and their extremities connected by a line1 we obtain1 not a smooth and flowing curve1 such as we should have if the observations contained only the rigorous results of regular laws2 but a broken and irregular line1 full of sudden and capricious twistings1 and bearing on its face marks of irregularities dependent1 not upon law1 but upon chance4 ,yet these irregular and abrupt deviations in the curve are1 in most cases1 but small in extent1 when compared with those bendings which denote the effects of regular law4 ,and this circumstance is one of the great grounds of advantage in the ,method of ,curves4 ,for when the observations thus laid down present to the eye such a broken and irregular line1 we can still see1 often with great ease and certainty1 what twistings of the line are probably due to the irregular errours of observation2 and can at once reject these1 by drawing a more regular curve1 cutting off all such small and irregular sinuosities1 leaving some to the right and some to the left2 and then proceeding as if this regular curve1 and not the irregular one1 expressed the observations4 ,in this manner1 we suppose the errours of observation to balance each other2 some of our corrected measures being too great and others too small1 but with no great preponderance either way4 ,we draw our main regular curve1 not through the points given by our observations1 but among them3 drawing it1 as has been said by one of the philosophers#cjc who first systematically used this method1 'with a bold but careful hand4' #bjg ,the regular curve which we thus obtain1 thus freed from the casual errours of observation1 is that in which we endeavour to discover the laws of change and succession4 ,note #cjc3 ,sir ,j4 ,herschel1 ,ast4 ,soc4 ,trans4 vol4 v4 p4 #a4 #d4 ,by this method1 thus getting rid at once1 in a great measure1 of errours of observation1 we obtain data which are more true than the individual facts themselves4 ,the philosopher's business is to compare his hypotheses with facts1 as we have often said4 ,but if we make the comparison with separate special facts1 we are liable to be perplexed or misled1 to an unknown amount1 by the errours of observation2 which may cause the hypothetical and the observed result to agree1 or to disagree1 when otherwise they would not do so4 ,if1 however1 we thus take the whole mass of the facts1 and remove the errours of actual observation#cac1 by making the curve which expresses the supposed observation regular and smooth1 we have the separate facts corrected by their general tendency4 ,we are put in possession1 as we have said1 of something more true than any fact by itself is4 ,note #cac3 ,ib4 vol4 v4 p4 #d4 ,one of the most admirable examples of the use of this ,method of ,curves is found in ,sir ,john ,herschel's ,investigation of the ,orbits of ,double ,stars#cbc4 ,the author there shows how far inferior the direct observations of the angle of position are1 to the observations corrected by a curve in the manner above stated4 ',this curve once drawn1' he says1 'must represent1 it is evident1 the law of variation of the angle of position1 with the time1 not only for instants intermediate between the dates of observations1 but even at the moments of observation themselves1 much better than the individual raw observations can possibly 7on an average7 do4 ,it is only requisite to try a case or two1 to be satisfied that by substituting the curve for the points1 we have made a nearer approach to nature1 and in a great measure eliminated errours of observation4' ',in following the graphical process1' he adds1 'we have a conviction almost approaching to moral certainty that #bjh we cannot be greatly misled4' ,again1 having thus corrected the raw observations1 he makes another use of the graphical method1 by trying whether an ellipse can be drawn 'if not through1 at least among the points1 so as to approach tolerably near them all2 and thus approaching to the orbit which is the subject of investigation4' ,note #cbc3 ,ib4 #e4 ,the ,obstacles which principally impede the application of the ,method of ,curves are 7,i47 our ignorance of the arguments of the changes1 and 7,,ii47 the complication of several laws with one another4 7,i47 ,if we do not know on what quantity those changes depend which we are studying1 we may fail entirely in detecting the law of the changes1 although we throw the observations into curves4 ,for the true argument of the change should1 in fact1 be made the abscissa of the curve4 ,if we were to express1 by a series of ordinates1 the hour of high water on successive days1 we should not obtain1 or should obtain very imperfectly1 the law which these times follow2 for the real argument of this change is not the solar hour1 but the hour at which the moon passes the meridian4 ,but if we are supposed to be aware that this is the argument1 7which theory suggests and trial instantly confirms7 we then do immediately obtain the primary ,rules of the ,time of ,high ,water1 by throwing a series of observations into a ,curve1 with the ,hour of the ,moon's ,transit for the abscissa4 ,in like manner1 when we have obtained the first great or ,semi-mensual ,inequality of the tides1 if we endeavour to discover the laws of other ,inequalities by means of curves1 we must take from theory the suggestion that the ,arguments of such inequalities will probably be the parallax and the declination of the moon4 ,this suggestion again is confirmed by trial2 but if we were supposed to be entirely ignorant of the dependence of the changes of the tide on the ,distance and ,declination of the moon1 the curves would exhibit unintelligible and seemingly capricious changes4 ,for by the effect of the ,inequality arising from the ,parallax1 the convexities of the curves which belong to the #bji spring tides1 are in some years made alternately greater and less all the year through2 while in other years they are made all nearly equal4 ,this difference does not betray its origin1 till we refer it to the ,parallax2 and the same difficulty in proceeding would arise if we were ignorant that the moon's ,declination is one of the ,arguments of tidal changes4 ,in like manner1 if we try to reduce to law any meteorological changes1 those of the ,height of the ,barometer for instance1 we find that we can make little progress in the investigation1 precisely because we do not know the ,argument on which these changes depend4 ,that there is a certain regular diurnal change of small amount1 we know2 but when we have abstracted this ,inequality1 7of which the ,argument is the time of day17 we find far greater ,changes left behind1 from day to day and from hour to hour2 and we express these in curves1 but we cannot reduce them to ,rule1 because we cannot discover on what numerical quantity they depend4 ,the assiduous study of barometrical observations1 thrown into curves1 may perhaps hereafter point out to us what are the relations of time and space by which these variations are determined2 but in the mean time1 this subject exemplifies to us our remark1 that the method of curves is of comparatively small use1 so long as we are in ignorance of the real ,arguments of the ,inequalities4 #f4 7,,ii47 ,in the next place1 ,i remark that a difficulty is thrown in the way of the ,method of ,curves by the ,combination of several laws one with another4 ,it will readily be seen that such a cause will produce a complexity in the curves which exhibit the succession of facts4 ,if1 for example1 we take the case of the ,tides1 the ,height of high water increases and diminishes with the ,approach of the sun to1 and its ,recess from1 the syzygies of the moon4 ,again1 this ,height increases and diminishes as the moon's ,parallax increases and diminishes2 and again1 the ,height diminishes when the ,declination increases1 and vice versa2 and all these ,arguments of change1 the ,distance from ,syzygy1 the ,parallax1 the ,declination1 complete their circuit and #baj return into themselves in different periods4 ,hence the curve which represents the ,height of high water has not any periodical interval in which it completes its changes and commences a new cycle4 ,the sinuosity which would arise from each ,inequality separately considered1 interferes with1 disguises1 and conceals the others2 and when we first cast our eyes on the curve of observation1 it is very far from offering any obvious regularity in its form4 ,and it is to be observed that we have not yet enumerated all the elements of this complexity3 for there are changes of the tide depending upon the ,parallax and ,declination of the ,sun as well as of the ,moon4 ,again2 besides these changes1 of which the ,arguments are obvious1 there are others1 as those depending upon the ,barometer and the ,wind1 which follow no known regular law1 and which constantly affect and disturb the results produced by other laws4 ,in the ,tides1 and in like manner in the motions of the ,moon1 we have very eminent examples of the way in which the discovery of laws may be rendered difficult by the number of laws which operate to affect the same quantity4 ,in such cases1 the ,inequalities are generally picked out in succession1 nearly in the order of their magnitudes4 ,in this way there were successively collected1 from the study of the ,moon's motions by a series of astronomers1 those ,inequalities which we term the ,equation of the ,center1 the ,evection1 the ,variation1 and the ,annual ,equation4 ,these ,inequalities were not1 in fact1 obtained by the application of the ,method of ,curves2 but the ,method of ,curves might have been applied to such a case with great advantage4 ,the ,method has been applied with great industry and with remarkable success to the investigation of the laws of the ,tides2 and by the use of it1 a series of ,inequalities both of the ,times and of the ,heights of high water has been detected1 which explain all the main features of the observed facts4 #baa ,,sect4 ,,ii4--,the ,method of ,means4 #g4 ,the ,method of ,curves1 as we have endeavoured to explain above1 frees us from the casual and extraneous irregularities which arise from the imperfection of observation2 and thus lays bare the results of the laws which really operate1 and enables us to proceed in search of those laws4 ,but the ,method of ,curves is not the only one which effects such a purpose4 ,the errours arising from detached observations may be got rid of1 and the additional accuracy which multiplied observations give may be obtained1 by operations upon the observed numbers1 without expressing them by spaces4 ,the process of curves assumes that the errours of observation balance each other2--that the accidental excesses and defects are nearly equal in amount2--that the true quantities which would have been observed if all accidental causes of irregularity were removed1 are obtained1 exactly or nearly1 by selecting quantities1 upon the whole1 equally distant from the extremes of great and small1 which our imperfect observations offer to us4 ,but when1 among a number of unequal quantities1 we take a quantity equally distant from the greater and the smaller1 this quantity is termed the ,mean of the unequal quantities4 ,hence the correction of our observations by the method of curves consists in taking the ,mean of the observations4 #h4 ,now without employing curves1 we may proceed arithmetically to take the ,mean of all the observed numbers of each class4 ,thus1 if we wished to know the ,height of the spring tide at a given place1 and if we found that four different spring tides were measured as being of the height of ten1 thirteen1 eleven1 and fourteen feet1 we should conclude that the true height of the tide was the ,mean of these numbers1--namely1 twelve feet2 and we should suppose that the deviation from this height1 in the individual cases1 arose from the accidents of weather1 the imperfections of observation1 or the operation of other laws1 besides the alternation of spring and neap tides4 #bab ,this process of finding the ,mean of an assemblage of observed numbers is much practised in discovering1 and still more in confirming and correcting1 laws of phenomena4 ,we shall notice a few of its peculiarities4 #i4 ,the ,method of ,means requires a knowledge of the ,argument of the changes which we would study2 for the numbers must be arranged in certain ,classes1 before we find the ,mean of each ,class2 and the principle on which this arrangement depends is the ,argument4 ,this knowledge of the ,argument is more indispensably necessary in the ,method of ,means than in the ,method of ,curves2 for when ,curves are drawn1 the eye often spontaneously detects the law of recurrence in their sinuosities2 but when we have collections of ,numbers1 we must divide them into classes by a selection of our own4 ,thus1 in order to discover the law which the heights of the tide follow1 in the progress from spring to neap1 we arrange the observed tides according to the day of the moon's age2 and we then take the mean of all those which thus happen at the same period of the ,moon's ,revolution4 ,in this manner we obtain the law which we seek2 and the process is very nearly the same in all other applications of this ,method of ,means4 ,in all cases1 we begin by assuming the ,classes of measures which we wish to compare1 the ,law which we could confirm or correct1 the ,formula of which we would determine the coefficients4 #aj4 ,the ,argument being thus assumed1 the ,method of ,means is very efficacious in ridding our inquiry of errours and irregularities which would impede and perplex it4 ,irregularities which are altogether accidental1 or at least accidental with reference to some law which we have under consideration1 compensate each other in a very remarkable way1 when we take the ,means of many observations4 ,if we have before us a collection of observed tides1 some of them may be elevated1 some depressed by the wind1 some noted too high and some too low by the observer1 some augmented and some diminished by uncontemplated changes in the moon's distance or motion3 but in the course of a year or two at the longest1 all these causes of irregularity balance #bac each other2 and the law of succession1 which runs through the observations1 comes out as precisely as if those disturbing influences did not exist4 ,in any particular case1 there appears to be no possible reason why the deviation should be in one way1 or of one moderate amount1 rather than another4 ,but taking the mass of observations together1 the deviations in opposite ways will be of equal amount1 with a degree of exactness very striking4 ,this is found to be the case in all inquiries where we have to deal with observed numbers upon a large scale4 ,in the progress of the population of a country1 for instance1 what can appear more inconstant1 in detail1 than the causes which produce births and deaths8 yet in each country1 and even in each province of a country1 the proportions of the whole numbers of births and deaths remain nearly constant4 ,what can be more seemingly beyond the reach of rule than the occasions which produce letters that cannot find their destination8 yet it appears that the number of 'dead letters' is nearly the same from year to year4 ,and the same is the result when the deviations arise1 not from mere accident1 but from laws perfectly regular1 though not contemplated in our investigation#ccc4 ,thus the effects of the ,moon's ,parallax upon the ,tides1 sometimes operating one way and sometimes another1 according to certain rules1 are quite eliminated by taking the ,means of a long series of observations2 the excesses and defects neutralizing each other1 so far as concerns the effect upon any law of the tides which we would investigate4 ,note #ccc3 ,provided the argument of the law which we neglect have no coincidence with the argument of the law which we would determine4 #aa4 ,in order to obtain very great accuracy1 very large masses of observations are often employed by philosophers1 and the accuracy of the result increases with the multitude of observations4 ,the immense collections of astronomical observations which have in this manner been employed in order to form and correct the ,tables of the celestial motions are perhaps the most signal instances of the attempts to obtain #bad accuracy by this accumulation of observations4 ,delambre's ,tables of the ,sun are founded upon nearly #cjjj observations2 ,burg's ,tables of the ,moon upon above #djjj4 ,but there are other instances hardly less remarkable4 ,mr4 ,lubbock's first investigations of the laws of the tides of ,london#cdc1 included above #ac1jjj observations1 extending through nineteen years2 it being considered that this large number was necessary to remove the effects of accidental causes#cec4 ,and the attempts to discover the laws of change in the barometer have led to the performance of labours of equal amount3 ,laplace and ,bouvard examined this question by means of observations made at the ,observatory of ,paris1 four times every day for eight years4 ,note #cdc3 ,phil4 ,trans4 #ahca4 ,note #cec3 ,this period of nineteen years was also selected for a reason which is alluded to in a former note4 ,it was thought that this period secured the inquirer from the errours which might be produced by the partial coincidence of the ,arguments of different irregularities2 for example1 those due to the moon's ,parallax and to the moon's ,declination4 ,it has since been found 7,phil4 ,tr4 #ahch4 ,on the ,determination of the ,laws of the ,tides from ,short ,series of ,observations71 that with regard to ,parallax at least1 the ,means of one year give sufficient accuracy4 #ab4 ,we may remark one striking evidence of the accuracy thus obtained by employing large masses of observations4 ,in this way we may often detect inequalities much smaller than the errours by which they are encumbered and concealed4 ,thus the ,diurnal ,oscillations of the ,barometer were discovered by the comparison of observations of many days1 classified according to the hours of the day2 and the result was a clear and incontestable proof of the existence of such oscillations although the differences which these oscillations produce at different hours of the day are far smaller than the casual changes1 hitherto reduced to no law1 which go on from hour to hour and from day to day4 ,the effect of law1 operating incessantly and steadily1 makes itself more and more felt as we give it a longer range2 while the effect of accident1 followed out in the #bae same manner1 is to annihilate itself1 and to disappear altogether from the result4 ,,sect4 ,,iii4--,the ,method of ,least ,squares4 #ac4 ,the ,method of ,least ,squares is in fact a method of means1 but with some peculiar characters4 ,its object is to determine the best ,mean of a number of observed quantities2 or the most probable ,law derived from a number of observations1 of which some1 or all1 are allowed to be more or less imperfect4 ,and the method proceeds upon this supposition2--that all errours are not equally probable1 but that small errours are more probable than large ones4 ,by reasoning mathematically upon this ground1 we find that the best result is obtained 7since we cannot obtain a result in which the errours vanish7 by making1 not the ,errours themselves1 but the ,sum of their ,squares1 of the smallest possible amount4 #ad4 ,an example may illustrate this4 ,let a quantity which is known to increase uniformly1 7as the distance of a star from the meridian at successive instants17 be measured at equal intervals of time1 and be found to be successively #d1 #ab1 #ad4 ,it is plain1 upon the face of these observations1 that they are erroneous2 for they ought to form an arithmetical progression1 but they deviate widely from such a progression4 ,but the question then occurs1 what arithmetical progression do they most probably represent3 for we may assume several arithmetical progressions which more or less approach the observed series2 as for instance1 these three2 #d1 #i1 #ad2 #f1 #aj1 #ad2 #e1 #aj1 #ae4 ,now in order to see the claims of each of these to the truth1 we may tabulate them thus4 ,sums of ,sums of ,squares ,observation #d1 #ab1 #ad ,errours ,errours4 of ,errours4 ,series 7#a7 #d1 #i1 #ad #j1 #c1 #j #c #i 7#b7 #f1 #aj1 #ad #b1 #b1 #j #d #h 7#c7 #e1 #aj1 #ae #a1 #b1 #a #d #f ,here1 although the first series gives the sum of the #baf errours less than the others1 the third series gives the sum of the squares of the errours least2 and is therefore1 by the proposition on which this ,method depends1 the most probable series of the three4 ,this ,method1 in more extensive and complex cases1 is a great aid to the calculator in his inferences from facts1 and removes much that is arbitrary in the ,method of ,means4 ,,sect4 ,,iv4--,the ,method of ,residues4 #ae4 ,by either of the preceding ,methods we obtain1 from observed facts1 such ,laws as readily offer themselves2 and by the ,laws thus discovered1 the most prominent changes of the observed quantities are accounted for4 ,but in many cases we have1 as we have noticed already1 several ,laws of nature operating at the same time1 and combining their influences to modify those quantities which are the subjects of observation4 ,in these cases we may1 by successive applications of the ,methods already pointed out1 detect such ,laws one after another3 but this successive process1 though only a repetition of what we have already described1 offers some peculiar features which make it convenient to consider it in a separate ,section1 as the ,method of ,residues4 #af4 ,when we have1 in a series of changes of a variable quantity1 discovered one ,law which the changes follow1 detected its ,argument1 and determined its ,magnitude1 so as to explain most clearly the course of observed facts1 we may still find that the observed changes are not fully accounted for4 ,when we compare the results of our ,law with the observations1 there may be a difference1 or as we may term it1 a ,residue1 still unexplained4 ,but this ,residue being thus detached from the rest1 may be examined and scrutinized in the same manner as the whole observed quantity was treated at first3 and we may in this way detect in it also a ,law of change4 ,if we can do this1 we must accommodate this new found ,law as nearly as possible to the ,residue to which it belongs2 and #bag this being done1 the difference of our ,rule and of the ,residue itself1 forms a ,second ,residue4 ,this ,second ,residue we may again bring under our consideration2 and may perhaps in it also discover some ,law of change by which its alterations may be in some measure accounted for4 ,if this can be done1 so as to account for a large portion of this ,residue1 the remaining unexplained part forms a ,third ,residue2 and so on4 #ag4 ,this course has really been followed in various inquiries1 especially in those of ,astronomy and ,tidology4 ,the ,equation of the ,center1 for the ,moon1 was obtained out of the ,residue of the ,longitude1 which remained when the ,mean ,anomaly was taken away4 ,this ,equation being applied and disposed of1 the ,second ,residue thus obtained1 gave to ,ptolemy the ,evection4 ,the ,third ,residue1 left by the ,equation of the ,center and the ,evection1 supplied to ,tycho the ,variation and the ,annual ,equation4 ,and the ,residue1 remaining from these1 has been exhausted by other ,equations1 of various arguments1 suggested by theory or by observation4 ,in this case1 the successive generations of astronomers have gone on1 each in its turn executing some step in this ,method of ,residues4 ,in the examination of the ,tides1 on the other hand1 this method has been applied systematically and at once4 ,the observations readily gave the ,semimensual ,inequality2 the ,residue of this supplied the corrections due to the ,moon's ,parallax and ,declination2 and when these were determined1 the remaining ,residue was explored for the law of the ,solar ,correction4 #ah4 ,in a certain degree1 the ,method of ,residues and the ,method of ,means are opposite to each other4 ,for the ,method of ,residues extricates ,laws from their combination1 bringing them into view in succession2 while the ,method of ,means discovers each ,law1 not by bringing the others into view1 but by destroying their effect through an accumulation of observations4 ,by the ,method of ,residues we should first extract the ,law of the ,parallax ,correction of the ,tides1 and then1 from the ,residue left by this1 obtain the ,declination ,correction4 ,but we might at once employ the ,method #bah of ,means1 and put together all the cases in which the ,declination was the same2 not allowing for the ,parallax in each case1 but taking for granted that the ,parallaxes belonging to the same ,declination would neutralize each other2 as many falling above as below the mean ,parallax4 ,in cases like this1 where the ,method of ,means is not impeded by a partial coincidence of the ,arguments of different unknown ,inequalities1 it may be employed with almost as much success as the ,method of ,residues4 ,but still1 when the ,arguments of the ,laws are clearly known1 as in this instance1 the ,method of ,residues is more clear and direct1 and is the rather to be recommended4 #ai4 ,if for example1 we wish to learn whether the ,height of the ,barometer exerts any sensible influence on the ,height of the ,sea's ,surface1 it would appear that the most satisfactory mode of proceeding1 must be to subtract1 in the first place1 what we know to be the effects of the ,moon's ,age1 ,parallax and ,declination1 and other ascertained causes of change2 and to search in the unexplained ,residue for the effects of barometrical pressure4 ,the contrary course has1 however1 been adopted1 and the effect of the ,barometer on the ocean has been investigated by the direct application of the ,method of ,means1 classing the observed heights of the water according to the corresponding heights of the ,barometer without any previous reduction4 ,in this manner1 the suspicion that the tide of the sea is affected by the pressure of the atmosphere1 has been confirmed4 ,this investigation must be looked upon as a remarkable instance of the efficacy of the ,method of ,means1 since the amount of the barometrical effect is much smaller than the other changes from among which it was by this process extricated4 ,but an application of the ,method of ,residues would still be desirable on a subject of such extent and difficulty4 #bj4 ,sir ,john ,herschel1 in his ,discourse on the ,study of ,natural ,philosophy 7,articles #aeh-afa71 has pointed out the mode of making discoveries by studying ,residual ,phenomena2 and has given several illustrations of the process4 ,in some of these1 he has also #bai considered this method in a wider sense than we have done2 treating it as not applicable to quantity only1 but to properties and relations of different kinds4 ,we likewise shall proceed to offer a few remarks on ,methods of ,induction applicable to other relations than those of quantity4 #bbj ,,chapter ,,viii4 ,,methods ,,of ,,induction ,,depending ,,on ,,resemblance4 ,,aphorism ,,xlix4 ,the ,law of ,continuity is this3--that a quantity cannot pass from one amount to another by any change of conditions1 without passing through all intermediate magnitudes according to the intermediate conditions4 ,this ,law may often be employed to disprove distinctions which have no real foundation4 ,,aphorism ,l4 ,the ,method of ,gradation consists in taking a number of stages of a property in question1 intermediate between two extreme cases which appear to be different4 ,this ,method is employed to determine whether the extreme cases are really distinct or not4 ,,aphorism ,,li4 ,the ,method of ,gradation1 applied to decide the question1 whether the existing geological phenomena arise from existing causes1 leads to this result3--,that the phenomena do appear to arise from ,existing ,causes1 but that the action of existing causes may1 in past times1 have transgressed1 to any extent1 their recorded limits of intensity4 ,,aphorism ,,lii4 ,the ,method of ,natural ,classification consists in classing cases1 not according to any assumed ,definition1 but according to the connexion of the facts themselves1 so as to make them the means of asserting general truths4 #bba ,,sect4 ,i4--,the ,law of ,continuity4 #a4 ,,the ,law of ,continuity is applicable to quantity primarily1 and therefore might be associated with the methods treated of in the last chapter3 but inasmuch as its inferences are made by a transition from one degree to another among contiguous cases1 it will be found to belong more properly to the ,methods of ,induction of which we have now to speak4 ,the ,law of ,continuity consists in this proposition1--,that a quantity cannot pass from one amount to another by any change of conditions1 without passing through all intermediate degrees of magnitude according to the intermediate conditions4 ,and this law may often be employed to correct inaccurate inductions1 and to reject distinctions which have no real foundation in nature4 ,for example1 the ,aristotelians made a distinction between motions according to nature1 7as that of a body falling vertically downwards17 and motions contrary to nature1 7as that of a body moving along a horizontal plane37 the former1 they held1 became naturally quicker and quicker1 the latter naturally slower and slower4 ,but to this it might be replied1 that a horizontal line may pass1 by gradual motion1 through various inclined positions1 to a vertical position3 and thus the retarded motion may pass into the accelerated2 and hence there must be some inclined plane on which the motion downwards is naturally uniform3 which is false1 and therefore the distinction of such kinds of motion is unfounded4 ,again1 the proof of the ,first ,law of ,motion depends upon the ,law of ,continuity3 for since1 by diminishing the resistance to a body moving on a horizontal plane1 we diminish the retardation1 and this without limit1 the law of continuity will bring us at the same time to the case of no resistance and to the case of no retardation4 #b4 ,the ,law of ,continuity is asserted by ,galileo in a particular application2 and the assertion which it #bbb suggests is by him referred to ,plato2--namely#cfc that a moveable body cannot pass from rest to a determinate degree of velocity without passing through all smaller degrees of velocity4 ,this law1 however1 was first asserted in a more general and abstract form by ,leibnitz#cgc3 and was employed by him to show that the laws of motion propounded by ,descartes must be false4 ,the ,third ,cartesian ,law of ,motion was this#chc3 that when one moving body meets another1 if the first body have a less momentum than the second1 it will be reflected with its whole motion3 but if the first have a greater momentum than the second1 it will lose a part of its motion1 which it will transfer to the second4 ,now each of these cases leads1 by the ,law of ,continuity1 to the case in which the two bodies have equal momentums3 but in this case1 by the first part of the law the body would retain all its motion2 and by the second part of the law it would lose a portion of it3 hence the ,cartesian ,law is false4 ,note #cfc3 ,dialog4 iii4 #aej4 iv4 #cb4 ,note #cgc3 ,opera1 i4 #cff4 ,note #chc3 ,cartes1 ,prin4 p4 #ce4 #c4 ,i shall take another example of the application of this ,law from ,professor ,playfair's ,dissertation on the ,history of ,mathematical and ,physical ,science#cic4 ',the ,academy of ,sciences at ,paris having 7in #agbd7 proposed1 as a ,prize ,question1 the ,investigation of the ,laws of the ,communication of ,motion1 ,john ,bernoulli presented an ,essay on the subject very ingenious and profound2 in which1 however1 he denied the existence of hard bodies1 because in the collision of such bodies1 a finite change of motion must take place in an instant3 an event which1 on the principle just explained1 he maintained to be impossible4' ,and this reasoning was justifiable3 for we can form a continuous transition from cases in which the impact manifestly occupies a finite time1 7as when we strike a large soft body7 to cases in which it is apparently instantaneous4 ,maclaurin and others are disposed1 in order to avoid the conclusion of ,bernoulli1 to reject the ,law of #bbc ,continuity4 ,this1 however1 would not only be1 as ,playfair says1 to deprive ourselves of an auxiliary1 commonly useful though sometimes deceptive2 but what is much worse1 to acquiesce in false propositions1 from the want of clear and patient thinking4 ,for the ,law of ,continuity1 when rightly interpreted1 is never violated in actual fact4 ,there are not really any such bodies as have been termed perfectly hard3 and if we approach towards such cases1 we must learn the laws of motion which rule them by attending to the ,law of ,continuity1 not by rejecting it4 ,note #cic3 ,in the ,encyc4 ,brit4 p4 #ecg4 #d4 ,newton used the ,law of ,continuity to suggest1 but not to prove1 the doctrine of universal gravitation4 ,let1 he said1 a terrestrial body be carried as high as the moon3 will it not still fall to the earth8 and does not the moon fall by the same force#djc8 ,again3 if any one says that there is a material ether which does not gravitate#dac1 this kind of matter1 by condensation1 may be gradually transmuted to the density of the most intensely gravitating bodies3 and these gravitating bodies1 by taking the internal texture of the condensed ether1 may cease to gravitate2 and thus the weight of bodies depends1 not on their quantity of matter1 but on their texture2 which doctrine ,newton conceived he had disproved by experiment4 ,note #djc3 ,principia1 lib4 iii4 prop4 #f4 ,note #dac3 ,ib4 cor4 #b4 #e4 ,the evidence of the ,law of ,continuity resides in the universality of those ,ideas1 which enter into our apprehension of ,laws of ,nature4 ,when1 of two quantities1 one depends upon the other1 the ,law of ,continuity necessarily governs this dependence4 ,every philosopher has the power of applying this law1 in proportion as he has the faculty of apprehending the ,ideas which he employs in his induction1 with the same clearness and steadiness which belong to the fundamental ideas of ,quantity1 ,space and ,number4 ,to those who possess this faculty1 the ,law is a ,rule of very wide and decisive application4 ,its use1 as has appeared in the above examples1 is seen rather in the disproof of erroneous views1 and in the correction of false propositions1 #bbd than in the invention of new truths4 ,it is a test of truth1 rather than an instrument of discovery4 ,methods1 however1 approaching very near to the ,law of ,continuity may be employed as positive means of obtaining new truths2 and these ,i shall now describe4 ,,sect4 ,,ii4--,the ,method of ,gradation4 #f4 ,to gather together the cases which resemble each other1 and to separate those which are essentially distinct1 has often been described as the main business of science2 and may1 in a certain loose and vague manner of speaking1 pass for a description of some of the leading procedures in the acquirement of knowledge4 ,the selection of instances which agree1 and of instances which differ1 in some prominent point or property1 are important steps in the formation of science4 ,but when classes of things and properties have been established in virtue of such comparisons1 it may still be doubtful whether these classes are separated by distinctions of opposites1 or by differences of degree4 ,and to settle such questions1 the ,method of ,gradation is employed2 which consists in taking intermediate stages of the properties in question1 so as to ascertain by experiment whether1 in the transition from one class to another1 we have to leap over a manifest gap1 or to follow a continuous road4 #g4 ,thus for instance1 one of the early ,divisions established by electrical philosophers was that of ,electrics and ,conductors4 ,but this division ,dr4 ,faraday has overturned as an essential opposition4 ,he takes#dbc a ,gradation which carries him from ,conductors to ,non-conductors4 ,sulphur1 or ,lac1 he says1 are held to be non-conductors1 but are not rigorously so4 ,spermaceti is a bad conductor3 ice or water better than spermaceti3 metals so much better that they are put in a different class4 ,but even in metals the transit of the electricity is not instantaneous3 we have in them proof of a retardation of the electric current3 'and what #bbe reason1 ,mr4 ,faraday asks1 why this retardation should not be of the same kind as that in spermaceti1 or in lac1 or sulphur8 ,but as1 in them1 retardation is insulation1 and insulation is induction#dcc why should we refuse the same relation to the same exhibitions of force in the metals8 ,note #dbc3 ,researches1 #abth series1 art4 #acbh4 ,note #dcc3 ,these words refer to another proposition1 also established by the ,method of ,gradation4 ,the process employed by the same sagacious philosopher to show the identity of ,voltaic and ,franklinic electricity1 is another example of the same kind#ddc4 ,machine ,franklinic electricity was made to exhibit the same phenomena as ,voltaic electricity1 by causing the discharge to pass through a bad conductor1 into a very extensive discharging train3 and thus it was clearly shown that ,franklinic electricity1 not so conducted1 differs from the other kinds1 only in being in a state of successive tension and explosion instead of a state of continued current4 ,note #ddc3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 ix4 sect4 #b4 ,again2 to show that the decomposition of bodies in the ,voltaic circuit was not due to the ,attraction of the ,poles#dec1 ,mr4 ,faraday devised a beautiful series of experiments1 in which these supposed ,poles were made to assume all possible electrical conditions3--in some cases the decomposition took place against air1 which according to common language is not a conductor1 nor is decomposed2--in others1 against the metallic poles1 which are excellent conductors but undecomposable2--and so on3 and hence he infers that the decomposition cannot justly be considered as due to the ,attraction1 or ,attractive ,powers1 of the ,poles4 ,note #dec3 ,ibid4 ,researches1 art4 #dig4 #h4 ,the reader of the ,novum ,organon may perhaps1 in looking at such examples of the ,rule1 be reminded of some of ,bacon's ,classes of ,instances1 as his instanti absenti in proximo1 and his instanti migrantes4 ,but we may remark that ,instances classed and treated as ,bacon recommends in those parts of his work1 could hardly lead to scientific truth4 ,his #bbf processes are vitiated by his proposing to himself the form or cause of the property before him1 as the object of his inquiry2 instead of being content to obtain1 in the first place1 the law of phenomena4 ,thus his example#dfc of a ,migrating ,instance is thus given4 ,let the ,nature inquired into be that of ,whiteness2 an ,instance ,migrating to the production of this property is glass1 first whole1 and then pulverized2 or plain water1 and water agitated into a foam2 for glass and water are transparent1 and not white2 but glass powder and foam are white1 and not transparent4 ,hence we must inquire what has happened to the glass or water in that ,migration4 ,for it is plain that the ,form of ,whiteness is conveyed and induced by the crushing of the glass and shaking of the water4 ,no real knowledge has resulted from this line of reasoning3--from taking the ,natures and ,forms of things and of their qualities for the primary subject of our researches4 ,note #dfc3 ,nov4 ,org4 lib4 ii4 ,aph4 #bh4 #i4 ,we may easily give examples from other subjects in which the ,method of ,gradation has been used to establish1 or to endeavour to establish1 very extensive propositions4 ,thus ,laplace's ,nebular ,hypothesis1--that systems like our solar system are formed by gradual condensation from diffused masses1 such as the nebul among the stars1--is founded by him upon an application of this ,method of ,gradation4 ,we see1 he conceives1 among these nebul1 instances of all degrees of condensation1 from the most loosely diffused fluid1 to that separation and solidification of parts by which suns1 and satellites1 and planets are formed3 and thus we have before us instances of systems in all their stages2 as in a forest we see trees in every period of growth4 ,how far the examples in this case satisfy the demands of the ,method of ,gradation1 it remains for astronomers and philosophers to examine4 ,again2 this method was used with great success by ,macculloch and others to refute the opinion1 put in currency by the ,wernerian school of geologists1 that #bbg the rocks called trap rocks must be classed with those to which a sedimentary origin is ascribed4 ,for it was shown that a gradual transition might be traced from those examples in which trap rocks most resembled stratified rocks1 to the lavas which have been recently ejected from volcanoes3 and that it was impossible to assign a different origin to one portion1 and to the other1 of this kind of mineral masses2 and as the volcanic rocks were certainly not sedimentary1 it followed1 that the trap rocks were not of that nature4 ,again2 we have an attempt of a still larger kind made by ,sir ,c4 ,lyell1 to apply this ,method of ,gradation so as to disprove all distinction between the causes by which geological phenomena have been produced1 and the causes which are now acting at the earth's surface4 ,he has collected a very remarkable series of changes which have taken place1 and are still taking place1 by the action of water1 volcanoes1 earthquakes1 and other terrestrial operations2 and he conceives he has shown in these a gradation which leads1 with no wide chasm or violent leap1 to the state of things of which geological researches have supplied the evidence4 #aj4 ,of the value of this ,method in geological speculations1 no doubt can be entertained4 ,yet it must still require a grave and profound consideration1 in so vast an application of the ,method as that attempted by ,sir ,c4 ,lyell1 to determine what extent we may allow to the steps of our gradation2 and to decide how far the changes which have taken place in distant parts of the series may exceed those of which we have historical knowledge1 without ceasing to be of the same kind4 ,those who1 dwelling in a city1 see1 from time to time1 one house built and another pulled down1 may say that such existing causes1 operating through past time1 sufficiently explain the existing condition of the city4 ,yet we arrive at important political and historical truths1 by considering the origin of a city as an event of a different order from those daily changes4 ,the causes which are now working to produce geological results1 may be supposed to have been1 at some former epoch1 so far exaggerated in their operation1 that the changes #bbh should be paroxysms1 not degrees2--that they should violate1 not continue1 the gradual series4 ,and we have no kind of evidence whether the duration of our historical times is sufficient to give us a just measure of the limits of such degrees2--whether the terms which we have under our notice enable us to ascertain the average rate of progression4 #aa4 ,the result of such considerations seems to be this3--that we may apply the ,method of ,gradation in the investigation of geological causes1 provided we leave the ,limits of the ,gradation undefined4 ,but1 then1 this is equivalent to the admission of the opposite hypothesis3 for a continuity of which the successive intervals are not limited1 is not distinguishable from discontinuity4 ,the geological sects of recent times have been distinguished as uniformitarians and catastrophists3 the ,method of ,gradation seems to prove the doctrine of the uniformitarians2 but then1 at the same time that it does this1 it breaks down the distinction between them and the catastrophists4 ,there are other exemplifications of the use of gradations in ,science which well deserve notice3 but some of them are of a kind somewhat different1 and may be considered under a separate head4 ,,sect4 ,,iii4 ,the ,method of ,natural ,classification4 #ab4 ,the ,method of ,natural ,classification consists1 as we have seen1 in grouping together objects1 not according to any selected properties1 but according to their most important resemblances2 and in combining such grouping with the assignation of certain marks of the classes thus formed4 ,the examples of the successful application of this method are to be found in the ,classificatory ,sciences through their whole extent2 as1 for example1 in framing the ,genera of plants and animals4 ,the same method1 however1 may often be extended to other sciences4 ,thus the classification of ,crystalline ,forms1 according to their ,degree of ,symmetry1 7which is really an important distinction17 as introduced by ,mohs and ,weiss1 was a great improvement #bbi upon ,hay's arbitrary division according to certain assumed primary forms4 ,sir ,david ,brewster was led to the same distinction of crystals by the study of their optical properties2 and the scientific value of the classification was thus strongly exhibited4 ,mr4 ,howard's classification of ,clouds appears to be founded in their real nature1 since it enables him to express the laws of their changes and successions4 ,as we have elsewhere said1 the criterion of a true classification is1 that it makes general propositions possible4 ,one of the most prominent examples of the beneficial influence of a right classification1 is to be seen in the impulse given to geology by the distinction of strata according to the organic fossils which they contain#dgc3 which1 ever since its general adoption1 has been a leading principle in the speculations of geologists4 ,note #dgc3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 ii4 sect4 #c4 #ac4 ,the mode in which1 in this and in other cases1 the ,method of ,natural ,classification directs the researches of the philosopher1 is this3--his arrangement being adopted1 at least as an instrument of inquiry and trial1 he follows the course of the different members of the classification1 according to the guidance which ,nature herself offers2 not prescribing beforehand the marks of each part1 but distributing the facts according to the total resemblances1 or according to those resemblances which he finds to be most important4 ,thus1 in tracing the course of a series of strata from place to place1 we identify each stratum1 not by any single character1 but by all taken together2--texture1 colour1 fossils1 position1 and any other circumstances which offer themselves4 ,and if1 by this means1 we come to ambiguous cases1 where different indications appear to point different ways1 we decide so as best to preserve undamaged those general relations and truths which constitute the value of our system4 ,thus although we consider the organic fossils in each stratum as its most important characteristic1 we are not prevented1 by the disappearance of some fossils1 or the addition of others1 or by the total absence of fossils1 #bcj from identifying strata in distant countries1 if the position and other circumstances authorize us to do so4 ,and by this ,method of ,classification1 the doctrine of ,geological ,equivalents#dhc has been applied to a great part of ,europe4 ,note #dhc3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 iii4 sect4 #d4 #ad4 ,we may further observe1 that the same method of natural classification which thus enables us to identify strata in remote situations1 notwithstanding that there may be great differences in their material and contents1 also forbids us to assume the identity of the series of rocks which occur in different countries1 when this identity has not been verified by such a continuous exploration of the component members of the series4 ,it would be in the highest degree unphilosophical to apply the special names of the ,english or ,german strata to the rocks of ,india1 or ,america1 or even of southern ,europe1 till it has appeared that in those countries the geological series of northern ,europe really exists4 ,in each separate country1 the divisions of the formations which compose the crust of the earth must be made out1 by applying the ,method of ,natural ,arrangement to that particular case1 and not by arbitrarily extending to it the nomenclature belonging to another case4 ,it is only by such precautions1 that we can ever succeed in obtaining geological propositions1 at the same time true and comprehensive2 or can obtain any sound general views respecting the physical history of the earth4 #ae4 ,the ,method of ,natural ,classification1 which we thus recommend1 falls in with those mental habits which we formerly described as resulting from the study of ,natural ,history4 ,the method was then termed the ,method of ,type1 and was put in opposition to the ,method of ,definition4 ,the ,method of ,natural ,classification is directly opposed to the process in which we assume and apply arbitrary definitions2 for in the former ,method1 we find our classes in nature1 and do not make them by marks of our own imposition4 ,nor can any advantage #bca to the progress of knowledge be procured1 by laying down our characters when our arrangements are as yet quite loose and unformed4 ,nothing was gained by the attempts to define ,metals by their weight1 their hardness1 their ductility1 their colour2 for to all these marks1 as fast as they were proposed1 exceptions were found1 among bodies which still could not be excluded from the list of ,metals4 ,it was only when elementary substances were divided into ,natural ,classes1 of which classes ,metals were one1 that a true view of their distinctive characters was obtained4 ,definitions in the outset of our examination of nature are almost always1 not only useless1 but prejudicial4 #af4 ,when we obtain a ,law of ,nature by induction from phenomena1 it commonly happens1 as we have already seen1 that we introduce1 at the same time1 a ,proposition and a ,definition4 ,in this case1 the two are correlative1 each giving a real value to the other4 ,in such cases1 also1 the ,definition1 as well as the ,proposition1 may become the basis of rigorous reasoning1 and may lead to a series of deductive truths4 ,we have examples of such ,definitions and ,propositions in the ,laws of ,motion1 and in many other cases4 #ag4 ,when we have established ,natural ,classes of objects1 we seek for ,characters of our classes2 and these ,characters may1 to a certain extent1 be called the ,definitions of our classes4 ,this is to be understood1 however1 only in a limited sense3 for these ,definitions are not absolute and permanent4 ,they are liable to be modified and superseded4 ,if we find a case which manifestly belongs to our ,natural ,class1 though violating our ,definition1 we do not shut out the case1 but alter our definition4 ,thus1 when we have made it part of our ,definition of the ,rose family1 that they have alternate stipulate leaves1 we do not1 therefore1 exclude from the family the genus ,lowa1 which has no stipul4 ,in ,natural ,classifications1 our ,definitions are to be considered as temporary and provisional only4 ,when ,sir ,c4 ,lyell established the distinctions of the tertiary strata1 which he termed ,eocene1 ,miocene1 and ,pliocene1 he took a numerical criterion #bcb 7the proportion of recent species of shells contained in those strata7 as the basis of his division4 ,but now that those kinds of strata have become1 by their application to a great variety of cases1 a series of ,natural ,classes1 we must1 in our researches1 keep in view the natural connexion of the formations themselves in different places2 and must by no means allow ourselves to be governed by the numerical proportions which were originally contemplated2 or even by any amended numerical criterion equally arbitrary2 for however amended1 ,definitions in natural history are never immortal4 ,the etymologies of ,pliocene and ,miocene may1 hereafter1 come to have merely an historical interest2 and such a state of things will be no more inconvenient1 provided the natural connexions of each class are retained1 than it is to call a rock oolite or porphyry1 when it has no roelike structure and no fiery spots4 ,the ,methods of ,induction which are treated of in this and the preceding chapter1 and which are specially applicable to causes governed by relations of ,quantity or of ,resemblance1 commonly lead us to ,laws of ,phenomena only4 ,inductions founded upon other ideas1 those of ,substance and ,cause for example1 appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things4 ,but before we speak of these1 we shall say a few words respecting the way in which inductive propositions1 once obtained1 may be verified and carried into effect by their application4 #bcc ,,chapter ,,ix4 ,,of ,,the ,,application ,,of ,,inductive ,,truths4 ,,aphorism ,,liii4 ,when the theory of any subject is established1 the observations and experiments which are made in applying the science to use and to instruction1 supply a perpetual verification of the theory4 ,,aphorism ,,liv4 ,such observations and experiments1 when numerous and accurate1 supply also corrections of the constants involved in the theory2 and sometimes1 7by the ,method of ,residues17 additions to the theory4 ,,aphorism ,,lv4 ,it is worth considering1 whether a continued and connected system of observation and calculation1 like that of astronomy1 might not be employed with advantage in improving our knowledge of other subjects2 as ,tides1 ,currents1 ,winds1 ,clouds1 ,rain1 ,terrestrial ,magnetism1 ,aurora ,borealis1 ,composition of ,crystals1 and many other subjects4 ,,aphorism ,,lvi4 ,an extension of a well-established theory to the explanation of new facts excites admiration as a discovery2 but it is a discovery of a lower order than the theory itself4 ,,aphorism ,,lvii4 ,the practical inventions which are most important in ,art may be either unimportant parts of ,science1 or results not explained by ,science4 #bcd ,,aphorism ,,lviii4 ,in modern times1 in many departments4 ,art is constantly guided1 governed and advanced by ,science4 ,,aphorism ,,lix4 ,recently several ,new ,arts have been invented1 which may be regarded as notable verifications of the anticipations of material benefits to be derived to man from the progress of ,science4 #a4 ,,by the application of inductive truths1 we here mean1 according to the arrangement given in chap4 ,i4 of this book1 those steps1 which in the natural order of science1 follow the discovery of each truth4 ,these steps are1 the verification of the discovery by additional experiments and reasonings1 and its extension to new cases1 not contemplated by the original discoverer4 ,these processes occupy that period1 which1 in the history of each great discovery1 we have termed the ,sequel of the epoch2 as the collection of facts1 and the elucidation of conceptions1 form its ,prelude4 #b4 ,it is not necessary to dwell at length on the processes of the ,verification of ,discoveries4 ,when the ,law of ,nature is once stated1 it is far easier to devise and execute experiments which prove it1 than it was to discern the evidence before4 ,the truth becomes one of the standard doctrines of the science to which it belongs1 and is verified by all who study or who teach the science experimentally4 ,the leading doctrines of ,chemistry are constantly exemplified by each chemist in his ,laboratory2 and an amount of verification is thus obtained of which books give no adequate conception4 ,in ,astronomy1 we have a still stronger example of the process of verifying discoveries4 ,ever since the science assumed a systematic form1 there have been ,observatories1 in which the consequences of the theory were habitually compared with the results of observation4 ,and to facilitate this comparison1 ,tables of great extent have been calculated1 with immense labour1 from each theory1 showing the place which the #bce theory assigned to the heavenly bodies at successive times2 and thus1 as it were1 challenging nature to deny the truth of the discovery4 ,in this way1 as ,i have elsewhere stated1 the continued prevalence of an errour in the systematic parts of astronomy is impossible#dic4 ,an errour1 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 for ever4 ,note #dic3 ,hist4 ,ind4 ,sc4 b4 vii4 c4 vi4 sect4 #f4 #c4 ,in these last expressions1 we suppose the theory1 not only to be tested1 but also to be corrected when it is found to be imperfect4 ,and this also is part of the business of the observing astronomer4 ,from his accumulated observations1 he deduces more exact values than had previously been obtained1 of the ,constants or ,coefficients of these ,inequalities of which the ,argument is already known4 ,this he is enabled to do by the methods explained in the fifth chapter of this book2 the ,method of ,means1 and especially the ,method of ,least ,squares4 ,in other cases1 he finds1 by the ,method of ,residues1 some new ,inequality2 for if no change of the ,coefficients will bring the ,tables and the observation to a coincidence1 he knows that a new ,term is wanting in his formula4 ,he obtains1 as far as he can1 the law of this unknown ,term2 and when its existence and its law have been fully established1 there remains the task of tracing it to its cause4 #d4 ,the condition of the science of ,astronomy1 with regard to its security and prospect of progress1 is one of singular felicity4 ,it is a question well worth our consideration1 as regarding the interests of science1 whether1 in other branches of knowledge also1 a continued and corrected system1 of observation and calculation1 imitating the system employed by astronomers1 might not be adopted4 ,but the discussion of this question would involve us in a digression too wide for the present occasion4 #bcf #e4 ,there is another mode of application of true theories after their discovery1 of which we must also speak2 ,i mean the process of showing that facts1 not included in the original induction1 and apparently of a different kind1 are explained by reasonings founded upon the theory3--extensions of the theory as we may call them4 ,the history of physical astronomy is full of such events4 ,thus after ,bradley and ,wargentin had observed a certain cycle among the perturbations of ,jupiter's satellites1 ,laplace explained this cycle by the doctrine of universal gravitation#ejc4 ,the long inequality of ,jupiter and ,saturn1 the diminution of the obliquity of the ecliptic1 the acceleration of the moon's mean motion1 were in like manner accounted for by ,laplace4 ,the coincidence of the nodes of the moon's equator with those of her orbit was proved to result from mechanical principles by ,lagrange4 ,the motions of the recently-discovered planets1 and of comets1 shown by various mathematicians to be in exact accordance with the theory1 are ,verifications and ,extensions still more obvious4 ,note #ejc3 ,hist4 ,ind4 ,sc4 b4 vii4 c4 iv4 sect4 #c4 #f4 ,in many of the cases just noticed1 the consistency between the theory1 and the consequences thus proved to result from it1 is so far from being evident1 that the most consummate command of all the powers and aids of mathematical reasoning is needed1 to enable the philosopher to arrive at the result4 ,in consequence of this circumstance1 the labours just referred to1 of ,laplace1 ,lagrange1 and others1 have been the object of very great and very just admiration4 ,moreover1 the necessary connexion of new facts1 at first deemed inexplicable1 with principles already known to be true2--a connexion utterly invisible at the outset1 and yet at last established with the certainty of demonstration2--strikes us with the delight of a new discovery2 and at first sight appears no less admirable than an original induction4 ,accordingly1 men sometimes appear tempted to consider ,laplace and other great mathematicians as persons of a kindred genius to ,newton4 ,we must not #bcg forget1 however1 that there is a great and essential difference between inductive and deductive processes of the mind4 ,the discovery of a new theory1 which is true1 is a step widely distinct from any mere development of the consequences of a theory already invented and established4 #g4 ,in the other sciences also1 which have been framed by a study of natural phenomena1 we may find examples of the explanation of new phenomena by applying the principles of the science when once established4 ,thus1 when the laws of the reflection and refraction of light had been established1 a new and poignant exemplification of them was found in the explanation of the ,rainbow by the reflection and refraction of light in the spherical drops of a shower2 and again1 another1 no less striking1 when the intersecting ,luminous ,circles and ,mock ,suns1 which are seen in cold seasons1 were completely explained by the hexagonal crystals of ice which float in the upper regions of the atmosphere4 ,the ,darkness of the space between the primary and secondary rainbow is another appearance which optical theory completely explains4 ,and when we further include in our optical theory the doctrine of interferences1 we find the explanation of other phenomena2 for instance1 the ,supernumerary ,rainbows which accompany the primary rainbow on its inner side1 and the small ,halos which often surround the sun and moon4 ,and when we come to optical experiments1 we find many instances in which the doctrine of interferences and of undulations have been applied to explain the phenomena by calculations almost as complex as those which we have mentioned in speaking of astronomy3 with results as little foreseen at first and as entirely satisfactory in the end4 ,such are ,schwerdt's explanation of the diffracted images of a triangular aperture by the doctrine of interferences1 and the explanation of the coloured ,lemniscates seen by polarized light in biaxal crystals1 given by ,young and by ,herschel3 and still more marked is another case1 in which the curves are unsymmetrical1 namely1 the curves seen by passing polarized #bch light through plates of quartz1 which agree in a wonderful manner with the calculations of ,airy4 ,to these we may add the curious phenomena1 and equally curious mathematical explanation1 of ,conical ,refraction1 as brought to view by ,professor ,lloyd and ,sir ,w4 ,hamilton4 ,indeed1 the whole history both of ,physical ,optics and of ,physical ,astronomy is a series of felicities of this kind1 as we have elsewhere observed4 ,such applications of theory1 and unforeseen explanations of new facts by complicated trains of reasoning necessarily flowing from the theory1 are strong proof of the truth of the theory1 while it is in the course of being established2 but we are here rather speaking of them as applications of the theory after it has been established4 ,those who thus apply principles already discovered are not to be ranked in their intellectual achievements with those who discover new principles2 but still1 when such applications are masked by the complex relations of space and number1 it is impossible not to regard with admiration the clearness and activity of intellect which thus discerns in a remote region the rays of a central truth already unveiled by some great discoverer4 #h4 ,as examples in other fields of the application of a scientific discovery to the explanation of natural phenomena1 we may take the identification of ,lightning with electricity by ,franklin1 and the explanation of ,dew by ,wells4 ,for ,wells's ,inquiry into the ,cause of ,dew1 though it has sometimes been praised as an original discovery1 was1 in fact1 only resolving the phenomenon into principles already discovered4 ,the atmologists of the last century were aware#eac that the vapour which exists in air in an invisible state may be condensed into water by cold2 and they had noticed that there is always a certain temperature1 lower than that of the atmosphere1 to which if we depress bodies1 water forms upon them in fine drops4 ,this temperature is the limit of that which is #bci necessary to constitute vapour1 and is hence called the constituent temperature4 ,but these principles were not generally familiar in ,england till ,dr4 ,wells introduced them into his ,essay on ,dew1 published in #ahad2 having indeed been in a great measure led to them by his own experiments and reasonings4 ,his explanation of ,dew1--that it arises from the coldness of the bodies on which it settles1--was established with great ingenuity2 and is a very elegant confirmation of the ,theory of ,constituent ,temperature4 ,note #eac3;,hist4 ,ind4 ,sc4 b4 x4 c4 iii4 sect4 #e4 #i4 ,as other examples of such explanations of new phenomena by a theory1 we may point out ,ampre's ,theory that ,magnetism is transverse voltaic currents1 applied to explain the rotation of a voltaic wire round a magnet1 and of a magnet round a voltaic wire4 ,and again1 in the same subject1 when it had been proved that electricity might be converted into magnetism1 it seemed certain that magnetism might be converted into electricity2 and accordingly ,faraday found under what conditions this may be done2 though indeed here1 the theory rather suggested the experiment than explained it when it had been independently observed4 ,the production of an electric spark by a magnet was a very striking exemplification of the theory of the identity of these different polar agencies4 #aj4 ,in ,chemistry such applications of the principles of the science are very frequent2 for it is the chemist's business to account for the innumerable changes which take place in material substances by the effects of mixture1 heat1 and the like4 ,as a marked instance of such an application of the science1 we may take the explanation of the explosive force of gunpowder#ebc1 from the conversion of its materials into gases4 ,in ,mineralogy also we have to apply the #bdj principles of ,chemistry to the analysis of bodies3 and ,i may mention1 as a case which at the time excited much notice1 the analysis of a mineral called ,heavy ,spar4 ,it was found that different specimens of this mineral differed in their crystalline angles about three degrees and a half2 a difference which was at variance with the mineralogical discovery then recently made1 of the constancy of the angle of the same substance4 ,vauquelin solved this difficulty by discovering that the crystals with the different angles were really minerals chemically different2 the one kind being sulphate of barytes1 and the other1 sulphate of strontian4 ,note #ebc3 ,the explanation is1 that the force is due to the sudden development of a large volume of nitrogen and carbonic acid gases1 which at the ordinary temperature of the air would occupy a space equal to about #cjj times the bulk of the powder used1 but from the intense heat developed at the moment of the explosion1 the dilatation amounts to at least #aejj times the volume of the gunpowder employed4 #aa4 ,in this way a scientific theory1 when once established1 is perpetually finding new applications in the phenomena of nature2 and those who make such applications1 though1 as we have said1 they care not to be ranked with the great discoverers who establish theories new and true1 often receive a more prompt and general applause than great discoverers do2 because they have not to struggle with the perplexity and averseness which often encounter the promulgation of new truths4 #ab4 ,along with the verification and extension of scientific truths1 we are naturally led to consider the useful application of them4 ,the example of all the best writers who have previously treated of the philosophy of sciences1 from ,bacon to ,herschel1 draws our attention to those instances of the application of scientific truths1 which are subservient to the uses of practical life2 to the support1 the safety1 the pleasure of man4 ,it is well known in how large a degree the furtherance of these objects constituted the merit of the ,novum ,organon in the eyes of its author2 and the enthusiasm with which men regard these visible and tangible manifestations of the power and advantage which knowledge may bring1 has gone on increasing up to our own day4 ,and undoubtedly such applications of the discoveries of science to promote the preservation1 comfort1 power and dignity of man1 must always be objects of great philosophical as well as practical interest4 ,yet we may observe that those #bda practical inventions which are of most importance in the ,arts1 have not commonly1 in the past ages of the world1 been the results of theoretical knowledge1 nor have they tended very greatly to the promotion of such knowledge4 ,the use of bread and of wine has existed from the first beginning of man's social history2 yet men have not had--we may question whether they yet have--a satisfactory theory of the constitution and fabrication of bread and of wine4 ,from a very early period there have been workers in metal3 yet who could tell upon what principles depended the purifying of gold and silver by the fire1 or the difference between iron and steel8 ,in some cases1 as in the story of the brass produced by the ,corinthian conflagration1 some particular step in art is ascribed to a special accident2 but hardly ever to the thoughtful activity of a scientific speculator4 ,the ,dyeing of cloths1 the fabrication and colouring of earthenware and glass vessels was carried to a very high degree of completeness2 yet who had any sound theoretical knowledge respecting these processes8 ,are not all these arts still practised with a degree of skill which we can hardly or not at all surpass1 by nations which have1 properly speaking1 no science8 ,till lately1 at least1 if even now the case be different1 the operations by which man's comforts1 luxuries1 and instruments were produced1 were either mere practical processes1 which the artist practises1 but which the scientist cannot account for2 or1 as in astronomy and optics1 they depended upon a small portion only of the theoretical sciences1 and did not tend to illustrate1 or lead to1 any larger truths4 ,bacon mentions as recent discoveries1 which gave him courage and hope with regard to the future progress of human knowledge1 the invention of gunpowder1 glass1 and printing1 the introduction of silk1 and the discovery of ,america4 ,yet which of these can be said to have been the results of a theoretical enlargement of human knowledge8 except perhaps the discovery of the ,new ,world1 which was in some degree the result of ,columbus's conviction of the globular form of the earth4 ,this1 however1 was not a recent1 but a very ancient #bdb doctrine of all sound astronomers4 ,and which of these discoveries has been the cause of a great enlargement of our theoretical knowledge8--except any one claims such a merit for the discovery of printing2 in which sense the result is brought about in a very indirect manner1 in the same way in which the progress of freedom and of religion may be ascribed as consequences to the same discovery4 ,however great or striking1 then1 such discoveries have been1 they have not1 generally speaking1 produced any marked advance of the ,inductive ,sciences in the sense in which we here speak of them4 ,they have increased man's power1 it may be3 that is1 his power of adding to his comforts and communicating with his fellow-men4 ,but they have not necessarily or generally increased his theoretical knowledge4 ,and1 therefore1 with whatever admiration we may look upon such discoveries as these1 we are not to admire them as steps in ,inductive ,science4 ,and on the other hand1 we are not to ask of ,inductive ,science1 as a necessary result of her progress1 such additions as these to man's means of enjoyment and action4 ,it is said1 with a feeling of triumph1 that ,knowledge is ,power3 but in whatever sense this may truly be said1 we value ,knowledge1 not because it is ,power but because it is ,knowledge2 and we estimate wrongly both the nature and the dignity of that kind of science with which we are here concerned1 if we expect that every new advance in theory will forthwith have a market value3--that science will mark the birth of a new ,truth with some new birthday present1 such as a softer stuff to wrap our limbs1 a brighter vessel to grace our table1 a new mode of communication with our friends and the world1 a new instrument for the destruction of our enemies1 or a new region which may be the source of wealth and interest4 #ac4 ,yet though1 as we have said1 many of the most remarkable processes which we reckon as the triumphs of ,art did not result from a previous progress of ,science1 we have1 at many points of the history of ,science1 applications of new views1 to enable man to do as well #bdc as to see4 ,when ,archimedes had obtained clear views of the theory of machines1 he forthwith expressed them in his bold practical boast2 ',give me whereon to stand1 and ,i will move the earth4' ,and his machines with which he is said to have handled the ,roman ships like toys1 and his burning mirrors with which he is reported to have set them on fire1 are at least possible applications of theoretical principles4 ,when he saw the waters rising in the bath as his body descended1 and rushed out crying1 ',i have found the way2' what he had found was the solution of the practical question of the quantity of silver mixed with the gold of ,hiero's crown4 ,but the mechanical inventions of ,hero of ,alexandria1 which moved by the force of air or of steam1 probably involved no exact theoretical notions of the properties of air or of steam4 ,he devised a toy which revolved by the action of steam2 but by the force of steam exerted in issuing from an orifice1 not by its pressure or condensation4 ,and the ,romans had no arts derived from science in addition to those which they inherited from the ,greeks4 ,they built aqueducts1 not indeed through ignorance of the principles of hydrostatics1 as has sometimes been said2 for we1 who know our hydrostatics1 build aqueducts still2 but their practice exemplified only ,archimedean hydrostatics4 ,their clepsydras or water-clocks were adjusted by trial only4 ,they used arches and vaults more copiously than the ,greeks had done1 but the principle of the arch appears1 by the most recent researches1 to have been known to the ,greeks4 ,domes and groined arches1 such as we have in the ,pantheon and in the ,baths of ,caracalla1 perhaps they invented2 certainly they practised them on a noble scale4 ,yet this was rather practical skill than theoretical knowledge2 and it was pursued by their successors in the middle ages in the same manner1 as practical skill rather than theoretical knowledge4 ,thus were produced flying buttresses1 intersecting pointed vaults1 and the other wonders of medival architecture4 ,the engineers of the fifteenth century1 as ,leonardo da ,vinci1 began to convert their practical into theoretical knowledge of ,mechanics2 but still #bdd clocks and watches1 flying machines and printing presses involved no new mechanical principle4 #ad4 ,but from this time the advances in ,science generally produced1 as their result1 new inventions of a practical kind4 ,thus the doctrine of the weight of air led to such inventions as the barometer used as a ,weather-glass1 the ,air-pump with its train of curious experiments1 the ,diving-,bell1 the ,balloon4 ,the telescope was perhaps in some degree a discovery due to accident1 but its principles had been taught by ,roger ,bacon1 and still more clearly by ,descartes4 ,newton invented a steady thermometer by attending to steady laws of nature4 ,and in the case of the improvements of the steam engine made by ,watt1 we have an admirable example how superior the method of improving ,art by ,science is1 to the blind gropings of mere practical habit4 ,of this truth1 the history of most of the useful arts in our time offers abundant proofs and illustrations4 ,all improvements and applications of the forces and agencies which man employs for his purposes are now commonly made1 not by blind trial but with the clearest theoretical as well as practical insight which he can obtain1 into the properties of the agents which he employs4 ,in this way he has constructed1 7using theory and calculation at every step of his construction17 steam engines1 steam boats1 screw-propellers1 locomotive engines1 railroads and bridges and structures of all kinds4 ,lightning-conductors have been improved and applied to the preservation of buildings1 and especially of ships1 with admirable effect1 by ,sir ,wm4 ,snow ,harris1 an experimenter who has studied with great care the theory of electricity4 ,the measurement of the quantity of oxygen1 that is1 of vital power1 in air1 has been taught by ,cavendish1 and by ,dr ,ure a skilful chemist of our time4 ,methods for measuring the bleaching power of a substance have been devised by eminent chemical philosophers1 ,gay ,lussac and ,mr ,graham4 ,davy used his discoveries concerning the laws of flame in order to construct his ,safety ,lamp3--his discoveries concerning the galvanic #bde battery in order to protect ships' bottoms from corrosion4 ,the skilled geologist has repeatedly given to those who were about to dig for coal where it could have no geological place1 advice which has saved them from ruinous expence4 ,sir ,roderick ,murchison1 from geological evidence1 declared the likelihood of gold being found abundantly in ,australia1 many years before the diggings began4 ,even the subtle properties of light as shewn in the recent discoveries of its interference and polarization1 have been applied to useful purposes4 ,young invented an ,eriometer1 an instrument which should measure the fineness of the threads of wool by the coloured fringes which they produce2 and substances which it is important to distinguish in the manufacture of sugar1 are discriminated by their effect in rotating the plane of polarization of light4 ,one substance has been termed ,dextrin1 from its impressing a right-handed rotation on the plane of polarization4 ,and in a great number of ,arts and ,manufactures1 the necessity of a knowledge of theory to the right conduct of practice is familiarly acknowledged and assumed4 ,in the testing and smelting of metals1 in the fabrication of soap1 of candles1 of sugar2 in the dyeing and printing of woollen1 linen1 cotton and silken stuffs2 the master manufacturer has always the scientific chemist at his elbow2--either a 'consulting chemist' to whom he may apply on a special occasion1 7for such is now a regular profession27 or a chemist who day by day superintends1 controls1 and improves the processes which his workmen daily carry on4 ,in these cases1 though ,art long preceded ,science1 ,science now guides1 governs and advances ,art4 #ae4 ,other ,arts and manufactures which have arisen in modern times have been new creations produced by ,science1 and requiring a complete acquaintance with scientific processes to conduct them effectually and securely4 ,such are the photographic ,arts1 now so various in their form2 beginning with those which1 from their authors1 are called ,daguerrotype and ,talbotype4 ,such are the ,arts of ,electrotype modelling #bdf and ,electrotype plating4 ,such are the ,arts of preparing fulminating substances2 gun-cotton2 fulminate of silver1 and of mercury2 and the application of those ,arts to use1 in the fabrication of percussion-caps for guns4 ,such is the ,art of ,electric ,telegraphy1 from its first beginning to its last great attempt1 the electric cord which connects ,england and ,america4 ,such is the ,art of imitating by the chemistry of the laboratory the vegetable chemistry of nature1 and thus producing the flavour of the pear1 the apple1 the pine-apple1 the melon1 the quince4 ,such is the ,art of producing in man a temporary insensibility to pain1 which was effected first through the means of sulphuric ether by ,dr ,jackson of ,america1 and afterwards through the use of chloroform by ,dr ,simpson of ,edinburgh4 ,in these cases and many others ,science has endowed man with ,new ,arts4 ,and though even in these ,arts1 which are thus the last results of ,science1 there is much which ,science cannot fully understand and explain2 still1 such cases cannot but be looked upon as notable verifications of the anticipations of those who ,in former times expected from the progress of ,science a harvest of material advantages to man4 ,we must now conclude our task by a few words on the subject of inductions involving ,ideas ulterior to those already considered4 #bdg ,,chapter ,x4 ,,of ,,the ,,induction ,,of ,,causes4 ,,aphorism ,,lx4 ,in the ,induction of ,causes the principal ,maxim is1 that we must be careful to possess1 and to apply1 with perfect clearness1 the ,fundamental ,idea on which the ,induction depends4 ,,aphorism ,,lxi4 ,the ,induction of ,substance1 of ,force1 of ,polarity1 go beyond mere laws of phenomena1 and may be considered as the ,induction of ,causes4 ,,aphorism ,,lxii4 ,the ,cause of certain phenomena being inferred1 we are led to inquire into the ,cause of this ,cause1 which inquiry must be conducted in the same manner as the previous one2 and thus we have the ,induction of ,ulterior ,causes4 ,,aphorism ,,lxiii4 ,in contemplating the series of ,causes which are themselves the effects of other causes1 we are necessarily led to assume a ,supreme ,cause in the ,order of ,causation1 as we assume a ,first ,cause in ,order of ,succession4 #a4 ,,we formerly#ecc stated the objects of the researches of ,science to be ,laws of ,phenomena and ,causes2 and showed the propriety and the necessity of not resting in the former object1 but extending our #bdh inquiries to the latter also4 ,inductions1 in which phenomena are connected by relations of ,space1 ,time1 ,number and ,resemblance1 belong to the former class2 and of the ,methods applicable to such ,inductions we have treated already4 ,in proceeding to ,inductions governed by any ulterior ,ideas1 we can no longer lay down any ,special ,methods by which our procedure may be directed4 ,a few general remarks are all that we shall offer4 ,note #ecc3 ,b4 ii4 c4 vii4 ,the principal ,maxim in such cases of ,induction is the obvious one3--that we must be careful to possess and to apply1 with perfect clearness and precision1 the ,fundamental ,idea on which the ,induction depends4 ,we may illustrate this in a few cases4 #b4 ,induction of ,substance4--,the ,idea of ,substance#edc involves this axiom1 that the weight of the whole compound must be equal to the weights of the separate elements1 whatever changes the composition or separation of the elements may have occasioned4 ,the application of this ,maxim we may term the ,method of the ,balance4 ,we have seen#eec elsewhere how the memorable revolution in ,chemistry1 the overthrow of ,phlogiston1 and the establishment of the ,oxygen ,theory1 was produced by the application of this ,method4 ,we have seen too#efc that the same ,idea leads us to this ,maxim2--that ,imponderable ,fluids are not to be admitted as chemical elements of bodies4 ,note #edc3 ,hist4 ,sc4 ,ideas1 ,book vi4 c4 iii4 ,note #eec3 ,ibid4 b4 vi4 c4 iv4 ,note #efc3 ,ibid4 ,whether those which have been termed ,imponderable ,fluids1--the supposed fluids which produce the phenomena of ,light1 ,heat1 ,electricity1 ,galvanism1 ,magnetism1--really exist or no1 is a question1 not merely of the ,laws1 but of the ,causes of ,phenomena4 ,it is1 as has already been shown1 a question which we cannot help discussing1 but which is at present involved in great obscurity4 ,nor does it appear at all likely that we shall obtain a true view of the cause of ,light1 ,heat1 and ,electricity1 till we have discovered precise and general laws connecting optical1 thermotical1 and #bdi electrical phenomena with those chemical doctrines to which the ,idea of ,substance is necessarily applied4 #c4 ,induction of ,force4--,the inference of ,mechanical ,forces from phenomena has been so abundantly practised1 that it is perfectly familiar among scientific inquirers4 ,from the time of ,newton1 it has been the most common aim of mathematicians2 and a persuasion has grown up among them1 that mechanical forces1--attraction and repulsion1--are the only modes of action of the particles of bodies which we shall ultimately have to consider4 ,i have attempted to show that this mode of conception is inadequate to the purposes of sound philosophy2--that the ,particles of crystals1 and the ,elements of chemical compounds1 must be supposed to be combined in some other way than by mere mechanical attraction and repulsion4 ,dr4 ,faraday has gone further in shaking the usual conceptions of the force exerted1 in well-known cases4 ,among the most noted and conspicuous instances of attraction and repulsion exerted at a distance1 were those which take place between electrized bodies4 ,but the eminent electrician just mentioned has endeavoured to establish1 by experiments of which it is very difficult to elude the weight1 that the action in these cases does not take place at a distance1 but is the result of a chain of intermediate particles connected at every point by forces of another kind4 #d4 ,induction of ,polarity4--,the forces to which ,dr4 ,faraday ascribes the action in these cases are ,polar ,forces#egc4 ,we have already endeavoured to explain the ,idea of ,polar ,forces2 which implies#ehc that at every point forces exactly equal act in opposite directions2 and thus1 in the greater part of their course1 neutralize and conceal each other2 while at the extremities of the line1 being by some cause liberated1 they are manifested1 still equal and opposite4 ,and the criterion by which this polar character of forces is recognized1 is implied in the reasoning of ,faraday1 on the question of one or two electricities1 of which we #bej formerly spoke#eic4 ,the maxim is this3--that in the action of polar forces1 along with every manifestation of force or property1 there exists a corresponding and simultaneous manifestation of an equal and opposite force or property4 ,note #egc3 ,researches1 #abth series4 ,note #ehc3 ,b4 v4 c4 i4 ,note #eic3 ,book v4 c4 i4 #e4 ,as it was the habit of the last age to reduce all action to mechanical forces1 the present race of physical speculators appears inclined to reduce all forces to polar forces4 ,mosotti has endeavoured to show that the positive and negative electricities pervade all bodies1 and that gravity is only an apparent excess of one of the kinds over the other4 ,as we have seen1 ,faraday has given strong experimental grounds for believing that the supposed remote actions of electrized bodies are really the effects of polar forces among contiguous particles4 ,if this doctrine were established with regard to all electrical1 magnetical1 and chemical forces1 we might ask1 whether1 while all other forces are polar1 gravity really affords a single exception to the universal rule8 ,is not the universe pervaded by an omnipresent antagonism1 a fundamental conjunction of contraries1 everywhere opposite1 nowhere independent8 ,we are1 as yet1 far from the position in which ,inductive ,science can enable us to answer such inquiries4 #f4 ,induction of ,ulterior ,causes4--,the first ,induction of a ,cause does not close the business of scientific inquiry4 ,behind proximate causes1 there are ulterior causes1 perhaps a succession of such4 ,gravity is the cause of the motions of the planets2 but what is the cause of gravity8 ,this is a question which has occupied men's minds from the time of ,newton to the present day4 ,earthquakes and volcanoes are the causes of many geological phenomena2 but what is the cause of those subterraneous operations8 ,this inquiry after ulterior causes is an inevitable result from the intellectual constitution of man4 ,he discovers mechanical causes1 but he cannot rest in them4 ,he must needs ask1 whence it is that matter has its universal power of attracting matter4 ,he discovers polar forces3 but even #bea if these be universal1 he still desires a further insight into the cause of this polarity4 ,he sees1 in organic structures1 convincing marks of adaptation to an end3 whence1 he asks1 is this adaptation8 ,he traces in the history of the earth a chain of causes and effects operating through time3 but what1 he inquires1 is the power which holds the end of this chain8 ,thus we are referred back from step to step in the order of causation1 in the same1 manner as1 in the paltiological sciences1 we were referred back in the order of time4 ,we make discovery after discovery in the various regions of science2 each1 it may be1 satisfactory1 and in itself complete1 but none final4 ,something always remains undone4 ,the last question answered1 the answer suggests still another question4 ,the strain of music from the lyre of ,science flows on1 rich and sweet1 full and harmonious1 but never reaches a close3 no cadence is heard with which the intellectual ear can feel satisfied4 ,of the ,supreme ,cause4--,in the utterance of ,science1 no cadence is heard with which the human mind can feel satisfied4 ,yet we cannot but go on listening for and expecting a satisfactory close4 ,the notion of a cadence appears to be essential to our relish of the music4 ,the idea of some closing strain seems to lurk among our own thoughts1 waiting to be articulated in the notes which flow from the knowledge of external nature4 ,the idea of something ultimate in our philosophical researches1 something in which the mind can acquiesce1 and which will leave us no further questions to ask1 of whence1 and why1 and by what power1 seems as if it belongs to us3--as if we could not have it withheld from us by any imperfection or incompleteness in the actual performances of science4 ,what is the meaning of this conviction8 ,what is the reality thus anticipated8 ,whither does the developement of this ,idea conduct us8 ,we have already seen that a difficulty of the same kind1 which arises in the contemplation of causes and effects considered as forming an historical series1 drives us to the assumption of a ,first ,cause1 as an ,axiom #beb to which our ,idea of ,causation in time necessarily leads4 ,and as we were thus guided to a ,first ,cause1 in order of ,succession1 the same kind of necessity directs us to a ,supreme ,cause in order of ,causation4 ,on this most weighty subject it is difficult to speak fitly2 and the present is not the proper occasion1 even for most of that which may be said4 ,but there are one or two remarks which flow from the general train of the contemplations we have been engaged in1 and with which this ,work must conclude4 ,we have seen how different are the kinds of cause to which we are led by scientific researches4 ,mechanical ,forces are insufficient without ,chemical ,affinities2 ,chemical ,agencies fail us1 and we are compelled to have recourse to ,vital ,powers2 ,vital ,powers cannot be merely physical1 and we must believe in something hyperphysical1 something of the nature of a ,soul4 ,not only do biological inquiries lead us to assume an animal soul1 but they drive us much further2 they bring before us ,perception1 and ,will evoked by ,perception4 ,still more1 these inquiries disclose to us ,ideas as the necessary forms of ,perception1 in the actions of which we ourselves are conscious4 ,we are aware1 we cannot help being aware1 of our ,ideas and our ,volitions as belonging to us1 and thus we pass from things to persons2 we have the idea of ,personality awakened4 ,and the idea of ,design and ,purpose1 of which we are conscious in our own minds1 we find reflected back to us1 with a distinctness which we cannot overlook1 in all the arrangements which constitute the frame of organized beings4 ,we cannot but reflect how widely diverse are the kinds of principles thus set before us2--by what vast strides we mount from the lower to the higher1 as we proceed through that series of causes which the range of the sciences thus brings under our notice4 ,yet we know how narrow is the range of these sciences when compared with the whole extent of human knowledge4 ,we cannot doubt that on many other subjects1 besides those included in physical speculation1 man has made out solid and satisfactory trains of #bec connexion2--has discovered clear and indisputable evidence of causation4 ,it is manifest1 therefore1 that1 if we are to attempt to ascend to the ,supreme ,cause--if we are to try to frame an idea of the ,cause of all these subordinate causes2--we must conceive it as more different from any of them1 than the most diverse are from each other2--more elevated above the highest1 than the highest is above the lowest4 ,but further2--though the ,supreme ,cause must thus be inconceivably different from all subordinate causes1 and immeasurably elevated above them all1 it must still include in itself all that is essential to each of them1 by virtue of that very circumstance that it is the ,cause of their ,causality4 ,time and ,space1--,infinite ,time and ,infinite ,space1--must be among its attributes2 for we cannot but conceive ,infinite ,time and ,space as attributes of the ,infinite ,cause of the universe4 ,force and ,matter must depend upon it for their efficacy2 for we cannot conceive the activity of ,force1 or the resistance of ,matter1 to be independent powers4 ,but these are its lower attributes4 ,the ,vital ,powers1 the ,animal ,soul1 which are the ,causes of the actions of living things1 are only the ,effects of the ,supreme ,cause of ,life4 ,and this ,cause1 even in the lowest forms of organized bodies1 and still more in those which stand higher in the scale1 involves a reference to ,ends and ,purposes1 in short1 to manifest ,final ,causes4 ,since this is so1 and since1 even when we contemplate ourselves in a view studiously narrowed1 we still find that we have ,ideas1 and ,will and ,personality1 it would render our philosophy utterly incoherent and inconsistent with itself1 to suppose that ,personality1 and ,ideas1 and ,will1 and ,purpose1 do not belong to the ,supreme ,cause from which we derive all that we have and all that we are4 ,but we may go a step further2--though1 in our present field of speculation1 we confine ourselves to knowledge founded on the facts which the external world presents to us1 we cannot forget1 in speaking of such a theme as that to which we have thus been led1 that these are but a small1 and the least significant #bed portion of the facts which bear upon it4 ,we cannot fail to recollect that there are facts belonging to the world within us1 which more readily and strongly direct our thoughts to the ,supreme ,cause of all things4 ,we can plainly discern that we have ,ideas elevated above the region of mechanical causation1 of animal existence1 even of mere choice and will1 which still have a clear and definite significance1 a permanent and indestructible validity4 ,we perceive as a fact1 that we have a ,conscience1 judging of ,right and ,wrong2 that we have ,ideas of ,moral ,good and ,evil1 that we are compelled to conceive the organization of the moral world1 as well as of the vital frame1 to be directed to an end and governed by a purpose4 ,and since the ,supreme ,cause is the cause of these facts1 the ,origin of these ,ideas1 we cannot refuse to recognize ,him as not only the ,maker1 but the ,governor of the ,world2 as not only a ,creative1 but a ,providential ,power2 as not only a ,universal ,father1 but an ,ultimate ,judge4 ,we have already passed beyond the boundary of those speculations which we proposed to ourselves as the basis of our conclusions4 ,yet we may be allowed to add one other reflection4 ,if we find in ourselves ,ideas of ,good and ,evil1 manifestly bestowed upon us to be the guides of our conduct1 which guides we yet find it impossible consistently to obey2--if we find ourselves directed1 even by our natural light1 to aim at a perfection of our moral nature from which we are constantly deviating through weakness and perverseness2 if1 when we thus lapse and err1 we can find1 in the region of human philosophy1 no power which can efface our aberrations1 or reconcile our actual with our ideal being1 or give us any steady hope and trust with regard to our actions1 after we have thus discovered their incongruity with their genuine standard2--if we discern that this is our condition1 how can we fail to see that it is in the highest degree consistent with all the indications supplied by such a philosophy as that of which we have been attempting to lay the foundations1 that the ,supreme ,cause1 through whom man exists as #bee a moral being of vast capacities and infinite ,hopes1 should have ,himself provided a teaching for our ignorance1 a propitiation for our sin1 a support for our weakness1 a purification and sanctification of our nature8 ,and thus1 in concluding our long survey of the grounds and structure of science1 and of the lessons which the study of it teaches us1 we find ourselves brought to a point of view in which we can cordially sympathize1 and more than sympathize1 with all the loftiest expressions of admiration and reverence and hope and trust1 which have been uttered by those who in former times have spoken of the elevated thoughts to which the contemplation of the nature and progress of human knowledge gives rise4 ,we can not only hold with ,galen1 and ,harvey1 and all the great physiologists1 that the organs of animals give evidence of a purpose2--not only assert with ,cuvier that this conviction of a purpose can alone enable us to understand every part of every living thing2--not only say with ,newton that 'every true step made in philosophy brings us nearer to the ,first ,cause1 and is on that account highly to be valued2'--and that 'the business of natural philosophy is to deduce causes from effects1 till we come to the very ,first ,cause1 which certainly is not mechanical2'--but we can go much farther1 and declare1 still with ,newton1 that 'this beautiful system could have its origin no other way than by the purpose and command of an intelligent and powerful ,being1 who governs all things1 not as the soul of the world1 but as the ,lord of the ,universe2 who is not only ,god1 but ,lord and ,governor4' ,when we have advanced so far1 there yet remains one step4 ,we may recollect the prayer of one1 the master in this school of the philosophy of science3 ',this also we humbly and earnestly beg2--that human things may not prejudice such as are divine2--neither that from the unlocking of the gates of sense1 and the kindling of a greater natural light1 anything may arise of incredulity or intellectual night towards divine mysteries2 but rather that by our minds thoroughly #bef purged and cleansed from fancy and vanity1 and yet subject and perfectly given up to the divine oracles1 there may be given unto faith the things that are faith's4' ,when we are thus prepared for a higher teaching1 we may be ready to listen to a greater than ,bacon1 when he says to those who have sought their ,god in the material universe1 ',whom ye ignorantly worship1 him declare ,i unto you4' ,and when we recollect how utterly inadequate all human language has been shown to be1 to express the nature of that ,supreme ,cause of the ,natural1 and ,rational1 and ,moral1 and ,spiritual world1 to which our ,philosophy points with trembling finger and shaded eyes1 we may receive1 with the less wonder but with the more reverence1 the declaration which has been vouchsafed to us3 ,a 1 ,i 1 ,i 4 #beg ,,novum ,,organon ,,renovatum4 ,,book ,,iv4 ,,of ,,the ,,language ,,of ,,science4 ,,introduction4 ,,it has been shown in the ,history of the ,sciences1 and has further appeared in the course of the ,history of ,ideas1 that almost every step in the progress of science is marked by the formation or appropriation of a technical term4 ,common language has1 in most cases1 a certain degree of looseness and ambiguity2 as common knowledge has usually something of vagueness and indistinctness4 ,in common cases too1 knowledge usually does not occupy the intellect alone1 but more or less interests some affection1 or puts in action the fancy2 and common language1 accommodating itself to the office of expressing such knowledge1 contains1 in every sentence1 a tinge of emotion or of imagination4 ,but when our knowledge becomes perfectly exact and purely intellectual1 we require a language which shall also be exact and intellectual2--which shall exclude alike vagueness and fancy1 imperfection and superfluity2--in which each term shall convey a meaning steadily fixed and rigorously limited4 ,such a language that of science becomes1 through the use of ,technical ,terms4 ,and we must now endeavour to lay down some maxims and suggestions1 by attention to which ,technical ,terms may be better fitted to answer their purpose4 ,in order to do this1 we shall in #beh the first place take a rapid survey of the manner in which ,technical ,terms have been employed from the earliest periods of scientific history4 ,the progress of the use of technical scientific language offers to our notice two different and successive periods2 in the first of which1 technical terms were formed casually1 as convenience in each case prompted2 while in the second period1 technical language was constructed intentionally1 with set purpose1 with a regard to its connexion1 and with a view of constructing a system4 ,though the casual and the systematic formation of technical terms cannot be separated by any precise date of time1 7for at all periods some terms in some sciences have been framed unsystematically17 we may1 as a general description1 call the former the ,ancient and the latter the ,modern ,period4 ,in illustrating the two following ,aphorisms1 ,i will give examples of the course followed in each of these periods4 ,,aphorism ,i4 ,in the ,ancient ,period of ,sciences1 ,technical ,terms were formed in three different ways3--by appropriating common words and fixing their meaning2--by constructing terms containing a description2--by constructing terms containing reference to a theory4 ,,the earliest sciences offer the earliest examples of technical terms4 ,these are ,geometry1 ,arithmetic1 and ,astronomy2 to which we have soon after to add ,harmonics1 ,mechanics1 and ,optics4 ,in these sciences1 we may notice the above-mentioned three different modes in which technical terms were formed4 ,i4 ,the simplest and first mode of acquiring technical terms1 is to take words current in common usage1 and by rigorously defining or otherwise fixing their meaning1 to fit them for the expression of scientific truths4 ,in this manner almost all the fundamental technical terms of ,geometry were formed4 ,a sphere1 a cone1 a cylinder1 had among the ,greeks1 at first1 #bei meanings less precise than those which geometers gave to these words1 and besides the mere designation of form1 implied some use or application4 ,a sphere 77 was a hand-ball used in games2 a cone 77 was a boy's spinning-top1 or the crest of a helmet2 a cylinder 77 was a roller2 a cube 77 was a die3 till these words were adopted by the geometers1 and made to signify among them pure modifications of space4 ,so an angle 77 was only a corner2 a point 77 was a signal2 a line 77 was a mark2 a straight line 77 was marked by an adjective which at first meant only direct4 ,a plane 77 is the neuter form of an adjective1 which by its derivation means on the ground1 and hence flat4 ,in all these cases1 the word adopted as a term of science has its sense rigorously fixed2 and where the common use of the term is in any degree vague1 its meaning may be modified at the same time that it is thus limited4 ,thus a rhombus 77 by its derivation1 might mean any figure which is twisted out of a regular form2 but it is confined by geometers to that figure which has four equal sides1 its angles being oblique4 ,in like manner1 a trapezium 77 originally signifies a table1 and thus might denote any form2 but as the tables of the ,greeks had one side shorter than the opposite one1 such a figure was at first called a trapezium4 ,afterwards the term was made to signify any figure with four unequal sides2 a name being more needful in geometry for this kind of figure than for the original form4 ,this class of technical terms1 namely1 words adopted from common language1 but rendered precise and determinate for purposes of science1 may also be exemplified in other sciences4 ,thus1 as was observed in the early portion of the history of astronomy#ad1 a day1 a month1 a year1 described at first portions of time marked by familiar changes1 but afterwards portions determined by rigorous mathematical definitions4 ,the conception of the heavens as a revolving sphere1 is so obvious1 #bfj that we may consider the terms which involve this conception as parts of common language2 as the pole 772 the arctic circle1 which includes the stars that never set#bd2 the horizon 77 a boundary1 applied technically to the circle bounding the visible earth and sky4 ,the turnings of the sun 7 71 which are mentioned by ,hesiod1 gave occasion to the term tropics1 the circles at which the sun in his annual motion turns back from his northward or southward advance4 ,the zones of the earth1 7the torrid1 temperate1 and frigid27 the gnomon of a dial2 the limb 7or border7 of the moon1 or of a circular instrument1 are terms of the same class4 ,an eclipse 77 is originally a deficiency or disappearance1 and joined with the name of the luminary1 an eclipse of the sun or of the moon1 described the phenomenon2 but when the term became technical1 it sufficed1 without addition1 to designate the phenomenon4 ,note #ad3 ,hist4 ,ind4 ,sci4 b4 iii4 c4 i4 ,note #bd3 ,hist4 ,ast4 b4 iii4 c4 i4 sect4 #h4 ,in ,mechanics1 the ,greeks gave a scientific precision to very few words3 we may mention weights 771 the arms of a lever 771 its fulcrum 771 and the verb to balance 774 ,other terms which they used1 as momentum 77 and force 771 did not acquire a distinct and definite meaning till the time of ,galileo1 or later4 ,we may observe that all abstract terms1 though in their scientific application expressing mere conceptions1 were probably at first derived from some word describing external objects4 ,thus the ,latin word for force1 vis1 seems to be connected with a ,greek word1 1 or 1 which often has nearly the same meaning2 but originally1 as it would seem1 signified a sinew or muscle1 the obvious seat of animal strength4 ,in later times1 the limitation imposed upon a word by its appropriation to scientific purposes1 is often more marked than in the cases above described4 ,thus the variation is made to mean1 in astronomy1 the second inequality of the moon's motion2 in magnetism1 the variation signifies the angular deviation of the #bfa compass-needle from the north2 in pure mathematics1 the variation of a quantity is the formula which expresses the result of any small change of the most general kind4 ,in like manner1 parallax 77 denotes a change in general1 but is used by astronomers to signify the change produced by the spectator's being removed from the center of the earth1 his theoretical place1 to the surface4 ,alkali at first denoted the ashes of a particular plant1 but afterwards1 all bodies having a certain class of chemical properties2 and1 in like manner1 acid1 the class opposed to alkali1 was modified in signification by chemists1 so as to refer no longer to the taste4 ,words thus borrowed from common language1 and converted by scientific writers into technical terms1 have some advantages and some disadvantages4 ,they possess this great convenience1 that they are understood after a very short explanation1 and retained in the memory without effort4 ,on the other hand1 they lead to some inconvenience2 for since they have a meaning in common language1 a careless reader is prone to disregard the technical limitation of this meaning1 and to attempt to collect their import in scientific books1 in the same vague and conjectural manner in which he collects the purpose of words in common cases4 ,hence the language of science1 when thus resembling common language1 is liable to be employed with an absence of that scientific precision which alone gives it value4 ,popular writers and talkers1 when they speak of force1 momentum1 action and reaction1 and the like1 often afford examples of the inaccuracy thus arising from the scientific appropriation of common terms4 ,,ii4 ,another class of technical terms1 which we find occurring as soon as speculative science assumes a distinct shape1 consists of those which are intentionally constructed by speculators1 and which contain some description or indication distinctive of the conception to which they are applied4 ,such are a parallelogram 771 which denotes a plane figure bounded by two pairs of parallel lines2 a parallelopiped #bfb 771 which signifies a solid figure bounded by three pairs of parallel planes4 ,a triangle 71 trigon7 and a quadrangle 71 tetragon7 were perhaps words invented independently of the mathematicians3 but such words extended to other cases1 pentagon1 decagon1 heccdecagon1 polygon1 are inventions of scientific men4 ,such also are tetrahedron1 hexahedron1 dodecahedron1 tesseracontaoctohedron1 polyhedron1 and the like4 ,these words being constructed by speculative writers1 explain themselves1 or at least require only some conventional limitation1 easily adopted4 ,thus parallelogram1 might mean a figure bounded by any number of sets of parallel lines1 but it is conventionally restricted to a figure of four sides4 ,so a great circle in a sphere means one which passes through the center of the sphere2 and a small circle is any other4 ,so in trigonometry1 we have the hypotenuse 771 or subtending line1 to designate the line subtending an angle1 and especially a right angle4 ,in this branch of mathematics we have many invented technical terms2 as complement1 supplement1 cosine1 cotangent1 a spherical angle1 the pole of a circle1 or of a sphere4 ,the word sine itself appears to belong to the class of terms already described as scientific appropriations of common terms1 although its origin is somewhat obscure4 ,mathematicians were naturally led to construct these and many other terms by the progress of their speculations4 ,in like manner1 when astronomy took the form of a speculative science1 words were invented to denote distinctly the conceptions thus introduced4 ,thus the sun's annual path among the stars1 in which not only solar1 but also all lunar eclipses occur1 was termed the ecliptic4 ,the circle which the sun describes in his diurnal motion1 when the days and nights are equal1 the ,greeks called the equidiurnal 717 the ,latin astronomers the equinoctial1 and the corresponding circle on the earth was the equator4 ,the ecliptic intersected the equinoctial in the equinoctial points4 ,the solstices 7in ,greek1 7 were the times when the sun arrested his motion northwards or #bfc southwards2 and the solstitial points 7 7 were the places1 in the ecliptic where he then was4 ,the name of meridians was given to circles passing through the poles of the equator2 the solstitial colure 71 curtailed71 was one of these circles1 which passes through the solstitial points1 and is intercepted by the horizon4 ,we have borrowed from the ,arabians various astronomical terms1 as ,zenith1 ,nadir1 ,azimuth1 ,almacantar4 ,and these words1 which among the ,arabians probably belonged to the first class1 of appropriated scientific terms1 are for us examples of the second class1 invented scientific terms2 although they differ from most that we have mentioned1 in not containing an etymology corresponding to their meaning in any language with which ,european cultivators of science are generally familiar4 ,indeed1 the distinction of our two classes1 though convenient1 is in a great measure1 casual4 ,thus most of the words we formerly mentioned1 as parallax1 horizon1 eclipse1 though appropriated technical terms among the ,greeks1 are to us invented technical terms4 ,in the construction of such terms as we are now considering1 those languages have a great advantage which possess a power of forming words by composition4 ,this was eminently the case with the ,greek language2 and hence most of the ancient terms of science in that language1 when their origin is once explained1 are clearly understood and easily retained4 ,of modern ,european languages1 the ,german possesses the greatest facility of composition2 and hence scientific authors in that language are able to invent terms which it is impossible to imitate in the other languages of ,europe4 ,thus ,weiss distinguishes his various systems of crystals as zwei-und-zwei-gliedrig1 ein-und-zwei-gliedrig1 drey-und-drey-gliedrig1 c41 7two-and-two-membered1 one-and-two-membered1 c47 ,and ,hessel1 also a writer on crystallography1 speaks of doubly-one-membered edges1 four-and-three spaced rays1 and the like4 ,how far the composition of words1 in such cases1 may be practised in the ,english language1 and the general question1 what are the best rules and artifices #bfd in such cases1 ,i shall afterwards consider4 ,in the mean time1 ,i may observe that this list of invented technical terms might easily be much enlarged4 ,thus in harmonics we have the various intervals1 as a ,fourth1 a ,fifth1 an ,octave1 7,diatessaron1 ,diapente1 ,diapason17 a ,comma1 which is the difference of a ,major and ,minor ,tone2 we have the various ,moods or ,keys1 and the notes of various lengths1 as ,minims1 ,breves1 ,semibreves1 ,quavers4 ,in chemistry1 ,gas was at first a technical term invented by ,van ,helmont1 though it has now been almost adopted into common language4 ,i omit many words which will perhaps suggest themselves to the reader1 because they belong rather to the next class1 which ,i now proceed to notice4 ,,iii4 ,the third class of technical terms consists of such as are constructed by men of science1 and involve some theoretical idea in the meaning which their derivation implies4 ,they do not merely describe1 like the class last spoken of1 but describe with reference to some doctrine or hypothesis which is accepted as a portion of science4 ,thus latitude and longitude1 according to their origin1 signify breadth and length2 they are used1 however1 to denote measures of the distance of a place on the earth's surface from the equator1 and from the first meridian1 of which distances1 one cannot be called length more properly than the other4 ,but this appropriation of these words may be explained by recollecting that the earth1 as known to the ancient geographers1 was much further extended from east to west than from north to south4 ,the ,precession of the equinoxes is a term which implies that the stars are fixed1 while the point which is the origin of the measure of celestial longitude moves backward4 ,the ,right ,ascension of a star is a measure of its position corresponding to terrestrial longitude2 this quantity is identical with the angular ascent of the equinoctial point1 when the star is in the horizon in a right sphere2 that is1 a sphere which supposes the spectator to be at the equator4 ,the ,oblique ,ascension 7a term now little used71 is derived in like manner from an oblique sphere4 ,the motion of a planet is direct or retrograde1 in #bfe consequentia 7signa71 or in antecedentia1 in reference to a certain assumed standard direction for celestial motions1 namely1 the direction opposite to that of the sun's daily motion1 and agreeing with his annual motion among the stars2 or with what is much more evident1 the moon's monthly motion4 ,the equation of time is the quantity which must be added to or subtracted from the time marked by the sun1 in order to reduce it to a theoretical condition of equable progress4 ,in like manner the equation of the center of the sun or of the moon is the angle which must be added to1 or subtracted from1 the actual advance of the luminary in the heavens1 in order to make its motion equable4 ,besides the equation of the center of the moon1 which represents the first and greatest of her deviations from equable motion1 there are many other equations1 by the application of which her motion is brought nearer and nearer to perfect uniformity4 ,the second of these equations is called the evection1 the third the variation1 the fourth the annual equation1 ,the motion of the sun as affected by its inequalities is called his anomaly1 which term denotes inequality4 ,in the ,history of ,astronomy1 we find that the inequable motions of the sun1 moon1 and planets were1 in a great measure1 reduced to rule and system by the ,greeks1 by the aid of an hypothesis of circles1 revolving1 and carrying in their motion other circles which also revolved4 ,this hypothesis introduced many technical terms1 as deferent1 epicycle1 eccentric4 ,in like manner1 the theories which have more recently taken the place of the theory of epicycles have introduced other technical terms1 as the elliptical orbit1 the radius vector1 and the equable description of areas by this radius1 which phrases express the true laws of the planetary motions4 ,there is no subject on which theoretical views have been so long and so extensively prevalent as astronomy1 and therefore no other science in which there are so many technical terms of the kind we are now considering4 ,but in other subjects also1 so far as theories have been established1 they have been accompanied by the introduction or fixation of technical terms4 ,thus1 as #bff we have seen in the examination of the foundations of mechanics1 the terms force and inertia derive their precise meaning from a recognition of the first law of motion2 accelerating force and composition of motion involve the second law2 moving force1 momentum1 action and reaction1 are expressions which imply the third law4 ,the term vis viva was introduced to express a general property of moving bodies2 and other terms have been introduced for like purposes1 as impetus by ,smeaton1 and work done1 by other engineers4 ,in the recent writings of several ,french engineers1 the term travail is much employed1 to express the work done and the force which does it3 this term has been rendered by labouring force4 ,the proposition which was termed the hydrostatic paradox had this name in reference to its violating a supposed law of the action of forces4 ,the verb to gravitate1 and the abstract term gravitation1 sealed the establishment of ,newton's theory of the solar system4 ,in some of the sciences1 opinions1 either false1 or disguised in very fantastical imagery1 have prevailed2 and the terms which have been introduced during the reign of such opinions1 bear the impress of the time4 ,thus in the days of alchemy1 the substances with which the operator dealt were personified2 and a metal when exhibited pure and free from all admixture was considered as a little king1 and was hence called a regulus1 a term not yet quite obsolete4 ,in like manner1 a substance from which nothing more of any value could be extracted1 was dead1 and was called a caput mortuum4 ,quick silver1 that is1 live silver 7argentum vivum71 was killed by certain admixtures1 and was revived when restored to its pure state4 ,we find a great number of medical terms which bear the mark of opinions formerly prevalent among physicians2 and though these opinions hardly form a part of the progress of science1 and were not presented in our ,history1 we may notice some of these terms as examples of the mode in which words involve in their derivation obsolete opinions4 ,such words as hysterics1 hypochondriac1 melancholy1 cholera1 colic1 quinsey #bfg 7squinantia1 1 a suffocation71 megrim1 migrane 7hemicranium1 the middle of the skull71 rickets1 7rachitis1 from 1 the backbone71 palsy1 7paralysis1 17 apoplexy 71 a stroke71 emrods1 71 hemorrhoids1 a flux of blood71 imposthume1 7corrupted from aposteme1 1 an abscess71 phthisis 71 consumption71 tympanum 71 swelling71 dropsy 7hydropsy1 17 sciatica1 isciatica 71 from 1 the hip71 catarrh 71 a flowing down71 diarrha 71 a flowing through71 diabetes 71 a passing through71 dysentery 71 a disorder of the entrails71 arthritic pains 7from 1 the joints71 are names derived from the supposed or real seat and circumstances of the diseases4 ,the word from which the first of the above names is derived 71 the last place17 signifies the womb1 according to its order in a certain systematic enumeration of parts4 ,the second word1 hypochondriac1 means something affecting the viscera below the cartilage of the breastbone1 which cartilage is called 2 melancholy and cholera derive their names from supposed affections of 1 the bile4 ,colic is that which affects the colon 771 the largest member of the bowels4 ,a disorder of the eye is called gutta serena 7the 'drop serene' of ,milton71 in contradistinction to gutta turbida1 in which the impediment to vision is perceptibly opake4 ,other terms also record the opinions of the ancient anatomists1 as duodenum1 a certain portion of the intestines1 which they estimated as twelve inches long4 ,we might add other allusions1 as the tendon of ,achilles4 ,astrology also supplied a number of words founded upon fanciful opinions2 but this study having been expelled from the list of sciences1 such words now survive1 only so far as they have found a place in common language4 ,thus men were termed mercurial1 martial1 jovial1 or saturnine1 accordingly as their characters were supposed to be determined by the influence of the planets1 ,mercury1 ,mars1 ,jupiter1 or ,saturn4 ,other expressions1 such as disastrous1 ill-starred1 exorbitant1 lord of the ascendant1 and hence ascendancy1 influence1 #bfh a sphere of action1 and the like1 may serve to show how extensively astrological opinions have affected language1 though the doctrine is no longer a recognized science4 ,the preceding examples will make it manifest that opinions1 even of a recondite and complex kind1 are often implied in the derivation of words2 and thus will show how scientific terms1 framed by the cultivators of science1 may involve received hypotheses and theories4 ,when terms are thus constructed1 they serve not only to convey with ease1 but to preserve steadily and to diffuse widely1 the opinions which they thus assume4 ,moreover1 they enable the speculator to employ these complex conceptions1 the creations of science1 and the results of much labour and thought1 as readily and familiarly as if they were convictions borrowed at once from the senses4 ,they are thus powerful instruments in enabling philosophers to ascend from one step of induction and generalization to another2 and hereby contribute powerfully to the advance of knowledge and truth4 ,it should be noticed1 before we proceed1 that the names of natural objects1 when they come to be considered as the objects of a science1 are selected according to the processes already enumerated4 ,for the most part1 the natural historian adopts the common names of animals1 plants1 minerals1 gems1 and the like1 and only endeavours to secure their steady and consistent application4 ,but many of these names imply some peculiar1 often fanciful1 belief respecting the object4 ,various plants derive their names from their supposed virtues1 as herniaria1 rupture-wort2 or from legends1 as herba ,sancti ,johannis1 ,st4 ,john's wort4 ,the same is the case with minerals3 thus the topaz was asserted to come from an island so shrouded in mists that navigators could only conjecture 77 where it was4 ,in these latter cases1 however1 the legend is often not the true origin of the name1 but is suggested by it4 ,the privilege of constructing names where they are wanted1 belongs to natural historians no less than to #bfi the cultivators of physical science2 yet in the ancient world1 writers of the former class appear rarely to have exercised this privilege1 even when they felt the imperfections of the current language4 ,thus ,aristotle repeatedly mentions classes of animals which have no name1 as co-ordinate with classes that have names2 but he hardly ventures to propose names which may supply these defects#cd4 ,the vast importance of nomenclature in natural history was not recognized till the modern period4 ,note #cd3 ,in his ,history of ,animals1 7b4 i4 c4 vi471 he says1 that the great classes of animals are ,quadrupeds1 ,birds1 ,fishes1 ,whales 7,cetaceans71 ,oysters 7,testaceans71 animals like crabs which have no general name 7,crustaceans71 soft animals 7,mollusks and ,insects74 ,he does1 however1 call the ,crustaces by a name 7,malacostraca1 soft-shelled7 which has since been adopted by ,naturalists4 ,we have1 however1 hitherto considered only the formation or appropriation of single terms in science2 except so far as several terms may in some instances be connected by reference to a common theory4 ,but when the value of technical terms began to be fully appreciated1 philosophers proceeded to introduce them into their sciences more copiously and in a more systematic manner4 ,in this way1 the modern history of technical language has some features of a different aspect from the ancient2 and must give rise to a separate ,aphorism4 ,,aphorism ,,ii4 ,in the ,modern ,period of ,science1 besides the three processes anciently employed in the formation of technical terms1 there have been introduced ,systematic ,nomenclature1 ,systematic ,terminology1 and the ,systematic ,modification of ,terms to express theoretical relations#dd4 ,note #dd3 ,on the subject of ,terminology and ,nomenclature1 see also ,aphorisms ,,lxxxviii and ,,xcviii concerning ,ideas1 and b4 viii4 c4 ii4 of the ,history of ,scientific ,ideas4 ,in those places ,i have spoken of the distinction of ,terminology and ,nomenclature4 ,,writers upon science have gone on up to modern times forming such technical terms as they had occasion for1 by the three processes above #bgj described2--namely1 appropriating and limiting words in common use2--constructing for themselves words descriptive of the conception which they wished to convey2--or framing terms which by their signification imply the adoption of a theory4 ,thus among the terms introduced by the study of the connexion between magnetism and electricity1 the word pole is an example of the first kind2 the name of the subject1 electro-magnetism1 of the second2 and the term current1 involving an hypothesis of the motion of a fluid1 is an instance of the third class4 ,in chemistry1 the term salt was adopted from common language1 and its meaning extended to denote any compound of a certain kind2 the term neutral salt implied the notion of a balanced opposition in the two elements of the compound2 and such words as subacid and superacid1 invented on purpose1 were introduced to indicate the cases in which this balance was not attained4 ,again1 when the phlogistic theory of chemistry was established1 the term phlogiston was introduced to express the theory1 and from this such terms as phlogisticated and dephlogisticated were derived1 exclusively words of science4 ,but in such instances as have just been given1 we approach towards a systematic modification of terms1 which is a peculiar process of modern times4 ,of this1 modern chemistry forms a prominent example1 which we shall soon consider1 but we shall first notice the other processes mentioned in the ,aphorism4 ,i4 ,in ancient times1 no attempt was made to invent or select a ,nomenclature of the objects of ,natural ,history which should be precise and permanent4 ,the omission of this step by the ancient naturalists gave rise to enormous difficulty and loss of time when the sciences resumed their activity4 ,we have seen in the history of the sciences of classification1 and of botany in especial#ed1 that the early cultivators of that study in modern times endeavoured to identify all the plants described by ,greek and ,roman writers with those which grow in the north of ,europe2 and were involved #bga in endless confusion#fd1 by the multiplication of names of plants1 at the same time superfluous and ambiguous4 ,the ,synonymies which botanists 7,bauhin and others7 found it necessary to publish1 were the evidences of these inconveniences4 ,in consequence of the defectiveness of the ancient botanical nomenclature1 we are even yet uncertain with respect to the identification of some of the most common trees mentioned by classical writers#gd4 ,the ignorance of botanists respecting the importance of nomenclature operated in another manner to impede the progress of science4 ,as a good nomenclature presupposes a good system of classification1 so1 on the other hand1 a system of classification cannot become permanent without a corresponding nomenclature4 ,csalpinus1 in the sixteenth century#hd1 published an excellent system of arrangement for plants2 but this1 not being connected with any system of names1 was never extensively accepted1 and soon fell into oblivion4 ,the business of framing a scientific botanical classification was in this way delayed for about a century4 ,in the same manner1 ,willoughby's classification of fishes1 though1 as ,cuvier says1 far better than any which preceded it1 was never extensively adopted1 in consequence of having no nomenclature connected with it4 ,note #ed3 ,hist4 ,ind4 ,sc4 b4 xvi4 c4 ii4 ,note #fd3 ,hist4 ,ind4 ,sc4 b4 xvi4 c4 iii4 sect4 #c4 ,note #gd3 ,for instance1 whether the fagus of the ,latins be the beech or the chestnut4 ,note #hd3 ,ib4 b4 xvi4 c4 iii4 sect4 #b4 ,,ii4 ,probably one main cause which so long retarded the work of fixing at the same time the arrangement and the names of plants1 was the great number of minute and diversified particulars in the structure of each plant which such a process implied4 ,the stalks1 leaves1 flowers1 and fruits of vegetables1 with their appendages1 may vary in so many ways1 that common language is quite insufficient to express clearly and precisely their resemblances and differences4 ,hence botany required not only a fixed system of names of plants1 but also an artificial system of phrases fitted to describe their parts3 not only a ,nomenclature1 but also #bgb a ,terminology4 ,the ,terminology was1 in fact1 an instrument indispensably requisite in giving fixity to the ,nomenclature4 ,the recognition of the kinds of plants must depend upon the exact comparison of their resemblances and differences2 and to become a part of permanent science1 this comparison must be recorded in words4 ,the formation of an exact descriptive language for botany was thus the first step in that systematic construction of the technical language of science1 which is one of the main features in the intellectual history of modern times4 ,the ancient botanists1 as ,de ,candolle#id says1 did not make any attempt to select terms of which the sense was rigorously determined2 and each of them employed in his descriptions the words1 metaphors1 or periphrases which his own genius suggested4 ,in the ,history of ,botany#ajd1 ,i have noticed some of the persons who contributed to this improvement4 ',clusius1' it is there stated1 'first taught botanists to describe well4 ,he introduced exactitude1 precision1 neatness1 elegance1 method3 he says nothing superfluous2 he omits nothing necessary4' ,this task was further carried on by ,jung and ,ray#aad4 ,in these authors we see the importance which began to be attached to the exact definition of descriptive terms2 for example1 ,ray quotes ,jung's definition of ,caulis1 a stalk4 ,note #id3 ,theor4 ,elem4 de ,bot4 p4 #cbg4 ,note #ajd3 ,hist4 ,ind4 ,sc4 b4 xvi4 c4 iii4 sect4 #c4 ,note #aad3 ,hist4 ,ind4 ,sc4 b4 xvi4 c4 iii4 sect4 #c 7about ,a4,d4 #affj74 ,the improvement of descriptive language1 and the formation of schemes of classification of plants1 went on gradually for some time1 and was much advanced by ,tournefort4 ,but at last ,linnus embodied and followed out the convictions which had gradually been accumulating in the breasts of botanists2 and by remodelling throughout both the terminology and the nomenclature of botany1 produced one of the greatest reforms which ever took place in any science4 ,he thus supplied a conspicuous example of such a reform1 and a most admirable model of a language1 from which #bgc other sciences may gather great instruction4 ,i shall not here give any account of the terms and words introduced by ,linnus4 ,they have been exemplified in the ,history of ,science#abd2 and the principles which they involve ,i shall consider separately hereafter4 ,i will only remind the reader that the great simplification in nomenclature which was the result of his labours1 consisted in designating each kind of plant by a binary term consisting of the name of the genus combined with that of the species3 an artifice seemingly obvious1 but more convenient in its results than could possibly have been anticipated4 ,note #abd3 ,ib4 c4 iv4 sect4 #a-c4 ,since ,linnus1 the progress of ,botanical ,anatomy and of ,descriptive ,botany have led to the rejection of several inexact expressions1 and to the adoption of several new terms1 especially in describing the structure of the fruit and the parts of cryptogamous plants4 ,hedwig1 ,medikus1 ,necker1 ,desvaux1 ,mirbel1 and especially ,grtner1 ,link1 and ,richard1 have proposed several useful innovations1 in these as in other parts of the subject2 but the general mass of the words now current consists still1 and will probably continue to consist1 of the terms established by the ,swedish ,botanist#acd4 ,note #acd3 ,de ,candolle1 ,th4 ,elem4 p4 #cjg4 ,when it was seen that botany derived so great advantages from a systematic improvement of its language1 it was natural that other sciences1 and especially classificatory sciences1 should endeavour to follow its example4 ,this attempt was made in ,mineralogy by ,werner1 and afterwards further pursued by ,mohs4 ,werner's innovations in the descriptive language of ,mineralogy were the result of great acuteness1 an intimate acquaintance with minerals1 and a most methodical spirit3 and were in most respects great improvements upon previous practices4 ,yet the introduction of them into ,mineralogy was far from regenerating that science1 as ,botany had been regenerated by the ,linnan reform4 ,it would seem that the perpetual #bgd scrupulous attention to most minute differences1 7as of lustre1 colour1 fracture17 the greater part of which are not really important1 fetters the mind1 rather than disciplines it or arms it for generalization4 ,cuvier has remarked#add that ,werner1 after his first ,essay on the ,characters of ,minerals1 wrote little2 as if he had been afraid of using the system which he had created1 and desirous of escaping from the chains which he had imposed upon others4 ,and he justly adds1 that ,werner dwelt least1 in his descriptions1 upon that which is really the most important feature of all1 the crystalline structure4 ,this1 which is truly a definite character1 like those of ,botany1 does1 when it can be clearly discerned1 determine the place of the mineral in a system4 ,this1 therefore1 is the character which1 of all others1 ought to be most carefully expressed by an appropriate language4 ,this task1 hardly begun by ,werner1 has since been fully executed by others1 especially by ,rom de l',isle1 ,hay1 and ,mohs4 ,all the forms of crystals can be described in the most precise manner by the aid of the labours of these writers and their successors4 ,but there is one circumstance well worthy our notice in these descriptions4 ,it is found that the language in which they can best be conveyed is not that of words1 but of symbols4 ,the relations of space which are involved in the forms of crystalline bodies1 though perfectly definite1 are so complex and numerous1 that they cannot be expressed1 except in the language of mathematics3 and thus we have an extensive and recondite branch of mathematical science1 which is1 in fact1 only a part of the ,terminology of the mineralogist4 ,note #add3 loges1 ii4 #acd4 ,the ,terminology of ,mineralogy being thus reformed1 an attempt was made to improve its ,nomenclature also1 by following the example of ,botany4 ,professor ,mohs was the proposer of this innovation4 ,the names framed by him were1 however1 not composed of two but of three elements1 designating respectively the ,species1 the ,genus1 and the ,order#aed3 thus he has such species as #bge ,rhombohedral ,lime ,haloide1 ,octahedral ,fluor ,haloide1 ,prismatic ,hal ,baryte4 ,these names have not been generally adopted2 nor is it likely that any names constructed on such a scheme will find acceptance among mineralogists1 till the higher divisions of the system are found to have some definite character4 ,we see no real mineralogical significance in ,mohs's ,genera and ,orders1 and hence we do not expect them to retain a permanent place in the science4 ,note #aed3 ,hist4 ,ind4 ,sc4 b4 xv4 c4 ix4 ,the only systematic names which have hitherto been generally admitted in ,mineralogy1 are those expressing the chemical constitution of the substance2 and these belong to a system of technical terms different from any we have yet spoken of1 namely to terms formed by systematic modification4 ,,iii4 ,the language of ,chemistry was already1 as we have seen1 tending to assume a systematic character1 even under the reign of the phlogiston theory4 ,but when oxygen succeeded to the throne1 it very fortunately happened that its supporters had the courage and the foresight to undertake a completely new and systematic recoinage of the terms belonging to the science4 ,the new nomenclature was constructed upon a principle hitherto hardly applied in science1 but eminently commodious and fertile2 namely1 the principle of indicating a modification of relations of elements1 by a change in the termination of the word4 ,thus the new chemical school spoke of sulphuric and sulphurous acids2 of sulphates and sulphites of bases2 and of sulphurets of metals2 and in like manner1 of phosphoric and phosphorous acids1 of phosphates1 phosphites1 phosphurets4 ,in this manner a nomenclature was produced1 in which the very name of a substance indicated at once its constitution and place in the system4 ,the introduction of this chemical language can never cease to be considered one of the most important steps ever made in the improvement of technical terms2 and as a signal instance of the advantages which may result from artifices apparently trivial1 if employed in a manner conformable to the laws of phenomena1 and systematically pursued4 ,it was1 however1 proved that #bgf this language1 with all its merits1 had some defects4 ,the relations of elements in composition were discovered to be more numerous than the modes of expression which the terminations supplied4 ,besides the sulphurous and sulphuric acids1 it appeared there were others2 these were called the hyposulphurous and hyposulphuric3 but these names1 though convenient1 no longer implied1 by their form1 any definite relation4 ,the compounds of ,nitrogen and ,oxygen are1 in order1 the ,protoxide1 the ,deutoxide or ,binoxide2 ,hyponitrous ,acid1 ,nitrous ,acid1 and ,nitric ,acid4 ,the nomenclature here ceases to be systematic4 ,we have three oxides of ,iron1 of which we may call the first the ,protoxide1 but we cannot call the others the ,deutoxide and ,trioxide1 for by doing so we should convey a perfectly erroneous notion of the proportions of the elements4 ,they are called the ,protoxide1 the ,black ,oxide1 and the ,peroxide4 ,we are here thrown back upon terms quite unconnected with the system4 ,other defects in the nomenclature arose from errours in the theory2 as for example the names of the muriatic1 oxymuriatic1 and hyperoxymuriatic acids2 which1 after the establishment of the new theory of chlorine1 were changed to hydrochloric acid1 chlorine1 and chloric acid4 ,thus the chemical system of nomenclature1 founded upon the oxygen theory1 while it shows how much may be effected by a good and consistent scheme of terms1 framed according to the real relations of objects1 proves also that such a scheme can hardly be permanent in its original form1 but will almost inevitably become imperfect and anomalous1 in consequence of the accumulation of new facts1 and the introduction of new generalizations4 ,still1 we may venture to say that such a scheme does not1 on this account1 become worthless2 for it not only answers its purpose in the stage of scientific progress to which it belongs3--so far as it is not erroneous1 or merely conventional1 but really systematic and significant of truth1 its terms can be translated at once into the language of any higher generalization which is afterwards arrived at4 ,if terms express #bgg relations really ascertained to be true1 they can never lose their value by any change of the received theory4 ,they are like coins of pure metal1 which1 even when carried into a country which does not recognize the sovereign whose impress they bear1 are still gladly received1 and may1 by the addition of an explanatory mark1 continue part of the common currency of the country4 ,these two great instances of the reform of scientific language1 in ,botany and in ,chemistry1 are much the most important and instructive events of this kind which the history of science offers4 ,it is not necessary to pursue our historical survey further4 ,our remaining ,aphorisms respecting the ,language of ,science will be collected and illustrated indiscriminately1 from the precepts and the examples of preceding philosophers of all periods#afd4 ,note #afd3 ,see at the end of these ,aphorisms1 further illustrations of them from the recent history of ,comparative ,anatomy and ,chemistry4 ,we may1 however1 remark that ,aphorisms ,,iii41 ,,iv41 ,v41 ,,vi41 ,,vii41 respect peculiarly the ,formation of ,technical ,terms by the ,appropriation of ,common ,words1 while the remaining ones apply to the ,formation of ,new ,terms4 ,it does not appear possible to lay down a system of rules which may determine and regulate the construction of all technical terms1 on all the occasions on which the progress of science makes them necessary or convenient4 ,but if we can collect a few maxims such as have already offered themselves to the minds of philosophers1 or such as may be justified by the instances by which we shall illustrate them1 these maxims may avail to guide us in doubtful cases1 and to prevent our aiming at advantages which are unattainable1 or being disturbed by seeming imperfections which are really no evils4 ,i shall therefore state such maxims of this kind as seem most sound and useful4 #bgh ,,aphorism ,,iii4 ,in framing scientific terms1 the appropriation of old words is preferable to the invention of new ones4 ,,this maxim is stated by ,bacon in his usual striking manner4 ,after mentioning ,metaphysic1 as one of the divisions of ,natural ,philosophy1 he adds#agd3 ',wherein ,i desire it may be conceived that ,i use the word metaphysic in a different sense from that that is received3 and in like manner ,i doubt not but it will easily appear to men of judgment that in this and other particulars1 wheresoever my conception and notion may differ from the ancient1 yet ,i am studious to keep the ancient terms4 ,for1 hoping well to deliver myself from mistaking by the order and perspicuous expressing of that ,i do propound2 ,i am otherwise zealous and affectionate to recede as little from antiquity1 either in terms or opinions1 as may stand with truth1 and the proficience of knowledge1 4 4 4 ,to me1 that do desire1 as much as lieth in my pen1 to ground a sociable intercourse between antiquity and proficience1 it seemeth best to keep a way with antiquity usque ad aras2 and therefore to retain the ancient terms1 though ,i sometimes alter the uses and definitions2 according to the moderate proceeding in civil governments1 when1 although there be some alteration1 yet that holdeth which ,tacitus wisely noteth1 eadem magistratuum vocabula4' ,note #agd3 ,de ,augm4 lib4 iii4 c4 iv4 ,we have had before us a sufficient number of examples of scientific terms thus framed2 for they formed the first of three classes which we described in the ,first ,aphorism4 ,and we may again remark1 that science1 when she thus adopts terms which are in common use1 always limits and fixes their meaning in a technical manner4 ,we may also repeat here the warning already given respecting terms of this kind1 that they are peculiarly liable to mislead readers who #bgi do not take care to understand them in their technical instead of their common signification4 ,force1 momentum1 inertia1 impetus1 vis viva1 are terms which are very useful1 if we rigorously bear in mind the import which belongs to each of them in the best treatises on ,mechanics2 but if the reader content himself with conjecturing their meaning from the context1 his knowledge will be confused and worthless4 ,in the application of this ,third ,aphorism1 other rules are to be attended to1 which ,i add4 ,,aphorism ,,iv4 ,when common words are appropriated as technical terms1 their meaning and relations in common use should be retained as far as can conveniently be done4 ,i ,,will state an example in which this rule seems to be applicable4 ,mr ,davies ,gilbert#ahd has recently proposed the term efficiency to designate the work which a machine1 according to the force exerted upon it1 is capable of doing2 the work being measured by the weight raised1 and the space through which it is raised1 jointly4 ,the usual term employed among engineers for the work which a machine actually does1 measured in the way just stated1 is duty4 ,but as there appears to be a little incongruity in calling that work efficiency which the machine ought to do1 when we call that work duty which it really does1 ,i have proposed to term these two quantities theoretical efficiency and practical efficiency1 or theoretical duty and practical duty#aid4 ,note #ahd3 ,phil4 ,trans4 #ahbg1 p4 #be4 ,note #aid3 ,the term travail is used by ,french engineers1 to express efficiency or theoretical duty4 ,this term has been rendered in ,english by labouring force4 ,since common words are often vague in their meaning1 ,i add as a necessary accompaniment to the ,third ,aphorism the following3-- #bhj ,,aphorism ,v4 ,when common words are appropriated as technical terms1 their meaning may be modified1 and must be rigorously fixed4 ,,this is stated by ,bacon in the above extract3 'to retain the ancient terms1 though ,i sometimes alter the uses and definitions4' ,the scientific use of the term is in all cases much more precise than the common use4 ,the loose notions of velocity and force for instance1 which are sufficient for the usual purposes of language1 require to be fixed by exact measures when these are made terms in the science of ,mechanics4 ,this scientific fixation of the meaning of words is to be looked upon as a matter of convention1 although it is in reality often an inevitable result of the progress of science4 ,momentum is conventionally defined to be the product of the numbers expressing the weight and the velocity2 but then1 it could be of no use in expressing the laws of motion if it were defined otherwise4 ,hence it is no valid objection to a scientific term that the word in common language does not mean exactly the same as in its common use4 ,it is no sufficient reason against the use of the term acid for a class of bodies1 that all the substances belonging to this class are not sour4 ,we have seen that a trapezium is used in geometry for any four-sided figure1 though originally it meant a figure with two opposite sides parallel and the two others equal4 ,a certain stratum which lies below the chalk is termed by ,english geologists the green sand4 ,it has sometimes been objected to this denomination that the stratum has very frequently no tinge of green1 and that it is often composed of lime with little or no sand4 ,yet the term is a good technical term in spite of these apparent improprieties2 so long as it is carefully applied to that stratum which is geologically equivalent to the greenish sandy bed to which the appellation was originally applied4 ,when it appeared that geometry would have to be employed as much at least about the heavens as the earth1 ,plato exclaimed against the folly of calling the #bha science by such a name2 since the word signifies 'earth-measuring2' yet the word geometry has retained its place and answered its purpose perfectly well up to the present day4 ,but though the meaning of the term may be modified or extended1 it must be rigorously fixed when it is appropriated to science4 ,this process is most abundantly exemplified by the terminology of ,natural ,history1 and especially of ,botany1 in which each term has a most precise meaning assigned to it4 ,thus ,linnus established exact distinctions between fasciculus1 capitulum1 racemus1 thyrsus1 paniculus1 spica1 amentum1 corymbus1 umbella1 cyma1 verticillus2 or1 in the language of ,english ,botanists1 a tuft1 a head1 a cluster1 a bunch1 a panicle1 a spike1 a catkin1 a corymb1 an umbel1 a cyme1 a whorl4 ,and it has since been laid down as a rule#bjd1 that each organ ought to have a separate and appropriate name2 so that the term leaf1 for instance1 shall never be applied to a leaflet1 a bractea1 or a sepal of the calyx4 ,note #bjd3 ,de ,candolle1 ,theor4 ,el4 #cbh4 ,botanists have not been content with fixing the meaning of their terms by verbal definition1 but have also illustrated them by figures1 which address the eye4 ,of these1 as excellent modern examples1 may be mentioned those which occur in the works of ,mirbel#bad1 and ,lindley#bbd4 ,note #bad3 lmens de ,botanique4 ,note #bbd3 ,elements of ,botany4 ,,aphorism ,,vi4 ,when common words are appropriated as technical terms1 this must be done so that they are not ambiguous in their application4 ,,an example will explain this maxim4 ,the conditions of a body1 as a solid1 a liquid1 and an air1 have been distinguished as different forms of the body4 ,but the word form1 as applied to bodies1 has other meanings2 so that if we were to inquire in what form water exists in a snow-cloud1 it might be doubted whether the forms of crystallization were meant1 or #bhb the different forms of ice1 water1 and vapour4 ,hence ,i have proposed#bcd to reject the term form in such cases1 and to speak of the different consistence of a body in these conditions4 ,the term consistence is usually applied to conditions between solid and fluid2 and may without effort be extended to those limiting conditions4 ,and though it may appear more harsh to extend the term consistence to the state of air1 it may be justified by what has been said in speaking of ,aphorism ,v4 ,note #bcd3 ,hist4 ,ind4 ,sc4 b4 x4 c4 ii4 sect4 #b4 ,i may notice another example of the necessity of avoiding ambiguous words4 ,a philosopher who makes method his study1 would naturally be termed a methodist2 but unluckily this word is already appropriated to a religious sect3 and hence we could hardly venture to speak of ,csalpinus1 ,ray1 ,morison1 ,rivinus1 ,tournefort1 ,linnus1 and their successors1 as botanical methodists4 ,again1 by this maxim1 we are almost debarred from using the term physician for a cultivator of the science of physics1 because it already signifies a practiser of physic4 ,we might1 perhaps1 still use physician as the equivalent of the ,french physicien1 in virtue of ,aphorism ,v42 but probably it would be better to form a new word4 ,thus we may say1 that while the ,naturalist employs principally the ideas of resemblance and life1 the ,physicist proceeds upon the ideas of force1 matter1 and the properties of matter4 ,whatever may be thought of this proposal1 the maxim which it implies is frequently useful4 ,it is this4 ,,aphorism ,,vii4 ,it is better to form new words as technical terms1 than to employ old ones in which the last three ,aphorisms cannot be complied with4 ,,the principal inconvenience attending the employment of new words constructed expressly for the use of science1 is the difficulty of effectually introducing them4 ,readers will not readily take the trouble to learn the meaning of a word1 in which the memory is #bhc not assisted by some obvious suggestion connected with the common use of language4 ,when this difficulty is overcome1 the new word is better than one merely appropriated2 since it is more secure from vagueness and confusion4 ,and in cases where the inconveniences belonging to a scientific use of common words become great and inevitable1 a new word must be framed and introduced4 ,the ,maxims which belong to the construction of such words will be stated hereafter2 but ,i may notice an instance or two tending to show the necessity of the ,maxim now before us4 ,the word ,force has been appropriated in the science of ,mechanics in two senses3 as indicating the cause of motion2 and again1 as expressing certain measures of the effects of this cause1 in the phrases accelerating force and moving force4 ,hence we might have occasion to speak of the accelerating or moving force of a certain force2 for instance1 if we were to say that the force which governs the motions of the planets resides in the sun2 and that the accelerating force of this force varies only with the distance1 but its moving force varies as the product of the mass of the sun and the planet4 ,this is a harsh and incongruous mode of expression2 and might have been avoided1 if1 instead of accelerating force and moving force1 single abstract terms had been introduced by ,newton3 if1 for instance1 he had said that the velocity generated in a second measures the accelerativity of the force which produces it1 and the momentum produced in a second measures the motivity of the force4 ,the science which treats of heat has hitherto had no special designation3 treatises upon it have generally been termed treatises ,on ,heat4 ,but this practice of employing the same term to denote the property and the science which treats of it1 is awkward1 and often ambiguous4 ,and it is further attended with this inconvenience1 that we have no adjective derived from the name of the science1 as we have in other cases1 when we speak of acoustical experiments and optical theories4 ,this inconvenience has led various persons to suggest names for the ,science of ,heat4 ,m4 ,comte #bhd terms it ,thermology4 ,in the ,history of the ,sciences1 ,i have named it ,thermotics1 which appears to me to agree better with the analogy of the names of other corresponding sciences1 ,acoustics and ,optics4 ,electricity is in the same condition as ,heat2 having only one word to express the property and the science4 ,m4 ,le ,comte proposes ,electrology3 for the same reason as before1 ,i should conceive ,electrics more agreeable to analogy4 ,the coincidence of the word with the plural of ,electric would not give rise to ambiguity2 for ,electrics1 taken as the name of a science1 would be singular1 like ,optics and ,mechanics4 ,but a term offers itself to express common or machine ,electrics1 which appears worthy of admission1 though involving a theoretical view4 ,the received doctrine of the difference between ,voltaic and ,common ,electricity is1 that in the former case the fluid must be considered as in motion1 in the latter as at rest4 ,the science which treats of the former class of subjects is commonly termed ,electrodynamics1 which obviously suggests the name ,electrostatics for the latter4 ,the subject of the ,tides is1 in like manner1 destitute of any name which designates the science concerned about it4 ,i have ventured to employ the term ,tidology1 having been much engaged in tidological researches4 ,many persons possess a peculiarity of vision1 which disables them from distinguishing certain colours4 ,on examining many such cases1 we find that in all such persons the peculiarities are the same2 all of them confounding scarlet with green1 and pink with blue4 ,hence they form a class1 which1 for the convenience of physiologists and others1 ought to have a fixed designation4 ,instead of calling them1 as has usually been done1 'persons having a peculiarity of vision1' we might take a ,greek term implying this meaning1 and term them ,idiopts4 ,but my business at present is not to speak of the selection of new terms when they are introduced1 but to illustrate the maxim that the necessity for their introduction often arises4 ,the construction of new terms will be treated of subsequently4 #bhe ,,aphorism ,,viii4 ,terms must be constructed and appropriated so as to be fitted to enunciate simply and clearly true general propositions4 ,,this ,aphorism may be considered as the fundamental principle and supreme rule of all scientific terminology4 ,it is asserted by ,cuvier1 speaking of a particular case4 ,thus he says#bdd of ,gmelin1 that by placing the lamantin in the genus of morses1 and the siren in the genus of eels1 he had rendered every general proposition respecting the organization of those genera impossible4 ,note #bdd3 ,rgne ,animal1 ,introd4 viii4 ,the maxim is true of words appropriated as well as invented1 and applies equally to the mathematical1 chemical1 and classificatory sciences4 ,with regard to most of these1 and especially the two former classes1 it has been abundantly exemplified already1 in what has previously been said1 and in the ,history of the ,sciences4 ,for we have there had to notice many technical terms1 with the occasions of their introduction2 and all these occasions have involved the intention of expressing in a convenient manner some truth or supposed truth4 ,the terms of ,astronomy were adopted for the purpose of stating and reasoning upon the relations of the celestial motions1 according to the doctrine of the sphere1 and the other laws which were discovered by astronomers4 ,the few technical terms which belong to ,mechanics1 force1 velocity1 momentum1 inertia1 c41 were employed from the first with a view to the expression of the laws of motion and of rest2 and were1 in the end1 limited so as truly and simply to express those laws when they were fully ascertained4 ,in ,chemistry1 the term phlogiston was useful1 as has been shown in the ,history1 in classing together processes which really are of the same nature2 and the nomenclature of the oxygen theory was still preferable1 because it enabled the chemist to express a still greater number of general truths4 #bhf ,to the connexion here asserted1 of theory and nomenclature1 we have the testimony of the author of the oxygen theory4 ,in the ,preface to his ,chemistry1 ,lavoisier says3--',thus while ,i thought myself employed only in forming a ,nomenclature1 and while ,i proposed to myself nothing more than to improve the chemical language1 my work transformed itself by degrees1 without my being able to prevent it1 into a ,treatise on the ,elements of ,chemistry4' ,and he then proceeds to show how this happened4 ,it is1 however1 mainly through the progress of ,natural ,history in modern times1 that philosophers have been led to see the importance and necessity of new terms in expressing new truths4 ,thus ,harvey1 in the ,preface to his work on ,generation1 says3--',be not offended if in setting out the ,history of the ,egg ,i make use of a new method1 and sometimes of unusual terms4 ,for as they which find out a new plantation and new shores call them by names of their own coining1 which posterity afterwards accepts and receives1 so those that find out new secrets have good title to their compellation4 ,and here1 methinks1 ,i hear ,galen advising3 ,if we consent in the things1 contend not about the words4' ,the ,nomenclature which answers the purposes of ,natural ,history is a ,systematic ,nomenclature1 and will be further considered under the next ,aphorism4 ,but we may remark1 that the ,aphorism now before us governs the use of words1 not in science only1 but in common language also4 ,are we to apply the name fish to animals of the whale kind8 ,the answer is determined by our present rule3 we are to do so1 or not1 accordingly as we can best express true propositions4 ,if we are speaking of the internal structure and physiology of the animal1 we must not call them fish2 for in these respects they deviate widely from fishes3 they have warm blood1 and produce and suckle their young as land quadrupeds do4 ,but this would not prevent our speaking of the whale-fishery1 and calling such animals fish on all occasions connected with this employment2 for the relations thus arising depend upon the animal's living in the water1 and being caught in a #bhg manner similar to other fishes4 ,a plea that human laws which mention fish do not apply to whales1 would be rejected at once by an intelligent judge4 ,a bituminiferous deposit which occurs amongst the coal measures in the neighbourhood of ,edinburgh was used as coal1 and called ',boghead ,cannel ,coal4' ,but a lawsuit arose upon the question whether this1 which geologically was not the coal1 should be regarded in law as coal4 ,the opinions of chemists and geologists1 as well as of lawyers1 were discrepant1 and a direct decision of the case was evaded4#bed ,note #bed3 ,miller's ,chemistry1 iii4 #ih4 ,,aphorism ,,ix4 ,in the ,classificatory ,sciences1 a ,systematic ,nomenclature is necessary2 and the ,system and the ,nomenclature are each essential to the utility of the other4 ,,the inconveniences arising from the want of a good ,nomenclature were long felt in ,botany1 and are still felt in ,mineralogy4 ,the attempts to remedy them by ,synonymies are very ineffective1 for such comparisons of synonyms do not supply a systematic nomenclature2 and such a one alone can enable us to state general truths respecting the objects of which the classificatory sciences treat4 ,the ,system and the ,names ought to be introduced together2 for the former is a collection of asserted analogies and resemblances1 for which the latter provide simple and permanent expressions4 ,hence it has repeatedly occurred in the progress of ,natural ,history1 that good ,systems did not take root1 or produce any lasting effect among naturalists1 because they were not accompanied by a corresponding ,nomenclature4 ,in this way1 as we have already noticed1 the excellent botanical ,system of ,csalpinus was without immediate effect upon the science4 ,the work of ,willoughby1 as ,cuvier says#bfd1 forms an epoch1 and #bhh a happy epoch in ,ichthyology2 yet because ,willoughby had no ,nomenclature of his own1 and no fixed names for his genera1 his immediate influence was not great4 ,again1 in speaking of ,schlotheim's work containing representations of fossil vegetables1 ,m4 ,adolphe ,brongniart observes#bgd that the figures and descriptions are so good1 that if the author had established a nomenclature for the objects he describes1 his work would have become the basis of all succeeding labours on the subject4 ,note #bfd3 ,hist4 des ,poissons1 ,pref4 ,note #bgd3 ,prodrom4 ,veg4 ,foss4 p4 #c4 ,as additional examples of cases in which the improvement of classification1 in recent times1 has led philosophers to propose new names1 ,i may mention the term ,pcilite1 proposed by ,mr4 ,conybeare to designate the group of strata which lies below the oolites and lias1 including the new red or variegated sandstone1 with the keuper above1 and the magnesian limestone below it4 ,again1 the transition districts of our island have recently been reduced to system by ,professor ,sedgwick and ,mr4 ,murchison2 and this step has been marked by the terms ,cambrian system1 and ,silurian system1 applied to the two great groups of formations which they have respectively examined1 and by several other names of the subordinate members of these formations4 ,thus ,system and ,nomenclature are each essential to the other4 ,without ,nomenclature1 the system is not permanently incorporated into the general body of knowledge1 and made an instrument of future progress4 ,without ,system1 the names cannot express general truths1 and contain no reason why they should be employed in preference to any other names4 ,this has been generally acknowledged by the most philosophical naturalists of modern times4 ,thus ,linnus begins that part of his ,botanical ,philosophy in which names are treated of1 by stating that the foundation of botany is twofold1 ,disposition and ,denomination2 and he adds this ,latin line1 ,nomina si nescis perit et cognitio rerum4 #bhi ,and ,cuvier1 in the ,preface to his ,animal ,kingdom1 explains1 in a very striking manner1 how the attempt to connect zoology with anatomy led him1 at the same time1 to reform the classifications1 and to correct the nomenclature of preceding zoologists4 ,i have stated that in ,mineralogy we are still destitute of a good nomenclature generally current4 ,from what has now been said1 it will be seen that it may be very far from easy to supply this defect1 since we have1 as yet1 no generally received system of mineralogical classification4 ,till we know what are really different species of minerals1 and in what larger groups these species can be arranged1 so as to have common properties1 we shall never obtain a permanent mineralogical nomenclature4 ,thus ,leucocyclite and ,tesselite are minerals previously confounded with ,apophyllite1 which ,sir ,john ,herschel and ,sir ,david ,brewster distinguished by those names1 in consequence of certain optical properties which they exhibit4 ,but are these properties definite distinctions8 and are there any external differences corresponding to them8 ,if not1 can we consider them as separate species8 and if not separate species1 ought they to have separate names8 ,in like manner1 we might ask if ,augite and ,hornblende are really the same species1 as ,gustavus ,rose has maintained8 if ,diallage and ,hypersthene are not definitely distinguished1 which has been asserted by ,kobell8 ,till such questions are settled1 we cannot have a fixed nomenclature in mineralogy4 ,what appears the best course to follow in the present state of the science1 ,i shall consider when we come to speak of the form of technical terms4 ,i may1 however1 notice here that the main ,forms of systematic nomenclature are two3--terms which are produced by combining words of higher and lower generality1 as the binary names1 consisting of the name of the genus and the species1 generally employed by natural historians since the time of ,linnus2--and terms in which some relation of things is indicated by a change in the form of the word1 for example1 an alteration of its termination1 of which kind of #bij nomenclature we have a conspicuous example in the modern chemistry4 ,,aphorism ,x4 ,new terms and changes of terms1 which are not needed in order to express truth1 are to be avoided4 ,,as the ,seventh ,aphorism asserted that novelties in language may be and ought to be introduced1 when they aid the enunciation of truths1 we now declare that they are not admissible in any other case4 ,new terms and new systems of terms are not to be introduced1 for example1 in virtue of their own neatness or symmetry1 or other merits1 if there is no occasion for their use4 ,i may mention1 as an old example of a superfluous attempt of this kind1 an occurrence in the history of ,astronomy4 ,in #afbh ,john ,bayer and ,julius ,schiller devised a ,clum ,christianum1 in which the common names of the planets1 c41 were replaced by those of ,adam1 ,moses1 and the ,patriarchs4 ,the twelve ,signs became the twelve ,apostles1 and the constellations became sacred places and things4 ,peireskius1 who had to pronounce upon the value of this proposal1 praised the piety of the inventors1 but did not approve1 he said#bhd1 the design of perverting and confounding whatever of celestial information from the period of the earliest memory is found in books4 ,note #bhd3 ,gassendi1 ,vita ,peireskii1 #cjj4 ,nor are slight anomalies in the existing language of science sufficient ground for a change1 if they do not seriously interfere with the expression of our knowledge4 ,thus ,linnus says#bid that a fair generic name is not to be exchanged for another though apter one3 and#cjd if we separate an old genus into several1 we must try to find names for them among the synonyms which describe the old genus4 ,this maxim excludes the restoration of ancient names long disused1 no less than the needless invention of new ones4 ,linnus #bia lays down this rule#cad2 and adds1 that the botanists of the sixteenth century well nigh ruined botany by their anxiety to recover the ancient names of plants4 ,in like manner ,cuvier#cbd laments it as a misfortune1 that he has had to introduce many new names2 and declares earnestly that he has taken great pains to preserve those of his predecessors4 ,note #bid3 ,phil4 ,bot4 #bdf4 ,note #cjd3 ,ib4 #bdg4 ,note #cad3 ,phil4 ,bot4 #bdh4 ,note #cbd3 ,rgne ,anim4 ,pref4 xvi4 ,the great bulk which the ,synonymy of botany and of mineralogy have attained1 shows us that this maxim has not been universally attended to4 ,in these cases1 however1 the multiplication of different names for the same kind of object has arisen in general from ignorance of the identity of it under different circumstances1 or from the want of a system which might assign to it its proper place4 ,but there are other instances1 in which the multiplication of names has arisen not from defect1 but from excess1 of the spirit of system4 ,the love which speculative men bear towards symmetry and completeness is constantly at work1 to make them create systems of classification more regular and more perfect than can be verified by the facts3 and as good systems are closely connected with a good nomenclature1 systems thus erroneous and superfluous lead to a nomenclature which is prejudicial to science4 ,for although such a nomenclature is finally expelled1 when it is found not to aid us in expressing the true laws of nature1 it may obtain some temporary sway1 during which1 and even afterwards1 it may be a source of much confusion4 ,we have a conspicuous example of such a result in the geological nomenclature of ,werner and his school4 ,thus it was assumed1 in ,werner's system1 that his ,first1 ,second1 and ,third ,fltz ,limestone1 his ,old and ,new ,red ,sandstone1 were universal formations2 and geologists looked upon it as their business to detect these strata in other countries4 ,names were thus assigned to the rocks of various parts of ,europe1 which created immense perplexity before they were again ejected4 ,the geological terms which now prevail1 for #bib instance1 those of ,smith1 are for the most part not systematic1 but are borrowed from accidents1 as localities1 or popular names2 as ,oxford ,clay and ,cornbrash2 and hence they are not liable to be thrust out on a change of system4 ,on the other hand we do not find sufficient reason to accept the system of names of strata proposed by ,mr4 ,conybeare in the ,introduction to the ,geology of ,england and ,wales1 according to which the ,carboniferous ,rocks are the ,medial ,order1--having above them the ,supermedial ,order 7,new ,red ,sand1 ,oolites and ,chalk71 and above these the ,superior ,order 7,tertiary ,rocks72 and again1--having below1 the ,submedial ,order 7the ,transition ,rocks71 and the ,inferior ,order 7,mica ,slate1 ,gneiss1 ,granite74 ,for though these names have long been proposed1 it does not appear that they are useful in enunciating geological truths4 ,we may1 it would seem1 pronounce the same judgment respecting the system of geological names proposed by ,m4 ,alexander ,brongniart1 in his ,tableau des ,terrains qui composent l'corce du ,globe4 ,he divides these strata into nine classes1 which he terms ,terrains ,alluviens1 ,lysiens1 ,pyrogenes1 ,clysmiens1 ,yzemiens1 ,hemilysiens1 ,agalysiens1 ,plutoniques1 ,vulcaniques4 ,these classes are again variously subdivided3 thus the ,terrains ,yzemiens are ,thalassiques1 ,pelagiques1 and ,abyssiques2 and the ,abyssiques are subdivided into ,lias1 ,keuper1 ,conchiliens1 ,pciliens1 ,peneens1 ,rudimentaires1 ,entritiques1 ,houillers1 ,carbonifers and ,gres ,rouge ,ancien4 ,scarcely any amount of new truths would induce geologists to burthen themselves at once with this enormous system of new names3 but in fact1 it is evident that any portion of truth1 which any author can have brought to light1 may be conveyed by means of a much simpler apparatus4 ,such a nomenclature carries its condemnation on its own face4 ,nearly the same may be said of the systematic nomenclature proposed for mineralogy by ,professor ,mohs4 ,even if all his ,genera be really natural groups1 7a doctrine which we can have no confidence in till they are confirmed by the evidence of chemistry17 there is no #bic necessity to make so great a change in the received names of minerals4 ,his proceeding in this respect1 so different from the temperance of ,linnus and ,cuvier1 has probably ensured a speedy oblivion to this part of his system4 ,in crystallography1 on the other hand1 in which ,mohs's improvements have been very valuable1 there are several terms introduced by him1 as rhombohedron1 scalenohedron1 hemihedral1 systems of crystallization1 which will probably be a permanent portion of the language of science4 ,i may remark1 in general1 that the only persons who succeed in making great alterations in the language of science1 are not those who make names arbitrarily and as an exercise of ingenuity1 but those who have much new knowledge to communicate2 so that the vehicle is commended to general reception by the value of what it contains4 ,it is only eminent discoverers to whom the authority is conceded of introducing a new system of names2 just as it is only the highest authority in the state which has the power of putting a new coinage in circulation4 ,i will here quote some judicious remarks of ,mr4 ,howard1 which fall partly under this ,aphorism1 and partly under some which follow4 ,he had proposed1 as names for the kinds of clouds1 the following3 ,cirrus1 ,cirrocumulus1 ,cirrostratus1 ,cumulostratus1 ,cumulus1 ,nimbus1 ,stratus4 ,in an abridgment of his views1 given in the ,supplement to the ,encyclopdia ,britannica1 ,english names were proposed as the equivalents of these2 ,curlcloud1 ,sondercloud1 ,wanecloud1 ,twaincloud1 ,stackencloud1 ,raincloud1 ,fallcloud4 ,upon these ,mr4 ,howard observes3 ',i mention these1 in order to have the opportunity of saying that ,i do not adopt them4 ,the names for the clouds which ,i deduced from the ,latin1 are but seven in number1 and very easy to remember4 ,they were intended as arbitrary terms for the structure of clouds1 and the meaning of them was carefully fixed by a definition4 ,the observer having once made himself master of this1 was able to apply the term with correctness1 after a little experience1 to the subject under all its varieties of form1 colour1 or position4 ,the #bid new names1 if meant to be another set of arbitrary terms1 are superfluous2 if intended to convey in themselves an explanation in ,english1 they fail in this1 by applying to some part or circumstance only of the definition2 the whole of which must be kept in view to study the subject with success4 ,to take for an example the first of the modifications4 ,the term cirrus very readily takes an abstract meaning1 equally applicable to the rectilinear as to the flexuous forms of the subject4 ,but the name of curl-cloud will not1 without some violence to its obvious sense1 acquire this more extensive one3 and will therefore be apt to mislead the reader rather than further his progress4 ,others of these names are as devoid of a meaning obvious to the ,english reader1 as the ,latin terms themselves4 ,but the principal objection to ,english or any other local terms1 remains to be stated4 ,they take away from the nomenclature its general advantage of constituting1 as far as it goes1 an universal language1 by means of which the intelligent of every country may convey to each other their ideas without the necessity of translation4' ,i here adduce these as examples of the arguments against changing an established nomenclature4 ,as grounds of selecting a new one1 they may be taken into account hereafter4 ,,aphorism ,,xi4 ,terms which imply theoretical views are admissible1 as far as the theory is proved4 ,,it is not unfrequently stated that the circumstances from which the names employed in science borrow their meaning1 ought to be facts and not theories4 ,but such a recommendation implies a belief that facts are rigorously distinguished from theories and directly opposed to them2 which belief1 we have repeatedly seen1 is unfounded4 ,when theories are firmly established1 they become facts2 and names founded on such theoretical views are unexceptionable4 ,if we speak of the minor #bie axis of ,jupiter's orbit1 or of his density1 or of the angle of refraction1 or the length of an undulation of red light1 we assume certain theories2 but inasmuch as the theories are now the inevitable interpretation of ascertained facts1 we can have no better terms to designate the conceptions thus referred to4 ,and hence the rule which we must follow is1 not that our terms must involve no theory1 but that they imply the theory only in that sense in which it is the interpretation of the facts4 ,for example1 the term polarization of light was objected to1 as involving a theory4 ,perhaps the term was at first suggested by conceiving light to consist of particles having poles turned in a particular manner4 ,but among intelligent speculators1 the notion of polarization soon reduced itself to the simple conception of opposite properties in opposite positions1 which is a bare statement of the fact3 and the term being understood to have this meaning1 is a perfectly good term1 and indeed the best which we can imagine for designating what is intended4 ,i need hardly add the caution1 that names involving theoretical views not in accordance with facts are to be rejected4 ,the following instances exemplify both the positive and the negative application of this maxim4 ,the distinction of primary and secondary rocks in geology was founded upon a theory2 namely1 that those which do not contain any organic remains were first deposited1 and afterwards1 those which contain plants and animals4 ,but this theory was insecure from the first4 ,the difficulty of making the separation which it implied1 led to the introduction of a class of transition rocks4 ,and the recent researches of geologists lead them to the conclusion1 that those rocks which are termed primary1 may be the newest1 not the oldest1 productions of nature4 ,in order to avoid this incongruity1 other terms have been proposed as substitutes for these4 ,sir ,c4 ,lyell remarks#ccd1 that granite1 gneiss1 and the like1 form a class #bif which should be designated by a common name2 which name should not be of chronological import4 ,he proposes hypogene1 signifying 'nether-formed2' and thus he adopts the theory that they have not assumed their present form and structure at the surface1 but determines nothing of the period when they were produced4 ,note #ccd3 ,princ4 ,geol4 iv4 #chf4 ,these hypogene rocks1 again1 he divides into unstratified or plutonic1 and altered stratified1 or metamorphic2 the latter term implying the hypothesis that the stratified rocks to which it is applied have been altered1 by the effect of fire or otherwise1 since they were deposited4 ,that fossiliferous strata1 in some cases at least1 have undergone such a change1 is demonstrable from facts#cdd4 ,note #cdd3 ,elem4 ,geol4 p4 #ag4 ,the modern nomenclature of chemistry implies the oxygen theory of chemistry4 ,hence it has sometimes been objected to4 ,thus ,davy1 in speaking of the ,lavoisierian nomenclature1 makes the following remarks1 which1 however plausible they may sound1 will be found to be utterly erroneous#ced4 ',simplicity and precision ought to be the characteristics of a scientific nomenclature3 words should signify things1 or the analogies of things1 and not opinions4 4 4 4 ,a substance in one age supposed to be simple1 in another is proved to be compound1 and vice vers4 ,a theoretical nomenclature is liable to continual alterations3 oxygenated muriatic acid is as improper a term as dephlogisticated marine acid4 ,every school believes itself to be in the right3 and if every school assumes to itself the liberty of altering the names of chemical substances in consequence of new ideas of their composition1 there can be no permanency in the language of the science2 it must always be confused and uncertain4 ,bodies which are similar to each other should always be classed together2 and there is a presumption that their composition is analogous4 ,metals1 earths1 alkalis1 are appropriate names for the bodies they represent1 and independent of all speculation3 whereas oxides1 sulphurets1 and muriates are terms founded upon opinions of the composition of bodies1 some of which have been already found erroneous4 #big ,the least dangerous mode of giving a systematic form to a language seems to be to signify the analogies of substances by some common sign affixed to the beginning or the termination of the word4 ,thus as the metals have been distinguished by a termination in um1 as aurum1 so their calciform or oxidated state might have been denoted by a termination in a1 as aura3 and no progress1 however great1 in the science could render it necessary that such a mode of appellation should be changed4' ,note #ced3 ,elements of ,chem4 ,phil4 p4 #df4 ,these remarks are founded upon distinctions which have no real existence4 ,we cannot separate things from their properties1 nor can we consider their properties and analogies in any other way than by having opinions about them4 ,by contrasting analogies with opinions1 it might appear as if the author maintained that there were certain analogies about which there was no room for erroneous opinions4 ,yet the analogies of chemical compounds1 are1 in fact1 those points which have been most the subject of difference of opinion1 and on which the revolutions of theories have most changed men's views4 ,as an example of analogies which are still recognized under alterations of theory1 the writer gives the relation of a metal to its oxide or calciform state4 ,but this analogy of metallic oxides1 as ,red ,copper or ,iron ,ore1 to ,calx1 or burnt lime1 is very far from being self-evident2--so far indeed1 that the recognition of the analogy was a great step in chemical theory4 ,the terms which he quotes1 oxygenated muriatic acid 7and the same may be said of dephlogisticated marine acid17 if improper1 are so not because they involve theory1 but because they involve false theory2--not because those who framed them did not endeavour to express analogies1 but because they expressed analogies about which they were mistaken4 ,unconnected names1 as metals1 earths1 alkalis1 are good as the basis of a systematic nomenclature1 but they are not substitutes for such a nomenclature4 ,a systematic nomenclature is an instrument of great utility and power1 as the modern history of chemistry has shown4 ,it would be highly unphilosophical to reject #bih the use of such an instrument1 because1 in the course of the revolutions of science1 we may have to modify1 or even to remodel it altogether4 ,its utility is not by that means destroyed4 ,it has retained1 transmitted1 and enabled us to reason upon1 the doctrines of the earlier theory1 so far as they are true2 and when this theory is absorbed into a more comprehensive one1 7for this1 and not its refutation1 is the end of a theory so far as it is true17 the nomenclature is easily translated into that which the new theory introduces4 ,we have seen1 in the history of astronomy1 how valuable the theory of epicycles was1 in its time3 the nomenclature of the relations of a planet's orbit1 which that theory introduced1 was one of ,kepler's resources in discovering the elliptical theory2 and1 though now superseded1 is still readily intelligible to astronomers4 ,this is not the place to discuss the reasons for the form of scientific terms2 otherwise we might ask1 in reference to the objections to the ,lavoisierian nomenclature1 if such forms as aurum and aura are good to represent the absence or presence of oxygen1 why such forms as sulphite and sulphate are not equally good to represent the presence of what we may call a smaller or larger dose of oxygen1 so long as the oxygen theory is admitted in its present form2 and to indicate still the difference of the same substances1 if under any change of theory it should come to be interpreted in a new manner4 ,but ,i do not now dwell upon such arguments1 my object in this place being to show that terms involving theory are not only allowable1 if understood so far as the theory is proved1 but of great value1 and indeed of indispensable use1 in science4 ,the objection to them is inconsistent with the objects of science4 ,if1 after all that has been done in chemistry or any other science1 we have arrived at no solid knowledge1 no permanent truth2--if all that we believe now may be proved to be false to-morrow2--then indeed our opinions and theories are corruptible elements1 on which it would be unwise to rest any thing important1 and which we might wish to exclude1 even from our names4 ,but if #bii our knowledge has no more security than this1 we can find no reason why we should wish at all to have names of things1 since the names are needed mainly that we may reason upon and increase our knowledge such as it is4 ,if we are condemned to endless alternations of varying opinions1 then1 no doubt1 our theoretical terms may be a source of confusion2 but then1 where would be the advantage of their being otherwise8 what would be the value of words which should express in a more precise manner opinions equally fleeting8 ,it will perhaps be said1 our terms must express facts1 not theories3 but of this distinction so applied we have repeatedly shown the futility4 ,theories firmly established are facts4 ,is it not a fact that the rusting of iron arises from the metal combining with the oxygen of the atmosphere8 ,is it not a fact that a combination of oxygen and hydrogen produces water8 ,that our terms should express such facts1 is precisely what we are here inculcating4 ,our examination of the history of science has led us to a view very different from that which represents it as consisting in the succession of hostile opinions4 ,it is1 on the contrary1 a progress1 in which each step is recognized and employed in the succeeding one4 ,every theory1 so far as it is true1 7and all that have prevailed extensively and long1 contain a large portion of truth17 is taken up into the theory which succeeds and seems to expel it4 ,all the narrower inductions of the first are included in the more comprehensive generalizations of the second4 ,and this is performed mainly by means of such terms as we are now considering2--terms involving the previous theory4 ,it is by means of such terms1 that the truths at first ascertained become so familiar and manageable1 that they can be employed as elementary facts in the formation of higher inductions4 ,these principles must be applied also1 though with great caution1 and in a temperate manner1 even to descriptive language4 ,thus the mode of describing the forms of crystals adopted by ,werner and ,rom de l',isle was to consider an original form1 from which other forms are derived by truncations of the edges and the #cjj angles4 ,hay's method of describing the same forms1 was to consider them as built up of rows of small solids1 the angles being determined by the decrements of these rows4 ,both these methods of description involve hypothetical views2 and the last was intended to rest on a true physical theory of the constitution of crystals4 ,both hypotheses are doubtful or false3 yet both these methods are good as modes of description3 nor is ,hay's terminology vitiated1 if we suppose 7as in fact we must suppose in many instances17 that crystalline bodies are not really made up of such small solids4 ,the mode of describing an octahedron of fluor spar1 as derived from the cube1 by decrements of one row on all the edges1 would still be proper and useful as a description1 whatever judgment we should form of the material structure of the body4 ,but then1 we must consider the solids which are thus introduced into the description as merely hypothetical geometrical forms1 serving to determine the angles of the faces4 ,it is in this way alone that ,hay's nomenclature can now be retained4 ,in like manner we may admit theoretical views into the descriptive phraseology of other parts of ,natural ,history3 and the theoretical terms will replace the obvious images1 in proportion as the theory is generally accepted and familiarly applied4 ,for example1 in speaking of the ,honeysuckle1 we may say that the upper leaves are perfoliate1 meaning that a single round leaf is perforated by the stalk1 or threaded upon it4 ,here is an image which sufficiently conveys the notion of the form4 ,but it is now generally recognized that this apparent single leaf is1 in fact1 two opposite leaves joined together at their bases4 ,if this were doubted1 it may be proved by comparing the upper leaves with the lower1 which are really separate and opposite4 ,hence the term connate is applied to these conjoined opposite leaves1 implying that they grow together2 or they are called connato-perfoliate4 ,again2 formerly the corolla was called monopetalous or polypetalous1 as it consisted of one part or of several3 but it is now agreed among botanists that those corollas which #cja appear to consist of a single part1 are1 in fact1 composed of several soldered together2 hence the term gamopetalous is now employed 7by ,de ,candolle and his followers7 instead of monopetalous#cfd4 ,note #cfd3 ,on this subject1 see ,illiger1 ,versuch einer ,systematischen ,vollstndigen ,terminologie fr das ,thierreich und ,pflanzenreich 7#ahaj74 ,de ,candolle1 ,thorie lmentaire de la ,botanique4 ,in this way the language of ,natural ,history not only expresses1 but inevitably implies1 general laws of nature2 and words are thus fitted to aid the progress of knowledge in this1 as in other provinces of science4 ,,aphorism ,,xii4 ,if terms are systematically good1 they are not to be rejected because they are etymologically inaccurate4 ,,terms belonging to a system are defined1 not by the meaning of their radical words1 but by their place in the system4 ,that they should be appropriate in their signification1 aids the processes of introducing and remembering them1 and should therefore be carefully attended to by those who invent and establish them2 but this once done1 no objections founded upon their etymological import are of any material weight4 ,we find no inconvenience in the circumstance that geometry means the measuring of the earth1 that the name porphyry is applied to many rocks which have no fiery spots1 as the word implies1 and oolite to strata which have no roelike structure4 ,in like manner1 if the term pcilite were already generally received1 as the name of a certain group of strata1 it would be no valid ground for quarrelling with it1 that this group was not always variegated in colour1 or that other groups were equally variegated3 although undoubtedly in introducing such a term1 care should be taken to make it as distinctive as possible4 ,it often happens1 as we have seen1 that by the natural progress of changes in language1 a word is steadily confirmed in a sense quite different from its etymological import4 ,but though #cjb we may accept such instances1 we must not wantonly attempt to imitate them4 ,i say1 not wantonly3 for if the progress of scientific identification compel us to follow any class of objects into circumstances where the derivation of the term is inapplicable1 we may still consider the term as an unmeaning sound1 or rather an historical symbol1 expressing a certain member of our system4 ,thus if1 in following the course of the mountain or carboniferous limestone1 we find that in ,ireland it does not form mountains nor contain coal1 we should act unwisely in breaking down the nomenclature in which our systematic relations are already expressed1 in order to gain1 in a particular case1 a propriety of language which has no scientific value4 ,all attempts to act upon the maxim opposite to this1 and to make our scientific names properly descriptive of the objects1 have failed and must fail4 ,for the marks which really distinguish the natural classes of objects1 are by no means obvious4 ,the discovery of them is one of the most important steps in science2 and when they are discovered1 they are constantly liable to exceptions1 because they do not contain the essential differences of the classes4 ,the natural order ,umbellat1 in order to be a natural order1 must contain some plants which have not umbels1 as ,eryngium#cgd4 ',in such cases1' said ,linnus1 'it is of small import what you call the order1 if you take a proper series of plants1 and give it some name which is clearly understood to apply to the plants you have associated4' ',i have1' he adds1 'followed the rule of borrowing the name fortiori1 from the principal feature4' ,note #cgd3 ,see ,hist4 ,ind4 ,sc4 b4 xvi4 c4 iv4 sect4 #e4 ,the distinction of crystals into systems according to the degree of symmetry which obtains in them1 has been explained elsewhere4 ,two of these systems1 of which the relation as to symmetry might be expressed by saying that one is square pyramidal and the other oblong pyramidal1 or the first square prismatic and the second oblong prismatic1 are termed by ,mohs1 the first1 ,pyramidal1 and the second ,prismatic4 ,and it may #cjc be doubted whether it is worth while to invent other terms1 though these are thus defective in characteristic significance4 ,as an example of a needless rejection of old terms in virtue of a supposed impropriety in their meaning1 ,i may mention the attempt made in the last edition of ,hay's ,mineralogy1 to substitute autopside and heteropside for metallic and unmetallic4 ,it was supposed to be proved that all bodies have a metal for their basis2 and hence it was wished to avoid the term unmetallic4 ,but the words metallic and unmetallic may mean that minerals seem metallic and unmetallic1 just as well as if they contained the element opside to imply this seeming4 ,the old names express all that the new express1 and with more simplicity1 and therefore should not be disturbed4 ,the maxim on which we are now insisting1 that we are not to be too scrupulous about the etymology of scientific terms1 may1 at first sight1 appear to be at variance with our ,fourth ,aphorism1 that words used technically are to retain their common meaning as far as possible4 ,but it must be recollected1 that in the ,fourth ,aphorism we spoke of common words appropriated as technical terms2 we here speak of words constructed for scientific purposes4 ,and although it is1 perhaps1 impossible to draw a broad line between these two classes of terms1 still the rule of propriety may be stated thus3 ,in technical terms1 deviations from the usual meaning of words are bad in proportion as the words are more familiar in our own language4 ,thus we may apply the term ,cirrus to a cloud composed of filaments1 even if these filaments are straight2 but to call such a cloud a ,curl cloud would be much more harsh4 ,since the names of things1 and of classes of things1 when constructed so as to involve a description1 are constantly liable to become bad1 the natural classes shifting away from the descriptive marks thus prematurely and casually adopted1 ,i venture to lay down the following maxim4 #cjd ,,aphorism ,,xiii4 ,the fundamental terms of a system of ,nomenclature may be conveniently borrowed from casual or arbitrary circumstances4 ,,for instance1 the names of plants1 of minerals1 and of geological strata1 may be taken from the places where they occur conspicuously or in a distinct form2 as ,parietaria1 ,parnassia1 ,chalcedony1 ,arragonite1 ,silurian system1 ,purbeck limestone4 ,these names may be considered as at first supplying standards of reference2 for in order to ascertain whether any rock be ,purbeck limestone1 we might compare it with the rocks in the ,isle of ,purbeck4 ,but this reference to a local standard is of authority only till the place of the object in the system1 and its distinctive marks1 are ascertained4 ,it would not vitiate the above names1 if it were found that the ,parnassia does not grow on ,parnassus2 that ,chalcedony is not found in ,chalcedon2 or even that ,arragonite no longer occurs in ,arragon2 for it is now firmly established as a mineral species4 ,even in geology such a reference is arbitrary1 and may be superseded1 or at least modified1 by a more systematic determination4 ,alpine limestone is no longer accepted as a satisfactory designation of a rock1 now that we know the limestone of the ,alps to be of various ages4 ,again1 names of persons1 either casually connected with the object1 or arbitrarily applied to it1 may be employed as designations4 ,this has been done most copiously in botany1 as for example1 ,nicotiana1 ,dahlia1 ,fuchsia1 ,jungermannia1 ,lonicera4 ,and ,linnus has laid down rules for restricting this mode of perpetuating the memory of men1 in the names of plants4 ,those generic names1 he says#chd1 which have been constructed to preserve the memory of persons who have deserved well of botany1 are to be religiously retained4 ,this1 he adds1 is the sole and supreme reward of the botanist's labours1 and must be carefully guarded and #cje scrupulously bestowed1 as an encouragement and an honour4 ,still more arbitrary are the terms borrowed from the names of the gods and goddesses1 heroes and heroines of antiquity1 to designate new genera in those departments of natural history in which so many have been discovered in recent times as to weary out all attempts at descriptive nomenclature4 ,cuvier has countenanced this method4 ',i have had to frame many new names of genera and sub-genera1' he says#cid1 'for the sub-genera which ,i have established were so numerous and various1 that the memory is not satisfied with numerical indications4 ,these ,i have chosen either so as to indicate some character1 or among the usual denominations1 which ,i have latinized1 or finally1 after the example of ,linnus1 among the names of mythology1 which are in general agreeable to the ear1 and which are far from being exhausted4' ,note #chd3 ,phil4 ,bot4 #bda4 ,note #cid3 ,rgne ,an4 p4 #af4 ,this mode of framing names from the names of persons to whom it was intended to do honour1 has been employed also in the mathematical and chemical sciences2 but such names have rarely obtained any permanence1 except when they recorded an inventor or discoverer4 ,some of the constellations1 indeed1 have retained such appellations1 as ,berenice's ,hair2 and the new star which shone out in the time of ,csar1 would probably have retained the name given to it1 of the ,julian ,star1 if it had not disappeared again soon after4 ,in the map of the ,moon1 almost all the parts have had such names imposed upon them by those who have constructed such maps1 and these names have very properly been retained4 ,but the names of new planets and satellites thus suggested have not been generally accepted2 as the ,medicean stars1 the name employed by ,galileo for the satellites of ,jupiter2 the ,georgium ,sidus1 the appellation proposed by ,herschel for ,uranus when first discovered#djd2 ,ceres ,ferdinandea1 #cjf the name which ,piazzi wished to impose on the small planet ,ceres4 ,the names given to astronomical ,tables by the astronomers who constructed them have been most steadily adhered to1 being indeed names of books1 and not of natural objects4 ,thus there were the ,ilchanic1 the ,alphonsine1 the ,rudolphine1 the ,carolinian ,tables4 ,comets which have been ascertained to be periodical1 have very properly had assigned to them the name of the person who established this point2 and of these we have thus1 ,halley's1 ,encke's ,comet1 and ,biela's or ,gambart's ,comet4 ,note #djd3 ,in this case1 the name ,uranus1 selected with a view to symmetry according to the mythological order of descent of the persons 7,uranus1 ,saturn1 ,jupiter1 ,mars7 was adopted by astronomers in general1 though not proposed or sanctioned by the discoverer of the new planet4 ,in the cases of the smaller planets1 ,ceres1 ,pallas1 ,juno1 and ,vesta1 the names were given either by the discoverer1 or with his sanction4 ,following this rule1 ,bessel gave the name of ,astra to a new planet discovered in the same region by ,mr4 ,hencke1 as mentioned in the additions to book vii4 of the ,history 7#bnd ,ed474 ,following the same rule1 and adhering as much as possible to mythological connexion1 the astronomers of ,europe have with the sanction of ,m4 ,le ,verrier1 given the name of ,neptune to the planet revolving beyond ,uranus1 and discovered in consequence of his announcement of its probable existence1 which had been inferred by ,mr4 ,adams and him 7calculating in ignorance of each other's purpose7 from the perturbations of ,uranus2 as ,i have stated in the ,additions to the ,third ,edition of the ,history4 ,in the case of discoveries in science or inventions of apparatus1 the name of the inventor is very properly employed as the designation4 ,thus we have the ,torricellian ,vacuum1 the ,voltaic ,pile1 ,fahrenheit's ,thermometer4 ,and in the same manner with regard to laws of nature1 we have ,kepler's ,laws1 ,boyle or ,mariotte's law of the elasticity of air1 ,huyghens's law of double refraction1 ,newton's scale of colours4 ,descartes' law of refraction is an unjust appellation2 for the discovery of the law of sines was made by ,snell4 ,in deductive mathematics1 where the invention of a theorem is generally a more definite step than an induction1 this mode of designation is more common1 as ,demoivre's ,theorem1 ,maclaurin's ,theorem1 ,lagrange's ,theorem1 ,eulerian ,integrals4 ,in the ,history of ,science#dad ,i have remarked that in the discovery of what is termed galvanism1 ,volta's #cjg office was of a higher and more philosophical kind than that of ,galvani2 and ,i have1 on this account1 urged the propriety of employing the term voltaic1 rather than galvanic electricity4 ,i may add that the electricity of the common machine is often placed in contrast with this1 and appears to require an express name4 ,mr4 ,faraday calls it common or machine electricity2 but ,i think that franklinic electricity would form a more natural correspondence with voltaic1 and would be well justified by ,franklin's place in the history of that part of the subject4 ,note #dad3 b4 xiii4 c4 #a4 ,,aphorism ,,xiv4 ,the ,binary ,method of ,nomenclature 7,names by ,genus and ,species7 is the most convenient hitherto employed in ,classification4 ,,the number of species in every province of ,natural ,history is so vast that we cannot distinguish them and record the distinctions without some artifice4 ,the known species of plants1 for instance1 were #aj1jjj in the time of ,linnus1 and are now probably #fj1jjj4 ,it would be useless to endeavour to frame and employ separate names for each of these species4 ,the division of the objects into a subordinated system of classification enables us to introduce a ,nomenclature which does not require this enormous number of names4 ,the artifice employed is1 to name a specimen by means of two 7or it might be more7 steps of the successive division4 ,thus in ,botany1 each of the ,genera has its name1 and the species are marked by the addition of some epithet to the name of the genus4 ,in this manner about #a1gjj ,generic ,names1 with a moderate number of ,specific ,names1 were found by ,linnus sufficient to designate with precision all the species of vegetables known at his time4 ,and this ,binary ,method of ,nomenclature has been found so convenient1 that it has been universally adopted in every other department of the ,natural ,history of organized beings4 #cjh ,many other modes of ,nomenclature have been tried1 but no other has at all taken root4 ,linnus himself appears at first to have intended marking each species by the ,generic ,name1 accompanied by a characteristic ,descriptive ,phrase2 and to have proposed the employment of a ,trivial ,specific ,name1 as he termed it1 only as a method of occasional convenience4 ,the use of these trivial names1 however1 has become universal1 as we have said2 and is by many persons considered the greatest improvement introduced at the ,linnan reform4 ,,aphorism ,,xv4 ,the ,maxims of ,linnus concerning the ,names to be used in ,botany1 7,philosophia ,botanica1 ,nomina4 ,sections #baj to #bee7 are good examples of ,aphorisms on this subject4 ,,both ,linnus and other writers 7as ,adanson7 have given many maxims with a view of regulating the selection of generic and specific names4 ,the maxims of ,linnus were intended as much as possible to exclude barbarism and confusion1 and have1 upon the whole1 been generally adopted4 ,these canons1 and the sagacious modesty of great botanists1 like ,robert ,brown1 in conforming to them1 have kept the majority of good botanists within salutary limits2 though many of these canons were objected to by the contemporaries of ,linnus 7,adanson and others#dbd7 as capricious and unnecessary restrictions4 ,note #dbd3 ,pref4 cxxix4 clxxii4 ,many of the names introduced by ,linnus certainly appear fanciful enough4 ,thus he gives the name ,bauhinia to a plant which has leaves in pairs1 because the ,bauhins were a pair of brothers4 ,banisteria is the name of a climbing plant in honour of ,banister1 who travelled among mountains4 ,but such names once established by adequate authority lose all their inconvenience and easily become permanent1 and hence the reasonableness of one of the ,linnan rules#dcd3-- ,that as such a perpetuation of the names of persons #cji by the names of plants is the only honour that botanists have to bestow1 it ought to be used with care and caution1 and religiously respected4 ,note #dcd3 ,phil4 ,bot4 s4 #bci4 #crd ed4 ,it may serve to show how sensitive botanists are to the allusions contained in such names1 that it has been charged against ,linnus1 as a proof of malignity towards ,buffon1 that he changed the name of the genus ,buffonia1 established by ,sauvages1 into ,bufonia1 which suggested a derivation from ,bufo1 a toad4 ,it appears to be proved that the spelling was not ,linnus's doing4 ,another ,linnan maxim is 7,art4 #bai71 that the generic name must be fixed before we attempt to form a specific name2 'the latter without the former is like the clapper without the bell4' ,the name of the genus being fixed1 the species may be marked 7,art4 #beg7 by adding to it 'a single word taken at will from any quarter2' that is1 it need not involve a description or any essential property of the plant1 but may be a casual or arbitrary appellation4 ,thus the various species of ,hieracium#ddd are ,hieracium ,alpinum1 ,h4 ,halleri1 ,h4 ,pilosella1 ,h4 dubium1 ,h4 murorum1 c41 where we see how different may be the kind of origin of the words4 ,note #ddd3 ,hooker1 ,fl4 ,scot4 #bbh4 ,attempts have been made at various times to form the names of species from those of genera in some more symmetrical manner4 ,but these have not been successful1 nor are they likely to be so2 and we shall venture to propound an axiom in condemnation of such names4 ,,aphorism ,,xvi4 ,numerical names in ,classification are bad2 and the same may be said of other names of kinds1 depending upon any fixed series of notes of order4 ,,with regard to numerical names of kinds1 of species for instance1 the objections are of this nature4 ,besides that such names offer nothing for the imagination to take hold of1 new discoveries will probably alter the #caj numeration1 and make the names erroneous4 ,thus1 if we call the species of a genus #a1 #b1 #c1 a new species intermediate between #a and #b1 #b and #c1 c4 cannot be put in its place without damaging the numbers4 ,the geological term ,trias1 lately introduced to designate the group consisting of the three members 7,bunter ,sandstein1 ,muschelkalk1 and ,keuper7 becomes improper if1 as some geologists hold1 two of these members cannot be separated4 ,objections resembling those which apply to numerical designations of species1 apply to other cases of fixed series3 for instance1 when it has been proposed to mark the species by altering the termination of the genus4 ,thus ,adanson#ded1 denoting a genus by the name ,fonna 7,lychnidea71 conceived he might mark five of its species by altering the last syllable1 ,fonna1 ,fonna-e1 ,fonna-i1 ,fonna-o1 ,fonna-u2 then others by ,fonna-ba1 ,fonna-ka1 and so on4 ,this would be liable to the same evils which have been noticed as belonging to the numerical method#dfd4 ,note #ded3 ,pref4 clxxvi4 ,note #dfd3 ,in like manner the names assigned by ,mr4 ,rickman to the successive of styles of ,gothic architecture in ,england1--,early ,english1 ,decorated1 and ,perpendicular1--cannot be replaced by numerical designations1 ,first ,pointed1 ,second ,pointed1 ,third ,pointed4 ,for--besides that he who first distinctly establishes classes has the right of naming them1 and that ,mr4 ,rickman's names are really appropriate and significant--these new names would confound all meaning of language4 ,we should not be able to divide ,early ,english1 or ,decorated1 or ,perpendicular into sub-styles2--for who could talk of ,first ,second ,pointed and ,second ,second ,pointed2 and what should we call that pointed style--the ,transition from the ,norman--which precedes the ,first ,pointed8 ,,aphorism ,,xvii4 ,in any classificatory science names including more than two steps of the classification may be employed if it be found convenient4 ,,linn,,us1 in his canons for botanical nomenclature 7,art4 #bab71 says that the names of the class and the order are to be mute1 while the names of the ,genus and ,species are sonorous4 ,and accordingly the names #caa of plants 7and the same is true of animals7 have in common practice been binary only1 consisting of a generic and a specific name4 ,the class and the order have not been admitted to form part of the appellation of the species4 ,indeed it is easy to see that a name1 which must be identical in so many instances as that of an ,order would be1 would be felt as superfluous and burthensome4 ,accordingly1 ,linnus makes it one of his maxims#dgd1 that the name of the ,class and ,order must not be expressed but understood1 and hence1 he says1 ,royen1 who took ,lilium for the name of a ,class1 rightly rejected this word as a generic name1 and substituted ,lirium with the ,greek termination4 ,note #dgd3 ,phil4 ,bot4 s4 #bae4 ,yet we must not too peremptorily assume such maxims as these to be universal for all classificatory sciences4 ,it is very possible that it may be found advisable to use three terms1 that of ,order1 ,genus1 and ,species in designating minerals1 as is done in ,mohs's nomenclature1 for example1 ,rhombohedral ,calc ,haloide1 ,paratomous ,hal ,baryte4 ,it is possible also that it may be found useful in the same science 7,mineralogy7 to mark some of the steps of classification by the termination4 ,thus it has been proposed to confine the termination ite to the ,order ,silicides of ,naumann1 as ,apophyllite1 ,stilbite1 ,leucite1 c41 and to use names of different form in other orders1 as ,talc ,spar for ,brennerite1 ,pyramidal ,titanium ,oxide for ,octahedrite4 ,some such method appears to be the most likely to give us a tolerable mineralogical nomenclature4 ,,aphorism ,,xviii4 ,in forming a ,terminology1 words may be invented when necessary1 but they cannot be conveniently borrowed from casual or arbitrary circumstances#dhd4 ,note #dhd3 ,i may also refer to ,hist4 ,sc4 ,id4 b4 viii4 c4 ii4 sec4 #b1 for some remarks on ,terminology4 ,,it will be recollected that ,terminology is a language employed for describing objects1 ,nomenclature1 a body #cab of names of the objects themselves4 ,the names1 as was stated in the last maxim1 may be arbitrary2 but the descriptive terms must be borrowed from words of suitable meaning in the modern or the classical languages4 ,thus the whole terminology which ,linnus introduced into botany1 is founded upon the received use of ,latin words1 although he defined their meaning so as to make it precise when it was not so1 according to ,aphorism ,v4 ,but many of the terms were invented by him and other botanists1 as ,perianth1 ,nectary1 ,pericarp2 so many1 indeed1 as to form1 along with the others1 a considerable language4 ,many of the terms which are now become familiar were originally invented by writers on botany4 ,thus the word ,petal1 for one division of the corolla1 was introduced by ,fabius ,columna4 ,the term ,sepal was devised by ,necker to express each of the divisions of the calyx4 ,and up to the most recent times1 new denominations of parts and conditions of parts have been devised by botanists1 when they found them necessary1 in order to mark important differences or resemblances4 ,thus the general ,receptacle of the flower1 as it is termed by ,linnus1 or ,torus by ,salisbury1 is continued into organs which carry the stamina and pistil1 or the pistil alone1 or the whole flower2 this organ has hence been termed#did ,gonophore1 ,carpophore1 and ,anthophore1 in these cases4 ,note #did3 ,de ,candolle's ,th4 ,el4 #dje4 ,in like manner when ,cuvier had ascertained that the lower jaws of ,saurians consisted always of six pieces having definite relations of form and position1 he gave names to them1 and termed them respectively the ,dental1 the ,angular1 the ,coronoid1 the ,articular1 the ,complementary1 and the ,opercular ,bones4 ,in all these cases1 the descriptive terms thus introduced have been significant in their derivation4 ,an attempt to circulate a perfectly arbitrary word as a means of description would probably be unsuccessful4 ,we have1 indeed1 some examples approaching to arbitrary designations1 in the ,wernerian names of colours1 #cac which are a part of the terminology of ,natural ,history4 ,many of these names are borrowed from natural resemblances1 as ,auricula purple1 ,apple green1 ,straw yellow2 but the names of others are taken from casual occurrences1 mostly1 however1 such as were already recognized in common language1 as ,prussian blue1 ,dutch orange1 ,king's yellow4 ,the extension of arbitrary names in scientific terminology is by no means to be encouraged4 ,i may mention a case in which it was very properly avoided4 ,when ,mr4 ,faraday's researches on ,voltaic electricity had led him to perceive the great impropriety of the term poles1 as applied to the apparatus1 since the processes have not reference to any opposed points1 but to two opposite directions of a path1 he very suitably wished to substitute for the phrases positive pole and negative pole1 two words ending in ode1 from 1 a way4 ,a person who did not see the value of our present maxim1 that descriptive terms should be descriptive in their origin1 might have proposed words perfectly arbitrary1 as ,alphode1 and ,betode3 or1 if he wished to pay a tribute of respect to the discoverers in this department of science1 ,galvanode and ,voltaode1 ,but such words would very justly have been rejected by ,mr4 ,faraday1 and would hardly have obtained any general currency among men of science4 ,zincode and ,platinode1 terms derived from the metal which1 in one modification of the apparatus1 forms what was previously termed the pole1 are to be avoided1 because in their origin too much is casual2 and they are not a good basis for derivative terms4 ,the pole at which the zinc is1 is the ,anode or ,cathode1 according as it is associated with different metals4 ,either the ,zincode must sometimes mean the pole at which the ,zinc is1 and at other times that at which the ,zinc is not1 or else we must have as many names for poles as there are metals4 ,anode and ,cathode1 the terms which ,mr4 ,faraday adopted1 were free from these objections2 for they refer to a natural standard of the direction of the voltaic current1 in a manner which1 though perhaps not obvious at first sight1 is easily understood and #cad retained4 ,anode and ,cathode1 the rising and the setting way1 are the directions which correspond to east and west in that voltaic current to which we must ascribe terrestrial magnetism4 ,and with these words it was easy to connect ,anon and ,cathon1 to designate the opposite elements which are separated and liberated at the two ,electrodes4 ,,aphorism ,,xix4 ,the meaning of ,technical ,terms must be fixed by convention1 not by casual reference to the ordinary meaning of words4 ,,in fixing the meaning of the ,technical ,terms which form the ,terminology of any science1 at least of the descriptive ,terms1 we necessarily fix1 at the same time1 the perceptions and notions which the ,terms are to convey to a hearer4 ,what do we mean by apple-green or ,french grey8 ,it might1 perhaps1 be supposed that1 in the first example1 the term apple1 referring to so familiar an object1 sufficiently suggests the colour intended4 ,but it may easily be seen that this is not true2 for apples are of many different hues of green1 and it is only by a conventional selection that we can appropriate the term to one special shade4 ,when this appropriation is once made1 the term refers to the sensation1 and not to the parts of this term2 for these enter into the compound merely as a help to the memory1 whether the suggestion be a natural connexion as in 'apple-green1' or a casual one as in ',french grey4' ,in order to derive due advantage from technical terms of this kind1 they must be associated immediately with the perception to which they belong2 and not connected with it through the vague usages of common language4 ,the memory must retain the sensation2 and the technical word must be understood as directly as the most familiar word1 and more distinctly4 ,when we find such terms as tin-white or pinchbeck-brown1 the metallic colour so denoted ought to start up in our memory without delay or search4 #cae ,this1 which it is most important to recollect with respect to the simpler properties of bodies1 as colour and form1 is no less true with respect to more compound notions4 ,in all cases the term is fixed to a peculiar meaning by convention2 and the student1 in order to use the word1 must be completely familiar with the convention1 so that he has no need to frame conjectures from the word itself4 ,such conjectures would always be insecure1 and often erroneous4 ,thus the term papilionaceous1 applied to a flower1 is employed to indicate1 not only a resemblance to a butterfly1 but a resemblance arising from five petals of a certain peculiar shape and arrangement2 and even if the resemblance to a butterfly were much stronger than it is in such cases1 yet if it were produced in a different way1 as1 for example1 by one petal1 or two only1 instead of a 'standard1' two 'wings1' and a 'keel' consisting of two parts more or less united into one1 we should no longer be justified in speaking of it as a 'papilionaceous' flower4 ,the formation of an exact and extensive descriptive language for botany has been executed with a degree of skill and felicity1 which1 before it was attained1 could hardly have been dreamt of as attainable4 ,every part of a plant has been named2 and the form of every part1 even the most minute1 has had a large assemblage of descriptive terms appropriated to it1 by means of which the botanist can convey and receive knowledge of form and structure1 as exactly as if each minute part were presented to him vastly magnified4 ,this acquisition was part of the ,linnan ,reform1 of which we have spoken in the ,history4 ',tournefort1' says ,de ,candolle#ejd1 'appears to have been the first who really perceived the utility of fixing the sense of terms in such a way as always to employ the same word in the same sense1 and always to express the same idea by the same word2 but it was ,linnus who really created and fixed this botanical language1 and this is his fairest claim to glory1 for by this fixation of language he has shed clearness and precision over all parts of the science4' ,note #ejd3 ,thor4 lm4 p4 #cbg4 #caf ,it is not necessary here to give any detailed account of the terms of botany4 ,the fundamental ones have been gradually introduced1 as the parts of plants were more carefully and minutely examined4 ,thus the flower was successively distinguished into the calyx1 the corolla1 the stamens1 and the pistils3 the sections of the corolla were termed petals by ,columna2 those of the calyx were called sepals by ,necker#ead4 ,sometimes terms of greater generality were devised2 as perianth to include the calyx and corolla1 whether one or both of these were present#ebd2 pericarp for the part inclosing the grain1 of whatever kind it be1 fruit1 nut1 pod1 c4 ,and it may easily be imagined that descriptive terms may1 by definition and combination1 become very numerous and distinct4 ,thus leaves may be called pinnatifid#ecd1 pinnnatipartite1 pinnatisect1 pinnatilobate1 palmatifid1 palmatipartite1 c41 and each of these words designates different combinations of the modes and extent of the divisions of the leaf with the divisions of its outline4 ,in some cases arbitrary numerical relations are introduced into the definition3 thus a leaf is called bilobate#edd when it is divided into two parts by a notch2 but if the notch go to the middle of its length1 it is bifid2 if it go near the base of the leaf1 it is bipartite2 if to the base1 it is bisect4 ,thus1 too1 a pod of a cruciferous plant is a silica#eed if it be four times as long as it is broad1 but if it be shorter than this it is a silicula4 ,such terms being established1 the form of the very complex leaf or frond of a fern is exactly conveyed1 for example1 by the following phrase3 'fronds rigid pinnate1 pinn recurved subunilateral pinnatifid1 the segments linear undivided or bifid spinuloso-serrate#efd4' ,note #ead3 ,de ,candolle1 #cbi4 ,note #ebd3 ,for this ,erhart and ,de ,candolle use ,perigone4 ,note #ecd3 ,de ,candolle1 #cah4 ,note #edd3 ,ibid4 #dic4 ,note #eed3 ,ibid4 #dbb4 ,note #efd3 ,hooker1 ,brit4 ,flo4 p4 #dej4 ,hymenophyllum ,wilsoni1 ,scottish filmy fern1 abundant in the highlands of ,scotland and about ,killarney4 ,other characters1 as well as form1 are conveyed with the like precision3 ,colour by means of a classified scale of colours1 as we have seen in speaking of the ,measures #cag of ,secondary ,qualities2 to which1 however1 we must add1 that the naturalist employs arbitrary names1 7such as we have already quoted17 and not mere numerical exponents1 to indicate a certain number of selected colours4 ,this was done with most precision by ,werner1 and his scale of colours is still the most usual standard of naturalists4 ,werner also introduced a more exact terminology with regard to other characters which are important in mineralogy1 as lustre1 hardness4 ,but ,mohs improved upon this step by giving a numerical scale of hardness1 in which talc is #a1 gypsum1 #b1 calc spar #c1 and so on1 as we have already explained in the ,history of ,mineralogy4 ,some properties1 as specific gravity1 by their definition give at once a numerical measure2 and others1 as crystalline form1 require a very considerable array of mathematical calculation and reasoning1 to point out their relations and gradations4 ,in all cases the features of likeness in the objects must be rightly apprehended1 in order to their being expressed by a distinct terminology4 ,thus no terms could describe crystals for any purpose of natural history1 till it was discovered that in a class of minerals the proportion of the faces might vary1 while the angle remained the same4 ,nor could crystals be described so as to distinguish species1 till it was found that the derived and primitive forms are connected by very simple relations of space and number4 ,the discovery of the mode in which characters must be apprehended so that they may be considered as fixed for a class1 is an important step in the progress of each branch of ,natural ,history2 and hence we have had1 in the ,history of ,mineralogy and ,botany1 to distinguish as important and eminent persons those who made such discoveries1 ,rom de ,lisle and ,hay1 ,csalpinus and ,gesner4 ,by the continued progress of that knowledge of minerals1 plants1 and other natural objects1 in which such persons made the most distinct and marked steps1 but which has been constantly advancing in a more gradual and imperceptible manner1 the most important and essential features of similarity and dissimilarity in such objects have been selected1 arranged1 and fitted with #cah names2 and we have thus in such departments1 systems of ,terminology which fix our attention upon the resemblances which it is proper to consider1 and enable us to convey them in words4 ,the following ,aphorisms respect the ,form of ,technical ,terms4 ,by the ,form of terms1 ,i mean their philological conditions2 as1 for example1 from what languages they may be borrowed1 by what modes of inflexion they must be compounded1 how their derivatives are to be formed1 and the like4 ,in this1 as in other parts of the subject1 ,i shall not lay down a system of rules1 but shall propose a few maxims4 ,,aphorism ,,xx4 ,the two main conditions of the ,form of technical terms are1 that they must be generally intelligible1 and susceptible of such grammatical relations as their scientific use requires4 ,,these conditions may at first appear somewhat vague1 but it will be found that they are as definite as we could make them1 without injuriously restricting ourselves4 ,it will appear1 moreover1 that they have an important bearing upon most of the questions respecting the form of the words which come before us2 and that if we can succeed in any case in reconciling the two conditions1 we obtain terms which are practically good1 whatever objections may be urged against them from other considerations4 #a4 ,the former condition1 for instance1 bears upon the question whether scientific terms are to be taken from the learned languages1 ,greek and ,latin1 or from our own4 ,and the latter condition very materially affects the same question1 since in ,english we have scarcely any power of inflecting our words2 and therefore must have recourse to ,greek or ,latin in order to obtain terms which admit of grammatical modification4 ,if we were content with the term ,heat1 to express the science of heat1 still it would be a bad technical term1 for we cannot derive from it an adjective like #cai thermotical4 ,if bed or layer were an equally good term with stratum1 we must still retain the latter1 in order that we may use the derivative ,stratification1 for which the ,english words cannot produce an equivalent substitute4 ,we may retain the words lime and flint1 but their adjectives for scientific purposes are not limy and flinty1 but calcareous and siliceous2 and hence we are able to form a compound1 as calcareo-siliceous1 which we could not do with indigenous words4 ,we might fix the phrases bent back and broken to mean 7of optical rays7 that they are reflected and refracted2 but then we should have no means of speaking of the angles of ,reflection and ,refraction1 of the ,refractive ,indices1 and the like4 ,in like manner1 so long as anatomists described certain parts of a vertebra as vertebral lamin1 or vertebral plates1 they had no adjective whereby to signify the properties of these parts2 the term ,neurapophysis1 given to them by ,mr4 ,owen1 supplies the corresponding expression neurapophysial4 ,so again1 the term ,basisphenoid1 employed by the same anatomist1 is better than basilar or basial process of the sphenoid1 because it gives us the adjective basisphenoidal4 ,and the like remark applies to other changes recently proposed in the names of portions of the skeleton4 ,thus one of the advantages of going to the ,greek and ,latin languages for the origin of our scientific terms is1 that in this way we obtain words which admit of the formation of adjectives and abstract terms1 and of composition1 and of other inflexions4 ,another advantage of such an origin is1 that such terms1 if well selected1 are readily understood over the whole lettered world4 ,for this reason1 the descriptive language of science1 of botany for instance1 has been1 for the most part1 taken from the ,latin2 many of the terms of the mathematical and chemical sciences have been derived from the ,greek2 and when occasion occurs to construct a new term1 it is generally to that language that recourse is had4 ,the advantage of such terms is1 as has already been intimated1 that they constitute an universal language1 by means of which #cbj cultivated persons in every country may convey to each other their ideas without the need of translation4 ,on the other hand1 the advantage of indigenous terms is1 that so far as the language extends1 they are intelligible much more clearly and vividly than those borrowed from any other source1 as well as more easily manageable in the construction of sentences4 ,in the descriptive language of botany1 for example1 in an ,english work1 the terms drooping1 nodding1 one-sided1 twining1 straggling1 appear better than cernuous1 nutant1 secund1 volubile1 divaricate4 ,for though the latter terms may by habit become as intelligible as the former1 they cannot become more so to any readers2 and to most ,english readers they will give a far less distinct impression4 #b4 ,since the advantage of indigenous over learned terms1 or the contrary1 depends upon the balance of the capacity of inflexion and composition on the one hand1 against a ready and clear significance on the other1 it is evident that the employment of scientific terms of the one class or of the other may very properly be extremely different in different languages4 ,the ,german possesses in a very eminent degree that power of composition and derivation1 which in ,english can hardly be exercised at all1 in a formal manner4 ,hence ,german scientific writers use native terms to a far greater extent than do our own authors4 ,the descriptive terminology of botany1 and even the systematic nomenclature of chemistry1 are represented by the ,germans by means of ,german roots and inflexions4 ,thus the description of ,potentilla anserina1 in ,english botanists1 is that it has ,leaves interruptedly pinnate1 serrate1 silky1 stem creeping1 stalks axilllar1 one-flowered4 ,here we have words of ,saxon and ,latin origin mingled pretty equally4 ,but the ,german description is entirely ,teutonic4 ,die ,blume in ,achsel2 die ,bltter unterbrochen gefiedert1 die ,blttchen scharf gesagt1 die ,stmme kriechend1 die ,bluthenstiele einblumig4 ,we could imitate this in our own language1 by saying brokenly-feathered1 sharp-sawed2 by using threed for ternate1 as the ,germans employ gedreit2 by saying #cba fingered-feathered for digitato-pinnate1 and the like4 ,but the habit which we have1 in common as well as scientific language1 of borrowing words from the ,latin for new cases1 would make such usages seem very harsh and pedantic4 ,we may add that1 in consequence of these different practices in the two languages1 it is a common habit of the ,german reader to impose a scientific definiteness upon a common word1 such as our ,fifth ,aphorism requires2 whereas the ,english reader expects rather that a word which is to have a technical sense shall be derived from the learned languages4 ,die ,kelch and die ,blume 7the cup and the flower7 easily assume the technical meaning of calyx and corolla2 die ,griffel 7the pencil7 becomes the pistil2 and a name is easily found for the pollen1 the anthers1 and the stamens1 by calling them the dust1 the dust-cases1 and the dust-threads 7der ,staub1 die ,staub-beutel1 or ,staub-fcher1 and die ,staub-fden71 ,this was formerly done in ,english to a greater extent than is now possible without confusion and pedantry4 ,thus1 in ,grew's book on the ,anatomy of ,plants1 the calyx is called the impalement1 and the sepals the impalers2 the petals are called the leaves of the flower2 the stamens with their anthers are the seminiform attire4 ,but the ,english language1 as to such matters1 is now less flexible than it was2 partly in consequence of its having adopted the ,linnan terminology almost entire1 without any endeavour to naturalize it4 ,any attempt at idiomatic description would interfere with the scientific language now generally received in this country4 ,in ,germany1 on the other hand1 those who first wrote upon science in their own language imitated the ,latin words which they found in foreign writers1 instead of transferring new roots into their own language4 ,thus the ,numerator and ,denominator of a fraction they call the ,namer and the ,counter 7,nenner and ,zhler74 ,this course they pursued even where the expression was erroneous4 ,thus that portion of the intestines which ancient anatomists called ,duodenum1 because they falsely estimated its length at twelve inches1 the #cbb ,germans also term ,zwlffingerdarm 7twelve-inch-gut71 though this intestine in a whale is twenty feet long1 and in a frog not above twenty lines4 ,as another example of this process in ,german1 we may take the word ,muttersackbauchblatte1 the uterine peritonum4 ,it is a remarkable evidence of this formative power of the ,german language1 that it should have been able to produce an imitation of the systematic chemical nomenclature of the ,french school1 so complete1 that it is used in ,germany as familiarly as the original system is in ,france and ,england4 ,thus ,oxygen and ,hydrogen are ,sauerstoff and 9999,wasserstoff2 ,azote is ,stickstoff 7suffocating matter72 ,sulphuric and ,sulphurous ,acid are ,schwefel-sure and ,schwefelichte-sure4 ,the ,sulphate and ,sulphite of ,baryta1 and ,sulphuret of ,baryum1 are ,schwefel-sure ,baryterde1 ,schwefelichte-sure ,baryterde1 and ,schwefel-baryum4 ,carbonate of ,iron is ,kohlen-sures ,eisenoxydul2 and we may observe that1 in such cases1 the ,german name is much more agreeable to analogy than the ,english one2 for the ,protoxide of ,iron1 7,eisenoxydul17 and not the ,iron itself1 is the base of the salt4 ,and the ,german language has not only thus imitated the established nomenclature of chemistry1 but has shown itself capable of supplying new forms to meet the demands which the progress of theory occasions4 ,thus the ,hydracids are ,wasserstoff-suren2 and of these1 the ,hydriodic ,acid is ,iodwasserstoff-sure1 and so of the rest4 ,in like manner1 the translator of ,berzelius has found ,german names for the sulpho-salts of that chemist2 thus he has ,wasserstoffschwefliges ,schewefellithium1 which would be 7if we were to adopt his theoretical view7 hydro-sulphuret of sulphuret of lithium3 and a like nomenclature for all other similar cases4 #c4 ,in ,english we have no power of imitating this process1 and must take our technical phrases from some more flexible language1 and generally from the ,latin or ,greek4 ,we are indeed so much accustomed to do this1 that except a word has its origin in one of these languages1 it hardly seems to us a technical #cbc term2 and thus by employing indigenous terms1 even descriptive ones1 we may1 perhaps1 lose in precision more than we gain in the vividness of the impression4 ,perhaps it may be better to say cuneate1 lunate1 hastate1 sagittate1 reniform1 than wedge-shaped1 crescent-shaped1 halbert-headed1 arrow-headed1 kidney-shaped4 ,ringent and personate are better than any ,english words which we could substitute for them2 labiate is more precise than lipped would readily become4 ,urceolate1 trochlear1 are more compact than pitcher-shaped1 pulley-shaped2 and infundibuliform1 hypocrateriform1 though long words1 are not more inconvenient than funnel-shaped and salver-shaped4 ,in the same way it is better to speak 7with ,dr4 ,prichard#egd17 of repent and progressive animals1 than of creeping and progressive3 the two ,latin terms make a better pair of correlatives4 ,note #egd3 ,researches1 p4 #fi4 #d4 ,but wherever we may draw the line between the proper use of ,english and ,latin terms in descriptive phraseology1 we shall find it advisable to borrow almost all other technical terms from the learned languages4 ,we have seen this in considering the new terms introduced into various sciences in virtue of our ,ninth ,maxim4 ,we may add1 as further examples1 the names of the various animals of which a knowledge has been acquired from the remains of them which exist in various strata1 and which have been reconstructed by ,cuvier and his successors4 ,such are the ,palotherium1 the ,anoplotherium1 the ,megatherium1 the ,dinotherium1 the ,chirotherium1 the ,megalichthys1 the ,mastodon1 the ,ichthyosaurus1 the ,plesiosaurus1 the ,pterodactylus4 ,to these others are every year added2 as1 for instance1 very recently1 the ,toxodon1 ,zeuglodon1 and ,phascolotherium of ,mr4 ,owen1 and the ,thylacotherium of ,m4 ,valenciennes4 ,still more recently the terms ,glyptodon1 ,mylodon1 ,dicynodon1 ,paloplotherium1 ,rhynchosaurus1 have been added by ,mr4 ,owen to designate fossil animals newly determined by him4 #cbd ,the names of species1 as well as of genera1 are thus formed from the ,greek3 as the ,plesiosaurus dolichodeirus 7long-necked71 ,ichthyosaurus platyodon 7broad-toothed71 the ,irish elk1 termed ,cervus megaceros 7large-horned74 ,but the descriptive specific names are also taken from the ,latin1 as ,plesiosaurus brevirostris1 longirostris1 crassirostris2 besides which there are arbitrary specific names1 which we do not here consider4 ,these names being all constructed at a period when naturalists were familiar with an artificial system1 the standard language of which is ,latin1 have not been taken from modern language4 ,but the names of living animals1 and even of their classes1 long ago formed in the common language of men1 have been in part adopted in the systems of naturalists1 agreeably to ,aphorism ,third4 ,hence the language of systems in natural history is mixed of ancient and modern languages4 ,thus ,cuvier's divisions of the vertebrated animals are ,mammifres 7,latin71 ,oiseaux1 ,reptiles1 ,poissons2 ,bimanes1 ,quadrumanes1 ,carnassires1 ,rongeurs1 ,pachydermes 7,greek71 ,ruminans 7,latin71 ,ctacs 7,latin74 ,in the subordinate divisions the distribution being more novel1 the names are less idiomatic3 thus the kinds of ,reptiles are ,cheloniens1 ,sauriens1 ,ophidiens1 ,batraciens1 all which are of ,greek origin4 ,in like manner4 ,fish are divided into ,chondropterygiens1 ,malacopterygiens1 ,acanthopterygiens4 ,the unvertebrated animals are ,mollusques1 ,animaux articuls1 and ,animaux rayonns2 and the ,mollusques are divided into six classes1 chiefly according to the position or form of their foot2 namely1 ,cephalopodes1 ,pteropodes1 ,gasteropodes1 ,acephales1 ,brachiopodes1 ,cirrhopodes4 ,in transferring these terms into ,english1 when the term is new in ,french as well as ,english1 we have little difficulty2 for we may take nearly the same liberties in ,english which are taken in ,french2 and hence we may say mammifers 7rather mammals71 cetaceans or cetaces1 batracians 7rather batrachians71 using the words as substantives4 ,but in other cases we must go back to the ,latin3 thus we say radiate #cbe animals1 or radiata 7rather radials71 for rayonns4 ,these changes1 however1 rather refer to another ,aphorism4 7,mr4 ,kirby has proposed radiary1 radiaries1 for radiata47 #e4 ,when new ,mineral ,species have been established in recent times1 they have generally had arbitrary names assigned to them1 derived from some person or places4 ,in some instances1 however1 descriptive names have been selected2 and then these have been generally taken from the ,greek1 as ,augite1 ,stilbite1 ,diaspore1 ,dichroite1 ,dioptase4 ,several of these ,greek names imposed by ,hay1 refer to some circumstances1 often fancifully selected1 in his view of the crystallization of the substance1 as ,epidote1 ,peridote1 ,pleonast4 ,similar terms of ,greek origin have been introduced by others1 as ,orthite1 ,anorthite1 ,periklin4 ,greek names founded on casual circumstances are less to be commended4 ,berzelius has termed a mineral ,eschynite from 1 shame1 because it is1 he conceives1 a shame for chemists not to have separated its elements more distinctly than they did at first4 #f4 ,in ,botany1 the old names of genera of ,greek origin are very numerous1 and many of them are descriptive1 as ,glycyrhiza 7 and 1 sweet root7 liquorice1 ,rhododendron 7rose-tree71 ,hmatoxylon 7bloody wood71 ,chrysocoma 7golden hair71 ,alopecurus 7fox-tail71 and many more4 ,in like manner there are names which derive a descriptive significance from the ,latin1 either adjectives1 as ,impatiens1 ,gloriosa1 ,sagittaria1 or substantives irregularly formed1 as ,tussilago 7 tussis domatione71 ,urtica 7ab urendo tactu71 ,salsola 7 salsedine74 ,but these1 though good names when they are established by tradition1 are hardly to be imitated in naming new plants4 ,in most instances1 when this is to be done1 arbitrary or local names have been selected1 as ,strelitzia4 #g4 ,in ,chemistry1 new substances have of late had names assigned them from ,greek roots1 as ,iodine1 from its violet colour1 ,chlorine from its green colour4 ,in like manner fluorine has by the ,french chemists been called ,phthor1 from its destructive properties4 ,so the #cbf new metals1 ,chrome1 ,rhodium1 ,iridium1 ,osmium1 had names of ,greek derivation descriptive of their properties4 ,some such terms1 however1 were borrowed from localities1 as ,strontia1 ,yttria1 the names of new earths4 ,others have a mixed origin1 as ,pyrogallic1 ,pyroacetic1 and ,pyroligneous ,spirit4 ,in some cases the derivation has been extravagantly capricious4 ,thus in the process for making ,pyrogallic ,acid1 a certain substance is left behind1 from which ,m4 ,braconnot extracted an acid which he called ,ellagic ,acid1 framing the root of the name by reading the word ,galle backwards4 ,the new laws which the study of ,electro-chemistry brought into view1 required a new terminology to express their conditions3 and in this case1 as we have observed in speaking of the ,twelfth ,maxim1 arbitrary words are less suitable4 ,mr4 ,faraday very properly borrowed from the ,greek his terms ,electrolyte1 ,electrode1 ,anode1 ,cathode1 ,anon1 ,cathon1 ,dielectric4 ,in the mechanico-chemical and mechanical sciences1 however1 new terms are less copiously required than in the sciences of classification1 and when they are needed1 they are generally determined by analogy from existing terms4 ,thermo-electricity and ,electro-dynamics were terms which very naturally offered themselves2 ,nobili's thermo-multiplier1 ,snow ,harris's unit-jar1 were almost equally obvious names4 ,in such cases1 it is generally possible to construct terms both compendious and descriptive1 without introducing any new radical words4 #h4 ,the subject of ,crystallography has inevitably given rise to many new terms1 since it brings under our notice a great number of new relations of a very definite but very complex form4 ,hay attempted to find names for all the leading varieties of crystals1 and for this purpose introduced a great number of new terms1 founded on various analogies and allusions4 ,thus the forms of calc-spar are termed by him primitive1 equiaxe1 inverse1 metastatique1 contrastante1 imitable1 birhomboidale1 prismatique1 apophane1 uniternaire1 bisunitaire1 dodcadre1 contracte1 dilate1 sexduodecimale1 bisalterne1 binoternaire1 and many others4 ,the #cbg want of uniformity in the origin and scheme of these denominations would be no valid objection to them1 if any general truth could be expressed by means of them3 but the fact is1 that there is no definite distinction of these forms4 ,they pass into each other by insensible gradations1 and the optical and physical properties which they possess are common to all of them4 ,and as a mere enunciation of laws of form1 this terminology is insufficient4 ,thus it does not at all convey the relation between the bisalterne and the binoternaire1 the former being a combination of the metastatique with the prismatique1 the latter1 of the metastatique with the contrastante3 again1 the contrastante1 the mixte1 the cuboide1 the contracte1 the dilate1 all contain faces generated by a common law1 the index being respectively altered so as to be in these cases1 #c1 #c_/b1 #d_/e1 #i_/d1 #e_/i2 and this1 which is the most important geometrical relation of these forms1 is not at all recorded or indicated by the nomenclature4 ,the fact is1 that it is probably impossible1 the subject of crystallography having become so complex as it now is1 to devise a system of names which shall express the relations of form4 ,numerical symbols1 such as those of ,weiss or ,naumann1 or ,professor ,miller1 are the proper ways of expressing these relations1 and are the only good crystallographic terminology for cases in detail4 ,the terms used in expressing crystallographic laws have been for the most part taken from the ,greek by all writers except some of the ,germans4 ,these1 we have already stated1 have constructed terms in their own language1 as zwei-und-ein gliedrig1 and the like4 ,in ,optics we have some new terms connected with crystalline laws1 as uniaxal and biaxal crystals1 optical axes1 which offered themselves without any effort on the part of the discoverers4 ,in the whole history of the undulatory theory1 very few innovations in language were found necessary1 except to fix the sense of a few phrases1 as plane-polarized light in opposition to circularly-polarized1 and the like4 ,this is still more the case in ,mechanics1 ,astronomy1 #cbh and pure mathematics4 ,in these sciences1 several of the primary stages of generalization being already passed over1 when any new steps are made1 we have before us some analogy by which we may frame our new terms4 ,thus when the plane of maximum areas was discovered1 it had not some new arbitrary denomination assigned it1 but the name which obviously described it was fixed as a technical name4 ,the result of this survey of the scientific terms of recent formation seems to be this2--that indigenous terms may be employed in the descriptions of facts and phenomena as they at first present themselves2 and in the first induction from these2 but that when we come to generalize and theorize1 terms borrowed from the learned languages are more readily fixed and made definite1 and are also more easily connected with derivatives4 ,our native terms are more impressive1 and at first more intelligible2 but they may wander from their scientific meaning1 and are capable of little inflexion4 ,words of classical origin are precise to the careful student1 and capable of expressing1 by their inflexions1 the relations of general ideas2 but they are unintelligible1 even to the learned man1 without express definition1 and convey instruction only through an artificial and rare habit of thought4 ,since in the balance between words of domestic and of foreign origin so much depends upon the possibility of inflexion and derivation1 ,i shall consider a little more closely what are the limits and considerations which we have to take into account in reference to that subject4 ,,aphorism ,,xxi4 ,in the composition and inflexion of technical terms1 philological analogies are to be preserved if possible1 but modified according to scientific convenience4 ,,in the language employed or proposed by writers upon subjects of science1 many combinations and forms of derivation occur1 which would be rejected and condemned by those who are careful of the purity and #cbi correctness of language4 ,such anomalies are to be avoided as much as possible2 but it is impossible to escape them altogether1 if we are to have a scientific language which has any chance of being received into general use4 ,it is better to admit compounds which are not philologically correct1 than to invent many new words1 all strange to the readers for whom they are intended3 and in writing on science in our own language1 it is not possible to avoid making additions to the vocabulary of common life2 since science requires exact names for many things which common language has not named4 ,and although these new names should1 as much as possible1 be constructed in conformity with the analogies of the language1 such extensions of analogy can hardly sound1 to the grammarian's ear1 otherwise than as solecisms4 ,but1 as our maxim indicates1 the analogy of science is of more weight with us than the analogy of language3 and although anomalies in our phraseology should be avoided as much as possible1 innovations must be permitted wherever a scientific language1 easy to acquire1 and convenient to use1 is unattainable without them4 ,i shall proceed to mention some of the transgressions of strict philological rules1 and some of the extensions of grammatical forms1 which the above conditions appear to render necessary4 #a4 ,the combination of different languages in the derivation of words1 though to be avoided in general1 is in some cases admissible4 ,such words are condemned by ,quintilian and other grammarians1 under the name of hybrids1 or things of a mixed race2 as biclinium from bis and 2 epitogium1 from and toga4 ,nor are such terms to be unnecessarily introduced in science4 ,whenever a homogeneous word can be formed and adopted with the same ease and convenience as a hybrid1 it is to be preferred4 ,hence we must have ichthyology1 not piscology1 entomology1 not insectology1 insectivorous1 not insectophagous4 ,in like manner1 it would be better to say unoculus than monoculus1 though the latter has the sanction of ,linnus1 who was a purist in such matters4 #ccj ,dr4 ,turner1 in his ,chemistry1 speaks of protoxides and binoxides1 which combination violates the rule for making the materials of our terms as homogeneous as possible2 protoxide and deutoxide would be preferable1 both on this and on other accounts4 ,yet this rule admits of exceptions4 ,mineralogy1 with its ,greek termination1 has for its root minera1 a medieval ,latin word of ,teutonic origin1 and is preferable to ,oryctology4 ,terminology appears to be better than ,glossology3 which according to its derivation would be rather the science of language in general than of technical terms2 and ,horology1 from 1 a term1 would not be immediately intelligible1 even to ,greek scholars2 and is already employed to indicate the science which treats of horologes1 or time-pieces4 ,indeed1 the ,english reader is become quite familiar with the termination ology1 the names of a large number of branches of science and learning having that form4 ,this termination is at present rather apprehended as a formative affix in our own language1 indicating a science1 than as an element borrowed from foreign language4 ,hence1 when it is difficult or impossible to find a ,greek term which clearly designates the subject of a science1 it is allowable to employ some other1 as in ,tidology1 the doctrine of the ,tides4 ,the same remark applies to some other ,greek elements of scientific words3 they are so familiar to us that in composition they are almost used as part of our own language4 ,this naturalization has taken place very decidedly in the element arch1 7 a leader17 as we see in archbishop1 archduke4 ,it is effected in a great degree for the preposition anti3 thus we speak of anti-slavery societies1 anti-reformers1 anti-bilious1 or anti-acid medicines1 without being conscious of any anomaly4 ,the same is the case with the ,latin preposition pr or pre1 as appears from such words as pre-engage1 pre-arrange1 pre-judge1 pre-paid2 and in some measure with pro1 for in colloquial language we speak of pro-catholics and anti-catholics4 ,also the preposition ante is similarly used1 as ante-nicene fathers4 ,the preposition co1 abbreviated from con1 and #cca implying things to be simultaneous or connected1 is firmly established as part of the language1 as we see in coexist1 coheir1 coordinate2 hence ,i have called those lines cotidal lines which pass through places where the high water of the tide occurs simultaneously4 #b4 ,as in the course of the mixture by which our language has been formed1 we have thus lost all habitual consciousness of the difference of its ingredients1 7,greek1 ,latin1 ,norman-,french1 and ,anglo-,saxon73 we have also ceased to confine to each ingredient the mode of grammatical inflexion which originally belonged to it4 ,thus the termination ive belongs peculiarly to ,latin adjectives1 yet we say sportive1 talkative4 ,in like manner1 able is added to words which are not ,latin1 as eatable1 drinkable1 pitiable1 enviable4 ,also the termination al and ical are used with various roots1 as loyal1 royal1 farcical1 whimsical2 hence we may make the adjective tidal from tide4 ,this ending1 al1 is also added to abstract terms in ion1 as occasional1 provisional1 intentional1 national2 hence we may1 if necessary1 use such words as educational1 terminational4 ,the ending ic appears to be suited to proper names1 as ,pindaric1 ,socratic1 ,platonic2 hence it may be used when scientific words are derived from proper names1 as ,voltaic or ,galvanic electricity3 to which ,i have proposed to add ,franklinic4 ,in adopting scientific adjectives from the ,latin1 we have not much room for hesitation2 for1 in such cases1 the habits of derivation from that language into our own are very constant2 ivus becomes ive1 as decursive2 inus becomes ine1 as in ferine2 atus becomes ate1 as hastate2 and us often becomes ous1 as rufous2 aris becomes ary1 as axillary2 ens becomes ent1 as ringent4 ,and in adopting into our language1 as scientific terms1 words which in another language1 the ,french for instance1 have a ,latin origin familiar to us1 we cannot do better than form them as if they were derived directly from the ,latin4 ,hence the ,french adjectives ctac1 crustac1 testac1 may become either cetaceous1 crustaceous1 testaceous1 according to the analogy of farinaceous1 predaceous1 or else cetacean1 crustacean1 #ccb testacean1 imitating the form of patrician4 ,since1 as ,i shall soon have to notice1 we require substantives as well as adjectives from these words1 we must1 at least for that use1 take the forms last suggested4 ,in pursuance of the same remark1 rongeur becomes rodent2 and edent would become edentate1 but that this word is rejected on another account3 the adjectives bimane and quadrumane are bimanous and quadrumanous4 #c4 ,there is not much difficulty in thus forming adjectives3 but the purposes of ,natural ,history require that we should have substantives corresponding to these adjectives2 and these cannot be obtained without some extension of the analogies of our language4 ,we cannot in general use adjectives or participles as singular substantives4 ,the happy or the doomed would1 according to good ,english usage1 signify those who are happy and those who are doomed in the plural4 ,hence we could not speak of a particular scaled animal as the squamate1 and still less could we call any such animal a squamate1 or speak of squamates in the plural4 ,some of the forms of our adjectives1 however1 do admit of this substantive use4 ,thus we talk of ,europeans1 plebeians1 republicans2 of divines and masculines2 of the ultramontanes2 of mordants and brilliants2 of abstergents and emollients2 of mercenaries and tributaries2 of animals1 mammals1 and officials2 of dissuasives and motives4 ,we cannot generally use in this way adjectives in ous1 nor in ate 7though reprobates is an exception71 nor ,english participles1 nor adjectives in which there is no termination imitating the ,latin1 as happy1 good4 ,hence1 if we have1 for purposes of science1 to convert adjectives into substantives1 we ought to follow the form of examples like these1 in which it has already appeared in fact1 that such usage1 though an innovation at first1 may ultimately become a received part of the language4 ,by attention to this rule we may judge what expressions to select in cases where substantives are needed4 ,i will take as an example the division of the mammalian animals into ,orders4 ,these ,orders1 #ccc according to ,cuvier1 are ,bimanes1 ,quadrumanes1 ,carnassiers1 ,rongeurs1 ,edents1 ,ruminants1 ,pachydermes1 ,ctacs2 and of these1 ,bimanes1 ,quadrumanes1 ,rodents1 ,ruminants1 ,pachyderms are admissible as ,english substantives on the grounds just stated4 ,cetaceous could not be used substantively2 but ,cetacean in such a usage is sufficiently countenanced by such cases as we have mentioned1 patrician1 c42 hence we adopt this form4 ,we have no ,english word equivalent to the ,french ,carnassiers3 the ,english translator of ,cuvier has not provided ,english words for his technical terms2 but has formed a ,latin word1 ,carnaria1 to represent the ,french terms4 ,from this we might readily form ,carnaries2 but it appears much better to take the ,linnan name ,fer as our root1 from which we may take ,ferine1 substantive as well as adjective2 and hence we call this order ,ferines4 ,the word for which it is most difficult to provide a proper representation is ,edent1 ,edentata3 for1 as we have said1 it would be very harsh to speak of the order as the ,edentates2 and if we were to abbreviate the word into edent1 we should suggest a false analogy with rodent1 for as rodent is quod rodit1 that which gnaws1 edent would be quod edit1 that which eats4 ,and even if we were to take edent as a substantive1 we could hardly use it as an adjective3 we should still have to say1 for example1 the edentate form of head4 ,for these reasons it appears best to alter the form of the word1 and to call the ,order the ,edentals1 which is quite allowable1 both as adjective and substantive4 ,an objection might be made to this term1 both in its ,latin1 ,french and ,english form3 namely1 that the natural group to which it is applied includes many species1 both existing and extinct1 well provided with teeth4 ,thus the armadillo is remarkable for the number of its teeth2 the megatherium1 for their complex structure4 ,but the analogy of scientific language readily permits us to fix1 upon the word edentata1 a special meaning1 implying the absence of one particular kind of teeth1 namely1 incisive teeth4 ,linnus called the equivalent order ,bruta4 ,we could not #ccd apply in this case the term ,brutes2 for common language has already attached to the word a wider meaning1 too fixedly for scientific use to trifle with it4 ,there are several other words in ate about which there is the same difficulty in providing substantive forms4 ,are we to speak of ,vertebrates8 or would it not be better1 in agreement with what has been said above1 to call these ,vertebrals1 and the opposite class ,invertebrals8 ,there are similar difficulties with regard to the names of subordinate portions of zoological classification2 thus the ,ferines are divided by ,cuvier into ,cheiroptres1 ,insectivores1 ,carnivores2 and these latter into ,plantigrades1 ,digitigrades1 ,amphibies1 ,marsupiaux4 ,there is not any great harshness in naturalizing these substantives as ,chiropters1 ,insectivores1 ,carnivores1 ,plantigrades1 ,digitigrades1 ,amphibians1 and ,marsupials4 ,these words ,carnivores and ,insectivores are better1 because of more familiar origin1 than ,greek terms2 otherwise we might1 if necessary1 speak of ,zoophagans and ,entomophagans4 ,it is only with certain familiar adjectival terminations1 as ous and ate1 that there is a difficulty in using the word as substantive4 ,when this can be avoided1 we readily accept the new word1 as ,pachyderms1 and in like manner ,mollusks4 ,if we examine the names of the ,orders of ,birds1 we find that they are in ,latin1 ,predatores or ,accipitres1 ,passeres1 ,scansores1 ,rasores or ,gallin1 ,grallatores1 ,palmipedes and ,anseres3 ,cuvier's ,orders are1 ,oiseaux de ,proie1 ,passereaux1 ,grimpeurs1 ,gallinacs1 chassiers1 ,palmipedes4 ,these may be englished conveniently as ,predators1 ,passerines1 ,scansors1 ,gallinaceans1 7rather than ,rasors17 ,grallators1 ,palmipedans1 or rather ,palmipeds1 like ,bipeds4 ,scansors1 ,grallators1 and ,rasors1 are better1 as technical terms1 than ,climbers1 ,waders1 and ,scratchers4 ,we might venture to anglicize the terminations of the names which ,cuvier gives to the divisions of these ,orders3 thus the ,predators are the ,diurnals and the ,nocturnals2 the ,passerines are the ,dentirostres1 the ,fissirostres1 the #cce ,conirostres1 the ,tenuirostres1 and the ,syndactyls3 the word lustre showing that the former termination is allowable4 ,the ,scansors are not sub-divided1 nor are the ,gallinaceans4 ,the ,grallators are ,pressirostres1 ,cultrirostres1 ,macrodactyls4 ,the ,palmipeds are the ,plungers1 the ,longipens1 the ,totipalmes and the ,lamellirostres4 ,the next class of ,vertebrals is the ,reptiles1 and these are either ,chelonians1 ,saurians1 ,ophidians1 or ,batrachians4 ,cuvier writes ,batraciens1 but we prefer the spelling to which the ,greek word directs us4 ,the last or lowest class is the ,fishes1 in which province ,cuvier has himself been the great systematist1 and has therefore had to devise many new terms4 ,many of these are of ,greek or ,latin origin1 and can be anglicized by the analogies already pointed out1 as ,chondropterygians1 ,malacopterygians1 ,lophobranchs1 ,plectognaths1 ,gymnodonts1 ,scleroderms4 ,discoboles and ,apodes may be ,english as well as ,french4 ,there are other cases in which the author has formed the names of ,families1 either by forming a word in ides from the name of a genus1 as ,gadoides1 ,gobiides1 or by gallicizing the ,latin name of the genus1 as ,salmones from ,salmo1 ,clupes from ,clupea1 soces from ,esox1 ,cyprins from ,cyprinus4 ,in these cases ,agassiz's favourite form of names for families of fishes has led ,english writers to use the words ,gadoids1 ,gobioids1 ,salmonoids1 ,clupeoids1 ,lucioids 7for soces71 ,cyprinoids1 c4 ,there is a taint of hybridism in this termination1 but it is attended with this advantage1 that it has begun to be characteristic of the nomenclature of family groups in the class ,pisces4 ,one of the orders of fishes1 co-ordinate with the ,chondropterygians and the ,lophobranchs1 is termed ,osseux by ,cuvier4 ,it appears hardly worth while to invent a substantive word for this1 when ,bony ,fishes is so simple a phrase1 and may readily be understood as a technical name of a systematic order4 ,the ,mollusks are the next ,class2 and these are divided into ,cephallopods1 ,gasteropods1 and the like4 ,the ,gasteropods are ,nudibranchs1 ,inferobranchs1 #ccf ,tectibranchs1 ,pectinibranchs1 ,scutibranchs1 and ,cyclobranchs4 ,in framing most of these terms ,cuvier has made hybrids by a combination of a ,latin word with branchi which is the ,greek name for the gills of a fish2 and has thus avoided loading the memory with words of an origin not obvious to most naturalists1 as terms derived from the ,greek would have been4 ,another division of the ,gasteropods is ,pulmons1 which we must make ,pulmonians4 ,in like manner the subdivisions of the ,pectinibranchs are the ,trochoidans and ,buccinoidans1 7,trochodes1 ,buccinodes74 ,the ,acphales1 another order of ,mollusks1 may be ,acephals in ,english4 ,after these comes the third grand division1 ,articulated ,animals1 and these are ,annelidans1 ,crustaceans1 ,arachnidans1 and ,insects4 ,i shall not dwell upon the names of these1 as the form of ,english words which is to be selected must be sufficiently obvious from the preceding examples4 ,finally1 we have the fourth grand division of animals1 the ,rayonns1 or ,radiata2 which1 for reasons already given1 we may call ,radials1 or ,radiaries4 ,these are ,echinoderms1 ,intestinals1 7or rather ,entozoans17 ,acalephes1 and ,polyps4 ,the ,polyps1 which are composite animals in which many gelatinous individuals are connected so as to have a common life1 have1 in many cases1 a more solid framework belonging to the common part of the animal4 ,this framework1 of which coral is a special example1 is termed in ,french ,polypier2 the word has been anglicized by the word polypary1 after the analogy of aviary and apiary4 ,thus ,polyps are either ,polyps with ,polyparies or ,naked ,polyps4 ,any common kind of ,polyps has usually in the ,english language been called ,polypus1 the ,greek termination being retained4 ,this termination in us1 however1 whether ,latin or ,greek1 is to be excluded from the ,english as much as possible1 on account of the embarrassment which it occasions in the formation of the plural4 ,for if we say ,polypi the word ceases to be ,english1 while ,polypuses is harsh3 and there is the additional inconvenience1 that both these forms would indicate the plural of individuals rather than of classes4 #ccg ,if we were to say1 ',the ,corallines are a ,family of the ,polypuses with ,polyparies1' it would not at once occur to the reader that the last three words formed a technical phrase4 ,this termination us which must thus be excluded from the names of families1 may be admitted in the designation of genera2 of animals1 as ,nautilus1 ,echinus1 ,hippopotamus2 and of plants1 as ,crocus1 ,asparagus1 ,narcissus1 ,acanthus1 ,ranunculus1 ,fungus4 ,the same form occurs in other technical words1 as ,fucus1 ,mucus1 sophagus1 ,hydrocephalus1 ,callus1 ,calculus1 ,uterus1 ,ftus1 ,radius1 ,focus1 ,apparatus4 ,it is1 however1 advisable to retain this form only in cases where it is already firmly established in the language2 for a more genuine ,english form is preferable4 ,hence we say1 with ,mr4 ,lyell1 ,ichthyosaur1 ,plesiosaur1 ,pterodactyl4 ,in like manner ,mr4 ,owen anglicizes the termination erium1 and speaks of the ,anoplothere and ,paleothere4 ,since the wants of science thus demand adjectives which can be used also as substantive names of classes1 this consideration may sometimes serve to determine our selection of new terms4 ,thus ,mr4 ,lyell's names for the subdivisions of the tertiary strata1 ,miocene1 ,pliocene1 can be used as substantives2 but if such words as ,mioneous1 ,plioneous1 had suggested themselves1 they must have been rejected1 though of equivalent signification1 as not fulfilling this condition4 #d4 7a47 ,abstract substantives can easily be formed from adjectives3 from electric we have electricity2 from galvanic1 galvanism2 from organic1 organization2 velocity1 levity1 gravity1 are borrowed from ,latin adjectives4 ,caloric is familiarly used for the matter of heat1 though the form of the word is not supported by any obvious analogy4 7b47 ,it is intolerable to have words regularly formed1 in opposition to the analogy which their meaning offers2 as when bodies are said to have conductibility or conducibility with regard to heat4 ,the bodies are conductive1 and their property is conductivity4 7c47 ,the terminations ize 7rather than ise71 ism1 and ist1 are applied to words of all origins3 thus we have to #cch pulverize1 to colonize1 ,witticism1 ,heathenism1 ,journalist1 ,tobacconist4 ,hence we may make such words when they are wanted4 ,as we cannot use physician for a cultivator of physics1 ,i have called him a ,physicist4 ,we need very much a name to describe a cultivator of science in general4 ,i should incline to call him a ,scientist4 ,thus we might say1 that as an ,artist is a ,musician1 ,painter1 or ,poet1 a ,scientist is a ,mathematician1 ,physicist1 or ,naturalist4 7d47 ,connected with verbs in ize1 we have abstract nouns in ization1 as polarization1 crystallization4 ,these it appears proper to spell in ,english with z rather than s2 governing our practice by the ,greek verbal termination which we imitate4 ,but we must observe that verbs and substantives in yse1 7analyse71 belong to a different analogy1 giving an abstract noun in ysis and an adjective ytic or ytical2 7analysis1 analytic1 analytical74 ,hence electrolyse is more proper than electrolyze4 7e47 ,the names of many sciences end in ics after the analogy of ,mathematics1 ,metaphysics2 as ,optics1 ,mechanics4 ,but these1 in most other languages1 as in our own formerly1 have the singular form ,optice1 l',optique1 ,optik1 ,optick3 and though we now write ,optics1 we make such words of the singular number3 ',newton's ,opticks is an example4' ,as1 however1 this connexion in new words is startling1 as when we say ',thermo-electrics is now much cultivated1' it appears better to employ the singular form1 after the analogy of ,logic and ,rhetoric1 when we have words to construct4 ,hence we may call the science of languages ,linguistic1 as it is called by the best ,german writers1 for instance1 ,william ,von ,humboldt4 #e4 ,in the derivation of ,english from ,latin or ,greek words1 the changes of letters are to be governed by the rules which have generally prevailed in such cases4 ,the ,greek and 1 the ,latin oe and ae1 are all converted into a simple e1 as in ,economy1 ,geodesy1 penal1 ,cesar4 ,hence1 according to common usage1 we should write phenomena1 not phnomena1 paleontology1 not palontology1 miocene not miocne1 pekilite not #cci pkilite4 ,but in order to keep more clearly in view the origin of our terms1 it may be allowable to deviate from these rules of change1 especially so long as the words are new and unfamiliar4 ,dr4 ,buckland speaks of the poikilitic1 not pecilitic1 group of strata3 palontology is the spelling commonly adopted2 and in imitation of this ,i have written paltiology4 ,the diphthong was by the ,latins changed into i1 as in ,aristides2 and hence this has been the usual form in ,english4 ,some recent authors indeed 7,mr4 ,mitford for instance7 write ,aristeides2 but the former appears to be the more legitimate4 ,hence we write miocene1 pliocene1 not meiocene1 pleiocene4 ,the ,greek becomes y1 and becomes u1 in ,english as in ,latin1 as crystal1 colure4 ,the consonants and become c and ch according to common usage4 ,hence we write crystal1 not chrystal1 batrachian1 not batracian1 cryolite1 not chryolite4 ,as1 however1 the letter c before e and i differs from k1 which is the sound we assign to the ,greek 1 it may be allowable to use k in order to avoid this confusion4 ,thus1 as we have seen1 poikilite has been used1 as well as pecilite4 ,even in common language some authors write skeptic1 which appears to be better than sceptic with our pronunciation1 and is preferred by ,dr4 ,johnson4 ,for the same reason1 namely1 to avoid confusion in the pronunciation1 and also1 in order to keep in view the connexion with cathode1 the elements of an electrolyte which go to the anode and cathode respectively may be termed the anion and cathion2 although the ,greek would suggest caton1 774 #f4 ,the example of chemistry has shown that we have in the terminations of words a resource of which great use may be made in indicating the relations of certain classes of objects3 as sulphurous and sulphuric acids2 sulphates1 sulphites1 and sulphurets4 ,since the introduction of the artifice by the ,lavoisierian school1 it has been extended to some new cases4 ,the ,chlorine1 ,fluorine1 ,bromine1 ,iodine1 had their names put into that shape in consequence of their supposed analogy3 and for the same reason have been termed ,chlore1 #cdj ,phlore1 ,brome1 ,iode1 by ,french chemists4 ,in like manner1 the names of metals in their ,latin form have been made to end in um1 as ,osmium1 ,palladium2 and hence it is better to say ,platinum1 ,molybdenum1 than ,platina1 ,molybdena4 ,it has been proposed to term the basis of ,boracic acid ,boron2 and those who conceive that the basis of ,silica has an analogy with ,boron have proposed to term it ,silicon1 while those who look upon it as a metal would name it ,silicium4 ,selenium was so named when it was supposed to be a metal3 as its analogies are now acknowledged to be of another kind1 it would be desirable1 if the change were not too startling1 to term it ,selen1 as it is in ,german4 ,phosphorus in like manner might be ,phosphur1 which would indicate its analogy with ,sulphur4 ,the resource which terminations offer has been applied in other cases4 ,the names of many species of minerals end in lite1 or ite1 as ,staurolite1 ,augite4 ,hence ,adolphe ,brongniart1 in order to form a name for a genus of fossil plants1 has given this termination to the name of the recent genus which they nearly resemble1 as ,zamites1 from ,zamia1 ,lycopodites from ,lycopodium4 ,names of different genera which differ in termination only are properly condemned by ,linnus#ehd2 as ,alsine1 ,alsinoides1 ,alsinella1 ,alsinastrum2 for there is no definite relation marked by those terminations4 ,linnus gives to such genera distinct names1 ,alsine1 ,bufonia1 ,sagina1 ,elatine4 ,note #ehd3 ,phil4 ,bot4 #bca4 ,terminations are well adapted to express definite systematic relations1 such as those of chemistry1 but they must be employed with a due regard to all the bearings of the system4 ,davy proposed to denote the combinations of other substances with chlorine by peculiar terminations2 using ane for the smallest proportion of ,chlorine1 and anea for the larger1 as ,cuprane1 ,cupranea4 ,in this nomenclature1 common salt would be ,sodane1 and ,chloride of ,nitrogen would be ,azotane4 ,this suggestion never found favour4 ,it was #cda objected that it was contrary to the ,linnan precept1 that a specific name must not be united to a generic termination4 ,but this was not putting the matter exactly on its right ground2 for the rules of nomenclature of natural history do not apply to chemistry2 and the ,linnan rule might with equal propriety have been adduced as a condemnation of such terms as ,sulphurous1 ,sulphuric4 ,but ,davy's terms were bad2 for it does not appear that ,chlorine enters1 as ,oxygen does1 into so large a portion of chemical compounds1 that its relations afford a key to their nature1 and may properly be made an element in their names4 ,this resource1 of terminations1 has been abused1 wherever it has been used wantonly1 or without a definite significance in the variety4 ,this is the case in ,m4 ,beudant's ,mineralogy4 ,among the names which he has given to new species1 we find the following 7besides many in ite71 ,scolexerose1 ,opsimose1 ,exanthelose1 c42 ,diacrase1 ,panabase1 ,neoplase2 ,neoclese2 ,rhodoise1 ,stibiconise1 c42 ,marceline1 ,wilhelmine1 c42 ,exitele1 and many others4 ,in addition to other objections which might be made to these names1 their variety is a material defect3 for to make this variety depend on caprice alone1 as in those cases it does1 is to throw away a resource of which chemical nomenclature may teach us the value4 ,,aphorism ,,xxii4 ,when alterations in technical terms become necessary1 it is desirable that the new term should contain in its form some memorial of the old one4 ,,we have excellent examples of the advantageous use of this maxim in ,linnus's reform of botanical nomenclature4 ,his innovations were very extensive1 but they were still moderated as much as possible1 and connected in many ways with the names of plants then in use4 ,he has himself given several rules of nomenclature1 which tend to establish this connexion of the #cdb old and new in a reform4 ,thus he says1 ',generic names which are current1 and are not accompanied with harm to botany1 should be tolerated#eid4' ',a passable generic name is not to be changed for another1 though more apt#fjd'4 ',new generic names are not to be framed so long as passable synonyms are at hand#fad4' ',a generic name of one genus1 except it be superfluous1 is not to be transferred to another genus1 though it suit the other better#fbd4' ',if a received genus requires to be divided into several1 the name which before included the whole1 shall be applied to the most common and familiar kind#fcd4' ,and though he rejects all generic names which have not a ,greek or ,latin root#fdd1 he is willing to make an exception in favour of those which from their form might be supposed to have such a root1 though they are really borrowed from other languages1 as ,thea1 which is the ,greek for goddess2 ,coffea1 which might seem to come from a ,greek word denoting silence 772 ,cheiranthus1 which appears to mean hand-flower1 but is really derived from the ,arabic ,keiri3 and many others4 ,note #eid3 ,philosophia ,botanica1 ,art4 #bdb4 ,note #fjd3 ,art4 #bdf4 ,note #fad3 ,art4 #bdg4 ,note #fbd3 ,art4 #bdi4 ,note #fcd3 ,art4 #bdi4 ,note #fdd3 ,art4 #bcb4 ,as we have already said1 the attempt at a reformation of the nomenclature of ,mineralogy made by ,professor ,mohs will probably not produce any permanent effect1 on this account amongst others1 that it has not been conducted in this temperate mode2 the innovations bear too large a proportion to the whole of the names1 and contain too little to remind us of the known appellations4 ,yet in some respects ,professor ,mohs has acted upon this maxim4 ,thus he has called one of his classes ,spar1 because ,felspar belongs to it4 ,i shall venture to offer a few suggestions on this subject of ,mineralogical ,nomenclature4 ,it has already been remarked that the confusion and complexity which prevail in this subject render a reform very desirable4 ,but it will be seen1 from the reasons assigned under the ,ninth ,aphorism1 that no permanent system of names can be looked for1 till a #cdc sound system of classification be established4 ,the best mineralogical systems recently published1 however1 appear to converge to a common point2 and certain classes have been formed which have both a natural-historical and a chemical significance4 ,these ,classes1 according to ,naumann1 whose arrangement appears the best1 are ,hydrolytes1 ,haloids1 ,silicides1 ,oxides of ,metals1 ,metals1 ,sulphurides 7,pyrites1 ,glances1 and ,blendes71 and ,anthracides4 ,now we find2--that the ,hydrolytes are all compounds1 such as are commonly termed ,salts2--that the ,haloids are1 many of them1 already called ,spars1 as ,calc ,spar1 ,heavy ,spar1 ,iron ,spar1 ,zinc ,spar2--that the ,silicides1 the most numerous and difficult class1 are denoted for the most part1 by single words1 many of which end in ite2--that the other classes1 or subclasses1 ,oxides1 ,pyrites1 ,glances1 and ,blendes1 have commonly been so termed2 as ,red ,iron ,oxide1 ,iron ,pyrites1 ,zinc ,blende2--while pure metals have usually had the adjective native prefixed1 as ,native ,gold1 ,native ,copper4 ,these obvious features of the current names appear to afford us a basis for a systematic nomenclature4 ,the ,salts and ,spars might all have the word salt or spar included in their name1 as ,natron ,salt1 ,glauber ,salt1 ,mock ,salt2 ,calc ,spar1 ,bitter ,spar1 7,carbonate of ,lime and ,magnesia71 ,fluor ,spar1 ,phosphor ,spar 7,phosphate of ,lime71 ,heavy ,spar1 ,celestine ,spar 7,sulphate of ,strontian71 ,chromic ,lead ,spar 7,chromate of ,lead72 the ,silicides might all have the name constructed so as to be a single word ending in ite1 as ,chabasite 7,chabasie71 ,natrolite 7,mesotype71 ,sommite 7,nepheline71 ,pistacite 7,epidote72 from this rule might be excepted the ,gems1 as ,topaz1 ,emerald1 ,corundum1 which might retain their old names4 ,the ,oxides1 ,pyrites1 ,glances1 and ,blendes1 might be so termed2 thus we should have ,tungstic ,iron ,oxide 7usually called ,tungstate of ,iron71 ,arsenical ,iron ,pyrites 7,mispickel71 ,tetrahedral ,copper ,glance 7,fahlerz71 ,quicksilver ,blende 7,cinnabar71 and the metals might be termed native1 as ,native ,copper1 ,native ,silver4 ,such a nomenclature would take in a very large #cdd proportion of commonly received appellations1 especially if we were to select among the synonyms1 as is proposed above in the case of ,glauber ,salt1 ,bitter ,spar1 ,sommite1 ,pistacite1 ,natrolite4 ,hence it might be adopted without serious inconvenience4 ,it would make the name convey information respecting the place of the mineral in the system2 and by imposing this condition1 would limit the extreme caprice1 both as to origin and form1 which has hitherto been indulged in imposing mineralogical names4 ,the principle of a mineralogical nomenclature determined by the place of the species in the system1 has been recognized by ,mr4 ,beudant as well as ,mr4 ,mohs4 ,the former writer has proposed that we should say ,carbonate ,calcaire1 ,carbonate ,witherite1 ,sulphate ,couperose1 ,silicate ,stilbite1 ,silicate ,chabasie1 and so on4 ,but these are names in which the part added for the sake of the system1 is not incorporated with the common name1 and would hardly make its way into common use4 ,we have already noticed ,mr4 ,mohs's designations for two of the ,systems of ,crystallization1 the ,pyramidal and the ,prismatic1 as not characteristic4 ,if it were thought advisable to reform such a defect1 this might be done by calling them the ,square ,pyramidal and the ,oblong ,prismatic1 which terms1 while they expressed the real distinction of the systems1 would be intelligible at once to those acquainted with the ,mohsian terminology4 ,i will mention another suggestion respecting the introduction of an improvement in scientific language4 ,the term ,depolarization was introduced1 because it was believed that the effect of certain crystals1 when polarized light was incident upon them in certain positions1 was to destroy the peculiarity which polarization had produced4 ,but it is now well known1 that the effect of the second crystal in general is to divide the polarized ray of light into two rays1 polarized in different planes4 ,still this effect is often spoken of as ,depolarization1 no better term having been yet devised4 ,i have proposed and used the term ,dipolarization1 #cde which well expresses what takes place1 and so nearly resembles the elder word1 that it must sound familiar to those already acquainted with writings on this subject4 ,i may mention one term in another department of literature which it appears desirable to reform in the same manner4 ,the theory of the ,fine ,arts1 or the philosophy which speculates concerning what is beautiful in painting1 sculpture or architecture1 and other arts1 often requires to be spoken of in a single word4 ,baumgarten and other ,german writers have termed this province of speculation sthetics2 1 to perceive1 being a word which appeared to them fit to designate the perception of beauty in particular4 ,since1 however1 sthetics would naturally denote the ,doctrine of ,perception in general2 since this ,doctrine requires a name2 since the term sthetics has actually been applied to it by other ,german writers 7as ,kant72 and since the essential point in the philosophy now spoken of is that it attends to ,beauty2--it appears desirable to change this name4 ,in pursuance of the maxim now before us1 ,i should propose the term ,callsthetics1 or rather 7in agreement with what was said in page #cch7 ,callsthetic1 the science of the perception of beauty4 #cdf ,,further ,,illustrations ,,of ,,the ,,aphorisms ,,on ,,scientific ,,language1 ,,from ,,the ,,recent ,,course ,,of ,,sciences4 #a4 ,,botany4 ,,the nomenclature of ,botany as rescued from confusion by ,linnus1 has in modern times been in some danger of relapsing into disorder or becoming intolerably extensive1 in consequence of the multiplication of genera by the separation of one old genus into several new ones1 and the like subdivisions of the higher groups1 as subclasses and classes4 ,this inconvenience1 and the origin of it1 have been so well pointed out by ,mr4 ,g4 ,bentham#fed1 that ,i shall venture to adopt his judgment as an ,aphorism1 and give his reasons for it4 ,note #fed3 ,linnan ,society's ,proceedings1 vol4 ii4 p4 #cj 7,june1 #aheg74 ,,aphorism ,,xxiii4 ,it is of the greatest importance that the ,groups which give their substantive names to every included species should remain large4 ,,it will be recollected that according to the ,linnan nomenclature1 the genus is marked by a substantive1 7as ,rosa71 and the species designated by an adjective added to this substantive1 7as ,rosa ,alpina72 while the natural orders are described by adjectives taken substantively1 7as ,rosace71 ,but this rule1 though it has been universally assented to in theory1 has often been deviated from in practice4 ,the number of known species having much increased1 and the language of ,linnus and the principles of ,jussieu having much augmented the facilities for the study of affinities1 botanists have become aware that the species of a genus and the genera of an order can be collected into intermediate groups #cdg as natural and as well defined as the genera and orders themselves1 and names are required for these subordinate groups as much as for the genera and orders4 ,now two courses have been followed in providing names for these subordinate groups4 #a4 ,the original genera 7considering the case of genera in the first place7 have been preserved1 7if well founded72 and the lower groups have been called subgenera1 sections1 subsections1 divisions1 c43 and the original names of the genera have been maintained for the purpose of nomenclature1 in order to retain a convenient and stable language4 ,but when these subordinate groups are so well defined and so natural1 that except for the convenience of language1 they might be made good genera1 there are given also to these subordinate groups1 substantive or substantively-taken adjective names4 ,when these subordinate groups are less defined or less natural1 either no names at all are given1 and they are distinguished by figures or signs such as 991 99991 or #a1 #b1 c4 or there are given them mere adjective names4 ,or1 #b1 ,to regard these intermediate groups between species and the original genera1 as so many independent genera2 and to give them substantive names1 to be used in ordinary botanical nomenclature4 ,now the second course is that which has produced the intolerable multiplication of genera in modern times2 and the first course is the only one which can save botanical nomenclature from replunging into the chaos in which ,linnus found it4 ,it was strongly advocated by the elder ,de ,candolle2 although in the latter years of his life1 seeing how general was the disposition to convert his subgenera and sections into genera1 he himself more or less gave in to the general practice4 ,the same principle was adopted by ,endlichen1 but he again was disposed to go far in giving substantive names to purely technical or ill-defined subsections of genera4 ,the multiplication of genera has been much too common4 ,botanists have a natural pride in establishing new genera 7or orders72 and besides this1 it is felt how useful it is1 in the study of affinities1 to define and #cdh name all natural groups in every grade1 however numerous they may be3 and in the immense variety of language it is found easy to coin names indefinitely4 ,but the arguments on the other side much preponderate4 ,in attempting to introduce all these new names into ordinary botanical language1 the memory is taxed beyond the capabilities of any mind1 and the original and legitimate object of the ,linnan nomenclature is wholly lost sight of4 ,in a purely scientific view it matters little if the ,orders are converted into ,classes or ,alliances1 the ,genera into ,orders1 and the ,sections or ,subsections into ,genera3 their relative importance does not depend on the names given to them1 but on their height in the scale of comprehensiveness4 ,but for language1 the great implement without which science cannot work1 it is of the greatest importance1 as our ,aphorism declares1 ,that the groups which give their substantive names to every species which they include1 should remain large4 ,if1 independently of the inevitable increase of ,genera by new discoveries1 such old ones as ,ficus1 ,begonia1 ,arum1 ,erica1 c4 are divided into #aj1 #bj1 #cj1 or #dj independent ,genera1 with names and characters which are to be recollected before any one species can be spoken of2--if ,genera are to be reckoned by tens of thousands instead of by thousands2--the range of any individual botanist will be limited to a small portion of the whole field of the sciences4 ,and in like manner with regard to ,orders1 so long as the number of ,orders can be kept within1 or not much beyond a couple of hundred1 it may reasonably be expected that a botanist of ordinary capacity shall obtain a sufficient general idea of their nature and characters to call them at any time individually to his mind for the purpose of comparison3 but if we double the number of ,orders1 all is confusion4 ,the inevitable confusion and the necessity of maintaining in some way the larger groups1 have been perceived by those even who have gone the furthest in lowering the scale of ,orders and ,genera4 ,as a remedy for this confusion1 they propose to erect the old genera into independent orders1 and the old orders into classes #cdi or divisions4 ,but this is but an incomplete resumption of the old principles1 without the advantage of the old nomenclature4 ,and it will not be asserted1 with regard to these new genera1 formed by cutting up the old ones1 that the new group is better defined than the group above it3 on the contrary1 it is frequently less so4 ,it is not pretended that ,urostigma or ,phannacosyce1 new genera formed out of the old genus ,ficus1 are better defined than the genus ,ficus3 or that the new genera which have lately been cut out of the old genus ,begonia1 form more natural groups than ,begonia itself does4 ,the principle which seems to be adopted in such subdivisions of old genera is this3 that the lowest definable group above a species is a genus4 ,if we were to go a step further1 every species becomes a genus with a substantive name4 ,it ought always to be recollected that though the analytical process carried to the uttermost1 and separating groups by observation of differences1 is necessary for the purpose of ascertaining the facts upon which botany or any other classificatory science is based1 it is a judicious synthesis alone1 associating individuals by the ties of language1 which can enable the human mind to take a comprehensive view of these facts1 to deduce from them the principles of the science1 or to communicate to others either facts or principles4 #b4 ,,comparative ,,anatomy4 ,the ,language of ,botany1 as framed by ,linnus1 and regulated by his ,canons1 is still the most notable and successful example of scientific terminology which has obtained general reception among naturalists4 ,but the ,language of ,anatomy1 and especially of the ,comparative ,anatomy of the skeleton1 has of late been an object of great attention to physiologists2 and especially to ,mr4 ,owen2 and the collection of terms which he has proposed are selected with so much thought and care1 that they may minister valuable lessons to us in this part of our subject4 ,there is1 at first sight1 this broad difference between the descriptive language of ,botany and of ,comparative #cej ,anatomy2 that in the former science1 we have comparatively few parts to describe1 7calyx1 corolla1 stamen1 pistil1 pericarp1 seed1 c473 while each of these parts is susceptible of many forms1 for describing which with precision many terms must be provided3 in ,comparative ,anatomy1 on the other hand1 the skeletons of many animals are to be regarded as modifications of a common type1 and the terms by which their parts are described are to mark this community of type4 ,the terminology of ,botany has for its object description2 the language of ,comparative ,anatomy must have for its basis morphology4 ,accordingly1 ,mr4 ,owen's terms are selected so as to express the analogies1 or1 as he calls them1 the homologies of the skeleton2 those parts of the skeleton being termed homologues1 which have the same place in the general type1 and therefore ought to have the same name4 ,yet this distinction of the basis of botanical and anatomical terminology is not to be pushed too far4 ,the primary definitions in botany1 as given by ,linnus1 are founded on morphological views2 and imply a general type of the structure of plants4 ,these are his definitions 7,phil4 ,bot4 ,art4 #hf74 ,,calyx1 ,cortex plant in ,fructificatione prsens4 ,,corolla1 ,liber plant in ,flora prsens4 ,,stamen1 ,viscus pro ,pollinis prparatione4 ,,pistillum1 ,viscus fructui adherens pro ,pollinis receptione4 ,,pericarpium1 ,viscus gravidum seminibus1 qu matura dimittit4 ,but in what follows these leading definitions1 the terms are descriptive merely4 ,now in ,comparative ,anatomy1 an important object of terms is1 to express what part of the type each bone represents--to answer the question1 what is it8 before we proceed1 assuming that we know what it is1 to describe its shape4 ,the difficulty of this previous question is very great when we come to the bones of the head2 and when we assume1 as morphology leads us to do1 that the heads of all vertebrated animals1 including even fishes1 are composed of homologous bones4 ,and1 as ,i have already #cea said in the ,history 7b4 xvii4 c4 #g71 speaking of ,animal ,morphology1 the best physiologists are now agreed that the heads of vertebrates may be resolved into a series of vertebr1 homologically repeated and modified in different animals4 ,this doctrine has been gradually making its way among anatomists1 through a great variety of views respecting details2 and hence1 with great discrepancies in the language by which it has been expressed4 ,mr4 ,owen has proposed a complete series of terms for the bones of the head of all vertebrates2 and these names are supported by reasons which are full of interest and instruction to the physiologist1 on account of the comprehensive and precise knowledge of comparative osteology which they involve2 but they are also1 as ,i have said1 interesting and instructive to us1 as exemplifying the reasons which may be given for the adoption of words in scientific language4 ,the reasons thus given agree with several of the aphorisms which ,i have laid down1 and may perhaps suggest a few others4 ,mr4 ,owen has done me the great honour to quote with approval some of these aphorisms4 ,the terms which he has proposed belong1 as ,i have already said1 to the ,terminology1 not to the ,nomenclature of ,zoology4 ,in the latter subject1 the ,nomenclature 7the names of species7 the binary nomenclature established by ,linnus remains1 in its principle1 unshaken1 simple and sufficient4 ,i shall best derive from ,mr4 ,owen's labours and reflexions some of the instruction which they supply with reference to the ,language of ,science1 by making remarks on his terminology with reference to such aphorisms as ,i have propounded on the subject1 and others of a like kind4 ,mr4 ,owen1 in his ,homologies of the ,vertebrate ,skeleton1 has given in a ,tabular ,form his views of the homology of the bones of the head of vertebrates1 and the names which he consequently proposes for each bone1 with the synonyms as they occur in the writings of some of the most celebrated anatomical philosophers1 ,cuvier1 ,geoffroy1 ,hallmann1 ,meckel and ,wagner1 ,agassiz and ,soemmering4 ,and he has added to this ,table his reasons for dissenting from his predecessors #ceb to the extent to which he has done so4 ,he has done this1 he says1 only where nature seemed clearly to refuse her sanction to them2 acting upon the maxim 7our ,aphorism ,x47 that new terms and changes of terms which are not needed in order to express truth1 are to be avoided4 ,the illustrations which ,i have there given1 however1 of this maxim1 apply rather to the changes in nomenclature than in terminology2 and though many considerations apply equally to these two subjects1 there are some points in which the reasons differ in the two cases3 especially in this point3--the names1 both of genera and of species1 in a system of nomenclature1 may be derived from casual or arbitrary circumstances1 as ,i have said in ,aphorism ,,xiii4 ,but the terms of a scientific terminology ought to cohere as a system1 and therefore should not commonly be derived from anything casual or arbitrary1 but from some analogy or connexion4 ,hence it seems unadvisable to apply to bones terms derived from the names of persons1 as ossa wormiana2 or even from an accident in anatomical history1 as os innominatum4 ,it is further desirable that in establishing such a terminology1 each bone should be designated by a single word1 and not by a descriptive phrase1 consisting of substantive and adjective4 ,on this ground ,mr4 ,owen proposes presphenoid for sphenide anterieur4 ,so also prefrontal is preferred to anterior frontal1 and postfrontal to posterior frontal4 ,and the reason which he gives for this is worthy of being stated as an ,aphorism1 among those which should regulate this subject4 ,i shall therefore state it thus3 ,,aphorism ,,xxiv4 ,it is advisable to substitute definite single names for descriptive phrases as better instruments of thought4 ,,it will be recollected by the reader that in the case of the ,linnan reform of the botanical nomenclature of species1 this was one of the great improvements which was introduced4 ,again3 some of the first of the terms which ,mr4 ,owen proposes illustrate1 and confirm by their manifest claim #cec to acceptance1 a maxim which we stated as ,aphorism ,,xxii43 namely1 ,when alterations in technical terms become necessary1 it is desirable that the new term should contain in its form some memorial of the old one4 ,thus for 'basilaire1' which ,cuvier exclusively applies to the 'pars basilaris' of the occiput1 and which ,geoffroy as exclusively applies 7in birds7 to the 'pars basilaris' of the sphenoid1 ,mr4 ,owen substitutes the term basioccipital4 ,again3 for the term 'suroccipital' of ,geoffroy1 ,mr4 ,owen proposes paroccipital1 to avoid confusion and false suggestion3 and with reference to this word1 he makes a remark in agreement with what we have said in the discussion of ,aphorism ,,xxi43 namely1 that the combination of different languages in the derivation of words1 though to be avoided in general1 is in some cases admissible4 ,he says1 ',if the purists who are distressed by such harmless hybrids as mineralogy1 terminology1 and mammalogy1 should protest against the combination of the ,greek prefix to the ,latin noun1 ,i can only plead that servility to a particular source of the fluctuating sounds of vocal language is a matter of taste3 and that it seems no unreasonable privilege to use such elements as the servants of thought2 and in the interests of science to combine them1 even though they come from different countries1 when the required duty is best and most expeditiously performed by their combination4' ,so again we have illustrations of our ,aphorism ,,xii41 that if terms are systematically good they are not to be rejected because they are etymologically inaccurate4 ,in reference to that bone of the skull which has commonly been called vomer1 the ploughshare3 a term which ,geoffroy rejected1 but which ,mr4 ,owen retains1 he says1 ',when ,geoffrey was induced to reject the term vomer as being applicable only to the peculiar form of the bone in a small portion of the vertebrata1 he appears not to have considered that the old term1 in its wider application1 would be used without reference to its primary allusion to the ploughshare1 and that becoming1 as it #ced has1 a purely arbitrary term1 it is superior and preferable to any partially descriptive one4' ,another condition which ,i have mentioned in ,aphorism ,,xx41 as valuable in technical terms is1 that they should be susceptible of such grammatical relations as their scientific use requires4 ,this is1 in fact1 one of the grounds of the ,aphorism which we have already borrowed from ,mr4 ,owen1 that we are to prefer single substantives to descriptive phrases4 ,for from such substantives we can derive adjectives1 and other forms2 and thus the term becomes1 as ,mr4 ,owen says1 a better instrument of thought4 ,hence1 he most consistently mentions it as a recommendation of his system of names1 that by them the results of a long series of investigations into the special homologies of the bones of the head are expressed in simple and definite terms1 capable of every requisite inflection to express the proportion of the parts4 ,i may also1 in reference to this same passage in ,mr4 ,owen's appeal in behalf of his terminology1 repeat what ,i have said under ,aphorism ,x43 that the persons who may most properly propose new scientific terms1 are those who have much new knowledge to communicate3 so that the vehicle is commended to general reception by the value of what it contains4 ,it is only to eminent discoverers and profound philosophers that the authority is conceded of introducing a new system of terms2 just as it is only the highest authority in the state which has the power of putting a new coinage into circulation4 ,the long series of investigations of which the results are contained in ,mr4 ,owen's table of synonyms1 and the philosophical spirit of his generalizations1 entitles him to a most respectful hearing when he appeals to the ,professors and ,demonstrators of ,human ,anatomy for an unbiassed consideration of the advantages of the terms proposed by him1 as likely to remedy the conflicting and unsettled synonymy which has hitherto pervaded the subject4 ,there is another remark which is suggested by the works on ,comparative ,anatomy1 which ,i am now considering4 ,i have said in various places that ,technical #cee ,terms are a necessary condition of the progress of a science4 ,but we may say much more than this3 and the remark is so important1 that it deserves to be stated as one of our ,aphorisms1 as follows3 ,,aphorism ,,xxv4 ,in an advanced ,science1 the history of the ,language of the ,science is the history of the ,science itself4 ,i ,,have already stated in previous ,aphorisms 7,,viii4 and ,,xi47 that ,terms must be constructed so as to be fitted to enunciate general propositions1 and that ,terms which imply theoretical views are admissible for this purpose4 ,and hence it happens that the history of ,terms in any science which has gone through several speculative stages1 is really the history of the generalizations and theories which have had currency among the cultivators of the science4 ,this appears in ,comparative ,anatomy from what we have been saying4 ,the recent progress of that science is involved in the rise and currency of the ,terms which have been used by the anatomists whose synonyms ,mr4 ,owen has to discuss2 and the reasons for selecting among these1 or inventing others1 include those truths and generalizations which are the important recent steps of the science4 ,the terms which are given by ,mr4 ,owen in his table to denote the bones of the head are good terms1 if they are good terms1 because their adoption and use is the only complete way of expressing the truths of homology3 namely1 of that ,special ,homology1 according to which all vertebrate skeletons are referred to the human skeleton as their type1 and have their parts designated accordingly4 ,but further3 there is another kind of homology which ,mr4 ,owen calls ,general ,homology1 according to which the primary type of a vertebrate animal is merely a series of vertebr2 and all limbs and other appendages are only developements of the parts of one or another of the vertebr4 ,and in order to express this view1 and in proportion as the doctrine has become current amongst #cef anatomists1 the parts of vertebr have been described by terms of a degree of generality which admit of such an interpretation4 ,and here1 also1 ,mr4 ,owen has proposed a terminology for the parts of the vertebr1 which seems to convey more systematically and comprehensively than those of preceding writers the truths to which they have been tending4 ,each vertebra is composed of a centrum1 neurapophysis1 parapophysis1 pleurapophysis1 hmaphysis1 neural spine and hmal spine1 with certain exogenous parts4 ,the opinion that the head1 as well as the other parts of the frame of vertebrates1 is composed of vertebr1 is now generally accepted among philosophical anatomists4 ,in the ,history 7,hist4 ,i4 ,s4 b4 xvii4 c4 #g1 sect4 #a71 ,i have mentioned this opinion as proposed by some writers2 and ,i have stated that ,oken1 in #ahjg published a ',program' ,on the signification of the bones of the ,skull1 in which he maintained1 that these bones are equivalent to four vertebr3 while ,meckel1 ,spix1 and ,geoffroy took views somewhat different4 ,cuvier and ,agassiz opposed this doctrine1 but ,mr4 ,owen has in his ,archetype and ,homologies of the ,vertebrate ,skeleton 7#ahdh71 accepted the views of ,oken1 and argued at length against the objections of ,cuvier1 and also those of ,mr4 ,agassiz4 ,as ,i have noted in the last edition of the ,history of the ,inductive ,sciences 7b4 xvii4 c4 #g71 he gives a ,table in which the ,bones of the ,head are resolved into four vertebr1 which he terms the ,occipital1 ,parietal1 ,frontal and ,nasal ,vertebr respectively3 the neural arches of which agree with what ,oken called the ,ear-vertebra1 the ,jaw-vertebra1 the ,eye-vertebra1 and the ,nose-vertebra4 ,besides these doctrines of ,special ,homology by which the bones of all vertebrates are referred to their corresponding bones in the human skeleton1 and of ,general ,homology1 by which the bones are referred to the parts of vertebr which they represent1 ,mr4 ,owen treats of ,serial ,homology1 the recognition of the same elements throughout the series of segments of the same skeleton2 as when we shew in what manner the arms correspond to the legs4 ,and thus1 he says1 in the head also1 the basioccipital1 basisphenoid1 presphenoid and vomer are #ceg homotypes with the centrums of all succeeding vertebr4 ,the excoccipitals1 alisphenoids1 orbitosphenoids1 and prefrontals1 are homotypes with the neurapophyses of all the succeeding vertebr4 ,the paroccipitals1 mactoids and postfrontals1 with the transverse processes of all the succeeding vertebr3 and so on4 ,perhaps these examples may exemplify sufficiently for the general reader both ,mr4 ,owen's terminology1 and the intimate manner in which it is connected with the widest generalizations to which anatomical philosophy has yet been led4 ,the same doctrine1 that the history of the ,language of a ,science is the history of the ,science1 appears also in the recent progress of ,chemistry2 but we shall be better able to illustrate our ,aphorism in this case by putting forward previously one or two other ,aphorisms bearing upon the history of that ,science4 ,,aphorism ,,xxvi4 ,in the ,terminology of ,science it may be necessary to employ letters1 numbers1 and algebraical symbols4 #a4 ,,mineralogy4 ,i ,,have already said1 in ,aphorism ,,xv41 that symbols have been found requisite as a part of the terminology of ,mineralogy4 ,the names proposed by ,hay1 borrowed from the crystalline laws1 were so inadequate and unsystematic that they could not be retained4 ,he himself proposed a notation for crystalline forms1 founded upon his principle of the derivation of such forms from a primitive form1 by decrements1 on its edges or its angles4 ,to denote this derivation he took the first letters of the three syllables to mark the faces of the ,pri,mi,tive form1 ,p1 ,m1 ,t2 the vowels ,a1 ,e1 ,i1 ,o to mark the angles2 the consonants ,b1 ,c1 ,d1 c4 to mark the edges2 and numerical exponents1 annexed in various positions to these letters1 represented the law and manner of derivation4 ,thus when the primitive form was a cube1 #a ,b represented the result of a derivation by a decrement of one row #ceh on an edge2 that is1 a rhombic octahedron2 and #a ,,bp represented the combination of this octahedron with the primitive cube4 ,in this way the pentagonal dodecahedron1 produced by decrements of #b to #a on half the edges of the cube1 was represented by ,b ,c ,g ,g4 ,not only1 however1 was the hypothesis of primitive forms and decrements untenable1 but this notation was too unsystematic to stand long4 ,and when ,weiss and ,mohs established the distinction of ,systems of ,crystallography#ffd1 they naturally founded upon that distinction a notation for crystalline forms4 ,mohs had several followers2 but his algebraical notation so barbarously violated all algebraical meaning1 that it was not likely to last4 ,thus1 from a primitive rhombohedron which he designated by ,r1 he derived1 by a certain process1 a series of other rhombohedrons1 which he denoted by ,r #a1 ,r #b1 ,r #a1 c42 and then1 by another mode of derivation from them1 he obtained forms which he marked as 7,r #b71 7,r #b71 c4 ,in doing this he used the algebraical marks of addition and involution without the smallest ground2 besides many other proposals no less transgressing mathematical analogy and simplicity4 ,note #ffd3 ,hist4 ,ind4 ,sc4 b4 xv4 c4 #d4 ,but this notation might easily suggest a better4 ,if we take a primitive form1 we can generally1 by two steps of derivation1 each capable of numerical measure1 obtain any possible face2 and therefore any crystalline form bounded by such faces4 ,hence all that we need indicate in our crystalline laws is the primitive form1 and two numerical exponents2 and rejecting all superfluity in our symbols1 instead of 7,r #b7 we might write #b ,r #c4 ,nearly of this kind is the notation of ,naumann4 ,the systems of crystallization1 the octahedral or tessular1 the rhombic1 and the prismatic1 are marked by the letters ,o1 ,r1 ,p2 and from these are derived1 by certain laws1 such symbols as #c ,o 1 ,r #b1 ,p #b1 #cei which have their definite signification flowing from the rules of the notation4 ,but ,professor ,miller1 who has treated the subject of ,crystallography in the most general and symmetrical manner1 adopts the plan of marking each crystalline plane by three numerical indices4 ,thus in the ,octahedral ,system1 the cube is #ajj2 the octahedron is #aaa2 the rhombic dodecahedron is #jaa2 the pentagonal dodecahedron is #jab2 where indicates that the form is not holohedral but hemihedral1 only half the number of faces being taken which the law of derivation would give4 ,this system is the most mathematically consistent1 and affords the best means of calculation1 as ,professor ,miller has shown2 but there appears to be in it this defect1 that though an essential part of the scheme is the division of crystalline forms into ,systems1--the ,octahedral1 ,pyramidal1 ,rhombohedral and ,prismatic1--this division does not at all appear in the notation4 ,but whatever be the notation which the crystallographer adopts1 it is evident that he must employ some notation2 and that1 without it1 he will be unable to express the forms and relations of forms with which he has to deal4 #b4 ,,chemistry4 ,the same has long been the case in ,chemistry4 ,as ,i have stated elsewhere#fgd1 the chemical nomenclature of the oxygen theory was for a time very useful and effective4 ,but yet it had defects which could not be overlooked1 as ,i have already stated under ,aphorism ,,ii4 ,the relations of elements were too numerous1 and their numerical properties too important1 to be expressed by terminations and other modifications of words4 ,thus the compounds of ,nitrogen and ,oxygen are the ,protoxide1 the ,deutoxide1 ,nitrous ,acid1 ,peroxide of ,nitrogen1 ,nitric ,acid4 ,the systematic nomenclature here1 even thus loosely extended1 does not express our knowledge4 ,and the ,atomic ,theory1 when established1 brought to view numerical #cfj relations which it was very important to keep in sight4 ,if ,n represents ,nitrogen and ,o ,oxygen1 the compounds of the two elements just mentioned might be denoted by ,n ,o1 ,n #b,o1 ,n #c,o1 ,n #d,o1 ,n #e,o4 ,and by adopting a letter for each of the elementary substances1 all the combinations of them might be expressed in this manner4 ,note #fgd3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 #f4 ,but in chemistry there are different orders of combination4 ,a salt1 for instance1 is a compound of a base and an acid1 each of which is already compound4 ,if ,fe be iron and ,c be carbon1 ,fe ,o will be the protoxide of iron1 and ,c #b,o will be carbonic acid2 and the carbonate of iron 7more properly carbonate of protoxide of iron71 may be represented by 7,fe ,o7 7,c #b,o7 where the brackets indicate the first stage of composition4 ,but these brackets and signs of addition1 in complex cases1 would cumber the page in an inconvenient degree2 and oxygen is of such very wide occurrence1 that it seems desirable to abridge the notation so far as it is concerned4 ,hence ,berzelius proposed#fhd that in the first stage of composition the oxygen should be expressed by dots over the letter2 and thus the carbonate of iron would be 4,fe 44,c4 ,but ,berzelius further introduced into his notation indexes such as in algebra denote involution to the square1 cube1 c4 ,thus ,cu being copper1 the sulphate of copper is represented by 444,s44,cu4 ,this notation1 when first proposed1 was strongly condemned by ,english chemists1 and ,berzelius's reply to them may be taken as stating the reasons in favour of such notation4 ,he says#fid1 ',we answer to the opponents1 that undoubtedly the matter may be looked at in various lights4 ,the use of ,formul has always1 for a person who has not accustomed himself to them1 something repulsive2 but this is easy to overcome4 ,i agree with my opponent1 #cfa who says that nothing can be understood in a ,formula which cannot be expressed in words2 and that if the words express it as easily as the ,formula1 the use of the latter would be a folly4 ,but there are cases in which this is not so2 in which the ,formula says in a glance what it would take many lines to express in words2 and in which the expression of the ,formula is clearer and more easily apprehended by the reader than the longer description in words4 ,let us examine such a ,formula1 and compare it with the equivalent description in words4 ,take1 for example1 crystallized sulphate of copper1 of which the ,formula is 44,cu444,s #aj;,h,o4 ,now this ,formula expresses the following propositions3 ',that the salt consists of one atom of copper-oxide combined with #b atoms of sulphuric acid and with #aj atoms of water2 that the copper-oxide contains two atoms of oxygen2 and that the sulphuric acid contains #c atoms of oxygen for one atom of sulphur2 that its oxygen is three times as much as that of the oxide2 and that the number of atoms of oxygen in the acid is #f2 and that the number of atoms of oxygen in the water is #aj2 that is1 #e times the number in the oxide2 and that finally the salt contains1 of simple atoms1 #a copper1 #b sulphur1 #bj hydrogen1 and #ah oxygen4 ,note #fhd3 ,system of ,mineralogy1 #ahaf4 ,note #fid3 ,jahresbericht1 #ahbd1 p4 #aai4 ',since so much is expressed in this brief ,formula1 how very long would the explanation be for a more composite body1 for example1 ,alum2 for which the ,formula is 44,k444,s #b444;,al444,s #dh;,h,o4 ,it would take half a page to express all which this ,formula contains4 ',perhaps it may be objected that it is seldom that any one wants to know all this at once4 ,but it might reasonably be said in reply1 that the peculiar value of the ,formula consists in this1 that it contains answers to all the questions which can be asked with regard to the composition of the body4 #cfb ',but these ,formul have also another application1 of which ,i have sometimes had occasion to make use4 ,experiments sometimes bring before us combinations which cannot be foreseen from the nomenclature1 and for which it is not always easy to find a consistent and appropriate name4 ,in writing1 the ,formula may be applied instead of a ,name3 and the reader understands it better than if one made a new name4 ,in my treatise upon the sulphuretted alkalies ,i found ,degrees of ,sulphur-combination1 for which ,nomenclature has no name4 ,i expressed them1 for example1 by ,,ks#f1 ,,ks#h1 ,,ks#aj and ,i believed that every one understood what was thereby meant4 ,moreover1 ,i found another class of bodies in which an electro-negative sulphuretted metal played the part of an ,acid with respect to an electro-positive sulphuretted metal1 for which a whole new nomenclature was needed2 while yet it were not prudent to construct such a nomenclature1 till more is known on the subject4 ,instead of new names ,i used formulas2 for example1 ,,ks #b;,as ,s1 instead of saying the combination of #b atoms of ,sulphuret of ,arsenic containing #c atoms of ,sulphur1 with one atom of ,sulphuret of ,potassium 7,kali7 with the least dose of sulphur4' ,berzelius goes on to say that the ,english chemists had found themselves unable to find any substitutes for his formul when they translated his papers4 ,our ,english chemists have not generally adopted the notation of oxygen by dots2 but have employed commas or full stops and symbols 71 or 4 and 71 to denote various degrees of union1 and numerical indices4 ,thus the double sulphate of copper and potash is ,cu ,o1 ,,so#c ,,ko1 ,,so#c4 ,what has been said is applicable mainly to inorganic bodies 7as salts and minerals7#gjd4 ,in these bodies there is 7at least according to the views of many intelligent chemists7 a binary plan of combination1 union taking #cfc place between pairs of elements1 and the compounds so produced again uniting themselves to other compound bodies in the same manner4 ,thus1 in the above example1 copper and oxygen combine into oxide of copper1 potassium and oxygen into potash1 sulphur and oxygen into sulphuric acid2 sulphuric acid in its turn combines both with oxide of copper and oxide of potassium1 generating a pair of salts which are capable of uniting to form the double compound ,cu ,o1 ,,so#c ,,ko1 ,,so#c4 ,note #gjd3 ,fownes's ,chemistry4 ,part iii4 ,the most complicated products of inorganic chemistry may be thus shown to be built up by this repeated pairing on the part of their constituents4 ,but with organic bodies the case is remarkably different2 no such arrangement can here be traced4 ,in sugar1 which is ,c#ab ,h#aa ,o#aa1 or morphia#gad1 which is ,c#ce ,h#bj ,,no#f1 the elements are as it were bound together into a single whole1 which can enter into combination with other substances1 and be thence discharged with properties unaltered2 the elements not being obviously arranged in any subordinate groups4 ,hence the symbols for those substances are such as ,i have given above1 no marks of combination being used4 ,note #gad3 ,fownes's ,chemistry1 p4 #ced4 ,it is perhaps a consequence of this peculiarity that organic compounds are unstable in comparison with inorganic4 ,in unorganic substances generally the elements are combined in such a way that the most powerful affinities are satisfied#gbd1 and hence arises a state of very considerable permanence and durability4 ,but in an organic substance containing three or four elements1 there are often opposing affinities nearly balanced1 and when one of these tendencies by some accident obtains a preponderance and the equilibrium is destroyed1 then the organic body breaks up into two or more new bodies of simpler and more permanent constitution4 ,note #gbd3 ,see ,hist4 ,ind4 ,sc4 b4 xiv4 c4 #c4 ,there is another property of many organic substances which is called the ,law of ,substitution4 ,the #cfd ,hydrogen of the organic substance may often be replaced by ,chlorine1 ,bromine1 ,iodine1 or some other elements1 without the destruction of the primitive type or constitution of the compound so modified4 ,and this substitution may take place by several successive steps1 giving rise to a series of substitution-compounds1 which depart more and more in properties from the original substance4 ,this ,law also gives rise to a special notation4 ,thus a certain compound called ,dutch liquid has the elements ,c#d ,h#d ,cl#b3 but this substance is affected by chlorine 7,cl7 in obedience to the law of substitution2 one and two equivalents of hydrogen being successively removed by the prolonged action of chlorine gas aided by sunshine4 ,the successive products may be thus written ,h#c ,h#b ,c#d ,h#d ,cl#b2 ,c#d ,cl#b2 ,c#d ,cl#b4 ,cl ,cl#b ,perhaps at a future period1 chemical symbols1 and especially those of organic bodies1 may be made more systematic and more significant than they at present are4 ,,aphorism ,,xxvii4 ,in using algebraical symbols as a part of scientific language1 violations of algebraical analogy are to be avoided1 but may be admitted when necessary4 ,,as we must in scientific language conform to etymology1 so must we to algebra2 and as we are not to make ourselves the slaves of the former1 so also1 not to the latter4 ,hence we reject such crystallographical notation as that of ,mohs2 and in chemistry we use ,c#b1 ,o#c rather than ,c1 ,o1 which signify the square of ,c and the cube of ,o4 ,but we may use1 as we have said1 both the comma and the sign of addition1 for chemical combination1 for the sake of brevity1 though both steps of combination are really addition4 #cfe ,,aphorism ,,xxviii4 ,in a complex science1 which is in a state of transition1 capricious and detached derivations of terms are common2 but are not satisfactory4 ,,in this remark ,i have especial reference to ,chemistry2 in which the discoveries made1 especially in organic chemistry1 and the difficulty of reducing them to a system1 have broken up in several instances the old nomenclature1 without its being possible at present to construct a new set of terms systematically connected4 ,hence it has come to pass that chemists have constructed words in a capricious and detached way3 as by taking fragments of words1 and the like4 ,i shall give some examples of such derivations1 and also of some attempts which have more of a systematic character4 ,i have mentioned 7,aph4 9999,,xx4 sect4 #g7 the word ,ellagic 7acid71 made by inverting the word ,galle4 ,several words have recently been formed by chemists by taking syllables from two or more different words4 ,thus ,chevreul discovered a substance to which he gave the name 9999,ethal1 from the first syllables of the words ether and alcohol1 because of its analogy to those liquids in point of composition#gcd4 ,so ,liebig has the word chloral#gdd4 ,note3 #gcd3 ,turner's ,chemistry1 #ahcd1 p4 #iee ,note3 #gdd3 ,berzelius' ,jahresbericht1 xv4 p4 #cgb4 ,liebig1 examining the product of distillation of alcohol1 sulphuric acid and amber1 found a substance which he termed ,aldehyd1 from the words ,alcohol dehydrogenated#ged4 ,this mode of making ,words has been strongly objected to by ,mr4 ,dumas#gfd4 ,still more has he objected to the word ,mercaptan 7of ,zeise71 which #cff he says rests upon a mere play of words2 for it means both mercurium captans and mercurio aptum4 ,note #ged3 ,ibid4 xvi4 p4 #cjh4 ,note #gfd3 ,leons de ,chimie1 p4 #ced4 ,dumas and ,peligot1 working on pyroligneous acids1 found reason to believe the existence of a substance#ggd which they called methylene1 deriving the name from methy1 a spirituous fluid1 and hyle1 wood4 ,berzelius remarks that the name should rather be methyl1 and that may be taken in its signification of matter1 to imply the ,radical of ,wine3 and he proposes that the older ther-,radical1 ,c#d ,h#aj shall be called thyl1 the newer1 ,c#b ,h#f1 ,methyl4 ,note #ggd3 ,berzelius' ,jahresbericht1 xv4 7#ahcf74 ,this notion of marking by the termination yl the hypothetical compound radical of a series of chemical compounds has been generally adopted2 and1 as we see from the above reference1 it must be regarded as representing the ,greek word 3 and such hypothetical radicals of bases have been termed in general basyls4 ,bunsen obtained from ,cadet's fuming liquid a substance which he called ,alkarsin 7alkali-arsenic873 and the substance produced from this by oxidation he called ,alkargen#ghd4 ,berzelius was of opinion1 that the true view of its composition was that it contained a compound ternary radical ,c#f ,h#ab ,as#b1 after the manner of organic bodies2 and he proposed for this the name#gid ,kakodyl4 ,alkarsin is ,kakodyl-oxyd1 4,kd1 ,alkargen is ,kakodyl-acid1 ,kd4 ,note #ghd3 ,ibid4 xviii4 p4 #dig4 ,note #gid3 ,ibid4 xx4 p4 #ebg4 ,the discovery of ,kakodyl was the first instance of the insulation of an organic metallic basyl#hjd4 ,note #hjd3 ,miller's ,chemistry1 iii4 #bbj4 ,the first of the ,hydrocarbon ,radicals of the ,alcohols was the radical of ,tetrylic alcohol obtained by ,kolbe from ,valerate of ,potash1 and hence called ,valyl ,c#af ,h#ah4 ,chloroform is perchloride of formyl1 the hypothetical radical of formic acid#had4 ,note #had3 ,dumas1 ,leons sur la ,phil4 ,chim4 p4 #cef4 #cfg ,the discovery of such bases goes back to #ahae4 ,the substance formerly called ,prussiate of ,mercury1 being treated in a particular manner1 was resolved into metallic mercury and ,cyanogen4 ,this substance1 ,cyanogen1 is1 according to the older nomenclature1 ,bicarburet of ,nitrogen2 but chemists are agreed that its most convenient name is ,cyanogen1 proposed by its discoverer1 ,gay-,lussac1 in #ahaehbd4 ,the importance of the discovery consists in this2 that this substance was the first compound body which was distinctly proved to enter into combination with elementary substances in a manner similar to that in which they combine with each other4 ,note #hbd3 ,turner's ,chemistry 7#ahcd71 p4 #dbj4 ,miller's ,chemistry1 ii4 #ff4 ,the truth of our ,aphorism 7,,xxv47 that in such a science as chemistry1 the history of the scientific nomenclature is the history of the science1 appears from this2 that the controversies with respect to chemical theories and their application take the form of objections to the common systematic names and proposals of new names instead4 ,thus a certain compound of potassa1 sulphur1 hydrogen1 and oxygen1 may be regarded either as ,hydrosulphate of ,potassa1 or as ,sulphide of ,potassium in solution1 according to different views#hcd4 ,in some cases indeed1 changes are made merely for the sake of clearness4 ,instead of ,hydrochloric and ,hydrocyanic acid1 many ,french writers1 following ,thenard1 transpose the elements of these terms2 they speak of ,chlorhydric and ,cyanhydric acid2 by this means they avoid any ambiguity which might arise from the use of the prefix ,hydro1 which has sometimes been applied to compounds which contain water#hdd4 ,note #hcd3 ,miller's ,chemistry1 vol4 ii4 p4 #ehc4 ,note #hdd3 ,ibid4 ii4 #dcc4 ,an incompleteness in chemical nomenclature was further felt1 when it appeared1 from the properties of various substances1 that mere identity in chemical composition is not sufficient to produce identity of chemical character or properties#hed4 ,the doctrine of #cfh the existence of compounds identical in ultimate composition1 but different in chemical properties1 was termed ,isomerism4 ,thus chemists enumerate the following compounds1 all of which contain carbon and hydrogen in the proportion of single equivalents of each#hfd2--,methylene1 ,olefiant gas1 ,propylene1 ,oil gas1 ,amylene1 ,caproylene1 ,naphthene1 ,eleene1 ,peramylene1 ,cetylene1 ,cerotylene1 ,melissine4 ,note #hed3 ,ibid4 ii4 #fec4 ,note #hfd3 ,miller's ,chemistry1 ii4 p4 #fed4 ,i will1 in the last place1 propound an ,aphorism which has already offered itself in considering the history of ,chemistry#hgd as having a special bearing upon that ,science1 but which may be regarded as the supreme and ultimate rule with regard to the language of ,science4 ,note #hgd3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 #a4 ,,aphorism ,,xxix4 ,in learning the meaning of ,scientific ,terms1 the history of science is our ,dictionary3 the steps of scientific induction are our ,definitions4 ,,it is usual for unscientific readers to complain that the technical terms which they meet with in books of science are not accompanied by plain definitions such as they can understand4 ,but such definitions cannot be given4 ,for definitions must consist of words2 and1 in the case of scientific terms1 must consist of words which require again to be defined3 and so on1 without limit4 ,elementary substances in chemistry1 for instance1 what are they8 ,the substances into which bodies can be analysed1 and by the junction of which they are composed4 ,but what is analysis8 what is composition8 ,we have seen that it required long and laborious courses of experiment to answer these questions2 and that finally the balance decided among rival answers4 ,and so it is in other cases4 ,in entering upon each science1 we come upon a new set of words4 ,and how are we to learn #cfi 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 or familiar language4 ,here1 as in all other branches of knowledge1 the meaning of words is to be sought in the progress of thought4 ,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 can 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 the same is the case in other subjects4 ,to take the instance of ,morphology4 ,when the beginner is told that every group of animals may be reduced to an ,archetype1 he will seek for a definition of ,archetype4 ,such a definition has been offered1 to this effect3 the ,archetype of a group of animals is a diagram embodying all the organs and parts which are found in the group in such a relative position as they would have had if none had attained an excessive development4 ,but1 then1 we are led further to ask1 ,how are we in each case to become acquainted with the diagram2 to know of what parts it consists1 and how they are related2 and further2 ,what is the standard of excess8 ,it is by a wide examination of particular species1 and by several successive generalizations of observed facts1 that we are led to a diagram of an animal form of a certain kind1 7for example1 a vertebrate27 and of the various ways1 excessive and defective1 in which the parts may be developed4 ,this craving for definitions1 as we have already said1 arises in a great degree from the acquaintance with geometry which most persons acquire at an early age4 ,the definitions of geometry are easily intelligible by a beginner1 because the idea of space1 of which they are modifications1 is clearly possessed without any special culture4 ,but this is not and cannot be the case in other sciences founded upon a wide and exact observation of facts4 #cgj ,it was formerly said that there was no ,royal ,road to ,geometry3 in modern times we have occasion often to repeat that there is no ,popular ,road--no road easy1 pleasant1 offering no difficulty and demanding no toil1--to ,comparative ,anatomy1 ,chemistry or any other of the ,inductive ,sciences4 ,,the ,,end4 ,,cambridge3 ,,printed ,,by ,c4 ,j4 ,,clay1 ,m4,a4 ,,at ,,the ,,university ,,press4 ,transcriber's ,notes ,whewell published the first edition of the ,philosophy of the ,inductive ,sciences in #ahdj in two volumes1 as a companion to the #ahcg ,history of the ,inductive ,sciences4 ,revised second editions of both works appeared in #ahdg4 ,the third editions saw a major reshaping of the ,philosophy3 a two volume ,history of ,scientific ,ideas 7#aheh2 in ,project ,gutenberg as #fijic71 ,novum ,organon ,renovatum 7#aheh2 the present text1 relying upon resources kindly provided by the ,internet ,archive71 and ,on the ,philosophy of ,discovery3 chapters historical and critical 7#ahfj2 long since in ,project ,gutenberg's collection as #eaee74 7,the third edition of the ,history of the ,inductive ,sciences is available in ,,pg as #fhfic47 ,adaptations in this text ,in the present text footnotes are numbered by ,book and are placed after the paragraph to which they attach2 in the original1 notes were numbered by chapter4 ,page numbers appear in 1 or when the number is not printed4 ,where a word was hyphenated across pages the number has been placed before the word4 ,fractions have been transcribed as numerator denominator2 the original usually has numerator over a line with denominator below4 ,some unusual symbols occur4 ,on pages #ceg and #ceh1 there are italic letters with a number written above them4 ,on two occasions ,b has a #a above it1 and once ,c has above it4 ,on page #cfd a formula is written with two entries containing ,h on a line above ,cl4 ,these superpositions have been preserved at the cost of some short lines4 ,the other oddities have been captured by using to indicate items above the following character4 7,they should not be confused with the use of for footnote anchors47 ,for superscripts has been used except for expressions using only the superscripted numbers available in ,unicode4 ,subscripts are indicated by a preceding the character4 7,this unfortunately results in double when the preceding characters are in italics47 ,on pages #aeb and #aig ,whewell uses a raised dot as a decimal point and in footnote #bfc a comma4 ,these have been replaced by a mid dot4 ,inductive ,charts ,at the end of ,book ,,ii41 ,whewell included two very large inserts1 described in some detail in the ,book itself4 ,they were not captured by the scans available in the ,internet ,archive4 ,i was kindly provided with photographs of them4 ,those charts were four times as wide as the normal page and a quarter as long4 ,in the html version they have been fairly accurately represented via tables2 but with up to #be columns these tables will be very difficult to decipher on small screens4 ,in the text version1 coded structure diagrams have been used1 which again utilise the full #gj spaces ,project ,gutenberg allows4 ,rather than the tree shape ,whewell used1 the diagrams have been made to flow from left to right4 ,corrections ,corrections are comparatively few4 ,apart from the silent ones1 they have been marked by 9999 and are listed below4 ,page ,printed text ,corrected text xiii v iii ,,lxx4 ,,lxxiii4 ,,lxxxv4 ,,lxxxii4 p4 #ab of and p4 #abh word work note #bac i4 ii4 p4 #cbb ,wafferstoff ,wasserstoff p4 #cfe ,,xv4 ,,xx4 ,ethol ,ethal ,given the various editions1 some of the internal cross-references turn out to be obsolete or erroneous3 note #aac reads ,b4 viii4 c4 iii4 but it refers actually to ,book viii4 c4 ii4 article #c in earlier editions and in the ,history of ,scientific ,ideas1 cf4 ,aphorism #hh in ,book ,i4 of the present volume4 ,compare also ,aphorism #ai in this volume's ,book ,,iv4 notes #ehc and #eic refer to ,book v4 c4 i4 ,for the present third edition they should have been aimed at that chapter of the ,history of ,scientific ,ideas4 ,there are some inconsistencies1 notably in spelling1 which have in general not been adjusted2 nor have ,whewell's unbalanced quotation marks and positioning of footnote anchors been modernized4