,,history ,,of ,,scientific ,,ideas4 ,,volume ,i4 ,cambridge2 ,,printed ,,by ,c4 ,j4 ,,clay1 ,m4,a4 ,,at ,,the ,,university ,,press4 ,,history ,,of ,,scientific ,,ideas4 ,,by ,,william ,,whewell1 ,d4,d41 ,,master ,,of ,,trinity ,,college1 ,,cambridge1 ,,and ,,corresponding ,,member ,,of ,,the ,,institute ,,of ,,france4 ,,being ,,the ,,first ,,part ,,of ,,the ,,philosophy ,,of ,,the ,,inductive ,,sciences4 ,,the ,,third ,,edition4 ,,in ,,two ,,volumes4 ,i ,i,i ,i ,,volume ,i4 ,,london3 ,,john ,w4 ,,parker ,,and ,,son1 ,,west ,,strand4 #aheh4 v ,,preface ,,to ,,this ,,edition4 ,,the ,chapters now offered to the ,reader were formerly published as a portion of ,the ,philosophy of the ,inductive ,sciences1 founded upon their ,history3 but the nature and subject of these ,chapters are more exactly described by the present title1 ,the ,history of ,scientific ,ideas4 ,for this part of the work is mainly historical1 and was1 in fact1 collected from the body of scientific literature1 at the same time that the ,history of the ,inductive ,sciences was so collected4 ,the present work contains the history of ,science so far as it depends on ,ideas2 the former work contains the same history so far as it is derived from ,observation4 ,the leading features in that were ,theories inferred from ,facts2 the leading features of this are ,discussions of ,theories tending to make them consistent with the conditions of human thought4 ,the ,ideas of which the ,history is here given are mainly the following3 ,space1 ,time1 ,number1 ,motion1 ,cause1 ,force1 ,matter1 ,medium1 ,intensity1 ,scale1 ,polarity1 ,element1 ,affinity1 ,substance1 ,atom1 ,symmetry1 ,likeness1 ,natural ,classes1 ,species1 ,life1 ,function1 ,vital ,forces1 ,final vi ,causes1 ,historical ,causation1 ,catastrophe and ,uniformity1 ,first ,cause4 ,the controversies to which the exact fixation of these ,ideas and their properties have given occasion form a large and essential part of the ,history of ,science3 but they also form an important part of the ,philosophy of ,science1 for no ,philosophy of ,science can be complete which does not solve the difficulties1 antitheses1 and paradoxes on which such controversies have turned4 ,i have given a survey of such controversies1 generally carried from their earliest origin to their latest aspect2 and have stated what appeared to me the best solution of each problem4 ,this has necessarily involved me in much thorny metaphysics2 but such metaphysics is a necessary part of the progress of ,science4 ,the human mind deriving its knowledge of ,truth from the observation of nature1 cannot evade the task of determining at every step how ,truth is consistent with itself4 ,this is the ,metaphysics of ,progressive ,knowledge1 and this is the matter of this present ,history4 ,of the remaining part of what was formerly published as the ,philosophy of the ,inductive ,sciences1 an additional part1 described in the ,introduction to the present work1 will shortly be published4 ,,trinity ,,lodge1 ,may #bd1 #aheh4 ,,erratum1 p4 #aeg1 l4 #aa from top1 for sciences read science4 ,,contents ,,of ,,the ,,first ,,volume4 ,,page ,,preface v ,,part ,i4 ,,of ,,ideas4 ,,introduction #c ,,book ,i4 ,,of ,,ideas ,,in ,,general4 ,,chap4 ,i4 ,,of ,,the ,,fundamental ,,antithesis ,,of ,,philosophy #bc ,sect4 #a4 ,thoughts and ,things -- #b4 ,necessary and ,experiential ,truths #be #c4 ,deduction and ,induction #bg #d4 ,theories and ,facts #bi #e4 ,ideas and ,sensations #cj #f4 ,reflexion and ,sensation #cc #g4 ,subjective and ,objective #ce #h4 ,matter and ,form #ch #i4 ,man the ,interpreter of ,nature #da #aj4 ,the ,fundamental ,antithesis is inseparable #dc #aa4 ,successive ,generalization #di viii ,,chap4 ,,ii4 ,,of ,,technical ,,terms #ed ,art4 #a4 ,examples4 #b4 ,use of ,terms4 ,,chap4 ,,iii4 ,,of ,,necessary ,,truths #eg ,art4 #a4 ,the two ,elements of ,knowledge1 #b4 ,shown by necessary ,truths4 #c4 ,examples of necessary ,truths in numbers4 #d4 ,the opposite cannot be distinctly conceived4 #e4 ,other ,examples4 #f4 ,universal ,truths4 ,,chap4 ,,iv4 ,,of ,,experience #fe ,art4 #a4 ,experience cannot prove necessary ,truths1 #b4 ,except when aided by ,ideas4 ,,chap4 ,v4 ,,of ,,the ,,grounds ,,of ,,necessary ,,truths #fi ,art4 #a4 ,these ,grounds are ,fundamental ,ideas4 #b4 ,these are to be reviewed4 #c4 ,definitions and ,axioms4 #d4 ,syllogism1 #e4 ,produces no new ,truths4 #f4 ,axioms needed4 #g4 ,axioms depend on ,ideas3 #h4 ,so do ,definitions4 #i4 ,idea not completely expressed4 ,,chap4 ,,vi4 ,,the ,,fundamental ,,ideas ,,are ,,not ,,derived ,,from ,,experience #gf ,art4 #a4 ,no connexion observed4 #b4 ,faculties implied in observation4 #c4 ,we are to examine our ,faculties4 ,,chap4 ,,vii4 ,,of ,,the ,,philosophy ,,of ,,the ,,sciences #ha ,sciences arranged according to ,ideas4 ix ,,book ,,ii4 ,,the ,,philosophy ,,of ,,the ,,pure ,,sciences4 ,,chap4 ,i4 ,,of ,,the ,,pure ,,sciences #hh ,art4 #a4 ,geometry1 ,arithmetic1 ,algebra1 #b4 ,are not ,inductive ,sciences3 #c4 ,are ,mathematical ,sciences4 #d4 ,mixed ,mathematics4 #e4 ,space1 ,time1 ,number4 ,,chap4 ,,ii4 ,,of ,,the ,,idea ,,of ,,space #ia ,art4 #a4 ,space is an ,idea1 #b4 ,not derived from ,experience1 #c4 ,as ,geometrical ,truth shows4 #d4 ,space is a ,form of ,experience4 #e4 ,the phrase not essential4 ,,chap4 ,,iii4 ,,of ,,some ,,peculiarities ,,of ,,the ,,idea ,,of ,,space #ie ,art4 #a4 ,space is not an ,abstract ,notion4 #b4 ,space is infinite4 #c4 ,space is real4 #d4 ,space is a ,form of ,intuition4 #e4 ,figure4 #f4 ,three ,dimensions4 ,,chap4 ,,iv4 ,,of ,,the ,,definitions ,,and ,,axioms ,,which ,,relate ,,to ,,space #ih ,art4 #a4 ,geometry4 #b4 ,definitions4 #c4 ,axioms4 #d4 ,not ,hypotheses4 #e4 ,axioms necessary4 #f4 ,straight ,lines4 #g4 ,planes4 #h4 ,elementary ,geometry4 ,,chap4 ,v4 ,,of ,,some ,,objections ,,which ,,have ,,been ,,made ,,to ,,the ,,doctrines ,,stated ,,in ,,the ,,previous ,,chapter #ajg ,art4 #a4 ,how is ,geometry hypothetical8 #b4 ,what was ,stewart's view8 x #c4 ',legitimate filiations' of ,definitions4 #d4 ,is a ,definition a complete explanation8 #e4 ,are some ,axioms ,definitions8 #f4 ,axiom concerning ,circles4 #g4 ,can ,axioms become truisms8 #h4 ,use of such4 ,,chap4 ,,vi4 ,,of ,,the ,,perception ,,of ,,space #aag ,art4 #a4 ,which ,senses apprehend ,space8 #b4 ,perception of solid figure4 #c4 ,is an interpretation4 #d4 ,may be analysed4 #e4 ,outline4 #f4 ,reversed convexity4 #g4 ,do we perceive ,space by ,touch8 #h4 ,brown's ,opinion4 #i4 ,the ,muscular ,sense4 #aj4 ,bell's ,opinion4 #aa4 ,perception includes ,activity4 #ab4 ,perception of the ,skyey ,dome4 #ac4 ,reid's ,idomenians4 #ad4 ,motion of the ,eye4 #ae4 ,searching ,motion4 #af4 ,sensible ,spot4 #ag4 ,expressions implying ,motion4 ,,chap4 ,,vii4 ,,of ,,the ,,idea ,,of ,,time #aca ,art4 #a4 ,time an ,idea not derived from ,experience4 #b4 ,time is a ,form of ,experience4 #c4 ,number4 #d4 ,is ,time derived from ,motion8 ,,chap4 ,,viii4 ,,of ,,some ,,peculiarities ,,in ,,the ,,idea ,,of ,,time #acd ,art4 #a4 ,time is not an ,abstract ,notion4 #b4 ,time is infinite4 #c4 ,time is a ,form of ,intuition4 #d4 ,time is of one ,dimension1 #e4 ,and no more4 #f4 ,rhythm4 #g4 ,alternation4 #h4 ,arithmetic4 xi ,,chap4 ,,ix4 ,,of ,,the ,,axioms ,,which ,,relate ,,to ,,number #ach ,art4 #a4 ,grounds of ,arithmetic4 #b4 ,intuition4 #c4 ,arithmetical ,axioms1 #d4 ,are ,conditions of ,numerical ,reasoning #e4 ,in all ,arithmetical ,operations4 #f4 ,higher ,numbers4 ,,chap4 ,x4 ,,of ,,the ,,perception ,,of ,,time ,,and ,,number #ada ,art4 #a4 ,memory4 #b4 ,sense of ,successiveness #c4 ,implies ,activity4 #d4 ,number also does so4 #e4 ,and apprehension of ,rhythm4 ,note to ,chapter ,x4 #ade ,,chap4 ,,xi4 ,,of ,,mathematical ,,reasoning #adg ,art4 #a4 ,discursive ,reasoning4 #b4 ,technical ,terms of ,reasoning4 #c4 ,geometrical ,analysis and ,synthesis4 ,,chap4 ,,xii4 ,,of ,,the ,,foundations ,,of ,,the ,,higher ,,mathematics #aea ,art4 #a4 ,the ,idea of a ,limit4 #b4 ,the use of ,general ,symbols4 #c4 ,connexion of ,symbols and ,analysis4 ,,chap4 ,,xiii4 ,,the ,,doctrine ,,of ,,motion #aef ,art4 #a4 ,pure ,mechanism4 #b4 ,formal ,astronomy4 ,,chap4 ,,xiv4 ,,of ,,the ,,application ,,of ,,mathematics ,,to ,,the ,,inductive ,,sciences #aei ,art4 #a4 ,the ,ideas of ,space and ,number are clear from the first4 #b4 ,their application in ,astronomy4 #c4 ,conic ,sections1 c4 #d4 ,arabian ,numerals4 #e4 ,newton's ,lemmas4 #f4 ,tides4 #g4 ,mechanics4 #h4 ,optics4 #i4 ,conclusion4 xii ,,book ,,iii4 ,,the ,,philosophy ,,of ,,the ,,mechanical ,,sciences4 ,,chap4 ,i4 ,,of ,,the ,,mechanical ,,sciences #aga ,,chap4 ,,ii4 ,,of ,,the ,,idea ,,of ,,cause #agc ,art4 #a4 ,not derived from ,observation1 #b4 ,as appears by its use4 #c4 ,cause cannot be observed4 #d4 ,is ,cause only constant succession8 #e4 ,other reasons4 ,,chap4 ,,iii4 ,,modern ,,opinions ,,respecting ,,the ,,idea ,,of ,,cause #agh ,art4 #a4 ,hume's ,doctrine4 #b4 ,stewart and ,brown4 #c4 ,kant4 #d4 ,relation of ,kant and ,brown4 #e4 ,axioms flow from the ,idea4 #f4 ,the ,idea implies activity in the ,mind4 ,,chap4 ,,iv4 ,,of ,,the ,,axioms ,,which ,,relate ,,to ,,the ,,idea ,,of ,,cause #ahd ,art4 #a4 ,causes are ,abstract ,conceptions4 #b4 ,first ,axiom4 #c4 ,second ,axiom4 #d4 ,limitation of the ,second ,axiom4 #e4 ,third ,axiom4 #f4 ,extent of the ,third ,axiom4 ,,chap4 ,v4 ,,of ,,the ,,origin ,,of ,,our ,,conceptions ,,of ,,force ,,and ,,matter #bje ,art4 #a4 ,force4 #b4 ,matter4 #c4 ,solidity4 #d4 ,inertia4 #e4 ,application4 xiii ,,chap4 ,,vi4 ,,of ,,the ,,establishment ,,of ,,the ,,principles ,,of ,,statics #bab ,art4 #a4 ,object of the ,chapter4 #b4 ,statics and ,dynamics4 #c4 ,equilibrium4 #d4 ,measure of ,statical ,forces4 #e4 ,the ,center of ,gravity4 #f4 ,oblique ,forces4 #g4 ,force acts at any point of its ,direction4 #h4 ,the ,parallelogram of ,forces #i4 ,is a necessary ,truth4 #aj4 ,center of ,gravity descends4 #aa4 ,stevinus's ,proof4 #ab4 ,principle of ,virtual ,velocities4 #ac4 ,fluids press equally4 #ad4 ,foundation of this ,axiom4 ,,chap4 ,,vii4 ,,of ,,the ,,establishment ,,of ,,the ,,principles ,,of ,,dynamics #bce ,art4 #a4 ,history4 #b4 ,the ,first ,law of ,motion4 #c4 ,gravity is a ,uniform ,force4 #d4 ,the ,second ,law of ,motion4 #e4 ,the ,third ,law of ,motion4 #f4 ,action and ,reaction in ,moving ,bodies4 #g4 ,d',alembert's ,principle4 #h4 ,connexion of ,statics and ,dynamics4 #i4 ,mechanical ,principles grow more evident4 #aj4 ,controversy of the ,measure of ,force4 ,,chap4 ,,viii4 ,,of ,,the ,,paradox ,,of ,,universal ,,propositions ,,obtained ,,from ,,experience #bfc ,art4 #a4 ,experience cannot establish necessary ,truths2 #b4 ,but can interpret ,axioms4 #c4 ,gives us the ,matter of ,truths4 #d4 ,exemplifies ,truths4 #e4 ,cannot shake ,axioms4 #f4 ,is this applicable in other cases8 ,,chap4 ,,ix4 ,,of ,,the ,,establishment ,,of ,,the ,,law ,,of ,,universal ,,gravitation #bgb ,art4 #a4 ,general course of the ,history4 xiv #b4 ,particulars as to the ,law4 #c4 ,as to the ,gravity of ,matter4 #d4 ,universality of the ,law4 #e4 ,is ,gravity an essential quality8 #f4 ,newton's ,rule of ,philosophizing4 #g4 ,hypotheses respecting ,gravity4 #h4 ,do ,bodies act at a distance8 ,,chap4 ,x4 ,,of ,,the ,,general ,,diffusion ,,of ,,clear ,,mechanical ,,ideas #bgi ,art4 #a4 ,nature of the ,process #b4 ,among the ,ancients4 #c4 ,kepler1 c4 #d4 ,lord ,monboddo1 c4 #e4 ,schelling1 c4 #f4 ,common usage4 #g4 ,effect of ,phrases4 #h4 ,contempt of ,predecessors4 #i4 ,less detail hereafter4 #aj4 ,mechanico-,chemical ,sciences4 #aa4 ,secondary ,mechanical ,sciences4 ,,book ,,iv4 ,,the ,,philosophy ,,of ,,the ,,secondary ,,mechanical ,,sciences4 ,,chap4 ,i4 ,,of ,,the ,,idea ,,of ,a ,,medium ,,as ,,commonly ,,employed #bic ,art4 #a4 ,of ,primary and ,secondary ,qualities4 #b4 ,the ,idea of ,externality4 #c4 ,sensation by a ,medium4 #d4 ,process of ,perception of ,secondary ,qualities4 ,,chap4 ,,ii4 ,,on ,,peculiarities ,,in ,,the ,,perceptions ,,of ,,the ,,different ,,senses #cjb ,art4 #a4 ,difference of ,senses4 ,sect4 ,i4 ,prerogatives of ,sight4 ,art4 #b4 ,position4 #c4 ,distance4 xv ,sect4 ,,ii4 ,prerogatives of ,hearing4 ,art4 #d4 ,musical ,intervals4 #e4 ,chords4 #f4 ,rhythm4 ,sect4 ,,iii4 ,the ,paradoxes of ,vision4 ,art4 #g4 ,first ,paradox4 #h4 ,second ,paradox4 #i4 ,the same for near ,objects4 #aj4 ,objections answered4 ,sect4 ,,iv4 ,the ,perception of ,visible ,figures4 ,art4 #aa4 ,brown's ,opinion4 ,,chap4 ,,iii4 ,,successive ,,attempts ,,at ,,the ,,scientific ,,application ,,of ,,the ,,idea ,,of ,a ,,medium #cbb ,art4 #a4 ,introduction4 #b4 ,sound4 #c4 ,light4 #d4 ,heat4 ,,chap4 ,,iv4 ,,of ,,the ,,measure ,,of ,,secondary ,,qualities #ccc ,sect4 ,i4 ,scales of ,qualities in ,general4 ,art4 #a4 ,intensity4 #b4 ,quantity and ,quality4 ,sect4 ,,ii4 ,the ,musical ,scale4 ,art4 #c4 ,musical ,relations4 #d4 ,musical ,standard4 ,sect4 ,,iii4 ,scales of ,colour4 ,art4 #e4 ,the ,prismatic ,scale4 #f4 ,newton's ,scale4 #g4 ,scales of ,impure ,colours4 #h4 ,chromatometer4 ,sect4 ,,iv4 ,scales of ,light4 ,art4 #i4 ,photometer4 #aj4 ,cyanometer4 ,sect4 ,v4 ,scales of ,heat4 ,art4 #aa4 ,thermometers4 #ab4 ,their progress4 #ac4 ,fixed ,points4 #ad4 ,concordance of ,thermometers4 #ae4 ,natural ,measure4 #af4 ,law of ,cooling4 xvi #ag4 ,theory of ,exchanges4 #ah4 ,air ,thermometer4 #ai4 ,theory of ,heat4 #bj4 ,other ,instruments4 ,sect4 ,,vi4 ,scales of other ,quantities4 ,art4 #ba4 ,tastes and ,smells4 #bb4 ,quality of ,sounds4 #bc4 ,articulate ,sounds4 #bd4 ,transition4 ,,book ,v4 ,,of ,,the ,,philosophy ,,of ,,the ,,mechanico-,,chemical ,,sciences4 ,,chap4 ,i4 ,,attempts ,,at ,,the ,,scientific ,,application ,,of ,,the ,,idea ,,of ,,polarity #cei ,art4 #a4 ,introduction of the ,idea4 #b4 ,magnetism4 #c4 ,electricity4 #d4 ,voltaic ,electricity4 #e4 ,light4 #f4 ,crystallization4 #g4 ,chemical ,affinity4 #h4 ,general ,remarks4 #i4 ,like repels like4 ,,chap4 ,,ii4 ,,of ,,the ,,connexion ,,of ,,polarities #cga ,art4 #a4 ,different ,polar ,phenomena from one ,cause4 #b4 ,connexion of ,magnetic and ,electric ,polarity4 #c4 ,ampre's ,theory4 #d4 ,faraday's views4 #e4 ,connexion of ,electrical and ,chemical ,polarity4 #f4 ,davy's and ,faraday's views #g4 ,depend upon ,ideas as well as ,experiments4 #h4 ,faraday's ,anticipations4 #i4 ,connexion of ,chemical and ,crystalline ,polarities4 #aj4 ,connexion of ,crystalline and ,optical ,polarities4 #aa4 ,connexion of ,polarities in general4 #ab4 ,schelling's ,speculations4 #ac4 ,hegel's vague notions4 #ad4 ,ideas must guide ,experiment4 #a ,,the ,,philosophy ,,of ,,the ,,inductive ,,sciences4 ,,introduction4 #c ,,introduction4 ,,the ,,philosophy ,,of ,,science1 if the phrase were to be understood in the comprehensive sense which most naturally offers itself to our thoughts1 would imply nothing less than a complete insight into the essence and conditions of all real knowledge1 and an exposition of the best methods for the discovery of new truths4 ,we must narrow and lower this conception1 in order to mould it into a form in which we may make it the immediate object of our labours with a good hope of success2 yet still it may be a rational and useful undertaking1 to endeavour to make some advance towards such a ,philosophy1 even according to the most ample conception of it which we can form4 ,the present work has been written with a view of contributing1 in some measure1 however small it may be1 towards such an undertaking4 ,but in this1 as in every attempt to advance beyond the position which we at present occupy1 our hope of success must depend mainly upon our being able to profit1 to the fullest extent1 by the progress already made4 ,we may best hope to understand the nature and conditions of real knowledge1 by studying the nature and conditions of the most certain and stable portions of knowledge which we already possess3 and we are most likely to learn the best methods of discovering truth1 by examining how truths1 now universally recognized1 have really been discovered4 ,now there do exist among us doctrines of solid and acknowledged certainty1 and truths of which the discovery has been received with universal applause4 ,these constitute what we commonly term ,sciences2 and of these bodies of exact and enduring knowledge1 we have within our #d reach so large and varied a collection1 that we may examine them1 and the history of their formation1 with a good prospect of deriving from the study such instruction as we seek4 ,we may best hope to make some progress towards the ,philosophy of ,science1 by employing ourselves upon ,,the ,,philosophy ,,of ,,the ,,sciences4 ,the ,sciences to which the name is most commonly and unhesitatingly given1 are those which are concerned about the material world2 whether they deal with the celestial bodies1 as the sun and stars1 or the earth and its products1 or the elements2 whether they consider the differences which prevail among such objects1 or their origin1 or their mutual operation4 ,and in all these ,sciences it is familiarly understood and assumed1 that their doctrines are obtained by a common process of collecting general truths from particular observed facts1 which process is termed ,induction4 ,it is further assumed that both in these and in other provinces of knowledge1 so long as this process is duly and legitimately performed1 the results will be real substantial truth4 ,and although this process1 with the conditions under which it is legitimate1 and the general laws of the formation of ,sciences1 will hereafter be subjects of discussion in this work1 ,i shall at present so far adopt the assumption of which ,i speak1 as to give to the ,sciences from which our lessons are to be collected the name of ,inductive ,sciences4 ,and thus it is that ,i am led to designate my work as ,,the ,,philosophy ,,of ,,the ,,inductive ,,sciences4 ,the views respecting the nature and progress of knowledge1 towards which we shall be directed by such a course of inquiry as ,i have pointed out1 though derived from those portions of human knowledge which are more peculiarly and technically termed ,sciences1 will by no means be confined1 in their bearing1 to the domain of such ,sciences as deal with the material world1 nor even to the whole range of ,sciences now existing4 ,on the contrary1 we shall be led to believe that the nature of truth is in all subjects the same1 and that its discovery involves1 in all cases1 the like #e conditions4 ,on one subject of human speculation after another1 man's knowledge assumes that exact and substantial character which leads us to term it ,science2 and in all these cases1 whether inert matter or living bodies1 whether permanent relations or successive occurrences1 be the subject of our attention1 we can point out certain universal characters which belong to truth1 certain general laws which have regulated its progress among men4 ,and we naturally expect that1 even when we extend our range of speculation wider still1 when we contemplate the world within us as well as the world without us1 when we consider the thoughts and actions of men as well as the motions and operations of unintelligent bodies1 we shall still find some general analogies which belong to the essence of truth1 and run through the whole intellectual universe4 ,hence we have reason to trust that a just ,philosophy of the ,sciences may throw light upon the nature and extent of our knowledge in every department of human speculation4 ,by considering what is the real import of our acquisitions1 where they are certain and definite1 we may learn something respecting the difference between true knowledge and its precarious or illusory semblances2 by examining the steps by which such acquisitions have been made1 we may discover the conditions under which truth is to be obtained2 by tracing the boundary-line between our knowledge and our ignorance1 we may ascertain in some measure the extent of the powers of man's understanding4 ,but it may be said1 in such a design there is nothing new2 these are objects at which inquiring men have often before aimed4 ,to determine the difference between real and imaginary knowledge1 the conditions under which we arrive at truth1 the range of the powers of the human mind1 has been a favourite employment of speculative men from the earliest to the most recent times4 ,to inquire into the original1 certainty1 and compass of man's knowledge1 the limits of his capacity1 the strength and weakness of his reason1 has been the professed purpose of many of the most conspicuous and valued labours of the philosophers of #f all periods up to our own day4 ,it may appear1 therefore1 that there is little necessity to add one more to these numerous essays2 and little hope that any new attempt will make any very important addition to the stores of thought upon such questions1 which have been accumulated by the profoundest and acutest thinkers of all ages4 ,to this ,i reply1 that without at all disparaging the value or importance of the labours of those who have previously written respecting the foundations and conditions of human knowledge1 it may still be possible to add something to what they have done4 ,the writings of all great philosophers1 up to our own time1 form a series which is not yet terminated4 ,the books and systems of philosophy which have1 each in its own time1 won the admiration of men1 and exercised a powerful influence upon their thoughts1 have had each its own part and functions in the intellectual history of the world2 and other labours which shall succeed these may also have their proper office and useful effect4 ,we may not be able to do much1 and yet still it may be in our power to effect something4 ,perhaps the very advances made by former inquirers may have made it possible for us1 at present1 to advance still further4 ,in the discovery of truth1 in the development of man's mental powers and privileges1 each generation has its assigned part2 and it is for us to endeavour to perform our portion of this perpetual task of our species4 ,although the terms which describe our undertaking may be the same which have often been employed by previous writers to express their purpose1 yet our position is different from theirs1 and thus the result may be different too4 ,we have1 as they had1 to run our appropriate course of speculation with the exertion of our best powers2 but our course lies in a more advanced part of the great line along which ,philosophy travels from age to age4 ,however familiar and old1 therefore1 be the design of such a work as this1 the execution may have1 and if it be performed in a manner suitable to the time1 will have1 something that is new and not unimportant4 #g ,indeed1 it appears to be absolutely necessary1 in order to check the prevalence of grave and pernicious errour1 that the doctrines which are taught concerning the foundations of human knowledge and the powers of the human mind1 should be from time to time revised and corrected or extended4 ,erroneous and partial views are promulgated and accepted2 one portion of the truth is insisted upon to the undue exclusion of another2 or principles true in themselves are exaggerated till they produce on men's minds the effect of falsehood4 ,when evils of this kind have grown to a serious height1 a ,reform is requisite4 ,the faults of the existing systems must be remedied by correcting what is wrong1 and supplying what is wanting4 ,in such cases1 all the merits and excellencies of the labours of the preceding times do not supersede the necessity of putting forth new views suited to the emergency which has arrived4 ,the new form which errour has assumed makes it proper to endeavour to give a new and corresponding form to truth4 ,thus the mere progress of time1 and the natural growth of opinion from one stage to another1 leads to the production of new systems and forms of philosophy4 ,it will be found1 ,i think1 that some of the doctrines now most widely prevalent respecting the foundations and nature of truth are of such a kind that a ,reform is needed4 ,the present age seems1 by many indications1 to be called upon to seek a sounder ,philosophy of ,knowledge than is now current among us4 ,to contribute towards such a ,philosophy is the object of the present work4 ,the work is1 therefore1 like all works which take into account the most recent forms of speculative doctrine1 invested with a certain degree of novelty in its aspect and import1 by the mere time and circumstances of its appearance4 ,but1 moreover1 we can point out a very important peculiarity by which this work is1 in its design1 distinguished from preceding essays on like subjects2 and this difference appears to be of such a kind as may well entitle us to expect some substantial addition to our knowledge as the result of our labours4 ,the peculiarity #h of which ,i speak has already been announced2--it is this3 that we purpose to collect our doctrines concerning the nature of knowledge1 and the best mode of acquiring it1 from a contemplation of the ,structure and ,history of those ,sciences 7the ,material ,sciences71 which are universally recognized as the clearest and surest examples of knowledge and of discovery4 ,it is by surveying and studying the whole mass of such ,sciences1 and the various steps of their progress1 that we now hope to approach to the true ,philosophy of ,science4 ,now this1 ,i venture to say1 is a new method of pursuing the philosophy of human knowledge4 ,those who have hitherto endeavoured to explain the nature of knowledge1 and the process of discovery1 have1 it is true1 often illustrated their views by adducing special examples of truths which they conceived to be established1 and by referring to the mode of their establishment4 ,but these examples have1 for the most part1 been taken at random1 not selected according to any principle or system4 ,often they have involved doctrines so precarious or so vague that they confused rather than elucidated the subject2 and instead of a single difficulty1--,what is the nature of ,knowledge8 these attempts at illustration introduced two1--,what was the true analysis of the ,doctrines thus adduced8 and1--,whether they might safely be taken as types of real ,knowledge8 ,this has usually been the case when there have been adduced1 as standard examples of the formation of human knowledge1 doctrines belonging to supposed sciences other than the material sciences2 doctrines1 for example1 of ,political ,economy1 or ,philology1 or ,morals1 or the ,philosophy of the ,fine ,arts4 ,i am very far from thinking that1 in regard to such subjects1 there are no important truths hitherto established3 but it would seem that those truths which have been obtained in these provinces of knowledge1 have not yet been fixed by means of distinct and permanent phraseology1 and sanctioned by universal reception1 and formed into a connected system1 and traced through the steps of their gradual discovery and establishment1 so as to make #i them instructive examples of the nature and progress of truth in general4 ,hereafter we trust to be able to show that the progress of moral1 and political1 and philological1 and other knowledge1 is governed by the same laws as that of physical science4 ,but since1 at present1 the former class of subjects are full of controversy1 doubt1 and obscurity1 while the latter consist of undisputed truths clearly understood and expressed1 it may be considered a wise procedure to make the latter class of doctrines the basis of our speculations4 ,and on the having taken this course1 is1 in a great measure1 my hope founded1 of obtaining valuable truths which have escaped preceding inquirers4 ,but it may be said that many preceding writers on the nature and progress of knowledge have taken their examples abundantly from the ,physical ,sciences4 ,it would be easy to point out admirable works1 which have appeared during the present and former generations1 in which instances of discovery1 borrowed from the ,physical ,sciences1 are introduced in a manner most happily instructive4 ,and to the works in which this has been done1 ,i gladly give my most cordial admiration4 ,but at the same time ,i may venture to remark that there still remains a difference between my design and theirs3 and that ,i use the ,physical ,sciences as exemplifications of the general progress of knowledge in a manner very materially different from the course which is followed in works such as are now referred to4 ,for the conclusions stated in the present work1 respecting knowledge and discovery1 are drawn from a connected and systematic survey of the whole range of ,physical ,science and its ,history2 whereas1 hitherto1 philosophers have contented themselves with adducing detached examples of scientific doctrines1 drawn from one or two departments of science4 ,so long as we select our examples in this arbitrary and limited manner1 we lose the best part of that philosophical instruction1 which the sciences are fitted to afford when we consider them as all members of one series1 and as governed by rules which are the same for all4 ,mathematical and chemical truths1 physical and physiological doctrines1 the sciences of #aj classification and of causation1 must alike be taken into our account1 in order that we may learn what are the general characters of real knowledge4 ,when our conclusions assume so comprehensive a shape that they apply to a range of subjects so vast and varied as these1 we may feel some confidence that they represent the genuine form of universal and permanent truth4 ,but if our exemplification is of a narrower kind1 it may easily cramp and disturb our philosophy4 ,we may1 for instance1 render our views of truth and its evidence so rigid and confined as to be quite worthless1 by founding them too much on the contemplation of mathematical truth4 ,we may overlook some of the most important steps in the general course of discovery1 by fixing our attention too exclusively upon some one conspicuous group of discoveries1 as1 for instance1 those of ,newton4 ,we may misunderstand the nature of physiological discoveries1 by attempting to force an analogy between them and discoveries of mechanical laws1 and by not attending to the intermediate sciences which fill up the vast interval between these extreme terms in the series of material sciences4 ,in these and in many other ways1 a partial and arbitrary reference to the material sciences in our inquiry into human knowledge may mislead us2 or at least may fail to give us those wider views1 and that deeper insight1 which should result from a systematic study of the whole range of sciences with this particular object4 ,the design of the following work1 then1 is to form a ,philosophy of ,science1 by analyzing the substance and examining the progress of the existing body of the sciences4 ,as a preliminary to this undertaking1 a survey of the history of the sciences was necessary4 ,this1 accordingly1 ,i have already performed2 and the result of the labour thus undertaken has been laid before the public as a ,history of the ,inductive ,sciences4 ,in that work ,i have endeavoured to trace the steps by which men acquired each main portion of that knowledge on which they now look with so much confidence and satisfaction4 ,the events which that ,history relates1 the speculations and controversies #aa which are there described1 and discussions of the same kind1 far more extensive1 which are there omitted1 must all be taken into our account at present1 as the prominent and standard examples of the circumstances which attend the progress of knowledge4 ,with so much of real historical fact before us1 we may hope to avoid such views of the processes of the human mind as are too partial and limited1 or too vague and loose1 or too abstract and unsubstantial1 to represent fitly the real forms of discovery and of truth4 ,of former attempts1 made with the same view of tracing the conditions of the progress of knowledge1 that of ,bacon is perhaps the most conspicuous3 and his labours on this subject were opened by his book on the ,advancement of ,learning1 which contains1 among other matter1 a survey of the then existing state of knowledge4 ,but this review was undertaken rather with the object of ascertaining in what quarters future advances were to be hoped for1 than of learning by what means they were to be made4 ,his examination of the domain of human knowledge was conducted rather with the view of discovering what remained undone1 than of finding out how so much had been done4 ,bacon's survey was made for the purpose of tracing the boundaries1 rather than of detecting the principles of knowledge4 ',i will now attempt1' he says#a;,i1 'to make a general and faithful perambulation of learning1 with an inquiry what parts thereof lie fresh and waste1 and not improved and converted by the industry of man2 to the end that such a plot made and recorded to memory1 may both minister light to any public designation1 and also serve to excite voluntary endeavours4' ,nor will it be foreign to our scheme also hereafter to examine with a like purpose the frontier-line of man's intellectual estate4 ,but the object of our perambulation in the first place1 is not so much to determine the extent of the field1 as the sources of its fertility4 ,we would learn by what plan and rules #ab of culture1 conspiring with the native forces of the bounteous soil1 those rich harvests have been produced which fill our garners4 ,bacon's maxims1 on the other hand1 respecting the mode in which he conceived that knowledge was thenceforth to be cultivated1 have little reference to the failures1 still less to the successes1 which are recorded in his ,review of the learning of his time4 ,his precepts are connected with his historical views in a slight and unessential manner4 ,his ,philosophy of the ,sciences is not collected from the ,sciences which are noticed in his survey4 ,nor1 in truth1 could this1 at the time when he wrote1 have easily been otherwise4 ,at that period1 scarce any branch of physics existed as a science1 except ,astronomy4 ,the rules which ,bacon gives for the conduct of scientific researches are obtained1 as it were1 by divination1 from the contemplation of subjects with regard to which no sciences as yet were4 ,his instances of steps rightly or wrongly made in this path1 are in a great measure cases of his own devising4 ,he could not have exemplified his ,aphorisms by references to treatises then extant1 on the laws of nature2 for the constant burden of his exhortation is1 that men up to his time had almost universally followed an erroneous course4 ,and however we may admire the sagacity with which he pointed the way along a better path1 we have this great advantage over him2--that we can interrogate the many travellers who since his time have journeyed on this road4 ,at the present day1 when we have under our notice so many sciences1 of such wide extent1 so well established2 a ,philosophy of the ,sciences ought1 it must seem1 to be founded1 not upon conjecture1 but upon an examination of many instances2--should not consist of a few vague and unconnected maxims1 difficult and doubtful in their application1 but should form a system of which every part has been repeatedly confirmed and verified4 ,note #a;,i3 ,advancement of ,learning1 b4 i4 p4 #gd4 ,this accordingly it is the purpose of the present work to attempt4 ,but ,i may further observe1 that as my hope of making any progress in this undertaking is #ac founded upon the design of keeping constantly in view the whole result of the past history and present condition of science1 ,i have also been led to draw my lessons from my examples in a manner more systematic and regular1 as appears to me1 than has been done by preceding writers4 ,bacon1 as ,i have just said1 was led to his maxims for the promotion of knowledge by the sagacity of his own mind1 with little or no aid from previous examples4 ,succeeding philosophers may often have gathered useful instruction from the instances of scientific truths and discoveries which they adduced1 but their conclusions were drawn from their instances casually and arbitrarily4 ,they took for their moral any which the story might suggest4 ,but such a proceeding as this cannot suffice for us1 whose aim is to obtain a consistent body of philosophy from a contemplation of the whole of ,science and its ,history4 ,for our purpose it is necessary to resolve scientific truths into their conditions and ingredients1 in order that we may see in what manner each of these has been and is to be provided1 in the cases which we may have to consider4 ,this accordingly is necessarily the first part of our task3--to analyse ,scientific ,truth into its ,elements4 ,this attempt will occupy the earlier portion of the present work2 and will necessarily be somewhat long1 and perhaps1 in many parts1 abstruse and uninviting4 ,the risk of such an inconvenience is inevitable2 for the inquiry brings before us many of the most dark and entangled questions in which men have at any time busied themselves4 ,and even if these can now be made clearer and plainer than of yore1 still they can be made so only by means of mental discipline and mental effort4 ,moreover this analysis of scientific truth into its elements contains much1 both in its principles and in its results1 different from the doctrines most generally prevalent among us in recent times3 but on that very account this analysis is an essential part of the doctrines which ,i have now to lay before the reader3 and ,i must therefore crave his indulgence towards any portion of it which may appear to him obscure or repulsive4 #ad ,there is another circumstance which may tend to make the present work less pleasing than others on the same subject1 in the nature of the examples of human knowledge to which ,i confine myself2 all my instances being1 as ,i have said1 taken from the material sciences4 ,for the truths belonging to these sciences are1 for the most part1 neither so familiar nor so interesting to the bulk of readers as those doctrines which belong to some other subjects4 ,every general proposition concerning politics or morals at once stirs up an interest in men's bosoms1 which makes them listen with curiosity to the attempts to trace it to its origin and foundation4 ,every rule of art or language brings before the mind of cultivated men subjects of familiar and agreeable thought1 and is dwelt upon with pleasure for its own sake1 as well as on account of the philosophical lessons which it may convey4 ,but the curiosity which regards the truths of physics or chemistry1 or even of physiology or astronomy1 is of a more limited and less animated kind4 ,hence1 in the mode of inquiry which ,i have prescribed to myself1 the examples which ,i have to adduce will not amuse and relieve the reader's mind as much as they might do1 if ,i could allow myself to collect them from the whole field of human knowledge4 ,they will have in them nothing to engage his fancy1 or to warm his heart4 ,i am compelled to detain the listener in the chilly air of the external world1 in order that we may have the advantage of full daylight4 ,but although ,i cannot avoid this inconvenience1 so far as it is one1 ,i hope it will be recollected how great are the advantages which we obtain by this restriction4 ,we are thus enabled to draw all our conclusions from doctrines which are universally allowed to be eminently certain1 clear1 and definite4 ,the portions of knowledge to which ,i refer are well known1 and well established among men4 ,their names are familiar1 their assertions uncontested4 ,astronomy and ,geology1 ,mechanics and ,chemistry1 ,optics and ,acoustics1 ,botany and ,physiology1 are each recognized as large and substantial collections of undoubted truths4 ,men are #ae wont to dwell with pride and triumph on the acquisitions of knowledge which have been made in each of these provinces2 and to speak with confidence of the certainty of their results4 ,and all can easily learn in what repositories these treasures of human knowledge are to be found4 ,when1 therefore1 we begin our inquiry from such examples1 we proceed upon a solid foundation4 ,with such a clear ground of confidence1 we shall not be met with general assertions of the vagueness and uncertainty of human knowledge2 with the question1 ,what truth is1 and ,how we are to recognize it2 with complaints concerning the hopelessness and unprofitableness of such researches4 ,we have1 at least1 a definite problem before us4 ,we have to examine the structure and scheme1 not of a shapeless mass of incoherent materials1 of which we doubt whether it be a ruin or a natural wilderness1 but of a fair and lofty palace1 still erect and tenanted1 where hundreds of different apartments belong to a common plan1 where every generation adds something to the extent and magnificence of the pile4 ,the certainty and the constant progress of science are things so unquestioned1 that we are at least engaged in an intelligible inquiry1 when we are examining the grounds and nature of that certainty1 the causes and laws of that progress4 ,to this inquiry1 then1 we now proceed4 ,and in entering upon this task1 however our plan or our principles may differ from those of the eminent philosophers who have endeavoured1 in our own or in former times1 to illustrate or enforce the philosophy of science1 we most willingly acknowledge them as in many things our leaders and teachers4 ,each reform must involve its own peculiar principles1 and the result of our attempts1 so far as they lead to a result1 must be1 in some respects1 different from those of former works4 ,but we may still share with the great writers who have treated this subject before us1 their spirit of hope and trust1 their reverence for the dignity of the subject1 their belief in the vast powers and boundless destiny of man4 ,and we may once more venture to use the #af words of hopeful exhortation1 with which the greatest of those who have trodden this path encouraged himself and his followers when he set out upon his way4 ',concerning ourselves we speak not2 but as touching the matter which we have in hand1 this we ask2--that men deem it not to be the setting up an ,opinion1 but the performing of a ,work3 and that they receive this as a certainty2 that we are not laying the foundations of any sect or doctrine1 but of the profit and dignity of mankind4 ,furthermore1 that being well disposed to what shall advantage themselves1 and putting off factions and prejudices1 they take common counsel with us1 to the end that being by these our aids and appliances freed and defended from wanderings and impediments1 they may lend their hands also to the labours which remain to be performed3 and yet further1 that they be of good hope2 neither imagine to themselves this our ,reform as something of infinite dimension1 and beyond the grasp of mortal man1 when in truth it is the end and true limit of infinite errour2 and is by no means unmindful of the condition of mortality and humanity1 not confiding that such a thing can be carried to its perfect close in the space of one single age1 but assigning it as a task to a succession of generations4' ,the ,philosophy of the ,inductive ,sciences1 according to our view1 must be founded upon the ,history of such ,sciences2 which history we have attempted in a former work4 ,the events of that history may be described generally as the rise of ,theories out of ,facts4 ,but besides this1 which we may term the external history of ,theories1 there is an internal history of ,theories1 namely1 the series of steps by which the human mind becomes capable of forming each ,theory4 ,hence to complete the ,history of the ,sciences as derived from ,facts1 we require a history of the ,ideas by which such derivation has been made possible3 and thus1 the ,first ,part of our ,philosophy must be a ,history of ,scientific ,ideas2--a labour no less historical than our former work1 and concerned with the same events2 but which has been purposely kept separate during the #ag composition1 in order that it might be afterwards presented in a more systematic form1 which ,i have here attempted to do4 ,scientific ,ideas are the ,conditions of the derivation of ,sciences from ,facts3 but can any method or methods be given by which such a ,derivation can be ensured1 or at least1 aided8 ,many such methods have been proposed2 of which the most celebrated is the ,novum ,organon of ,bacon1 of which the title was intended to imply that its scope goes much beyond the ,organon of ,aristotle4 ,with the experience of the formation of ,science which the world has had since ,bacon's time1 it does not appear presumptuous to suppose that we can now improve or correct his methods2 nor to term such an attempt ,novum ,organon ,renovatum4 ,the ,philosophy of the ,inductive ,sciences1 then1 contains these two parts1 ,the ,history of ,scientific ,ideas1 and the ,novum ,organon ,renovatum4 #ai ,,the ,,philosophy ,,of ,,the ,,inductive ,,sciences4 ,,part ,i4 ,,history ,,of ,,scientific ,,ideas4 ,we have just spoken of ,theories and ,facts1 of ,ideas and ,facts1 and of ,inductive ,sciences1 which imply the opposition of ,induction and ,deduction4 ,the explanation of these antitheses must be the starting point of our ,philosophy4 ,knowledge grows1 and through the ages one increasing purpose runs1 ,and the thoughts of men are widen'd with the process of the ,suns4 ,,book ,i4 ,,of ,,ideas ,,in ,,general4 ,qu adhuc inventa sunt in ,scientiis1 ea hujusmodi sunt ut ,notionibus ,vulgaribus fere subjaceant3 ut vero ad interiora et remotiora ,natur penetretur1 necesse est ut tam ,,notiones quam ,,axiomata magis cert et munit vi a particularibus abstrahantur2 atque omnino melior et certior intellects adoperatio in usum veniat4 ,,bacon1 ,nov4 ,org41 ,lib4 #a4 ,aphor4 xviii4 #bc ,,book ,i4 ,,of ,,ideas ,,in ,,general4 ,,chapter ,i4 ,,of ,,the ,,fundamental ,,antithesis ,,of ,,philosophy4 ,sect4 #a4--,thoughts and ,things4 ,,in order that we may do something towards determining the nature and conditions of human knowledge1 7which ,i have already stated as the purpose of this work17 ,i shall have to refer to an antithesis or opposition1 which is familiar and generally recognized1 and in which the distinction of the things opposed to each other is commonly considered very clear and plain4 ,i shall have to attempt to make this opposition sharper and stronger than it is usually conceived1 and yet to shew that the distinction is far from being so clear and definite as it is usually assumed to be3 ,i shall have to point the contrast1 yet shew that the things which are contrasted cannot be separated3--,i must explain that the antithesis is constant and essential1 but yet that there is no fixed and permanent line dividing its members4 ,i may thus appear1 in different parts of my discussion1 to be proceeding in opposite directions1 but ,i hope that the reader who gives me a patient attention will see that both steps lead to the point of view to which ,i wish to lead him4 ,the antithesis or opposition of which ,i speak is denoted1 with various modifications1 by various pairs of terms3 ,i shall endeavour to shew the connexion of these different modes of expression1 and ,i will begin with that form which is the simplest and most idiomatic4 #bd ,the simplest and most idiomatic expression of the antithesis to which ,i refer is that in which we oppose to each other ,,things and ,,thoughts4 ,the opposition is familiar and plain4 ,our thoughts are something which belongs to ourselves2 something which takes place within us2 they are what we think2 they are actions of our minds4 ,things1 on the contrary1 are something different from ourselves and independent of us2 something which is without us2 they are2 we see them1 touch them1 and thus know that they exist2 but we do not make them by seeing or touching them1 as we make our ,thoughts by thinking them2 we are passive1 and ,things act upon our organs of perception4 ,now what ,i wish especially to remark is this3 that in all human ,,knowledge both ,thoughts and ,things are concerned4 ,in every part of my knowledge there must be some thing about which ,i know1 and an internal act of me who know4 ,thus1 to take simple yet definite parts of our knowledge1 if ,i know that a solar year consists of #cfe days1 or a lunar month of #cj days1 ,i know something about the sun or the moon2 namely1 that those objects perform certain revolutions and go through certain changes1 in those numbers of days2 but ,i count such numbers and conceive such revolutions and changes by acts of my own thoughts4 ,and both these elements of my knowledge are indispensable4 ,if there were not such external ,things as the sun and the moon ,i could not have any knowledge of the progress of time as marked by them4 ,and however regular were the motions of the sun and moon1 if ,i could not count their appearances and combine their changes into a cycle1 or if ,i could not understand this when done by other men1 ,i could not know anything about a year or a month4 ,in the former case ,i might be conceived as a human being1 possessing the human powers of thinking and reckoning1 but kept in a dark world with nothing to mark the progress of existence4 ,the latter is the case of brute animals1 which see the sun and moon1 but do not know how many days make a month or a year1 because they have not human powers of thinking and reckoning4 #be ,the two elements which are essential to our knowledge in the above cases1 are necessary to human knowledge in all cases4 ,in all cases1 ,knowledge implies a combination of ,thoughts and ,things4 ,without this combination1 it would not be ,knowledge4 ,without ,thoughts1 there could be no connexion2 without ,things1 there could be no reality4 ,thoughts and ,things are so intimately combined in our ,knowledge1 that we do not look upon them as distinct4 ,one single act of the mind involves them both2 and their contrast disappears in their union4 ,but though ,knowledge requires the union of these two elements1 ,philosophy requires the separation of them1 in order that the nature and structure of ,knowledge may be seen4 ,therefore ,i begin by considering this separation4 ,and ,i now proceed to speak of another way of looking at the antithesis of which ,i have spoken2 and which ,i may1 for the reasons which ,i have just mentioned1 call the ,,fundamental ,,antithesis ,,of ,,philosophy4 ,sect4 #b4--,necessary and ,experiential ,truths4 ,,most persons are familiar with the distinction of necessary and contingent truths4 ,the former kind are ,truths which cannot but be true2 as that #ai and #aa make #cj2--that parallelograms upon the same base and between the same parallels are equal2--that all the angles in the same segment of a circle are equal4 ,the latter are ,truths which it happens 7contingit7 are true2 but which1 for anything which we can see1 might have been otherwise2 as that a lunar month contains #cj days1 or that the stars revolve in circles round the pole4 ,the latter kind of ,truths are learnt by experience1 and hence we may call them ,truths of ,experience1 or1 for the sake of convenience1 ,experiential ,truths1 in contrast with ,necessary ,truths4 ,geometrical propositions are the most manifest examples of ,necessary ,truths4 ,all persons who have read and understood the elements of geometry1 know that the propositions above stated 7that parallelograms #bf upon the same base and between the same parallels are equal2 that all the angles in the same segment of a circle are equal17 are necessarily true2 not only they are true1 but they must be true4 ,the meaning of the terms being understood1 and the proof being gone through1 the truth of the propositions must be assented to4 ,we learn these propositions to be true by demonstrations deduced from definitions and axioms2 and when we have thus learnt them1 we see that they could not be otherwise4 ,in the same manner1 the truths which concern numbers are necessary truths3 #ai and #aa not only do make #cj1 but must make that number1 and cannot make anything else4 ,in the same manner1 it is a necessary truth that half the sum of two numbers added to half their difference is equal to the greater number4 ,it is easy to find examples of ,experiential ,truths2-- propositions which we know to be true1 but know by experience only4 ,we know1 in this way1 that salt will dissolve in water2 that plants cannot live without light2-- in short1 we know in this way all that we do know in chemistry1 physiology1 and the material sciences in general4 ,i take the ,sciences as my examples of human knowledge1 rather than the common truths of daily life1 or moral or political truths2 because1 though the latter are more generally interesting1 the former are much more definite and certain1 and therefore better starting-points for our speculations1 as ,i have already said4 ,and we may take elementary astronomical truths as the most familiar examples of ,experiential ,truths in the domain of science4 ,with these examples1 the distinction of ,necessary and ,experiential ,truths is1 ,i hope1 clear4 ,the former kind1 we see to be true by thinking about them1 and see that they could not be otherwise4 ,the latter kind1 men could never have discovered to be true without looking at them2 and having so discovered them1 still no one will pretend to say they might not have been otherwise4 ,for aught we can see1 the astronomical truths which express the motions and periods of the sun1 moon and stars1 might have been otherwise4 ,if we had been placed in another part of the solar system1 our #bg experiential truths respecting days1 years1 and the motions of the heavenly bodies1 would have been other than they are1 as we know from astronomy itself4 ,it is evident that this distinction of ,necessary and ,experiential ,truths involves the same antithesis which we have already considered2--the antithesis of ,thoughts and ,things4 ,necessary ,truths are derived from our own ,thoughts3 ,experiential truths are derived from our observation of ,things about us4 ,the opposition of ,necessary and ,experiential ,truths is another aspect of the ,fundamental ,antithesis of ,philosophy4 ,sect4 #c4--;,deduction and ,induction4 ,i ,,have already stated that geometrical truths are established by demonstrations deduced from definitions and axioms4 ,the term ,deduction is specially applied to such a course of demonstration of truths from definitions and axioms4 ,in the case of the parallelograms upon the same base and between the same parallels1 we prove certain triangles to be equal1 by supposing them placed so that their two bases have the same extremities2 and hence1 referring to an ,axiom respecting straight lines1 we infer that the bases coincide4 ,we combine these equal triangles with other equal spaces1 and in this way make up both the one and the other of the parallelograms1 in such a manner as to shew that they are equal4 ,in this manner1 going on step by step1 deducing the equality of the triangles from the axiom1 and the equality of the parallelograms from that of the triangles1 we travel to the conclusion4 ,and this process of successive deduction is the scheme of all geometrical proof4 ,we begin with ,definitions of the notions which we reason about1 and with ,axioms1 or self-evident truths1 respecting these notions2 and we get1 by reasoning from these1 other truths which are demonstratively evident2 and from these truths again1 others of the same kind1 and so on4 ,we begin with our own ,thoughts1 which supply us with ,axioms to start from2 and we reason from these1 till we come to propositions #bh which are applicable to the ,things about us2 as for instance1 the propositions respecting circles and spheres applicable to the motions of the heavenly bodies4 ,this is ,deduction1 or ,deductive ,reasoning4 ,experiential truths are acquired in a very different way4 ,in order to obtain such truths1 we begin with ,things4 ,in order to learn how many days there are in a year1 or in a lunar month1 we must begin by observing the sun and the moon4 ,we must observe their changes day by day1 and try to make the cycle of change fit into some notion of number which we supply from our own ,thoughts4 ,we shall find that a cycle of #cj days nearly will fit the changes of phase of the moon2--that a cycle of #cfe days nearly will fit the changes of daily motion of the sun4 ,or1 to go on to experiential truths of which the discovery comes within the limits of the history of science--we shall find 7as ,hipparchus found7 that the unequal motion of the sun among the stars1 such as observation shews it to be1 may be fitly represented by the notion of an eccentric2--a circle in which the sun has an equable annual motion1 the spectator not being in the center of the circle4 ,again1 in the same manner1 at a later period1 ,kepler started from more exact observations of the sun1 and compared them with a supposed motion in a certain ellipse2 and was able to shew that1 not a circle about an eccentric point1 but an ellipse1 supplied the mode of conception which truly agreed with the motion of the sun about the earth2 or rather1 as ,copernicus had already shewn1 of the earth about the sun4 ,in such cases1 in which truths are obtained by beginning from observation of external things and by finding some notion with which the ,things1 as observed1 agree1 the truths are said to be obtained by ,induction4 ,the process is an ,inductive ,process4 ,the contrast of the ,deductive and ,inductive process is obvious4 ,in the former1 we proceed at each step from general truths to particular applications of them2 in the latter1 from particular observations to a general truth which includes them4 ,in the former case we may be said to reason downwards1 in the latter case1 #bi upwards2 for general notions are conceived as standing above particulars4 ,necessary truths are proved1 like arithmetical sums1 by adding together the portions of which they consist4 ,an inductive truth is proved1 like the guess which answers a riddle1 by its agreeing with the facts described4 ,demonstration is irresistible in its effect on the belief1 but does not produce surprize1 because all the steps to the conclusion are exhibited1 before we arrive at the conclusion4 ,inductive inference is not demonstrative1 but it is often more striking than demonstrative reasoning1 because the intermediate links between the particulars and the inference are not shewn4 ,deductive truths are the results of relations among our own ,thoughts4 ,inductive truths are relations which we discern among existing ,things2 and thus1 this opposition of ,deduction and ,induction is again an aspect of the ,fundamental ,antithesis already spoken of4 ,sect4 #d4--,theories and ,facts4 ,,general experiential ,truths1 such as we have just spoken of1 are called ,theories1 and the particular observations from which they are collected1 and which they include and explain1 are called ,facts4 ,thus ,hipparchus's doctrine1 that the sun moves in an eccentric about the earth1 is his ,theory of the ,sun1 or the ,eccentric ,theory4 ,the doctrine of ,kepler1 that the ,earth moves in an ,ellipse about the ,sun1 is ,kepler's ,theory of the ,earth1 the ,elliptical ,theory4 ,newton's doctrine that this elliptical motion of the ,earth about the ,sun is produced and governed by the ,sun's attraction upon the ,earth1 is the ,newtonian theory1 the ,theory of ,attraction4 ,each of these ,theories was accepted1 because it included1 connected and explained the ,facts2 the ,facts being1 in the two former cases1 the motions of the ,sun as observed2 and in the other case1 the elliptical motion of the ,earth as known by ,kepler's ,theory4 ,this antithesis of ,theory and ,fact is included in what has just been said of ,inductive ,propositions4 ,a ,theory is an ,inductive ,proposition1 and the ,facts #cj are the particular observations from which1 as ,i have said1 such ,propositions are inferred by ,induction4 ,the ,antithesis of ,theory and ,fact implies the fundamental ,antithesis of ,thoughts and ,things2 for a ,theory 7that is1 a true ,theory7 may be described as a ,thought which is contemplated distinct from ,things and seen to agree with them2 while a ,fact is a combination of our ,thoughts with ,things in so complete agreement that we do not regard them as separate4 ,thus the antithesis of ,theory and ,fact involves the antithesis of ,thoughts and ,things1 but is not identical with it4 ,facts involve ,thoughts1 for we know ,facts only by thinking about them4 ,the ,fact that the year consists of #cfe days2 the ,fact that the month consists of #cj days1 cannot be known to us1 except we have the ,thoughts of ,time1 ,number and ,recurrence4 ,but these ,thoughts are so familiar1 that we have the fact in our mind as a simple ,thing without attending to the ,thought which it involves4 ,when we mould our ,thoughts into a ,theory1 we consider the thought as distinct from the ,facts2 but yet1 though distinct1 not independent of them2 for it is a true ,theory1 only by including and agreeing with the ,facts4 ,sect4 #e4--;,ideas and ,sensations4 ,,we have just seen that the antithesis of ,theory and ,fact1 although it involves the antithesis of ,thoughts and ,things1 is not identical with it4 ,there are other modes of expression also1 which involve the same ,fundamental ,antithesis1 more or less modified4 ,of these1 the pair of words which in their relations appear to separate the members of the antithesis most distinctly are ,ideas and ,sensations4 ,we see and hear and touch external things1 and thus perceive them by our senses2 but in perceiving them1 we connect the impressions of sense according to relations of space1 time1 number1 likeness1 cause1 c4 ,now some at least of these kinds of connexion1 as space1 time1 number1 may be contemplated distinct from the things to which they are applied2 and so contemplated1 ,i term them ,ideas4 ,and #ca the other element1 the impressions upon our senses which they connect1 are called ,sensations4 ,i term space1 time1 cause1 c41 ,ideas1 because they are general relations among our sensations1 apprehended by an act of the mind1 not by the senses simply4 ,these relations involve something beyond what the senses alone could furnish4 ,by the sense of sight we see various shades and colours and shapes before us1 but the outlines by which they are separated into distinct objects of definite forms1 are the work of the mind itself4 ,and again1 when we conceive visible things1 not only as surfaces of a certain form1 but as solid bodies1 placed at various distances in space1 we again exert an act of the mind upon them4 ,when we see a body move1 we see it move in a path or orbit1 but this orbit is not itself seen2 it is constructed by the mind4 ,in like manner when we see the motions of a needle towards a magnet1 we do not see the attraction or force which produces the effects2 but we infer the force1 by having in our minds the ,idea of ,cause4 ,such acts of thought1 such ,ideas1 enter into our perceptions of external things4 ,but though our perceptions of external things involve some act of the mind1 they must involve something else besides an act of the mind4 ,if we must exercise an act of thought in order to see force exerted1 or orbits described by bodies in motion1 or even in order to see bodies existing in space1 and to distinguish one kind of object from another1 still the act of thought alone does not make the ,bodies4 ,there must be something besides1 on which the thought is exerted4 ,a colour1 a form1 a sound1 are not produced by the mind1 however they may be moulded1 combined1 and interpreted by our mental acts4 ,a philosophical poet has spoken of ,all the world ,of eye and ear1 both what they half create1 ,and what perceive4 ,but it is clear1 that though they half create1 they do not wholly create3 there must be an external world of colour and sound to give impressions to the eye and ear1 as well as internal powers by which we perceive #cb what is offered to our organs4 ,the mind is in some way passive as well as active3 there are objects without as well as faculties within2--,sensations1 as well as acts of ,thought4 ,indeed this is so far generally acknowledged1 that according to common apprehension1 the mind is passive rather than active in acquiring the knowledge which it receives concerning the material world4 ,its sensations are generally considered more distinct than its operations4 ,the world without is held to be more clearly real than the faculties within4 ,that there is something different from ourselves1 something external to us1 something independent of us1 something which no act of our minds can make or can destroy1 is held by all men to be at least as evident1 as that our minds can exert any effectual process in modifying and appreciating the impressions made upon them4 ,most persons are more likely to doubt whether the mind be always actively applying ,ideas to the objects which it perceives1 than whether it perceive them passively by means of ,sensations4 ,but yet a little consideration will show us that an activity of the mind1 and an activity according to certain ,ideas1 is requisite in all our knowledge of external objects4 ,we see objects1 of various solid forms1 and at various distances from us4 ,but we do not thus perceive them by sensation alone4 ,our visual impressions cannot1 of themselves1 convey to us a knowledge of solid form1 or of distance from us4 ,such knowledge is inferred from what we see3--inferred by conceiving the objects as existing in space1 and by applying to them the ,idea of ,space4 ,again3--day after day passes1 till they make up a year3 but we do not know that the days are #cfe1 except we count them2 and thus apply to them our ,idea of ,number4 ,again3--we see a needle drawn to a magnet3 but1 in truth1 the drawing is what we cannot see4 ,we see the needle move1 and infer the attraction1 by applying to the fact our ,idea of ,force1 as the cause of motion4 ,again3--we see two trees of different kinds2 but we cannot know that they are so1 except by applying to them our ,idea of the resemblance #cc and difference which makes kinds4 ,and thus ,ideas1 as well as ,sensations1 necessarily enter into all our knowledge of objects3 and these two words express1 perhaps more exactly than any of the pairs before mentioned1 that ,fundamental ,antithesis1 in the union of which1 as ,i have said1 all knowledge consists4 ,sect4 #f4--,reflexion and ,sensation4 ,,it will hereafter be my business to show what the ,ideas are1 which thus enter into our knowledge2 and how each ,idea has been1 as a matter of historical fact1 introduced into the ,science to which it especially belongs4 ,but before ,i proceed to do this1 ,i will notice some other terms1 besides the phrases already noticed1 which have a reference1 more or less direct1 to the ,fundamental ,antithesis of ,ideas and ,sensations4 ,i will mention some of these1 in order that if they should come under the reader's notice1 he may not be perplexed as to their bearing upon the view here presented to him4 ,the celebrated doctrine of ,locke1 that all our ',ideas1' 7that is1 in his use of the word1 all our objects of thinking17 come from ,sensation or ,reflexion1 will naturally occur to the reader as connected with the antithesis of which ,i have been speaking4 ,but there is a great difference between ,locke's account of ,sensation and ,reflexion1 and our view of ,sensation and ,ideas4 ,he is speaking of the origin of our knowledge2--we1 of its nature and composition4 ,he is content to say that all the knowledge which we do not receive directly by ,sensation1 we obtain by ,reflex ,acts of the mind1 which make up his ,reflexion4 ,but we hold that there is no ,sensation without an act of the mind1 and that the mind's activity is not only reflexly exerted upon itself1 but directly upon objects1 so as to perceive in them connexions and relations which are not ,sensations4 ,he is content to put together1 under the name of ,reflexion1 everything in our knowledge which is not ,sensation3 we are to attempt to analyze all that is not ,sensation2 not only to say it consists of ,ideas1 but #cd to point out what those ,ideas are1 and to show the mode in which each of them enters into our knowledge4 ,his purpose was1 to prove that there are no ,ideas1 except the reflex acts of the mind3 our endeavour will be to show that the acts of the mind1 both direct and reflex1 are governed by certain ,laws1 which may be conveniently termed ,ideas4 ,his procedure was1 to deny that any knowledge could be derived from the mind alone3 our course will be1 to show that in every part of our most certain and exact knowledge1 those who have added to our knowledge in every age have referred to principles which the mind itself supplies4 ,i do not say that my view is contrary to his3 but it is altogether different from his4 ,if ,i grant that all our knowledge comes from ,sensation and ,reflexion1 still my task then is only begun2 for ,i want further to determine1 in each science1 what portion comes1 not from mere ,sensation1 but from those ,ideas by the aid of which either ,sensation or ,reflexion can lead to ,science4 ,locke's use of the word 'idea' is1 as the reader will perceive1 different from ours4 ,he uses the word1 as he says1 which 'serves best to stand for whatsoever is the object of the understanding when a man thinks4' ',i have used it1' he adds1 'to express whatever is meant by phantasm1 notion1 species1 or whatever it is to which the mind can be employed about in thinking4' ,it might be shown that this separation of the mind itself from the ideal objects about which it is employed in thinking1 may lead to very erroneous results4 ,but it may suffice to observe that we use the word ,ideas1 in the manner already explained1 to express that element1 supplied by the mind itself1 which must be combined with ,sensation in order to produce knowledge4 ,for us1 ,ideas are not ,objects of ,thought1 but rather ,laws of ,thought4 ,ideas are not synonymous with ,notions2 they are ,principles which give to our ,notions whatever they contain of truth4 ,but our use of the term ,idea will be more fully explained hereafter4 #ce ,sect4 #g4--,subjective and ,objective4 ,,the ,fundamental ,antithesis of ,philosophy of which ,i have to speak has been brought into great prominence in the writings of modern ,german philosophers1 and has conspicuously formed the basis of their systems4 ,they have indicated this antithesis by the terms subjective and objective4 ,according to the technical language of old writers1 a thing and its qualities are described as subject and attributes2 and thus a man's faculties and acts are attributes of which he is the subject4 ,the mind is the subject in which ideas inhere4 ,moreover1 the man's faculties and acts are employed upon external objects2 and from objects all his sensations arise4 ,hence the part of a man's knowledge which belongs to his own mind1 is subjective3 that which flows in upon him from the world external to him1 is objective4 ,and as in man's contemplation of nature1 there is always some act of thought which depends upon himself1 and some matter of thought which is independent of him1 there is1 in every part of his knowledge1 a subjective and an objective element4 ,the combination of the two elements1 the subjective or ideal1 and the objective or observed1 is necessary1 in order to give us any insight into the laws of nature4 ,but different persons1 according to their mental habits and constitution1 may be inclined to dwell by preference upon the one or the other of these two elements4 ,it may perhaps interest the reader to see this difference of intellectual character illustrated in two eminent men of genius of modern times1 ,gthe and ,schiller4 ,gthe himself gives us the account to which ,i refer1 in his history of the progress of his speculations concerning the ,metamorphosis of ,plants2 a mode of viewing their structure by which he explained1 in a very striking and beautiful manner1 the relations of the different parts of a plant to each other2 as has been narrated in the ,history of the ,inductive ,sciences4 ,gthe felt a delight in the passive contemplation of nature1 unmingled with the desire of reasoning and theorizing2 a delight such as naturally belongs to those poets who #cf merely embody the images which a fertile genius suggests1 and do not mix with these pictures1 judgments and reflexions of their own4 ,schiller1 on the other hand1 both by his own strong feeling of the value of a moral purpose in poetry1 and by his adoption of a system of metaphysics in which the subjective element was made very prominent1 was well disposed to recognize fully the authority of ideas over external impressions4 ,gthe for a time felt a degree of estrangement towards ,schiller1 arising from this contrariety in their views and characters4 ,but on one occasion they fell into discussion on the study of natural history2 and ,gthe endeavoured to impress upon his companion his persuasion that nature was to be considered1 not as composed of detached and incoherent parts1 but as active and alive1 and unfolding herself in each portion1 in virtue of principles which pervade the whole4 ,schiller objected that no such view of the objects of natural history had been pointed out by observation1 the only guide which the natural historians recommended2 and was disposed on this account to think the whole of their study narrow and shallow4 ',upon this1' says ,gthe1 ',i expounded to him1 in as lively a way as ,i could1 the metamorphosis of plants1 drawing on paper for him1 as ,i proceeded1 a diagram to represent that general form of a plant which shows itself in so many and so various transformations4 ,schiller attended and understood2 and1 accepting the explanation1 he said1 ,this is not observation1 but an idea4 ,i replied1' adds ,gthe1 'with some degree of irritation2 for the point which separated us was most luminously marked by this expression3 but ,i smothered my vexation1 and merely said1 ,i was happy to find that ,i had got ideas without knowing it2 nay1 that ,i saw them before my eyes4' ,gthe then goes on to say1 that he had been grieved to the very soul by maxims promulgated by ,schiller1 that no observed fact ever could correspond with an idea4 ,since he himself loved best to wander in the domain of external observation1 he had been led to look with repugnance and hostility upon anything which professed to depend upon ideas4 ',yet1' he #cg observes1 'it occurred to me that if my ,observation was identical with his ,idea1 there must be some common ground on which we might meet4' ,they went on with their mutual explanations1 and became intimate and lasting friends4 ',and thus1' adds the poet1 by means of that mighty and interminable controversy between object and subject1 we two concluded an alliance which remained unbroken1 and produced much benefit to ourselves and others4' ,the general diagram of a plant1 of which ,gthe here speaks1 must have been a combination of lines and marks expressing the relations of position and equivalence among the elements of vegetable forms1 by which so many of their resemblances and differences may be explained4 ,such a symbol is not an ,idea in that general sense in which we propose to use the term1 but is a particular modification of the general ,ideas of symmetry1 developement1 and the like2 and we shall hereafter see1 according to the phraseology which we shall explain in the next chapter1 how such a diagram might express the ideal conception of a plant4 ,the antithesis of subjective and objective is very familiar in the philosophical literature of ,germany and ,france2 nor is it uncommon in any age of our own literature4 ,but though efforts have recently been made to give currency among us to this phraseology1 it has not been cordially received1 and has been much complained of as not of obvious meaning4 ,nor is the complaint without ground3 for when we regard the mind as the subject in which ideas inhere1 it becomes for us an object1 and the antithesis vanishes4 ,we are not so much accustomed to use subject in this sense1 as to make it a proper contrast to object4 ,the combination 'ideal and objective1' would more readily convey to a modern reader the opposition which is intended between the ideas of the mind itself1 and the objects which it contemplates around it4 ,to the antitheses already noticed--,thoughts and ,things2 ,necessary and ,experiential ,truths2 ,deduction and ,induction2 ,theory and ,fact2 ,ideas and ,sensations2 ,reflexion and ,sensation2 ,subjective and #ch ,objective2 we may add others1 by which distinctions depending more or less upon the fundamental antithesis have been denoted4 ,thus we speak of the internal and external sources of our knowledge2 of the world within and the world without us2 of ,man and ,nature4 ,some of the more recent metaphysical writers of ,germany have divided the universe into the ,me and ,not-me 7,ich and ,nicht-ich74 ,upon such phraseology we may observe1 that to have the fundamental antithesis of which we speak really understood1 is of the highest consequence to philosophy1 but that little appears to be gained by expressing it in any novel manner4 ,the most weighty part of the philosopher's task is to analyze the operations of the mind2 and in this task1 it can aid us but little to call it1 instead of the mind1 the subject1 or the me4 ,sect4 #h4--,matter and ,form4 ,,there are some other ways of expressing1 or rather of illustrating1 the fundamental antithesis1 which ,i may briefly notice4 ,the antithesis has been at different times presented by means of various images4 ,one of the most ancient of these1 and one which is still very instructive1 is that which speaks of ,sensations as the ,matter1 and ,ideas as the ,form1 of our knowledge2 just as ivory is the matter1 and a cube the form1 of a die4 ,this comparison has the advantage of showing that two elements of an antithesis which cannot be separated in fact1 may yet be advantageously separated in our reasonings4 ,for ,matter and ,form cannot by any means be detached from each other4 ,all matter must have some form2 all form must be the form of some material thing4 ,if the ivory be not a cube1 it must have a spherical or some other form4 ,and the cube1 in order to be a cube1 must be of some material2--if not of ivory1 of wood1 or stone1 for instance1 ,a figure without matter is merely a geometrical conception2--a modification of the idea of space4 ,matter without figure is a mere abstract term2--a supposed union of certain sensible qualities which1 so insulated #ci from others1 cannot exist4 ,yet the distinction of ,matter and ,form is real2 and1 as a subject of contemplation1 clear and plain4 ,nor is the distinction by any means useless4 ,the speculations which treat of the two subjects1 ,matter and ,figure1 are very different4 ,matter is the subject of the sciences of ,mechanics and ,chemistry2 ,figure1 of ,geometry4 ,these two classes of ,sciences have quite different sets of principles4 ,if we refuse to consider the ,matter and the ,form of bodies separately1 because we cannot exhibit ,matter and ,form separately1 we shut the door to all philosophy on such subjects4 ,in like manner1 though ,sensations and ,ideas are necessarily united in all our knowledge1 they can be considered as distinct2 and this distinction is the basis of all philosophy concerning knowledge4 ,this illustration of the relation of ,ideas and ,sensations may enable us to estimate a doctrine which has been put forwards at various times4 ,in a certain school of speculators there has existed a disposition to derive all our ,ideas from our ,sensations1 the term ,idea1 being1 in this school1 used in its wider sense1 so as to include all modifications and limitations of our ,fundamental ,ideas4 ,the doctrines of this school have been summarily expressed by saying that ',every ,idea is a transformed ,sensation4' ,now1 even supposing this assertion to be exactly true1 we easily see1 from what has been said1 how little we are likely to answer the ends of philosophy by putting forward such a maxim as one of primary importance4 ,for we might say1 in like manner1 that every statue is but a transformed block of marble1 or every edifice but a collection of transformed stones4 ,but what would these assertions avail us1 if our object were to trace the rules of art by which beautiful statues were formed1 or great works of architecture erected8 ,the question naturally occurs1 ,what is the nature1 the principle1 the law of this ,transformation8 ,in what faculty resides the transforming power8 ,what train of ideas of beauty1 and symmetry1 and stability1 in the mind of the statuary or the architect1 has produced those great works which #dj mankind look upon as among their most valuable possessions2--the ,apollo of the ,belvidere1 the ,parthenon1 the ,cathedral of ,cologne8 ,when this is what we want to know1 how are we helped by learning that the ,apollo is of ,parian marble1 or the ,cathedral of basaltic stone8 ,we must know much more than this1 in order to acquire any insight into the principles of statuary or of architecture4 ,in like manner1 in order that we may make any progress in the philosophy of knowledge1 which is our purpose1 we must endeavour to learn something further respecting ideas than that they are transformed sensations1 even if they were this4 ,but1 in reality1 the assertion that our ideas are transformed sensations1 is erroneous as well as frivolous4 ,for it conveys1 and is intended to convey1 the opinion that our sensations have one form which properly belongs to them2 and that1 in order to become ideas1 they are converted into some other form4 ,but the truth is1 that our sensations1 of themselves1 without some act of the mind1 such as involves what we have termed an ,idea1 have no form4 ,we cannot see one object without the idea of space2 we cannot see two without the idea of resemblance or difference2 and space and difference are not sensations4 ,thus1 if we are to employ the metaphor of ,matter and ,form1 which is implied in the expression to which ,i have referred1 our sensations1 from their first reception1 have their ,form not changed1 but given by our ,ideas4 ,without the relations of thought which we here term ,ideas1 the sensations are matter without form4 ,matter without form cannot exist3 and in like manner sensations cannot become perceptions of objects1 without some formative power of the mind4 ,by the very act of being received as perceptions1 they have a formative power exercised upon them1 the operation of which might be expressed1 by speaking of them1 not as transformed1 but simply as formed2--as invested with form1 instead of being the mere formless material of perception4 ,the word inform1 according to its ,latin etymology1 at first implied this process by which matter is #da invested with form4 ,thus ,virgil#aa speaks of the thunderbolt as informed by the hands of ,brontes1 and ,steropes1 and ,pyracmon4 ,and ,dryden introduces the word in another place3-- ,let others better mould the running mass ,of metals1 or inform the breathing brass4 ,even in this use of the word1 the form is something superior to the brute manner1 and gives it a new significance and purpose4 ,and hence the term is again used to denote the effect produced by an intelligent principle of a still higher kind3-- 4 4 4 4 ,he informed ,this ill-shaped body with a daring soul4 ,and finally even the soul itself1 in its original condition1 is looked upon as matter1 when viewed with reference to education and knowledge1 by which it is afterwards moulded2 and hence these are1 in our language1 termed information4 ,if we confine ourselves to the first of these three uses of the term1 we may correct the erroneous opinion of which we have just been speaking1 and retain the metaphor by which it is expressed1 by saying1 that ideas are not transformed1 but informed sensations4 ,note #aa3 ,ferrum exercebant vasto ,cyclopes in ,antro ,brontesque ,steropesque et nudus membra ,pyracmon2 ,his informatum manibus1 jam parte polita ,fulmen erat4--n4 viii4 #dbd4 ,sect4 #i4--,man the ,interpreter of ,nature4 ,,there is another image by which writers have represented the acts of thought through which knowledge is obtained from the observation of the external world4 ,nature is the ,book1 and ,man is the ,interpreter4 ,the facts of the external world are marks1 in which man discovers a meaning1 and so reads them4 ,man is the ,interpreter of ,nature1 and ,science is the right ,interpretation4 ,and this image also is1 in many respects1 #db instructive4 ,it exhibits to us the necessity of both elements2--the marks which man has to look at1 and the knowledge of the alphabet and language which he must possess and apply before he can find any meaning in what he sees4 ,moreover this image presents to us1 as the ideal element1 an activity of the mind of that very kind which we wish to point out4 ,indeed the illustration is rather an example than a comparison of the composition of our knowledge4 ,the letters and symbols which are presented to the ,interpreter are really objects of sensation3 the notion of letters as signs of words1 the notion of connexions among words by which they have meaning1 really are among our ,ideas2--,signs and ,meaning are ,ideas1 supplied by the mind1 and added to all that sensation can disclose in any collection of visible marks4 ,the ,sciences are not figuratively1 but really1 ,interpretations of ,nature4 ,but this image1 whether taken as example or comparison1 may serve to show both the opposite character of the two elements of knowledge1 and their necessary combination1 in order that there may be knowledge4 ,this illustration may also serve to explain another point in the conditions of human knowledge which we shall have to notice3--namely1 the very different degrees in which1 in different cases1 we are conscious of the mental act by which our sensations are converted into knowledge4 ,for the same difference occurs in reading an inscription4 ,if the inscription were entire and plain1 in a language with which we were familiar1 we should be unconscious of any mental act in reading it4 ,we should seem to collect its meaning by the sight alone4 ,but if we had to decipher an ancient inscription1 of which only imperfect marks remained1 with a few entire letters among them1 we should probably make several suppositions as to the mode of reading it1 before we found any mode which was quite successful2 and thus1 our guesses1 being separate from the observed facts1 and at first not fully in agreement with them1 we should be clearly aware that the conjectured meaning1 on the one hand1 and the observed marks on the other1 were distinct things1 though these #dc two things would become united as elements of one act of knowledge when we had hit upon the right conjecture4 ,sect4 #aj4--,the ,fundamental ,antithesis inseparable4 ,,the illustration just referred to1 as well as other ways of considering the subject1 may help us to get over a difficulty which at first sight appears perplexing4 ,we have spoken of the common opposition of ,theory and ,fact as important1 and as involving what we have called the ,fundamental ,antithesis of ,philosophy4 ,but after all1 it may be asked1 ,is this distinction of ,theory and ,fact really tenable8 ,is it not often difficult to say whether a special part of our knowledge is a ,fact or a ,theory8 ,is it a ,fact or a ,theory that the stars revolve round the pole8 ,is it a ,fact or a ,theory that the earth is a globe revolving on its axis8 ,is it a ,fact or a ,theory that the earth travels in an ellipse round the sun8 ,is it a ,fact or a ,theory that the sun attracts the earth8 ,is it a ,fact or a ,theory that the loadstone attracts the needle8 ,in all these cases1 probably some persons would answer one way1 and some persons the other4 ,there are many persons by whom the doctrine of the globular form of the earth1 the doctrine of the earth's elliptical orbit1 the doctrine of the sun's attraction on the earth1 would be called theories1 even if they allowed them to be true theories4 ,but yet if each of these propositions be true1 is it not a fact8 ,and even with regard to the simpler facts1 as the motion of the stars round the pole1 although this may be a ,fact to one who has watched and measured the motions of the stars1 one who has not done this1 and who has only carelessly looked at these stars from time to time1 may naturally speak of the circles which the astronomer makes them describe as ,theories4 ,it would seem1 then1 that we cannot in such cases expect general assent1 if we say1 ,this is a ,fact and not a ,theory1 or ,this is a ,theory and not a ,fact4 ,and the same is true in a vast range of cases4 ,it would seem1 therefore1 that we cannot rest any reasoning upon this distinction of ,theory #dd and ,fact2 and we cannot avoid asking whether there is any real distinction in this antithesis1 and if so1 what it is4 ,to this ,i reply3 the distinction between ,theory 7that is1 true ,theory7 and ,fact1 is this3 that in ,theory the ,ideas are considered as distinct from the ,facts3 in ,facts1 though ,ideas may be involved1 they are not1 in our apprehension1 separated from the sensations4 ,in a ,fact1 the ,ideas are applied so readily and familiarly1 and incorporated with the sensations so entirely1 that we do not see them1 we see through them4 ,a person who carefully notes the motion of a star all night1 sees the circle which it describes1 as he sees the star1 though the circle is1 really1 a result of his own ,ideas4 ,a person who has in his mind the measures of different lines and countries on the earth's surface1 and who can put them1 together into one conception1 finds that they can make no figure but a globular one3 to him1 the earth's globular form is a ,fact1 as much as the square form of his chamber4 ,a person to whom the grounds of believing the earth to travel round the sun are as familiar as the grounds for believing the movements of the mail-coaches in this country1 looks upon the former event as a ,fact1 just as he looks upon the latter events as ,facts4 ,and a person who1 knowing the ,fact of the earth's annual motion1 refers it distinctly to its mechanical cause1 conceives the sun's attraction as a ,fact1 just as he conceives as a ,fact1 the action of the wind which turns the sails of a mill4 ,he cannot see the force in either case2 he supplies it out of his own ,ideas4 ,and thus1 a true ,theory is a ,fact2 a ,fact is a familiar ,theory4 ,that which is a ,fact under one aspect1 is a ,theory under another4 ,the most recondite ,theories when firmly established are ,facts3 the simplest ,facts involve something of the nature of ,theory4 ,theory and ,fact correspond1 in a certain degree1 with ,ideas and ,sensations1 as to the nature of their opposition4 ,but the ,facts are ,facts1 so far as the ,ideas have been combined with the ,sensations and absorbed in them3 the ,theories are ,theories1 so far as the ,ideas are kept distinct from the ,sensations1 and so far as it is #de considered still a question whether those can be made to agree with these4 ,we may1 as ,i have said1 illustrate this matter by considering man as interpreting the phenomena which he sees4 ,he often interprets without being aware that he does so4 ,thus when we see the needle move towards the magnet1 we assert that the magnet exercises an attractive force on the needle4 ,but it is only by an interpretative act of our own minds that we ascribe this motion to attraction4 ,that1 in this case1 a force is exerted--something of the nature of the pull which we could apply by our own volition--is our interpretation of the phenomena2 although we may be conscious of the act of interpretation1 and may then regard the attraction as a ,fact4 ,nor is it in such cases only that we interpret phenomena in our own way1 without being conscious of what we do4 ,we see a tree at a distance1 and judge it to be a chestnut or a lime2 yet this is only an inference from the colour or form of the mass according to preconceived classifications of our own4 ,our lives are full of such unconscious interpretations4 ,the farmer recognizes a good or a bad soil2 the artist a picture of a favourite master2 the geologist a rock of a known locality1 as we recognize the faces and voices of our friends2 that is1 by judgments formed on what we see and hear2 but judgments in which we do not analyze the steps1 or distinguish the inference from the appearance4 ,and in these mixtures of observation and inference1 we speak of the judgment thus formed1 as a ,fact directly observed4 ,even in the case in which our perceptions appear to be most direct1 and least to involve any interpretations of our own1--in the simple process of seeing1--who does not know how much we1 by an act of the mind1 add to that which our senses receive8 ,does any one fancy that he sees a solid cube8 ,it is easy to show that the solidity of the figure1 the relative position of its faces and edges to each other1 are inferences of the spectator2 no more conveyed to his conviction by the eye alone1 than they would be if he were looking at #df a painted representation of a cube4 ,the scene of nature is a picture without depth of substance1 no less than the scene of art2 and in the one case as in the other1 it is the mind which1 by an act of its own1 discovers that colour and shape denote distance and solidity4 ,most men are unconscious of this perpetual habit of reading the language of the external world1 and translating as they read4 ,the draughtsman1 indeed1 is compelled1 for his purposes1 to return back in thought from the solid bodies which he has inferred1 to the shapes of surface which he really sees4 ,he knows that there is a mask of theory over the whole face of nature1 if it be theory to infer more than we see4 ,but other men1 unaware of this masquerade1 hold it to be a fact that they see cubes and spheres1 spacious apartments and winding avenues4 ,and these things are facts to them1 because they are unconscious of the mental operation by which they have penetrated nature's disguise4 ,and thus1 we still have an intelligible distinction of ,fact and ,theory1 if we consider ,theory as a conscious1 and ,fact as an unconscious inference1 from the phenomena which are presented to our senses4 ,but still1 ,theory and ,fact1 ,inference and ,perception1 ,reasoning and ,observation1 are antitheses in none of which can we separate the two members by any fixed and definite line4 ,even the simplest terms by which the antithesis is expressed cannot be separated4 ,ideas and ,sensations1 ,thoughts and ,things1 ,subject and ,object1 cannot in any case be applied absolutely and exclusively4 ,our ,sensations require ,ideas to bind them together1 namely1 ,ideas of space1 time1 number1 and the like4 ,if not so bound together1 ,sensations do not give us any apprehension of ,things or ,objects4 ,all ,things1 all ,objects1 must exist in space and in time--must be one or many4 ,now space1 time1 number1 are not ,sensations or ,things4 ,they are something different from1 and opposed to ,sensations and ,things4 ,we have termed them ,ideas4 ,it may be said they are ,relations of ,things1 or of ,sensations4 ,but granting this form of expression1 still a ,relation is not a ,thing or a #dg ,sensation2 and therefore we must still have another and opposite element1 along with our ,sensations4 ,and yet1 though we have thus these two elements in every act of perception1 we cannot designate any portion of the act as absolutely and exclusively belonging to one of the elements4 ,perception involves ,sensation1 along with ,ideas of time1 space1 and the like2 or1 if any one prefers the expression1 we may say1 ,perception involves ,sensations along with the apprehension of ,relations4 ,perception is ,sensation1 along with such ,ideas as make ,sensation into an apprehension of ,things or ,objects4 ,and as ,perception of ,objects implies ,ideas1--as ,observation implies ,reasoning2--so1 on the other hand1 ,ideas cannot exist where ,sensation has not been2 ,reasoning cannot go on when there has not been previous ,observation4 ,this is evident from the necessary order of developement of the human faculties4 ,sensation necessarily exists from the first moments of our existence1 and is constantly at work4 ,observation begins before we can suppose the existence of any ,reasoning which is not involved in ,observation4 ,hence1 at whatever period we consider our ,ideas1 we must consider them as having been already engaged in connecting our ,sensations1 and as having been modified by this employment4 ,by being so employed1 our ,ideas are unfolded and defined2 and such developement and definition cannot be separated from the ,ideas themselves4 ,we cannot conceive space1 without boundaries or forms2 now ,forms involve ,sensations4 ,we cannot conceive time1 without events which mark the course of time2 but events involve ,sensations4 ,we cannot conceive number1 without conceiving things which are numbered2 and ,things imply sensations4 ,and the forms1 things1 events1 which are thus implied in our ,ideas1 having been the objects of ,sensation constantly in every part of our life1 have modified1 unfolded1 and fixed our ,ideas1 to an extent which we cannot estimate1 but which we must suppose to be essential to the processes which at present go on in our minds4 ,we cannot say that ,objects create ,ideas2 for to perceive ,objects we must already have ,ideas4 ,but we may #dh say1 that ,objects and the constant ,perception of ,objects have so far modified our ,ideas1 that we cannot1 even in thought1 separate our ,ideas from the perception of ,objects4 ,we cannot say of any ,ideas1 as of the ,idea of space1 or time1 or number1 that they are absolutely and exclusively ,ideas4 ,we cannot conceive what space1 or time1 or number1 would be in our minds1 if we had never perceived any ,thing or ,things in space or time4 ,we cannot conceive ourselves in such a condition as never to have perceived any ,thing or ,things in space or time4 ,but1 on the other hand1 just as little can we conceive ourselves becoming acquainted with space and time or numbers as objects of ,sensation4 ,we cannot reason without having the operations of our minds affected by previous ,sensations2 but we cannot conceive ,reasoning to be merely a series of ,sensations4 ,in order to be used in ,reasoning1 ,sensation must become ,observation2 and1 as we have seen1 ,observation already involves ,reasoning4 ,in order to be connected by our ,ideas1 ,sensations must be ,things or ,objects1 and ,things or ,objects already include ,ideas4 ,and thus1 none of the terms by which the fundamental antithesis is expressed can be absolutely and exclusively applied4 ,i will make a remark suggested by the views which have thus been presented4 ,since1 as we have just seen1 none of the terms which express the fundamental antithesis can be applied absolutely and exclusively1 the absolute application of the antithesis in any particular case can never be a conclusive or immoveable principle4 ,this remark is the more necessary to be borne in mind1 as the terms of this antithesis are often used in a vehement and peremptory manner4 ,thus we are often told that such a thing is a ,fact2 ,a ,,fact and not a ,theory1 with all the emphasis which1 in speaking or writing1 tone or italics or capitals can give4 ,we see from what has been said1 that when this is urged1 before we can estimate the truth1 or the value of the assertion1 we must ask to whom is it a ,fact8 what habits of thought1 what previous information1 what ,ideas does it imply1 to conceive the ,fact as a ,fact8 #di ,does not the apprehension of the ,fact imply assumptions which may with equal justice be called ,theory1 and which are perhaps false ,theory8 in which case1 the ,fact is no ,fact4 ,did not the ancients assert it as a ,fact1 that the earth stood still1 and the stars moved8 and can any ,fact have stronger apparent evidence to justify persons in asserting it emphatically than this had8 ,these remarks are by no means urged in order to show that no ,fact can be certainly known to be true2 but only1 to show that no ,fact can be certainly shown to be a ,fact1 merely by calling it a ,fact1 however emphatically4 ,there is by no means any ground of general skepticism with regard to truth1 involved in the doctrine of the necessary combination of two elements in all our knowledge4 ,on the contrary1 ,ideas are requisite to the essence1 and ,things to the reality of our knowledge in every case4 ,the proportions of ,geometry and ,arithmetic are examples of knowledge respecting our ,ideas of space and number1 with regard to which there is no room for doubt4 ,the doctrines of ,astronomy are examples of truths not less certain respecting the ,facts of the external world4 ,sect4 #aa4--,successive ,generalization4 ,,in the preceding pages we have been led to the doctrine1 that though1 in the ,antithesis of ,theory and ,fact1 there is involved an essential opposition2 namely the opposition of the thoughts within us and the phenomena without us2 yet that we cannot distinguish and define the members of this antithesis separately4 ,theories become ,facts1 by becoming certain and familiar3 and thus1 as our knowledge becomes more sure and more extensive1 we are constantly transferring to the class of facts1 opinions which were at first regarded as theories4 ,now we have further to remark1 that in the progress of human knowledge respecting any branch of speculation1 there may be several such steps in succession1 each depending upon and including the preceding4 #ej ,the theoretical views which one generation of discoverers establishes1 become the facts from which the next generation advances to new theories4 ,as men rise from the particular to the general1 so1 in the same manner1 they rise from what is general to what is more general4 ,each induction supplies the materials of fresh inductions2 each generalization1 with all that it embraces in its circle1 may be found to be but one of many circles1 comprehended within the circuit of some wider generalization4 ,this remark has already been made1 and illustrated1 in the ,history of the ,inductive ,sciences#ba2 and1 in truth1 the whole of the history of science is full of suggestions and exemplifications of this course of things4 ,it may be convenient1 however1 to select a few instances which may further explain and confirm this view of the progress of scientific knowledge4 ,note #ba3 ,hist4 ,inductive ,sciences1 b4 vii4 c4 ii4 sect4 #e4 ,the most conspicuous instance of this succession is to be found in that science which has been progressive from the beginning of the world to our own times1 and which exhibits by far the richest collection of successive discoveries3 ,i mean ,astronomy4 ,it is easy to see that each of these successive discoveries depended on those antecedently made1 and that in each1 the truths which were the highest point of the knowledge of one age were the fundamental basis of the efforts of the age which came next4 ,thus we find1 in the days of ,greek discovery1 ,hipparchus and ,ptolemy combining and explaining the particular facts of the motion of the sun1 moon1 and planets1 by means of the theory of epicycles and eccentrics2--a highly important step1 which gave an intelligible connexion and rule to the motions of each of these luminaries4 ,when these cycles and epicycles1 thus truly representing the apparent motions of the heavenly bodies1 had accumulated to an inconvenient amount1 by the discovery of many inequalities in the observed motions1 ,copernicus showed that their effects might all be more simply included1 by making the sun the center of motion of the planets1 instead of #ea the earth4 ,but in this new view1 he still retained the epicycles and eccentrics which governed the motion of each body4 ,tycho ,brahe's observations1 and ,kepler's calculations1 showed that1 besides the vast number of facts which the epicyclical theory could account for1 there were some which it would not exactly include1 and ,kepler was led to the persuasion that the planets move in ellipses4 ,but this view of motion was at first conceived by ,kepler as a modification of the conception of epicycles4 ,on one occasion he blames himself for not sooner seeing that such a modification was possible4 ',what an absurdity on my part6' he cries#ca2 'as if libration in the diameter of the epicycle might not come to the same thing as motion in the ellipse4' ,but again2 ,kepler's laws of the elliptical motion of the planets were established2 and these laws immediately became the facts on which the mathematicians had to found their mechanical theories4 ,from these facts1 ,newton1 as we have related1 proved that the central force of the sun retains the planets in their orbits1 according to the law of the inverse square of the distance4 ,the same law was shown to prevail in the gravitation of the earth4 ,it was shown1 too1 by induction from the motions of ,jupiter and ,saturn1 that the planets attract each other2 by calculations from the figure of the earth1 that the parts of the earth attract each other2 and1 by considering the course of the tides1 that the sun and moon attract the waters of the ocean4 ,and all these curious discoveries being established as facts1 the subject was ready for another step of generalization4 ,by an unparalleled rapidity in the progress of discovery in this case1 not only were all the inductions which we have first mentioned made by one individual1 but the new advance1 the higher flight1 the closing victory1 fell to the lot of the same extraordinary person4 ,note #ca3 ,hist4 ,inductive ,sciences1 b4 v4 c4 iv4 sect4 #c4 ,the attraction of the sun upon the planets1 of the moon upon the earth1 of the planets on each other1 of the parts of the earth on themselves1 of the sun and #eb moon upon the ocean2--all these truths1 each of itself a great discovery1 were included by ,newton in the higher generalization1 of the universal gravitation of matter1 by which each particle is drawn to every other according to the law of the inverse square3 and thus this long advance from discovery to discovery1 from truths to truths1 each justly admired when new1 and then rightly used as old1 was closed in a worthy and consistent manner1 by a truth which is the most worthy admiration1 because it includes all the researches of preceding ages of ,astronomy4 ,we may take another example of a succession of this kind from the history of a science1 which1 though it has made wonderful advances1 has not yet reached its goal1 as physical astronomy appears to have done1 but seems to have before it a long prospect of future progress4 ,i now refer to ,chemistry1 in which ,i shall try to point out how the preceding discoveries afforded the materials of the succeeding2 although this subordination and connexion is1 in this case1 less familiar to men's minds than in ,astronomy1 and is1 perhaps1 more difficult to present in a clear and definite shape4 ,sylvius saw1 in the facts which occur1 when an acid and an alkali are brought together1 the evidence that they neutralize each other4 ,but cases of neutralization1 and acidification1 and many other effects of mixture of the ingredients of bodies1 being thus viewed as facts1 had an aspect of unity and law given them by ,geoffroy and ,bergman#da1 who introduced the conception of the ,chemical ,affinity or ,elective ,attraction1 by which certain elements select other elements1 as if by preference4 ,that combustion1 whether a chemical union or a chemical separation of ingredients1 is of the same nature with acidification1 was the doctrine of ,beccher and ,stahl1 and was soon established as a truth which must form a part of every succeeding physical theory4 ,that the rules of affinity and chemical composition may include gaseous elements1 was established by ,black and ,cavendish4 ,and all these truths1 thus brought to light by #ec chemical discoverers1--affinity1 the identity of acidification and combustion1 the importance of gaseous elements1--along with all the facts respecting the weight of ingredients and compounds which the balance disclosed1--were taken up1 connected1 and included as particulars in the oxygen theory of ,lavoisier4 ,again1 the results of this theory1 and the quantity of the several ingredients which entered into each compound--7such results1 for the most part1 being now no longer mere theoretical speculations1 but recognized facts7--were the particulars from which ,dalton derived that wide law of chemical combination which we term the ,atomic ,theory4 ,and this law1 soon generally accepted among chemists1 is already in its turn become one of the facts included in ,faraday's ,theory of the identity of ,chemical ,affinity and ,electric ,attraction4 ,note #da3 ,hist4 ,inductive ,sciences1 b4 xiv4 c4 iii4 ,it is unnecessary to give further exemplifications of this constant ascent from one step to a higher2 this perpetual conversion of true theories into the materials of other and wider theories4 ,it will hereafter be our business to exhibit1 in a more full and formal manner1 the mode in which this principle determines the whole scheme and structure of all the most exact sciences4 ,and thus1 beginning with the facts of sense1 we gradually climb to the highest forms of human knowledge1 and obtain from experience and observation a vast collection of the most wide and elevated truths4 ,there are1 however1 truths of a very different kind1 to which we must turn our attention1 in order to pursue our researches respecting the nature and grounds of our knowledge4 ,but before we do this1 we must notice one more feature in that progress of science which we have already in part described4 #ed ,,chapter ,,ii4 ,,of ,,technical ,,terms4 #a4 ,,it has already been stated that we gather knowledge from the external world1 when we are able to apply1 to the facts which we observe1 some ideal conception1 which gives unity and connexion to multiplied and separate perceptions4 ,we have also shown that our conceptions1 thus verified by facts1 may themselves be united and connected by a new bond of the same nature2 and that man may thus have to pursue his way from truth to truth through a long progression of discoveries1 each resting on the preceding1 and rising above it4 ,each of these steps1 in succession1 is recorded1 fixed1 and made available1 by some peculiar form of words2 and such words1 thus rendered precise in their meaning1 and appropriated to the service of science1 we may call ,technical ,terms4 ,it is in a great measure by inventing such ,terms that men not only best express the discoveries they have made1 but also enable their followers to become so familiar with these discoveries1 and to possess them so thoroughly1 that they can readily use them in advancing to ulterior generalizations4 ,most of our ideal conceptions are described by exact and constant words or phrases1 such as those of which we here speak4 ,we have already had occasion to employ many of these4 ,thus we have had instances of technical ,terms expressing geometrical conceptions1 as ,ellipsis1 ,radius ,vector1 ,axis1 ,plane1 the ,proportion of the ,inverse ,square1 and the like4 ,other ,terms have described mechanical conceptions1 as ,accelerating ,force and ,attraction4 ,again1 chemistry exhibits 7as do all sciences7 a series of ,terms which mark the steps of our #ee progress4 ,the views of the first real founders of the science are recorded by the ,terms which are still in use1 ,neutral ,salts1 ,affinity1 and the like4 ,the establishment of ,dalton's theory has produced the use of the word ,atom in a peculiar sense1 or of some other word1 as ,proportion1 in a sense equally technical4 ,and ,mr4 ,faraday has found it necessary1 in order to expound his electro-chemical theory1 to introduce such terms as ,anode and ,cathode1 ,anon and ,cathon4 #b4 ,i need not adduce any further examples1 for my object at present is only to point out the use and influence of such language3 its rules and principles ,i shall hereafter try1 in some measure1 to fix4 ,but what we have here to remark is1 the extraordinary degree in which the progress of science is facilitated1 by thus investing each new discovery with a compendious and steady form of expression4 ,these terms soon become part of the current language of all who take an interest in speculation4 ,however strange they may sound at first1 they soon grow familiar in our ears1 and are used without any effort1 or any recollection of the difficulty they once involved4 ,they become as common as the phrases which express our most frequent feelings and interests1 while yet they have incomparably more precision than belongs to any terms which express feelings2 and they carry with them1 in their import1 the results of deep and laborious trains of research4 ,they convey the mental treasures of one period to the generations that follow2 and laden with this1 their precious freight1 they sail safely across gulfs of time in which empires have suffered shipwreck1 and the languages of common life have sunk into oblivion4 ,we have still in constant circulation among us the ,terms which belong to the geometry1 the astronomy1 the zoology1 the medicine of the ,greeks1 and the algebra and chemistry of the ,arabians4 ,and we can in an instant1 by means of a few words1 call to our own recollection1 or convey to the apprehension of another person1 phenomena and relations of phenomena in optics1 mineralogy1 chemistry1 which are so complex and abstruse1 that it might seem to require the utmost subtlety of the human mind to #ef grasp them1 even if that were made the sole object of its efforts4 ,by this remarkable effect of ,technical ,language1 we have the results of all the labours of past times not only always accessible1 but so prepared that we may 7provided we are careful in the use of our instrument7 employ what is really useful and efficacious for the purpose of further success1 without being in any way impeded or perplexed by the length and weight of the chain of past connexions which we drag along with us4 ,by such means1--by the use of the ,inductive ,process1 and by the aid of ,technical ,terms1--man has been constantly advancing in the path of scientific truth4 ,in a succeeding part of this work we shall endeavour to trace the general rules of this advance1 and to lay down the maxims by which it may be most successfully guided and forwarded4 ,but in order that we may do this to the best advantage1 we must pursue still further the analysis of knowledge into its elements2 and this will be our employment in the first part of the work4 #eg ,,chapter ,,iii4 ,,of ,,necessary ,,truths4 #a4 ,,every advance in human knowledge consists1 as we have seen1 in adapting new ideal conceptions to ascertained facts1 and thus in superinducing the ,form upon the ,matter1 the active upon the passive processes of our minds4 ,every such step introduces into our knowledge an additional portion of the ideal element1 and of those relations which flow from the nature of ,ideas4 ,it is1 therefore1 important for our purpose to examine more closely this element1 and to learn what the relations are which may thus come to form part of our knowledge4 ,an inquiry into those ,ideas which form the foundations of our sciences2--into the reality1 independence1 extent1 and principal heads of the knowledge which we thus acquire2 is a task on which we must now enter1 and which will employ us for several of the succeeding ,books4 ,in this inquiry our object will be to pass in review all the most important ,fundamental ,ideas which our sciences involve2 and to prove more distinctly in reference to each1 what we have already asserted with regard to all1 that there are everywhere involved in our knowledge acts of the mind as well as impressions of sense2 and that our knowledge derives1 from these acts1 a generality1 certainty1 and evidence which the senses could in no degree have supplied4 ,but before ,i proceed to do this in particular cases1 ,i will give some account of the argument in its general form4 ,we have already considered the separation of our knowledge into its two elements1--,impressions of ,sense and ,ideas1--as evidently indicated by this2 that all knowledge possesses characters which neither of these #eh elements alone could bestow4 ,without our ideas1 our sensations could have no connexion2 without external impressions1 our ideas would have no reality2 and thus both ingredients of our knowledge must exist4 #b4 ,there is another mode in which the distinction of the two elements of knowledge appears1 as ,i have already said 7c4 i4 sect4 #b73 namely in the distinction of necessary1 and contingent or experiential1 truths4 ,for of these two classes of truths1 the difference arises from this2--that the one class derives its nature from the one1 and the other from the other1 of the two elements of knowledge4 ,i have already stated briefly the difference of these two kinds of truths3--namely1 that the former are truths which1 we see1 must be true3--the latter are true1 but so far as we can see1 might be otherwise4 ,the former are true necessarily and universally3 the latter are learnt from experience and limited by experience4 ,now with regard to the former kind of truths1 ,i wish to show that the universality and necessity which distinguish them can by no means be derived from experience2 that these characters do in reality flow from the ideas which these truths involve2 and that when the necessity of the truth is exhibited in the way of logical demonstration1 it is found to depend upon certain fundamental principles1 7,definitions and ,axioms17 which may thus be considered as expressing1 in some measure1 the essential characters of our ideas4 ,these fundamental principles ,i shall afterwards proceed to discuss and to exhibit in each of the principal departments of science4 ,i shall begin by considering ,necessary ,truths more fully than ,i have yet done4 ,as ,i have already said1 necessary truths are those in which we not only learn1 that the proposition is true1 but see that it must be true2 in which the negation of the truth is not only false1 but impossible2 in which we cannot1 even by an effort of imagination1 or in a supposition1 conceive the reverse of that which is asserted4 #c4 ,that there are such truths cannot be doubted4 ,we may take1 for example1 all relations of number4 ,three and ,two added together make ,five4 ,we cannot #ei conceive it to be otherwise4 ,we cannot1 by any freak of thought1 imagine ,three and ,two to make ,seven4 ,it may be said that this assertion merely expresses what we mean by our words2 that it is a matter of definition2 that the proposition is an identical one4 ,but this is by no means so4 ,the definition of ,five is not ,three and ,two1 but ,four and ,one4 ,how does it appear that ,three and ,two is the same number as ,four and ,one8 ,it is evident that it is so2 but why is it evident8--not because the proposition is identical2 for if that were the reason1 all numerical propositions must be evident for the same reason4 ,if it be a matter of definition that #c and #b make #e1 it must be a matter of definition that #ci and #bg make #ff4 ,but who will say that the definition of #ff is #ci and #bg8 ,yet the magnitude of the numbers can make no difference in the ground of the truth4 ,how do we know that the product of #ac and #ag is #d less than the product of #ae and #ae8 ,we see that it is so1 if we perform certain operations by the rules of arithmetic2 but how do we know the truth of the rules of arithmetic8 ,if we divide #abccge by #ihg according to the process taught us at school1 how are we assured that the result is correct1 and that the number #abe thus obtained is really the number of times one number is contained in the other8 ,the correctness of the rule1 it may be replied1 can be rigorously demonstrated4 ,it can be shown that the process must inevitably give the true quotient4 ,certainly this can be shown to be the case4 ,and precisely because it can be shown that the result must be true1 we have here an example of a necessary truth2 and this truth1 it appears1 is not therefore necessary because it is itself evidently identical1 however it may be possible to prove it by reducing it to evidently identical propositions4 ,and the same is the case with all other numerical propositions2 for1 as we have said1 the nature of all of them is the same4 ,here1 then1 we have instances of truths which are not only true1 but demonstrably and necessarily true4 ,now such truths are1 in this respect at least1 altogether #fj different from truths1 which1 however certain they may be1 are learnt to be so only by the evidence of observation1 interpreted1 as observation must be interpreted1 by our own mental faculties4 ,there is no difficulty in finding examples of these merely observed truths4 ,we find that sugar dissolves in water1 and forms a transparent fluid1 but no one will say that we can see any reason beforehand why the result must be so4 ,we find that all animals which chew the cud have also the divided hoof2 but could any one have predicted that this would be universally the case8 or supposing the truth of the rule to be known1 can any one say that he cannot conceive the facts as occurring otherwise8 ,water expands when it crystallizes1 some other substances contract in the same circumstances2 but can any one know that this will be so otherwise than by observation8 ,we have here propositions rigorously true1 7we will assume17 but can any one say they are necessarily true8 ,these1 and the great mass of the doctrines established by induction1 are actual1 but so far as we can see1 accidental laws2 results determined by some unknown selection1 not demonstrable consequences of the essence of things1 inevitable and perceived to be inevitable4 ,according to the phraseology which has been frequently used by philosophical writers1 they are contingent1 not necessary truths4 ,it is requisite to insist upon this opposition1 because no insight can be obtained into the true nature of knowledge1 and the mode of arriving at it1 by any one who does not clearly appreciate the distinction4 ,the separation of truths which are learnt by observation1 and truths which can be seen to be true by a pure act of thought1 is one of the first and most essential steps in our examination of the nature of truth1 and the mode of its discovery4 ,if any one does not clearly comprehend this distinction of necessary and contingent truths1 he will not be able to go along with us in our researches into the foundations of human knowledge2 nor1 indeed1 to pursue with success any speculation on the subject4 ,but1 in fact1 this distinction is one that can hardly fail to be at once understood4 ,it #fa is insisted upon by almost all the best modern1 as well as ancient1 metaphysicians#ea1 as of primary importance4 ,and if any person does not fully apprehend1 at first1 the different kinds of truth thus pointed out1 let him study1 to some extent1 those sciences which have necessary truth for their subject1 as geometry1 or the properties of numbers1 so as to obtain a familiar acquaintance with such truth2 and he will then hardly fail to see how different the evidence of the propositions which occur in these sciences1 is from the evidence of the facts which are merely learnt from experience4 ,that the year goes through its course in #cfe days1 can only be known by observation of the sun or stars3 that #cfe days is #eb weeks and a day1 it requires no experience1 but only a little thought to perceive4 ,that bees build their cells in the form of hexagons1 we cannot know without looking at them2 that regular hexagons may be arranged so as to fill space1 may be proved with the utmost rigour1 even if there were not in existence such a thing as a material hexagon4 ,note #ea3 ,aristotle1 ,dr ,whately1 ,dugald ,stewart1 c4 #d4 ,as ,i have already said1 one mode in which we may express the difference of necessary truths and truths of experience1 is1 that necessary truths are those of which we cannot distinctly conceive the contrary4 ,we can very readily conceive the contrary of experiential truths4 ,we can conceive the stars moving about the pole or across the sky in any kind of curves with any velocities2 we can conceive the moon always appearing during the whole month as a luminous disk1 as she might do if her light were inherent and not borrowed4 ,but we cannot conceive one of the parallelograms on the same base and between the same parallels larger than the other2 for we find that1 if we attempt to do this1 when we separate the parallelograms into parts1 we have to conceive one triangle larger than another1 both having all their parts equal2 which we cannot conceive at all1 if we conceive the triangles distinctly4 ,we make this impossibility more clear by conceiving #fb the triangles to be placed so that two sides of the one coincide with two sides of the other2 and it is then seen1 that in order to conceive the triangles unequal1 we must conceive the two bases which have the same extremities both ways1 to be different lines1 though both straight lines4 ,this it is impossible to conceive3 we assent to the impossibility as an axiom1 when it is expressed by saying1 that two straight lines cannot inclose a space2 and thus we cannot distinctly conceive the contrary of the proposition just mentioned respecting parallelograms4 ,but it is necessary1 in applying this distinction1 to bear in mind the terms of it2--that we cannot distinctly conceive the contrary of a necessary truth4 ,for in a certain loose1 indistinct way1 persons conceive the contrary of necessary geometrical truths1 when they erroneously conceive false propositions to be true4 ,thus1 ,hobbes erroneously held that he had discovered a means of geometrically 'doubling the cube1' as it is called1 that is1 finding two mean proportionals between two given lines2 a problem which cannot be solved by plane geometry4 ,hobbes not only proposed a construction for this purpose1 but obstinately maintained that it was right1 when it had been proved to be wrong4 ,but then1 the discussion showed how indistinct the geometrical conceptions of ,hobbes were2 for when his critics had proved that one of the lines in his diagram would not meet the other in the point which his reasoning supposed1 but in another point near to it2 he maintained1 in reply1 that one of these points was large enough to include the other1 so that they might be considered as the same point4 ,such a mode of conceiving the opposite of a geometrical truth1 forms no exception to the assertion1 that this opposite cannot be distinctly conceived4 ,in like manner1 the indistinct conceptions of children and of rude savages do not invalidate the distinction of necessary and experiential truths4 ,children and savages make mistakes even with regard to numbers2 and might easily happen to assert that #bg and #ch are equal to #fc or #fd4 ,but such mistakes cannot #fc make arithmetical truths cease to be necessary truths4 ,when any person conceives these numbers and their addition distinctly1 by resolving them into parts1 or in any other way1 he sees that their sum is necessarily #fe4 ,if1 on the ground of the possibility of children and savages conceiving something different1 it be held that this is not a necessary truth1 it must be held on the same ground1 that it is not a necessary truth that #g and #d are equal to #aa2 for children and savages might be found so unfamiliar with numbers as not to reject the assertion that #g and #d are #aj1 or even that #d and #c are #f1 or #h4 ,but ,i suppose that no persons would on such grounds hold that these arithmetical truths are truths known only by experience4 #e4 ,i have taken examples of necessary truths from the properties of number and space2 but such truths exist no less in other subjects1 although the discipline of thought which is requisite to perceive them distinctly1 may not be so usual among men with regard to the sciences of mechanics and hydrostatics1 as it is with regard to the sciences of geometry and arithmetic4 ,yet every one may perceive that there are such truths in mechanics4 ,if ,i press the table with my hand1 the table presses my hand with an equal force3 here is a self-evident and necessary truth4 ,in any machine1 constructed in whatever manner to increase the force which ,i can exert1 it is certain that what ,i gain in force ,i must lose in the velocity which ,i communicate4 ,this is not a contingent truth1 borrowed from and limited by observation2 for a man of sound mechanical views applies it with like confidence1 however novel be the construction of the machine4 ,when ,i come to speak of the ideas which are involved in our mechanical knowledge1 ,i may1 perhaps1 be able to bring more clearly into view the necessary truth of general propositions on such subjects4 ,that reaction is equal and opposite to action1 is as necessarily true as that two straight lines cannot inclose a space2 it is as impossible theoretically to make a perpetual motion by mere mechanism as to make the diagonal of a square commensurable with the side4 #fd #f4 ,necessary truths must be universal truths4 ,if any property belong to a right-angled triangle necessarily1 it must belong to all right-angled triangles4 ,and it shall be proved in the following ,chapter1 that truths possessing these two characters1 of ,necessity and ,universality1 cannot possibly be the mere results of experience4 ,necessary truths are not considered as a portion of the ,inductive ,sciences4 ,they are ,deductions from our ,ideas4 ,thus the necessary truths which constitute the ,science of ,geometry are ,deductions from our ,idea of ,space3 the necessary truths which constitute the ,science of ,arithmetic are ,deductions from our notions of ,number2 which perhaps involves necessarily the ,idea of ,time4 ,but though we do not call those ,sciences ,inductive which involve properties of ,space1 ,number and ,time alone1 the properties of ,space1 ,time and ,number enter in many very important ways into the ,inductive ,sciences2 and therefore the ,ideas of ,space1 ,time and ,number require to be considered in the first place4 ,and moreover the examination of these ,ideas is an essential step towards the examination of other ,ideas3 and the conditions of the possibility and certainty of truth1 which are exemplified in ,geometry and ,arithmetic1 open to us important views respecting the conditions of the possibility and certainty of all ,scientific ,truth4 ,we shall therefore in the next ,book examine the ,ideas on which the ,pure ,sciences1 ,geometry and ,arithmetic1 are founded4 ,but we must first say a little more of ,ideas in general4 #fe ,,chapter ,,iv4 ,,of ,,experience4 #a4 ,i ,,here employ the term ,experience in a more definite and limited sense than that which it possesses in common usage2 for ,i restrict it to matters belonging to the domain of science4 ,in such cases1 the knowledge which we acquire1 by means of experience1 is of a clear and precise nature2 and the passions and feelings and interests1 which make the lessons of experience in practical matters so difficult to read aright1 no longer disturb and confuse us4 ,we may1 therefore1 hope1 by attending to such cases1 to learn what efficacy experience really has1 in the discovery of truth4 ,that from experience 7including intentional experience1 or observation17 we obtain much knowledge which is highly important1 and which could not be procured from any other source1 is abundantly clear4 ,we have already taken several examples of such knowledge4 ,we know by experience that animals which ruminate are cloven-hoofed2 and we know this in no other manner4 ,we know1 in like manner1 that all the planets and their satellites revolve round the sun from west to east4 ,it has been found by experience that all meteoric stones contain chrome4 ,many similar portions of our knowledge might be mentioned4 ,now what we have here to remark is this2--that in no case can experience prove a proposition to be necessarily or universally true4 ,however many instances we may have observed of the truth of a proposition1 yet if it be known merely by observation1 there is nothing to assure us that the next case shall not be an exception to the rule4 ,if it be strictly true that every ruminant animal yet known has cloven hoofs1 we #ff still cannot be sure that some creature will not hereafter be discovered which has the first of these attributes without having the other4 ,when the planets and their satellites1 as far as ,saturn1 had been all found to move round the sun in one direction1 it was still possible that there might be other such bodies not obeying this rule2 and1 accordingly1 when the satellites of ,uranus were detected1 they appeared to offer an exception of this kind4 ,even in the mathematical sciences1 we have examples of such rules suggested by experience1 and also of their precariousness4 ,however far they may have been tested1 we cannot depend upon their correctness1 except we see some reason for the rule4 ,for instance1 various rules have been given1 for the purpose of pointing out prime numbers2 that is1 those which cannot be divided by any other number4 ,we may try1 as an example of such a rule1 this one--any odd power of the number two1 diminished by one4 ,thus the third power of two1 diminished by one1 is seven2 the fifth power1 diminished by one1 is thirty-one2 the seventh power so diminished is one hundred and twenty-seven4 ,all these are prime numbers3 and we might be led to suppose that the rule is universal4 ,but the next example shows us the fallaciousness of such a belief4 ,the ninth power of two1 diminished by one1 is five hundred and eleven1 which is not a prime1 being divisible by seven4 ,experience must always consist of a limited number of observations4 ,and1 however numerous these may be1 they can show nothing with regard to the infinite number of cases in which the experiment has not been made4 ,experience being thus unable to prove a fact to be universal1 is1 as will readily be seen1 still more incapable of proving a truth to be necessary4 ,experience cannot1 indeed1 offer the smallest ground for the necessity of a proposition4 ,she can observe and record what has happened2 but she cannot find1 in any case1 or in any accumulation of cases1 any reason for what must happen4 ,she may see objects side by side2 but she cannot see a reason why they must ever be side by side4 ,she finds certain events to occur in succession2 but the succession supplies1 in its occurrence1 no #fg reason for its recurrence4 ,she contemplates external objects2 but she cannot detect any internal bond1 which indissolubly connects the future with the past1 the possible with the real4 ,to learn a proposition by experience1 and to see it to be necessarily true1 are two altogether different processes of thought4 #b4 ,but it may be said1 that we do learn by means of observation and experience many universal truths2 indeed1 all the general truths of which science consists4 ,is not the doctrine of universal gravitation learnt by experience8 ,are not the laws of motion1 the properties of light1 the general principles of chemistry1 so learnt8 ,how1 with these examples before us1 can we say that experience teaches no universal truths8 ,to this we reply1 that these truths can only be known to be general1 not universal1 if they depend upon experience alone4 ,experience cannot bestow that universality which she herself cannot have1 and that necessity of which she has no comprehension4 ,if these doctrines are universally true1 this universality flows from the ideas which we apply to our experience1 and which are1 as we have seen1 the real sources of necessary truth4 ,how far these ideas can communicate their universality and necessity to the results of experience1 it will hereafter be our business to consider4 ,it will then appear1 that when the mind collects from observation truths of a wide and comprehensive kind1 which approach to the simplicity and universality of the truths of pure science2 she gives them this character by throwing upon them the light of her own ,fundamental ,ideas4 ,but the truths which we discover by observation of the external world1 even when most strikingly simple and universal1 are not necessary truths4 ,is the doctrine of universal gravitation necessarily true8 ,it was doubted by ,clairaut 7so far as it refers to the moon71 when the progression of the apogee in fact appeared to be twice as great as the theory admitted4 ,it has been doubted1 even more recently1 with respect to the planets1 their mutual perturbations appearing to indicate a deviation from the law4 ,it is doubted still1 by some #fh persons1 with respect to the double stars4 ,but suppose all these doubts to be banished1 and the law to be universal2 is it then proved to be necessary8 ,manifestly not3 the very existence of these doubts proves that it is not so4 ,for the doubts were dissipated by reference to observation and calculation1 not by reasoning on the nature of the law4 ,clairaut's difficulty was removed by a more exact calculation of the effect of the sun's force on the motion of the apogee4 ,the suggestion of ,bessel1 that the intensity of gravitation might be different for different planets1 was found to be unnecessary1 when ,professor ,airy gave a more accurate determination of the mass of ,jupiter4 ,and the question whether the extension of the law of the inverse square to the double stars be true1 7one of the most remarkable questions now before the scientific world17 must be answered1 not by any speculations concerning what the laws of attraction must necessarily be1 but by carefully determining the actual laws of the motion of these curious objects1 by means of the observations such as those which ,sir ,john ,herschel has collected for that purpose1 by his unexampled survey of both hemispheres of the sky4 ,and since the extent of this truth is thus to be determined by reference to observed facts1 it is clear that no mere accumulation of them can make its universality certain1 or its necessity apparent4 ,thus no knowledge of the necessity of any truths can result from the observation of what really happens4 ,this being clearly understood1 we are led to an important inquiry4 ,the characters of universality and necessity in the truths which form part of our knowledge1 can never be derived from experience1 by which so large a part of our knowledge is obtained4 ,but since1 as we have seen1 we really do possess a large body of truths which are necessary1 and because necessary1 therefore universal1 the question still recurs1 from what source these characters of universality and necessity are derived4 ,the answer to this question we will attempt to give in the next chapter4 #fi ,,chapter ,v4 ,,of ,,the ,,grounds ,,of ,,necessary ,,truths4 #a4 ,,to the question just stated1 ,i reply1 that the necessity and universality of the truths which form a part of our knowledge1 are derived from the ,fundamental ,ideas which those truths involve4 ,these ideas entirely shape and circumscribe our knowledge2 they regulate the active operations of our minds1 without which our passive sensations do not become knowledge4 ,they govern these operations1 according to rules which are not only fixed and permanent1 but which may be expressed in plain and definite terms2 and these rules1 when thus expressed1 may be made the basis of demonstrations by which the necessary relations imparted to our knowledge by our ,ideas may be traced to their consequences in the most remote ramifications of scientific truth4 ,these enunciations of the necessary and evident conditions imposed upon our knowledge by the ,fundamental ,ideas which it involves1 are termed ,axioms4 ,thus the ,axioms of ,geometry express the necessary conditions which result from the ,idea of ,space2 the ,axioms of ,mechanics express the necessary conditions which flow from the ,ideas of ,force and ,motion2 and so on4 #b4 ,it will be the office of several of the succeeding ,books of this work to establish and illustrate in detail what ,i have thus stated in general terms4 ,i shall there pass in review many of the most important fundamental ideas on which the existing body of our science depends2 and ,i shall endeavour to show1 for each such idea in succession1 that knowledge involves an active as well as a passive element2 that it is not possible without an act of the mind1 regulated by certain #gj laws4 ,i shall further attempt to enumerate some of the principal fundamental relations which each idea thus introduces into our thoughts1 and to express them by means of definitions and axioms1 and other suitable forms4 ,i will only add a remark or two to illustrate further this view of the ideal grounds of our knowledge4 #c4 ,to persons familiar with any of the demonstrative sciences1 it will be apparent that if we state all the ,definitions and ,axioms which are employed in the demonstrations1 we state the whole basis on which those reasonings rest4 ,for the whole process of demonstrative or deductive reasoning in any science1 7as in geometry1 for instance17 consists entirely in combining some of these first principles so as to obtain the simplest propositions of the science2 then combining these so as to obtain other propositions of greater complexity2 and so on1 till we advance to the most recondite demonstrable truths2 these last1 however intricate and unexpected1 still involving no principles except the original definitions and axioms4 ,thus1 by combining the ,definition of a triangle1 and the ,definitions of equal lines and equal angles1 namely1 that they are such as when applied to each other1 coincide1 with the ,axiom respecting straight lines 7that two such lines cannot inclose a space17 we demonstrate the equality of triangles1 under certain assumed conditions4 ,again1 by combining this result with the ,definition of parallelograms1 and with the ,axiom that if equals be taken from equals the wholes are equal1 we prove the equality of parallelograms between the same parallels and upon the same base4 ,from this proposition1 again1 we prove the equality of the square on the hypotenuse of a triangle to the squares on the two sides containing the right angle4 ,but in all this there is nothing contained which is not rigorously the result of our geometrical ,definitions and ,axioms4 ,all the rest of our treatises of geometry consists only of terms and phrases of reasoning1 the object of which is to connect those first principles1 and to exhibit the effects of their combination in the shape of demonstration4 #ga #d4 ,this combination of first principles takes place according to the forms and rules of ,logic4 ,all the steps of the demonstration may be stated in the shape in which logicians are accustomed to exhibit processes of reasoning in order to show their conclusiveness1 that is1 in ,syllogisms4 ,thus our geometrical reasonings might be resolved into such steps as the following3-- ,all straight lines drawn from the centre of a circle to its circumference are equal3 ,but the straight lines ,,ab1 ,,ac1 are drawn from the centre of a circle to its circumference3 ,therefore the straight lines ,,ab1 ,,ac1 are equal4 ,each step of geometrical1 and all other demonstrative reasoning1 may be resolved into three such clauses as these2 and these three clauses are termed respectively1 the major premiss1 the minor premiss1 and the conclusion2 or1 more briefly1 the major1 the minor1 and the 9999conclusion4 ,the principle which justifies the reasoning when exhibited in this syllogistic form1 is this3--that a truth which can be asserted as generally1 or rather as universally true1 can be asserted as true also in each particular case4 ,the minor only asserts a certain particular case to be an example of such conditions as are spoken of in the major2 and hence the conclusion1 which is true of the major by supposition1 is true of the minor by consequence2 and thus we proceed from syllogism to syllogism1 in each one employing some general truth in some particular instance4 ,any proof which occurs in geometry1 or any other science of demonstration1 may thus be reduced to a series of processes1 in each of which we pass from some general proposition to the narrower and more special propositions which it includes4 ,and this process of deriving truths by the mere combination of general principles1 applied in particular hypothetical cases1 is called deduction2 being opposed to induction1 in which1 as we have seen 7chap4 i4 sect4 #c71 a new general principle is introduced at every step4 #e4 ,now we have to remark that1 this being so1 however far we follow such deductive reasoning1 we can #gb never have1 in our conclusion any truth which is not virtually included in the original principles from which the reasoning started4 ,for since at any step we merely take out of a general proposition something included in it1 while at the preceding step we have taken this general proposition out of one more general1 and so on perpetually1 it is manifest that our last result was really included in the principle or principles with which we began4 ,i say principles1 because1 although our logical conclusion can only exhibit the legitimate issue of our first principles1 it may1 nevertheless1 contain the result of the combination of several such principles1 and may thus assume a great degree of complexity1 and may appear so far removed from the parent truths1 as to betray at first sight hardly any relationship with them4 ,thus the proposition which has already been quoted respecting the squares on the sides of a right-angled triangle1 contains the results of many elementary principles2 as1 the definitions of parallels1 triangle1 and square2 the axioms respecting straight lines1 and respecting parallels2 and1 perhaps1 others4 ,the conclusion is complicated by containing the effects of the combination of all these elements2 but it contains nothing1 and can contain nothing1 but such elements and their combinations4 ,this doctrine1 that logical reasoning produces no new truths1 but only unfolds and brings into view those truths which were1 in effect1 contained in the first principles of the reasoning1 is assented to by almost all who1 in modern times1 have attended to the science of logic4 ,such a view is admitted both by those who defend1 and by those who depreciate the value of logic4 ',whatever is established by reasoning1 must have been contained and virtually asserted in the premises#fa4' ',the only truth which such propositions can possess consists in conformity to the original principles4' ,note #fa3 ,whately's ,logic1 pp4 #bcg1 #bch4 ,in this manner the whole substance of our geometry is reduced to the ,definitions and ,axioms which we employ in our elementary reasonings2 and in like #gc manner we reduce the demonstrative truths of any other science to the definitions and axioms which we there employ4 #f4 ,but in reference to this subject1 it has sometimes been said that demonstrative sciences do in reality depend upon ,definitions only2 and that no additional kind of principle1 such as we have supposed ,axioms to be1 is absolutely required4 ,it has been asserted that in geometry1 for example1 the source of the necessary truth of our propositions is this1 that they depend upon definitions alone1 and consequently merely state the identity of the same thing under different aspects4 ,that in the sciences which admit of demonstration1 as geometry1 mechanics1 and the like1 ,axioms as well as ,definitions are needed1 in order to express the grounds of our necessary convictions1 must be shown hereafter by an examination of each of these sciences in particular4 ,but that the propositions of these sciences1 those of geometry for example1 do not merely assert the identity of the same thing1 will1 ,i think1 be generally allowed1 if we consider the assertions which we are enabled to make4 ,when we declare that 'a straight line is the shortest distance between two points1' is this merely an identical proposition8 the definition of a straight line in another form8 ,not so3 the definition of a straight line involves the notion of form only1 and does not contain anything about magnitude2 consequently1 it cannot contain anything equivalent to 'shortest4' ,thus the propositions of geometry are not merely identical propositions2 nor have we in their general character anything to countenance the assertion1 that they are the results of definitions alone4 ,and when we come to examine this and other sciences more closely1 we shall find that axioms1 such as are usually in our treatises made the fundamental principles of our demonstrations1 neither have ever been1 nor can be1 dispensed with4 ,axioms1 as well as ,definitions1 are in all cases requisite1 in order properly to exhibit the grounds of necessary truth4 #g4 ,thus the real logical basis of every body of demonstrated truths are the ,definitions and ,axioms #gd which are the first principles of the reasonings4 ,but when we are arrived at this point1 the question further occurs1 what is the ground of the truth of these ,axioms8 ,it is not the logical1 but the philosophical1 not the formal1 but the real foundation of necessary truth1 which we are seeking4 ,hence this inquiry necessarily comes before us1 ,what is the ground of the ,axioms of ,geometry1 of ,mechanics1 and of any other demonstrable science8 ,the answer which we are led to give1 by the view which we have taken of the nature of knowledge1 has already been stated4 ,the ground of the axioms belonging to each science is the ,idea which the axiom involves4 ,the ground of the ,axioms of ,geometry is the ,idea of ,space3 the ground of the ,axioms of ,mechanics is the ,idea of ,force1 of ,action and ,reaction1 and the like4 ,and hence these ,ideas are ,fundamental ,ideas2 and since they are thus the foundations1 not only of demonstration but of truth1 an examination into their real import and nature is of the greatest consequence to our purpose4 #h4 ,not only the ,axioms1 but the definitions which form the basis of our reasonings1 depend upon our ,fundamental ,ideas4 ,and the ,definitions are not arbitrary definitions1 but are determined by a necessity no less rigorous than the ,axioms themselves4 ,we could not think of geometrical truths without conceiving a circle2 and we could not reason concerning such truths without defining a circle in some mode equivalent to that which is commonly adopted4 ,the ,definitions of parallels1 of right angles1 and the like1 are quite as necessarily prescribed by the nature of the case1 as the ,axioms which these ,definitions bring with them4 ,indeed we may substitute one of these kinds of principles for another4 ,we cannot always put a ,definition in the place of an ,axiom2 but we may always find an ,axiom which shall take the place of a ,definition4 ,if we assume a proper ,axiom respecting straight lines1 we need no ,definition of a straight line4 ,but in whatever shape the principle appear1 as ,definition or as ,axiom1 it has about it nothing casual or #ge arbitrary1 but is determined to be what it is1 as to its import1 by the most rigorous necessity1 growing out of the ,idea of ,space4 #i4 ,these principles1--,definitions1 and ,axioms1--thus exhibiting the primary developments of a fundamental idea1 do in fact express the idea1 so far as its expression in words forms part of our science4 ,they are different views of the same body of truth2 and though each principle1 by itself1 exhibits only one aspect of this body1 taken together they convey a sufficient conception of it for our purposes4 ,the ,idea itself cannot be fixed in words2 but these various lines of truth proceeding from it1 suggest sufficiently to a fitly-prepared mind1 the place where the idea resides1 its nature1 and its efficacy4 ,it is true that these principles1--our elementary ,definitions and ,axioms1--even taken all together1 express the ,idea incompletely4 ,thus the ,definitions and ,axioms of ,geometry1 as they are stated in our elementary works1 do not fully express the ,idea of ,space as it exists in our minds4 ,for1 in addition to these1 other ,axioms1 independent of these1 and no less evident1 can be stated2 and are in fact stated when we come to the ,higher ,geometry4 ,such1 for instance1 is the ,axiom of ,archimedes--that a curve line which joins two points is less than a broken line which joins the same points and includes the curve4 ,and thus the ,idea is disclosed but not fully revealed1 imparted but not transfused1 by the use we make of it in science4 ,when we have taken from the fountain so much as serves our purpose1 there still remains behind a deep well of truth1 which we have not exhausted1 and which we may easily believe to be inexhaustible4 #gf ,,chapter ,,vi4 ,,the ,,fundamental ,,ideas ,,are ,,not ,,derived ,,from ,,experience4 #a4 ,,by the course of speculation contained in the last three ,chapters1 we are again led to the conclusion which we have already stated1 that our knowledge contains an ideal element1 and that this element is not derived from experience4 ,for we have seen that there are propositions which are known to be necessarily true2 and that such knowledge is not1 and cannot be1 obtained by mere observation of actual facts4 ,it has been shown1 also1 that these necessary truths are the results of certain fundamental ideas1 such as those of space1 number1 and the like4 ,hence it follows inevitably that these ideas and others of the same kind are not derived from experience4 ,for these ideas possess a power of infusing into their developments that very necessity which experience can in no way bestow4 ,this power they do not borrow from the external world1 but possess by their own nature4 ,thus we unfold out of the ,idea of ,space the propositions of geometry1 which are plainly truths of the most rigorous necessity and universality4 ,but if the idea of space were merely collected from observation of the external world1 it could never enable or entitle us to assert such propositions3 it could never authorize us to say that not merely some lines1 but all lines1 not only have1 but must have1 those properties which geometry teaches4 ,geometry in every proposition speaks a language which experience never dares to utter2 and indeed of which she but half comprehends the meaning4 ,experience sees that the assertions are true1 but she sees not how profound and absolute is their truth4 #gg ,she unhesitatingly assents to the laws which geometry delivers1 but she does not pretend to see the origin of their obligation4 ,she is always ready to acknowledge the sway of pure scientific principles as a matter of fact1 but she does not dream of offering her opinion on their authority as a matter of right2 still less can she justly claim to be herself the source of that authority4 ,david ,hume asserted#ga1 that we are incapable of seeing in any of the appearances which the world presents anything of necessary connexion2 and hence he inferred that our knowledge cannot extend to any such connexion4 ,it will be seen from what we have said that we assent to his remark as to the fact1 but we differ from him altogether in the consequence to be drawn from it4 ,our inference from ,hume's observation is1 not the truth of his conclusion1 but the falsehood of his premises2--not that1 therefore1 we can know nothing of natural connexion1 but that1 therefore1 we have some other source of knowledge than experience3--not1 that we can have no idea of connexion or causation1 because1 in his language1 it cannot be the copy of an impression2 but that since we have such an idea1 our ideas are not the copies of our impressions4 ,note #ga3 ,essays1 vol4 ii4 p4 #gj4 ,since it thus appears that our fundamental ideas are not acquired from the external world by our senses1 but have some separate and independent origin1 it is important for us to examine their nature and properties1 as they exist in themselves2 and this it will be our business to do through a portion of the following pages4 ,but it may be proper first to notice one or two objections which may possibly occur to some readers4 #b4 ,it may be said that without the use of our senses1 of sight and touch1 for instance1 we should never have any idea of space2 that this idea1 therefore1 may properly be said to be derived from those senses4 ,and to this ,i reply1 by referring to a parallel instance4 ,without light we should have no perception of visible #gh figure2 yet the power of perceiving visible figure cannot be said to be derived from the light1 but resides in the structure of the eye4 ,if we had never seen objects in the light1 we should be quite unaware that we possessed a power of vision2 yet we should not possess it the less on that account4 ,if we had never exercised the senses of sight and touch 7if we can conceive such a state of human existence7 we know not that we should be conscious of an idea of space4 ,but the light reveals to us at the same time the existence of external objects and our own power of seeing4 ,and in a very similar manner1 the exercise of our senses discloses to us1 at the same time1 the external world1 and our own ideas of space1 time1 and other conditions1 without which the external world can neither be observed nor conceived4 ,that light is necessary to vision1 does not1 in any degree1 supersede the importance of a separate examination of the laws of our visual powers1 if we would understand the nature of our own bodily faculties and the extent of the information they can give us4 ,in like manner1 the fact that intercourse with the external world is necessary for the conscious employment of our ideas1 does not make it the less essential for us to examine those ideas in their most intimate structure1 in order that we may understand the grounds and limits of our knowledge4 ,even before we see a single object1 we have a faculty of vision2 and in like manner1 if we can suppose a man who has never contemplated an object in space or time1 we must still assume him to have the faculties of entertaining the ideas of space and time1 which faculties are called into play on the very first occasion of the use of the senses4 #c4 ,in answer to such remarks as the above1 it has sometimes been said that to assume separate faculties in the mind for so many different processes of thought1 is to give a mere verbal explanation1 since we learn nothing concerning our idea of space by being told that we have a faculty of forming such an idea4 ,it has been said that this course of explanation leads to an endless multiplication of elements in man's nature1 without any advantage to our knowledge of his true #gi constitution4 ,we may1 it is said1 assert man to have a faculty of walking1 of standing1 of breathing1 of speaking2 but what1 it is asked1 is gained by such assertions8 ,to this ,i reply1 that we undoubtedly have such faculties as those just named2 that it is by no means unimportant to consider them2 and that the main question in such cases is1 whether they are separate and independent faculties1 or complex and derivative ones2 and1 if the latter be the case1 what are the simple and original faculties by the combination of which the others are produced4 ,in walking1 standing1 breathing1 for instance1 a great part of the operation can be reduced to one single faculty2 the voluntary exercise of our muscles4 ,but in breathing this does not appear to be the whole of the process4 ,the operation is1 in part at least1 involuntary2 and it has been held that there is a certain sympathetic action of the nerves1 in addition to the voluntary agency which they transmit1 which is essential to the function4 ,to determine whether or no this sympathetic faculty is real and distinct1 and if so1 what are its laws and limits1 is certainly a highly philosophical inquiry1 and well deserving the attention which has been bestowed upon it by eminent physiologists4 ,and just of the same nature are the inquiries with respect to man's intellectual constitution1 on which we propose to enter4 ,for instance1 man has a faculty of apprehending time1 and a faculty of reckoning numbers3 are these distinct1 or is one faculty derived from the other8 ,to analyze the various combinations of our ideas and observations into the original faculties which they involve2 to show that these faculties are original1 and not capable of further analysis3 to point out the characters which mark these faculties and lead to the most important features of our knowledge2--these are the kind of researches on which we have now to enter1 and these1 we trust1 will be found to be far from idle or useless parts of our plan4 ,if we succeed in such attempts1 it will appear that it is by no means a frivolous or superfluous step to distinguish separate faculties in the mind4 ,if we do not learn much by being told that we have a faculty #hj of forming the idea of space1 we at least1 by such a commencement1 circumscribe a certain portion of the field of our investigations1 which1 we shall afterwards endeavour to show1 requires and rewards a special examination4 ,and though we shall thus have to separate the domain of our philosophy into many provinces1 these are1 as we trust it will appear1 neither arbitrarily assigned1 nor vague in their limits1 nor infinite in number4 #ha ,,chapter ,,vii4 ,,of ,,the ,,philosophy ,,of ,,the ,,sciences4 ,,we proceed1 in the ensuing ,books1 to the closer examination of a considerable number of those ,fundamental ,ideas on which the sciences1 hitherto most successfully cultivated1 are founded4 ,in this task1 our objects will be to explain and analyze such ,ideas so as to bring into view the ,definitions and ,axioms1 or other forms1 in which we may clothe the conditions to which our speculative knowledge is subjected4 ,i shall also try to prove1 for some of these ,ideas in particular1 what has been already urged respecting them in general1 that they are not derived from observation1 but necessarily impose their conditions upon that knowledge of which observation supplies the materials4 ,i shall further1 in some cases1 endeavour to trace the history of these ,ideas as they have successively come into notice in the progress of science2 the gradual development by which they have arrived at their due purity and clearness2 and1 as a necessary part of such a history1 ,i shall give a view of some of the principal controversies which have taken place with regard to each portion of knowledge4 ,an exposition and discussion of the ,fundamental ,ideas of each ,science may1 with great propriety1 be termed the ,,philosophy ,,of such ,,science4 ,these ideas contain in themselves the elements of those truths which the science discovers and enunciates2 and in the progress of the sciences1 both in the world at large and in the mind of each individual student1 the most important steps consist in apprehending these ideas clearly1 and in bringing them into accordance with the observed facts4 ,i shall1 therefore1 in a series of ,books1 #hb treat of the ,philosophy of the ,pure ,sciences1 the ,philosophy of the ,mechanical ,sciences1 the ,philosophy of ,chemistry1 and the like1 and shall analyze and examine the ideas which these sciences respectively involve4 ,in this undertaking1 inevitably somewhat long1 and involving many deep and subtle discussions1 ,i shall take1 as a chart of the country before me1 by which my course is to be guided1 the scheme of the sciences which ,i was led to form by travelling over the history of each in order#ha4 ,each of the sciences of which ,i then narrated the progress1 depends upon several of the ,fundamental ,ideas of which ,i have to speak3 some of these ,ideas are peculiar to one field of speculation1 others are common to more4 ,a previous enumeration of ,ideas thus collected may serve both to show the course and limits of this part of our plan1 and the variety of interest which it offers4 ,note #ha3 ,history of the ,inductive ,sciences4 ,i shall1 then1 successively1 have to speak ,of the ,ideas which are the foundation of ,geometry and ,arithmetic1 7and which also regulate all sciences depending upon these1 as ,astronomy and ,mechanics27 namely1 the ,ideas of ,space1 ,time1 and ,number 7,book ,,ii473 ,of the ,ideas on which the ,mechanical ,sciences 7as ,mechanics1 ,hydrostatics1 ,physical ,astronomy7 more peculiarly rest2 the ideas of ,force and ,matter1 or rather the idea of ,cause1 which is the basis of these 7,book ,,iii473 ,of the ,ideas which the ,secondary ,mechanical ,sciences 7,acoustics1 ,optics1 and ,thermotics7 involve2 namely1 the ,ideas of the ,externality of objects1 and of the ,media by which we perceive their qualities 7,book ,,iv473 ,of the ,ideas which are the basis of ,mechanico-chemical and ,chemical ,science2 ,polarity1 ,chemical ,affinity1 and ,substance2 and the ,idea of ,symmetry1 a necessary part of the ,philosophy of ,crystallography 7,books ,v4 ,,vi473 ,of the ,ideas on which the ,classificatory ,sciences proceed 7,mineralogy1 ,botany1 and ,zoology72 namely1 #hc the ,ideas of ,resemblance1 and of its gradations1 and of ,natural ,affinity 7,books ,,vii4 ,,viii473 ,finally1 of those ,ideas on which the ,physiological ,sciences are founded2 the ,ideas of separate ,vital ,powers1 such as ,assimilation and ,irritability2 and the ,idea of ,final ,cause 7,book ,,ix473 ,we have1 besides these1 the ,paltiological ,sciences1 which proceed mainly on the conception of ,historical ,causation 7,book ,x473 ,it is plain that when we have proceeded so far as this1 we have advanced to the verge of those speculations which have to do with mind as well as body4 ,the extension of our philosophy to such a field1 if it can be justly so extended1 will be one of the most important results of our researches2 but on that very account we must fully study the lessons which we learn in those fields of speculation where our doctrines are most secure1 before we venture into a region where our principles will appear to be more precarious1 and where they are inevitably less precise4 ,we now proceed to the examination of the above ,ideas1 and to such essays towards the philosophy of each ,science as this course of investigation may suggest4 #he ,,book ,,ii4 ,,the ,,philosophy ,,of ,,the ,,pure ,,sciences4 ,the way in which we are led to regard human knowledge is like the way in which ,copernicus was led to regard the heavens4 ,when the explanation of the celestial motions could not be made to go right so long as he assumed that all the host of stars turns round the spectator1 he tried whether it would not answer better if he made the spectator turn1 and left the stars at rest4 ,we may make a similar trial in ,metaphysics1 as to our way of looking at objects4 ,if our view of them must be governed altogether by the properties of the objects themselves1 ,i see not how man can know anything about them priori4 ,but if the thing1 as an object of the senses1 is regulated by the constitution of our power of knowing1 ,i can very readily represent to myself this possibility4 ,,kant1 ,kritik d4 ,r4 ,v4 ,pref4 #hg ,,book ,,ii4 ,,the ,,philosophy ,,of ,,the ,,pure ,,sciences4 ,the principal question discussed in the last ,book was this 7see chaps4 ,v4 and ,,vi473 ,how are necessary and universal truths possible8 ,and the answer then given was3 that the necessity and universality of truths are derived from the ,fundamental ,ideas which they involve4 ,and we proceed in this ,book to exemplify this doctrine in the case of the truths of ,geometry and ,arithmetic1 which derive their necessity and universality from the ,fundamental ,ideas of ,space1 and ,time1 or ,number4 ,the question thus examined is that which ,kant undertook to deal with in his celebrated work1 ,kritik der reinen ,vernunft 7,examination of the ,pure ,reason73 and our solution of the ,problem1 so far as the ,ideas of ,space and ,time are concerned1 agrees in the main with his4 ,the arguments contained in chapters ,,ii4 and 9999,,vii4 of this ,book1 are the leading arguments respecting ,space and ,time1 in ,kant's ,kritik4 ,kant1 however1 instead of calling ,space and ,time ,ideas1 calls them the necessary ,forms of our experience1 as ,i have stated in the text4 ,but though ,i have adopted ,kant's arguments as to ,space and ,time1 all that follows in the succeeding ,books1 with regard to other ,ideas1 has no resemblance to any doctrines of ,kant or his school 7with the exception1 perhaps1 of some of the views on the ,idea of ,cause74 ,the nature and character of the other ,scientific ,ideas which ,i have examined1 in the succeeding ,books1 have been established by an analysis of the history of the several ,sciences to which those ,ideas are essential1 and an examination of the writings of the principal discoverers in those ,sciences4 #hh ,,chapter ,i4 ,,of ,,the ,,pure ,,sciences4 #a4 ,,all external objects and events which we can contemplate are viewed as having relations of ,space1 ,time1 and ,number2 and are subject to the general conditions which these ,ideas impose1 as well as to the particular laws which belong to each class of objects and occurrences4 ,the special laws of nature1 considered under the various aspects which constitute the different sciences1 are obtained by a mixed reference to ,experience and to the ,fundamental ,ideas of each science4 ,but besides the sciences thus formed by the aid of special experience1 the conditions which flow from those more comprehensive ideas first mentioned1 ,space1 ,time1 and ,number1 constitute a body of science1 applicable to objects and changes of all kinds1 and deduced without recurrence being had to any observation in particular4 ,these sciences1 thus unfolded out of ideas alone1 unmixed with any reference to the phenomena of matter1 are hence termed ,pure ,sciences4 ,the principal sciences of this class are ,geometry1 ,theoretical ,arithmetic1 and ,algebra considered in its most general sense1 as the investigation of the relations of space and number by means of general symbols4 #b4 ,these ,pure ,sciences were not included in our survey of the history of the sciences1 because they are not inductive sciences4 ,their progress has not consisted in collecting laws from phenomena1 true theories from observed facts1 and more general from more limited laws2 but in tracing the consequences of the ideas themselves1 and in detecting the most general and intimate analogies and connexions which prevail #hi among such conceptions as are derivable from the ideas4 ,these sciences have no principles besides definitions and axioms1 and no process of proof but deduction2 this process1 however1 assuming here a most remarkable character2 and exhibiting a combination of simplicity and complexity1 of rigour and generality1 quite unparalleled in other subjects4 #c4 ,the universality of the truths1 and the rigour of the demonstrations of these pure sciences1 attracted attention in the earliest times2 and it was perceived that they offered an exercise and a discipline of the intellectual faculties1 in a form peculiarly free from admixture of extraneous elements4 ,they were strenuously cultivated by the ,greeks1 both with a view to such a discipline1 and from the love of speculative truth which prevailed among that people3 and the name mathematics1 by which they are designated1 indicates this their character of disciplinal studies4 #d4 ,as has already been said1 the ideas which these sciences involve extend to all the objects and changes which we observe in the external world2 and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature1 as ,astronomy1 ,optics1 and ,mechanics4 ,such sciences are hence often termed ,mixed ,mathematics1 the relations of space and number being1 in these branches of knowledge1 combined with principles collected from special observation2 while ,geometry1 ,algebra1 and the like subjects1 which involve no result of experience1 are called ,pure ,mathematics4 #e4 ,space1 time1 and number1 may be conceived as forms by which the knowledge derived from our sensations is moulded1 and which are independent of the differences in the matter of our knowledge1 arising from the sensations themselves4 ,hence the sciences which have these ideas for their subject may be termed ,formal ,sciences4 ,in this point of view1 they are distinguished from sciences in which1 besides these mere formal laws by which appearances are corrected1 we endeavour to apply to the phenomena the idea of cause1 #ij or some of the other ideas which penetrate further into the principles of nature4 ,we have thus1 in the ,history1 distinguished ,formal ,astronomy and ,formal ,optics from ,physical ,astronomy and ,physical ,optics4 ,we now proceed to our examination of the ,ideas which constitute the foundation of these formal or pure mathematical sciences1 beginning with the ,idea of ,space4 #ia ,,chapter ,,ii4 ,,of ,,the ,,idea ,,of ,,space4 #a4 ,,by speaking of space as an ,idea1 ,i intend to imply1 as has already been stated1 that the apprehension of objects as existing in space1 and of the relations of position1 c41 prevailing among them1 is not a consequence of experience1 but a result of a peculiar constitution and activity of the mind1 which is independent of all experience in its origin1 though constantly combined with experience in its exercise4 ,that the idea of space is thus independent of experience1 has already been pointed out in speaking of ideas in general3 but it may be useful to illustrate the doctrine further in this particular case4 ,i assert1 then1 that space is not a notion obtained by experience4 ,experience gives us information concerning things without us3 but our apprehending them as without us1 takes for granted their existence in space4 ,experience acquaints us what are the form1 position1 magnitude of particular objects3 but that they have form1 position1 magnitude1 presupposes that they are in space4 ,we cannot derive from appearances1 by the way of observation1 the habit of representing things to ourselves as in space2 for no single act of observation is possible any otherwise than by beginning with such a representation1 and conceiving objects as already existing in space4 #b4 ,that our mode of representing space to ourselves is not derived from experience1 is clear also from this3 that through this mode of representation we arrive at propositions which are rigorously universal and necessary4 ,propositions of such a kind could not possibly be obtained from experience2 for experience can #ib only teach us by a limited number of examples1 and therefore can never securely establish a universal proposition3 and again1 experience can only inform us that anything is so1 and can never prove that it must be so4 ,that two sides of a triangle are greater than the third is a universal and necessary geometrical truth3 it is true of all triangles2 it is true in such a way that the contrary cannot be conceived4 ,experience could not prove such a proposition4 ,and experience has not proved it2 for perhaps no man ever made the trial as a means of removing doubts3 and no trial could1 in fact1 add in the smallest degree to the certainty of this truth4 ,to seek for proof of geometrical propositions by an appeal to observation proves nothing in reality1 except that the person who has recourse to such grounds has no due apprehension of the nature of geometrical demonstration4 ,we have heard of persons who convinced themselves by measurement that the geometrical rule respecting the squares on the sides of a right-angled triangle was true3 but these were persons whose minds had been engrossed by practical habits1 and in whom the speculative development of the idea of space had been stifled by other employments4 ,the practical trial of the rule may illustrate1 but cannot prove it4 ,the rule will of course be confirmed by such trial1 because what is true in general is true in particular3 but the rule cannot be proved from any number of trials1 for no accumulation of particular cases makes up a universal case4 ,to all persons who can see the force of any proof1 the geometrical rule above referred to is as evident1 and its evidence as independent of experience1 as the assertion that sixteen and nine make twenty-five4 ,at the same time1 the truth of the geometrical rule is quite independent of numerical truths1 and results from the relations of space alone4 ,this could not be if our apprehension of the relations of space were the fruit of experience3 for experience has no element from which such truth and such proof could arise4 #c4 ,thus the existence of necessary truths1 such as those of geometry1 proves that the idea of space from #ic which they flow is not derived from experience4 ,such truths are inconceivable on the supposition of their being collected from observation2 for the impressions of sense include no evidence of necessity4 ,but we can readily understand the necessary character of such truths1 if we conceive that there are certain necessary conditions under which alone the mind receives the impressions of sense4 ,since these conditions reside in the constitution of the mind1 and apply to every perception of an object to which the mind can attain1 we easily see that their rules must include1 not only all that has been1 but all that can be1 matter of experience4 ,our sensations can each convey no information except about itself2 each can contain no trace of another additional sensation2 and thus no relation and connexion between two sensations can be given by the sensations themselves4 ,but the mode in which the mind perceives these impressions as objects1 may and will introduce necessary relations among them3 and thus by conceiving the idea of space to be a condition of perception in the mind1 we can conceive the existence of necessary truths1 which apply to all perceived objects4 #d4 ,if we consider the impressions of sense as the mere materials of our experience1 such materials may be accumulated in any quantity and in any order4 ,but if we suppose that this matter has a certain form given it1 in the act of being accepted by the mind1 we can understand how it is that these materials are subject to inevitable rules2--how nothing can be perceived exempt from the relations which belong to such a form4 ,and since there are such truths applicable to our experience1 and arising from the nature of space1 we may thus consider space as a form which the materials given by experience necessarily assume in the mind2 as an arrangement derived from the perceiving mind1 and not from the sensations alone4 #e4 ,thus this phrase1--that space is a form belonging to our perceptive power1--may be employed to express that we cannot perceive objects as in space1 without an operation of the mind as well as of the senses--without active as well as passive faculties4 ,this phrase1 however1 #id is not necessary to the exposition of our doctrines4 ,whether we call the conception of space a ,condition of perception1 a ,form of perception1 or an ,idea1 or by any other term1 it is something originally inherent in the mind perceiving1 and not in the objects perceived4 ,and it is because the apprehension of all objects is thus subjected to certain mental conditions1 forms or ideas1 that our knowledge involves certain inviolable relations and necessary truths4 ,the principles of such truths1 so far as they regard space1 are derived from the idea of space1 and we must endeavour to exhibit such principles in their general form4 ,but before we do this1 we may notice some of the conditions which belong1 not to our ,ideas in general1 but to this ,idea of ,space in particular4 #ie ,,chapter ,,iii4 ,,of ,,some ,,peculiarities ,,of ,,the ,,idea ,,of ,,space4 #a4 ,,some of the ,ideas which we shall have to examine involve conceptions of certain relations of objects1 as the idea of ,cause and of ,likeness2 and may appear to be suggested by experience1 enabling us to abstract this general relation from particular cases4 ,but it will be seen that ,space is not such a general conception of a relation4 ,for we do not speak of ,spaces as we speak of ,causes and ,likenesses1 but of ,space4 ,and when we speak of spaces1 we understand by the expression1 parts of one and the same identical everywhere-extended ,space4 ,we conceive a universal ,space2 which is not made up of these partial spaces as its component parts1 for it would remain if these were taken away2 and these cannot be conceived without presupposing absolute space4 ,absolute ,space is essentially one2 and the complication which exists in it1 and the conception of various spaces1 depends merely upon boundaries4 ,space must1 therefore1 be1 as we have said1 not a general conception abstracted from particulars1 but a universal mode of representation1 altogether independent of experience4 #b4 ,space is infinite4 ,we represent it to ourselves as an infinitely great magnitude4 ,such an idea as that of ,likeness or ,cause1 is1 no doubt1 found in an infinite number of particular cases1 and so far includes these cases4 ,but these ideas do not include an infinite number of cases as parts of an infinite whole4 ,when we say that all bodies and partial spaces exist in infinite space1 we use an expression which is not applied in the same sense to any cases except those of ,space and ,time4 #if #c4 ,what is here said may appear to be a denial of the real existence of space4 ,it must be observed1 however1 that we do not deny1 but distinctly assert1 the existence of space as a real and necessary condition of all objects perceived2 and that we not only allow that objects are seen external to us1 but we found upon the fact of their being so seen1 our view of the nature of space4 ,if1 however1 it be said that we deny the reality of space as an object or thing1 this is true4 ,nor does it appear easy to maintain that space exists as a thing1 when it is considered that this thing is infinite in all its dimensions2 and1 moreover1 that it is a thing1 which1 being nothing in itself1 exists only that other things may exist in it4 ,and those who maintain the real existence of space1 must also maintain the real existence of time in the same sense4 ,now two infinite things1 thus really existing1 and yet existing only as other things exist in them1 are notions so extravagant that we are driven to some other mode of explaining the state of the matter4 #d4 ,thus space is not an object of which we perceive the properties1 but a form of our perception2 not a thing which affects our senses1 but an idea to which we conform the impressions of sense4 ,and its peculiarities appear to depend upon this1 that it is not only a form of sensation1 but of intuition2 that in reference to space1 we not only perceive but contemplate objects4 ,we see objects in space1 side by side1 exterior to each other2 space1 and objects in so far as they occupy space1 have parts exterior to other parts2 and have the whole thus made up by the juxtaposition of parts4 ,this mode of apprehension belongs only to the ideas of space and time4 ,space and ,time are made up of parts1 but ,cause and ,likeness are not apprehended as made up of parts4 ,and the term intuition 7in its rigorous sense7 is applicable only to that mode of contemplation in which we thus look at objects as made up of parts1 and apprehend the relations of those parts at the same time and by the same act by which we apprehend the objects themselves4 #e4 ,as we have said1 space limited by boundaries #ig gives rise to various conceptions which we have often to consider4 ,thus limited1 space assumes form or figure2 and the variety of conceptions thus brought under our notice is infinite4 ,we have every possible form of line1 straight line1 and curve2 and of curves an endless number2--circles1 parabolas1 hyperbolas1 spirals1 helices4 ,we have plane surfaces of various shapes1--parallelograms1 polygons1 ellipses2 and we have solid figures1--cubes1 cones1 cylinders1 spheres1 spheroids1 and so on4 ,all these have their various properties1 depending on the relations of their boundaries2 and the investigation of their properties forms the business of the science of ,geometry4 #f4 ,space has three dimensions1 or directions in which it may be measured2 it cannot have more or fewer4 ,the simplest measurement is that of a straight line1 which has length alone4 ,a surface has both length and breadth3 and solid space has length1 breadth1 and thickness or depth4 ,the origin of such a difference of dimensions will be seen if we reflect that each portion of space has a boundary1 and is extended both in the direction in which its boundary extends1 and also in a direction from its boundary2 for otherwise it would not be a boundary4 ,a point has no dimensions4 ,a line has but one dimension1--the distance from its boundary1 or its length4 ,a plane1 bounded by a straight line1 has the dimension which belongs to this line1 and also has another dimension arising from the distance of its parts from this boundary line2 and this may be called breadth4 ,a solid1 bounded by a plane1 has the dimensions which this plane has2 and has also a third dimension1 which we may call height or depth1 as we consider the solid extended above or below the plane2 or thickness1 if we omit all consideration of up and down4 ,and no space can have any dimensions which are not resoluble into these three4 ,we may now proceed to consider the mode in which the idea of space is employed in the formation of ,geometry4 #ih ,,chapter ,,iv4 ,,of ,,the ,,definitions ,,and ,,axioms ,,which ,,relate ,,to ,,space4 #a4 ,,the relations of space have been apprehended with peculiar distinctness and clearness from the very first unfolding of man's speculative powers4 ,this was a consequence of the circumstance which we have just noticed1 that the simplest of these relations1 and those on which the others depend1 are seen by intuition4 ,hence1 as soon as men were led to speculate concerning the relations of space1 they assumed just principles1 and obtained true results4 ,it is said that the science of geometry had its origin in ,egypt1 before the dawn of the ,greek philosophy3 but the knowledge of the early ,egyptians 7exclusive of their mythology7 appears to have been purely practical2 and1 probably1 their geometry consisted only in some maxims of land-measuring1 which is what the term implies4 ,the ,greeks of the time of ,plato1 had1 however1 not only possessed themselves of many of the most remarkable elementary theorems of the science2 but had1 in several instances1 reached the boundary of the science in its elementary form2 as when they proposed to themselves the problems of doubling the cube and squaring the circle4 ,but the deduction of these theorems by a systematic process1 and the primary exhibition of the simplest principles involved in the idea of space1 which such a deduction requires1 did not take place1 so far as we are aware1 till a period somewhat later4 ,the ,elements of ,geometry of ,euclid1 in which this task was performed1 are to this day the standard work on the subject3 the author of this work taught mathematics with great applause at ,alexandria1 in the reign of ,ptolemy ,lagus1 #ii about #bhj years before ,christ4 ,the principles which ,euclid makes the basis of his system have been very little simplified since his time2 and all the essays and controversies which bear upon these principles1 have had a reference to the form in which they are stated by him4 #b4 ,definitions4--,the first principles of ,euclid's geometry are1 as the first principles of any system of geometry must be1 definitions and axioms respecting the various ideal conceptions which he introduces2 as straight lines1 parallel lines1 angles1 circles1 and the like4 ,but it is to be observed that these definitions and axioms are very far from being arbitrary hypotheses and assumptions4 ,they have their origin in the idea of space1 and are merely modes of exhibiting that idea in such a manner as to make it afford grounds of deductive reasoning4 ,the axioms are necessary consequences of the conceptions respecting which they are asserted2 and the definitions are no less necessary limitations of conceptions2 not requisite in order to arrive at this or that consequence2 but necessary in order that it may be possible to draw any consequences1 and to establish any general truths4 ,for example1 if we rest the end of one straight staff upon the middle of another straight staff1 and move the first staff into various positions1 we1 by so doing1 alter the angles which the first staff makes with the other to the right hand and to the left4 ,but if we place the staff in that special position in which these two angles are equal1 each of them is a right angle1 according to ,euclid2 and this is the definition of a right angle1 except that ,euclid employs the abstract conception of straight lines1 instead of speaking1 as we have done1 of staves4 ,but this selection of the case in which the two angles are equal is not a mere act of caprice2 as it might have been if he had selected a case in which these angles are unequal in any proportion4 ,for the consequences which can be drawn concerning the cases of unequal angles1 do not lead to general truths1 without some reference to that peculiar case in which the angles are equal3 and thus it becomes necessary to #ajj single out and define that special case1 marking it by a special phrase4 ,and this definition not only gives complete and distinct knowledge what a right angle is1 to any one who can form the conception of an angle in general2 but also supplies a principle from which all the properties of right angles may be deduced4 #c4 ,axioms4--,with regard to other conceptions also1 as circles1 squares1 and the like1 it is possible to lay down definitions which are a sufficient basis for our reasoning1 so far as such figures are concerned4 ,but1 besides these definitions1 it has been found necessary to introduce certain axioms among the fundamental principles of geometry4 ,these are of the simplest character2 for instance1 that two straight lines cannot cut each other in more than one point1 and an axiom concerning parallel lines4 ,like the definitions1 these axioms flow from the ,idea of ,space1 and present that idea under various aspects4 ,they are different from the definitions2 nor can the definitions be made to take the place of the axioms in the reasoning by which elementary geometrical properties are established4 ,for example1 the definition of parallel straight lines is1 that they are such as1 however far continued1 can never meet3 but1 in order to reason concerning such lines1 we must further adopt some axiom respecting them3 for example1 we may very conveniently take this axiom2 that two straight lines which cut one another are not both of them parallel to a third straight line#ab4 ,the definition and the axiom are seen to be inseparably connected by our intuition of the properties of space2 but the axiom cannot be proved from the definition1 by any rigorous deductive demonstration4 ,and if we were to take any other definition of two parallel straight lines1 7as that they are both perpendicular to a third straight line17 we should still1 at some point or other of our progress1 fall in with the same difficulty of demonstratively establishing their properties without some further assumption4 ,note #ab3 ,this axiom is simpler and more convenient than that of ,euclid4 ,it is employed by the late ,professor ,playfair in his ,geometry4 #aja #d4 ,thus the elementary properties of figures1 which are the basis of our geometry1 are necessary results of our ,idea of ,space2 and are connected with each other by the nature of that idea1 and not merely by our hypotheses and constructions4 ,definitions and axioms must be combined1 in order to express this idea so far as the purposes of demonstrative reasoning require4 ,these verbal enunciations of the results of the idea cannot be made to depend on each other by logical consequence2 but have a mutual dependence of a more intimate kind1 which words cannot fully convey4 ,it is not possible to resolve these truths into certain hypotheses1 of which all the rest shall be the necessary logical consequence4 ,the necessity is not hypothetical1 but intuitive4 ,the axioms require not to be granted1 but to be seen4 ,if any one were to assent to them without seeing them to be true1 his assent would be of no avail for purposes of reasoning3 for he would be also unable to see in what cases they might be applied4 ,the clear possession of the ,idea of ,space is the first requisite for all geometrical reasoning2 and this clearness of idea may be tested by examining whether the axioms offer themselves to the mind as evident4 #e4 ,the necessity of ideas added to sensations1 in order to produce knowledge1 has often been overlooked or denied in modern times4 ,the ground of necessary truth which ideas supply being thus lost1 it was conceived that there still remained a ground of necessity in definitions2--that we might have necessary truths1 by asserting especially what the definition implicitly involved in general4 ,it was held1 also1 that this was the case in geometry3--that all the properties of a circle1 for instance1 were implicitly contained in the definition of a circle4 ,that this alone is not the ground of the necessity of the truths which regard the circle1--that we could not in this way unfold a definition into proportions1 without possessing an intuition of the relations to which the definition led1--has already been shown4 ,but the insufficiency of the above account of the grounds of necessary geometrical truth appeared in another way also4 ,it was found impossible to lay #ajb down a system of definitions out of which alone the whole of geometrical truth could be evolved4 ,it was found that axioms could not be superseded4 ,no definition of a straight line could be given which rendered the axiom concerning straight lines superfluous4 ,and thus it appeared that the source of geometrical truths was not definition alone2 and we find in this result a confirmation of the doctrine which we are here urging1 that this source of truth is to be found in the form or conditions of our perception2--in the idea which we unavoidably combine with the impressions of sense2--in the activity1 and not in the passivity of the mind#bb4 ,note #bb3 ,i formerly stated views similar to these in some ',remarks' appended to a work which ,i termed ,the ,mechanical ,euclid1 published in #ahcg4 ,these ,remarks1 so far as they bear upon the question here discussed1 were noticed and controverted in ,no4 #ace of the ,edinburgh ,review4 ,as an examination of the reviewer's objections may serve further to illustrate the subject1 ,i shall annex to this chapter an answer to the article to which ,i have referred4 #f4 ,this will appear further when we come to consider the mode in which we exercise our observation upon the relations of space4 ,but we may1 in the first place1 make a remark which tends to show the connexion between our conception of a straight line1 and the axiom which is made the foundation of our reasonings concerning space4 ,the axiom is this2--that two straight lines1 which have both their ends joined1 cannot have the intervening parts separated so as to inclose a space4 ,the necessity of this axiom is of exactly the same kind as the necessity of the definition of a right angle1 of which we have already spoken4 ,for as the line standing on another makes right angles when it makes the angles on the two sides of it equal2 so a line is a straight line when it makes the two portions of space1 on the two sides of it1 similar4 ,and as there is only a single position of the line first mentioned1 which can make the angles equal1 so there is only a single form of a line which can make the spaces near the line similar on one side and on the other3 and #ajc therefore there cannot be two straight lines1 such as the axiom describes1 which1 between the same limits1 give two different boundaries to space thus separated4 ,and thus we see a reason for the axiom4 ,perhaps this view may be further elucidated if we take a leaf of paper1 double it1 and crease the folded edge4 ,we shall thus obtain a straight line at the folded edge2 and this line divides the surface of the paper1 as it was originally spread out1 into two similar spaces4 ,and that these spaces are similar so far as the fold which separates them is concerned1 appears from this2--that these two parts coincide when the paper is doubled4 ,and thus a fold in a sheet of paper at the same time illustrates the definition of a straight line according to the above view1 and confirms the axiom that two such lines cannot inclose a space4 ,if the separation of the two parts of space were made by any other than a straight line2 if1 for instance1 the paper were cut by a concave line2 then1 on turning one of the parts over1 it is easy to see that the edge of one part being concave one way1 and the edge of the other part concave the other way1 these two lines would enclose a space4 ,and each of them would divide the whole space into two portions which were not similar2 for one portion would have a concave edge1 and the other a convex edge4 ,between any two points1 there might be innumerable lines drawn1 some1 convex one way1 and some1 convex the other way2 but the straight line is the line which is not convex either one way or the other2 it is the single medium standard from which the others may deviate in opposite directions4 ,such considerations as these show sufficiently that the singleness of the straight line which connects any two points is a result of our fundamental conceptions of space4 ,but yet the above conceptions of the similar form of the two parts of space on the two sides of a line1 and of the form of a line which is intermediate among all other forms1 are of so vague a nature1 that they cannot fitly be made the basis of our elementary geometry2 and they are far more conveniently replaced1 as they have been in almost all treatises of #ajd geometry1 by the axiom1 that two straight lines cannot inclose a space4 #g4 ,but we may remark that1 in what precedes1 we have considered space only under one of its aspects3--as a plane4 ,the sheet of paper which we assumed in order to illustrate the nature of a straight line1 was supposed to be perfectly plane or flat3 for otherwise1 by folding it1 we might obtain a line not straight4 ,now this assumption of a plane appears to take for granted that very conception of a straight line which the sheet was employed to illustrate2 for the definition of a plane given in the ,elements of ,geometry is1 that it is a surface on which lie all straight lines drawn from one point of the surface to another4 ,and thus the explanation above given of the nature of a straight line1--that it divides a plane space into similar portions on each side1--appears to be imperfect or nugatory4 ,to this we reply1 that the explanation must be rendered complete and valid by deriving the conception of a plane from considerations of the same kind as those which we employed for a straight line4 ,any portion of solid space may be divided into two portions by surfaces passing through any given line or boundaries4 ,and these surfaces may be convex either on one side or on the other1 and they admit of innumerable changes from being convex on one side to being convex on the other in any degree4 ,so long as the surface is convex either way1 the two portions of space which it separates are not similar1 one having a convex and the other a concave boundary4 ,but there is a certain intermediate position of the surface1 in which position the two portions of space which it divides have their boundaries exactly similar4 ,in this position1 the surface is neither convex nor concave1 but plane4 ,and thus a plane surface is determined by this condition--of its being that single surface which is the intermediate form among all convex and concave surfaces by which solid space can be divided1--and of its separating such space into two portions1 of which the boundaries1 though they are the same surface in two opposite positions1 are exactly similar4 #aje ,thus a plane is the simplest and most symmetrical boundary by which a solid can be divided2 and a straight line is the simplest and most symmetrical boundary by which a plane can be separated4 ,these conceptions are obtained by considering the boundaries of an interminable space1 capable of imaginary division in every direction4 ,and as a limited space may be separated into two parts by a plane1 and a plane again separated into two parts by a straight line1 so a line is divided into two portions by a point1 which is the common boundary of the two portions2 the end of the one and the beginning of the other portion having itself no magnitude1 form1 or parts4 #h4 ,the geometrical properties of planes and solids are deducible from the first principles of the ,elements1 without any new axioms2 the definition of a plane above quoted1--that all straight lines joining its points lie in the plane1--being a sufficient basis for all reasoning upon these subjects4 ,and thus1 the views which we have presented of the nature of space being verbally expressed by means of certain definitions and axioms1 become the groundwork of a long series of deductive reasoning1 by which is established a very large and curious collection of truths1 namely1 the whole science of ,elementary ,plane and ,solid ,geometry4 ,this science is one of indispensable use and constant reference1 for every student of the laws of nature2 for the relations of space and number are the alphabet in which those laws are written4 ,but besides the interest and importance of this kind which geometry possesses1 it has a great and peculiar value for all who wish to understand the foundations of human knowledge1 and the methods by which it is acquired4 ,for the student of geometry acquires1 with a degree of insight and clearness which the unmathematical reader can but feebly imagine1 a conviction that there are necessary truths1 many of them of a very complex and striking character2 and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend1 may1 by systematic deduction1 lead to the most remote and unexpected results4 #ajf ,in pursuing such philosophical researches as that in which we are now engaged1 it is of great advantage to the speculator to have cultivated to some extent the study of geometry2 since by this study he may become fully aware of such features in human knowledge as those which we have mentioned4 ,by the aid of the lesson thus learned from the contemplation of geometrical truths1 we have been endeavouriug to establish those further doctrines2--that these truths are but different aspects of the same ,fundamental ,idea1 and that the grounds of the necessity which these truths possess reside in the ,idea from which they flow1 this ,idea not being a derivative result of experience1 but its primary rule4 ,when the reader has obtained a clear and satisfactory view of these doctrines1 so far as they are applicable to our knowledge concerning space1 he has1 we may trust1 overcome the main difficulty which will occur in following the course of the speculations now presented to him4 ,he is then prepared to go forwards with us2 to see over how wide a field the same doctrines are applicable3 and how rich and various a harvest of knowledge springs from these seemingly scanty principles4 ,but before we quit the subject now under our consideration1 we shall endeavour to answer some objections which have been made to the views here presented2 and shall attempt to illustrate further the active powers which we have ascribed to the mind4 #ajg ,,chapter ,v4 ,,of ,,some ,,objections ,,which ,,have ,,been ,,made ,,to ,,the ,,doctrines ,,stated ,,in ,,the ,,previous ,,chapter4#cb ,note #cb3 ,in order to render the present chapter more intelligible1 it may be proper to state briefly the arguments which gave occasion to the review4 ,after noticing ,stewart's assertions1 that the certainty of mathematical reasoning arises from its depending upon definitions1 and that mathematical truth is hypothetical2 ,i urged1--that no one has yet been able to construct a system of mathematical truths by the aid of definitions alone2 that a definition would not be admissible or applicable except it agreed with a distinct conception in the mind2 that the definitions which we employ in mathematics are not arbitrary or hypothetical1 but necessary definitions2 that if ,stewart had taken as his examples of axioms the peculiar geometrical axioms1 his assertions would have been obviously erroneous2 and that the real foundation of the truths of mathematics is the ,idea of ,space1 which may be expressed 7for purposes of demonstration7 partly by definitions and partly by axioms4 ,,the ,edinburgh ,review1 ,no4 cxxxv41 contains a critique on a work termed ,the ,mechanical ,euclid1 in which opinions were delivered to nearly the same effect as some of those stated in the last chapter1 and hereafter in ,chapter xi4 ,although ,i believe that there are no arguments used by the reviewer to which the answers will not suggest themselves in the mind of any one who has read with attention what has been said in the preceding chapters 7except1 perhaps1 one or two remarks which have reference to mechanical ideas71 it may serve to illustrate the subject if ,i reply to the objections directly1 taking them as the reviewer has stated them4 ,i4 ,i had dissented from ,stewart's assertion that mathematical truth is hypothetical1 or depends upon arbitrary definitions2 since we understand by an #ajh hypothesis a supposition1 not only which we may make1 but may abstain from making1 or may replace by a different supposition2 whereas the definitions and hypotheses of geometry are necessarily such as they are1 and cannot be altered or excluded4 ,the reviewer 7p4 #hd7 informs us that he understands ,stewart1 when he speaks of hypotheses and definitions being the foundation of geometry1 to speak of the hypothesis that real objects correspond to our geometrical definitions4 ',if a crystal be an exact hexahedron1 the geometrical properties of the hexahedron may be predicated of that crystal4' ,to this ,i reply1--that such hypotheses as this are the grounds of our applications of geometrical truths to real objects1 but can in no way be said to be the foundation of the truths themselves2--that ,i do not think that the sense which the reviewer gives was ,stewart's meaning2--but that if it was1 this view of the use of mathematics does not at all affect the question which both he and ,i proposed to discuss1 which was1 the ground of mathematical certainty4 ,i may add1 that whether a crystal be an exact hexahedron1 is a matter of observation and measurement1 not of definition4 ,i think the reader can have no difficulty in seeing how little my doctrine is affected by the connexion on which the reviewer thus insists4 ,i have asserted that the proposition which affirms the square on the diagonal of a rectangle to be equal to the squares on two sides1 does not rest upon arbitrary hypotheses2 the objector answers1 that the proposition that the square on the diagonal of this page is equal to the squares on the sides1 depends upon the arbitrary hypothesis that the page is a rectangle4 ,even if this fact were a matter of arbitrary hypothesis1 what could it have to do with the general geometrical proposition8 ,how could a single fact1 observed or hypothetical1 affect a universal and necessary truth1 which would be equally true if the fact were false8 ,if there be nothing arbitrary or hypothetical in geometry till we come to such steps in its application1 it is plain that the truths themselves are not hypothetical2 which is the question for us to decide4 #aji #b4 ,the reviewer then 7p4 #he7 considers the doctrine that axioms as well as definitions are the foundations of geometry2 and here he strangely narrows and confuses the discussion by making himself the advocate of ,stewart1 instead of arguing the question itself4 ,i had asserted that some axioms are necessary as the foundations of mathematical reasoning1 in addition to the definitions4 ,if ,stewart did not intend to discuss this question1 ,i had no concern with what he had said about axioms4 ,but ,i had every reason to believe that this was the question which ,stewart did intend to discuss4 ,i conceive there is no doubt that he intended to give an opinion upon the grounds of mathematical reasoning in general4 ,for he begins his discussions 7,elements1 vol4 ii4 p4 #ch7 by contesting ,reid's opinion on this subject1 which is stated generally2 and he refers again to the same subject1 asserting in general terms1 that the first principles of mathematics are not axioms but definitions4 ,if1 then1 afterwards1 he made his proof narrower than his assertion2--if having declared that no axioms are necessary1 he afterwards limited himself to showing that seven out of twelve of ,euclid's axioms are barren truisms1 it was no concern of mine to contest this assertion1 which left my thesis untouched4 ,i had asserted that the proper geometrical axioms 7that two straight lines cannot inclose a space1 and the axiom about parallel lines7 are indispensable in geometry4 ,what account the reviewer gives of these axioms we shall soon see2 but if ,stewart allowed them to be axioms necessary to geometrical reasoning1 he overturned his own assertion as to the foundations of such reasoning2 and if he said nothing decisive about these axioms1 which are the points on which the battle must turn1 he left his assertion altogether unproved2 nor was it necessary for me to pursue the war into a barren and unimportant corner1 when the metropolis was surrendered4 ,the reviewer's exultation that ,i have not contested the first seven axioms is an amusing example of the self-complacent zeal of advocacy4 #c4 ,but let us turn to the material point1--the proper geometrical axioms4 ,what is the reviewer's account of #aaj these8 ,which side of the alternative does he adopt8 ,do they depend upon the definitions1 and is he prepared to show the dependence8 ,or are they superfluous1 and can he erect the structure of geometry without their aid8 ,one of these two courses1 it would seem1 he must take4 ,for we both begin by asserting the excellence of geometry as an example of demonstrated truth4 ,it is precisely this attribute which gives an interest to our present inquiry4 ,how1 then1 does the reviewer explain this excellence on his views8 ,how does he reckon the foundation courses of the edifice which we agree in considering as a perfect example of intellectual building8 ,i presume ,i may take1 as his answer to this question1 his hypothetical statement of what ,stewart would have said 7p4 #hg71 on the supposition that there had been1 among the foundations of geometry1 self-evident indemonstrable truths3 although it is certainly strange that the reviewer should not venture to make up his mind as to the truth or falsehood of this supposition4 ,if there were such truths they would be1 he says1 'legitimate filiations' of the definitions4 ,they would be involved in the definitions4 ,and again he speaks of the foundation of the geometrical doctrine of parallels as a flaw1 and as a truth which requires1 but has not received demonstration4 ,and yet again1 he tells us that each of these supposed axioms 7,euclid's twelfth1 for instance7 is 'merely an indication of the point at which geometry fails to perform that which it undertakes to perform' 7p4 #ia72 and that in reality her truths are not yet demonstrated4 ,the amount of this is1 that the geometrical axioms are to be held to be legitimate filiations of the definitions1 because though certainly true1 they cannot be proved from the definitions2 that they are involved in the definitions1 although they cannot be evolved out of them2 and that rather than admit that they have any other origin than the definitions1 we are to proclaim that geometry has failed to perform what she undertakes to perform4 ,to this ,i reply--that ,i cannot understand what is meant by 'legitimate filiations' of principles1 if the #aaa phrase do not mean consequences of such principles established by rigorous and formal demonstrations2--that the reviewer1 if he claims any real signification for his phrase1 must substantiate the meaning of it by such a demonstration2 he must establish his 'legitimate filiation' by a genealogical table in a satisfactory form4 ,when this cannot be done1 to assert1 notwithstanding1 that the propositions are involved in the definitions1 is a mere begging the question2 and to excuse this defect by saying that geometry fails to perform what she has promised1 is to calumniate the character of that science which we profess to make our standard1 rather than abandon an arbitrary and unproved assertion respecting the real grounds of her excellence4 ,i add1 further1 that if the doctrine of parallel lines1 or any other geometrical doctrine of which we see the truth1 with the most perfect insight of its necessity1 have not hitherto received demonstration to the satisfaction of any school of reasoners1 the defect must arise from their erroneous views of the nature of demonstrations1 and the grounds of mathematical certainty4 #d4 ,i conceive1 then1 that the reviewer has failed altogether to disprove the doctrine that the axioms of geometry are necessary as a part of the foundations of the science4 ,i had asserted further that these axioms supply what the definitions leave deficient2 and that they1 along with definitions1 serve to present the idea of space under such aspects that we can reason logically concerning it4 ,to this the reviewer opposes 7p4 #if7 the common opinion that a perfect definition is a complete explanation of a name1 and that the test of its perfection is1 that we may substitute the definition for the name wherever it occurs4 ,i reply1 that my doctrine1 that a definition expresses a part1 but not the whole1 of the essential characters of an idea1 is certainly at variance with an opinion sometimes maintained1 that a definition merely explains a word1 and should explain it so fully that it may always replace it4 ,the error of this common opinion may1 ,i think1 be shown from considerations such as these2--that if #aab we undertake to explain one word by several1 we may be called upon1 on the same ground1 to explain each of these several by others1 and that in this way we can reach no limit nor resting-place2--that in point of fact1 it is not found to lead to clearness1 but to obscurity1 when in the discussion of general principles1 we thus substitute definitions for single terms2--that even if this be done1 we cannot reason without conceiving what the terms mean2--and that1 in doing this1 the relations of our conceptions1 and not the arbitrary equivalence of two forms of expression1 are the foundations of our reasoning4 #e4 ,the reviewer conceives that some of the so-called axioms are really definitions4 ,the axiom1 that 'magnitudes which coincide with each other1 that is1 which fill the same space1 are equal1' is a definition of geometrical equality3 the axiom1 that 'the whole is greater than its part1' is a definition of whole and part4 ,but surely there are very serious objections to this view4 ,it would seem more natural to say1 if the former axiom is a definition of the word equal1 that the latter is a definition of the word greater4 ,and how can one short phrase define two terms8 ,if ,i say1 'the heat of summer is greater than the heat of winter1' does this assertion define anything1 though the proposition is perfectly intelligible and distinct8 ,i think1 then1 that this attempt to reduce these axioms to definitions is quite untenable4 #f4 ,i have stated that a definition can be of no use1 except we can conceive the possibility and truth of the property connected with it2 and that if we do conceive this1 we may rightly begin our reasonings by stating the property as an axiom2 which ,euclid does1 in the case of straight lines and of parallels4 ,the reviewer inquires 7p4 #ib71 whether ,i am prepared to extend this doctrine to the case of circles1 for which the reasoning is usually rested upon the definition2--whether ,i would replace this definition by an axiom1 asserting the possibility of such a circle4 ,to this ,i might reply1 that it is not at all incumbent upon me to assent to such a change2 for ,i have all along stated that it is indifferent #aac whether the fundamental properties from which we reason be exhibited as definitions or as axioms1 provided the necessity be clearly seen4 ,but ,i am ready to declare that ,i think the form of our geometry would be not at all the worse1 if1 instead of the usual definition of a circle1--'that it is a figure contained by one line1 which is called the circumference1 and which is such1 that all straight lines drawn from a certain point within the circumference are equal to one another1'--we were to substitute an axiom and a definition1 as follows3-- ,axiom4 ,if a line be drawn so as to be at every point equally distant from a certain point1 this line will return into itself or will be one line including a space4 ,definition4 ,the space is called a circle1 the line the circumference1 and the point the center4 ,and this being done1 it would be true1 as the reviewer remarks1 that geometry cannot stir one step without resting on an axiom4 ,and ,i do not at all hesitate to say1 that the above axiom1 expressed or understood1 is no less necessary than the definition1 and is tacitly assumed in every proposition into which circles enter4 #g4 ,i have1 ,i think1 now disposed of the principal objections which bear upon the proper axioms of geometry4 ,the principles which are stated as the first seven axioms of ,euclid's ,elements1 need not1 as ,i have said1 be here discussed4 ,they are principles which refer1 not to ,space in particular1 but to ,quantity in general3 such1 for instance1 as these2 ',if equals be added to equals the wholes are equal2'--',if equals be taken from equals the remainders are equal4' ,but ,i will make an observation or two upon them before ,i proceed4 ,both ,locke and ,stewart have spoken of these axioms as barren truisms3 as propositions from which it is not possible to deduce a single inference3 and the reviewer asserts that they are not first principles1 but laws of thought 7p4 #hh74 ,to this last expression ,i am #aad willing to assent2 but ,i would add1 that not only these1 but all the principles which express the fundamental conditions of our knowledge1 may with equal propriety be termed laws of thought2 for these principles depend upon our ideas1 and regulate the active operations of the mind1 by which coherence and connexion are given to its passive impressions4 ,but the assertion that no conclusions can be drawn from simple axioms1 or laws of human thought1 which regard quantity1 is by no means true4 ,the whole of arithmetic1--for instance1 the rules for the multiplication and division of large numbers1 the rule for finding a common measure1 and1 in short1 a vast body of theory respecting numbers1--rests upon no other foundation than such axioms as have been just noticed1 that if equals be added to equals the wholes will be equal4 ,and even when ,locke's assertion1 that from these axioms no truths can be deduced1 is modified by ,stewart and the reviewer1 and limited to geometrical truths1 it is hardly tenable 7although1 in fact1 it matters little to our argument whether it is or no74 ,for the greater part of the ,seventh ,book of ,euclid's ,elements1 7on ,commensurable and ,incommensurable ,quantities17 and the ,fifth ,book1 7on ,proportion17 depend upon these axioms1 with the addition only of the definition or axiom 7for it may be stated either way7 which expresses the idea of proportionality in numbers4 ,so that the attempt to disprove the necessity and use of axioms1 as principles of reasoning1 fails even when we take those instances which the opponents consider as the more manifestly favourable to their doctrine4 #h4 ,but perhaps the question may have already suggested itself to the reader's mind1 of what use can it be formally to state such principles as these1 7for example1 that if equals be added to equals the wholes are equal17 since1 whether stated or no1 they will be assumed in our reasoning8 ,and how can such principles be said to be necessary1 when our proof proceeds equally well without any reference to them8 ,and the answer is1 that it is precisely because these are the #aae common principles of reasoning1 which we naturally employ without specially contemplating them1 that they require to be separated from the other steps and formally stated1 when we analyse the demonstrations which we have obtained4 ,in every mental process many principles are combined and abbreviated1 and thus in some measure concealed and obscured4 ,in analysing these processes1 the combination must be resolved1 and the abbreviation expanded1 and thus the appearance is presented of a pedantic and superfluous formality4 ,but that which is superfluous for proof1 is necessary for the analysis of proof4 ,in order to exhibit the conditions of demonstration distinctly1 they must be exhibited formally4 ,in the same manner1 in demonstration we do not usually express every step in the form of a syllogism1 but we see the grounds of the conclusiveness of a demonstration1 by resolving it into syllogisms4 ,neither axioms nor syllogisms are necessary for conviction2 but they are necessary to display the conditions under which conviction becomes inevitable4 ,the application of a single one of the axioms just spoken of is so minute a step in the proof1 that it appears pedantic to give it a marked place2 but the very essence of demonstration consists in this1 that it is composed of an indissoluble succession of such minute steps4 ,the admirable circumstance is1 that by the accumulation of such apparently imperceptible advances1 we can in the end make so vast and so sure a progress4 ,the completeness of the analysis of our knowledge appears in the smallness of the elements into which it is thus resolved4 ,the minuteness of any of these elements of truth1 of axioms for instance1 does not prevent their being as essential as others which are more obvious4 ,and any attempt to assume one kind of element only1 when the course of our analysis brings before us two or more kinds1 is altogether unphilosophical4 ,axioms and definitions are the proximate constituent principles of our demonstrations2 and the intimate bond which connects together a definition and an axiom on the same subject is not truly expressed #aaf by asserting the latter to be derived from the former4 ,this bond of connexion exists in the mind of the reasoner1 in his conception of that to which both definition and axiom refer1 and consequently in the general ,fundamental ,idea of which that conception is a modification4 #aag ,,chapter ,,vi4 ,,of ,,the ,,perception ,,of ,,space4 #a4 ,,according to the views above explained1 certain of the impressions of our senses convey to us the perception of objects as existing in space2 inasmuch as by the constitution of our minds we cannot receive those impressions otherwise than in a certain form1 involving such a manner of existence4 ,but the question deserves to be asked1 ,what are the impressions of sense by which we thus become acquainted with space and its relations8 ,and as we have seen that this idea of space implies an act of the mind as well as an impression on the sense1 what manifestations do we find of this activity of the mind1 in our observation of the external world8 ,it is evident that sight and touch are the senses by which the relations of space are perceived1 principally or entirely4 ,it does not appear that an odour1 or a feeling of warmth or cold1 would1 independently of experience1 suggest to us the conception of a space surrounding us4 ,but when we see objects1 we see that they are extended and occupy space2 when we touch them1 we feel that they are in a space in which we also are4 ,we have before our eyes any object1 for instance1 a board covered with geometrical diagrams2 and we distinctly perceive1 by vision1 those lines of which the relations are the subjects of our mathematical reasoning4 ,again1 we see before us a solid object1 a cubical box for instance2 we see that it is within reach2 we stretch out the hand and perceive by the touch that it has sides1 edges1 corners1 which we had already perceived by vision4 #aah #b4 ,probably most persons do not generally apprehend that there is any material difference in these two cases2--that there are any different acts of mind concerned in perceiving by sight a mathematical diagram upon paper1 and a solid cube lying on a table4 ,yet it is not difficult to show that1 in the latter case at least1 the perception of the shape of the object is not immediate4 ,a very little attention teaches us that there is an act of judgment as well as a mere impression of sense requisite1 in order that we may see any solid object4 ,for there is no visible appearance which is inseparably connected with solidity4 ,if a picture of a cube be rightly drawn1 in perspective and skilfully shaded1 the impression upon the sense is the same as if it were a real cube4 ,the picture may be mistaken for a solid object4 ,but it is clear that1 in this case1 the solidity is given to the object by an act of mental judgment4 ,all that is seen is outline and shade1 figures and colours on a flat board4 ,the solid angles and edges1 the relation of the faces of the figure by which they form a cube1 are matters of inference4 ,this1 which is evident in the case of the pictured cube1 is true in all vision whatever4 ,we see a scene before us on which are various figures and colours1 but the eye cannot see more4 ,it sees length and breadth1 but no third dimension4 ,in order to know that there are solids1 we must infer as well as see4 ,and this we do readily and constantly2 so familiarly1 indeed1 that we do not perceive the operation4 ,yet we may detect this latent process in many ways2 for instance1 by attending to cases in which the habit of drawing such inferences misleads us4 ,most persons have experienced this delusion in looking at a scene in a theatre1 and especially that kind of scene which is called a diorama1 when the interior of a building is represented4 ,in these cases1 the perspective representations of the various members of the architecture and decoration impress us almost irresistibly with the conviction that we have before us a space of great extent and complex form1 instead of a flat painted canvass4 ,here1 at least1 the space is our own creation2 but yet here1 it is #aai manifestly created by the same act of thought as if we were really in the palace or the cathedral of which the halls and aisles thus seem to inclose us4 ,and the act by which we thus create space of three dimensions out of visible extent of length and breadth1 is constantly and imperceptibly going on4 ,we are perpetually interpreting in this manner the language of the visible world4 ,from the appearances of things which we directly see1 we are constantly inferring that which we cannot directly see1--their distance from us1 and the position of their parts4 #c4 ,the characters which we thus interpret are various4 ,they are1 for instance1 the visible forms1 colours1 and shades of the parts1 understood according to the maxims of perspective2 7for of perspective every one has a practical knowledge1 as every one has of grammar27 the effort by which we fix both our eyes on the same object1 and adjust each eye to distinct vision2 and the like4 ,the right interpretation of the information which such circumstances give us respecting the true forms and distances of things1 is gradually learned2 the lesson being begun in our earliest infancy1 and inculcated upon us every hour during which we use our eyes4 ,the completeness with which the lesson is mastered is truly admirable2 for we forget that our conclusion is obtained indirectly1 and mistake a judgment on evidence for an intuitive perception4 ,we see the breadth of the street1 as clearly and readily as we see the house on the other side of it2 and we see the house to be square1 however obliquely it be presented to us4 ,this1 however1 by no means throws any doubt or difficulty on the doctrine that in all these cases we do interpret and infer4 ,the rapidity of the process1 and the unconsciousness of the effort1 are not more remarkable in this case than they are when we understand the meaning of the speech which we hear1 or of the book which we read4 ,in these latter cases we merely hear noises or see black marks2 but we make1 out of these elements1 thought and feeling1 without being aware of the act by which we do so4 ,and by an exactly similar process we see a variously-coloured #abj expanse1 and collect from it a space occupied by solid objects4 ,in both cases the act of interpretation is become so habitual that we can hardly stop short at the mere impression of sense4 #d4 ,but yet there are various ways in which we may satisfy ourselves that these two parts of the process of seeing objects are distinct4 ,to separate these operations is precisely the task which the artist has to execute1 in making a drawing of what he sees4 ,he has to recover the consciousness of his real and genuine sensations1 and to discern the lines of objects as they appear4 ,this at first he finds difficult2 for he is tempted to draw what he knows of the forms of visible objects1 and not what he sees3 but as he improves in his art1 he learns to put on paper what he sees only1 separated from what he infers1 in order that thus the inference1 and with it a conception like that of the reality1 may be left to the spectator4 ,and thus the natural process of vision is the habit of seeing that which cannot be seen2 and the difficulty of the art of drawing consists in learning not to see more than is visible4 #e4 ,but again2 even in the simplest drawing we exhibit something which we do not see4 ,however slight is our representation of objects1 it contains something which we create for ourselves4 ,for we draw an outline4 ,now an outline has no existence in nature4 ,there are no visible lines presented to the eye by a group of figures4 ,we separate each figure from the rest1 and the boundary by which we do this is the outline of the figure2 and the like may be said of each member of every figure4 ,a painter of our own times has made this remark in a work upon his art#db3 ',the effect which natural objects produce upon our sense of vision is that of a number of parts1 or distinct masses of form and colour1 and not of lines4 ,but when we endeavour to represent by painting the objects which are before us1 or which invention supplies to our minds1 #aba the first and the simplest means we resort to is this picture1 by which we separate the form of each object from those that surround it1 marking its boundary1 the extreme extent of its dimensions in every direction1 as impressed on our vision3 and this is termed drawing its outline4' ,note #db3 ,phillips ,on ,painting4 #f4 ,again1 there are other ways in which we see clear manifestations of the act of thought by which we assign to the parts of objects their relations in space1 the impressions of sense being merely subservient to this act4 ,if we look at a medal through a glass which inverts it1 we see the figures upon it become concave depressions instead of projecting convexities2 for the light which illuminates the nearer side of the convexity will be transferred to the opposite side by the apparent inversion of the medal1 and will thus imply a hollow in which the side nearest the light gathers the shade4 ,here our decision as to which part is nearest to us1 has reference to the side from which the light comes4 ,in other cases the decision is more spontaneous4 ,if we draw black outlines1 such as represent the edges of a cube seen in perspective1 certain of the lines will cross each other2 and we may make this cube appear to assume two different positions1 by determining in our own mind that the lines which belong to one end of the cube shall be understood to be before or to be behind those which they cross4 ,here an act of the will1 operating upon the same sensible image1 gives us two cubes1 occupying two entirely different positions4 ,again1 many persons may have observed that when a windmill in motion at a distance from us1 7so that the outline of the sails only is seen17 stands obliquely to the eye1 we may1 by an effort of thought1 make the obliquity assume one or the other of two positions2 and as we do this1 the sails1 which in one instance appear to turn from right to left1 in the other case turn from left to right4 ,a person a little familiar with this mental effort1 can invert the motion as often as he pleases1 so long as the conditions of form and light do not offer a manifest contradiction to either position4 #abb4 ,thus we have these abundant and various manifestations of the activity of the mind1 in the process by which we collect from vision the relations of solid space of three dimensions4 ,but we must further make some remarks on the process by which we perceive mere visible figure2 and also1 on the mode in which we perceive the relations of space by the touch2 and first1 of the latter subject4 #g4 ,the opinion above illustrated1 that our sight does not give us a direct knowledge of the relations of solid space1 and that this knowledge is acquired only by an inference of the mind1 was first clearly taught by the celebrated ,bishop ,berkeley#eb1 and is a doctrine now generally assented to by metaphysical speculators4 ,note #eb3 ,theory of ,vision4 ,but does the sense of touch give us directly a knowledge of space8 ,this is a question which has attracted considerable notice in recent times2 and new light has been thrown upon it in a degree which is very remarkable1 when we consider that the philosophy of perception has been a prominent subject of inquiry from the earliest times4 ,two philosophers1 advancing to this inquiry from different sides1 the one a metaphysician1 the other a physiologist1 have independently arrived at the conviction that the long current opinion1 according to which we acquire a knowledge of space by the sense of touch1 is erroneous4 ,and the doctrine which they teach instead of the ancient errour1 has a very important bearing upon the principle which we are endeavouring to establish1--that our knowledge of space and its properties is derived rather from the active operations than from the passive impressions of the percipient mind4 ,undoubtedly the persuasion that we acquire a knowledge of form by the touch is very obviously suggested by our common habits4 ,if we wish to know the form of any body in the dark1 or to correct the impressions conveyed by sight1 when we suspect them to be false1 we have only1 it seems to us1 at least at first1 to stretch forth the hand and touch the object2 and we learn its #abc shape with1 no chance of errour4 ,in these cases1 form appears to be as immediate a perception of the sense of touch1 as colour is of the sense of sight4 #h4 ,but is this perception really the result of the passive sense of touch merely8 ,against such an opinion ,dr4 ,brown1 the metaphysician of whom ,i speak1 urges#fb that the feeling of touch alone1 when any object is applied to the hand1 or any other part of the body1 can no more convey the conception of form or extension1 than the sensation of an odour or a taste can do1 except we have already some knowledge of the relative position of the parts of our bodies2 that is1 except we are already in possession of an idea of space1 and have1 in our minds1 referred our limbs to their positions2 which is to suppose the conception of form already acquired4 ,note #fb3 ,lectures1 ,vol4 i4 p4 #dei1 7#ahbd74 #i4 ,by what faculty then do we originally acquire our conceptions of the relations of position8 ,brown answers by the muscular sense2 that is1 by the conscious exertions of the various muscles by which we move our limbs4 ,when we feel out the form and position of bodies by the hand1 our knowledge is acquired1 not by the mere touch of the body1 but by perceiving the course the fingers must take in order to follow the surface of the body1 or to pass from one body to another4 ,we are conscious of the slightest of the volitions by which we thus feel out form and place2 we know whether we move the finger to the right or left1 up or down1 to us or from us1 through a large or a small space2 and all these conscious acts are bound together and regulated in our minds by an idea of an extended space in which they are performed4 ,that this idea of space is not borrowed from the sight1 and transferred to the muscular feelings by habit1 is evident4 ,for a man born blind can feel out his way with his staff1 and has his conceptions of position determined by the conditions of space1 no less than one who has the use of his eyes4 ,and the muscular consciousness which reveals to us the position of objects and parts of objects1 #abd when we feel them out by means of the hand1 shows itself in a thousand other ways1 and in all our limbs3 for our habits of standing1 walking1 and all other attitudes and motions1 are regulated by our feeling of our position and that of surrounding objects4 ,and thus1 we cannot touch any object without learning something respecting its position2 not that the sense of touch directly conveys such knowledge2 but we have already learnt1 from the muscular sense1 constantly exercised1 the position of the limb which the object thus touches4 #aj4 ,the justice of this distinction will1 ,i think1 be assented to by all persons who attend steadily to the process itself1 and might be maintained by many forcible reasons4 ,perhaps one of the most striking evidences in its favour is that1 as ,i have already intimated1 it is the opinion to which another distinguished philosopher1 ,sir ,charles ,bell1 has been led1 reasoning entirely upon physiological principles4 ,from his researches it resulted that besides the nerves which convey the impulse of the will from the brain to the muscle1 by which every motion of our limbs is produced1 there is another set of nerves which carry back to the brain a sense of the condition of the muscle1 and thus regulate its activity2 and give us the consciousness of our position and relation to surrounding objects4 ,the motion of the hand and fingers1 or the consciousness of this motion1 must be combined with the sense of touch properly so called1 in order to make an inlet to the knowledge of such relations4 ,this consciousness of muscular exertion1 which he has called a sixth sense#gb1 is our guide1 ,sir ,c4 ,bell shows1 in the common practical government of our motions2 and he states that having given this explanation of perception as a physiological doctrine1 he had afterwards with satisfaction seen it confirmed by ,dr4 ,brown's speculations4 ,note #gb3 ,bridgewater ,treatise1 p4 #aie4 ,phil4 ,trans4 #ahbf1 ,pt4 ii4 p4 #afg4 #aa4 ,thus it appears that our consciousness of the relations of space is inseparably and fundamentally connected with our own actions in space4 ,we perceive #abe only while we act2 our sensations require to be interpreted by our volitions4 ,the apprehension of extension and figure is far from being a process in which we are inert and passive4 ,we draw lines with our fingers2 we construct surfaces by curving our hands2 we generate spaces by the motion of our arms4 ,when the geometer bids us form lines1 or surfaces1 or solids by motion1 he intends his injunction to be taken as hypothetical only2 we need only conceive such motions4 ,but yet this hypothesis represents truly the origin of our knowledge2 we perceive spaces by motion at first1 as we conceive spaces by motion afterwards3--or if not always by actual motion1 at least by potential4 ,if we perceive the length of a staff by holding its two ends in our two hands without running the finger along it1 this is because by habitual motion we have already acquired a measure of the distance of our hands in any attitude of which we are conscious4 ,even in the simplest case1 our perceptions are derived not from the touch1 but from the sixth sense2 and this sixth sense at least1 whatever may be the case with the other five1 implies an active mind along with the passive sense4 #ab4 ,upon attentive consideration1 it will be clear that a large portion of the perceptions respecting space which appear at first to be obtained by sight alone1 are1 in fact1 acquired by means of this sixth sense4 ,thus we consider the visible sky as a single surface surrounding us and returning into itself1 and thus forming a hemisphere4 ,but such a mode of conceiving an object of vision could never have occurred to us1 if we had not been able to turn our heads1 to follow this surface1 to pursue it till we find it returning into itself4 ,and when we have done this1 we necessarily present it to ourselves as a concave inclosure within which we are4 ,the sense of sight alone1 without the power of muscular motion1 could not have led us to view the sky as a vault or hemisphere4 ,under such circumstances1 we should have perceived only what was presented to the eye in one position2 and if different appearances had been presented in succession1 we could #abf not have connected them as parts of the same picture1 for want of any perception of their relative position4 ,they would have been so many detached and incoherent visual sensations4 ,the muscular sense connects their parts into a whole1 making them to be only different portions of one universal scene#hb4 ,note #hb3 ,it has been objected to this view that we might obtain a conception of the sky as a hemisphere1 by being ourselves turned round1 7as on a music-stool1 for instance17 and thus seeing in succession all parts of the sky4 ,but this assertion ,i conceive to be erroneous4 ,by being thus turned round1 we should see a number of pictures which we should put together as parts of a plane picture2 and when we came round to the original point1 we should have no possible means of deciding that it was the same point3 it would appear only as a repetition of the picture4 ,that sight1 of itself1 can give us only a plane picture1 the doctrine of ,berkeley1 appears to be indisputable2 and1 no less so1 the doctrine that it is the consciousness of our own action in space which puts together these pictures so that they cover the surface of a solid body4 ,we can see length and breadth with our eyes1 but we must thrust out our arm towards the flat surface1 in order that we may1 in our thoughts1 combine a third dimension with the other two4 #ac4 ,these considerations point out the fallacy of a very curious representation made by ,dr4 ,reid1 of the convictions to which man would be led1 if he possessed vision without the sense of touch4 ,to illustrate this subject1 ,reid uses the fiction of a nation whom he terms the ,idomenians1 who have no sense except that of sight4 ,he describes their notions of the relations of space as being entirely different from ours4 ,the axioms of their geometry are quite contradictory to our axioms4 ,for example1 it is held to be self-evident among them that two straight lines which intersect each other once1 must intersect a second time2 that the three angles of any triangle are greater than two right angles2 and the like4 ,these paradoxes are obtained by tracing the relations of lines on the surface of a concave sphere1 which surrounds the spectator1 and on which all visible appearances may be supposed to be presented to him4 ,but from what is said above it appears that the notion of such a sphere1 and such a connexion of visible objects which are seen in different #abg directions1 cannot be arrived at by sight alone4 ,when the spectator combines in his conception the relations of long-drawn lines and large figures1 as he sees them by turning his head to the right and to the left1 upwards and downwards1 he ceases to be an ,idomenian4 ,and thus our conceptions of the properties of space1 derived through the exercise of one mode of perception1 are not at variance with those obtained in another way2 but all such conceptions1 however produced or suggested1 are in harmony with each other2 being1 as has already been said1 only different aspects of the same idea4 #ad4 ,if our perceptions of the position of objects around us do not depend on the sense of vision alone1 but on the muscular feeling brought into play when we turn our head1 it will obviously follow that the same is true when we turn the eye instead of the head4 ,and thus we may learn the form of objects1 not by looking at them with a fixed gaze1 but by following the boundary of them with the eye4 ,while the head is held perfectly still1 the eye can rove along the outlines of visible objects1 scrutinize each point in succession1 and leap from one point to another2 each such act being accompanied by a muscular consciousness which makes us aware of the direction in which the look is travelling4 ,and we may thus gather information concerning the figures and places which we trace out with the visual ray1 as the blind man learns the forms of things which he traces out with his staff1 being conscious of the motions of his hand4 #ae4 ,this view of the mode in which the eye perceives position1 which is thus supported by the analogy of other members employed for the same purpose1 is further confirmed by ,sir ,charles ,bell by physiological reasons4 ,he teaches us that#ib when an object is seen we employ two senses3 there is an impression on the retina2 but we receive also the idea of position or relation in space1 which it is not the office of the retina to give1 by our consciousness of the efforts of the voluntary #abh muscles of the eye3 and he has traced in detail the course of the nerves by which these muscles convey their information4 ,the constant searching motion of the eye1 as he terms it#ajb1 is the means by which we become aware of the position of objects about us4 ,note #ib3 ,phil4 ,trans4 #ahbc4 ,on the ,motions of the ,eye4 ,note #ajb3 ,bridgewater ,treatise1 p4 #bhb4 ,i have adopted1 in writing the above1 the views and expressions of ,sir ,charles ,bell4 ,the essential part of the doctrine there presented is1 that the eye constantly makes efforts to turn1 so that the image of an object to which our attention is drawn1 shall fall upon a certain particular point of the retina2 and that when the image falls upon any other point1 the eye turns away from this oblique into the direct position4 ,other writers have maintained that the eye thus turns not because the point on which the image falls in direct vision is the most sensible point1 but that it is the point of greatest distinctness of vision4 ,they urge that a small star1 which disappears when the eye is turned full upon it1 may often be seen by looking a little away from it3 and hence1 they infer that the parts of the retina removed from the spot of direct vision1 are more sensible than it is4 ,the facts are very curious1 however they be explained1 but they do not disturb the doctrine delivered in the text4 #af4 ,it is not to our present purpose to follow the physiology of this subject2 but we may notice that ,sir ,c4 ,bell has examined the special circumstances which belong to this operation of the eye4 ,we learn from him that the particular point of the eye which thus traces the forms of visible objects is a part of the retina which has been termed the sensible spot2 being that part which is most distinctly sensible to the impressions of light and colour4 ,this part1 indeed1 is not a spot of definite size and form1 for it appears that proceeding from a certain point of the retina1 the distinct sensibility diminishes on every side by degrees4 ,and the searching motion of the eye arises from the desire which we instinctively feel of receiving upon the sensible spot the image of the object to which the attention is directed4 ,we are uneasy and impatient till the eye is turned so that this is effected4 ,and as our attention is transferred from point to point of the scene before us1 the eye1 and this point of the eye in particular1 travel along with the thoughts2 and the muscular sense1 which tells us of these movements of the organ of #abi vision1 conveys to us a knowledge of the forms and places which we thus successively survey4 #ag4 ,how much of activity there is in the process by which we perceive the outlines of objects appears further from the language by which we describe their forms4 ,we apply to them not merely adjectives of form1 but verbs of motion4 ,an abrupt hill starts out of the plain2 a beautiful figure has a gliding outline4 ,we have ,the windy summit1 wild and high1 ,roughly rushing on the sky4 ,these terms express the course of the eye as it follows the lines by which such forms are bounded and marked4 ,in like manner another modern poet#aab says of ,soracte1 that it ,from out the plain ,heaves like a long-swept wave about to break1 ,and on the curl hangs pausing4 ,note #aab3 ,byron1 ,ch4 ,har4 vi4 st4 #ge4 ,thus the muscular sense1 which is inseparably connected with an act originating in our own mind1 not only gives us all that portion of our perceptions of space in which we use the sense of touch1 but also1 at least in a great measure1 another large portion of such perceptions1 in which we employ the sense of sight4 ,as we have before seen that our knowledge of solid space and its properties is not conceivable in any other way than as the result of a mental act1 governed by conditions depending on its own nature2 so it now appears that our perceptions of visible figure are not obtained without an act performed under the same conditions4 ,the sensations of touch and sight are subordinated to an idea which is the basis of our speculative knowledge concerning space and its relations2 and this same idea is disclosed to our consciousness by its practically regulating our intercourse with the external world4 ,by considerations such as have been adduced and referred to1 it is proved beyond doubt1 that in a great #acj number of cases our knowledge of form and position is acquired from the muscular sense1 and not from sight directly3--for instance1 in all cases in which we have before us objects so large and prospects so extensive that we cannot see the whole of them in one position of the eye#abb4 ,note #abb3 ,the expression in the first edition was 'large objects and extensive spaces4' ,in the text as now given1 ,i state a definite size and extent1 within which the sight by itself can judge of position and figure4 ,the doctrine1 that we require the assistance of the muscular sense to enable us to perceive space of three dimensions1 is not at all inconsistent with this other doctrine1 that within the space which is seen by the fixed eye1 we perceive the relative positions of points directly by vision1 and that1 consequently1 we have a perception of visible figure4 ,sir ,charles ,bell has said1 7,phil4 ,trans4 #ahbc1 p4 #aha17 ',it appears to me that the utmost ingenuity will be at a loss to devise an explanation of that power by which the eye becomes acquainted with the position and relation of objects1 if the sense of muscular activity be excluded which accompanies the motion of the eyeball4' ,but surely we should have no difficulty in perceiving the relation of the sides and angles of a small triangle1 placed before the eye1 even if the muscles of the eyeball were severed4 ,this subject is resumed b4 iv4 c4 ii4 sect4 #aa4 ,we now quit the consideration of the properties of ,space1 and consider the ,idea of ,time4 #aca ,,chapter ,,vii4 ,,of ,,the ,,idea ,,of ,,time4 #a4 ,,respecting the ,idea of ,time1 we may make several of the same remarks which we made concerning the idea of space1 in order to show that it is not borrowed from experience1 but is a bond of connexion among the impressions of sense1 derived from a peculiar activity of the mind1 and forming a foundation both of our experience and of our speculative knowledge4 ,time is not a notion obtained by experience4 ,experience1 that is1 the impressions of sense and our consciousness of our thoughts1 gives us various perceptions2 and different successive perceptions considered together exemplify the notion of change4 ,but this very connexion of different perceptions1--this successiveness1--presupposes that the perceptions exist in time4 ,that things happen either together1 or one after the other1 is intelligible only by assuming time as the condition under which they are presented to us4 ,thus time is a necessary condition in the presentation of all occurrences to our minds4 ,we cannot conceive this condition to be taken away4 ,we can conceive time to go on while nothing happens in it2 but we cannot conceive anything to happen while time does not go on4 ,it is clear from this that time is not an impression derived from experience1 in the same manner in which we derive from experience our information concerning the objects which exist1 and the occurrences which take place in time4 ,the objects of experience can easily be conceived to be1 or not to be3--to be absent as well as present4 ,time always is1 and always is #acb present1 and even in our thoughts we cannot form the contrary supposition4 #b4 ,thus time is something distinct from the matter or substance of our experience1 and may be considered as a necessary form which that matter 7the experience of change7 must assume1 in order to be an object of contemplation to the mind4 ,time is one of the necessary conditions under which we apprehend the information which our senses and consciousness give us4 ,by considering time as a form which belongs to our power of apprehending occurrences and changes1 and under which alone all such experience can be accepted by the mind1 we explain the necessity1 which we find to exist1 of conceiving all such changes as happening in time2 and we thus see that time is not a property perceived as existing in objects1 or as conveyed to us by our senses2 but a condition impressed upon our knowledge by the constitution of the mind itself2 involving an act of thought as well as an impression of sense4 #c4 ,we showed that space is an idea of the mind1 or form of our perceiving power1 independent of experience1 by pointing out that we possess necessary and universal truths concerning the relations of space1 which could never be given by means of experience2 but of which the necessity is readily conceivable1 if we suppose them to have for their basis the constitution of the mind4 ,there exist also respecting number1 many truths absolutely necessary1 entirely independent of experience and anterior to it2 and so far as the conception of number depends upon the idea of time1 the same argument might be used to show that the idea of time is not derived from experience1 but is a result of the native activity of the mind3 but we shall defer all views of this kind till we come to the consideration of ,number4 #d4 ,some persons have supposed that we obtain the notion of time from the perception of motion4 ,but it is clear that the perception of motion1 that is1 change of place1 presupposes the conception of time1 and is not capable of being presented to the mind in any other #acc way4 ,if we contemplate the same body as being in different places at different times1 and connect these observations1 we have the conception of motion1 which thus presupposes the necessary conditions that existence in time implies4 ,and thus we see that it is possible there should be necessary truths concerning all ,motion1 and consequently1 concerning those motions which are the objects of experience2 but that the source of this necessity is the ,ideas of ,time and ,space1 which1 being universal conditions of knowledge residing in the mind1 afford a foundation for necessary truths4 #acd ,,chapter ,,viii4 ,,of ,,some ,,peculiarities ,,of ,,the ,,idea ,,of ,,time4 #a4 ,,the ,idea of ,time1 like the ,idea of ,space1 offers to our notice some characters which do not belong to our fundamental ideas generally1 but which are deserving of remark4 ,these characters are1 in some respects1 closely similar with regard to ,time and to ,space1 while1 in other respects1 the peculiarities of these two ideas are widely different4 ,we shall point out some of these characters4 ,time is not a general abstract notion collected from experience2 as1 for example1 a certain general conception of the relations of things4 ,for we do not consider particular times as examples of ,time in general1 7as we consider particular causes to be examples of ,cause17 but we conceive all particular times to be parts of a single and endless ,time4 ,this continually-flowing and endless time is what offers itself to us when we contemplate any series of occurrences4 ,all actual and possible times exist as ,parts1 in this original and general ,time4 ,and since all particular times are considered as derivable from time in general1 it is manifest that the notion of time in general cannot be derived from the notions of particular times4 ,the notion of time in general is therefore not a general conception gathered from experience4 #b4 ,time is infinite4 ,since all actual and possible times exist in the general course of time1 this general time must be infinite4 ,all limitation merely divides1 and does not terminate1 the extent of absolute time4 ,time has no beginning and no end2 but the beginning and the end of every other existence takes place in it4 #c4 ,time1 like space1 is not only a form of perception1 but of intuition4 ,we contemplate events as #ace taking place in time4 ,we consider its parts as added to one another1 and events as filling a larger or smaller extent of such parts4 ,the time which any event takes up is the sum of all such parts1 and the relation of the same to time is fully understood when we can clearly see what portions of time it occupies1 and what it does not4 ,thus the relation of known occurrences to time is perceived by intuition2 and time is a form of intuition of the external world4 #d4 ,time is conceived as a quantity of one dimension2 it has great analogy with a line1 but none at all with a surface or solid4 ,time may be considered as consisting of a series of instants1 which are before and after one another2 and they have no other relation than this1 of before and after4 ,just the same would be the case with a series of points taken along a line2 each would be after those on one side of it1 and before those on another4 ,indeed the analogy between time1 and space of one dimension1 is so close1 that the same terms are applied to both ideas1 and we hardly know to which they originally belong4 ,times and lines are alike called long and short2 we speak of the beginning and end of a line2 of a point of time1 and of the limits of a portion of duration4 #e4 ,but1 as has been said1 there is nothing in time which corresponds to more than one dimension in space1 and hence nothing which has any obvious analogy with figure4 ,time resembles a line indefinitely extended both ways2 all partial times are portions of this line2 and no mode of conceiving time suggests to us a line making any angle with the original line1 or any other combination which might give rise to figures of any kind4 ,the analogy between time and space1 which in many circumstances is so clear1 here disappears altogether4 ,spaces of two and of three dimensions1 planes and solids1 have nothing to which we can compare them in the conceptions arising out of time4 #f4 ,as figure is a conception solely appropriate to space1 there is also a conception which peculiarly belongs to time1 namely1 the conception of recurrence of times similarly marked2 or1 as it may be termed1 #acf rhythm1 using this word in a general sense4 ,the term rhythm is most commonly used to designate the recurrence of times marked by the syllables of a verse1 or the notes of a melody3 but it is easy to see that the general conception of such a recurrence does not depend on the mode in which it is impressed upon the sense4 ,the forms of such recurrence are innumerable4 ,thus in such a line as ,qudrupednte putrm sonit quatit ngula cmpum1 we have alternately one long or forcible syllable1 and two short or light ones1 recurring over and over4 ,in like manner in our own language1 in the line ,at the clse of the dy when the hmlet is still1 we have two light and one strong syllable repeated four times over4 ,such repetition is the essence of versification4 ,the same kind of rhythm is one of the main elements of music1 with this difference only1 that in music the forcible syllables are made so for the purposes of rhythm by their length only or principally2 for example1 if either of the above lines were imitated by a melody in the most simple and obvious manner1 each strong syllable would occupy exactly twice as much time as two of the weaker ones4 ,something very analogous to such rhythm may be traced in other parts of poetry and art1 which we need not here dwell upon4 ,but in reference to our present subject1 we may remark that by the introduction of such rhythm1 the flow of time1 which appears otherwise so perfectly simple and homogeneous1 admits of an infinite number of varied yet regular modes of progress4 ,all the kinds of versification which occur in all languages1 and the still more varied forms of recurrence of notes of different lengths1 which are heard in all the varied strains of melodies1 are only examples of such modifications1 or configurations as we may call them1 of time4 ,they involve relations of various portions of time1 as figures involve relations of various portions of space4 ,but yet the analogy between rhythm and figure is by no means very close2 for in rhythm we have relations of quantity alone in the parts of time1 whereas in figure we have #acg relations not only of quantity1 but of a kind altogether different1--namely1 of position4 ,on the other hand1 a repetition of similar elements1 which does not necessarily occur in figures1 is quite essential in order to impress upon us that measured progress of time of which we here speak4 ,and thus the ideas of time and space have each its peculiar and exclusive relations2 position and figure belonging only to space1 while repetition and rhythm are appropriate to time4 #g4 ,one of the simplest forms of recurrence is alternation1 as when we have alternate strong and slight syllables4 ,for instance1-- ,awke1 arse1 or b for ver fll'n4 ,or without any subordination1 as when we reckon numbers1 and call them in succession1 odd1 even1 odd1 even4 #h4 ,but the simplest of all forms of recurrence is that which has no variety2--in which a series of units1 each considered as exactly similar to the rest1 succeed each other2 as one1 one1 one1 and so on4 ,in this case1 however1 we are led to consider each unit with reference to all that have preceded2 and thus the series one1 one1 one1 and so forth1 becomes one1 two1 three1 four1 five1 and so on2 a series with which all are familiar1 and which may be continued without limit4 ,we thus collect from that repetition of which time admits1 the conception of ,number4 #i4 ,the relations of position and figure are the subject of the science of geometry2 and are1 as we have already said1 traced into a very remarkable and extensive body of truths1 which rests for its foundations on axioms involved in the ,idea of ,space4 ,there is1 in like manner1 a science of great complexity and extent1 which has its foundation in the ,idea of ,time4 ,but this science1 as it is usually pursued1 applies only to the conception of ,number1 which is1 as we have said1 the simplest result of repetition4 ,this science is ,theoretical ,arithmetic1 or the speculative doctrine of the properties and relations of numbers2 and we must say a few words concerning the principles which it is requisite to assume as the basis of this science4 #ach ,,chapter ,,ix4 ,,of ,,the ,,axioms ,,which ,,relate ,,to ,,number4 #a4 ,,the foundations of our speculative knowledge of the relations and properties of ,number1 as well as of ,space1 are contained in the mode in which we represent to ourselves the magnitudes which are the subjects of our reasonings4 ,to express these foundations in axioms in the case of number1 is a matter requiring some consideration1 for the same reason as in the case of geometry2 that is1 because these axioms are principles which we assume as true1 without being aware that we have made any assumption2 and we cannot1 without careful scrutiny1 determine when we have stated1 in the form of axioms1 all that is necessary for the formation of the science1 and no more than is necessary4 ,we will1 however1 attempt to detect the principles which really must form the basis of theoretical arithmetic4 #b4 ,why is it that three and two are equal to four and one8 ,because if we look at five things of any kind1 we see that it is so4 ,the five are four and one2 they are also three and two4 ,the truth of our assertion is involved in our being able to conceive the number five at all4 ,we perceive this truth by intuition1 for we cannot see1 or imagine we see1 five things1 without perceiving also that the assertion above stated is true4 ,but how do we state in words this fundamental principle of the doctrine of numbers8 ,let us consider a very simple case4 ,if we wish to show that seven and two are equal to four and five1 we say that seven are four and three1 therefore seven and two are four and three and two2 and because three and two are #aci five1 this is four and five4 ,mathematical reasoners justify the first inference 7marked by the conjunctive word therefore71 by saying that ,when equals are added to equals the wholes are equal1 and that thus1 since seven is equal to three and four1 if we add two to both1 seven and two are equal to four and three and two4 #c4 ,such axioms as this1 that when equals are added to equals the wholes are equal1 are1 in fact1 expressions of the general condition of intuition1 by which a whole is contemplated as made up of parts1 and as identical with the aggregate of the parts4 ,and a yet more general form in which we might more adequately express this condition of intuition would be this2 that ',two magnitudes are equal when they can be divided into parts which are equal1 each to each4' ,thus in the above example1 seven and two are equal to four and five1 because each of the two sums can be divided into the parts1 four1 three1 and two4 #d4 ,in all these cases1 a person who had never seen such axioms enunciated in a verbal form would employ the same reasoning as a practised mathematician1 in order to satisfy himself that the proposition was true4 ,the steps of the reasoning1 being seen to be true by intuition1 would carry an entire conviction1 whether or not the argument were made verbally complete4 ,hence the axioms may appear superfluous1 and on this account such axioms have often been spoken contemptuously of1 as empty and barren assertions4 ,in fact1 however1 although they cannot supply the deficiency of the clear intuition of number and space in the reasoner himself1 and although when he possesses such a faculty1 he will reason rightly if he have never heard of such axioms1 they still have their place properly at the beginning of our treatises on the science of quantity2 since they express1 as simply as words can express1 those conditions of the intuition of magnitudes on which all reasoning concerning quantity must be based2 and are necessary when we want1 not only to see the truth of the elementary reasonings on these subjects1 but to put such reasonings in a formal and logical shape4 #adj #e4 ,we have considered the above-mentioned axioms as the basis of all arithmetical operations of the nature of addition4 ,but it is easily seen that the same principle may be carried into other cases2 as for instance1 multiplication1 which is merely a repeated addition1 and admits of the same kind of evidence4 ,thus five times three are equal to three times five2 why is this8 ,if we arrange fifteen things in five rows of three1 it is seen by looking1 or by imaginary looking1 which is intuition1 that they may also be taken as three rows of five4 ,and thus the principle that those wholes are equal which can be resolved into the same partial magnitudes1 is immediately applicable in this as in the other case4 #f4 ,we may proceed to higher numbers1 and may find ourselves obliged to use artificial nomenclature and notation in order to represent and reckon them2 but the reasoning in these cases also is still the same4 ,and the usual artifice by which our reasoning in such instances is assisted is1 that the number which is the root of our scale of notation 7which is ten in our usual system71 is alternately separated into parts and treated as a single thing4 ,thus #dg and #ce are #hb2 for #dg is four tens and seven2 #ce is three tens and five2 whence #dg and #ce are seven tens and twelve2 that is1 #g tens1 #a ten1 and #b2 which is #h tens and #b1 or #hb4 ,the like reasoning is applicable in other cases4 ,and since the most remote and complex properties of numbers are obtained by a prolongation of a course of reasoning exactly similar to that by which we thus establish the most elementary propositions1 we have1 in the principles just noticed1 the foundation of the whole of ,theoretical ,arithmetic4 #ada ,,chapter ,x4 ,,of ,,the ,,perception ,,of ,,time ,,and ,,number4 #a4 ,,our perception of the passage of time involves a series of acts of memory4 ,this is easily seen and assented to1 when large intervals of time and a complex train of occurrences are concerned4 ,but since memory is requisite in order to apprehend time in such cases1 we cannot doubt that the same faculty must be concerned in the shortest and simplest cases of succession2 for it will hardly be maintained that the process by which we contemplate the progress of time is different1 when small1 and when large intervals are concerned4 ,if memory be absolutely requisite to connect two events which begin and end a day1 and to perceive a tract of time between them1 it must be equally indispensable to connect the beginning and end of a minute1 or a second2 though in this case the effort may be smaller1 and consequently more easily overlooked4 ,in common cases1 we are unconscious of the act of thought by which we recollect the preceding instant1 though we perceive the effort when we recollect some distant event4 ,and this is analogous to what happens in other instances4 ,thus1 we walk without being conscious of the volitions by which we move our muscles2 but1 in order to leap1 a distinct and manifest exertion of the same muscles is necessary4 ,yet no one will doubt that we walk as well as leap by an act of the will exerted through the muscles2 and in like manner1 our consciousness of small as well as large intervals of time involves something of the nature of an act of memory4 #b4 ,but this constant and almost imperceptible kind of memory1 by which we connect the beginning and #adb end of each instant as it passes1 may very fitly be distinguished in common cases from manifest acts of recollection1 although it may be difficult or impossible to separate the two operations in general4 ,this perpetual and latent kind of memory may be termed a sense of successiveness2 and must be considered as an internal sense by which we perceive ourselves existing in time1 much in the same way as by our external and muscular sense we perceive ourselves existing in space4 ,and both our internal thoughts and feelings1 and the events which take place around us1 are apprehended as objects of this internal sense1 and thus as taking place in time4 #c4 ,in the same manner in which our interpretation of the notices of the muscular sense implies the power of moving our limbs1 and of touching at will this object or that2 our apprehension of the relations of time1 by means of the internal sense of successiveness1 implies a power of recalling what has past1 and of retaining what is passing4 ,we are able to seize the occurrences which have just taken place1 and to hold them fast in our minds so as mentally to measure their distance in time from occurrences now present4 ,and thus1 this sense of successiveness1 like the muscular sense with which we have compared it1 implies activity of the mind itself1 and is not a sense passively receiving impressions4 #d4 ,the conception of ,number appears to require the exercise of the same sense of succession4 ,at first sight1 indeed1 we seem to apprehend ,number without any act of memory1 or any reference to time3 for example1 we look at a horse1 and see that his legs are four2 and this we seem to do at once1 without reckoning them4 ,but it is not difficult to see that this seeming instantaneousness of the perception of small numbers is an illusion4 ,this resembles the many other cases in which we perform short and easy acts so rapidly and familiarly that we are unconscious of them2 as in the acts of seeing1 and of articulating our words4 ,and this is the more manifest1 since we begin our acquaintance with number by counting even the #adc smallest numbers4 ,children and very rude savages must use an effort to reckon even their five fingers1 and find a difficulty in going further4 ,and persons have been known who were able by habit1 or by a peculiar natural aptitude1 to count by dozens as rapidly as common persons can by units4 ,we may conclude1 therefore1 that when we appear to catch a small number by a single glance of the eye1 we do in fact count the units of it in a regular1 though very brief succession4 ,to count requires an act of memory4 ,of this we are sensible when we count very slowly1 as when we reckon the strokes of a church-clock2 for in such a case we may forget in the intervals of the strokes1 and miscount4 ,now it will not be doubted that the nature of the process in counting is the same whether we count fast or slow4 ,there is no definite speed of reckoning at which the faculties which it requires are changed2 and therefore memory1 which is requisite in some cases1 must be so in all#acb4 ,note #acb3 ,i have considered ,number as involving the exercise of the sense of succession1 because ,i cannot draw any line between those cases of large numbers1 in which1 the process of counting being performed1 there is a manifest apprehension of succession2 and those cases of small numbers1 in which we seem to see the number at one glance4 ,but if any one holds ,number to be apprehended by a direct act of intuition1 as ,space and ,time are1 this view will not disturb the other doctrines delivered in the text4 ,the act of counting1 7one1 two1 three1 and so on17 is the foundation of all our knowledge of number4 ,the intuition of the relations of number involves this act of counting2 for1 as we have just seen1 the conception of number cannot be obtained in any other way4 ,and thus the whole of theoretical arithmetic depends upon an act of the mind1 and upon the conditions which the exercise of that act implies4 ,these have been already explained in the last chapter4 #e4 ,but if the apprehension of number be accompanied by an act of the mind1 the apprehension of rhythm is so still more clearly4 ,all the forms of versification and the measures of melodies are the creations of man1 who thus realizes in words and sounds the #add forms of recurrence which rise within his own mind4 ,when we hear in a quiet scene any rapidly-repeated sound1 as those made by the hammer of the smith or the saw of the carpenter1 every one knows how insensibly we throw these noises into a rhythmical form in our own apprehension4 ,we do this even without any suggestion from the sounds themselves4 ,for instance1 if the beats of a clock or watch be ever so exactly alike1 we still reckon them alternately tick-tack1 tick-tack4 ,that this is the case1 may be proved by taking a watch or clock of such a construction that the returning swing of the pendulum is silent1 and in which therefore all the beats are rigorously alike3 we shall find ourselves still reckoning its sounds as tick-tack4 ,in this instance it is manifest that the rhythm is entirely of our own making4 ,in melodies1 also1 and in verses in which the rhythm is complex1 obscure and difficult1 we perceive something is required on our part2 for we are often incapable of contributing our share1 and thus lose the sense of the measure altogether4 ,and when we consider such cases1 and attend to what passes within us when we catch the measure1 even of the simplest and best-known air1 we shall no longer doubt that an act of our own thoughts is requisite in such cases1 as well as impressions on the sense4 ,and thus the conception of this peculiar modification of time1 which we have called rhythm1 like all the other views which we have taken of the subject1 shows that we must1 in order to form such conceptions1 supply a certain idea by our own thoughts1 as well as merely receive by senses1 whether external or internal1 the impressions of appearances and collections of appearances4 #ade ,,note ,,to ,,chapter ,x4 ,i ,,have in the last ten chapters described ,space1 ,time1 and ,number by various expressions1 all intended to point out their office as exemplifying the ,ideal ,element of human knowledge4 ,i have called them ,fundamental ,ideas2 ,forms of ,perception2 ,forms of ,intuition2 and perhaps other names4 ,i might add yet other phrases4 ,i might say that the properties of ,space1 ,time1 and ,number are ,laws of the ,mind's ,activity in apprehending what is4 ,for the mind cannot apprehend any thing or event except conformably to the properties of space1 time1 and number4 ,it is not only that it does not1 but it can not3 and this impossibility shows that the law is a law of the mind1 and not of objects extraneous to the mind4 ,it is usual for some of those who reject the doctrines here presented to say that the axioms of geometry1 and of other sciences1 are obtained by ,induction from facts constantly presented by experience4 ,but ,i do not see how ,induction can prove that a proposition must be true4 ,the only intelligible usage of the word ,induction appears to me to be1 that in which it is applied to a proposition which1 being separable from the facts in our apprehension1 and being compared with them1 is seen to agree with them4 ,but in the cases now spoken of1 the proposition is not separable from the facts4 ,we cannot infer by induction that two straight lines cannot inclose a space1 because we cannot contemplate special cases of two lines inclosing a space1 in which it remains to be determined whether or not the proposition1 that both are straight1 is true4 ,i do not deny that the activity of the mind by which it perceives objects and events as related according to the laws of space1 time1 and number1 is awakened and developed by being constantly exercised2 and that we cannot imagine a stage of human existence in which the powers have not been awakened and #adf developed by such exercise4 ,in this way1 experience and observation are necessary conditions and prerequisites of our apprehension of geometrical 7and other7 axioms4 ,we cannot see the truth of these axioms without some experience1 because we cannot see any thing1 or be human beings1 without some experience4 ,this might be expressed by saying that such truths are acquired necessarily in the course of all experience2 but ,i think it is very undesirable to apply1 to such a case1 the word ,induction1 of which it is so important to us to keep the scientific meaning free from confusion4 ,induction cannot give demonstrative proofs1 as ,i have already stated in ,book #a4 ,c4 i4 sect4 #c1 and therefore cannot be the ground of necessary truths4 ,another expression which may be used to describe the ,fundamental ,ideas here spoken of is suggested by the language of a very profound and acute ,review of the former edition4 ,the ,reviewer holds that we pass from special experiences to universal truths in virtue of 'the inductive propensity--the irresistible impulse of the mind to generalize ad infinitum4' ,i have already given reasons why ,i cannot adopt the former expression2 but ,i do not see why space1 time1 number1 cause1 and the rest1 may not be termed different forms of the impulse of the mind to generalize4 ,but if we put together all the ,fundamental ,ideas as results of the ,generalizing ,impulse1 we must still separate them as different modes of action of that ,impulse1 showing themselves in various characteristic ways in the axioms and modes of reasoning which belong to different sciences4 ,the ,generalizing ,impulse in one case proceeds according to the ,idea of ,space2 in another1 according to the ,idea of ,mechanical ,cause2 and so in other subjects4 #adg ,,chapter ,,xi4 ,,of ,,mathematical ,,reasoning4 #a4 ,discursive ,reasoning4--,,we have thus seen that our notions of space1 time1 and their modifications1 necessarily involve a certain activity of the mind2 and that the conditions of this activity form the foundations of those sciences which have the relations of space1 time1 and number1 for their object4 ,upon the fundamental principles thus established1 the various sciences which are included in the term ,pure ,mathematics1 7,geometry1 ,algebra1 ,trigonometry1 ,conic ,sections1 and the rest of the ,higher ,geometry1 the ,differential ,calculus1 and the like17 are built up by a series of reasonings4 ,these reasonings are subject to the rules of ,logic1 as we have already remarked2 nor is it necessary here to dwell long on the nature and rules of such processes4 ,but we may here notice that such processes are termed discursive1 in opposition to the operations by which we acquire our fundamental principles1 which are1 as we have seen1 intuitive4 ,this opposition was formerly very familiar to our writers2 as ,milton1-- 4 4 4 ,thus the soul reason receives1 ,discursive or intuitive4--,paradise ,lost1 v4 #dch4 ,for in such reasonings we obtain our conclusions1 not by looking at our conceptions steadily in one view1 which is intuition1 but by passing from one view to another1 like those who run from place to place 7discursus74 ,thus a straight line may be at the same time a side of a triangle and a radius of a circle3 and in the first proposition of ,euclid a line is considered1 first in one of these relations1 and then in the other1 and thus the sides of a certain triangle are proved to be equal4 ,and by this 'discourse of reason1' as by our older #adh writers it was termed1 we set forth from those axioms which we perceive by intuition1 travel securely over a vast and varied region1 and become possessed of a copious store of mathematical truths4 #b4 ,technical ,terms of ,reasoning4--,the reasoning of mathematics1 thus proceeding from a few simple principles to many truths1 is conducted according to the rules of ,logic4 ,if it be necessary1 mathematical proofs may be reduced to logical forms1 and expressed in ,syllogisms1 consisting of major1 minor1 and conclusion4 ,but in most cases the syllogism is of that kind which is called by logical writers an ,enthymeme2 a word which implies something existing in the thoughts only1 and which designates a syllogism in which one of the premises is understood1 and not expressed4 ,thus we say in a mathematical proof1 'because the point ,c is the center of the circle ,,ab1 ,,ac is equal to ,,bc2' not stating the major1--that all lines drawn from the center of a circle to the circumference are equal2 or introducing it only by a transient reference to the definition of a circle4 ,but the enthymeme is so constantly used in all habitual forms of reasoning1 that it does not occur to us as being anything peculiar in mathematical works4 ,the propositions which are proved to be generally true are termed ,theorems3 but when anything is required to be done1 as to draw a line or a circle under given conditions1 this proposition is a ,problem4 ,a theorem requires demonstration2 a problem1 solution4 ,and for both purposes the mathematician usually makes a ,construction4 ,he directs us to draw certain lines1 circles1 or other curves1 on which is to be founded his demonstration that his theorem is true1 or that his problem is solved4 ,sometimes1 too1 he establishes some ,lemma1 or preparatory proposition1 before he proceeds to his main task2 and often he deduces from his demonstration some conclusion in addition to that which was the professed object of his proposition2 and this is termed a ,corollary4 ,these technical terms are noted here1 not as being very important1 but in order that they may not sound #adi strange and unintelligible if we should have occasion to use some of them4 ,there is1 however1 one technical distinction more peculiar1 and more important4 #c4 ,geometrical ,analysis and ,synthesis4--,in geometrical reasoning such as we have described1 we introduce at every step some new consideration2 and it is by combining all these considerations1 that we arrive at the conclusion1 that is1 the demonstration of the proposition4 ,each step tends to the final result1 by exhibiting some part of the figure under a new relation4 ,to what we have already proved1 is added something more2 and hence this process is called ,synthesis1 or putting together4 ,the proof flows on1 receiving at every turn new contributions from different quarters2 like a river fed and augmented by many tributary streams4 ,and each of these tributaries flows from some definition or axiom as its fountain1 or is itself formed by the union of smaller rivulets which have sources of this kind4 ,in descending along its course1 the synthetical proof gathers all these accessions into one common trunk1 the proposition finally proved4 ,but we may proceed in a different manner4 ,we may begin from the formed river1 and ascend to its sources4 ,we may take the proposition of which we require a proof1 and may examine what the supposition of its truth implies4 ,if this be true1 then something else may be seen to be true2 and from this1 something else1 and so on4 ,we may often1 in this way1 discover of what simpler propositions our theorem or solution is compounded1 and may resolve these in succession1 till we come to some proposition which is obvious4 ,this is geometrical ,analysis4 ,having succeeded in this analytical process1 we may invert it2 and may descend again from the simple and known propositions1 to the proof of a theorem1 or the solution of a problem1 which was our starting-place4 ,this process resembles1 as we have said1 tracing a river to its sources4 ,as we ascend the stream1 we perpetually meet with bifurcations2 and some sagacity is needed to enable us to see which1 in each case1 is the main stream3 but if we proceed in our research1 we #aej exhaust the unexplored valleys1 and finally obtain a clear knowledge of the place whence the waters flow4 ,analytical is sometimes confounded with symbolical reasoning1 on which subject we shall make a remark in the next chapter4 ,the object of that chapter is to notice certain other fundamental principles and ideas1 not included in those hitherto spoken of1 which we find thrown in our way as we proceed in our mathematical speculations4 ,it would detain us too long1 and involve us in subtle and technical disquisitions1 to examine fully the grounds of these principles2 but the ,mathematics hold so important a place in relation to the inductive sciences1 that ,i shall briefly notice the leading ideas which the ulterior progress of the subject involves4 #aea ,,chapter ,,xii4 ,,of ,,the ,,foundations ,,of ,,the ,,higher ,,mathematics4 #a4 ,the ,idea of a ,limit4--,,the general truths concerning relations of space which depend upon the axioms and definitions contained in ,euclid's ,elements1 and which involve only properties of straight lines and circles1 are termed ,elementary ,geometry3 all beyond this belongs to the ,higher ,geometry4 ,to this latter province appertain1 for example1 all propositions respecting the lengths of any portions of curve lines2 for these cannot be obtained by means of the principles of the ,elements alone4 ,here then we must ask to what other principles the geometer has recourse1 and from what source these are drawn4 ,is there any origin of geometrical truth which we have not yet explored8 ,the ,idea of a ,limit supplies a new mode of establishing mathematical truths4 ,thus with regard to the length of any portion of a curve1 a problem which we have just mentioned2 a curve is not made up of straight lines1 and therefore we cannot by means of any of the doctrines of elementary geometry measure the length of any curve4 ,but we may make up a figure nearly resembling any curve by putting together many short straight lines1 just as a polygonal building of very many sides may nearly resemble a circular room4 ,and in order to approach nearer and nearer to the curve1 we may make the sides more and more small1 more and more numerous4 ,we may then possibly find some mode of measurement1 some relation of these small lines to other lines1 which is not disturbed by the multiplication of the sides1 however far it be carried4 ,and thus1 we may do what is equivalent to measuring the curve itself2 for by multiplying the #aeb sides we may approach more and more closely to the curve till no appreciable difference remains4 ,the curve line is the ,limit of the polygon2 and in this process we proceed on the ,axiom1 that ',what is true up to the ,limit is true at the ,limit4' ,this mode of conceiving mathematical magnitudes is of wide extent and use2 for every curve may be considered as the limit of some polygon2 every varied magnitude1 as the limit of some aggregate of simpler forms2 and thus the relations of the elementary figures enable us to advance to the properties of the most complex cases4 ,a ,limit is a peculiar and fundamental conception1 the use of which in proving the propositions of the ,higher ,geometry cannot be superseded by any combination of other hypotheses and definitions#adb4 ,the axiom just noticed1 that what is true up to the limit is true at the limit1 is involved in the very conception of a ,limit3 and this principle1 with its consequences1 leads to all the results which form the subject of the higher mathematics1 whether proved by the consideration of evanescent triangles1 by the processes of the ,differential ,calculus1 or in any other way4 ,note #adb3 ,this assertion cannot be fully proved and illustrated without a reference to mathematical reasonings which would not be generally intelligible4 ,i have shown the truth of the assertion in my ,thoughts on the ,study of ,mathematics1 annexed to the ,principles of ,english ,university ,education4 ,the proof is of this kind3--,the ultimate equality of an arc of a curve and the corresponding periphery of a polygon1 when the sides of the polygon are indefinitely increased in number1 is evident4 ,but this truth cannot be proved from any other axiom4 ,for if we take the supposed axiom1 that a curve is always less than the including broken line1 this is not true1 except with a condition2 and in tracing the import of this condition1 we find its necessity becomes evident only when we introduce a reference to a ,limit4 ,and the same is the case if we attempt to supersede the notion of a ,limit in proving any other simple and evident proposition in which that notion is involved4 ,therefore these evident truths are self-evident1 in virtue of the ,idea of a ,limit4 ,the ancients did not expressly introduce this conception of a ,limit into their mathematical reasonings2 although in the application of what is termed the #aec ,method of ,exhaustions1 7in which they show how to exhaust the difference between a polygon and a curve1 or the like17 they were in fact proceeding upon an obscure apprehension of principles equivalent to those of the ,method of ,limits4 ,yet the necessary fundamental principle not having1 in their time1 been clearly developed1 their reasonings were both needlessly intricate and imperfectly satisfactory4 ,moreover they were led to put in the place of axioms1 assumptions which were by no means self-evident2 as when ,archimedes assumed1 for the basis of his measure of the circumference of the circle1 the proposition that a circular arc is necessarily less than two lines which inclose it1 joining its extremities4 ,the reasonings of the older mathematicians1 which professed to proceed upon such assumptions1 led to true results in reality1 only because they were guided by a latent reference to the limiting case of such assumptions4 ,and this latent employment of the conception of a ,limit1 reappeared in various forms during the early period of modern mathematics2 as for example1 in the ,method of ,indivisibles of ,cavalleri1 and the ,characteristic ,triangle of ,barrow2 till at last1 ,newton distinctly referred such reasonings to the conception of a ,limit1 and established the fundamental principles and processes which that conception introduces1 with a distinctness and exactness which required little improvement to make it as unimpeachable as the demonstrations of geometry4 ,and when such processes as ,newton thus deduced from the conception of a ,limit1 are represented by means of general algebraical symbols instead of geometrical diagrams1 we have then before us the ,method of ,fluxions1 or the ,differential ,calculus2 a mode of treating mathematical problems justly considered as the principal weapon by which the splendid triumphs of modern mathematics have been achieved4 #b4 ,the ,use of ,general ,symbols4--,the employment of algebraical symbols1 of which we have just spoken1 has been another of the main instruments to which the successes of modern mathematics are owing4 ,and here again the processes by which we obtain our #aed results depend for their evidence upon a fundamental conception1--the conception of arbitrary symbols as the ,signs of quantity and its relations2 and upon a corresponding axiom1 that ',the interpretation of such symbols must be perfectly general4' ,in this case1 as in the last1 it was only by degrees that mathematicians were led to a just apprehension of the grounds of their reasoning4 ,for symbols were at first used only to represent numbers considered with regard to their numerical properties2 and thus the science of ,algebra was formed4 ,but it was found1 even in cases belonging to common algebra1 that the symbols often admitted of an interpretation which went beyond the limits of the problem1 and which yet was not unmeaning1 since it pointed out a question closely analogous to the question proposed4 ,this was the case1 for example1 when the answer was a negative quantity2 for when ,descartes had introduced the mode of representing curves by means of algebraical relations among the symbols of the co-ordinates1 or distances of each of their points from fixed lines1 it was found that negative quantities must be dealt with as not less truly significant than positive ones4 ,and as the researches of mathematicians proceeded1 other cases also were found1 in which the symbols1 although destitute of meaning according to the original conventions of their institution1 still pointed out truths which could be verified in other ways2 as in the cases in which what are called impossible quantities occur4 ,such processes may usually be confirmed upon other principles1 and the truth in question may be established by means of a demonstration in which no such seeming fallacies defeat the reasoning4 ,but it has also been shown in many such cases1 that the process in which some of the steps appear to be without real meaning1 does in fact involve a valid proof of the proposition4 ,and what we have here to remark is1 that this is not true accidentally or partially only1 but that the results of systematic symbolical reasoning must always express general truths1 by their nature2 and do not1 for their justification1 require each of the steps of the process to represent #aee some definite operation upon quantity4 ,the absolute universality of the interpretation of symbols is the fundamental principle of their use4 ,this has been shown very ably by ,dr4 ,peacock in his ,algebra4 ,he has there illustrated1 in a variety of ways1 this principle3 that ',if general symbols express an identity when they are supposed to be of any special nature1 they must also express an identity when they are general in their nature4' ,and thus1 this universality of symbols is a principle in addition to those we have already noticed2 and is a principle of the greatest importance in the formation of mathematical science1 according to the wide generality which such science has in modern times assumed4 #c4 ,connexion of ,symbols and ,analysis4--,since in our symbolical reasoning our symbols thus reason for us1 we do not necessarily here1 as in geometrical reasoning1 go on adding carefully one known truth to another1 till we reach the desired result4 ,on the contrary1 if we have a theorem to prove or a problem to solve which can be brought under the domain of our symbols1 we may at once state the given but unproved truth1 or the given combination of unknown quantities1 in its symbolical form4 ,after this first process1 we may then proceed to trace1 by means of our symbols1 what other truth is involved in the one just stated1 or what the unknown symbols must signify2 resolving step by step the symbolical assertion with which we began1 into others more fitted for our purpose4 ,the former process is a kind of synthesis1 the latter is termed analysis4 ,and although symbolical reasoning does not necessarily imply such analysis2 yet the connexion is so familiar1 that the term analysis is frequently used to designate symbolical reasoning4 #aef ,,chapter ,,xiii4 ,,the ,,doctrine ,,of ,,motion4 #a4 ,pure ,mechanism4--,,the doctrine of ,motion1 of which we have here to speak1 is that in which motion is considered quite independently of its cause1 force2 for all consideration of force belongs to a class of ideas entirely different from those with which we are here concerned4 ,in this view it may be termed the pure doctrine of motion1 since it has to do solely with space and time1 which are the subjects of pure mathematics4 7,see c4 i4 of this book47 ,although the doctrine of motion in connexion with force1 which is the subject of mechanics1 is by far the most important form in which the consideration of motion enters into the formation of our sciences1 the ,pure ,doctrine of ,motion1 which treats of space1 time1 and velocity1 might be followed out so as to give rise to a very considerable and curious body of science4 ,such a science is the science of ,mechanism1 independent of force1 and considered as the solution of a problem which may be thus enunciated3 ',to communicate any given motion from a first mover to a given body4' ,the science which should have for its object to solve all the various cases into which this problem would ramify1 might be termed ,pure ,mechanism1 in contradistinction to ,mechanics ,proper1 or ,machinery1 in which ,force is taken into consideration4 ,the greater part of the machines which have been constructed for use in manufactures have been practical solutions of some of the cases of this problem4 ,we have also important contributions to such a science in the works of ,mathematicians2 for example1 the various investigations and demonstrations which have been published respecting the form of the ,teeth #aeg of ,wheels1 and ,mr4 ,babbage's memoir#aeb on the ,language of ,machinery4 ,there are also several works which contain collections of the mechanical contrivances which have been invented for the purpose of transmitting and modifying motion1 and these works may be considered as treatises on the science of ,pure ,mechanism4 ,but this science has not yet been reduced to the systematic simplicity which is desirable1 nor indeed generally recognized as a separate science4 ,it has been confounded1 under the common name of ,mechanics1 with the other 9999science1 ,mechanics ,proper1 or ,machinery1 which considers the effect of force transmitted by ,mechanism from one part of a material combination to another4 ,for example1 the ,mechanical ,powers1 as they are usually termed1 7the ,lever1 the ,wheel and ,axle1 the ,inclined ,plane1 the ,wedge1 and the ,screw17 have almost always been treated with reference to the relation between the ,power and the ,weight1 and not primarily as a mode of changing the velocity and kind of the motion4 ,the science of pure motion has not generally been separated from the science of motion viewed with reference to its causes4 ,note #aeb3 ,on a ,method of expressing by ,signs the action of ,machinery4 ,phil4 ,trans4 #ahbf1 p4 #bej4 ,recently1 indeed1 the necessity of such a separation has been seen by those who have taken a philosophical view of science4 ,thus this necessity has been urged by ,m4 ,ampre1 in his ,essai sur la ,philosophie des ,sciences 7#ahcd73 ',long1' he says1 7p4 #ej17 'before ,i employed myself upon the present work1 ,i had remarked that it is usual to omit1 in the beginning of all books treating of sciences which regard motion and force1 certain considerations which1 duly developed1 must constitute a special science3 of which science certain parts have been treated of1 either in memoirs or in special works2 such1 for example1 as that of ,carnot upon ,motion considered ,geometrically1 and the essay of ,lanz and ,betancourt upon the ,composition of ,machines4' ,he then proceeds to describe this science nearly as we have #aeh done1 and proposes to term it ,kinematics 7,cinmatique71 from 1 motion4 #b4 ,formal ,astronomy4--,i shall not attempt here further to develop the form which such a science must assume4 ,but ,i may notice one very large province which belongs to it4 ,when men had ascertained the apparent motions of the sun1 moon1 and stars1 to a moderate degree of regularity and accuracy1 they tried to conceive in their minds some mechanism by which these motions might be produced2 and thus they in fact proposed to themselves a very extensive problem in ,kinematics4 ,this1 indeed1 was the view originally entertained of the nature of the science of astronomy4 ,thus ,plato in the seventh ,book of his ,republic#afb1 speaks of astronomy as the doctrine of the motion of solids1 meaning thereby1 spheres4 ,and the same was a proper description of the science till the time of ,kepler1 and even later3 for ,kepler endeavoured in vain to conjoin with the knowledge of the motions of the heavenly bodies1 those true mechanical conceptions which converted formal into physical astronomy#agb4 ,note #afb3 ,p4 #ebh4 ,note #agb3 ,hist4 ,induc4 ,sc4 ii4 #acj4 ,the astronomy of the ancients admitted none but uniform circular motions1 and could therefore be completely cultivated by the aid of their elementary geometry4 ,but the pure science of motion might be extended to all motions1 however varied as to the speed or the path of the moving body4 ,in this form it must depend upon the doctrine of limits2 and the fundamental principle of its reasonings would be this3 ,that velocity is measured by the ,limit of the space described1 considered with reference to the time in which it is described4 ,i shall not further pursue this subject2 and in order to complete what ,i have to say respecting the ,pure ,sciences1 ,i have only a few words to add respecting their bearing on ,inductive ,science in general4 #aei ,,chapter ,,xiv4 ,,of ,,the ,,application ,,of ,,mathematics ,,to ,,the ,,inductive ,,sciences4 #a4 ,,all objects in the world which can be made the subjects of our contemplation are subordinate to the conditions of ,space1 ,time1 and ,number2 and on this account1 the doctrines of pure mathematics have most numerous and extensive applications in every department of our investigations of nature4 ,and there is a peculiarity in these ,ideas1 which has caused the mathematical sciences to be1 in all cases1 the first successful efforts of the awakening speculative powers of nations at the commencement of their intellectual progress4 ,conceptions derived from these ,ideas are1 from the very first1 perfectly precise and clear1 so as to be fit elements of scientific truths4 ,this is not the case with the other conceptions which form the subjects of scientific inquiries4 ,the conception of statical force1 for instance1 was never presented in a distinct form till the works of ,archimedes appeared3 the conception of accelerating force was confused1 in the mind of ,kepler and his contemporaries1 and only became clear enough for purposes of sound scientific reasoning in the succeeding century3 the just conception of chemical composition of elements gradually1 in modern times1 emerged from the erroneous and vague notions of the ancients4 ,if we take works published on such subjects before the epoch when the foundations of the true science were laid1 we find the knowledge not only small1 but worthless4 ,the writers did not see any evidence in what we now consider as the axioms of the science2 nor any inconsistency where we now see self-contradiction4 ,but this was never the case with speculations concerning #afj space and number4 ,from their first rise1 these were true as far as they went4 ,the ,geometry and ,arithmetic of the ,greeks and ,indians1 even in their first and most scanty form1 contained none but true propositions4 ,men's intuitions upon these subjects never allowed them to slide into error and confusion2 and the truths to which they were led by the first efforts of their faculties1 so employed1 form part of the present stock of our mathematical knowledge4 #b4 ,but we are here not so much concerned with mathematics in their pure form1 as with their application to the phenomena and laws of nature4 ,and here also the very earliest history of civilization presents to us some of the most remarkable examples of man's success in his attempts to attain to science4 ,space and time1 position and motion1 govern all visible objects2 but by far the most conspicuous examples of the relations which arise out of such elements1 are displayed by the ever-moving luminaries of the sky1 which measure days1 and months1 and years1 by their motions1 and man's place on the earth by their position4 ,hence the sciences of space and number were from the first cultivated with peculiar reference to ,astronomy4 ,i have elsewhere#ahb quoted ,plato's remark1--that it is absurd to call the science of the relations of space geometry1 the measure of the earth1 since its most important office is to be found in its application to the heavens4 ,and on other occasions also it appears how strongly he1 who may be considered as the representative of the scientific and speculative tendencies of his time and country1 had been impressed with the conviction1 that the formation of a science of the celestial motions must depend entirely upon the progress of mathematics4 ,in the ,epilogue to the ,dialogue on the ,laws#aib1 he declares mathematical knowledge to be the first and main requisite for the astronomer1 and describes the portions of it which he holds necessary for astronomical speculators to cultivate4 ,these seem to be1 ,plane ,geometry1 ,theoretical ,arithmetic1 the ,application of ,arithmetic #afa to planes and to solids1 and finally the doctrine of ,harmonics4 ,indeed the bias of ,plato appears to be rather to consider mathematics as the essence of the science of astronomy1 than as its instrument2 and he seems disposed1 in this as in other things1 to disparage observation1 and to aspire after a science founded upon demonstration alone4 ',an astronomer1' he says in the same place1 'must not be like ,hesiod and persons of that kind1 whose astronomy consists in noting the settings and risings of the stars2 but he must be one who understands the revolutions of the celestial spheres1 each performing its proper cycle4' ,note #ahb3 ,hist4 ,ind4 ,sc4 b4 iii4 c4 ii4 ,note #aib3 ,epinomis1 p4 #iij4 ,a large portion of the mathematics of the ,greeks1 so long as their scientific activity continued1 was directed towards ,astronomy4 ,besides many curious propositions of plane and solid ,geometry1 to which their astronomers were led1 their ,arithmetic1 though very inconvenient in its fundamental assumptions 7as being sexagesimal not decimal71 was cultivated to a great extent2 and the science of ,trigonometry1 in which problems concerning the relations of space were resolved by means of tables of numerical results previously obtained1 was created4 ,menelaus of ,alexandria wrote six ,books on ,chords1 probably containing methods of calculating ,tables of these quantities2 such ,tables were familiarly used by the later ,greek astronomers4 ,the same author also wrote three ,books on ,spherical ,trigonometry1 which are still extant4 #c4 ,the ,greeks1 however1 in the first vigour of their pursuit of mathematical truth1 at the time of ,plato and soon after1 had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature2 but had followed out many beautiful trains of research1 concerning various kinds of figures1 for the sake of their beauty alone2 as for instance in their doctrine of ,conic ,sections1 of which curves they had discovered all the principal properties4 ,but it is curious to remark1 that these investigations1 thus pursued at first as mere matters of curiosity and intellectual gratification1 were destined1 two thousand years later1 to play a very important part in #afb establishing that system of the celestial motions which succeeded the ,platonic scheme of cycles and epicycles4 ,if the properties of the conic sections had not been demonstrated by the ,greeks1 and thus rendered familiar to the mathematicians of succeeding ages1 ,kepler would probably not have been able to discover those laws respecting the orbits and motions of the planets which were the occasion of the greatest revolution that ever happened in the history of science4 #d4 ,the ,arabians1 who1 as ,i have elsewhere said1 added little of their own to the stores of science which they received from the ,greeks1 did however make some very important contributions in those portions of pure mathematics which are subservient to astronomy4 ,their adoption of the ,indian mode of computation by means of the ,ten ,digits1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i1 #j1 and by the method of ,local ,values1 instead of the cumbrous sexagesimal arithmetic of the ,greeks1 was an improvement by which the convenience and facility of numerical calculations were immeasurably augmented4 ,the ,arabians also rendered several of the processes of trigonometry much more commodious1 by using the ,sine of an arc instead of the ,chord2 an improvement which ,albategnius appears to claim for himself#bjb2 and by employing also the ,tangents of arcs1 or1 as they called them#bab1 upright shadows4 ,note #bjb3 ,delambre1 ,ast41 ,m4 ,a41 p4 #ab4 ,note #bab3 ,ibid4 p4 #ag4 #e4 ,the constant application of mathematical knowledge to the researches of ,astronomy1 and the mutual influence of each science on the progress of the other1 has been still more conspicuous in modern times4 ,newton's ,method of ,prime and ,ultimate ,ratios1 which we have already noticed as the first correct exposition of the doctrine of a ,limit1 is stated in a series of ,lemmas1 or preparatory theorems1 prefixed to his ,treatise on the ,system of the ,world4 ,both the properties of curve lines and the doctrines concerning force and motion1 which he had to establish1 required that the common mathematical processes should be methodized and extended4 ,if ,newton had not been a most #afc expert and inventive mathematician1 as well as a profound and philosophical thinker1 he could never have made any one of those vast strides in discovery of which the rapid succession in his work strikes us with wonder#bbb4 ,and if we see that the great task begun by him1 goes on more slowly in the hands of his immediate successors1 and lingers a little before its full completion1 we perceive that this arises1 in a great measure1 from the defect of the mathematical methods then used4 ,newton's synthetical modes of investigation1 as we have elsewhere observed1 were an instrument#bcb1 powerful indeed in his mighty hand1 but too ponderous for other persons to employ with effect4 ,the countrymen of ,newton clung to it the longest1 out of veneration for their master2 and ,english cultivators of physical astronomy were1 on that very account1 left behind the progress of mathematical science in ,france and ,germany1 by a wide interval1 which they have only recently recovered4 ,on the ,continent1 the advantages offered by a familiar use of symbols1 and by attention to their symmetry and other relations1 were accepted without reserve4 ,in this manner the ,differential ,calculus of ,leibnitz1 which was in its origin and signification identical with the ,method of ,fluxions of ,newton1 soon surpassed its rival in the extent and generality of its application to problems4 ,this ,calculus was applied to the science of mechanics1 to which it1 along with the symmetrical use of co-ordinates1 gave a new form2 for it was soon seen that the most difficult problems might in general be reduced to finding integrals1 which is the reciprocal process of that by which differentials are found2 so that all difficulties of physical astronomy were reduced to difficulties of symbolical calculation1 these1 indeed1 being often sufficiently stubborn4 ,clairaut1 ,euler1 and ,d',alembert employed the increased resources of mathematical science upon the ,theory of the ,moon1 and other questions relative to the system of the world2 and thus began to pursue such inquiries in the course in which mathematicians #afd are still labouring up to the present day4 ,this course was not without its checks and perplexities4 ,we have elsewhere quoted#bdb ,clairaut's expression when he had obtained the very complex differential equations which contain the solution of the problem of the moon's motion3 ',now integrate them who can6' ,but in no very long time they were integrated1 at least approximately2 and the methods of approximation have since then been improved2 so that now1 with a due expenditure of labour1 they may be carried to any extent which is thought desirable4 ,if the methods of astronomical observation should hereafter reach a higher degree of exactness than they now profess1 so that irregularities in the motions of the sun1 moon1 and planets1 shall be detected which at present escape us1 the mathematical part of the theory of universal gravitation is in such a condition that it can soon be brought into comparison with the newly-observed facts4 ,indeed at present the mathematical theory is in advance of such observations4 ,it can venture to suggest what may afterwards be detected1 as well as to explain what has already been observed4 ,this has happened recently2 for ,professor ,airy has calculated the law and amount of an inequality depending upon the mutual attraction of the ,earth and ,venus2 of which inequality 7so small is it17 it remains to be determined whether its effect can be traced in the series of astronomical observations4 ,note #bbb3 ,hist4 ,ind4 ,sc4 b4 vii4 c4 ii4 ,note #bcb3 ,ibid4 p4 #age4 ,note #bdb3 ,hist4 ,ind4 ,sc4 b4 vi4 c4 vi4 sect4 #g4 #f4 ,as the influence of mathematics upon the progress of astronomy is thus seen in the cases in which theory and observation confirm each other1 so this influence appears in another way1 in the very few cases in which the facts have not been fully reduced to an agreement with theory4 ,the most conspicuous case of this kind is the state of our knowledge of the ,tides4 ,this is a portion of astronomy3 for the ,newtonian theory asserts these curious phenomena to be the result of the attraction of the sun and moon4 ,nor can there be any doubt that this is true1 as a general statement2 yet the subject is up to the present time a blot #afe on the perfection of the theory of universal gravitation2 for we are very far from being able in this1 as in the other parts of astronomy1 to show that theory will exactly account for the time1 and magnitude1 and all other circumstances of the phenomenon at every place on the earth's surface4 ,and what is the portion of our mathematics which is connected with this solitary signal defect in astronomy8 ,it is the mathematics of the ,motion of ,fluids2 a portion in which extremely little progress has been made1 and in which all the more general problems of the subject have hitherto remained entirely insoluble4 ,the attempts of the greatest mathematicians1 ,newton1 ,maclaurin1 ,bernoulli1 ,clairaut1 ,laplace1 to master such questions1 all involve some gratuitous assumption1 which is introduced because the problem cannot otherwise be mathematically dealt with3 these assumptions confessedly render the result defective1 and how defective1 it is hard to say4 ,and it was probably precisely the absence of a theory which could be reasonably expected to agree with the observations1 which made ,observations of this very curious phenomenon1 the ,tides1 to be so much neglected as till very recently they were4 ,of late years such observations have been pursued1 and their results have been resolved into empirical laws1 so that the rules of the phenomena have been ascertained1 although the dependence of these rules upon the lunar and solar forces has not been shown4 ,here then we have a portion of our knowledge relating to facts undoubtedly dependent upon universal gravitation1 in which ,observation has outstripped ,theory in her progress1 and is compelled to wait till her usual companion overtakes her4 ,this is a position of which ,mathematical ,theory has usually been very impatient1 and we may expect that she will be no less so in the present instance4 #g4 ,it would be easy to show from the history of other sciences1 for example1 ,mechanics and ,optics1 how essential the cultivation of pure mathematics has been to their progress4 ,the parabola was already familiar among mathematicians when ,galileo discovered that it was the theoretical path of a ,projectile2 and the #aff extension and generalization of the ,laws of ,motion could never have been effected1 unless the ,differential and ,integral ,calculus had been at hand1 ready to trace the results of every hypothesis which could be made4 ,d',alembert's mode of expressing the ,third ,law of ,motion in its most general form#beb1 if it did not prove the law1 at least reduced the application of it to analytical processes which could be performed in most of those cases in which they were needed4 ,in many instances the demands of mechanical science suggested the extension of the methods of pure analysis4 ,the problem of ,vibrating ,strings gave rise to the ,calculus of ,partial ,differences1 which was still further stimulated by its application to the motions of fluids and other mechanical problems4 ,and we have in the writings of ,lagrange and ,laplace other instances equally remarkable of new analytical methods1 to which mechanical problems1 and especially cosmical problems1 have given occasion4 ,note #beb3 ,hist4 ,ind4 ,sc4 b4 vi4 c4 vi4 sect4 #g4 #h4 ,the progress of ,optics as a science has1 in like manner1 been throughout dependent upon the progress of pure mathematics4 ,the first rise of ,geometry was followed by some advances1 slight ones no doubt1 in the doctrine of ,reflection and in ,perspective4 ,the law of ,refraction was traced to its consequences by means of ,trigonometry1 which indeed was requisite to express the law in a simple form4 ,the steps made in ,optical science by ,descartes1 ,newton1 ,euler1 and ,huyghens1 required the geometrical skill which those philosophers possessed4 ,and if ,young and ,fresnel had not been1 each in his peculiar way1 persons of eminent mathematical endowments1 they would not have been able to bring the ,theory of ,undulations and ,interferences into a condition in which it could be tested by experiments4 ,we may see how unexpectedly recondite parts of pure mathematics may bear upon physical science1 by calling to mind a circumstance already noticed in the ,history of ,science#bfb2--that ,fresnel obtained one of the #afg most curious confirmations of the theory 7the laws of ,circular ,polarization by reflection7 through an interpretation of an algebraical expression1 which1 according to the original conventional meaning of the symbols1 involved an impossible quantity4 ,we have already remarked1 that in virtue of the principle of the generality of symbolical language1 such an interpretation may often point out some real and important analogy4 ,note #bfb3 ,hist4 ,ind4 ,sc4 b4 ix4 c4 xiii4 sect4 #b4 #i4 ,from this rapid sketch it may be seen how important an office in promoting the progress of the physical sciences belongs to mathematics4 ,indeed in the progress of many sciences1 every step has been so intimately connected with some advance in mathematics1 that we can hardly be surprised if some persons have considered mathematical reasoning to be the most essential part of such sciences2 and have overlooked the other elements which enter into their formation4 ,how erroneous this view is we shall best see by turning our attention to the other ,ideas besides those of space1 number1 and motion1 which enter into some of the most conspicuous and admired portions of what is termed exact science2 and by showing that the clear and distinct development of such ,ideas is quite as necessary to the progress of exact and real knowledge as an acquaintance with arithmetic and geometry4 #afi ,,book ,,iii4 ,,the ,,philosophy ,,of ,,the ,,mechanical ,,sciences4 ,,it is only because we subject trains of phenomena1 that is1 all change whatever1 to the law of causality--to the relation of cause and effect--that experience or empirical knowledge becomes possible4 ,,kant1 ,kr4 d4 ,r4 ,v4 #aa ,th4 #a ,abth4 #aa ,buch4 #b ,haupt4 ,quicquid premit vel trahit alterum1 tantundem ab eo premitur vel trahitur 444 ,si corpus aliquod in corpus aliud impingens motum ejus vi su quomodocunque mutaverit1 idem quoque vicissim in motu proprio eandem mutationem in partem contrariam vi alterius 7ob qualitatem pressionis1 mutu7 subibit 444 ,obtinet etiam hc ,lex in attractionibus4 ,,newton1 ,princip4 ad init4 #aga ,,book ,,iii4 ,,the ,,philosophy ,,of ,,the ,,mechanical ,,sciences4 ,,chapter ,i4 ,,of ,,the ,,mechanical ,,sciences4 ,,in the ,history of the ,sciences1 that class of which we here speak occupies a conspicuous and important place2 coming into notice immediately after those parts of ,astronomy which require for their cultivation merely the ideas of space1 time1 motion1 and number4 ,it appears from our ,history1 that certain truths concerning the equilibrium of bodies were established by ,archimedes2--that1 after a long interval of inactivity1 his principles were extended and pursued further in modern times3--and that to these doctrines concerning equilibrium and the forces which produce it1 7which constitute the science ,statics17 were added many other doctrines concerning the motions of bodies1 considered also as produced by forces1 and thus the science of ,dynamics was produced4 ,the assemblage of these sciences composes the province of ,mechanics4 ,moreover1 philosophers have laboured to make out the laws of the equilibrium of fluid as well as solid bodies2 and hence has arisen the science of ,hydrostatics4 ,and the doctrines of ,mechanics have been found to have a most remarkable bearing upon the motions of the heavenly bodies2 with reference to which1 indeed1 they were at first principally studied4 ,the explanation of those cosmical facts by means of mechanical #agb principles and their consequences1 forms the science of ,physical ,astronomy4 ,these are the principal examples of mechanical science2 although some other portions of ,physics1 as ,magnetism and ,electrodynamics1 introduce mechanical doctrines very largely into their speculations4 ,now in all these sciences we have to consider ,forces4 ,in all mechanical reasonings forces enter1 either as producing motion1 or as prevented from doing so by other forces4 ,thus force1 in its most general sense1 is the cause of motion1 or of tendency to motion2 and in order to discover the principles on which the mechanical sciences truly rest1 we must examine the nature and origin of our knowledge of ,causes4 ,in these sciences1 however1 we have not to deal with ,cause in its more general acceptation1 in which it applies to all kinds of agency1 material or immaterial2--to the influence of thought and will1 as well as of bodily pressure and attractive force4 ,our business at present is only with such causes as immediately operate upon matter4 ,we shall nevertheless1 in the first place1 consider the nature of ,cause in its most general form2 and afterwards narrow our speculations so as to direct them specially to the mechanical sciences4 #agc ,,chapter ,,ii4 ,,of ,,the ,,idea ,,of ,,cause4 #a4 ,,we see in the world around us a constant succession of causes and effects connected with each other4 ,the laws of this connexion we learn in a great measure from experience1 by observation of the occurrences which present themselves to our notice1 succeeding one another4 ,but in doing this1 and in attending to this succession of appearances1 of which we are aware by means of our senses1 we supply from our own minds the ,idea of ,cause4 ,this ,idea1 as we have already shown with respect to other ,ideas1 is not derived from experience1 but has its origin in the mind itself2--is introduced into our experience by the active1 and not by the passive part of our nature4 ,by ,cause we mean some quality1 power1 or efficacy1 by which a state of things produces a succeeding state4 ,thus the motion of bodies from rest is produced by a cause which we call ,force3 and in the particular case in which bodies fall to the earth1 this force is termed ,gravity4 ,in these cases1 the ,conceptions of ,force and ,gravity receive their meaning from the ,idea of ,cause which they involve3 for ,force is conceived as the ,cause of ,motion4 ,that this ,idea of ,cause is not derived from experience1 we prove 7as in former cases7 by this consideration3 that we can make assertions1 involving this idea1 which are rigorously necessary and universal2 whereas knowledge derived from experience can only be true as far as experience goes1 and can never contain in itself any evidence whatever of its necessity4 ,we assert that ',every event must have a cause3' and this proposition we know to be true1 not only probably1 and generally1 and as far as we can see3 #agd but we cannot suppose it to be false in any single instance4 ,we are as certain of it as of the truths of arithmetic or geometry4 ,we cannot doubt that it must apply to all events past and future1 in every part of the universe1 just as truly as to those occurrences which we have ourselves observed4 ,what causes produce what effects2--what is the cause of any particular event2--what will be the effect of any peculiar process2--these are points on which experience may enlighten us4 ,observation and experience may be requisite1 to enable us to judge respecting such matters4 ,but that every event has some cause1 ,experience cannot prove any more than she can disprove4 ,she can add nothing to the evidence of the truth1 however often she may exemplify it4 ,this doctrine1 then1 cannot have been acquired by her teaching2 and the ,idea of ,cause1 which the doctrine involves1 and on which it depends1 cannot have come into our minds from the region of observation4 #b4 ,that we do1 in fact1 apply the ,idea of ,cause in a more extensive manner than could be justified1 if it were derived from experience only1 is easily shown4 ,for from the principle that everything must have a cause1 we not only reason concerning the succession of the events which occur in the progress of the world1 and which form the course of experience2 but we infer that the world itself must have a cause2--that the chain of events connected by common causation1 must have a ,first ,cause of a nature different from the events themselves4 ,this we are entitled to do1 if our ,idea of ,cause be independent of1 and superior to1 experience3 but if we have no ,idea of ,cause except such as we gather from experience1 this reasoning is altogether baseless and unmeaning4 #c4 ,again2 by the use of our powers of observation1 we are aware of a succession of appearances and events4 ,but none of our senses or powers of external observation can detect in these appearances the power or quality which we call ,cause4 ,cause is that which connects one event with another2 but no sense or perception discloses to us1 or can disclose1 any connexion #age among the events which we observe4 ,we see that one occurrence follows another1 but we can never see anything which shows that one occurrence must follow another4 ,we have already noticed#ac1 that this truth has been urged by metaphysicians in modern times1 and generally assented to by those who examine carefully the connexion of their own thoughts4 ,the arguments are1 indeed1 obvious enough4 ,one ball strikes another and causes it to move forwards4 ,but by what compulsion8 ,where is the necessity8 ,if the mind can see any circumstance in this case which makes the result inevitable1 let this circumstance be pointed out4 ,but1 in fact1 there is no such discoverable necessity2 for we can conceive this event not to take place at all4 ,the struck ball may stand still1 for aught we can see4 ',but the laws of motion will not allow it to do so4' ,doubtless they will not4 ,but the laws of motion are learnt from experience1 and therefore can prove no necessity4 ,why should not the laws of motion be other than they are8 ,are they necessarily true8 ,that they are necessarily such as do actually regulate the impact of bodies1 is at least no obvious truth2 and therefore this necessity cannot be1 in common minds1 the ground of connecting the impact of one ball with the motion of another4 ,and assuredly1 if this fail1 no other ground of such necessary connexion can be shown4 ,in this case1 then1 the events are not seen to be necessarily connected4 ,but if this case1 where one ball moves another by impulse1 be not an instance of events exhibiting a necessary connexion1 we shall look in vain for any example of such a connexion4 ,there is1 then1 no case in which events can be observed to be necessarily connected3 our idea of causation1 which implies that the event is necessarily connected with the cause1 cannot be derived from observation4 ,note #ac3 ,book #c4 chap4 ii4 #d4 ,but it may be said1 we have not any such ,idea of ,cause1 implying necessary connexion with effect1 and a quality by which this connexion is produced4 #agf ,we see nothing but the succession of events2 and by cause we mean nothing but a certain succession of events2--namely1 a constant1 unvarying succession4 ,cause and effect are only two events of which the second invariably follows the first4 ,we delude ourselves when we imagine that our idea of causation involves anything more4 ,to this ,i reply by asking1 what then is the meaning of the maxim above quoted1 and allowed by all to be universally and necessarily true1 that every event must have a cause8 ,let us put this maxim into the language of the explanation just noticed2 and it becomes this3--',every event must have a certain other event invariably preceding it4' ,but why must it8 ,where is the necessity8 ,why must like events always be preceded by like1 except so far as other events interfere8 ,that there is such a necessity1 no one can doubt4 ,all will allow that if a stone ascend because it is thrown upwards in one case1 a stone which ascends in another case has also been thrown upwards1 or has undergone some equivalent operation4 ,all will allow that in this sense1 every kind of event must have some other specific kind of event preceding it4 ,but this turn of men's thoughts shows that they see in events a connexion which is not mere succession4 ,they see in cause and effect1 not merely what does1 often or always1 precede and follow1 but what must precede and follow4 ,the events are not only conjoined1 they are connected4 ,the cause is more than the prelude1 the effect is more than the sequel1 of the fact4 ,the cause is conceived not as a mere occasion2 it is a power1 an efficacy1 which has a real operation4 #e4 ,thus we have drawn from the maxim1 that ,every ,effect must have a ,cause1 arguments to show that we have an ,idea of ,cause which is not borrowed from experience1 and which involves more than mere succession4 ,similar arguments might be derived from any other maxims of universal and necessary validity1 which we can obtain concerning ,cause3 as1 for example1 the maxims that ,causes are measured by their ,effects1 and that ,reaction is equal and opposite to #agg ,action4 ,these maxims we shall soon have to examine2 but we may observe here1 that the necessary truth which belongs to them1 shows that they1 and the ,ideas which they involve1 are not the mere fruits of observation2 while their meaning1 including1 as it does1 something quite different from the mere conception of succession of events1 proves that such a conception is far from containing the whole import and signification of our ,idea of ,cause4 ,the progress of the opinions of philosophers on the points discussed in this chapter1 has been one of the most remarkable parts of the history of ,metaphysics in modern times3 and ,i shall therefore briefly notice some of its features4 #agh ,,chapter ,,iii4 ,,modern ,,opinions ,,respecting ,,the ,,idea ,,of ,,cause4 #a4 ,,towards the end of the seventeenth century there existed in the minds of many of the most vigorous and active speculators of the ,european literary world1 a strong tendency to ascribe the whole of our ,knowledge to the teaching of ,experience4 ,this tendency1 with its consequences1 including among them the reaction which was produced when the tenet had been pushed to a length manifestly absurd1 has exercised a very powerful influence upon the progress of metaphysical doctrines up to the present time4 ,i proceed to notice some of the most prominent of the opinions which have thus obtained prevalence among philosophers1 so far as the ,idea of ,cause is concerned4 ,locke was one of the metaphysicians who produced the greatest effect in diffusing this opinion1 of the exclusive dependence of our knowledge upon experience4 ,agreeably to this general system1 he taught#bc that our ideas of ,cause and ,effect are got from observation of the things about us4 ,yet notwithstanding this tenet of his1 he endeavoured still to employ these ideas in reasoning on subjects which are far beyond all limits of experience3 for he professed to prove1 from our idea of ,causation1 the existence of the ,deity#cc4 ,note #bc3 ,essay on the ,human ,understanding1 b4 ii4 c4 xxvi4 ,note #cc3 ,b4 iv4 c4 x4 ,hume noticed this obvious inconsistency2 but declared himself unable to discover any remedy for a defect so fatal to the most important parts of our knowledge4 ,he could see1 in our belief of the succession of cause and effect1 nothing but the habit of associating in our minds what had often been #agi associated in our experience4 ,he therefore maintained that we could not1 with logical propriety1 extend our belief of such a succession to cases entirely distinct from all those of which our experience consisted4 ,we see1 he said1 an actual conjunction of two events2 but we can in no way detect a necessary connexion2 and therefore we have no means of inferring cause from effect1 or effect from cause#dc4 ,the only way in which we recognize ,cause and ,effect in the field of our experience1 is as an unfailing ,sequence3 we look in vain for anything which can assure us of an infallible ,consequence4 ,and since experience is the only source of our knowledge1 we cannot with any justice assert that the world in which we live must necessarily have had a cause4 ,note #dc3 ,hume's ,phil4 of the ,human ,mind1 vol4 i4 p4 #id4 #b4 ,this doctrine1 taken in conjunction with the known skepticism of its author on religious points1 produced a considerable fermentation in the speculative world4 ,the solution of the difficulty thus thrown before philosophers1 was by no means obvious4 ,it was vain to endeavour to find in experience any other property of a ,cause1 than a constant sequence of the effect4 ,yet it was equally vain to try to persuade men that they had no idea of ,cause2 or even to shake their belief in the cogency of the familiar arguments concerning the necessity of an original cause of all that is and happens4 ,accordingly these hostile and apparently irreconcilable doctrines1--the indispensable necessity of a cause of every event1 and the impossibility of our knowing such a necessity1--were at last allowed to encamp side by side4 ,reid1 ,beattie1 and others1 formed one party1 who showed how widely and constantly the idea of a cause pervades all the processes of the human mind3 while another sect1 including ,brown1 and apparently ,stewart1 maintained that this idea is always capable of being resolved into a constant sequence2 and these latter reasoners tried to obviate the dangerous and shocking inferences which some persons might try to draw from their opinion1 by declaring the #ahj maxim that ,every event must have a cause1 to be an instinctive law of belief1 or a fundamental principle of the human mind#ec4 ,note #ec3 ,stewart's ,active ,powers1 vol4 i4 p4 #cdg4 ,browne's ,lectures1 vol4 i4 p4 #aae4 #c4 ,while this series of discussions was going on in ,britain1 a great metaphysical genius in ,germany was unravelling the perplexity in another way4 ,kant's speculations originated1 as he informs us1 in the trains of thought to which ,hume's writings gave rise2 and the ,kritik der ,reinen ,vernunft1 or ,examination of the ,pure ,reason1 was published in #aghg1 with the view of showing the true nature of our knowledge4 ,kant's solution of the difficulties just mentioned differs materially from that above stated4 ,according to ,brown#fc1 succession observed and cause inferred1--the memory of past conjunctions of events and the belief of similar future conjunctions1--are facts1 independent1 so far as we can discover1 but inseparably combined by a law of our mental nature4 ,according to ,kant1 causality is an inseparable condition of our experience3 a connexion in events is requisite to our apprehending them as events4 ,future occurrences must be connected by causation as the past have been1 because we cannot think of past1 present1 and future1 without such connexion4 ,we cannot fix the mind upon occurrences1 without including these occurrences in a series of causes and effects4 ,the relation of ,causation is a condition under which we think of events1 as the relations of space are a condition under which we see objects4 ,note #fc3 ,lectures1 vol4 i4 p4 #aad4 #d4 ,on a subject so abstruse1 it is not easy to make our distinctions very clear4 ,some of ,brown's illustrations appear to approach very near to the doctrine of ,kant4 ,thus he says#gc1 ',the form of bodies is the relation of their elements to each other in space1--the power of bodies is their relation to each other in time4' ,yet notwithstanding such approximations in expression1 the ,kantian doctrine appears to be different from #aha the views of ,stewart and ,brown1 as commonly understood4 ,according to the ,scotch philosophers1 the cause and the effect are two things1 connected in our minds by a law of our nature4 ,but this view requires us to suppose that we can conceive the law to be absent1 and the course of events to be unconnected4 ,if we can understand what is the special force of this law1 we must be able to imagine what the case would be if the law were non-existing4 ,we must be able to conceive a mind which does not connect effects with causes4 ,the ,kantian doctrine1 on the other hand1 teaches that we cannot imagine events liberated from the connexion of cause and effect3 this connexion is a condition of our conceiving any real occurrences3 we cannot think of a real sequence of things1 except as involving the operation of causes4 ,in the ,scotch system1 the past and the future are in their nature independent1 but bound together by a rule2 in the ,german system1 they share in a common nature and mutual relation1 by the act of thought which makes them past and future4 ,in the former doctrine cause is a tie which binds2 in the latter it is a character which pervades and shapes events4 ,the ,scotch metaphysicians only assert the universality of the relation2 the ,german attempts further to explain its necessity4 ,note #gc3 ,lectures1 vol4 i4 p4 #abg4 ,this being the state of the case1 such illustrations as that of ,dr4 ,brown quoted above1 in which he represents cause as a relation of the same kind with form1 do not appear exactly to fit his opinions4 ,can the relations of figure be properly said to be connected with each other by a law of our nature1 or a tendency of our mental constitution8 ,can we ascribe it to a law of our thoughts1 that we believe the three angles of a triangle to be equal to two right angles8 ,if so1 we must give the same reason for our belief that two straight lines cannot inclose a space2 or that three and two are five4 ,but will any one refer us to an ultimate law of our constitution for the belief that three and two are five8 ,do we not see that they are so1 as plainly as we see that they are three and two8 ,can we imagine laws of our constitution abolished1 so that three and two shall #ahb make something different from five2--so that an inclosed space shall lie between two straight lines2--so that the three angles of a plane triangle shall be greater than two right angles8 ,we cannot conceive this4 ,if the numbers are three and two2 if the lines are straight2 if the triangle is a rectilinear triangle1 the consequences are inevitable4 ,we cannot even imagine the contrary4 ,we do not want a law to direct that things should be what they are4 ,the relation1 then1 of cause and effect1 being of the same kind as the necessary relations of figure and number1 is not properly spoken of as established in our minds by a special law of our constitution3 for we reject that loose and inappropriate phraseology which speaks of the relations of figure and number as 'determined by laws of belief4' #e4 ,in the present work1 we accept and adopt1 as the basis of our inquiry concerning our knowledge1 the existence of necessary truths concerning causes1 as there exist necessary truths concerning figure and number4 ,we find such truths universally established and assented to among the cultivators of science1 and among speculative men in general4 ,all mechanicians agree that reaction is equal and opposite to action1 both when one body presses another1 and when one body communicates motion to another4 ,all reasoners join in the assertion1 not only that every observed change of motion has had a cause1 but that every change of motion must have a cause4 ,here we have certain portions of substantial and undoubted knowledge4 ,now the essential point in the view which we must take of the idea of cause is this1--that our view must be such as to form a solid basis for our knowledge4 ,we have1 in the ,mechanical ,sciences1 certain universal and necessary truths on the subject of causes4 ,now any view which refers our belief in causation to mere experience or habit1 cannot explain the possibility of such necessary truths1 since experience and habit can never lead to a perception of necessary connexion4 ,but a view which teaches us to acknowledge axioms concerning cause1 as we acknowledge axioms #ahc concerning space1 will lead us to look upon the science of mechanics as equally certain and universal with the science of geometry2 and will thus materially affect our judgment concerning the nature and claims of our scientific knowledge4 ,axioms concerning ,cause1 or concerning ,force1 which as we shall see1 is a modification of ,cause1 will flow from an ,idea of ,cause1 just as axioms concerning space and number flow from the ideas of space and number or time4 ,and thus the propositions which constitute the science of ,mechanics prove that we possess an idea of cause1 in the same sense in which the propositions of geometry and arithmetic prove our possession of the ideas of space and of time or number4 #f4 ,the idea of cause1 like the ideas of space and time1 is a part of the active powers of the mind4 ,the relation of cause and effect is a relation or condition under which events are apprehended1 which relation is not given by observation1 but supplied by the mind itself4 ,according to the views which explain our apprehension of cause by reference to habit1 or to a supposed law of our mental nature1 causal connexion is a consequence of agencies which the mind passively obeys2 but according to the view to which we are led1 this connexion is a result of faculties which the mind actively exercises4 ,and thus the relation of cause and effect is a condition of our apprehending successive events1 a part of the mind's constant and universal activity1 a source of necessary truths2 or1 to sum all this in one phrase1 a ,fundamental ,idea4 #ahd ,,chapter ,,iv4 ,,of ,,the ,,axioms ,,which ,,relate ,,to ,,the ,,idea ,,of ,,cause4 #a4 ,causes are abstract ,conceptions4--,,we have now to express1 as well as we can1 the fundamental character of that ,idea of ,cause of which we have just proved the existence4 ,this may be done1 at least for purposes of reasoning1 in this as in former instances1 by means of axioms4 ,i shall state the principal axioms which belong to this subject1 referring the reader to his own thoughts for the axiomatic evidence which belongs to them4 ,but ,i must first observe1 that in order to express general and abstract truths concerning cause and effect1 these terms1 cause and effect1 must be understood in a general and abstract manner4 ,when one event gives rise to another1 the first event is1 in common language1 often called the cause1 and the second the effect4 ,thus the meeting of two billiard-balls may be said to be the cause of one of them turning aside out of the path in which it was moving4 ,for our present purposes1 however1 we must not apply the term cause to such occurrences as this meeting and turning1 but to a certain conception1 force1 abstracted from all such special events1 and considered as a quality or property by which one body affects the motion of the other4 ,and in like manner in other cases1 cause is to be conceived as some abstract quality1 power1 or efficacy1 by which change is produced2 a quality not identical with the events1 but disclosed by means of them4 ,not only is this abstract mode of conceiving force and cause useful in expressing the fundamental principles of science2 but it supplies us with the only mode by which such principles can be #ahe stated in a general manner1 and made to lead to substantial truth and real knowledge4 ,understanding cause1 therefore1 in this sense1 we proceed to our ,axioms4 #b4 ,first ,axiom4 ,nothing can take place without a ,cause4 ,every event1 of whatever kind1 must have a cause in the sense of the term which we have just indicated2 and that it must1 is a universal and necessary proposition to which we irresistibly assent as soon as it is understood4 ,we believe each appearance to come into existence1--we conceive every change to take place1--not only with something preceding it1 but something by which it is made to be what it is4 ,an effect without a cause2--an event without a preceding condition involving the efficacy by which the event is produced2--are suppositions which we cannot for a moment admit4 ,that the connexion of effect with cause is universal and necessary1 is a universal and constant conviction of mankind4 ,it persists in the minds of all men1 undisturbed by all the assaults of sophistry and skepticism2 and1 as we have seen in the last chapter1 remains unshaken1 even when its foundations seem to be ruined4 ,this axiom expresses1 to a certain extent1 our ,idea of ,cause2 and when that idea is clearly apprehended1 the axiom requires no proof1 and indeed admits of none which makes it more evident4 ,that notwithstanding its simplicity1 it is of use in our speculations1 we shall hereafter see2 but in the first place1 we must consider the other axioms belonging to this subject4 #c4 ,second ,axiom4 ,effects are proportional to their ,causes1 and ,causes are measured by their ,effects4 ,we have already said that cause is that quality or power1 in the circumstances of each case1 by which the effect is produced2 and this power1 an abstract property of the condition of things to which it belongs1 can in no way fall directly under the cognizance of the senses4 ,cause1 of whatever kind1 is not apprehended as including objects and events which share its nature by being co-extensive with certain portions of it1 as space and time are4 ,it cannot therefore1 like them1 be #ahf measured by repetition of its own parts1 as space is measured by repetition of inches1 and time by repetition of minutes4 ,causes may be greater or less2 as1 for instance1 the force of a man is greater than the force of a child4 ,but how much is the one greater than the other8 ,how are we to compare the abstract conception1 force1 in such cases as these8 ,to this1 the obvious and only answer is1 that we must compare causes by means of their effects2--that we must compare force by something which force can do4 ,the child can lift one fagot2 the man can lift ten such fagots3 we have here a means of comparison4 ,and whether or not the rule is to be applied in this manner1 that is1 by the number of things operated on1 7a question which we shall have to consider hereafter17 it is clear that this form of rule1 namely1 a reference to some effect or other as our measure1 is the right1 because the only possible form4 ,the cause determines the effect4 ,the cause being the same1 the effect must be the same4 ,the connexion of the two is governed by a fixed and inviolable rule4 ,it admits of no ambiguity4 ,every degree of intensity in the cause has some peculiar modification of the effect corresponding to it4 ,hence the effect is an unfailing index of the amount of the cause2 and if it be a measurable effect1 gives a measure of the cause4 ,we can have no other measure2 but we need no other1 for this is exact1 sufficient and complete4 ,it may be said1 that various effects are produced by the same cause4 ,the sun's heat melts wax and expands quicksilver4 ,the force of gravity causes bodies to move downwards if they are free1 and to press down upon their supports if they are supported4 ,which of the effects is to be taken as the measure of heat1 or of gravity1 in these cases8 ,to this we reply1 that if we had merely different states of the same cause to compare1 any of the effects might be taken4 ,the sun's heat on different days might be measured by the expansion of quicksilver1 or by the quantity of wax melted4 ,the force of gravity1 if it were different at different places1 might be measured by the spaces through which a given weight would bend an elastic #ahg support1 or by the spaces through which a body would fall in a given time4 ,all these measures are consistent with the general character of our idea of cause4 #d4 ,limitation of the ,second ,axiom4--,but there may be circumstances in the nature of the case which may further determine the kind of effect which we must take for the measure of the cause4 ,for example1 if causes are conceived to be of such a nature as to be capable of addition1 the effects taken as their measure must conform to this condition4 ,this is the case with mechanical causes4 ,the weights of two bodies are the causes of the pressure which they exert downwards2 and these weights are capable of addition4 ,the weight of the two is the sum of the weight of each4 ,we are therefore not at liberty to say that weights shall be measured by the spaces through which they bend a certain elastic support1 except we have first ascertained that the whole weight bends it through a space equal to the sum of the inflections produced by the separate weights4 ,without this precaution1 we might obtain inconsistent results4 ,two weights1 each of the magnitude #c as measured by their effects1 might1 if we took the inflections of a spring for the effects1 be together equal to #e or to #g by the same kind of measurement4 ,for the inflection produced by two weights of #c might1 for aught we can see beforehand1 be more or less than twice as great as the inflection produced by one weight of #c4 ,that forces are capable of addition1 is a condition which limits1 and1 as we shall see1 in some cases rigorously fixes1 the kind of effects which are to be taken as their measures4 ,causes which are thus capable of addition are to be measured by the repeated addition of equal quantities4 ,two such causes are equal to each other when they produce exactly the same effect4 ,so far our axiom is applied directly4 ,but these two causes can be added together2 and being thus added1 they are double of one of them2 and the cause composed by addition of three such1 is three times as great as the first2 and so on for any measure whatever4 ,by this means1 and by this #ahh means only1 we have a complete and consistent measure of those causes which are so conceived as to be subject to this condition of being added and multiplied4 ,causes are1 in the present chapter1 to be understood in the widest sense of the term2 and the axiom now under our consideration applies to them1 whenever they are of such a nature as to admit of any measure at all4 ,but the cases which we have more particularly in view are mechanical causes1 the causes of the motion and of the equilibrium of bodies4 ,in these cases1 forces are conceived as capable of addition2 and what has been said of the measure of causes in such cases1 applies peculiarly to mechanical forces4 ,two weights1 placed together1 may be considered as a single weight1 equal to the sum of the two4 ,two pressures1 pushing a body in the same direction at the same point1 are identical in all respects with some single pressure1 their sum1 pushing in like manner2 and this is true whether or not they put the body in motion4 ,in the cases of mechanical forces1 therefore1 we take some certain effect1 velocity generated or weight supported1 which may fix the unit of force2 and we then measure all other forces by the successive repetition of this unit1 as we measure all spaces by the successive repetition of our unit of lineal measure4 ,but these steps in the formation of the science of ,mechanics will be further explained1 when we come to follow our axioms concerning cause into their application in that science4 ,at present we have1 perhaps1 sufficiently explained the axiom that causes are measured by their effects1 and we now proceed to a third axiom1 also of great importance4 #e4 ,third ,axiom4 ,reaction is equal and opposite to ,action4 ,in the case of mechanical forces1 the action of a cause often takes place by an operation of one body upon another2 and in this case1 the action is always and inevitably accompanied by an opposite action4 ,if ,i press a stone with my hand1 the stone presses my hand in return4 ,if one ball strike another and put it in motion1 the second ball diminishes the motion of #ahi the first4 ,in these cases the operation is mutual2 the ,action is accompanied by a ,reaction4 ,and in all such cases the ,reaction is a force of exactly the same nature as the ,action1 exerted in an opposite direction4 ,a pressure exerted upon a body at rest is resisted and balanced by another pressure2 when the pressure of one body puts another in motion1 the body1 though it yields to the force1 nevertheless exerts upon the pressing body a force like that which it suffers4 ,now the axiom asserts further1 that this ,reaction is equal1 as well as opposite1 to the ,action4 ,for the ,reaction is an effect of the ,action1 and is determined by it4 ,and since the two1 ,action and ,reaction1 are forces of the same nature1 each may be considered as cause and as effect2 and they must1 therefore1 determine each other by a common rule4 ,but this consideration leads necessarily to their equality3 for since the rule is mutual1 if we could for an instant suppose the ,reaction to be less than the ,action1 we must1 by the same rule1 suppose the ,action to be less than the ,reaction4 ,and thus ,action and ,reaction1 in every such case1 are rigorously equal to each other4 ,it is easily seen that this axiom is not a proposition which is1 or can be1 proved by experience2 but that its truth is anterior to special observation1 and depends on our conception of ,action and ,reaction4 ,like our other axioms1 this has its source in an ,idea2 namely1 the ,idea of ,cause1 under that particular condition in which cause and effect are mutual4 ,the necessary and universal truth which we cannot help ascribing to the axiom1 shows that it is not derived from the stores of experience1 which can never contain truths of this character4 ,accordingly1 it was asserted with equal confidence and generality by those who did not refer to experience for their principles1 and by those who did4 ,leonicus ,tomus1 a commentator of ,aristotle1 whose work was published in #aeeb1 and therefore at a period when no right opinions concerning mechanical reaction were current1 at least in his school1 says1 in his remarks on the ,author's ,questions concerning the communication of motion1 that ',reaction is equal and #aij contrary to ,action4' ,the same principle was taken for granted by all parties1 in all the controversies concerning the proper measure of force1 of which we shall have to speak3 and would be rigorously true1 as a law of motion1 whichever of the rival interpretations of the measure of the term ',action' we were to take4 #f4 ,extent of the ,third ,axiom4--,it may naturally be asked whether this third ,axiom respecting causation extends to any other cases than those of mechanical action1 since the notion of ,cause in general has certainly a much wider extent4 ,for instance1 when a hot body heats a cold one1 is there necessarily an equal reaction of the second body upon the first8 ,does the snowball cool the boy's hand exactly as much as the hand heats the snow8 ,to this we reply1 that1 in every case in which one body acts upon another by its physical qualities1 there must be some reaction4 ,no body can affect another without being itself also affected4 ,but in any physical change the action exerted is an abstract term which may be variously understood4 ,the hot hand may melt a cool body1 or may warm it3 which kind of effect is to be taken as action8 ,this remains to be determined by other considerations4 ,in all cases of physical change produced by one body in another1 it is generally possible to assume such a meaning of action1 that the reaction shall be of the same nature as the action2 and when this is done1 the third axiom of causation1 that reaction is equal to action1 is universally true4 ,thus if a hot body heat a cold one1 the change may be conceived as the transfer of a certain substance1 heat or caloric1 from the first body to the second4 ,on this supposition1 the first body loses just as much heat as the other gains2 action and reaction are equal4 ,but if the reaction be of a different kind to the action we can no longer apply the axiom4 ,if a hot body melt a cold one1 the latter cools the former3 here1 then1 is reaction2 but so long as the action and reaction are stated in this form1 we cannot assert any equality between them4 ,in treating of the secondary mechanical sciences1 we #aia shall see further in what way we may conceive the physical action of one body upon another1 so that the same axioms which are the basis of the science of ,mechanics shall apply to changes not at first sight manifestly mechanical4 ,the three axioms of causation which we have now stated are the fundamental maxims of all reasoning concerning causes as to their quantities2 and it will be shown in the sequel that these axioms form the basis of the science of ,mechanics1 determining its form1 extent1 and certainty4 ,we must1 however1 in the first place1 consider how we acquire those conceptions upon which the axioms now established are to be employed4 #b;d ,ed4 ,the ,axiom that ,reaction is equal and opposite to ,action1 may appear to be at variance with a maxim concerning ,cause which is commonly current2 namely1 that the ',cause precedes ,effect1 and ,effect follows ,cause4' ,for it may be said1 if ,a1 the ,action1 and ,r1 the ,reaction1 can be considered as mutually the cause of each other1 ,a must precede ,r1 and yet must follow it1 which is impossible4 ,but to this ,i reply1 that in those cases of direct ,causation to which the maxim applies1 the ,cause and ,effect are not successive1 but simultaneous4 ,if ,i press against some obstacle1 the obstacle resists and returns the pressure at the instant it is exerted1 not after any interval of time1 however small4 ,the common maxim1 that the effect follows the cause1 has arisen from the practice of considering1 as examples of cause and effect1 not instantaneous forces or causes1 and the instantaneous changes which they produce2 but taking1 instead of this latter1 the cumulative effects produced in the course of time1 and compared with like results occurring without the action of the cause4 ,thus1 if we alter the length of a clock-pendulum1 this change produces1 as its effect1 a subsequent change of rate in the clock3 because the rate is measured by the accumulated effects of the pendulum's gravity1 before and after the change4 ,but the pendulum produces its mechanical effect upon the escapement1 at the moment of its contact1 and each wheel upon the next1 at the moment of its contact4 ,as has #aib been said in a ,review of this work1 ',the time lost in cases of indirect physical causation is consumed in the movements which take place among the parts of the mechanism in action1 by which the active forces so transformed into momentum are transported over intervals of space to new points of action1 the motion of matter in such cases being regarded as a mere carrier of force4' 7,quarterly ,rev4 ,no4 cxxxv4 p4 #bab47 ,this subject ,i have further treated in the ,memoirs of the ,cambridge ,philosophical ,society1 vol4 vii4 part iii4 ,in this ,third ,edition ,i add this discussion4 ,discussion of the ,question3--,are ,cause and ,effect successive or simultaneous8 ,i ,,have at various times laid before this ,society dissertations on the metaphysical grounds and elements of our knowledge1 and especially on the foundations of the science of mechanics4 ,as these speculations have not failed to excite some attention1 both here and elsewhere1 ,i am tempted to bring forward in the same manner some additional disquisitions of the same kind4 ,indeed1 the immediate occasion of the present memoir is of itself an evidence that such subjects are not supposed to be without their interest for the general reader2 for ,i am led to the views and reasonings which ,i am now about to lay before the ,society1 by some remarks in one of our most popular ,reviews1 7,the ,quarterly ,review1 ,article on the ,history and ,philosophy of the ,inductive ,sciences1 ,june #ahda74 ,a writer of singular acuteness and comprehensiveness of view has there made remarks upon the doctrines which ,i had delivered in the ,philosophy of the ,inductive ,sciences1 which remarks appear to me in the highest degree instructive and philosophical4 ,i am not1 however1 going here to discuss fully the doctrines contained in this critique4 ,with respect to its general tendency1 ,i will only observe1 that the author does not accept1 in the form in which ,i had given it1 the account of the origin and ground of necessary and universal truths4 ,i had stated that our knowledge is derived from ,sensations and ,ideas2 and that ,ideas1 which are the conditions of perception1 such as space1 time1 likeness1 cause1 make universal and necessary knowledge possible2 whereas1 if knowledge were derived from ,sensation alone1 it could not have those characters4 ,i have moreover #aic enumerated a long series of ,fundamental ,ideas as the bases of a corresponding series of sciences1 of which sciences ,i have shown also1 by an historical survey1 that they claim to possess universal truths1 and have their claims allowed4 ,i have gone further3 for ,i have stated the ,axioms which flow from these ,fundamental ,ideas1 and which are the logical grounds of necessity and universality in the truths of each science1 when the science is presented in the form of a demonstrated system4 ,the ,reviewer does not assent to this doctrine1 nor to the argument by which it is supported2 namely1 that ,experience cannot lead to universal truths1 except by means of a universal ,idea supplied by the mind1 and infused into the particular facts which observation ministers4 ,he considers that the existence of universal truths in our knowledge may be explained otherwise4 ,he holds that it is a sufficient account of the matter to say that we pass from special experience to universal truth in virtue of 'the inductive propensity--the irresistible impulse of the mind to generalize ad infinitum4' ,i shall not here dwell upon very strong reasons which may be assigned1 as ,i conceive1 for not accepting this as a full and satisfactory explanation of the difficulty4 ,instead of doing so1 ,i shall here content myself with remarking1 that even if we adopt the ,reviewer's expressions1 we must still contend that there are different forms of the impulse of the mind to generalize1 corresponding to each of the ,fundamental ,ideas of our system4 ,these ,fundamental ,ideas1 if they be nothing else1 must at least be accepted as a classification of the modes of action of the ,inductive ,propensity1--as so many different paths and tendencies of the ,generalizing ,impulse3 and the ,axioms which ,i have stated as the express results of the ,fundamental ,ideas1 and as the steps by which those ,ideas make universal truths possible1 are still no less worthy of notice1 if they are stated as the results of our ,generalizing ,impulse2 and as the steps by which that ,impulse1 in its many various forms1 makes universal truths possible4 ,the ,generalizing ,impulse in that operation by which it leads us to the ,axioms of ,geometry1 and to those of ,mechanics1 takes very different courses2 and these courses may well deserve to be separately studied4 ,and perhaps1 even if we accept this view of the philosophy of our knowledge1 no simpler or clearer way can be found of describing and distinguishing these fundamentally different operations of the ,inductive ,propensity1 than by saying1 #aid that in the one case it proceeds according to the ,idea of ,space1 in another according to the ,idea of ,mechanical ,cause2 and the like phraseology may be employed for all the other cases4 ,this then being understood1 my present object is to consider some very remarkable1 and1 as appears to me1 novel views of the ,idea of ,cause which the ,reviewer propounds4 ,and these may be best brought under our discussion by considering them as an attempt to solve the question1 ,whether1 according to our fundamental apprehensions of the relation of ,cause and ,effect1 effect follows cause in the order of time1 or is simultaneous with it4 ,at first sight1 this question may seem to be completely decided by our fundamental convictions respecting cause and effect1 and by the axioms which have been propounded by almost all writers1 and have obtained universal currency among reasoners on this subject4 ,that the cause must precede the effect1--that the effect must follow the cause1--are1 it might seem1 self-evident truths1 assumed and assented to by all persons in all reasonings in which those notions occur4 ,such a doctrine is commonly asserted in general terms1 and seems to be verified in all the applications of the idea of cause4 ,a heavy body produces motion by its weight2 the motion produced is subsequent in time to the pressure which the weight exerts4 ,in a machine1 bodies push or strike each other1 and so produce a series of motions2 each motion1 in this case1 is the result of the motions and configurations which have preceded it4 ,the whole series of such motions employs time2 and this time is filled up and measured by the series of causes and effects1 the effects being1 in their turn1 causes of other effects4 ,this is the common mode of apprehending the universal course of events1 in which the chain of causation1 and the progress of time1 are contemplated as each the necessary condition and accompaniment of the other4 ,but this1 the ,critic remarks1 is not true in direct causation4 ',if the antecedence and consequence in question be understood as the interposition of an interval of time1 however small1 between the action of the cause and the production of the effect1 we regard it as inadmissible4 ,in the production of motion by force1 for instance1 though the effect be cumulative with continued exertion of the cause1 yet each elementary or individual action is1 to our apprehension1 instanter accompanied with its corresponding increment of momentum in the body moved4 ,in all dynamical #aie reasonings no one has ever thought of interposing an instant of time between the action and its resulting momentum2 nor does it appear necessary4' ,this is so evident1 that it appears strange it should have the air of novelty2 yet1 so far as ,i am aware1 the matter has never before been put in the same point of view4 ,but this being the case1 the question occurs1 how it is that time seems to be employed in the progress from cause to effect8 ,how is it that the opinion of the effect being subsequent to the cause has generally obtained8 ,and to this the ,critic's answer is obvious3--it is so in cases of indirect or of cumulative effect4 ,if a ball ,a strikes another1 ,b1 and puts it in motion1 and ,b strikes ,c1 and puts it in motion1 ,a's impact may be considered as the cause1 though not the direct cause1 of ,c's motion4 ,now time1 namely the time of ,b's motion after it is struck by ,a1 and before it strikes ,c1 intervenes between ,a's impact and the beginning of ,c's motion3 that is1 between the cause and its effect4 ,in this sense1 the effect is subsequent to the cause4 ,again1 if a body be put in motion by a series of impulses acting at finite intervals of time1 all in the same direction1 the motion at the end of all these intervals is the effect of all the impulses1 and exists after they have all acted4 ,it is the accumulated effect1 and subsequent to each separate action of the cause4 ,but in this case1 each impulse produces its effect instantaneously1 and the time is employed1 not in the transition from any cause to its effect1 but in the intervals between the action of the several causes1 during which intervals the body goes on with the velocity already communicated to it4 ,in each impulse1 force produces motion3 and the motion goes on till a new change takes place1 by the same kind of action4 ,the force may be said1 in the language employed by the ,critic1 to be transformed into momentum2 and in the successive impulses1 successive portions of force are thus transformed2 while in the intervening intervals1 the force thus transformed into momentum is carried by the body from one place to another1 where a new change awaits it4 ',the cause is absorbed and transformed into effect1 and therein treasured up4' ,hence1 as the ,writer says1 ',the time lost in cases of indirect physical causation is that consumed in the movements which take place among the parts of the mechanism set in action1 by which the active forces so transformed into mechanism are transported over intervals of space to new points of action1 the motion of matter in such cases being #aif regarded as a mere carrier of force'3--and when force is directly counteracted by force1 their mutual destruction must be conceived1 as the ,reviewer says1 to be instantaneous4 ,we can therefore hardly resist his conclusion1 that men have been misled in assuming sequence as a feature in the relation of cause and effect2 and we may readily assent to his suggestion1 that sequence1 when observed1 is to be held as a sure indication of indirect action1 accompanied with a movement of parts4 ,but yet if we turn for a moment to other kinds of causation1 we seem to be compelled at every step to recognize the truth of the usual maxim upon this subject1 that effects are subsequent to causes4 ,is not poison1 taken at a certain moment1 the cause of disorder and death which follow at a subsequent period8 ,is not a man's early prudence often the cause of his prosperity in later life1 and his folly1 though for a moment it may produce gratification1 finally the cause of his ruin8 ,and even in the case of mechanism1 if1 in a clock which goes rightly1 we alter the length of the pendulum1 is not this alteration the cause of an alteration which afterwards takes place in the rate of the clock's going8 ,are not all these1 and innumerable other cases1 instances in which the usual notion of the effect following the cause is verified8 and are they not irreconcileable with the new doctrine of cause and effect being simultaneous8 ,in order to disentangle this apparent confusion1 let us first consider the case last mentioned1 of a clock1 in which some alteration is made which affects the rate of going4 ,so long as the parts of the clock remain unaltered1 its rate will remain unaltered2 and any part which is considered as capable of alteration1 may be considered as1 if we please1 the cause of the unaltered rate1 by being itself unaltered4 ,but we do not usually introduce the positive idea of cause1 to correspond with this negation of change4 ,if we speak of the rate as unaltered1 we may also say that it is so because there is no cause of alteration4 ,the steady rate is the indication of the absence of any cause of alteration2 and the rate of going measures the progress of time1 in a state of things in which causes of change are thus excluded4 ,if an alteration takes place in any part of the clock1 once for all1 the rate is altered2 but the new rate is steady as the old rate was1 and1 like it1 measures the uniform progress of time4 ,but the difference between the new rate and the old is occasioned by #aig the difference of the parts of the clock2 and the new rate may very properly be said to be caused by the change of the parts1 and to be subsequent to it3 for it does prevail after the change1 and does not prevail before4 ,but how is this view to be reconciled with the one just quoted from the ,reviewer1 and1 as it appeared1 satisfactorily proved by him2 according to which all mechanical effects are simultaneous with their causes1 and not subsequent to them8 ,we have here the two views in close contact1 and in seeming opposition4 ,in the going of a clock1 the parts are in motion2 and these motions are determined by forces arising from the form and connexion of the parts of the mechanism4 ,each of the forces thus exerted at any instant produces its effect at the same instant2 and thus1 so far as the term cause refers to such instantaneous forces1 the cause and the effect are simultaneous4 ,but if such instantaneous forces act at successive intervals of time1 the motion during each interval is unaltered1 and by its uniform progress measures the progress of time4 ,and thus the motion of the machine consists of a series of intervals1 during each of which the motion is uniform1 and measures the time2 separated from each other by a series of changes1 at each of which the change measures the instantaneous force1 and is simultaneous with it4 ,and if1 in this case1 we suppose1 at any point of time1 the instantaneous forces to cease1 the succession of them being terminated1 from that point of time the motion would be uniform4 ,and since the rate of the motion in each interval of time is determined by the instantaneous force which last acted and by the preceding motion1 the rate of the motion in each interval of time is determined by all the preceding instantaneous forces4 ,hence1 when the series of instantaneous forces stops1 the rate at which the motion goes on permanently1 from that point of time1 is determined by the antecedent series of such forces1 which series may be considered as an aggregate cause2 and hence it appears1 that the permanent effect is determined by the aggregate cause2 and in this sense the effect is subsequent to the cause4 ,thus we obtain1 in this case1 a solution of the difficulty which is placed before us4 ,the instantaneous effect or change is simultaneous with the instantaneous force or cause by which it is #aih produced4 ,but if we consider a series of such instantaneous forces as a single aggregate cause1 and the final condition as a permanent effect of this cause1 the effect is subsequent to the cause4 ,in this case1 the cause is immediately succeeded by the effect4 ,the cause acts in time3 the effect goes on in time4 ,the times occupied by the cause and by the effect succeed each other1 the one ending at the point of time at which the other begins4 ,but the time which the cause occupies is really composed of a series of instants of uniform motion interposed between instantaneous forces2 and during the time that this series of causes is going on1 to make up the aggregate cause1 a series of effects is going on to make up the final effect4 ,there is a progressive cause and a progressive effect which go on together1 and occupy the same finite time2 and this simultaneous progression is composed of all the simultaneous instantaneous steps of cause and effect4 ,the aggregate cause is the sum of the progression of causes2 the final effect is the last term of the progression of effects4 ,at each step1 as the ,reviewer says1 cause is transformed into effect2 and it is treasured up in the results during the intermediate intervals2 and the time occupied is not the time which intervenes between cause and effect at each step1 but the time which intervenes between these transformations4 ,i have supposed forces to act at distinct instants1 and to cease to act in the intervals between2 and then1 the aggregate of such intervals to make up a finite time1 during which an aggregate force acts4 ,but if the action of the force be rigorously continuous1 it will easily be seen that all the consequences as to cause and effect will be the same2 the discontinuous action being merely the usual artifice by which1 in mathematical reasonings1 we obtain results respecting continuous changes4 ,it will still be true1 that the uniform motion which takes place after a continuous force has acted1 is the effect subsequent to the cause2 while the change which takes place at any instant by the action of the force1 is the instantaneous effect simultaneous with the cause4 ,it may be objected1 that this solution does not appear immediately to apply3 for the motion of a clock is not uniform during any portion of the time4 ,the parts move by intervals of varied motion and of rest2 or by oscillations backwards and forwards2 and the succession of forces which acts during any #aii oscillation1 or any cycle of motion1 is repeated during the succeeding oscillation or cycle1 and so on indefinitely2 and if an alteration be made in the parts1 it is not a change once for all1 but recurs in its operation in every cycle of the motion4 ,but it will be found that this circumstance does not prevent the same explanation from being still applicable with a slight modification4 ,instead of uniform motion in the intervals of causation1 we shall have to speak of steady going3 and instead of considering all the forces which affect the motion as causes of change of uniform motion1 we shall have to speak of changes in the parts of the mechanism as causes of change of rate of going4 ,with this modification1 it will still be true1 that any instantaneous cause produces its instantaneous effect simultaneously1 while the permanent effect is subsequent to the change which is its cause4 ,the steady going of the clock is assumed as a normal condition1 in which it measures the progress of time2 and in this assumption1 the notion of cause and effect is not brought into view4 ,but a steady rate thus denoting the mean passage of time1 a change in the rate indicates a cause of change4 ,the change of rate1 as an instantaneous transition from one rate to another1 is simultaneous with the change in the parts4 ,but then the changed rate as a continued condition in which1 no new change supervening1 the rate again measures the progress of time1 is subsequent to the change of parts1 for it begins when that ends1 and continues when the progress of that has ceased4 ,if1 however1 this be a satisfactory solution of the difficulty in the case of mechanism1 how shall we apply the same views to the other cases8 ,growth1 the effect of food1 is subsequent to the act of taking food2 disorder1 the effect of poison1 is subsequent to the introduction of poison into the system4 ,can we say that the animal would continue unchanged if it were not to take food2 and that food is the cause of a change1 namely1 of growth8 ,this is manifestly false2 for if the animal were not to take food1 it would soon perish4 ,but the analogy of the former case1 of the clock1 will enable us to avoid this perplexity4 ,as we assumed a steady rate of going in the clock to be the measure of time when we considered the effect of mechanism1 so we assume a steady rate of action in the animal functions to be the measure of the progress of time when we consider the causes which act upon the #bjj development and health of animals4 ,digestion1 and of course nutrition1 are a part of this normal condition2 they are involved in the steady going of the animal mechanism1 and we must suppose these functions to go regularly on1 in order that the animal may preserve its character of animal4 ,food and digestion may be considered as causes of the continued existence of the animal1 in the same way in which the form of the parts of a clock is the cause of the steady going of a clock4 ,and when we come to consider causes of change1 this kind of causation1 which produces a normal condition of things1 merely measuring the flow of time1 is left out of our account4 ,we can conceive an uniform condition of animal existence1 the animal neither growing nor wasting4 ,this being taken as the normal condition1 any deviation from this condition indicates a cause1 and is taken as the evidence and measure of the cause of change4 ,and thus1 in a growing animal1 the food partly keeps the animal in continued animal existence1 and partly1 and in addition to this1 causes its growth4 ,food1 in the former view1 is always circulating in the system1 and is supposed to be uniformly administered2 the cycles of nutrition being merged in the notion of uniform existence1 as the oscillations of the pendulum in a clock are merged in the notion of uniform going2 and the elementary steps of nutrition which are1 in this view1 supposed to take place at each instant1 produce their instantaneous effect1 for they are requisite in the cycle of animal processes which goes on from instant to instant4 ,but on the other hand1 in considering growth1 we compare the state of an animal with a preceding state1 and consider the nutriment taken in the intervening time as the cause of the change3 hence this nutriment1 as an aggregate1 is considered as the cause of growth of the animal2 and in this view the effect is subsequent to the cause4 ,but yet here1 as in the case of mechanism1 the progressive effect is simultaneous1 step by step1 with the progressive cause4 ,there is a series of operations2 as for instance1 intussusception1 digestion1 assimilation1 growth3 each of these is a progressive operation2 and in the progress of each operation1 the steps of the effect and the instantaneous forces are simultaneous4 ,but the end of one operation is the beginning of the next1 or at least in part1 and hence we have time occupied by the succession4 ,the end of intussusception is the beginning of digestion1 the end of digestion the beginning of assimilation1 #bja and so on4 ,these aggregate effects succeed each other2 and hence growth is subsequent to the taking of food2 though each instantaneous force of animal life1 no less than of mechanism1 produces an effect simultaneous with its action4 ,each of these separate operations is an aggregate operation1 and occupies time2 and each aggregate effect is a condition of the action of the cause in the next operation4 ,again2 if an animal in a permanent condition1 neither waxing nor wasting1 may be taken as the normal state in which the functions of life measure time1 in order that we may consider growth as an effect1 to be referred to food as cause2 we may1 for other purposes1 consider1 as the normal condition1 an animal waxing and then wasting1 according to the usual law of animal life3 and we must take this1 the healthy progress of an animal1 as our normal condition1 if we have to consider causes which produce disease4 ,if we have to refer the morbid condition of an animal to the influence of poison1 for example1 we must consider how far the condition deviates from what it would have been if the poison had not been taken into the frame4 ,the usual progress of the animal functions including its growth1 is the measure of time2 the deviation from this usual progress is the indication of cause2 and the effect of the poison is subsequent to the cause1 because the poison acts through the cycle of the animal functions just mentioned1 which occupies time2 and because the taking the poison into the system1 not any subsequent action of the animal forces in the system1 is considered as the event which we must contemplate as a cause4 ,to resume the analogy of the clock3 the rate of the clock is altered by altering the parts2 but this alteration itself may occupy time2 as if we alter the rate of a clock by applying a drop of acid1 which gradually eats off a part of the pendulum1 the corrosion1 as an aggregate effect1 occupies time2 and the rates before and after the change are separated by this time4 ,but the application of the drop is the cause2 and thus1 in this case the final effect is subsequent to the cause1 though here1 as in the case of mechanism1 the instantaneous forces always produce a simultaneous effect4 ,thus we have in every case a uniform state1 or a state which is considered as uniform1 or at least normal2 and which is taken as the indication and measure of time2 and we have also change1 #bjb which is contemplated as a deviation from uniformity1 and is taken as the indication and measure of cause4 ,the uniform state may be one which never exists1 being purely imaginary2 as the case in which no forces act2 and the case in which animal functions go on permanently1 the animal neither growing nor wasting4 ,the normal state may also be a state in which change is constantly taking place1 as1 in fact1 even a state of motion is a state of change2 such states also are1 in a further sense1 that of a clock going by starts1 and that of an animal constantly growing3 in these cases the changes are all merged in a wider view of uniformity1 so that these are taken as the normal states4 ,and in all these cases1 successive changes which take place are separated by intervals of time1 measured by the normal progress2 and each change is produced by some simultaneous instantaneous cause4 ,but taking the cause in a larger sense1 we group these instantaneous causes1 and perhaps omit in our contemplation some of the intervening intervals2 and thus assign the cause to a preceding1 and the effect to a succeeding time4 ,i may observe further1 as a corollary from what has been said1 that the measure of time is different1 when we consider different kinds of causation2 and in each case1 is homogeneous with the changes which causation effects4 ,in the consideration of mechanical causes1 we measure time by mechanical changes2--by uniform motion1 or uniform succession of cycles of motion2 by the rotation of a wheel1 or the oscillation of a pendulum4 ,but if we have to consider physiological changes1 the progress of time is physiologically measured2--by the normal progress of vital operations2 by the circulation1 digestion or development of the organized body2 by the pulse1 or by the growth4 ,these different measures of time give to time1 so far as it is exhibited by facts and events1 a different character in the different cases4 ,phenomenal time has a different nature and essence according to the kind of the changes which we consider1 and which gives us our sole phenomenal indication of cause4 ,i fear that ,i am travelling into matters too abstruse and metaphysical for the occasion3 but before ,i conclude1 ,i will present one other aspect of the subject4 ,in stating the difficulty1 ,i referred to cases of moral as well as physical causation2 as when prudence produces prosperity1 or #bjc when folly produces ruin4 ,it may be asked1 whether we are here to apply the same explanation2--whether we are to assume a normal condition of human existence1 in which neither prudence nor folly are displayed1 neither prosperity nor adversity produced2--whether we are to conceive the progress of such a state to measure the progress of time1 and deviations from it to denote causes of the kind mentioned4 ,it may be asked further1 whether1 if we do make this supposition1 we can resolve the influence of such causes as prudence or imprudence into instantaneous acts1 which produce their effects immediately3 and which occupy time only by being separated by intervals of the inactive normal moral condition4 ,to this ,i must here reply1 that the discussion of such questions would carry me too far1 and would involve speculations not included within the acknowledged domain of this ,society1 from which ,i therefore abstain4 ,but ,i may say1 before quitting the subject1 that ,i do not think the suppositions above suggested are untenable2 and that in order to include moral causation under the maxims of causation in general1 we must necessarily make some such hypothesis4 ,the peculiarity of that kind of causation which the will and the character exert1 and which is exerted upon the will and the character1 would make this case far more complex and difficult than those already considered2 but1 at the same time1 would offer us the means of explaining what may seem harsh1 in the above analogy4 ,for instance1 we should have to assume such a maxim as this3 that in moral causation1 time is not to be measured by the flow of mechanical or physiological events2--not by the clock1 or by the pulse4 ,moral causation has its own clock1 its own pulse1 in the progress of man's moral being2 and by this measure of time is the relation of moral cause and effect to be defined4 ,that in estimating moral causation1 the progress of time is necessarily estimated by moral changes1 and not by machinery1--by the progress of events1 and not by the going of the clock1--is a truth familiar as a practical maxim to all who give their thoughts to dramatic or narrative fictions4 ,who feels any thing incongruous or extravagantly hurried in the progress of events in that great exhibition of moral causation1 the tragedy of ,othello8 ,if we were asked what time those vast and terrible #bjd and complex changes of the being and feelings of the characters occupy1 we should say1 that1 measured on its own scale1 the event is of great extent2--that the transaction is of considerable magnitude in all ways4 ,but if1 with previous critics1 we look into the progress of time by the day and the hour--what is the measure of this history8 ,forty-eight hours4 #bje ,,chapter ,v4 ,,of ,,the ,,origin ,,of ,,our ,,conceptions ,,of ,,force ,,and ,,matter4 #a4 ,force4--,,when the faculties of observation and thought are developed in man1 the idea of causation is applied to those changes which we see and feel in the state of rest and motion of bodies around us4 ,and when our abstract conceptions are thus formed and named1 we adopt the term ,force1 and use it to denote that property which is the cause of motion produced1 changed1 or prevented4 ,this conception is1 it would seem1 mainly and primarily suggested by our consciousness of the exertions by which we put bodies in motion4 ,the ,latin and ,greek words for ,force1 ,vis1 1 were probably1 like all abstract terms1 derived at first from some sensible object4 ,the original meaning of the ,greek word was a muscle or tendon4 ,its first application as an abstract term is accordingly to muscular force3 ' ' 1 ' 4 ,then ,ajax a far heavier stone upheaved1 ,he whirled it1 and impressing ,force intense ,upon the mass1 dismist it4 ,the property by which bodies affect each other's motions1 was naturally likened to that energy which we exert upon them with similar effect3 and thus the labouring horse1 the rushing torrent1 the descending weight1 the elastic bow1 were said to exert force4 #bjf ,homer#hc speaks of the force of the river1 2 and ,hesiod#ic of the force of the north wind1 4 ,note #hc3 ,il4 xxi4 ,note #ic3 ,op4 et ,d4 ,thus man's general notion of force was probably first suggested by his muscular exertions1 that is1 by an act depending upon that muscular sense1 to which1 as we have already seen1 the perception of space is mainly due4 ,and this being the case1 it will be easily understood that the ,direction of the force thus exerted is perceived by the muscular sense1 at the same time that the force itself is perceived2 and that the direction of any other force is understood by comparison with force which man must exert to produce the same effect1 in the same manner as force itself is so understood4 ,this abstract notion of ,force long remained in a very vague and obscure condition1 as may be seen by referring to the ,history for the failures of attempts at a science of force and motion1 made by the ancients and their commentators in the middle ages4 ,by degrees1 in modern times1 we see the scientific faculty revive4 ,the conception of ,force becomes so far distinct and precise that it can be reasoned upon in a consistent manner1 with demonstrated consequences2 and a genuine science of ,mechanics comes into existence4 ,the foundations of this science are to be found in the ,axioms concerning causation which we have already stated2 these axioms being interpreted and fixed in their application by a constant reference to observed facts1 as we shall show4 ,but we must1 in the first place1 consider further those primary processes of observation by which we acquire the first materials of thought on such subjects4 #b4 ,matter4--,the conception of ,force1 as we have said1 arises with our consciousness of our own muscular exertions4 ,but we cannot imagine such exertions without also imagining some bodily substance against which they are exercised4 ,if we press1 we press something3 if we thrust or throw1 there must be something #bjg to resist the thrust or to receive the impulse4 ,without body1 muscular force cannot be exerted1 and force in general is not conceivable4 ,thus ,force cannot exist without ,body on which it acts4 ,the two conceptions1 ,force and ,matter1 are co-existent and correlative4 ,force implies resistance2 and the force is effective only when the resistance is called into play4 ,if we grasp a stone1 we have no hold of it till the closing of the hand is resisted by the solid texture of the stone4 ,if we push open a gate1 we must surmount the opposition which it exerts while turning on its hinges4 ,however slight the resistance be1 there must be some resistance1 or there would be no force4 ,if we imagine a state of things in which objects do not resist our touch1 they must also cease to be influenced by our strength4 ,such a state of things we sometimes imagine in our dreams2 and such are the poetical pictures of the regions inhabited by disembodied spirits4 ,in these1 the figures which appear are conspicuous to the eye1 but impalpable like shadow or smoke2 and as they do not resist the corporeal impressions1 so neither do they obey them4 ,the spectator tries in vain to strike or to grasp them4 ,et ni docta comes tenues sine corpore vitas ,admoneat volitare cav sub imagine form1 ,irruat ac frustra ferro diverberet umbras4 ,the ,sibyl warns him that there round him fly ,bodiless things1 but substance to the eye2 ,else had he pierced those shapes with life-like face1 ,and smitten1 fierce1 the unresisting space4 ,neque illum ,prensantem nequicquam umbras et multa volentem ,dicere1 preterea vidit4 ,he grasps her form1 and clutches but the shade4 ,such may be the circumstances of the unreal world of dreams1 or of poetical fancies approaching to dreams3 for in these worlds our imaginary perceptions are bound by no rigid conditions of force and reaction4 ,in #bjh such cases1 the mind casts off the empire of the idea of cause1 as it casts off even the still more familiar sway of the ideas of space and time4 ,but the character of the material world in which we live when awake is1 that we have at every instant and at every place1 force operating on matter and matter resisting force4 #c4 ,solidity4--,from our consciousness of muscular exertion1 we derive1 as we have seen1 the conception of force1 and with that also the conception of matter4 ,we have already shown1 in a former chapter1 that the same part of our frame1 the muscular system1 is the organ by which we perceive extension and the relations of space4 ,thus the same organ gives us the perception of body as resisting force1 and as occupying space2 and by combining these conditions we have the conception of solid extended bodies4 ,in reality1 this resistance is inevitably presented to our notice in the very facts from which we collect the notion of extension4 ,for the action of the hand and arm by which we follow the forms of objects1 implies that we apply our fingers to their surface2 and we are stopped there by the resistance which the body offers4 ,this resistance is precisely that which is requisite in order to make us conscious of cur muscular effort#ajc4 ,neither touch1 nor any other mere passive sensation1 could produce the perception of extent1 as we have already urged3 nor could the muscular sense lead to such a perception1 except the extension of the muscles were felt to be resisted4 ,and thus the perception of resistance enters the mind along with the perception of extended bodies4 ,all the objects with which we have to do are not only extended but solid4 ,note #ajc3 ,brown's ,lectures1 i4 #dff4 ,this sense of the term solidity1 7the general property of all matter17 is different to that in which we oppose solidity to fluidity4 ,we may avoid ambiguity by opposing rigid to fluid bodies4 ,by solid bodies1 as we now speak of them1 we mean only such as resist the pressure which we exert1 so long as their parts continue in their places4 ,by fluid bodies1 we mean those #bji whose parts are1 by a slight pressure1 removed out of their places4 ,a drop of water ceases to prevent the contact of our two hands1 not by ceasing to have solidity in this sense1 but by being thrust out of the way4 ,if it could remain in its place1 it could not cease to exercise its resistance to our pressure1 except by ceasing to be matter altogether4 ,the perception of solidity1 like the perception of extension1 implies an act of the mind1 as well as an impression of the senses3 as the perception of extension implies the idea of space1 so the perception of solidity implies the idea of action and reaction4 ,that an ,idea is involved in our knowledge on this subject1 appears1 as in other instances1 from this consideration1 that the convictions of persons1 even of those who allow of no ground of knowledge but experience1 do in fact go far beyond the possible limits of experience4 ,thus ,locke says#aac1 that 'the bodies which we daily handle hinder by an insurmountable force the approach of the parts of our hands that press them4' ,now it is manifest that our observation can never go to this length4 ,by our senses we can only perceive that bodies resist the greatest actual forces that we exert upon them4 ,but our conception of force carries us further3 and since1 so long as the body is there to receive the action of the force1 it must suffer the whole of that action1 and must react as much as it suffers3 it is therefore true1 that so long as the body remains there1 the force which is exerted upon it can never surmount the resistance which the body exercises4 ,and thus this doctrine1 that bodies resist the intrusion of other bodies by an insurmountable force1 is1 in fact1 a consequence of the axiom that the reaction is always equal to the action4 ,note #aac3 ,essay1 b4 ii4 c4 #d4 #d4 ,inertia4--,but this principle of the equality of action and reaction appears also in another way4 ,not only when we exert force upon bodies at rest1 but when1 by our exertions1 we put them in motion1 they react4 ,if we set a large stone in motion1 the stone #baj resists2 for the operation requires an effort4 ,by increasing the effort1 we can increase the effect1 that is1 the motion produced2 but the resistance still remains4 ,and the greater the stone moved1 the greater is the effort requisite to move it4 ,there is1 in every case1 a resistance to motion1 which shows itself1 not in preventing the motion1 but in a reciprocal force1 exerted backwards upon the agent by which the motion is produced4 ,and this resistance resides in each portion of matter1 for it is increased as we add one portion of matter to another4 ,we can push a light boat rapidly through the water2 but we may go on increasing its freight1 till we are barely able to stir it4 ,this property of matter1 then1 by which it resists the reception of motion1 or rather by which it reacts and requires an adequate force in order that any motion may result1 is called its inertness1 or inertia4 ,that matter has such a property1 is a conviction flowing from that idea of a reaction equal and opposite to the action1 which the conception of all force involves4 ,by what laws this inertia depends on the magnitude1 form1 and material of the body1 must be the subject of our consideration hereafter4 ,but that matter has this inertia1 in virtue of which1 as the matter is greater1 the velocity which the same effort can communicate to it is less1 is a principle inseparable from the notion of matter itself4 ,hermann says that ,kepler first introduced this 'most significant' inertia4 ,whether it is to be found in earlier writers ,i know not2 ,kepler certainly does use it familiarly in those attempts to assign physical reasons for the motions of the planets which were among the main occasions of the discovery of the true laws of mechanics4 ,he assumes the slowness of the motions of the planets to increase1 7other causes remaining the same17 as the inertia increases2 and though1 even in this assumption1 there is an errour involved1 7if we adopt that interpretation of the term inertia to which subsequent researches led17 the introduction of such a word was one step in determining and expressing those laws of motion which depend on the fundamental principle of the equality of action and reaction4 #baa #e4 ,we have thus seen1 ,i trust in a satisfactory manner1 the origin of our conceptions of ,force1 ,matter1 ,solidity1 and ,inertness4 ,it has appeared that the organ by which we obtain such conceptions is that very muscular frame1 which is the main instrument of our perceptions of space2 but that1 besides bodily sensations1 these ideal conceptions1 like all the others which we have hitherto considered1 involve also an habitual activity of the mind1 giving to our sensations a meaning which they could not otherwise possess4 ,and among the ideas thus brought into play1 is an idea of action with an equal and opposite reaction1 which forms a foundation for universal truths to be hereafter established respecting the conceptions thus obtained4 ,we must now endeavour to trace in what manner these fundamental principles and conceptions are unfolded by means of observation and reasoning1 till they become an extensive yet indisputable science4 #bab ,,chapter ,,vi4 ,,of ,,the ,,establishment ,,of ,,the ,,principles ,,of ,,statics4 #a4 ,object of the ,chapter4--,,in the present and the succeeding chapters we have to show how the general axioms of ,causation enable us to construct the science of ,mechanics4 ,we have to consider these axioms as moulding themselves1 in the first place1 into certain fundamental mechanical principles1 which are of evident and necessary truth in virtue of their dependence upon the general axioms of ,causation2 and thus as forming a foundation for the whole structure of the science2--a system of truths no less necessary than the fundamental principles1 because derived from these by rigorous demonstration4 ,this account of the construction of the science of ,mechanics1 however generally treated1 cannot be otherwise than technical in its details1 and will probably be imperfectly understood by any one not acquainted with ,mechanics as a mathematical science4 ,i cannot omit this portion of my survey without rendering my work incomplete2 but ,i may remark that the main purpose of it is to prove1 in a more particular manner1 what ,i have already declared in general1 that there are1 in ,mechanics no less than in ,geometry1 fundamental principles of axiomatic evidence and necessity2--that these principles derive their axiomatic character from the ,idea which they involve1 namely1 the ,idea of ,cause2--and that through the combination of principles of this kind1 the whole science of ,mechanics1 including its most complex and remote results1 exists as a body of solid and universal truths4 #bac #b4 ,statics and ,dynamics4--,we must first turn our attention to a technical distinction of ,mechanics into two portions1 according as the forces about which we reason produce rest1 or motion2 the former portion is termed ,statics1 the latter ,dynamics4 ,if a stone fall1 or a weight put a machine in motion1 the problem belongs to ,dynamics2 but if the stone rest upon the ground1 or a weight be merely supported by a machine1 without being raised higher1 the question is one of ,statics4 #c4 ,equilibrium4--,in ,statics1 forces balance each other1 or keep each other in equilibrium4 ,and forces which directly balance each other1 or keep each other in equilibrium1 are necessarily and manifestly equal4 ,if we see two boys pull at two ends of a rope so that neither of them in the smallest degree prevails over the other1 we have a case in which two forces are in equilibrium4 ,the two forces are evidently equal1 and are a statical exemplification of action and reaction1 such as are spoken of in the third axiom concerning causes4 ,now the same exemplification occurs in every case of equilibrium4 ,no point or body can be kept at rest except in virtue of opposing forces acting upon it2 and these forces must always be equal in their opposite effect4 ,when a stone lies on the floor1 the weight of the stone downwards is opposed and balanced by an equal pressure of the floor upwards4 ,if the stone rests on a slope1 its tendency to slide is counteracted by some equal and opposite force1 arising1 it may be1 from the resistance which the sloping ground opposes to any motion along its surface4 ,every case of rest is a case of equilibrium3 every case of equilibrium is a case of equal and opposite forces4 ,the most complex frame-work on which weights are supported1 as the roof of a building1 or the cordage of a machine1 are still examples of equilibrium4 ,in such cases we may have many forces all combining to balance each other2 and the equilibrium will depend on various conditions of direction and magnitude among the forces4 ,and in order to understand what are these conditions1 we must ask1 in the first place1 what #bad we understand by the magnitude of such forces2--what is the measure of statical forces4 #d4 ,measure of ,statical ,forces4--,at first we might expect1 perhaps1 that since statical forces come under the general notion of ,cause1 the mode of measuring them would be derived from the second axiom of ,causation1 that causes are measured by their effects4 ,but we find that the application of this axiom is controlled by the limitation which we noticed1 after stating that axiom2 namely1 the condition that the causes shall be capable of addition4 ,further1 as we have seen1 a statical force produces no other effect than this1 that it balances some other statical force2 and hence the measure of statical forces is necessarily dependent upon their balancing1 that is1 upon the equality of action and reaction4 ,that statical forces are capable of addition is involved in our conception of such forces4 ,when two men pull at a rope in the same direction1 the forces which they exert are added together4 ,when two heavy bodies are put into a basket suspended by a string1 their weights are added1 and the sum is supported by the string4 ,combining these considerations1 it will appear that the measure of statical forces is necessarily given at once by the fundamental principle of the equality of action and reaction4 ,since two opposite forces which balance each other are equal1 each force is measured by that which it balances2 and since forces are capable of addition1 a force of any magnitude is measured by adding together a proper number of such equal forces4 ,thus a heavy body which1 appended to some certain elastic branch of a tree1 would bend it down through one inch1 may be taken as a unit of weight4 ,then if we remove this first body1 and find a second heavy body which will also bend the branch through the same space1 this is also a unit of weight2 and in like manner we might go on to a third and a fourth equal body2 and adding together the two1 or the three1 or the four heavy bodies1 we have a force twice1 or three times1 or four times the unit of weight4 ,and with #bae such a collection of heavy bodies1 or weights1 we can readily measure all other forces2 for the same principle of the equality of action and reaction leads at once to this maxim1 that any statical force is measured by the weight which it would support4 ,as has been said1 it might at first have been supposed that we should have to apply1 in this case1 the axiom that causes are measured by their effects in another manner2 that thus1 if that body were a unit of weight which bent the bough of a tree through one inch1 that body would be two units which bent it through two inches1 and so on4 ,but1 as we have already stated1 the measures of weight must be subject to this condition1 that they are susceptible of being added3 and therefore we cannot take the deflexion of the bough for our measure1 till we have ascertained1 that which experience alone can teach us1 that under the burden of two equal weights1 the deflexion will be twice as great as it is with one weight1 which is not true1 or at least is neither obviously nor necessarily true4 ,in this1 as in all other cases1 although causes must be measured by their effects1 we learn from experience only how the effects are to be interpreted1 so as to give a true and consistent measure4 ,with regard1 however1 to the measure of statical force1 and of weight1 no difficulty really occurred to philosophers from the time when they first began to speculate on such subjects2 for it was easily seen that if we take any uniform material1 as wood1 or stone1 or iron1 portions of this which are geometrically equal1 must also be equal in statical effect2 since this was implied in the very hypothesis of a uniform material ,and a body ten times as large as another of the same substance1 will be of ten times the weight4 ,but before men could establish by reasoning the conditions under which weights would be in equilibrium1 some other principles were needed in addition to the mere measure of forces4 ,the principles introduced for this purpose still resulted from the conception of equal action and reaction2 but it required no small clearness of thought to select them rightly1 and to employ them #baf successfully4 ,this1 however1 was done1 to a certain extent1 by the ,greeks2 and the treatise of ,archimedes ,on the ,center of ,gravity1 is founded on principles which may still be considered as the genuine basis of statical reasoning4 ,i shall make a few remarks on the most important principle among those which ,archimedes thus employs4 #e4 ,the ,center of ,gravity4--,the most important of the principles which enter into the demonstration of ,archimedes is this3 that ,every body has a center of gravity2 meaning by the center of gravity1 a point at which the whole matter of the body may be supposed to be collected1 to all intents and purposes of statical reasoning4 ,this principle has been put in various forms by succeeding writers3 for instance1 it has been thought sufficient to assume a case much simpler than the general one2 and to assert that two equal bodies have their center of gravity in the point midway between them4 ,it is to be observed1 that this assertion not only implies that the two bodies will balance upon a support placed at that midway point1 but also1 that they will exercise1 upon such a support1 a pressure equal to their sum2 for this point being the center of gravity1 the whole matter of the two bodies may be conceived to be collected there1 and therefore the whole weight will press there4 ,and thus the principle in question amounts to this1 that when two equal heavy bodies are supported on the middle point between them1 the pressure upon the support is equal to the sum of the weights of the bodies4 ,a clear understanding of the nature and grounds of this principle is of great consequence3 for in it we have the foundation of a large portion of the science of ,mechanics4 ,and if this principle can be shown to be necessarily true1 in virtue of our ,fundamental ,ideas1 we can hardly doubt that there exist many other truths of the same kind1 and that no sound view of the evidence and extent of human knowledge can be obtained1 so long as we mistake the nature of these1 its first principles4 #bag ,the above principle1 that the pressure on the support is equal to the sum of the bodies supported1 is often stated as an axiom in the outset of books on ,mechanics4 ,and this appears to be the true place and character of this principle1 in accordance with the reasonings which we have already urged4 ,the axiom depends upon our conception of action and reaction4 ,that the two weights are supported1 implies that the supporting force must be equal to the force or weight supported4 ,in order further to show the foundation of this principle1 we may ask the question3--,if it be not an axiom1 deriving its truth from the fundamental conception of equal action and reaction1 which equilibrium always implies1 what is the origin of its certainty8 ,the principle is never for an instant denied or questioned3 it is taken for granted1 even before it is stated4 ,no one will doubt that it is not only true1 but true with the same rigour and universality as the axioms of ,geometry4 ,will it be said1 that it is borrowed from experience8 ,experience could never prove a principle to be universally and rigorously true4 ,moreover1 when from experience we prove a proposition to possess great exactness and generality1 we approach by degrees to this proof3 the conviction becomes stronger1 the truth more secure1 as we accumulate trials4 ,but nothing of this kind is the case in the instance before us4 ,there is no gradation from less to greater certainty2--no hesitation which precedes confidence4 ,from the first1 we know that the axiom is exactly and certainly true4 ,in order to be convinced of it1 we do not require many trials1 but merely a clear understanding of the assertion itself4 ,but in fact1 not only are trials not necessary to the proof1 but they do not strengthen it4 ,probably no one ever made a trial for the purpose of showing that the pressure upon the support is equal to the sum of the two weights4 ,certainly no person with clear mechanical conceptions ever wanted such a trial to convince him of the truth2 or thought the truth clearer after the trial had been made4 ,if to such a person1 an #bah experiment were shown which seemed to contradict the principle1 his conclusion would be1 not that the principle was doubtful1 but that the apparatus was out of order4 ,nothing can be less like collecting truth from experience than this4 ,we maintain1 then1 that this equality of mechanical action and reaction1 is one of the principles which do not flow from1 but regulate our experience4 ,to this principle1 the facts which we observe must conform2 and we cannot help interpreting them in such a manner that they shall be exemplifications of the principle4 ,a mechanical pressure not accompanied by an equal and opposite pressure1 can no more be given by experience1 than two unequal right angles4 ,with the supposition of such inequalities1 space ceases to be space1 force ceases to be force1 matter ceases to be matter4 ,and this equality of action and reaction1 considered in the case in which two bodies are connected so as to act on a single support1 leads to the axiom which we have stated above1 and which is one of the main foundations of the science of ,mechanics4 #b;d ed4 ,to the doctrine that mechanical principles1 such as the one here under consideration 7that the pressure on the point of support is equal to the sum of the weights71 are derived from our ,ideas1 and do not flow from but regulate our experience1 objections are naturally made by those who assert all our knowledge to be derived from experience4 ,how1 they ask1 can we know the properties of pressures1 levers and the like1 except from experience8 ,what but experience can possibly inform us that a force applied transversely to a lever will have any tendency to turn the lever on its center8 ,this cannot be1 except we suppose in the lever tenacity1 rigidity and the like1 which are qualities known only by experience4 ,and it is obvious that this line of argument might be carried on through the whole subject4 ,my answer to this objection is a remark of the same kind as one which ,i have made respecting the ,ideas of ,space1 ,time1 and ,number1 in the last ,book4 ,the mind1 in apprehending events as causes #bai and effects1 is governed by ,laws of its own ,activity2 and these ,laws govern the results of the mind's action2 and make these results conform to the ,axioms of ,causation4 ,but this activity of the mind is awakened and developed by being exercised2 and in dealing with the examples of cause and effect here spoken of1 7namely1 pressure and resistance1 force and motion17 the mind's activity is necessarily governed also by the bodily powers of perception and action4 ,we are human beings only in so far as we have existed in space and time2 and of our human faculties1 developed by our existence in space and time1 space and time are necessary conditions4 ,in like manner1 we are human beings only in so far as we have bodies1 and bodily organs2 and our bodies necessarily imply material objects external to us4 ,and hence our human faculties1 developed by our bodily existence in a material world1 have the conditions of matter for their necessary ,laws4 ,i have already said 7chap4 v47 that our conception of ,force arises with our consciousness of our own muscular exertions2--that ,force cannot be conceived without ,resistance to exercise itself upon2--and that this resistance is supplied by ,matter4 ,and thus the conception of ,matter1 and of the most general modes in which ,matter receives1 resists1 and transmits force1 are parts of our constitution which1 though awakened and unfolded by our being in a material world1 are not distinguishable from the original structure of the mind4 ,i do not ascribe to the mind innate ,ideas--,ideas which it would have1 even if it had no intercourse with the world of space1 time1 and matter2 because we cannot imagine a mind in such a state4 ,but ,i attempt to point out and classify those ,conditions of all ,experience1 to which the intercourse of all minds with the material world has necessarily given rise in all4 ,truths thus necessarily acquired in the course of all experience1 cannot be said to be learnt from experience1 in the same sense in which particular facts1 at definite times1 are learnt from experience--learnt by some persons and not by others--learnt with more or less of certainty4 ,these latter special truths of #bbj experience will be very important subjects of our consideration2 but our whole chance of discussing them with any profit depends upon our keeping them distinct from the necessary and universal conditions of experience4 ,here1 as everywhere1 we must keep in view the fundamental antithesis of ,ideas and ,facts4 #f4 ,oblique ,forces4--,by the aid of the above axiom and a few others1 the ,greeks made some progress in the science of ,statics4 ,but after a short advance1 they arrived at another difficulty1 that of ,oblique ,forces1 which they never overcame2 and which no mathematician mastered till modern times4 ,the unpublished manuscripts of ,leonardo da ,vinci1 written in the fifteenth century1 and the works of ,stevinus and ,galileo1 in the sixteenth1 are the places in which we find the first solid grounds of reasoning on the subject of forces acting obliquely to each other4 ,and from that period1 mathematicians1 having thus become possessed of all the mechanical principles which are requisite in problems respecting equilibrium1 soon framed a complete science of ,statics4 ,succeeding writers presented this science in forms variously modified2 for it was found1 in ,mechanics as in ,geometry1 that various propositions might be taken as the starting points2 and that the collection of truths which it was the mechanician's business to include in his course1 might thus be traversed by various routes1 each path offering a series of satisfactory demonstrations4 ,the fundamental conceptions of force and resistance1 like those of space and number1 could be contemplated under different aspects1 each of which might be made the basis of axioms1 or of principles employed as axioms4 ,hence the grounds of the truth of ,statics may be stated in various ways2 and it would be a task of some length to examine all these completely1 and to trace them to their ,fundamental ,ideas4 ,this ,i shall not undertake here to do2 but the philosophical importance of the subject makes it proper to offer a few remarks on some of the main principles involved in the different modes of presenting ,statics as a rigorously demonstrated science4 #bba #g4 ,a ,force may be supposed to act at any ,point of its ,direction4--,it has been stated in the history of ,mechanics#abc1 that ,leonardo da ,vinci and ,galileo obtained the true measure of the effect of oblique forces1 by reasonings which were1 in substance1 the same4 ,the principle of these reasonings is that expressed at the head of this paragraph2 and when we have a little accustomed ourselves to contemplate our conceptions of force1 and its action on matter1 in an abstract manner1 we shall have no difficulty in assenting to the principle in this general form4 ,but it may1 perhaps1 be more obvious at first in a special case4 ,note #abc3 ,hist4 ,ind4 ,sc4 b4 vi4 c4 i4 sect4 #b4 ,if we suppose a wheel1 moveable about its axis1 and carrying with it in its motion a weight1 7as1 for example1 one of the wheels by means of which the large bells of a church are rung17 this weight may be supported by means of a rope 7not passing along the circumference of the wheel1 as is usual in the case of bells17 but fastened to one of the spokes of the wheel4 ,now the principle which is enunciated above asserts1 that if the rope pass in a straight line across several of the spokes of the wheel1 it makes no difference in the mechanical effect of the force applied1 for the purpose of putting the bell in motion1 to which of these spokes the rope is fastened4 ,in each case1 the fastening of the rope to the wheel merely serves to enable the force to produce motion about the center2 and so long as the force acts in the same line1 the effect is the same1 at whatever point of the rope the line of action finishes4 ,this axiom very readily aids us in estimating the effect of oblique forces4 ,for when a force acts on one of the arms of a lever at any oblique angle1 we suppose another arm projecting from the center of motion1 like another spoke of the same wheel1 so situated that it is perpendicular to the force4 ,this arm we may1 with ,leonardo1 call the virtual lever2 for1 by the axiom1 we may suppose the force to act where the line of its direction meets this arm2 and thus we reduce the case #bbb to that in which the force acts perpendicularly on the arm4 ,the ground of this axiom is1 that matter1 in ,statics1 is necessarily conceived as transmitting force4 ,that force can be transmitted from one place to another1 by means of matter2--that we can push with a rod1 pull with a rope1--are suppositions implied in our conceptions of force and matter4 ,matter is1 as we have said1 that which receives the impression of force1 and the modes just mentioned1 are the simplest ways in which that impression operates4 ,and since1 in any of these cases1 the force might be resisted by a reaction equal to the force itself1 the reaction in each case would be equal1 and1 therefore1 the action in each case is necessarily equal2 and thus the forces must be transmitted1 from one point to another1 without increase or diminution4 ,this property of matter1 of transmitting the action of force1 is of various kinds4 ,we have the coherence of a rope which enables us to pull1 and the rigidity of a staff1 which enables us to push with it in the direction of its length2 and again1 the same staff has a rigidity of another kind1 in virtue of which we can use it as a lever2 that is1 a rigidity to resist flexure1 and to transmit the force which turns a body round a fulcrum4 ,there is1 further1 the rigidity by which a solid body resists twisting4 ,of these kinds of rigidity1 the first is that to which our axiom refers2 but in order to complete the list of the elementary principles of ,statics1 we ought also to lay down axioms respecting the other kinds of rigidity#acc4 ,these1 however1 ,i shall not here state1 as they do not involve any new principle4 ,like the one just considered1 they form part of our fundamental conception of matter2 they are not the results of any experience1 but are the hypotheses to which we are irresistibly led1 when we would liberate our reasonings concerning force and matter from a dependence on the special results of experience4 ,we cannot even #bbc conceive 7that is1 if we have any clear mechanical conceptions at all7 the force exerted by the point of a staff and resisting the force which we steadily impress on the head of it1 to be different from the impressed force4 ,note #acc3 ,such axioms are given in a little work 7,the ,mechanical ,euclid7 which ,i published on the ,elements of ,mechanics4 #h4 ,forces may have equivalent ,forces substituted for them4 ,the ,parallelogram of ,forces4--,it has already been observed1 that in order to prove the doctrines of ,statics1 we may take various principles as our starting points1 and may still find a course of demonstration by which the leading propositions belonging to the subject may be established4 ,thus1 instead of beginning our reasonings1 as in the last section we supposed them to commence1 with the case in which forces act upon different points of the same body in the same line of force1 and counteract each other in virtue of the intervening matter by which the effect of force is transferred from one point to another2 we may suppose different forces to act at the same point1 and may thus commence our reasonings with a case in which we have to contemplate force1 without having to take into our account the resistance or rigidity of matter4 ,two statical forces1 thus acting at a mathematical point1 are equivalent1 in all respects1 to some single force acting at the same point2 and would be kept in equilibrium by a force equal and opposite to that single force4 ,and the rule by which the single force is derived from the two1 is commonly termed the parallelogram of forces2 the proposition being this1--,that if the two forces be represented in magnitude and direction by the two sides of a parallelogram1 the resulting force will be represented in the same manner by the diagonal of the parallelogram4 ,this proposition has very frequently been made1 by modern writers1 the commencement of the science of ,mechanics3 a position for which1 by its simplicity1 it is well suited2 although1 in order to deduce from it the other elementary propositions of the science1 as1 for instance1 those respecting the lever1 we require the axiom stated in the last section4 #i4 ,the ,parallelogram of ,forces is a necessary ,truth4--,in the series of discussions in which we are #bbd here engaged1 our main business is to ascertain the nature and grounds of the certainty of scientific truths4 ,we have1 therefore1 to ask whether this proposition1 the parallelogram of forces1 be a necessary truth2 and if so1 on what grounds its necessity ultimately rests4 ,we shall find that this1 like the other fundamental doctrines of ,statics1 justly claim a demonstrative certainty4 ,daniel ,bernoulli1 in #agbf1 gave the first proof of this important proposition on pure statical principles2 and thus1 as he says#adc1 'proved that statical theorems are not less necessarily true than geometrical are4' ,if we examine this proof of ,bernoulli1 in order to discover what are the principles on which it rests1 we shall find that the reasoning employs in its progress such axioms as this2--,that if from forces which are in equilibrium at a point be taken away other forces which are in equilibrium at the same point1 the remainder will be in equilibrium2 and generally2--,that if forces can be resolved into other equivalent forces1 these may be separated1 grouped1 and recombined1 in any new manner1 and the result will still be identical with what it was at first4 ,thus in ,bernoulli's proof1 the two forces to be compounded are represented by ,p and ,q2 ,p is resolved into two other forces1 ,x and ,u2 and ,q into two others1 ,y and ,v1 under certain conditions4 ,it is then assumed that these forces may be grouped into the pairs ,x1 ,y1 and ,u1 ,v3 and when it has been shown that ,x and ,y are in equilibrium1 they may1 by what has been said1 be removed1 and the forces1 ,p1 ,q1 are equivalent to ,u1 ,v2 which1 being in the same direction by the course of the construction1 have a result equal to their sum4 ,note #adc3 ,comm4 ,petrop4 vol4 i4 ,it is clear that the principles here assumed are genuine axioms1 depending upon our conception of the nature of equivalence of forces1 and upon their being capable of addition and composition4 ,if the forces1 ,p1 ,q1 be equivalent to forces ,x1 ,u1 ,y1 ,v1 they are equivalent to these forces added and compounded in any order2 just as a geometrical figure is1 by our conception of #bbe space1 equivalent to its parts added together in any order4 ,the apprehension of forces as having magnitude1 as made up of parts1 as capable of composition1 leads to such axioms in ,statics1 in the same manner as the like apprehension of space leads to the axioms of ,geometry4 ,and thus the truths of ,statics1 resting upon such foundations1 are independent of experience in the same manner in which geometrical truths are so4 ,the proof of the parallelogram of forces thus given by ,daniel ,bernoulli1 as it was the first1 is also one of the most simple proofs of that proposition which have been devised up to the present day4 ,many other demonstrations1 however1 have been given of the same proposition4 ,jacobi1 a ,german mathematician1 has collected and examined eighteen of these#aec4 ,they all depend either upon such principles as have just been stated2 ,that forces may in every way be replaced by those which are equivalent to them2--or else upon those previously stated1 the doctrine of the lever1 and the transfer of a force from one point to another of its direction4 ,in either case1 they are necessary results of our statical conceptions1 independent of any observed laws of motion1 and indeed1 of the conception of actual motion altogether4 ,note #aec3 ,these are by the following mathematicians2 ,d4 ,bernoulli 7#agbf72 ,lambert 7#agga72 ,scarella 7#agef72 ,venini 7#agfd72 ,araldi 7#ahjf72 ,wachter 7#ahae72 ,kaestner2 ,marini2 ,eytelwein2 ,salimbeni2 ,duchayla2 two different proofs by ,foncenex 7#agfj72 three by ,d',alembert2 and those of ,laplace and ,m4 ,poisson4 ,there is another class of alleged proofs of the parallelogram of forces1 which involve the consideration of the motion produced by the forces4 ,but such reasonings are1 in fact1 altogether irrelevant to the subject of ,statics4 ,in that science1 forces are not measured by the motion which they produce1 but by the forces which they will balance1 as we have already seen4 ,the combination of two forces employed in producing motion in the same body1 either simultaneously or successively1 #bbf belongs to that part of ,mechanics which has motion for its subject1 and is to be considered in treating of the laws of motion4 ,the composition of motion1 7as when a man moves in a ship while the ship moves through the water17 has constantly been confounded with the composition of force4 ,but though it has been done by very eminent mathematicians1 it is quite necessary for us to keep the two subjects distinct1 in order to see the real nature of the evidence of truth in either case4 ,the conditions of equilibrium of two forces on a lever1 or of three forces at a point1 can be established without any reference whatever to any motions which the forces might1 under other circumstances1 produce4 ,and because this can be done1 to do so is the only scientific procedure4 ,to prove such propositions by any other course1 would be to support truth by extraneous and inconclusive reasons2 which would be foreign to our purpose1 since we seek not only knowledge1 but the grounds of our knowledge4 #aj4 ,the ,center of gravity seeks the lowest place4--,the principles which we have already mentioned afford a sufficient basis for the science of ,statics in its most extensive and varied applications2 and the conditions of equilibrium of the most complex combinations of machinery may be deduced from these principles with a rigour not inferior to that of geometry4 ,but in some of the more complex cases1 the results of long trains of reasoning may be foreseen1 in virtue of certain maxims which appear to us self-evident1 although it may not be easy to trace the exact dependence of these maxims upon our fundamental conceptions of force and matter4 ,of this nature is the maxim now stated2--,that in any combination of matter any how supported1 the ,center of ,gravity will descend into the lowest position which the connexion of the parts allows it to assume by descending4 ,it is easily seen that this maxim carries to a much greater extent the principle which the ,greek mathematicians assumed1 that every body has a ,center of ,gravity1 that is1 a point in which1 if the whole matter of the body be collected1 the effect will remain unchanged4 ,for the ,greeks asserted this of a #bbg single rigid mass only2 whereas1 in the maxim now under our notice1 it is asserted of any masses1 connected by strings1 rods1 joints1 or in any manner4 ,we have already seen that more modern writers on mechanics1 desirous of assuming as fundamental no wider principles than are absolutely necessary1 have not adopted the ,greek axiom in all its generality1 but have only asserted that two equal weights have a center of gravity midway between them4 ,yet the principle that every body1 however irregular1 has a center of gravity1 and will be supported if that center is supported1 and not otherwise1 is so far evident1 that it might be employed as a fundamental truth1 if we could not resolve it into any simpler truths3 and1 historically speaking1 it was assumed as evident by the ,greeks4 ,in like manner the still wider principle1 that a collection of bodies1 as1 for instance1 a flexible chain hanging upon one or more supports1 has a center of gravity2 and that this point will descend to the lowest possible situation1 as a single body would do1 has been adopted at various periods in the history of mechanics2 and especially at conjunctures when mathematical philosophers have had new and difficult problems to contend with4 ,for in almost every instance it has only been by repeated struggles that philosophers have reduced the solution of such problems to a clear dependence upon the most simple axioms4 #aa4 ,stevinus's ,proof for ,oblique ,forces4--,we have an example of this mode of dealing with problems1 in ,stevinus's mode of reasoning concerning the ,inclined ,plane2 which1 as we have stated in the ,history of ,mechanics1 was the first correct published solution of that problem4 ,stevinus supposes a loop of chain1 or a loop of string loaded with a series of equal balls at equal distances1 to hang over the ,inclined ,plane2 and his reasoning proceeds upon this assumption1--,that such a loop so hanging will find a certain position in which it will rest3 for otherwise1 says he#afc1 its motion must go on for ever1 which is absurd4 ,it may be asked how #bbh this absurdity of a perpetual motion appears2 and it will perhaps be added1 that although the impossibility of a machine with such a condition may be proved as a remote result of mechanical principles1 this impossibility can hardly be itself recognized as a self-evident truth4 ,but to this we may reply1 that the impossibility is really evident in the case contemplated by ,stevinus2 for we cannot conceive a loop of chain to go on through all eternity1 sliding round and round upon its support1 by the effect of its own weight4 ,and the ground of our conviction that this cannot be1 seems to be this consideration2 that when the chain moves by the effect of its weight1 we consider its motion as the result of an effort to reach some certain position1 in which it can rest2 just as a single ball in a bowl moves till it comes to rest at the lowest point of the bowl4 ,such an effect of weight in the chain1 we may represent to ourselves by conceiving all the matter of the chain to be collected in one single point1 and this single heavy point to hang from the support in some way or other1 so as fitly to represent the mode of support of the chain4 ,in whatever manner this heavy point 7the center of gravity of the chain7 be supported and controlled in its movements1 there will still be some position of rest which it will seek and find4 ,and thus there will be some corresponding position of rest for the chain2 and the interminable shifting from one position to another1 with no disposition to rest in any position1 cannot exist4 ,note #afc3 ,stevin4 ,statique1 livre i4 prop4 #ai4 ,thus the demonstration of the property of the ,inclined ,plane by ,stevinus1 depends upon a principle which1 though far from being the simplest of those to which the case can be reduced1 is still both true and evident3 and the evidence of this principle1 depending upon the assumption of a center of gravity1 is of the same nature as the evidence of the ,greek statical demonstrations1 the earliest real advances in the science4 #ab4 ,principle of ,virtual ,velocities4--,we have referred above to an assertion often made1 that we may1 from the simple principles of ,mechanics1 demonstrate the impossibility of a perpetual motion4 ,in reality1 #bbi however1 the simplest proof of that impossibility1 in a machine acted upon by weight only1 arises from the very maxim above stated1 that the center of gravity seeks and finds the lowest place2 or from some similar proposition4 ,for if1 as is done by many writers1 we profess to prove the impossibility of a perpetual motion by means of that proposition which includes the conditions of equilibrium1 and is called the ,principle of ,virtual ,velocities#agc1 we are under the necessity of first proving in a general manner that principle4 ,and if this be done by a mere enumeration of cases1 7as by taking those five cases which are called the ,mechanical ,powers17 there may remain some doubts whether the enumeration of possible mechanical combinations be complete4 ,accordingly1 some writers have attempted independent and general proofs of the ,principle of ,virtual ,velocities2 and these proofs rest upon assumptions of the same nature as that now under notice4 ,this is1 for example1 the case with ,lagrange's proof1 which depends upon what he calls the ,principle of ,pulleys4 ,for this principle is1--,that a weight any how supported1 as by a string passing round any number of pulleys any how placed1 will be at rest then only1 when it cannot get lower by any small motion of the pulleys4 ,and thus the maxim that a weight will descend if it can1 is assumed as the basis of this proof4 ,note #agc3 ,see ,hist4 ,ind ,sc4 b4 vi4 c4 ii4 sect4 #d4 ,there is1 as we have said1 no need to assume such principles as these for the foundation of our mechanical science4 ,but it is1 on various accounts1 useful to direct our attention to those cases in which truths1 apprehended at first in a complex and derivative form1 have afterwards been reduced to their simpler elements2--in which1 also1 sagacious and inventive men have fixed upon those truths as self-evident1 which now appear to us only certain in virtue of demonstration4 ,in these cases we can hardly doubt that such men were led to assert the doctrines which they discovered1 not by any capricious conjecture of arbitrary selection1 but by having a keener and deeper insight than other persons #bcj into the relations which were the object of their contemplation2 and in the science now spoken of1 they were led to their assumptions by possessing clearly and distinctly the conceptions of mechanical cause and effect1--action and reaction1--force1 and the nature of its operation4 #ac4 ,fluids press ,equally in all ,directions4--,the doctrines which concern the equilibrium of fluids depend on principles no less certain and simple than those which refer to the equilibrium of solid bodies2 and the ,greeks1 who1 as we have seen1 obtained a clear view of some of the principles of ,statics1 also made a beginning in the kindred subject of ,hydrostatics4 ,we still possess a treatise of ,archimedes ,on ,floating ,bodies1 which contains correct solutions of several problems belonging to this subject1 and of some which are by no means easy4 ,in this treatise1 the fundamental assumption is of this kind3 ',let it be assumed that the nature of a fluid is such1 that the parts which are less pressed yield to those which are more pressed4' ,in this assumption or axiom it is implied that a pressure exerted upon a fluid in one direction produces a pressure in another direction2 thus1 the weight of the fluid which arises from a downward force produces a lateral pressure against the sides of the containing vessel4 ,not only does the pressure thus diverge from its original direction into all other directions1 but the pressure is in all directions exactly equal1 an equal extent of the fluid being taken4 ,this principle1 which was involved in the reasoning of ,archimedes1 is still to the present day the basis of all hydrostatical treatises1 and is expressed1 as above1 by saying that fluids press equally in all directions4 ,concerning this1 as concerning previously-noticed principles1 we have to ask whether it can rightly be said to be derived from experience4 ,and to this the answer must still be1 as in the former cases1 that the proposition is not one borrowed from experience in any usual or exact sense of the phrase4 ,i will endeavour to illustrate this4 ,there are many elementary propositions in physics1 our knowledge of which #bca indisputably depends upon experience2 and in these cases there is no difficulty in seeing the evidence of this dependence4 ,in such cases1 the experiments which prove the law are prominently stated in treatises upon the subject3 they are given with exact measures1 and with an account of the means by which errours were avoided3 the experiments of more recent times have either rendered more certain the law originally asserted1 or have pointed out some correction of it as requisite3 and the names1 both of the discoverers of the law and of its subsequent reformers1 are well known4 ,for instance1 the proposition that ',the elastic force of air varies as the density1' was first proved by ,boyle1 by means of operations of which the detail is given in his ,defence of his ,pneumatical ,experiments#ahc2 and by 9999,mariotte in his ,trait de l'quilibre des ,liquides1 from whom it has generally been termed ,mariotte's law4 ,after being confirmed by many other experimenters1 this law was suspected to be slightly inaccurate1 and a commission of the ,french ,academy of ,sciences was appointed1 consisting of several distinguished philosophers#aic1 to ascertain the truth or falsehood of this suspicion4 ,the result of their investigations appeared to be1 that the law is exact1 as nearly as the inevitable inaccuracies of machinery and measures will allow us to judge4 ,here we have an example of a law which is of the simplest kind and form2 and which yet is not allowed to rest upon its simplicity or apparent probability1 but is rigorously tested by experience4 ,in this case1 the assertion1 that the law depends upon experience1 contains a reference to plain and notorious passages in the history of science4 ,note #ahc3 ,shaw's ,boyle1 ,vol4 ii4 p4 #fga4 ,note #aic3 ,the members were ,prony1 ,arago1 ,ampre1 ,girard1 and ,dulong4 ,the experiments were extended to a pressure of twenty-seven atmospheres2 and in no instance did the difference between the observed and calculated elasticity amount to one-hundredth of the whole2 nor did the difference appear to increase with the increase of pressure4--,fechner1 ,repertorium1 i4 #aaj4 ,now with regard to the principle that fluids press equally in all directions1 the case is altogether different4 #bcb ,it is1 indeed1 often asserted in works on hydrostatics1 that the principle is collected from experience1 and sometimes a few experiments are described as exhibiting its effect2 but these are such as to illustrate and explain1 rather than to prove1 the truth of the principle3 they are never related to have been made with that exactness of precaution and measurement1 or that frequency of repetition1 which are necessary to establish a purely experimental truth4 ,nor did such experiments occur as important steps in the history of science4 ,it does not appear that ,archimedes thought experiment necessary to confirm the truth of the law as he employed it3 on the contrary1 he states it in exactly the same shape as the axioms which he employs in statics1 and even in geometry2 namely1 as an assumption4 ,nor does any intelligent student of the subject find any difficulty in assenting to this fundamental principle of hydrostatics as soon as it is propounded to him4 ,experiment was not requisite for its discovery2 experiment is not necessary for its proof at present2 and we may add1 that experiment1 though it may make the proposition the more readily intelligible1 can add nothing to our conviction of its truth when it is once understood4 #ad4 ,foundation of the above ,axiom4--,but it will naturally be asked1 ,what then is the ground of our conviction of this doctrine of the equal pressure of a fluid in all directions8 ,and to this ,i reply1 that the reasons of this conviction are involved in our idea of a fluid1 which is considered as matter1 and therefore as capable of receiving1 resisting1 and transmitting force according to the general conception of matter2 and which is also considered as matter which has its parts perfectly moveable among one another4 ,for it follows from these suppositions1 that if the fluid be confined1 a pressure which thrusts in one side of the containing vessel1 may cause any other side to bulge outwards1 if there be a part of the surface which has not strength to resist this pressure from within4 ,and that this pressure1 when thus transferred into a direction different from the original one1 is not altered in intensity1 #bcc depends upon this consideration2 that any difference in the two pressures would be considered as a defect of perfect fluidity1 since the fluidity would be still more complete1 if this entire and undiminished transmission of pressure in all directions were supposed4 ,if1 for instance1 the lateral pressure were less than the vertical1 this could be conceived no other way than as indicating some rigidity or adhesion of the parts of the fluid4 ,when the fluidity is perfect1 the two pressures which act in the two different parts of the fluid exactly balance each other3 they are the action and the reaction2 and must hence be equal by the same necessity as two directly opposite forces in statics4 ,but it may be urged1 that even if we grant that this conception of a perfect fluid1 as a body which has its parts perfectly moveable among each other1 leads us necessarily to the principle of the equality of hydrostatic pressure in all directions1 still this conception itself is obtained from experience1 or suggested by observation4 ,and to this we may reply1 that the conception of a fluid1 as contemplated in mechanical theory1 cannot be said to be derived from experience1 except in the same manner as the conception of a solid and rigid body may be said to be acquired by experience4 ,for if we imagine a vessel full of small1 smooth spherical balls1 such a collection of balls would approach to the nature of a fluid1 in having its parts moveable among each other2 and would approach to perfect fluidity1 as the balls became smoother and smaller4 ,and such a collection of balls would also possess the statical properties of a fluid2 for it would transmit pressure out of a vertical into a lateral 7or any other7 direction1 in the same manner as a fluid would do4 ,and thus a collection of solid bodies has the same property which a fluid has2 and the science of ,hydrostatics borrows from experience no principles beyond those which are involved in the science of ,statics respecting solids4 ,and since in this latter portion of science1 as we have already seen1 none of the principles depend for their evidence upon any special experience1 the doctrines of ,hydrostatics also are not #bcd proved by experience1 but have a necessary truth borrowed from the relations of our ideas4 ,it is hardly to be expected that the above reasoning will1 at first sight1 produce conviction in the mind of the reader1 except he have1 to a certain extent1 acquainted himself with the elementary doctrines of the science of ,hydrostatics as usually delivered2 and have followed1 with clear and steady apprehension1 some of the trains of reasoning by which the pressures of fluids are determined2 as1 for instance1 the explanation of what is called the ,hydrostatic ,paradox4 ,the necessity of such a discipline in order that the reader may enter fully into this part of our speculations1 naturally renders them less popular2 but this disadvantage is inevitable in our plan4 ,we cannot expect to throw light upon philosophy by means of the advances which have been made in the mathematical and physical sciences1 except we really understand the doctrines which have been firmly established in those sciences4 ,this preparation for philosophizing may be somewhat laborious2 but such labour is necessary if we would pursue speculative truth with all the advantages which the present condition of human knowledge places within our reach4 ,we may add1 that the consequences to which we are directed by the preceding opinions1 are of very great importance in their bearing upon our general views respecting human knowledge4 ,i trust to be able to show1 that some important distinctions are illustrated1 some perplexing paradoxes solved1 and some large anticipations of the future extension of our knowledge suggested1 by means of the conclusions to which the preceding discussions have conducted us4 ,but before ,i proceed to these general topics1 ,i must consider the foundations of some of the remaining portions of the science of ,mechanics4 #bce ,,chapter ,,vii4 ,,of ,,the ,,establishment ,,of ,,the ,,principles ,,of ,,dynamics4 #a4 ,,in the ,history of ,mechanics1 ,i have traced the steps by which the three ,laws of ,motion and the other principles of mechanics were discovered1 established1 and extended to the widest generality of form and application4 ,we have1 in these laws1 examples of principles which were1 historically speaking1 obtained by reference to experience4 ,bearing in mind the object and the result of the preceding discussions1 we cannot but turn with much interest to examine these portions of science2 to inquire whether there be any real difference in the grounds and nature between the knowledge thus obtained1 and those truths which we have already contemplated2 and which1 as we have seen1 contain their own evidence1 and do not require proof from experiment4 #b4 ,the ,first ,law of ,motion4--,the first law of motion is1 that ,when a body moves not acted upon by any force1 it will go on perpetually in a straight line1 and with a uniform velocity4 ,now what is the real ground of our assent to this proposition8 ,that it is not at first sight a self-evident truth1 appears to be clear2 since from the time of ,aristotle to that of ,galileo the opposite assertion was held to be true2 and it was believed that all bodies in motion had1 by their own nature1 a constant tendency to move more and more slowly1 so as to stop at last4 ,this belief1 indeed1 is probably even now entertained by most persons1 till their attention is fixed upon the arguments by which the first law of motion is established4 ,it is1 however1 not difficult to lead any person of a speculative habit #bcf of thought to see that the retardation which constantly takes place in the motion of all bodies when left to themselves1 is1 in reality1 the effect of extraneous forces which destroy the velocity4 ,a top ceases to spin because the friction against the ground and the resistance of the air gradually diminish its motion1 and not because its motion has any internal principle of decay or fatigue4 ,this may be shown1 and was1 in fact1 shown by ,hooke before the ,royal ,society1 at the time when the laws of motion were still under discussion1 by means of experiments in which the weight of the top is increased1 and the resistance to motion offered by its support1 is diminished2 for by such contrivances its motion is made to continue much longer than it would otherwise do4 ,and by experiments of this nature1 although we can never remove the whole of the external impediments to continued motion1 and although1 consequently1 there will always be some retardation2 and an end of the motion of a body left to itself1 however long it may be delayed1 must at last come2 yet we can establish a conviction that if all resistance could be removed1 there would be no diminution of velocity1 and thus the motion would go on for ever4 ,if we call to mind the axioms which we formerly stated1 as containing the most important conditions involved in the idea of ,cause1 it will be seen that our conviction in this case depends upon the first axiom of ,causation1 that nothing can happen without a cause4 ,every change in the velocity of the moving body must have a cause2 and if the change can1 in any manner1 be referred to the presence of other bodies1 these are said to exert force upon the moving body3 and the conception of force is thus evolved from the general idea of cause4 ,force is any cause which has motion1 or change of motion1 for its effect2 and thus1 all the change of velocity of a body which can be referred to extraneous bodies1--as the air which surrounds it1 or the support on which it rests1--is considered as the effect of forces2 and this consideration is looked upon as explaining the difference between the motion which really takes places in the experiment1 and that motion #bcg which1 as the law asserts1 would take place if the body were not acted on by any forces4 ,thus the truth of the first law of motion depends upon the axiom that no change can take place without a cause2 and follows from the definition of force1 if we suppose that there can be none but an external cause of change4 ,but in order to establish the law1 it was necessary further to be assured that there is no internal cause of change of velocity belonging to all matter whatever1 and operating in such a manner that the mere progress of time is sufficient to produce a diminution of velocity in all moving bodies4 ,it appears from the history of mechanical science1 that this latter step required a reference to observation and experiment2 and that the first law of motion is so far1 historically at least1 dependent upon our experience4 ,but notwithstanding this historical evidence of the need which we have of a reference to observed facts1 in order to place this first law of motion out of doubt1 it has been maintained by very eminent mathematicians and philosophers1 that the law is1 in truth1 evident of itself1 and does not really rest upon experimental proof4 ,such1 for example1 is the opinion of d',alembert#bjc1 who offers what is called an priori proof of this law2 that is1 a demonstration derived from our ideas alone4 ,when a body is put in motion1 either1 he says1 the cause which puts it in motion at first1 suffices to make it move one foot1 or the continued action of the cause during this foot is requisite for the motion4 ,in the first case1 the same reason which made the body proceed to the end of the first foot will hold for its going on through a second1 a third1 a fourth foot1 and so on for any number4 ,in the second case1 the same reason which made the force continue to act during the first foot1 will hold for its acting1 and therefore for the body moving during each succeeding foot4 ,and thus the body1 once beginning to move1 must go on moving for ever4 ,note #bjc3 ,dynamique4 #bch ,it is obvious that we might reply to this argument1 that the reasons for the body proceeding during each succeeding foot may not necessarily be all the same2 for among these reasons may be the time which has elapsed2 and thus the velocity may undergo a change as the time proceeds3 and we require observation to inform us that it does not do so4 ,professor ,playfair has presented nearly the same argument1 although in a different and more mathematical form#bac4 ,if the velocity change1 says he1 it must change according to some expression of calculation depending upon the time1 or1 in mathematical language1 must be a function of the time4 ,if the velocity diminish as the time increases1 this may be expressed by stating the velocity in each case as a certain number1 from which another quantity1 or term1 increasing as the time increases1 is subtracted4 ,but1 ,playfair adds1 there is no condition involved in the nature of the case1 by which the coefficients1 or numbers which are to be employed1 along with the number representing the time1 in calculating this second term1 can be determined to be of one magnitude rather than of any other4 ,therefore he infers there can be no such coefficients1 and that the velocity is in each case equal to some constant number1 independent of the time2 and is therefore the same for all times4 ,note #bac3 ,outlines of ,natural ,philosophy1 p4 #bf4 ,in reply to this we may observe1 that the circumstance of our not seeing in the nature of the case anything which determines for us the coefficients above spoken of1 cannot prove that they have not some certain value in nature4 ,we do not see in the nature of the case anything which should determine a body to fall sixteen feet in a second of time1 rather than one foot or one hundred feet3 yet in fact the space thus run through by falling bodies is determined to a certain magnitude4 ,it would be easy to assign a mathematical expression for the velocity of a body1 implying that one-hundredth of the velocity1 or any other #bci fraction1 is lost in each second#bbc3 and where is the absurdity of supposing such an expression really to represent the velocity8 ,note #bbc3 ,this would be the case1 if1 t being the number of seconds elapsed1 and ,c some constant quantity1 the velocity were expressed by this mathematical formula1 ,c7#ii_/ajj7t4 ,most modern writers on mechanics have embraced the opposite opinion1 and have ascribed our knowledge of this first law of motion to experience4 ,thus ,m4 ,poisson1 one of the most eminent of the mathematicians who have written on this subject1 says#bcc1 ,we cannot affirm priori that the velocity communicated to a body will not become slower and slower of itself1 and end by being entirely extinguished4 ,it is only by experience and induction that this question can be decided4 ,note #bcc3 ,poisson1 ,dynamique1 ed4 #b1 art4 #aac4 ,yet it cannot be denied that there is much force in those arguments by which it is attempted to show that the ,first ,law of ,motion1 such as we find it1 is more consonant to our conceptions than any other would be4 ,the ,law1 as it exists1 is the most simple that we can conceive4 ,instead of having to determine by experiments what is the law of the natural change of velocity1 we find the ,law to be that it does not change at all4 ,to a certain extent1 the ,law depends upon the evident axiom1 that no change can take place without a cause4 ,but the question further occurs1 whether the mere lapse of time may not be a cause of change of velocity4 ,in order to ensure this1 we have recourse to experiment2 and the result is that time alone does not produce any such change4 ,in addition to the conditions of change which we collect from our own ,ideas1 we ask of ,experience what other conditions and circumstances she has to offer2 and the answer is1 that she can point out none2 ,when we have removed the alterations which external causes1 in our very conception of them1 occasion1 there are no longer any alterations4 ,instead of having to guide ourselves #bdj by experience1 we learn that on this subject she has nothing to tell us4 ,instead of having to take into account a number of circumstances1 we find that we have only to reject all circumstances4 ,the velocity of a body remains unaltered by time alone1 of whatever kind the body itself be4 ,but the doctrine that time alone is not a cause of change of velocity in any body is further recommended to us by this consideration2--that time is conceived by us not as a cause1 but only as a condition of other causes producing their effects4 ,causes operate in time2 but it is only when the cause exists1 that the lapse of time can give rise to alterations4 ,when therefore all external causes of change of velocity are supposed to be removed1 the velocity must continue identical with itself1 whatever the time which elapses4 ,an eternity of negation can produce no positive result4 ,thus1 though the discovery of the ,first ,law of ,motion was made1 historically speaking1 by means of experiment1 we have now attained a point of view in which we see that it might have been certainly known to be true independently of experience4 ,this law in its ultimate form1 when completely simplified and steadily contemplated1 assumes the character of a self-evident truth4 ,we shall find the same process to take place in other instances4 ,and this feature in the progress of science will hereafter be found to suggest very important views with regard both to the nature and prospects of our knowledge4 #c4 ,gravity is a ,uniform ,force4--,we shall find observations of the same kind offering themselves in a manner more or less obvious1 with regard to the other principles of ,dynamics4 ,the determination of the laws according to which bodies fall downwards by the common action of gravity1 has already been noticed in the ,history of ,mechanics#bdc1 as one of the earliest positive advances in the doctrine of motion4 ,these laws were first rightly stated by ,galileo1 and #bda established by reasoning and by experiment1 not without dissent and controversy4 ,the amount of these doctrines is this3 ,that gravity is a uniform accelerating force2 such a uniform force having this for its character1 that it makes the velocity increase in exact proportion to the time of motion4 ,the relation which the spaces described by the body bear to the times in which they are described1 is obtained by mathematical deduction from this definition of the force4 ,note #bdc3 ,hist4 ,ind4 ,sc4 b4 vi4 c4 ii4 sect4 #b4 ,the clear ,definition of a uniform accelerating force1 and the ,proposition that gravity is such a force1 were co-ordinate and contemporary steps in this discovery4 ,in defining accelerating force1 reference1 tacit or express1 was necessarily made to the second of the general axioms respecting causation1--,that causes are measured by their effects4 ,force1 in the cases now under our notice1 is conceived to be1 as we have already stated1 7p4 #bcf17 any cause which1 acting from without1 changes the motion of a body4 ,it must1 therefore1 in this acceptation1 be measured by the magnitude of the changes which are produced4 ,but in what manner the changes of motion are to be employed as the measures of force1 is learnt from observation of the facts which we see taking place in the world4 ,experience interprets the axiom of causation1 from which otherwise we could not deduce any real knowledge4 ,we may assume1 in virtue of our general conceptions of force1 that under the same circumstances1 a greater change of motion implies a greater force producing it2 but what are we to expect when the circumstances change8 ,the weight of a body makes it fall from rest at first1 and causes it to move more quickly as it descends lower4 ,we may express this by saying1 that gravity1 the universal force which makes all terrestrial bodies fall when not supported1 by its continuous action first gives velocity to the body when it has none1 and afterwards adds velocity to that which the body already has4 ,but how is the velocity added proportioned to the velocity which already exists8 ,force acting on a body at rest1 and on a body in motion1 appears under very different #bdb conditions2--how are the effects related8 ,let the force be conceived to be in both cases the same1 since force is conceived to depend upon the extraneous bodies1 and not upon the condition of the moving mass itself4 ,but the force being the same1 the effects may still be different4 ,it is at first sight conceivable that the body1 acted upon by the same gravity1 may receive a less addition of velocity when it is already moving in the direction in which this gravity impels it2 for if we ourselves push a body forwards1 we can produce little additional effect upon it when it is already moving rapidly away from us4 ,may it not be true1 in like manner1 that although gravity be always the same force1 its effect depends upon the velocity which the body under its influence already possesses8 ,observation and reasoning combined1 as we have said1 enabled ,galileo to answer these questions4 ,he asserted and proved that we may consistently and properly measure a force by the velocity which is by it generated in a body1 in some certain time1 as one second2 and further1 that if we adopt this measure1 gravity will be a force of the same value under all circumstances of the body which it affects2 since it appeared that1 in fact1 a falling body does receive equal increments of velocity in equal times from first to last4 ,if it be asked whether we could have known1 anterior to1 or independent of1 experiment1 that gravity is a uniform force in the sense thus imposed upon the term2 it appears clear that we must reply1 that we could not have attained to such knowledge1 since other laws of the motion of bodies downwards are easily conceivable1 and nothing but observation could inform us that one of these laws does not prevail in fact4 ,indeed1 we may add1 that the assertion that the force of gravity is uniform1 is so far from being self-evident1 that it is not even true2 for gravity varies according to the distance from the center of the earth2 and although this variation is so small as to be1 in the case of falling bodies1 imperceptible1 it negatives the rigorous uniformity of the force as completely1 though #bdc not to the same extent1 as if the weight of a body diminished in a marked degree1 when it was carried from the lower to the upper room of a house4 ,it cannot1 then1 be a truth independent of experience1 that gravity is uniform4 ,yet1 in fact1 the assertion that gravity is uniform was assented to1 not only before it was proved1 but even before it was clearly understood4 ,it was readily granted by all1 that bodies which fall freely are uniformly accelerated2 but while some held the opinion just stated1 that uniformly accelerated motion is that in which the velocity increases in proportion to the time1 others maintained1 that that is uniformly accelerated motion1 in which the velocity increases in proportion to the space2 so that1 for example1 a body in falling vertically through twenty feet should acquire twice as great a velocity as one which falls through ten feet4 ,these two opinions are both put forward by the interlocutors of ,galileo's ,dialogue on this subject#bec4 ,and the latter supposition is rejected1 the author showing1 not that it is inconsistent with experience1 but that it is impossible in itself3 inasmuch as it would inevitably lead to the conclusion1 that the fall through a large and a small vertical space would occupy exactly the same time4 ,note #bec3 ,dialogo1 iii4 p4 #ie4 ,indeed1 ,galileo assumes his definition of uniformly accelerated motion as one which is sufficiently recommended by its own simplicity4 ',if we attend carefully1' he says1 'we shall find that no mode of increase of velocity is more simple than that which adds equal increments in equal times4 ,which we may easily understand if we consider the close affinity of time and motion3 for as the uniformity of motion is defined by the equality of spaces described in equal times1 so we may conceive the uniformity of acceleration to exist when equal velocities are added in equal times4' ,galileo's mode of supporting his opinion1 that bodies falling by the action of gravity are thus uniformly #bdd accelerated1 consists1 in the first place1 in adducing the maxim that nature always employs the most simple means#bfc4 ,but he is far from considering this a decisive argument4 ',i1' says one of his speakers1 'as it would be very unreasonable in me to gainsay this or any other definition which any author may please to make1 since they are all arbitrary1 may still1 without offence1 doubt whether such a definition1 conceived and admitted in the abstract1 fits1 agrees1 and is verified in that kind of accelerated motion which bodies have when they descend naturally4' ,note #bfc3 ,dialogo1 iii4 p4 #ia4 ,the experimental proof that bodies1 when they fall downwards1 are uniformly accelerated1 is 7by ,galileo7 derived from the inclined plane2 and therefore assumes the proposition1 that if such uniform acceleration prevail in vertical motion1 it will also hold when a body is compelled to describe an oblique rectilinear path4 ,this proposition may be shown to be true1 if 7assuming by anticipation the ,third ,law of ,motion1 of which we shall shortly have to speak17 we introduce the conception of a uniform statical force as the cause of uniform acceleration4 ,for the force on the inclined plane bears a constant proportion to the vertical force1 and this proportion is known from statical considerations4 ,but in the work of which we are speaking1 ,galileo does not introduce this abstract conception of force as the foundation of his doctrines4 ,instead of this1 he proposes1 as a postulate sufficiently evident to be made the basis of his reasonings1 ,that bodies which descend down inclined planes of different inclinations1 but of the same vertical height1 all acquire the same velocity#bgc4 ,but when this postulate has been propounded by one of the persons of the dialogue1 another interlocutor says1 ',you discourse very probably2 but besides this likelihood1 ,i wish to augment the probability so far1 that it shall be almost as complete as a necessary demonstration4' ,he then proceeds to describe a very ingenious and simple experiment1 which shows that when a body is made to swing upwards at the end of #bde a string1 it attains to the same height1 whatever is the path it follows1 so long as it starts from the lowest point with the same velocity4 ,and thus ,galileo's postulate is experimentally confirmed1 so far as the force of gravity can be taken as an example of the forces which the postulate contemplates3 and conversely1 gravity is proved to be a uniform force1 so far as it can be considered clear that the postulate is true of uniform forces4 ,note #bgfc3 ,dialogo1 iii4 p4 #cf4 ,when we have introduced the conception and definition of accelerating force1 ,galileo's postulate1 that bodies descending down inclined planes of the same vertical height1 acquire the same velocity1 may1 by a few steps of reasoning1 be demonstrated to be true of uniform forces3 and thus the proof that gravity1 either in vertical or oblique motion1 is a uniform force1 is confirmed by the experiment above mentioned2 as it also is1 on like grounds1 by many other experiments1 made upon inclined planes and pendulums4 ,thus the propriety of ,galileo's conception of a uniform force1 and the doctrine that gravity is a uniform force1 were confirmed by the same reasonings and experiments4 ,we may make here two remarks2 ,first1 that the conception1 when established and rightly stated1 appears so simple as hardly to require experimental proof2 a remark which we have already made with regard to the ,first ,law of ,motion3 and ,second1 that the discovery of the real law of nature was made by assuming propositions which1 without further proof1 we should consider as very precarious1 and as far less obvious1 as well as less evident1 than the law of nature in its simple form4 #d4 ,the ,second ,law of ,motion4--,when a body1 instead of falling downwards from rest1 is thrown in any direction1 it describes a curve line1 till its motion is stopped4 ,in this1 and in all other cases in which a body describes a curved path in free space1 its motion is determined by the ,second ,law of ,motion4 ,the law1 in its general form1 is as follows3--,when a body is thus cast forth and acted upon by a force in a direction #bdf transverse to its motion1 the result is1 ,that there is combined with the motion with which the body is thrown1 another motion1 exactly the same as that which the same force would have communicated to a body at rest4 ,it will readily be understood that the basis of this law is the axiom already stated1 that effects are measured by their causes4 ,in virtue of this axiom1 the effect of gravity acting upon a body in a direction transverse to its motion1 must measure the accelerative or deflective force of gravity under those circumstances4 ,if this effect vary with the varying velocity and direction of the body thus acted upon1 the deflective force of gravity also will vary with those circumstances4 ,the more simple supposition is1 that the deflective force of gravity is the same1 whatever be the velocity and direction of the body which is subjected to its influence3 and this is the supposition which we find to be verified by facts4 ,for example1 a ball let fall from the top of a ship's upright mast1 when she is sailing steadily forward1 will fall at the foot of the mast1 just as if it were let fall while the ship were at rest2 thus showing that the motion which gravity gives to the ball is compounded with the horizontal motion which the ball shares with the ship from the first4 ,this general and simple conception of motions as compounded with one another1 represents1 it is proved1 the manner in which the motion produced by gravity modifies any other motion which the body may previously have had4 ,the discussions which terminated in the general reception of this ,second ,law of ,motion among mechanical writers1 were much mixed up with the arguments for and against the ,copernican system1 which system represented the earth as revolving upon its axis4 ,for the obvious argument against this system was1 that if each point of the earth's surface were thus in motion from west to east1 a stone dropt from the top of a tower would be left behind1 the tower moving away from it3 and the answer was1 that by this law of motion1 the stone would have the earth's motion impressed upon it1 as well as that motion which would #bdg arise from its gravity to the earth2 and that the motion of the stone relative to the tower would thus be the same as if both earth and tower were at rest4 ,galileo further urged1 as a presumption in favour of the opinion that the two motions1--the circular motion arising from the rotation of the earth1 and the downward motion arising from the gravity of the stone1 would be compounded in the way we have described1 7neither of them disturbing or diminishing the other17--that the first motion was in its own nature not liable to any change or diminution#bhc1 as we learn from the ,first ,law of ,motion4 ,nor was the subject lightly dismissed4 ,the experiment of the stone let fall from the top of the mast was made in various forms by ,gassendi2 and in his ,epistle1 ,de ,motu impresso a ,motore translato1 the rule now in question is supported by reference to these experiments4 ,in this manner1 the general truth1 the ,second ,law of ,motion1 was established completely and beyond dispute4 ,note #bhc3 ,dialogo1 ii4 p4 #aad4 ,but when this law had been proved to be true in a general sense1 with such accuracy as rude experiments1 like those of ,galileo and ,gassendi1 would admit1 it still remained to be ascertained 7supposing our knowledge of the law to be the result of experience alone17 whether it were true with that precise and rigorous exactness which more refined modes of experimenting could test4 ,we so willingly believe in the simplicity of laws of nature1 that the rigorous accuracy of such a law1 known to be at least approximately true1 was taken for granted1 till some ground for suspecting the contrary should appear4 ,yet calculations have not been wanting which might confirm the law as true to the last degree of accuracy4 ,laplace relates 7,syst4 du ,monde1 livre iv4 chap4 #af17 that at one time he had conceived it possible that the effect of gravity upon the moon might be slightly modified by the moon's direction and velocity2 and that in this way an explanation might be found for the moon's acceleration 7a deviation of her observed from her calculated place1 which long #bdh perplexed mathematicians74 ,but it was after some time discovered that this feature in the moon's motion arose from another cause2 and the second law of motion was confirmed as true in the most rigorous sense4 ,thus we see that although there were arguments which might be urged in favour of this law1 founded upon the necessary relations of ideas1 men became convinced of its truth only when it was verified and confirmed by actual experiment4 ,but yet in this case again1 as in the former ones1 when the law had been established beyond doubt or question1 men were very ready to believe that it was not a mere result of observation1--that the truth which it contained was not derived from experience1--that it might have been assumed as true in virtue of reasonings anterior to experience1--and that experiments served only to make the law more plain and intelligible1 as visible diagrams in geometry serve to illustrate geometrical truths2 our knowledge not being 7they deemed7 in mechanics1 any more than in geometry1 borrowed from the senses4 ,it was thought by many to be self-evident1 that the effect of a force in any direction cannot be increased or diminished by any motion transverse to the direction of the force which the body may have at the same time3 or1 to express it otherwise1 that if the motion of the body be compounded of a horizontal and vertical motion1 the vertical motion alone will be affected by the vertical force4 ,this principle1 indeed1 not only has appeared evident to many persons1 but even at the present day is assumed as an axiom by many of the most eminent mathematicians4 ,it is1 for example1 so employed in the ,mcanique ,cleste of ,laplace1 which may be looked upon as the standard of mathematical mechanics in our time2 and in the ,mcanique ,analytique of ,lagrange1 the most consummate example which has appeared of subtilty of thought on such subjects1 as well as of power of mathematical generalization#bic4 ,and #bdi thus we have here another example of that circumstance which we have already noticed in speaking of the ,first ,law of ,motion1 7,art4 #b of this chapter17 and of the ,law that ,gravity is a uniform ,force1 7,art4 #c72 namely1 that the law1 though historically established by experiments1 appears1 when once discovered and reduced to its most simple and general form1 to be self-evident4 ,i am the more desirous of drawing attention to this feature in various portions of the history of science1 inasmuch as it will be found to lead to some very extensive and important views1 hereafter to be considered4 ,note #bic3 ,i may observe that the rule that we may compound motions1 as the ,law supposes1 is involved in the step of resolving them2 which is done in the passage to which ,i refer4 7,mc4 ,analyt4 ptie4 i4 sect4 i4 art4 #c4 p4 #bbe47 ',si on conoit que le mouvement d'un corps et les forces qui le sollicitent soient decomposes suivant trois lignes droites perpendiculaires entre elles1 on pourra considrer sparment les mouvemens et les forces relatives chacun de ces trois directions4 ,car cause de la perpendicularit des directions il est visible que chacun de ces mouvemens partiels peut tre regard comme indpendant des deux autres1 et qu'il ne peut recevoir d'altration que de la part de la force qui agit dans la direction de ce mouvement2 l'on peut conclure que ces trois mouvemens doivent suivre1 chacun en particulier1 les lois des mouvemens rectilignes acclrs ou retards par les forces donnes4' ,laplace makes the same assumption in effect1 7,mc4 ,cl4 p4 i4 liv4 i4 art4 #g71 by resolving the forces which act upon a point in three rectangular directions1 and reasoning separately concerning each direction4 ,but in his mode of treating the subject is involved a principle which belongs to the ,third ,law of ,motion1 namely1 the doctrine that the velocity is as the force1 of which we shall have to speak elsewhere4 #e4 ,the ,third ,law of ,motion4--,we have1 in the definition of ,accelerating ,force1 a measure of ,forces1 so far as they are concerned in producing motion4 ,we had before1 in speaking of the principles of statics1 defined the measure of ,forces or ,pressures1 so far as they are employed in producing equilibrium4 ,but these two aspects of ,force are closely connected2 and we require a law which shall lay down the rule of their connexion4 ,by the same kind of muscular exertion by which we can support a heavy stone1 we can also put it in motion4 ,the question then occurs1 how is the rate and manner of its motion determined8 ,the answer to this question is contained in the ,third ,law #bej of ,motion1 and it is to this effect3 that the ,momentum which any pressure produces in the mass in a given time is proportional to the pressure4 ,by ,momentum is meant the product of the numbers which express the velocity and the mass of the body3 and hence1 if the mass of the body be the same in the instances which we compare1 the rule is1--,that the velocity is as the force which produces it2 and this is one of the simplest ways of expressing the ,third ,law of ,motion4 ,in agreement with our general plan1 we have to ask1 ,what is the ground of this rule8 ,what is the simplest and most satisfactory form to which we can reduce the proof of it8 ,or1 to take an instance2 if a double pressure be exerted against a given mass1 so disposed as to be capable of motion1 why must it produce twice the velocity in the same time8 ,to answer this question1 suppose the double pressure to be resolved into two single pressures3 one of these will produce a certain velocity2 and the question is1 why an equal pressure1 acting upon the same mass1 will produce an equal velocity in addition to the former8 ,or1 stating the matter otherwise1 the question is1 why each of the two forces will produce its separate effect1 unaltered by the simultaneous action of the other force8 ,this statement of the case makes it seem to approach very near to such cases as are included in the ,second ,law of ,motion1 and therefore it might appear that this ,third ,law has no grounds distinct from the ,second4 ,but it must be recollected that the word force has a different meaning in this case and in that2 in this place it signifies pressure2 in the statement of the ,second ,law its import was accelerative or deflective force1 measured by the velocity or deflexion generated4 ,and thus the ,third ,law of ,motion1 so far as our reasonings yet go1 appears to rest on a foundation different from the ,second4 ,accordingly1 that part of the ,third ,law of ,motion which we are now considering1 that the velocity generated is as the force1 was obtained1 in fact1 by a separate train of research4 ,the first exemplification of this #bea law which was studied by mathematicians1 was the motion of bodies upon inclined planes3 for the force which urges a body down an inclined plane is known by statics1 and hence the velocity of its descent was to be determined4 ,galileo originally#cjc in his attempts to solve this problem of the descent of a body down an inclined plane1 did not proceed from the principle which we have stated1 7the determination of the force which acts down the inclined plane from statical considerations17 obvious as it may seem2 but assumed1 as we have already seen1 a proposition apparently far more precarious2--namely1 that a body sliding down a smooth inclined plane acquires always the same velocity1 so long as the vertical height fallen through is the same4 ,and this conjecture 7for at first it was nothing more than a conjecture7 he confirmed by an ingenious experiment2 in which bodies acquired or lost the same velocity by descending or ascending through the same height1 although their paths were different in other respects4 ,note #cjc3 ,dial4 della ,sc4 ,nuov4 iii4 p4 #if4 ,see ,hist4 ,ind4 ,sci4 b4 vi4 c4 ii4 sect4 #e4 ,this was the form in which the doctrine of the motion of bodies down inclined planes was at first presented in ,galileo's ,dialogues on the ,science of ,motion4 ,but his disciple ,viviani was dissatisfied with the assumption thus introduced2 and in succeeding editions of the ,dialogues1 the apparent chasm in the reasoning was much narrowed1 by making the proof depend upon a principle nearly identical with the third law of motion as we have just stated it4 ,in the proof thus added1 ',we are agreed1' says the interlocutor#cac1 'that in a moving body the impetus1 energy1 momentum1 or propension to motion1 is as great as is the force or least resistance which suffices to sustain it2' and the impetus or momentum1 in the course of the proof1 being taken to be as the velocity produced in a given time1 it is manifest that the principle so stated amounts to this2 that the velocity produced is as the statical force4 ,and thus this law of motion appears1 #beb in the school of ,galileo1 to have been suggested and established at first by experiment1 but afterwards confirmed and demonstrated by priori considerations4 ,note #cac3 ,dialogo1 p4 #ajd4 ,we see1 in the above reasoning1 a number of abstract terms introduced which are not1 at first at least1 very distinctly defined1 as impetus1 momentum1 c4 ,of these1 momentum has been selected1 to express that quantity which1 in a moving body1 measures the statical force impressed upon the body4 ,this quantity is1 as we have just seen1 proportional to the velocity in a given body4 ,it is also1 in different bodies1 proportional to the mass of the body4 ,this part of the third law of motion follows from our conception of matter in general as consisting of parts capable of addition4 ,a double pressure must be required to produce the same velocity in a double mass2 for if the mass be halved1 each half will require an equal pressure2 and the addition1 both of the pressures and of the masses1 will take place without disturbing the effects4 ,the measure of the quantity of matter of a body considered as affecting the velocity which pressure produces in the body1 is termed its inertia1 as we have already stated 7c4 v474 ,inertia is the property by which a large mass of matter requires a greater force than a small mass1 to give it an equal velocity4 ,it belongs to each portion of matter2 and portions of inertia are added whenever portions of matter are added4 ,hence inertia is as the quantity of matter2 which is only another way of expressing this third law of motion1 so far as quantity of matter is concerned4 ,but how do we know the quantity of matter of a body8 ,we may reply1 that we take the weight as the measure of the quantity of matter3 but we may then be again asked1 how it appears that the weight is proportional to the inertia2 which it must be1 in order that the quantity of matter may be proportional to both one and the other4 ,we answer1 that this appears to be true experimentally1 because all bodies fall with equal velocities by gravity1 when the known causes of difference are removed4 ,the observations of falling #bec bodies1 indeed1 are not susceptible of much exactness3 but experiments leading to the same result1 and capable of great precision1 were made upon pendulums by ,newton2 as he relates in his ,principia1 ,book ,,iii4 prop4 #f4 ,they all agreed1 he says1 with perfect accuracy3 and thus the weight and the inertia are proportional in all cases1 and therefore each proportional to the quantity of matter as measured by the other4 ,the conception of inertia1 as we have already seen in chapter ,v41 involves the notion of action and reaction2 and thus the laws which involve inertia depend upon the idea of mutual causation4 ,the rule1 that the velocity is as the force1 depends upon the principle of causation1 that the effect is proportional to the cause2 the effect being here so estimated as to be consistent both with the other laws of motion and with experiment4 ,but here1 as in other cases1 the question occurs again2 ,is experiment really requisite for the proof of this law8 ,if we look to authorities1 we shall be not a little embarrassed to decide4 ,d',alembert is against the necessity of experimental proof4 ',why1' says he#cbc1 'should we have recourse to this principle employed1 at the present day1 by everybody1 that the force is proportional to the velocity8 444 a principle resting solely upon this vague and obscure axiom1 that the effect is proportional to the cause4 ,we shall not examine here1' he adds1 'if this principle is necessarily true2 we shall only avow that the proofs which have hitherto been adduced do not appear to us unexceptionable3 nor shall we1 with some geometers1 adopt it as a purely contingent truth2 which would be to ruin the certainty of mechanics1 and to reduce it to be nothing more than an experimental science4 ,we shall content ourselves with observing1' he proceeds1 'that certain or doubtful1 clear or obscure1 it is useless in mechanics1 and consequently ought to be banished from the science4' ,though ,d',alembert rejects the third law of motion in this form1 he accepts one of #bed equivalent import1 which appears to him to possess axiomatic certainty2 and this procedure is in consistence with the course which he takes1 of claiming for the science of mechanics more than mere experimental truth4 ,on the contrary1 ,laplace considers this third law as established by experiment4 ',is the force1' he says'#ccc1 'proportioned to the velocity8 ,this1' he replies1 'we cannot know priori1 seeing that we are in ignorance of the nature of moving force3 we must therefore1 for this purpose1 recur to experience2 for all which is not a necessary consequence of the few data we have respecting the nature of things1 is1 for us1 only a result of observation4' ,and again he says#cdc1 ',here1 then1 we have two laws of motion1--the law of inertia the first law of motion1 and the law of the force proportional to the velocity1--which are given by observation4 ,they are the most natural and the most simple laws which we can imagine1 and without doubt they flow from the very nature of matter2 but this nature being unknown1 they are1 for us1 only observed facts3 the only ones1 however1 which ,mechanics borrows from experience4' ,note #cbc3 ,dynamique1 ,pref4 p4 x4 ,note #ccc3 ,mc4 ,cl4 p4 #ae4 ,note #cdc3 p4 #ah4 ,it will appear1 ,i think1 from the views given in this and several other parts of the present work1 that we cannot with justice say that we have very 'few data respecting the nature of things1' in speculating concerning the laws of the universe2 since all the consequences which flow from the relations of our fundamental ideas1 necessarily regulate our knowledge of things1 so far as we have any such knowledge4 ,nor can we say that the nature of matter is unknown to us1 in any sense in which we can conceive knowledge as possible4 ,the nature of matter is no more unknown than the nature of space or of number4 ,in our conception of matter1 as of space and of number1 are involved certain relations1 which are the necessary groundwork of our knowledge2 and anything which is independent of these relations1 is not unknown1 but inconceivable4 #bee ,it must be already clear to the reader1 from the phraseology employed by these two eminent mathematicians1 that the question respecting the formation of the third law of motion can only be solved by a careful consideration of what we mean by observation and experience1 nature and matter4 ,but it will probably be generally allowed1 that1 taking into account the explanations already offered of the necessary conditions of experience and of the conception of inertia1 this law of motion1 that the inertia is as the quantity of matter1 is almost or altogether self-evident4 #f4 ,action and ,reaction are ,equal in ,moving ,bodies4--,when we have to consider bodies as acting upon one another1 and influencing each other's motions1 the third law of motion is still applied2 but along with this1 we also employ the general principle that action and reaction are equal and opposite4 ,action and reaction are here to be understood as momentum produced and destroyed1 according to the measure of action established by the ,third ,law of ,motion3 and the cases in which this principle is thus employed form so large a portion of those in which the third law of motion is used1 that some writers 7,newton at the head of them7 have stated the equality of action and reaction as the third law of motion4 ,the third law of motion being once established1 the equality of action and reaction1 in the sense of momentum gained and lost1 necessarily follows4 ,thus1 if a weight hanging by a string over the edge of a smooth level table draw another weight along the table1 the hanging weight moves more slowly than it would do if not so connected1 and thus loses velocity by the connexion2 while the other weight gains by the connexion all the velocity which it has1 for if left to itself it would rest4 ,and the pressures which restrain the descent of the first body and accelerate the motion of the second1 are equal at all instants of time1 for each of these pressures is the tension of the string3 and hence1 by the third law of motion1 the momentum gained by the one body1 and the momentum lost by the other in virtue of the action of this string1 are equal4 ,and similar #bef reasoning may be employed in any other case where bodies are connected4 ,the case where one body does not push or draw1 but strikes another1 appeared at first to mechanical reasoners to be of a different nature from the others2 but a little consideration was sufficient to show that a blow is1 in fact1 only a short and violent pressure2 and that1 therefore1 the general rule of the equality of momentum lost and gained applies to this as well as to the other cases4 ,thus1 in order to determine the case of the direct action of bodies upon one another1 we require no new law of motion4 ,the equality of action and reaction1 which enters necessarily into every conception of mechanical operation1 combined with the measure of action as given by the third law of motion1 enables us to trace the consequences of every case1 whether of pressure or of impact4 #g4 ,d',alembert's ,principle4--,but what will be the result when bodies do not act directly upon each other1 but are indirectly connected in any way by levers1 strings1 pulleys1 or in any other manner1 so that one part of the system has a mechanical advantage over another8 ,the result must still be determined by the principle that action and reaction balance each other4 ,the action and reaction1 being pressures in one sense1 must balance each other by the laws of statics1 for these laws determine the equilibrium of pressure4 ,now action and reaction1 according to their measures in the ,third ,law of ,motion1 are momentum gained and lost1 when the action is direct2 and except the indirect action introduce some modification of the law1 they must have the same measure still4 ,but1 in fact1 we cannot well conceive any modification of the law to take place in this case2 for direct action is only one 7the ultimate7 case of indirect action4 ,thus if two heavy bodies act at different points of a lever1 the action of each on the other is indirect2 but if the two points come together1 the action becomes direct4 ,hence the rule must be that which we have already stated2 for if the rule were false for indirect action1 it would #beg also be false for direct action1 for which case we have shown it to be true4 ,and thus we obtain the general principle1 that in any system of bodies which act on each other1 action and reaction1 estimated by momentum gained and lost1 balance each other according to the laws of equilibrium4 ,this principle1 which is so general as to supply a key to the solution of all possible mechanical problems1 is commonly called ,d',alembert's ,principle4 ,the experimental proofs which convinced men of the truth of the ,third ,law of ,motion were1 many or most of them1 proofs of the law in this extended sense4 ,and thus the proof of ,d',alembert's ,principle1 both from the idea of mechanical action and from experience1 is included in the proof of the law already stated4 #h4 ,connexion of ,dynamical and ,statical ,principles4--,the principle of equilibrium of ,d',alembert just stated1 is the law which he would substitute for the ,third ,law of ,motion2 and he would thus remove the necessity for an independent proof of that law4 ,in like manner1 the ,second ,law of ,motion is by some writers derived from the principle of the composition of statical forces2 and they would thus supersede the necessity of a reference to experiment in that case4 ,laplace takes this course1 and thus1 as we have seen1 rests only the ,first and ,third ,law of ,motion upon experience4 ,newton1 on the other hand1 recognizes the same connexion of propositions1 but for a different purpose2 for he derives the composition of statical forces from the ,second ,law of ,motion4 ,the close connexion of these three principles1 the composition of 7statical7 forces1 the composition of 7accelerating7 forces with velocities1 and the measure of 7moving7 forces by velocities1 cannot be denied2 yet it appears to be by no means easy to supersede the necessity of independent proofs of the last two of these principles4 ,both may be proved or illustrated by experiment3 and the experiments which prove the one are different from those which establish the other4 ,for example1 it appears by easy calculations1 that when we apply our principles to the oscillations of a pendulum1 #beh the ,second ,law is proved by the fact1 that the oscillations take place at the same rate in an east and west1 and in a north and south direction3 under the same circumstances1 the ,third ,law is proved by our finding that the time of a small oscillation is proportional to the square root of the length of a pendulum2 and similar differences might be pointed out in other experiments1 as to their bearing upon the one law or the other4 #i4 ,mechanical ,principles become gradually more simple and more evident4--,i will again point out in general two circumstances which ,i have already noticed in particular cases of the laws of motion4--,truths are often at first assumed in a form which is far from being the most obvious or simple2--and truths once discovered are gradually simplified1 so as to assume the appearance of self-evident truths4 ,the former circumstance is exemplified in several of the instances which we have had to consider4 ,the assumption1 that a perpetual motion is impossible1 preceded the knowledge of the first law of motion4 ,the assumed equality of the velocities acquired down two inclined planes of the same height1 was afterwards reduced to the third law of motion by ,galileo himself4 ,in the ,history#cec1 we have noted ,huyghens's assumption of the equality of the actual descent and potential ascent of the center of gravity3 this was afterwards reduced by ,herman and the ,bernoullis1 to the statical equivalence of the solicitations of gravity and the vicarious solicitations of the effective forces which act on each point2 and finally to the principle of ,d',alembert1 which asserts that the motions gained and lost balance each other4 ,note #cec3 ,b4 vi4 c4 v4 sect4 #b4 ,this early assertion of principles which now appear neither obvious nor self-evident1 is not to be considered as a groundless assumption on the part of the discoverers by whom it was made4 ,on the contrary1 it is evidence of the deep sagacity and clear thought which were #bei requisite in order to make such discoveries4 ,for these results are really rigorous consequences of the laws of motion in their simplest form3 and the evidence of them was probably present1 though undeveloped1 in the minds of the discoverers4 ,we are told of geometrical students1 who1 by a peculiar aptitude of mind1 perceived the evidence of some of the more advanced propositions of geometry without going through the introductory steps4 ,we must suppose a similar aptitude for mechanical reasonings1 which1 existing in the minds of ,stevinus1 ,galileo1 ,newton1 and ,huyghens1 led them to make those assumptions which finally resolved themselves into the laws of motion4 ,we may observe further1 that the simplicity and evidence which the laws of mechanics have at length assumed1 are much favoured by the usage of words among the best writers on such subjects4 ,terms which originally1 and before the laws of motion were fully known1 were used in a very vague and fluctuating sense1 were afterwards limited and rendered precise1 so that assertions which at first appear identical propositions become distinct and important principles4 ,thus force1 motion1 momentum1 are terms which were employed1 though in a loose manner1 from the very outset of mechanical speculation4 ,and so long as these words retained the vagueness of common language1 it would have been a useless and barren truism to say that 'the momentum is proportional to the force1' or that 'a body loses as much motion as it communicates to another4' ,but when 'momentum' and 'quantity of motion' are defined to mean the product of mass and velocity1 these two propositions immediately become distinct statements of the third law of motion and its consequences4 ,in like manner1 the assertion that 'gravity is a uniform force' was assented to1 before it was settled what a uniform force was2 but this assertion only became significant and useful when that point had been properly determined4 ,the statement that 'when different motions are communicated to the same body their effects are #bfj compounded1' becomes the second law of motion1 when we define what composition of motions is4 ,and the same process may be observed in other cases4 ,and thus we see how well the form which science ultimately assumes is adapted to simplify knowledge4 ,the definitions which are adopted1 and the terms which become current in precise senses1 produce a complete harmony between the matter and the form of our knowledge2 so that truths which were at first unexpected and recondite1 became familiar phrases1 and after a few generations sound1 even to common ears1 like identical propositions4 #aj4 ,controversy of the ,measure of ,force4--,in the ,history of ,mechanics#cfc1 we have given an account of the controversy which1 for some time1 occupied the mathematicians of ,europe1 whether the forces of bodies in motion should be reckoned proportional to the velocity1 or to the square of the velocity4 ,we need not here recall the events of this dispute2 but we may remark1 that its history1 as a metaphysical controversy1 is remarkable in this respect1 that it has been finally and completely settled2 for it is now agreed among mathematicians that both sides were right1 and that the results of mechanical action may be expressed with equal correctness by means of momentum and of vis viva4 ,it is1 in one sense1 as ,d',alembert has said#cgc1 a dispute about words2 but we are not to infer that1 on that account1 it was frivolous or useless2 for such disputes are one principal means of reducing the principles of our #bfa knowledge to their utmost simplicity and clearness4 ,the terms which are employed in the science of mechanics are now liberated for ever1 in the minds of mathematicians1 from that ambiguity which was the battleground in the war of the vis viva4 ,note #cfc3 ,b4 vi4 c4 v4 sect4 #b4 ,note #cgc3 ,d',alembert has also remarked 7,dynamique1 ,pref4 xxi47 that this controversy 'shows how little justice and precision there is in the pretended axiom that causes are proportional to their effects4' ,but this reflection is by no means well founded4 ,for since both measures are true1 it appears that causes may be justly measured by their effects1 even when very different kinds of effects are taken4 ,that the axiom does not point out one precise measure1 till illustrated by experience or by other considerations1 we grant3 but the same thing occurs in the application of other axioms also4 ,but we may observe that the real reason of this controversy was exactly that tendency which we have been noticing2--the disposition of man to assume in his speculations certain general propositions as true1 and to fix the sense of terms so that they shall fall in with this truth4 ,it was agreed1 on all hands1 that in the mutual action of bodies the same quantity of force is always preserved2 and the question was1 by which of the two measures this rule could best be verified4 ,we see1 therefore1 that the dispute was not concerning a definition merely1 but concerning a definition combined with a general proposition4 ,such a question may be readily conceived to have been by no means unimportant2 and we may remark1 in passing1 that such controversies1 although they are commonly afterwards stigmatized as quarrels about words and definitions1 are1 in reality1 events of considerable consequence in the history of science2 since they dissipate all ambiguity and vagueness in the use of terms1 and bring into view the conditions under which the fundamental principles of our knowledge can be most clearly and simply presented4 ,it is worth our while to pause for a moment on the prospect that we have thus obtained1 of the advance of knowledge1 as exemplified in the history of ,mechanics4 ,the general transformation of our views from vague to definite1 from complex to simple1 from unexpected discoveries to self-evident truths1 from seeming contradictions to identical propositions1 is very remarkable1 but it is by no means peculiar to our subject4 ,the same circumstances1 more or less prominent1 more or less developed1 appear in the history of other sciences1 according to the point of advance which each has reached4 ,they bear upon very important doctrines respecting the prospects1 the #bfb limits1 and the very nature of our knowledge4 ,and though these doctrines require to be considered with reference to the whole body of science1 yet the peculiar manner in which they are illustrated by the survey of the history of ,mechanics1 on which we have just been engaged1 appears to make this a convenient place for introducing them to the reader4 #bfc ,,chapter ,,viii4 ,,of ,,the ,,paradox ,,of ,,universal ,,propositions ,,obtained ,,from ,,experience4 #a4 ,,it was formerly stated#chc that experience cannot establish any universal or necessary truths4 ,the number of trials which we can make of any proposition is necessarily limited1 and observation alone cannot give us any ground of extending the inference to untried cases4 ,observed facts have no visible bond of necessary connexion1 and no exercise of our senses can enable us to discover such connexion4 ,we can never acquire from a mere observation of facts1 the right to assert that a proposition is true in all cases1 and that it could not be otherwise than we find it to be4 ,note #chc3 ,b4 i4 c4 iv4 ,of ,experience ,yet1 as we have just seen in the history of the laws of motion1 we may go on collecting our knowledge from observation1 and enlarging and simplifying it1 till it approaches or attains to complete universality and seeming necessity4 ,whether the laws of motion1 as we now know them1 can be rigorously traced to an absolute necessity in the nature of things1 we have not ventured absolutely to pronounce4 ,but we have seen that some of the most acute and profound mathematicians have believed that1 for these laws of motion1 or some of them1 there was such a demonstrable necessity compelling them to be such as they are1 and no other4 ,most of those who have carefully studied the principles of ,mechanics will allow that some at least of the primary laws of motion approach very near to this character of necessary truth2 and will confess that it would be difficult to imagine any other consistent #bfd scheme of fundamental principles4 ,and almost all mathematicians will allow to these laws an absolute universality2 so that we may apply them without scruple or misgiving1 in cases the most remote from those to which our experience has extended4 ,what astronomer would fear to refer to the known laws of motion1 in reasoning concerning the double stars2 although these objects are at an immeasurably remote distance from that solar system which has been the only field of our observation of mechanical facts8 ,what philosopher1 in speculating respecting a magnetic fluid1 or a luminiferous ether1 would hesitate to apply to it the mechanical principles which are applicable to fluids of known mechanical properties8 ,when we assert that the quantity of motion in the world cannot be increased or diminished by the mutual actions of bodies1 does not every mathematician feel convinced that it would be an unphilosophical restriction to limit this proposition to such modes of action as we have tried8 ,yet no one can doubt that1 in historical fact1 these laws were collected from experience4 ,that such is the case1 is no matter of conjecture4 ,we know the time1 the persons1 the circumstances1 belonging to each step of each discovery4 ,i have1 in the ,history1 given an account of these discoveries2 and in the previous chapters of the present work1 ,i have further examined the nature and the import of the principles which were thus brought to light4 ,here1 then1 is an apparent contradiction4 ,experience1 it would seem1 has done that which we had proved that she cannot do4 ,she has led men to propositions1 universal at least1 and to principles which appear to some persons necessary4 ,what is the explanation of this contradiction1 the solution of this paradox8 ,is it true that ,experience can reveal to us universal and necessary truths8 ,does she possess some secret virtue1 some unsuspected power1 by which she can detect connexions and consequences which we have declared to be out of her sphere8 ,can she see more than mere appearances1 and observe more than mere facts8 ,can #bfe she penetrate1 in some way1 to the nature of things8--descend below the surface of phenomena to their causes and origins1 so as to be able to say what can and what can not be2--what occurrences are partial1 and what universal8 ,if this be so1 we have indeed mistaken her character and powers2 and the whole course of our reasoning becomes precarious and obscure4 ,but1 then1 when we return upon our path we cannot find the point at which we deviated1 we cannot detect the false step in our deduction4 ,it still seems that by experience1 strictly so called1 we cannot discover necessary and universal truths4 ,our senses can give us no evidence of a necessary connexion in phenomena4 ,our observation must be limited1 and cannot testify concerning anything which is beyond its limits4 ,a general view of our faculties appears to prove it to be impossible that men should do what the history of the science of mechanics shows that they have done4 #b4 ,but in order to try to solve this ,paradox1 let us again refer to the ,history of ,mechanics4 ,in the cases belonging to that science1 in which propositions of the most unquestionable universality1 and most approaching to the character of necessary truths1 7as1 for instance1 the laws of motion17 have been arrived at1 what is the source of the axiomatic character which the propositions thus assume8 ,the answer to this question will1 we may hope1 throw some light on the perplexity in which we appear to be involved4 ,now the answer to this inquiry is1 that the laws of motion borrow their axiomatic character from their being merely interpretations of the ,axioms of ,causation4 ,those axioms1 being exhibitions of the ,idea of ,cause under various aspects1 are of the most rigorous universality and necessity4 ,and so far as the laws of motion are exemplifications of those axioms1 these laws must be no less universal and necessary4 ,how these axioms are to be understood2--in what sense cause and effect1 action and reaction1 are to be taken1 experience and observation did1 in fact1 teach inquirers on this subject2 and without this teaching1 the laws of motion could never have been distinctly known4 ,if two forces #bff act together1 each must produce its effect1 by the axiom of causation2 and1 therefore1 the effects of the separate forces must be compounded4 ,but a long course of discussion and experiment must instruct men of what kind this composition of forces is4 ,again2 action and reaction must be equal2 but much thought and some trial were needed to show what action and reaction are4 ,those metaphysicians who enunciated ,laws of motion without reference to experience1 propounded only such laws as were vague and inapplicable4 ,but yet these persons manifested the indestructible conviction1 belonging to man's speculative nature1 that there exist ,laws of motion1 that is1 universal formul1 connecting the causes and effects when motion takes place4 ,those mechanicians1 again1 who1 observed facts involving equilibrium and motion1 and stated some narrow rules1 without attempting to ascend to any universal and simple principle1 obtained laws no less barren and useless than the metaphysicians2 for they could not tell in what new cases1 or whether in any1 their laws would be verified2--they needed a more general rule1 to show them the limits of the rule they had discovered4 ,they went wrong in each attempt to solve a new problem1 because their interpretation of the terms of the axioms1 though true1 perhaps1 in certain cases1 was not right in general4 ,thus ,pappus erred in attempting to interpret as a case of the lever1 the problem of supporting a weight upon an inclined plane2 thus ,aristotle erred in interpreting the doctrine that the weight of bodies is the cause of their fall2 thus ,kepler erred in interpreting the rule that the velocity of bodies depends upon the force2 thus ,bernoulli#cic erred in interpreting the equality of action and reaction upon a lever in motion4 ,in each of these instances1 true doctrines1 already established1 7whether by experiment or otherwise17 were erroneously applied4 ,and the error was corrected by further reflection1 which pointed out that another mode of interpretation was requisite1 in order that the axiom #bfg which1 was appealed to in each case might retain its force in the most general sense4 ,and in the reasonings which avoided or corrected such errors1 and which led to substantial general truths1 the object of the speculator always was to give to the acknowledged maxims which the ,idea of ,cause suggested1 such a signification as should be consistent with their universal validity4 ,the rule was not accepted as particular at the outset1 and afterwards generalized more and more widely2 but from the very first1 the universality of the rule was assumed1 and the question was1 how it should be understood so as to be universally true4 ,at every stage of speculation1 the law was regarded as a general law4 ,this was not an aspect which it gradually acquired1 by the accumulating contributions of experience1 but a feature of its original and native character4 ,what should happen universally1 experience might be needed to show3 but that what happened should happen universally1 was implied in the nature of knowledge4 ,the universality of the laws of motion was not gathered from experience1 however much the laws themselves might be so4 ,note #cic3 ,hist4 ,ind4 ,sc4 b4 vi4 c4 v4 sect4 #b4 #c4 ,thus we obtain the solution of our ,paradox1 so far as the case before us is concerned4 ,the laws of motion borrow their form from the ,idea of ,causation1 though their matter may be given by experience3 and hence they possess a universality which experience cannot give4 ,they are certainly and universally valid2 and the only question for observation to decide is1 how they are to be understood4 ,they are like general mathematical formul1 which are known to be true1 even while we are ignorant what are the unknown quantities which they involve4 ,it must be allowed1 on the other hand1 that so long as these formul are not interpreted by a real study of nature1 they are not only useless but prejudicial2 filling men's minds with vague general terms1 empty maxims1 and unintelligible abstractions1 which they mistake for knowledge4 ,of such perversion of the speculative propensities of man's nature1 the world has seen too much in all ages4 ,yet we must not1 on that account1 despise these forms of #bfh truth1 since without them1 no general knowledge is possible4 ,without general terms1 and maxims1 and abstractions1 we can have no science1 no speculation2 hardly1 indeed1 consistent thought or the exercise of reason4 ,the course of real knowledge is1 to obtain from thought and experience the right interpretation of our general terms1 the real import of our maxims1 the true generalizations which our abstractions involve4 #d4 ,if it be asked1 ,how ,experience is able to teach us to interpret aright the general terms which the ,axioms of ,causation involve2--whence she derives the light which she is to throw on these general notions2 the answer is obvious2--namely1 that the relations of causation are the conditions of ,experience2--that the general notions are exemplified in the particular cases of which she takes cognizance4 ,the events which take place about us1 and which are the objects of our observation1 we cannot conceive otherwise than as subject to the laws of cause and effect4 ,every event must have a cause2--,every effect must be determined by its cause2--these maxims are true of the phenomena which form the materials of our experience4 ,it is precisely to them1 that these truths apply4 ,it is in the world which we have before our eyes1 that these propositions are universally verified2 and it is therefore by the observation of what we see1 that we must learn how these propositions are to be understood4 ,every fact1 every experiment1 is an example of these statements2 and it is therefore by attention to and familiarity with facts and experiments1 that we learn the signification of the expressions in which the statements are made2 just as in any other case we learn the import of language by observing the manner in which it is applied in known cases4 ,experience is the interpreter of nature2 it being understood that she is to make her interpretation in that comprehensive phraseology which is the genuine language of science4 #e4 ,we may return for an instant to the objection1 that experience cannot give us general truths1 since1 after any number of trials confirming a rule1 we may for aught we can foresee1 have one which violates the #bfi rule4 ,when we have seen a thousand stones fall to the ground1 we may see one which does not fall under the same apparent circumstances4 ,how then1 it is asked1 can experience teach us that all stones1 rigorously speaking1 will fall if unsupported8 ,and to this we reply1 that it is not true that we can conceive one stone to be suspended in the air1 while a thousand others fall1 without believing some peculiar cause to support it2 and that1 therefore1 such a supposition forms no exception to the law1 that gravity is a force by which all bodies are urged downwards4 ,undoubtedly we can conceive a body1 when dropt or thrown1 to move in a line quite different from other bodies3 thus a certain missile#djc used by the natives of ,australia1 and lately brought to this country1 when thrown from the hand in a proper manner1 describes a curve1 and returns to the place from whence it was thrown4 ,but did any one1 therefore1 even for an instant suppose that the laws of motion are different for this and for other bodies8 ,on the contrary1 was not every person of a speculative turn immediately led to inquire how it was that the known causes which modify motion1 the resistance of the air and the other causes1 produced in this instance so peculiar an effect8 ,and if the motion had been still more unaccountable1 it would not have occasioned any uncertainty whether it were consistent with the agency of gravity and the laws of motion4 ,if a body suddenly alter its direction1 or move in any other unexpected manner1 we never doubt that there is a cause of the change4 ,we may continue quite ignorant of the nature of this cause1 but this ignorance never occasions a moment's doubt that the cause exists and is exactly suited to the effect4 ,and thus experience can prove or discover to us general rules1 but she can never prove that general rules do not exist4 ,anomalies1 exceptions1 unexplained phenomena1 may remind us that we have much still to learn1 but they can never make us suppose that truths are not universal4 ,we may observe facts that show us we have not fully #bgj understood the meaning of our general laws1 but we can never find facts which show our laws to have no meaning4 ,our experience is bound in by the limits of cause and effect1 and can give us no information concerning any region where that relation does not prevail4 ,the whole series of external occurrences and objects1 through all time and space1 exists only1 and is conceived only1 as subject to this relation2 and therefore we endeavour in vain to imagine to ourselves when and where and how exceptions to this relation may occur4 ,the assumption of the connexion of cause and effect is essential to our experience1 as the recognition of the maxims which express this connexion is essential to our knowledge4 ,note #djc3 ,called the ,bo-me-rang4 #f4 ,i have thus endeavoured to explain in some measure how1 at least in the field of our mechanical knowledge1 experience can discover universal truths1 though she cannot give them their universality2 and how such truths1 though borrowing their form from our ideas1 cannot be understood except by the actual study of external nature4 ,and thus with regard to the laws of motion1 and other fundamental principles of ,mechanics1 the analysis of our ideas and the history of the progress of the science well illustrate each other4 ,if the paradox of the discovery of universal truths by experience be thus solved in one instance1 a much wider question offers itself to us2--,how far the difficulty1 and how far the solution1 are applicable to other subjects4 ,it is easy to see that this question involves most grave and extensive doctrines with regard to the whole compass of human knowledge3 and the views to which we have been led in the present ,book of this work are1 we trust1 fitted to throw much light upon the general aspect of the subject4 ,but after discussions so abstract1 and perhaps obscure1 as those in which we have been engaged for some chapters1 ,i willingly postpone to a future occasion an investigation which may perhaps appear to most readers more recondite and difficult still4 ,and we have1 in fact1 many other special fields of knowledge to survey1 before we are led by the order of our subject1 to #bga those general questions and doctrines1 those antitheses brought into view and again resolved1 which a view of the whole territory of human knowledge suggests1 and by which the nature and conditions of knowledge are exhibited4 ,before we quit the subject of mechanical science we shall make a few remarks on another doctrine which forms part of the established truths of the science1 namely1 the doctrine of universal gravitation4 #bgb ,,chapter ,,ix4 ,,of ,,the ,,establishment ,,of ,,the ,,law ,,of ,,universal ,,gravitation4 ,,the doctrine of universal gravitation is a feature of so much importance in the history of science that we shall not pass it by without a few remarks on the nature and evidence of the doctrine4 #a4 ,to a certain extent the doctrine of the attraction of bodies according to the law of the inverse square of the distance1 exhibits in its progress among men the same general features which we have noticed in the history of the laws of motion4 ,this doctrine was maintained priori on the ground of its simplicity1 and was asserted positively1 even before it was clearly understood3--notwithstanding this anticipation1 its establishment on the ground of facts was a task of vast labour and sagacity3--when it had been so established in a general way1 there occurred at later periods1 an occasional suspicion that it might be approximately true only3--these suspicions led to further researches1 which showed the rule to be rigorously exact3--and at present there are mathematicians who maintain1 not only that it is true1 but that it is a necessary property of matter4 ,a very few words on each of these points will suffice4 #b4 ,i have shown in the ,history of ,science#dac1 that the attraction of the sun according to the inverse square of the distance1 had been divined by ,bullialdus1 ,hooke1 ,halley1 and others1 before it was proved by ,newton4 ,probably the reason which suggested this conjecture was1 that gravity might be considered #bgc as a sort of emanation2 and that thus1 like light or any other effect diffused from a center1 it must follow the law just stated1 the efficacy of the force being weakened in receding from the center1 exactly in proportion to the space through which it is diffused4 ,it cannot be denied that such a view appears to be strongly recommended by analogy4 ,note #dac3 ,b4 vii4 c4 i4 ,when it had been proved by ,newton that the planets were really retained in their elliptical orbits by a central force1 his calculations also showed that the above-stated law of the force must be at least very approximately correct1 since otherwise the aphelia of the orbits could not be so nearly at rest as they were4 ,yet when it seemed as if the motion of the moon's apogee could not be accounted for without some new supposition1 the priori argument in favour of the inverse square did not prevent ,clairaut from trying the hypothesis of a small term added to that which expressed the ancient law3 but when1 in order to test the accuracy of this hypothesis1 the calculation of the motion of the moon's apogee was pushed to a greater degree of exactness than had been obtained before1 it was found that the new term vanished of itself2 and that the inverse square now accounted for the whole of the motion4 ,and thus1 as in the case of the second law of motion1 the most scrupulous examination terminated in showing the simplest rule to be rigorously true4 #c4 ,similar events occurred in the history of another part of the law of gravitation3 namely1 that the attraction is proportional to the quantity of matter attracted4 ,this part of the law may also be thus stated1 ,that the weight of bodies arising from gravity is proportional to their inertia2 and thus1 that the accelerating force on all bodies under the same circumstances is the same4 ,newton made experiments which proved this with regard to terrestrial bodies2 for he found that1 at the end of equal strings1 balls of all substances1 gold1 silver1 lead1 glass1 wood1 c41 oscillated in equal times#dbc4 ,but a few years ago1 doubts #bgd arose among the ,german astronomers whether this law was rigorously true with regard to the planetary bodies4 ,some calculations appeared to prove1 that the attraction of ,jupiter as shown by the perturbations which he produces in the small planets ,juno1 ,vesta1 and ,pallas1 was different from the attraction which he exerts on his own satellites4 ,nor did there appear to these philosophers anything inconceivable in the supposition that the attraction of a planet might be thus elective4 ,but when ,mr4 ,airy obtained a more exact determination of the mass of ,jupiter1 as indicated by his effect on his satellites1 it was found that this suspicion was unfounded2 and that there was1 in this case1 no exception to the universality of the rule1 that this cosmical attraction is in the proportion of the attracted mass4 ,note #dbc3 ,prin4 lib4 iii4 prop4 #f4 #d4 ,again3 when it had thus been shown that a mutual attraction of parts1 according to the law above mentioned1 prevailed throughout the extent of the solar system1 it might still be doubted whether the same law extended to other regions of the universe4 ,it might have been perhaps imagined that each fixed star had its peculiar law of force4 ,but the examination of the motions of double stars about each other1 by the two ,herschels and others1 appears to show that these bodies describe ellipses as the planets do2 and thus extends the law of the inverse squares to parts of the universe immeasurably distant from the whole solar system4 #e4 ,since every doubt which has been raised with regard to the universality and accuracy of the law of gravitation1 has thus ended in confirming the rule1 it is not surprizing that men's minds should have returned with additional force to those views which had at first represented the law as a necessary truth1 capable of being established by reason alone4 ,when it had been proved by ,newton that gravity is really a universal attribute of matter as far as we can learn1 his pupils were not content without maintaining it to be an essential quality4 ,this is the doctrine held by ,cotes in the preface to the second edition of the ,principia 7#agab73 #bge ',gravity1' he says1 'is a primary quality of bodies1 as extension1 mobility1 and impenetrability are4' ,but ,newton himself by no means went so far4 ,in his second ,letter to ,bentley 7#afic71 he says1 ',you sometimes speak of gravity as essential and inherent to matter2 pray do not ascribe that notion to me4 ,the cause of gravity1' he adds1 ',i do not pretend to know1 and would take more time to consider of it4' ,cotes maintains his opinion by urging1 that we learn by experience that all bodies possess gravity1 and that we do not learn in any other way that they are extended1 moveable1 or solid4 ,but we have already seen1 that the ideas of space1 time1 and reaction1 on which depend extension1 mobility1 and solidity1 are not results1 but conditions1 of experience4 ,we cannot conceive a body except as extended2 we cannot conceive it to exert mechanical action except with some kind of solidity4 ,but so far as our conceptions of body have hitherto been developed1 we find no difficulty in conceiving two bodies which do not attract each other4 #f4 ,newton lays down1 in the second edition of the ,principia1 this ',rule of ,philosophizing' 7book iii472 that ',the qualities of bodies which cannot be made more or less intense1 and which belong to all bodies on which we are able to make experiments1 are to be held to be qualities of all bodies in general4' ,and this ,rule is cited in the sixth ,proposition of the ,third ,book of the ,principia1 7,cor4 #b17 in order to prove that gravity1 proportional to the quantity of matter1 may be asserted to be a quality of all bodies universally4 ,but we may remark that a ,rule of ,philosophizing1 itself of precarious authority1 cannot authorize us in ascribing universality to an empirical result4 ,geometrical and statical properties are seen to be necessary1 and therefore universal3 but ,newton appears disposed to assert a like universality of gravity1 quite unconnected with any necessity4 ,it would be a very inadequate statement1 indeed a false representation1 of statical truth1 if we were to say1 that because every body which has hitherto been tried has been found to have a center of gravity1 we venture to assert that all bodies whatever #bgf have a center of gravity4 ,and if we are ever able to assert the absolute universality of the law of gravitation1 we shall have to rest this truth upon the clearer development of our ideas of matter and force2 not upon a ,rule of ,philosophizing1 which1 till otherwise proved1 must be a mere rule of prudence1 and which the opponent may refuse to admit4 #g4 ,other persons1 instead of asserting gravity to be in its own nature essential to matter1 have made hypotheses concerning some mechanism or other1 by which this mutual attraction of bodies is produced#dcc4 ,thus the ,cartesians ascribed to a vortex the tendency of bodies to a center2 ,newton himself seems to have been disposed to refer this tendency to the elasticity of an ether2 ,le ,sage propounded a curious hypothesis1 in which this attraction is accounted for by the impulse of infinite streams of particles flowing constantly through the universe in all directions4 ,in these speculations1 the force of gravity is resolved into the pressure or impulse of solids or fluids4 ,on the other hand1 hypotheses have been propounded1 in which the solidity1 and other physical qualities of bodies1 have been explained by representing the bodies as a collection of points1 from which points1 repulsive1 as well as attractive1 forces emanate4 ,this view of the constitution of bodies was maintained and developed by ,boscovich1 and is hence termed ',boscovich's ,theory3' and the discussion of it will more properly come under our review at a future period1 when we speak of the question whether bodies are made up of atoms4 ,but we may observe1 that ,newton himself appears to have inclined1 as his followers certainly did1 to this mode of contemplating the physical properties of bodies4 ,in his ,preface to the ,principia1 after speaking of the central forces which are exhibited in cosmical phenomena1 he says3 ',would that we could derive the other phenomena of ,nature from mechanical principles by the same mode of reasoning4 ,for many things move me #bgg so that ,i suspect all these phenomena may depend upon certain forces1 by which the particles of bodies1 through causes not yet known1 are either impelled to each other and cohere according to regular figures1 or are repelled and recede from each other3 which forces being unknown1 philosophers have hitherto made their attempts upon nature in vain4' ,note #dcc3 ,see ,vince1 ,observations on the ,hypothesis respecting ,gravitation1 and the ,critique of that work1 ,edinb4 ,rev4 vol4 xiii4 #h4 ,but both these hypotheses2--that by which cohesion and solidity are reduced to attractive and repulsive forces1 and that by which attraction is reduced to the impulse and pressure of media2--are hitherto merely modes of representing mechanical laws of nature2 and cannot1 either of them1 be asserted as possessing any evident truth or peremptory authority to the exclusion of the other4 ,this consideration may enable us to estimate the real weight of the difficulty felt in assenting to the mutual attraction of bodies not in contact with each other2 for it is often urged that this attraction of bodies at a distance is an absurd supposition4 ,the doctrine is often thus stigmatized1 both by popular and by learned writers4 ,it was long received as a maxim in philosophy 7as ,monboddo informs us#ddc71 that a body cannot act where it is not1 any more than when it is not4 ,but to this we reply1 that time is a necessary condition of our conception of causation1 in a different manner from space4 ,the action of force can only be conceived as taking place in a succession of moments1 in each of which cause and effect immediately succeed each other3 and thus the interval of time between a cause and its remote effect is filled up by a continuous succession of events connected by the same chain of causation4 ,but in space1 there is no such visible necessity of continuity2 the action and reaction may take place at a distance from each other2 all that is necessary being that they be equal and opposite4 ,note #ddc3 ,ancient ,metaphysics1 vol4 ii4 p4 #age4 ,undoubtedly the existence of attraction is rendered more acceptable to common apprehension by supposing #bgh some intermediate machinery1--a cord1 or rod1 or fluid1--by which the forces may be conveyed from one point to another4 ,but such images are rather fitted to satisfy those prejudices which arise from the earlier application of our ideas of force1 than to exhibit the real nature of those ideas4 ,if we suppose two bodies to pull each other by means of a rod or cord1 we only suppose1 in addition to those equal and opposite forces acting upon the two bodies1 7which forces are alone essential to mutual attraction7 a certain power of resisting transverse pressure at every point of the intermediate line3 which additional supposition is entirely useless1 and quite unconnected with the essential conditions of the case4 ,when the ,newtonians were accused of introducing into philosophy an unknown cause which they termed attraction1 they justly replied that they knew as much respecting attraction as their opponents did about impulse4 ,in each case we have a knowledge of the conception in question so far as we clearly apprehend it under the conditions of those axioms of mechanical causation which form the basis of our science on such subjects4 ,having thus examined the degree of certainty and generality to which our knowledge of the law of universal gravitation has been carried1 by the progress of mechanical discovery and speculation up to the present time1 we might proceed to the other branches of science1 and examine in like manner their grounds and conditions4 ,but before we do this1 it will be worth our while to attend for a moment to the effect which the progress of mechanical ideas among mathematicians and mechanical philosophers has produced upon the minds of other persons1 who share only in an indirect and derivative manner in the influence of science4 #bgi ,,chapter ,x4 ,,of ,,the ,,general ,,diffusion ,,of ,,clear ,,mechanical ,,ideas4 #a4 ,,we have seen how the progress of knowledge upon the subject of motion and force has produced1 in the course of the world's history1 a great change in the minds of acute and speculative men2 so that such persons can now reason with perfect steadiness and precision upon subjects on which1 at first1 their thoughts were vague and confused2 and can apprehend1 as truths of complete certainty and evidence1 laws which it required great labour and time to discover4 ,this complete development and clear manifestation of mechanical ideas has taken place only among mathematicians and philosophers4 ,but yet a progress of thought upon such subjects1--an advance from the obscure to the clear1 and from errour to truth1--may be traced in the world at large1 and among those who have not directly cultivated the exact sciences4 ,this diffused and collateral influence of science manifests itself1 although in a wavering and fluctuating manner1 by various indications1 at various periods of literary history4 ,the opinions and reasonings which are put forth upon mechanical subjects1 and above all1 the adoption1 into common language1 of terms and phrases belonging to the prevalent mechanical systems1 exhibit to us the most profound discoveries and speculations of philosophers in their effect upon more common and familiar trains of thought4 ,this effect is by no means unimportant1 and we shall point out some examples of such indications as we have mentioned4 #b4 ,the discoveries of the ancients in speculative mechanics were1 as we have seen1 very scanty2 and #bhj hardly extended their influence to the unmathematical world4 ,yet the familiar use of the term 'center of gravity' preserved and suggested the most important part of what the ,greeks had to teach4 ,the other phrases which they employed1 as momentum1 energy1 virtue1 force1 and the like1 never had any exact meaning1 even among mathematicians2 and therefore never1 in the ancient world1 became the means of suggesting just habits of thought4 ,i have pointed out1 in the ,history of ,science1 several circumstances which appear to denote the general confusion of ideas which prevailed upon mechanical subjects during the times of the ,roman empire4 ,i have there taken as one of the examples of this confusion1 the fable narrated by ,pliny and others concerning the echines1 a small fish1 which was said to stop a ship merely by sticking to it#dec4 ,this story was adduced as betraying the absence of any steady apprehension of the equality of action and reaction2 since the fish1 except it had some immoveable obstacle to hold by1 must be pulled forward by the ship1 as much as it pulled the ship backward4 ,if the writers who speak of this wonder had shown any perception of the necessity of a reaction1 either produced by the rapid motion of the fish's fins in the water1 or in any other way1 they would not be chargeable with this confusion of thought2 but from their expressions it is1 ,i think1 evident that they saw no such necessity#dfc4 ,their idea of mechanical action was not sufficiently distinct to enable them to see the absurdity of #bha supposing an intense pressure with no obstacle for it to exert itself against4 ,note #dec3 ,hist4 ,ind4 ,sc4 b4 iv4 c4 i4 sect4 #b4 ,note #dfc3 ,see ,prof4 ,powell1 ,on the ,nature and ,evidence of the ,laws of ,motion4 ,reports of the ,ashmolean ,society4 ,oxford4 #ahcg4 ,professor ,powell has made an objection to my use of this instance of confusion of thought2 the remark in the text seems to me to justify what ,i said in the ,history4 ,as an evidence that the fish was not supposed to produce its effect by its muscular power acting on the water1 we may take what ,pliny says1 ,nat4 ,hist4 xxxii4 #a1 ',domat mundi rabiem1 nullo suo labore2 non retinendo1 aut alio modo quam adhrendo3' and also what he states in another place 7ix4 #da71 that when it is preserved in pickle1 it may be used in recovering gold which has fallen into a deep well4 ,all this implies adhesion alone1 with no conception of reaction4 #c4 ,we may trace1 in more modern times also1 indications of a general ignorance of mechanical truths4 ,thus the phrase of shooting at an object 'point-blank1' implies the belief that a cannon-ball describes a path of which the first portion is a straight line4 ,this errour was corrected by the true mechanical principles which ,galileo and his followers brought to light2 but these principles made their way to popular notice1 principally in consequence of their application to the motions of the solar system1 and to the controversies which took place respecting those motions4 ,thus by far the most powerful argument against the reception of the ,copernican system of the universe1 was that of those who asked1 ,why a stone dropt from a tower was not left behind by the motion of the earth8 ,the answer to this question1 now universally familiar1 involves a reference to the true doctrine of the composition of motions4 ,again2 ,kepler's persevering and strenuous attempts#dgc to frame a physical theory of the universe were frustrated by his ignorance of the first law of motion1 which informs us that a body will retain its velocity without any maintaining force4 ,he proceeded upon the supposition that the sun's force was requisite to keep up the motion of the planets1 as well as to deflect and modify it2 and he was thus led to a system which represented the sun as carrying round the planets in their orbits by means of a vortex1 produced by his revolution4 ,the same neglect of the laws of motion presided in the formation of ,descartes' system of vortices4 ,although ,descartes had enunciated in words the laws of motion1 he and his followers showed that they had not the practical habit of referring to these mechanical principles2 and dared not trust the planets to move in free space without some surrounding machinery to support them#dhc4 ,note #dgc3 ,hist4 ,ind4 ,sc4 b4 v4 c4 iv4 and b4 vii4 c4 i4 ,note #dhc3 ,i have1 in the ,history1 applied to ,descartes the character which ,bacon gives to ,aristotle1 ',audax simul et pavidus3' though he was bold enough to enunciate the laws of motion without knowing them aright1 he had not the courage to leave the planets to describe their orbits by the agency of those laws1 without the machinery of contact4 #bhb #d4 ,when at last mathematicians1 following ,newton1 had ventured to consider the motion of each planet as a mechanical problem not different in its nature from the motion of a stone cast from the hand2 and when the solution of this problem and its immense consequences had become matters of general notoriety and interest2 the new views introduced1 as is usual1 new terms1 which soon became extensively current4 ,we meet with such phrases as 'flying off in the tangent1' and 'deflexion from the tangent2' with antitheses between 'centripetal' and 'centrifugal force1' or between 'projectile' and 'central force4' ',centers of force1' 'disturbing forces1' 'perturbations1' and 'perturbations of higher orders1' are not unfrequently spoken of3 and the expression 'to gravitate1' and the term 'universal gravitation1' acquired a permanent place in the language4 ,yet for a long time1 and even up to the present day1 we find many indications that false and confused apprehensions on such subjects are by no means extirpated4 ,arguments are urged against the mechanical system of the universe1 implying in the opponents an absence of all clear mechanical notions4 ,many of this class of writers retrograde to ,kepler's point of view4 ,this is1 for example1 the case with ,lord ,monboddo1 who1 arguing on the assumption that force is requisite to maintain1 as well as to deflect motion1 produced a series of attacks upon the ,newtonian philosophy2 which he inserted in his ,ancient ,metaphysics1 published in #aggi and the succeeding years4 ,this writer 7like ,kepler71 measures force by the velocity which the body has#dic1 not by that which it gains4 ,such a use of language would prevent our obtaining any laws of motion at all4 ,accordingly1 the author1 in the very next page to that which ,i have just quoted1 abandons this measure of force1 and1 in curvilinear motion1 measures #bhc force by 'the fall from the extremity of the arc4' ,again2 in his objections to the received theory1 he denies that curvilinear motion is compounded1 although his own mode of considering such motion assumes this composition in the only way in which it was ever intended by mathematicians4 ,many more instances might be adduced to show that a want of cultivation of the mechanical ideas rendered this philosopher incapable of judging of a mechanical system4 ,note #dic3 ,anc4 ,met4 vol4 ii4 b4 v4 c4 vi4 p4 #dac4 ,the following extract from the ,ancient ,metaphysics1 may be sufficient to show the value of the author's criticism on the subjects of which we are now speaking4 ,his object is to prove that there do not exist a centripetal and a centrifugal force in the case of elliptical motion4 ',let any man move in a circular or elliptical line described to him2 and he will find no tendency in himself either to the center or from it1 much less both4 ,if indeed he attempt to make the motion with great velocity1 or if he do it carelessly and inattentively1 he may go out of the line1 either towards the center or from it3 but this is to be ascribed1 not to the nature of the motion1 but to our infirmity2 or perhaps to the animal form1 which is more fitted for progressive motion in a right line than for any kind of curvilinear motion4 ,but this is not the case with a sphere or spheroid1 which is equally adapted to motion in all directions#ejc4' ,we need hardly remind the reader that the manner in which a man running round a small circle1 finds it necessary to lean inwards1 in order that there may be a centripetal inclination to counteract the centrifugal force1 is a standard example of our mechanical doctrines2 and this fact 7quite familiar in practice as well as theory7 is in direct contradiction of ,lord ,monboddo's assertion4 ,note #ejc3 ,anc4 ,met4 vol4 i4 b4 ii4 c4 #ai1 p4 #bfd4 #e4 ,a similar absence of distinct mechanical thought appears in some of the most celebrated metaphysicians of ,germany4 ,i have elsewhere noted#eac the opinion expressed by ,hegel1 that the glory which belongs to #bhd ,kepler has been unjustly transferred to ,newton2 and ,i have suggested1 as the explanation of this mode of thinking1 that ,hegel himself1 in the knowledge of mechanical truth1 had not advanced beyond ,kepler's point of view4 ,persons who possess conceptions of space and number1 but who have not learnt to deal with ideas of force and causation1 may see more value in the discoveries of ,kepler than in those of ,newton4 ,another exemplification of this state of mind may be found in ,professor ,schelling's speculations2 for instance1 in his ,lectures on the ,method of ,academical ,study4 ,in the twelfth ,lecture1 on the study of ,physics and ,chemistry1 he says1 7p4 #bff17 ',what the mathematical natural philosophy has done for the knowledge of the laws of the universe since the time that they were discovered by his 7,kepler's7 godlike genius1 is1 as is well known1 this3 it has attempted a construction of those laws which1 according to its foundations1 is altogether empirical4 ,we may assume it as a general rule1 that in any proposed construction1 that which is not a pure general form cannot have any scientific import or truth4 ,the foundation from which the centrifugal motion of the bodies of the world is derived1 is no necessary form1 it is an empirical fact4 ,the ,newtonian attractive force1 even if it be a necessary assumption for a merely reflective view of the subject1 is still of no significance for the ,reason1 which recognizes only absolute relations4 ,the grounds of the ,keplerian laws can be derived1 without any empirical appendage1 purely from the doctrine of ,ideas1 and of the two ,unities1 which are in themselves one ,unity1 and in virtue of which each being1 while it is absolute in itself1 is at the same time in the absolute1 and reciprocally4' ,note #eac3 ,hist4 ,ind4 ,sc4 b4 vii4 c4 ii4 sect4 #e4 ,it will be observed1 that in this passage our mechanical laws are objected to because they are not necessary results of our ideas2 which1 however1 as we have seen1 according to the opinion of some eminent mechanical philosophers1 they are4 ,but to assume this evident necessity as a condition of every advance in science1 is to mistake the last1 perhaps unattainable step1 for the first1 which lies before our feet4 ,and1 #bhe without inquiring further about 'the ,doctrine of the two ,unities1' or the manner in which from that doctrine we may deduce the ,keplerian laws1 we may be well convinced that such a doctrine cannot supply any sufficient reason to induce us to quit the inductive path by which all scientific truth up to the present time has been acquired4 #f4 ,but without going to schools of philosophy opposed to the ,inductive ,school1 we may find many loose and vague habits of thinking on mechanical subjects among the common classes of readers and reasoners4 ,and there are some familiar modes of employing the phraseology of mechanical science1 which are1 in a certain degree1 chargeable with inaccuracy1 and may produce or perpetuate confusion4 ,among such cases we may mention the way in which the centripetal and centrifugal forces1 and also the projectile and central forces of the planets1 are often compared or opposed4 ,such antitheses sometimes proceed upon the false notion that the two members of these pairs of forces are of the same kind3 whereas on the contrary the projectile force is a hypothetical impulsive force which may1 at some former period1 have caused the motion to begin2 while the central force is an actual force1 which must act continuously and during the whole time of the motion1 in order that the motion may go on in the curve4 ,in the same manner the centrifugal force is not a distinct force in a strict sense1 but only a certain result of the first law of motion1 measured by the portion of centripetal force which counteracts it4 ,comparisons of quantities so heterogeneous imply confusion of thought1 and often suggest baseless speculations and imagined reforms of the received opinions4 #g4 ,i might point out other terms and maxims1 in addition to those already mentioned1 which1 though formerly employed in a loose and vague manner1 are now accurately understood and employed by all just thinkers2 and thus secure and diffuse a right understanding of mechanical truths4 ,such are momentum1 inertia1 quantity of matter1 quantity of motion2 that force is proportional to its effects2 that action and #bhf reaction are equal2 that what is gained in force by machinery is lost in time2 that the quantity of motion in the world cannot be either increased or diminished4 ,when the expression of the truth thus becomes easy and simple1 clear and convincing1 the meanings given to words and phrases by discoverers glide into the habitual texture of men's reasonings1 and the effect of the establishment of true mechanical principles is felt far from the school of the mechanician4 ,if these terms and maxims are understood with tolerable clearness1 they carry the influence of truth to those who have no direct access to its sources4 ,many an extravagant project in practical machinery1 and many a wild hypothesis in speculative physics1 has been repressed by the general currency of such maxims as we have just quoted4 #h4 ,indeed so familiar and evident are the elementary truths of mechanics when expressed in this simple form1 that they are received as truisms2 and men are disposed to look back with surprise and scorn at the speculations which were carried on in neglect of them4 ,the most superficial reasoner of modern times thinks himself entitled to speak with contempt and ridicule of ,kepler's hypothesis concerning the physical causes of the celestial motions3 and gives himself credit for intellectual superiority1 because he sees1 as self-evident1 what such a man could not discover at all4 ,it is well for such a person to recollect1 that the real cause of his superior insight is not the pre-eminence of his faculties1 but the successful labours of those who have preceded him4 ,the language which he has learnt to use unconsciously1 has been adapted to1 and moulded on1 ascertained truths4 ,when he talks familiarly of accelerating forces and deflexions from the tangent1 he is assuming that which ,kepler did not know1 and which it cost ,galileo and his disciples so much labour and thought to establish4 ,language is often called an instrument of thought2 but it is also the nutriment of thought2 or rather1 it is the atmosphere in which thought lives3 a medium essential to the activity of our speculative power1 although invisible #bhg and imperceptible in its operation2 and an element modifying1 by its qualities and changes1 the growth and complexion of the faculties which it feeds4 ,in this way the influence of preceding discoveries upon subsequent ones1 of the past upon the present1 is most penetrating and universal1 though most subtle and difficult to trace4 ,the most familiar words and phrases are connected by imperceptible ties with the reasonings and discoveries of former men and distant times4 ,their knowledge is an inseparable part of ours2 the present generation inherits and uses the scientific wealth of all the past4 ,and this is the fortune1 not only of the great and rich in the intellectual world3 of those who have the key to the ancient storehouses1 and who have accumulated treasures of their own2--but the humblest inquirer1 while he puts his reasonings into words1 benefits by the labours of the greatest discoverers4 ,when he counts his little wealth1 he finds that he has in his hands coins which bear the image and superscription of ancient and modern intellectual dynasties2 and that in virtue of this possession1 acquisitions are in his power1 solid knowledge within his reach1 which none could ever have attained to1 if it were not that the gold of truth1 once dug out of the mine1 circulates more and more widely among mankind4 #i4 ,having so fully examined1 in the preceding instances1 the nature of the progress of thought which science implies1 both among the peculiar cultivators of science1 and in that wider world of general culture which receives only an indirect influence from scientific discoveries1 we shall not find it necessary to go into the same extent of detail with regard to the other provinces of human knowledge4 ,in the case of the ,mechanical ,sciences1 we have endeavoured to show1 not only that ,ideas are requisite in order to form into a science the ,facts which nature offers to us1 but that we can advance1 almost or quite1 to a complete identification of the ,facts with the ,ideas4 ,in the sciences to which we now proceed1 we shall not seek to fill up the chasm by which ,facts and ,ideas are separated2 but we shall endeavour to detect the ,ideas which our #bhh knowledge involves1 to show how essential these are2 and in some respects to trace the mode in which they have been gradually developed among men4 #aj4 ,the motions of the heavenly bodies1 their laws1 their causes1 are among the subjects of the first division of the ,mechanical ,sciences2 and of these sciences we formerly sketched the history1 and have now endeavoured to exhibit the philosophy4 ,if we were to take any other class of motions1 their laws and causes might give rise to sciences which would be mechanical sciences in exactly the same sense in which ,physical ,astronomy is so4 ,the phenomena of magnets1 of electrical bodies1 of galvanical apparatus1 seem to form obvious materials for such sciences2 and if they were so treated1 the philosophy of such branches of knowledge would naturally come under our consideration at this point of our progress4 ,but on looking more attentively at the sciences of ,electricity1 ,magnetism1 and ,galvanism1 we discover cogent reasons for transferring them to another part of our arrangement2 we find it advisable to associate them with ,chemistry1 and to discuss their principles when we can connect them with the principles of chemical science4 ,for though the first steps and narrower generalizations of these sciences depend upon mechanical ideas1 the highest laws and widest generalizations which we can reach respecting them1 involve chemical relations4 ,the progress of these portions of knowledge is in some respects opposite to the progress of ,physical ,astronomy4 ,in this1 we begin with phenomena which appear to indicate peculiar and various qualities in the bodies which we consider1 7namely1 the heavenly bodies17 and we find in the end that all these qualities resolve themselves into one common mechanical property1 which exists alike in all bodies and parts of bodies4 ,on the contrary1 in studying magnetical and electrical laws1 we appear at first to have a single extensive phenomenon1 attraction and repulsion3 but in our attempts to generalize this phenomenon1 we find that it is governed by conditions depending upon something quite separate from the bodies themselves1 upon #bhi the presence and distribution of peculiar and transitory agencies2 and1 so far as we can discover1 the general laws of these agencies are of a chemical nature1 and are brought into action by peculiar properties of special substances4 ,in cosmical phenomena1 everything1 in proportion as it is referred to mechanical principles1 tends to simplicity1--to permanent uniform forces1--to one common1 positive1 property4 ,in magnetical and electrical appearances1 on the contrary1 the application of mechanical principles leads only to a new complexity1 which requires a new explanation2 and this explanation involves changeable and various forces1--gradations and oppositions of qualities4 ,the doctrine of the universal gravitation of matter is a simple and ultimate truth1 in which the mind can acquiesce and repose4 ,we rank gravity among the mechanical attributes of matter1 and we see no necessity to derive it from any ulterior properties4 ,gravity belongs to matter1 independent of any conditions4 ,but the conditions of magnetic or electrical activity require investigation as much as the laws of their action4 ,of these conditions no mere mechanical explanation can be given2 we are compelled to take along with us chemical properties and relations also3 and thus magnetism1 electricity1 galvanism1 are mechanico-chemical sciences4 #aa4 ,before considering these1 therefore1 ,i shall treat of what ,i shall call ,secondary ,mechanical ,sciences2 by which expression ,i mean the sciences depending upon certain qualities which our senses discover to us in bodies2--,optics1 which has visible phenomena for its subject2 ,acoustics1 the science of hearing2 the doctrine of ,heat1 a quality which our touch recognizes3 to this last science ,i shall take the liberty of sometimes giving the name ,thermotics1 analogous to the names of the other two4 ,if our knowledge of the phenomena of ,smell and ,taste had been successfully cultivated and systematized1 the present part of our work would be the place for the philosophical discussion of those sensations as the subjects of science4 ,the branches of knowledge thus grouped in one class involve common ,fundamental ,ideas1 from which #bij their principles are derived in a mode analogous1 at least in a certain degree1 to the mode in which the principles of the mechanical sciences are derived from the fundamental ideas of causation and reaction4 ,we proceed now to consider these ,fundamental ,ideas1 their nature1 development1 and consequences4 #bia ,,book ,,iv4 ,,the ,,philosophy ,,of ,,the ,,secondary ,,mechanical ,,sciences4 ' 1 ' 1 ' 4 ' 1 4 1 1 4 ' 1 ' 1 ' ' 1 4 ,,aristot4 ,de ,anima1 ,,ii4 #g4 #bic ,,book ,,iv4 ,,the ,,philosophy ,,of ,,the ,,secondary ,,mechanical ,,sciences4 ,,chapter ,i4 ,,of ,,the ,,idea ,,of ,a ,,medium ,,as ,,commonly ,,employed4 #a4 ,of ,primary and ,secondary ,qualities4--,,in the same way in which the mechanical sciences depend upon the ,idea of ,cause1 and have their principles regulated by the development of that ,idea1 it will be found that the sciences which have for their subject ,sound1 ,light1 and ,heat1 depend for their principles upon the ,fundamental ,idea of ,media by means of which we perceive those qualities4 ,like the idea of cause1 this idea of a medium is unavoidably employed1 more or less distinctly1 in the common1 unscientific operations of the understanding2 and is recognized as an express principle in the earliest speculative essays of man4 ,but here also1 as in the case of the mechanical sciences1 the development of the idea1 and the establishment of the scientific truths which depend upon it1 was the business of a succeeding period1 and was only executed by means of long and laborious researches1 conducted with a constant reference to experiment and observation4 ,among the most prominent manifestations of the influence of the idea of a medium of which we have now to speak1 is the distinction of the qualities of bodies into primary1 and secondary qualities4 ,this distinction has #bid been constantly spoken of in modern times3 yet it has often been a subject of discussion among metaphysicians whether there be really such a distinction1 and what the true difference is4 ,locke states it thus#ad3 ,original or ,primary qualities of bodies are 'such as are utterly inseparable from the body in what estate soever it may be1--such as sense constantly finds in every particle of matter which has bulk enough to be perceived1 and the mind finds inseparable from every particle of matter1 though less than to make itself singly perceived by our senses3' and he enumerates them as solidity1 extension1 figure1 motion or rest1 and number4 ,secondary qualities1 on the other hand1 are such 'which in truth are nothing in the objects themselves1 but powers to produce various sensations in us by their primary qualities1 i4e4 by the bulk1 figure1 texture1 and motion of their insensible parts1 as colours1 sounds1 tastes1 c4' ,note #ad3 ,essay1 b4 ii4 ch4 viii4 s4 #i1 #aj4 ,dr4 ,reid#bd1 reconsidering this subject1 puts the difference in another way4 ,there is1 he says1 a real foundation for the distinction of ,primary and ,secondary qualities1 and it is this3 ',that our senses give us a direct and distinct notion of the primary qualities1 and inform us what they are in themselves2 but of the secondary qualities1 our senses give us only a relative and obscure notion4 ,they inform us only that they are qualities that affect us in a certain manner1 that is1 produce in us a certain sensation2 but as to what they are in themselves1 our senses leave us in the dark4' ,note #bd3 ,essays1 b4 ii4 c4 xvii4 ,dr4 ,brown#cd states the distinction somewhat otherwise4 ,we give the name of ,matter1 he observes1 to that which has extension and resistance3 these1 therefore1 are ,primary qualities of matter1 because they compose our definition of it4 ,all other qualities are ,secondary1 since they are ascribed to bodies only because we find them associated with the primary qualities which form our notion of those bodies4 ,note #cd3 ,lectures1 ii4 #ab4 #bie ,it is not necessary to criticize very strictly these various distinctions4 ,if it were1 it would be easy to find objections to them4 ,thus ,locke1 it may be observed1 does not point out any reason for believing that his secondary qualities are produced by the primary4 ,how are we to learn that the colour of a rose arises from the bulk1 figure1 texture1 and motion of its particles8 ,certainly our senses do not teach us this2 and in what other way1 on ,locke's principles1 can we learn it8 ,reid's statement is not more free from the same objection4 ,how does it appear that our notion of ,warmth is relative to our own sensations more than our notion of ,solidity8 ,and if we take ,brown's account1 we may still ask whether our selection of certain qualities to form our idea and definition of ,matter be arbitrary and without reason8 ,if it be1 how can it make a real distinction8 if it be not1 what is the reason8 ,i do not press these objections1 because ,i believe that any of the above accounts of the distinction of ,primary and ,secondary qualities is right in the main1 however imperfect it may be4 ,the difference between such qualities as ,extension and ,solidity on the one hand1 and ,colour or ,fragrance on the other1 is assented to by all1 with a conviction so firm and indestructible1 that there must be some fundamental principle at the bottom of the belief1 however difficult it may be to clothe the principle in words4 ,that successive efforts to express the real nature of the difference were made by men so clear-sighted and acute as those whom ,i have quoted1 even if none of them are satisfactory1 shows how strong and how deeply-seated is the perception of truth which impels us to such attempts4 ,the most obvious mode of stating the difference of ,primary and ,secondary qualities1 as it naturally offers itself to speculative minds1 appears to be that employed by ,locke1 slightly modified4 ,certain of the qualities of bodies1 as their bulk1 figure1 and motion1 are perceived immediately in the bodies themselves4 ,certain other qualities as sound1 colour1 heat1 are #bif perceived by means of some medium4 ,our conviction that this is the case is spontaneous and irresistible2 and this difference of qualities immediately and mediately perceived is the distinction of ,primary and ,secondary qualities4 ,we proceed further to examine this conviction4 #b4 ,the ,idea of ,externality4--,in reasoning concerning the ,secondary ,qualities of bodies1 we are led to assume the bodies to be external to us1 and to be perceived by means of some ,medium intermediate between us and them4 ,these assumptions are fundamental conditions of perception1 inseparable from perception even in thought4 ,that objects are external to us1 that they are without us1 that they have outness1 is as clear as it is that these words have any meaning at all4 ,this conviction is1 indeed1 involved in the exercise of that faculty by which we perceive all things as existing in space2 for by this faculty we place ourselves and other objects in one common space1 and thus they are exterior to us4 ,it may be remarked that this apprehension of objects as external to us1 although it assumes the idea of space1 is far from being implied in the idea of space4 ,the objects which we contemplate are considered as existing in space1 and by that means become invested with certain mutual relations of position2 but when we consider them as existing without us1 we make the additional step of supposing ourselves and the objects to exist in one common space4 ,the question respecting the ,ideal ,theory of ,berkeley has been mixed up with the recognition of this condition of the externality of objects4 ,that philosopher maintained1 as is well known1 that the perceptible qualities of bodies have no existence except in a perceiving mind4 ,this system has often been understood as if he had imagined the world to be a kind of optical illusion1 like the images which we see when we shut our eyes1 appearing to be without us1 though they are only in our organs2 and thus this ,ideal ,system has been opposed to a belief in an external world4 ,in truth1 however1 no such opposition exists4 ,the ,ideal ,system is an attempt to explain the #big mental process of perception1 and to get over the difficulty of mind being affected by matter4 ,but the author of that system did not deny that objects were perceived under the conditions of space and mechanical causation2--that they were external and material so far as those words describe perceptible qualities4 ,berkeley's system1 however visionary or erroneous1 did not prevent his entertaining views as just1 concerning optics or acoustics1 as if he had held any other doctrine of the nature of perception4 ,but when ,berkeley's theory was understood as a denial of the existence of objects without us1 how was it answered8 ,if we examine the answers which are given by ,reid and other philosophers to this hypothesis1 it will be found that they amount to this3 that objects are without us1 since we perceive that they are so2 that we perceive them to be external1 by the same act by which we perceive them to be objects4 ,and thus1 in this stage of philosophical inquiry1 the externality of objects is recognized as one of the inevitable conditions of our perception of them2 and hence the ,idea of ,externality is adopted as one of the necessary foundations of all reasoning concerning all objects whatever4 #c4 ,sensation by a ,medium4--,objects1 as we have just seen1 are necessarily apprehended as without us2 and in general1 as removed from us by a great or small distance4 ,yet they affect our bodily senses2 and this leads us irresistibly to the conviction that they are perceived by means of something intermediate4 ,vision1 or hearing1 or smell1 or the warmth of a fire1 must be communicated to us by some ,medium of ,sensation4 ,this unavoidable belief appears in all attempts1 the earliest and the latest alike1 to speculate upon such subjects4 ,thus1 for instance1 ,aristotle says#dd1 ',seeing takes place in virtue of some action which the sentient organ suffers3 now it cannot suffer action from the colour of the object directly3 the only remaining possible case then is1 that it is acted upon by an #bih intervening ,medium2 there must then be an intervening ,medium4' ',and the same may be said1' he adds1 'concerning sounding and odorous bodies2 for these do not produce sensation by touching the sentient organ1 but the intervening ,medium is acted on by the sound or the smell1 and the proper organ1 by the ,medium 444 ,in sound the ,medium is air2 in smell we have no name for it4' ,in the sense of taste1 the necessity of a ,medium is not at first so obviously seen1 because the object tasted is brought into contact with the organ2 but a little attention convinces us that the taste of a solid body can only be perceived when it is conveyed in some liquid vehicle4 ,till the fruit is crushed1 and till its juices are pressed out1 we do not distinguish its flavour4 ,in the case of heat1 it is still more clear that we are compelled to suppose some invisible fluid1 or other means of communication1 between the distant body which warms us and ourselves4 ,note #dd3 4 ii4 #g4 ,see the motto to this ,book4 ,it may appear to some persons that the assumption of an intermedium between the object perceived and the sentient organ results from the principles which form the basis of our mechanical reasonings1--that every change must have a cause1 and that bodies can act upon each other only by contact4 ,it cannot be denied that this principle does offer itself very naturally as the ground of our belief in media of sensation2 and it appears to be referred to for this purpose by ,aristotle in the passage quoted above4 ,but yet we cannot but ask1 ,does the principle1 that matter produces its effect by contact only1 manifestly apply here8 ,when we so apply it1 we include sensation among the effects which material contact produces2--a case so different from any merely mechanical effect1 that the principle1 so employed1 appears to acquire a new signification4 ,may we not1 then1 rather say that we have here a new axiom1--,that sensation implies a material cause immediately acting on the organ1--than a new application of our former proposition1--,that all mechanical change implies contact8 ,the solution of this doubt is not of any material consequence to our reasonings2 for whatever be the #bii ground of the assumption1 it is certain that we do assume the existence of media by which the sensations of sight1 hearing1 and the like1 are produced2 and it will be seen shortly that principles inseparably connected with this assumption are the basis of the sciences now before us4 ,this assumption makes its appearance in the physical doctrines of all the schools of philosophy4 ,it is exhibited perhaps most prominently in the tenets of the ,epicureans1 who were materialists1 and extended to all kinds of causation the axiom of the existence of a corporeal mechanism by which alone the effect is produced4 ,thus1 according to them1 vision is produced by certain images or material films which flow from the object1 strike upon the eyes1 and so become sensible4 ,this opinion is urged with great detail and earnestness by ,lucretius1 the poetical expositor of the ,epicurean creed among the ,romans4 ,his fundamental conviction of the necessity of a material medium is obviously the basis of his reasoning1 though he attempts to show the existence of such a medium by facts4 ,thus he argues#ed1 that by shouting loud we make the throat sore2 which shows1 he says1 that the voice must be material1 so that it can hurt the passage in coming out4 ,haud igitur dubium est quin voces verbaque constent ,corporeis e principiis ut ldere possint4 ,note #ed3 ,de ,rerum ,natur1 ,lib4 iv4 #ebi4 #d4 ,the ,process of ,perception of ,secondary ,qualities4--,the likenesses or representatives of objects by which they affect our senses were called by some writers species1 or sensible species1 a term which continued in use till the revival of science4 ,it may be observed that the conception of these species as films cast off from the object1 and retaining its shape1 was different1 as we have seen1 from the view which ,aristotle took1 though it has sometimes been called the ,peripatetic doctrine#fd4 ,we may add that the expression was latterly applied to express the supposition of an emanation of any kind1 and implied little #cjj more than that supposition of a ,medium of which we are now speaking4 ,thus ,bacon1 after reviewing the phenomena of sound1 says#gd1 ',videntur motus soni fieri per species spirituales3 ita enim loquendum donec certius quippiam inveniatur4' ,note #fd3 ,brown1 vol4 ii4 p4 #ih4 ,note #gd3 ,hist4 ,son4 et ,aud4 vol4 ix4 p4 #hg4 ,though the fundamental principles of several sciences depend upon the assumption of a ,medium of ,perception1 these principles do not at all depend upon any special view of the ,process of our perceptions4 ,the mechanism of that process is a curious subject of consideration2 but it belongs to physiology1 more properly than either to metaphysics1 or to those branches of physics of which we are now speaking4 ,the general nature of the process is the same for all the senses4 ,the object affects the appropriate intermedium2 the medium1 through the proper organ1 the eye1 the ear1 the nose1 affects the nerves of the particular sense2 and1 by these1 in some way1 the sensation is conveyed to the mind1 ,but to treat the impression upon the nerves as the act of sensation which we have to consider1 would be to mistake our object1 which is not the constitution of the human body1 but of the human mind4 ,it would be to mistake one link of the chain for the power which holds the end of the chain4 ,no anatomical analysis of the corporeal conditions of vision1 or hearing1 or feeling warm1 is necessary to the sciences of ,optics1 or ,acoustics1 or ,thermotics4 ,not only is this physiological research an extraneous part of our subject1 but a partial pursuit of such a research may mislead the inquirer4 ,we perceive objects by means of certain media1 and by means of certain impressions on the nerves3 but we cannot with propriety say that we perceive either the media or the impressions on the nerves4 ,what person in the act of seeing is conscious of the little coloured spaces on the retina8 or of the motions of the bones of the auditory apparatus whilst he is hearing8 ,surely1 no one4 ,this may appear obvious enough1 and yet a writer of no common acuteness1 ,dr4 ,brown1 has put forth several #cja very strange opinions1 all resting upon the doctrine that the coloured spaces on the retina are the objects which we perceive2 and there are some supposed difficulties and paradoxes on the same subject which have become quite celebrated 7as upright vision with inverted images71 arising from the same confusion of thought4 ,as the consideration of the difficulties which have arisen respecting the ,philosophy of ,perception may serve still further to illustrate the principles on which we necessarily reason respecting the secondary qualities of bodies1 ,i shall here devote a few pages to that subject4 #cjb ,,chapter ,,ii4 ,,on ,,peculiarities ,,in ,,the ,,perceptions ,,of ,,the ,,different ,,senses4 #a4 ,,we cannot doubt that we perceive all secondary qualities by means of immediate impressions made1 through the proper medium of sensation1 upon our organs4 ,hence all the senses are sometimes vaguely spoken of as modifications of the sense of feeling4 ,it will1 however1 be seen1 on reflection1 that this mode of speaking identifies in words things which in our conceptions have nothing in common4 ,no impression on the organs of touch can be conceived as having any resemblance to colour or smell4 ,no effort1 no ingenuity1 can enable us to describe the impressions of one sense in terms borrowed from another4 ,the senses have1 however1 each its peculiar powers1 and these powers may be in some respects compared1 so as to show their leading resemblances and differences1 and the characteristic privileges and laws of each4 ,this is what we shall do as briefly as possible4 ,,sect4 ,i4--,prerogatives of ,sight4 ,,the sight distinguishes colours1 as the hearing distinguishes tones2 the sight estimates degrees of brightness1 the ear1 degrees of loudness2 but with several resemblances1 there are most remarkable differences between these two senses4 #b4 ,position4--,the sight has this peculiar prerogative1 that it apprehends the place of its objects directly and primarily4 ,we see where an object is at the same instant that we see what it is4 ,if we see two objects1 we see their relative position4 ,we cannot help #cjc perceiving that one is above or below1 to the right or to the left of the other1 if we perceive them at all4 ,there is nothing corresponding to this in sound4 ,when we hear a noise1 we do not necessarily assign a place to it4 ,it may easily happen that we cannot tell from which side a thunder-clap comes4 ,and though we often can judge in what direction a voice is heard1 this is a matter of secondary impression1 and of inference from concomitant circumstances1 not a primary fact of sensation4 ,the judgments which we form concerning the position of sounding bodies are obtained by the conscious or unconscious comparison of the impressions made on the two ears1 and on the bones of the head in general2 they are not inseparable conditions of hearing4 ,we may hear sounds1 and be uncertain whether they are 'above1 around1 or underneath6' but the moment anything visible appears1 however unexpected1 we can say1 'see where it comes6' ,since we can see the relative position of things1 we can see figure1 which is but the relative position of the different parts of the boundary of the object4 ,and thus the whole visible world exhibits to us a scene of various shapes1 coloured and shaded according to their form and position1 but each having relations of position to all the rest2 and altogether1 entirely filling up the whole range which the eye can command4 #c4 ,distance4--,the distance of objects from us is no matter of immediate perception1 but is a judgment and inference formed from our sensations1 in something of the same way as our judgment of position by the ear1 though more precise4 ,that this is so1 was most distinctly shown by ,berkeley1 in his ,new ,theory of ,vision4 ,the elements on which we form our judgment are1 the effort by which we fix both eyes on the same object1 the effort by which we adjust each eye to distinct vision1 and the known forms1 colours1 and parts of objects1 as compared with their appearance4 ,the right interpretation of the information which these circumstances give us respecting the true distances and forms of things1 is gradually learnt by experience1 the lesson being begun in our earliest infancy1 and inculcated upon us every hour during which we #cjd use our eyes4 ,the completeness with which the lesson is learnt is truly admirable2 for we forget that our conclusion is obtained indirectly1 and mistake a judgment on evidence for an intuitive perception4 ,this1 however1 is not more surprizing than the rapidity and unconsciousness of effort with which we understand the meaning of the speech that we hear1 or the book that we read4 ,in both cases1 the habit of interpretation is become as familiar as the act of perception4 ,and this is the case with regard to vision4 ,we see the breadth of the street as clearly and readily as we see the house on the other side of it4 ,we see the house to be square1 however obliquely it be presented to us4 ,indeed the difficulty is1 to recover the consciousness of our real and original sensations2--to discover what is the apparent relation of the lines which appear before us4 ,as we have already said1 7book ii4 chap4 #f7 in the common process of vision we suppose ourselves to see that which cannot be seen2 and when we would make a picture of an object1 the difficulty is to represent what is visible and no more4 ,but perfect as is our habit of interpreting what we perceive1 we could not interpret if we did not perceive4 ,if the eye did not apprehend visible position1 it could not infer actual position1 which is collected from visible position as a consequence3 if we did not see apparent figure1 we could not arrive at any opinion concerning real form4 ,the perception of place1 which is the prerogative of the eye1 is the basis of all its other superiority4 ,the precision with which the eye can judge of apparent position is remarkable4 ,if we had before us two stars distant from each other by one-twentieth of the moon's diameter1 we could easily decide the apparent direction of the one from the other1 as above or below1 to the right or left4 ,yet eight millions of stars might be placed in the visible hemisphere of the sky at such distances from each other2 and thus the eye would recognize the relative position in a portion of its range not greater than one eight-millionth of the whole4 ,such is the accuracy of the sense of vision in this #cje respect2 and1 indeed1 we might with truth have stated it much higher4 ,our judgment of the position of distant objects in a landscape depends upon features far more minute than the magnitude we have here described4 ,as our object is to point out principally the differences of the senses1 we do not dwell upon the delicacy with which we distinguish tints and shades1 but proceed to another sense4 ,,sect4 ,,ii4--,prerogatives of ,hearing4 ,,the sense of hearing has two remarkable prerogatives2 it can perceive a definite and peculiar relation between certain tones1 and it can clearly perceive two tones together2 in both these circumstances it is distinguished from vision1 and from the other senses4 #d4 ,musical intervals4--,we perceive that two tones have1 or have not1 certain definite relations to each other1 which we call ,concords3 one sound is a ,fifth1 an ,octave1 c41 above the other4 ,and when this is the case1 our perception of the relation is extremely precise4 ,it is easy to perceive when a fifth is out of tune by one-twentieth of a tone2 that is1 by one-seventieth of itself4 ,to this there is nothing analogous in vision4 ,colours have certain vague relations to one another2 they look well together1 by contrast or by resemblance2 but this is an indefinite1 and in most cases a casual and variable feeling4 ,the relation of complementary colours to one another1 as of red to green1 is somewhat more definite2 but still1 has nothing of the exactness and peculiarity which belongs to a musical concord4 ,in the case of the two sounds1 there is an exact point at which the relation obtains2 when by altering one note we pass this point1 the concord does not gradually fade away1 but instantly becomes a discord2 and if we go further still1 we obtain another concord of quite a different character4 ,we learn from the theory of sound that concords occur when the times of vibration of the notes have exact simple ratios2 an octave has these times as #a to #cjf #b2 a fifth1 as #b to #c4 ,according to the undulatory theory of light1 such ratios occur in colours1 yet the eye is not affected by them in any peculiar way4 ,the times of the undulations of certain red and certain violet rays are as #b to #c1 but we do not perceive any peculiar harmony or connexion between those colours4 #e4 ,chords4--,again1 the ear has this prerogative1 that it can apprehend two notes together1 yet distinct4 ,if two notes1 distant by a fifth from each other1 are sounded on two wind instruments1 both they and their musical relation are clearly perceived4 ,there is not a mixture1 but a concord1 a musical interval4 ,in colours1 the case is otherwise4 ,if blue and yellow fall on the same spot1 they form green2 the colour is simple to the eye2 it can no more be decomposed by the vision than if it were the simple green of the prismatic spectrum3 it is impossible for us1 by sight1 to tell whether it is so or not4 ,these are very remarkable differences of the two senses3 two colours can be compounded into an apparently simple one2 two sounds cannot3 colours pass into each other by gradations and intermediate tints2 sounds pass from one concord to another by no gradations3 the most intolerable discord is that which is near a concord4 ,we shall hereafter see how these differences affect the scales of sound and of colour4 #f4 ,rhythm4--,we might remark1 that as we see objects in space1 we hear sounds in time2 and that we thus introduce an arrangement among sounds which has several analogies with the arrangement of objects in space4 ,but the conception of time does not seem to be peculiarly connected with the sense of hearing2 a faculty of apprehending tone and time1 or in musical phraseology tune and rhythm1 are certainly very distinct4 ,i shall not1 therefore1 here dwell upon such analogies4 ,the other ,senses have not any peculiar prerogatives1 at least none which bear on the formation of science4 ,i may1 however1 notice1 in the feeling of heat1 this circumstance2 that it presents us with two opposites1 heat and cold1 which graduate into each other4 ,this #cjg is not quite peculiar1 for vision also exhibits to us white and black1 which are clearly opposites1 and which pass into each other by the shades of gray4 ,,sect4 ,,iii4--,the ,paradoxes of ,vision4 #g4 ,first ,paradox of ,vision4 ,upright ,vision4--,all our senses appear to have this in common2 ,that they act by means of organs1 in which a bundle of nerves receives the impression of the appropriate medium of the sense4 ,in the construction of these organs there are great differences and peculiarities1 corresponding1 in part at least1 to the differences in the information given4 ,moreover1 in some cases1 as we have noted in the case of audible position and visible distance1 that which seems to be a perception is really a judgment founded on perceptions of which we are not directly aware4 ,it will be seen1 therefore1 that with respect to the peculiar powers of each sense1 it may be asked2--whether they can be explained by the construction of the peculiar organ2--whether they are acquired judgments and not direct perceptions2--or whether they are inexplicable in either of these ways1 and cannot1 at present at least1 be resolved into anything but conditions of the intellectual act of perception4 ,two of these questions with regard to vision1 have been much discussed by psychological writers3 the cause of our seeing objects upright by inverted images on the retina2 and of our seeing single with two such images4 ,physiologists have very completely explained the exquisitely beautiful mechanism of the eye1 considered as analogous to an optical instrument2 and it is indisputable that by means of certain transparent lenses and humours1 an inverted image of the objects which are looked at is formed upon the retina1 or fine net-work of nerve1 with which the back of the eye is lined4 ,we cannot doubt that the impression thus produced on these nerves is essential to the act of vision2 and so far as we consider the nerves #cjh themselves to feel or perceive by contact1 we may say that they perceive this image1 or the affections of light which it indicates4 ,but we cannot with any propriety say that we perceive1 or that our mind perceives1 this image2 for we are not conscious of it1 and none but anatomists are aware of its existence3 we perceive by means of it4 ,a difficulty has been raised1 and dwelt upon in a most unaccountable manner1 arising from the neglect of this obvious distinction4 ,it has been asked1 how is it that we see an object1 a man for instance1 upright1 when the immediate object of our sensation1 the image of the man on our retina1 is inverted8 ,to this we must answer1 that we see him upright because the image is inverted2 that the inverted image is the necessary means of seeing an upright object4 ,this is granted1 and where then is the difficulty8 ,perhaps it may be put thus3 ,how is it that we do not judge the man to be inverted1 since the sensible image is so8 ,to this we may reply1 that we have no notion of upright or inverted1 except that which is founded on experience1 and that all our experience1 without exception1 must have taught us that such a sensible image belongs to a man who is in an upright position4 ,indeed1 the contrary judgment is not conceivable2 a man is upright whose head is upwards and his feet downwards4 ,but what are the sensible images of upwards and downwards8 ,whatever be our standard of up and down1 the sensible representation of up will be an image moving on the retina towards the lower side1 and the sensible representation of down will be a motion towards the upper side4 ,the head of the man's image is towards the image of the sky1 its feet are towards the image of the ground2 how then should it appear otherwise than upright8 ,do we expect that the whole world should appear inverted8 ,be it so3 but if the whole be inverted1 how is the relation of the parts altered8 ,do we expect that we should think our own persons in particular8 ,this cannot be1 for we look at them as we do at other objects4 ,do we expect that things should appear to fall #cji upwards8 ,surely not4 ,for what do we know of upwards1 except that it is the direction in which bodies do not fall8 ,in short1 the whole of this difficulty1 though it has in no small degree embarrassed metaphysicians1 appears to result from a very palpable confusion of ideas2 from an attempt at comparison of what we see1 with that which the retina feels1 as if they were separately presentable4 ,it is a sufficient explanation to say1 that we do not see the image on the retina1 but see by means of it4 ,the perplexity does not require much more skill to disentangle1 than it does to see that a word written in black ink1 may signify white#hd4 ,note #hd3 ,the explanation of our seeing objects erect when the image is inverted has been put very simply1 by saying1 ',we call that the lower end of an object which is next the ground4' ,the observer cannot look into his own eye2 he knows by experience what kind of image corresponds to a man in an upright position4 ,the anatomist tells him that this image is inverted3 but this does not disturb the process of judging by experience4 ,it does not appear why any one should be perplexed at the notion of seeing objects erect by means of inverted images1 rather than at the notion of seeing objects large by means of small images2 or cubical and pyramidal1 by means of images on a spherical surface2 or green and red1 by means of images on a black surface4 ,indeed some persons have contrived to perplex themselves with these latter questions1 as well as the first4 ,the above explanation is not at all affected1 as to its substance1 if we adopt ,sir ,david ,brewster's expression1 and say that the line of visible direction is a line passing through the center of the spherical surface of the retina1 and therefore of course perpendicular to the surface4 ,in speaking of 'the inverted image1' it has always been supposed to be determined by such lines2 and though the point where they intersect may not have been ascertained with exactness by previous physiologists1 the philosophical view of the matter was not in any degree vitiated by this imperfection4 #h4 ,second ,paradox of ,vision4 ,single ,vision4--7#a47 ,small or ,distant ,objects4--,the other difficulty1 why with two images on the retina we see only one object1 is of a much more real and important kind4 ,this effect is manifestly limited by certain circumstances of a very precise nature2 for if we direct our eyes at an object which is very near the eye1 we see #caj all other objects double4 ,the fact is not1 therefore1 that we are incapable of receiving two impressions from the two images1 but that1 under certain conditions1 the two impressions form one4 ,a little attention shows us that these conditions are1 that with both eyes we should look at the same object2 and again1 we find that to look at an object with either eye1 is to direct the eye so that the image falls on or near a particular point about the middle of the retina4 ,thus these middle points in the two retinas correspond1 and we see an image single when the two images fall on the corresponding points4 ,again1 as each eye judges of position1 and as the two eyes judge similarly1 an object will be seen in the same place by one eye and by the other1 when the two images which it produces are similarly situated with regard to the corresponding points of the retina#id4 ,note #id3 ,the explanation of single vision with two eyes may be put in another form4 ,each eye judges immediately of the relative position of all objects within the field of its direct vision4 ,therefore when we look with both eyes at a distant prospect 7so distant that the distance between the eyes is small in comparison7 the two prospects1 being similar collections of forms1 will coincide altogether1 if a corresponding point in one and in the other coincide4 ,if this be the case1 the two images of every object will fall upon corresponding points of the retina1 and will appear single4 ,if the two prospects seen by the two eyes do not exactly coincide1 in consequence of nearness of the objects1 or distortion of the eyes1 but if they nearly coincide1 the stronger image of an object absorbs the weaker1 and the object is seen single2 yet modified by the combination1 as will be seen when we speak of the single vision of near objects4 ,when the two images of an object are considerably apart1 we see it double4 ,this explanation is not different in substance from the one given in the text2 but perhaps it is better to avoid the assertion that the law of corresponding points is 'a distinct and original principle of our constitution1' as ,i had stated in the first edition4 ,the simpler mode of stating the law of our constitution appears to be to say1 that each eye determines similarly the position of objects2 and that when the positions of an object1 as seen by the two eyes1 coincide 7or nearly coincide7 the object is seen single4 ,this is the ,law of ,single ,vision1 at least so far as regards small objects2 namely1 objects so small that in contemplating them we consider their position only1 #caa and not their solid dimensions4 ,single vision in such cases is a result of the law of vision simply3 and it is a mistake to call in1 as some have done1 the influence of habit and of acquired judgments1 in order to determine the result in such cases4 ,to ascribe the apparent singleness of objects to the impressions of vision corrected by the experience of touch#ajd1 would be to assert that a person who had not been in the habit of handling what he saw1 would see all objects double2 and also1 to assert that a person beginning with the double world which vision thus offers to him1 would1 by the continued habit of handling objects1 gradually and at last learn to see them single4 ,but all the facts of the case show such suppositions to be utterly fantastical4 ,no one can1 in this case1 go back from the habitual judgment of the singleness of objects1 to the original and direct perception of their doubleness1 as the draughtsman goes back from judgments to perception1 in representing solid distances and forms by means of perspective pictures4 ,no one can point out any case in which the habit is imperfectly formed2 even children of the most tender age look at an object with both eyes1 and see it as one4 ,note #ajd3 ,see ,brown1 vol4 ii4 p4 #ha4 ,in cases when the eyes are distorted 7in squinting71 one eye only is used1 or if both are employed1 there is double vision2 and thus any derangement of the correspondence of motion in the two eyes will produce double-sightedness4 ,brown is one of those#aad who assert that two images suggest a single object because we have always found two images to belong to a single object4 ,he urges as an illustration1 that the two words 'he conquered1' by custom excite exactly the same notion as the one ,latin word 'vicit2' and thus that two visual images1 by the effect of habit1 produce the same belief of a single object as one tactual impression4 ,but in order to make this pretended illustration of any value1 it ought to be true that when a person has thoroughly learnt the ,latin language1 he can no longer distinguish #cab any separate meaning in 'he' and in 'conquered4' ,we can by no effort perceive the double sensation1 when we look at the object with the two eyes4 ,those who squint1 learn by habit to see objects single3 but the habit which they acquire is that of attending to the impressions of one eye only at once1 not of combining the two impressions4 ,it is obvious1 that if each eye spreads before us the same visible scene1 with the same objects and the same relations of place1 then1 if one object in each scene coincide1 the whole of the two visible impressions will be coincident4 ,and here the remarkable circumstance is1 that not only each eye judges for itself of the relations of position which come within its field of view2 but that there is a superior and more comprehensive faculty which combines and compares the two fields of view2 which asserts or denies their coincidence2 which contemplates1 as in a relative position to one another1 these two visible worlds1 in which all other relative position is given4 ,this power of confronting two sets of visible images and figured spaces before a purely intellectual tribunal1 is one of the most remarkable circumstances in the sense of vision4 ,note #aad3 ,lectures1 vol4 ii4 p4 #ha4 #i4 7#b47 ,near ,objects4--,we have hitherto spoken of the singleness of objects whose images occupy corresponding positions on the retina of the two eyes4 ,but here occurs a difficulty4 ,if an object of moderate size1 a small thick book for example1 be held at a little distance from the eyes1 it produces an image on the retina of each eye2 and these two images are perspective representations of the book from different points of view1 7the positions of the two eyes17 and are therefore of different forms4 ,hence the two images cannot occupy corresponding points of the retina throughout their whole extent4 ,if the central parts of the two images occupy corresponding points1 the boundaries of the two wall not correspond4 ,how is it then consistent with the law above stated that in this case the object appears single8 ,it may be observed1 that the two images in such a case will differ most widely when the object is not a #cac mere surface1 but a solid4 ,if a book1 for example1 be held with one of its upright edges towards the face1 the right eye will see one side more directly than the left eye1 and the left eye will see another side more directly1 and the outline of the two images upon the two retinas will exhibit this difference4 ,and it may be further observed1 that this difference in the images received by the two eyes1 is a plain and demonstrative evidence of the solidity of the object seen2 since nothing but a solid object could 7without some special contrivance7 produce these different forms of the images in the two eyes4 ,hence the absence of exact coincidence in the two images on the retina is the necessary condition of the solidity of the object seen1 and must be one of the indications by means of which our vision apprehends an object as solid4 ,and that this is so1 ,mr4 ,wheatstone has proved experimentally1 by means of some most ingenious and striking contrivances4 ,he has devised#abd an instrument 7the stereoscope7 by which two images 7drawn in outline7 differing exactly as much as the two images of a solid body seen near the face would differ1 are conveyed1 one to one eye1 and the other to the other4 ,and it is found that when this is effected1 the object which the images represent is not only seen single1 but is apprehended as solid with a clearness and reality of conviction quite distinct from any impression which a mere perspective representation can give4 ,note #abd3 ,phil4 ,trans4 #ahci4 ,at the same time it is found that the object is then only apprehended as single when the two images are such as are capable of being excited by one single object placed in solid space1 and seen by the two eyes4 ,if the images differ more or otherwise than this condition allows1 the result is1 that both are seen1 their lines crossing and interfering with one another4 ,it may be observed1 too1 that if an object be of such large size as not to be taken in by a single glance of the eyes1 it is no longer apprehended as single by a direct act of perception2 but its parts are looked at #cad separately and successively1 and the impressions thus obtained are put together by a succeeding act of the mind4 ,hence the objects which are directly seen as solid1 will be of moderate size2 in which case it is not difficult to show that the outlines of the two images will differ from each other only slightly4 ,hence we are led to the following1 as the ,law of ,single ,vision for near objects3--,when the two images in the two eyes are situated 7part for part7 nearly1 but not exactly1 upon corresponding points1 the object is apprehended as single1 if the two images are such as are or would be given by a single solid object seen by the two eyes separately3 and in this case the object is necessarily apprehended as solid4 ,this law of vision does not contradict that stated above for distant objects3 for when an object is removed to a considerable distance1 the images in the two eyes coincide exactly1 and the object is seen as single1 though without any direct apprehension of its solidity4 ,the first law is a special case of the second4 ,under the condition of exactly corresponding points1 we have the perception of singleness1 but no evidence of solidity4 ,under the condition of nearly corresponding points1 we may have the perception of singleness1 and with it1 of solidity4 ,we have before noted it as an important feature in our visual perception1 that while we have two distinct impressions upon the sense1 which we can contemplate separately and alternately1 7the impressions on the two eyes17 we have a higher perceptive faculty which can recognize these two impressions1 exactly similar to each other1 as only two images of one and the same assemblage of objects4 ,but we now see that the faculty by which we perceive visible objects can do much more than this3--it can not only unite two impressions1 and recognize them as belonging to one object in virtue of their coincidence1 but it can also unite and identify them1 even when they do not exactly coincide4 ,it can correct and adjust their small difference1 so that they are both apprehended as representations of the same figure4 ,it can infer from them a real form1 not #cae agreeing with either of them2 and a solid space1 which they are quite incapable of exemplifying4 ,the visual faculty decides whether or not the two ocular images can be pictures of the same solid object1 and if they can1 it undoubtingly and necessarily accepts them as being so4 ,this faculty operates as if it had the power of calling before it all possible solid figures1 and of ascertaining by trial whether any of those will1 at the same time1 fit both the outlines which are given by the sense4 ,it assumes the reality of solid space1 and1 if it be possible1 reconciles the appearances with that reality4 ,and thus an activity of the mind of a very remarkable and peculiar kind is exercised in the most common act of seeing4 #aj4 ,it may be said that this doctrine1 of such a visual faculty as has been described1 is very vague and obscure1 since we are not told what are its limits4 ,it adjusts and corrects figures which nearly coincide1 so as to identify them4 ,but how nearly1 it may be asked1 must the figures approach each other1 in order that this adjustment may be possible8 ,what discrepance renders impossible the reconcilement of which we speak8 ,is it not impossible to give a definite answer to these questions1 and therefore impossible to lay down definitely such laws of vision as we have stated8 ,to this ,i reply1 that the indefiniteness thus objected to us1 is no new difficulty1 but one with which philosophers are familiar1 and to which they are already reconciled4 ,it is1 in fact1 no other than the indefiniteness of the limits of distinct vision4 ,how near to the face must an object be brought1 so that we shall cease to see it distinctly8 ,the distance1 it will be answered1 is indefinite3 it is different for different persons2 and for the same person1 it varies with the degree of effort1 attention1 and habit4 ,but this indefiniteness is only the indefiniteness1 in another form1 of the deviation of the two ocular images from one another3 and in reply to the question concerning them we must still say1 as before1 that in doubtful cases1 the power of apprehending an object as single1 when this can be done1 will vary with effort1 attention1 and habit4 ,the assumption #caf that the apparent object exists as a real figure1 in real space1 is to be verified1 if possible2 but1 in extreme cases1 from the unfitness of the point of view1 or from any other cause of visual confusion or deception1 the existence of a real object corresponding to the appearance may be doubtful2 as in any other kind of perception it may be doubtful whether our senses1 under disadvantageous circumstances1 give us true information4 ,the vagueness of the limits1 then1 within which this visual faculty can be successfully exercised1 is no valid argument against the existence of the faculty1 or the truth of the law which we have stated concerning its action4 ,,sect4 ,,iv4--,the ,perception of ,visible ,figure4 #aa4 ,visible ,figure4--,there is one tenet on the subject of vision which appears to me so extravagant and unphilosophical1 that ,i should not have thought it necessary to notice it1 if it had not been recently promulgated by a writer of great acuteness in a book which has obtained1 for a metaphysical work1 considerable circulation4 ,i speak of ,brown's opinion#acd that we have no immediate perception of visible figure4 ,i confess myself unable to comprehend fully the doctrine which he would substitute in the place of the one commonly received4 ,he states it thus#add3 ',when the simple affection of sight is blended with the ideas of suggestion those arising from touch1 c4 in what are termed the acquired perceptions of vision1 as1 for example1 in the perception of a sphere1 it is colour only which is blended with the large convexity1 and not a small coloured plane4' ,the doctrine which ,brown asserts in this and similar passages1 appears to be1 that we do not by vision perceive both colour and figure2 but that the colour which we see is blended with the figure which we learn the existence of by other means1 as by touch4 ,but if this were possible when we can call in other perceptions1 how is it possible when we cannot or do not touch the object8 #cag ,why does the moon appear round1 gibbous1 or horned8 ,what sense besides vision suggests to us the idea of her figure8 ,and even in objects which we can reach1 what is that circumstance in the sense of vision which suggests to us that the colour belongs to the sphere1 except that we see the colour where we see the sphere8 ,if we do not see figure1 we do not see position2 for figure is the relative position of the parts of a boundary4 ,if we do not see position1 why do we ascribe the yellow colour to the sphere on our left1 rather than to the cube on our right8 ,we associate the colour with the object1 says ,dr4 ,brown2 but if his opinion were true1 we could not associate two colours with two objects1 for we could not apprehend the colours as occupying two different places4 ,note #acd3 ,lectures1 vol4 ii4 p4 #hb4 ,note #add3 ,ib4 vol4 ii4 p4 #ij4 ,the whole of ,brown's reasoning on this subject is so irreconcilable with the first facts of vision1 that it is difficult to conceive how it could proceed from a person who has reasoned with great acuteness concerning touch4 ,in order to prove his assertion1 he undertakes to examine the only reasons which1 he says#aed1 he can imagine for believing the immediate perception of visible figure3 7#a7 ,that it is absolutely impossible1 in our present sensations of sight1 to separate colour from extension2 and 7#b7 ,that there are1 in fact1 figures on the retina corresponding to the apparent figures of objects4 ,note #aed3 ,lectures1 vol4 ii4 p4 #hc4 ,on the subject of the first reason1 he says1 that the figure which we perceive as associated with colour1 is the real1 and not the apparent figure4 ',is there1' he asks1 'the slightest consciousness of a perception of visible figure1 corresponding to the affected portion of the retina8' ,to which1 though he seems to think an affirmative answer impossible1 we cannot hesitate to reply1 that there is undoubtedly such a consciousness2 that though obscured by being made the ground of habitual inference as to the real figure1 this consciousness is constantly referred to by the draughtsman1 and easily recalled by any one4 ,we may separate colour1 he says #cah again#afd1 from the figures on the retina1 as we may separate it from length1 breadth1 and thickness1 which we do not see4 ,but this is altogether false3 we cannot separate colour from length1 breadth1 and thickness1 in any other way1 than by transferring it to the visible figure which we do see4 ,he cannot1 he allows1 separate the colour from the visible form of the trunk of a large oak2 but just as little1 he thinks1 can he separate it from the convex mass of the trunk1 which 7it is allowed on all hands7 he does not immediately see4 ,but in this he is mistaken3 for if he were to make a picture of the oak1 he would separate the colour from the convex shape1 which he does not imitate1 but he could not separate it from the visible figure1 which he does imitate2 and he would then perceive that the fact that he has not an immediate perception of the convex form1 is necessarily connected with the fact that he has an immediate perception of the apparent figure2 so far is the rejection of immediate perception in the former case from being a reason for rejecting it in the latter4 ,note #afd3 ,lectures1 vol4 ii4 p4 #hd4 ,again1 with regard to the second argument4 ,it does not1 he says1 follow1 that because a certain figured portion of the retina is affected by light1 we should see such a figure2 for if a certain figured portion of the olfactory organ were affected by odours1 we should not acquire by smell any perception of such figure#agd4 ,this is merely to say1 that because we do not perceive position and figure by one sense1 we cannot do so by another sense4 ,but this again is altogether erroneous4 ,it is an office of our sight to inform us of position1 and consequently of figure2 for this purpose1 the organ is so constructed that the position of the object determines the position of the point of the retina affected4 ,there is nothing of this kind in the organ of smell2 objects in different positions and of different forms do not affect different parts of the olfactory nerve1 or portions of different shape4 ,different objects1 remote from each other1 if perceived by smell1 affect the same #cai part of the olfactory organs4 ,this is all quite intelligible2 for it is not the office of smell to inform us of position4 ,of what use or meaning would be the curious and complex structure of the eye1 if it gave us only such vague and wandering notions of the colours and forms of the flowers in a garden1 as we receive from their odours when we walk among them blindfold8 ,it is1 as we have said1 the prerogative of vision to apprehend position3 the places of objects on the retina give this information4 ,we do not suppose that the affection of a certain shape of nervous expanse will necessarily and in all cases give us the impression of figure2 but we know that in vision it does2 and it is clear that if we did not acquire our acquaintance with visible figure in this way1 we could not acquire it in any way#ahd4 ,note #agd3 ,ib4 p4 #hg4 ,note #ahd3 ,when ,brown says further 7p4 #hg71 that we can indeed show the image in the dissected eye2 but that 'it is not in the dissected eye that vision takes place2' it is difficult to see what his drift is4 ,does he doubt that there is an image formed in the living as completely as in the dissected eye8 ,the whole of this strange mistake of ,brown's appears to arise from the fault already noticed2--that of considering the image on the retina as the object instead of the means of vision4 ,this indeed is what he says3 'the true object of vision is not the distant body itself1 but the light that has reached the expansive termination of the optic nerve#aid4' ,even if this were so1 we do not see why we should not perceive the position of the impression on this expanded nerve4 ,but as we have already said1 the impression on the nerve is the means of vision1 and enables us to assign a place1 or at least a direction1 to the object from which the light proceeds1 and thus makes vision possible4 ,brown1 indeed1 pursues his own peculiar view till he involves the subject in utter confusion4 ,thus he says#bjd1 ',according to the common theory that figure can be perceived by the eye1 a visible sphere is at once to my perception convex and plane2 and if the sphere be a one1 it is perceived at once to be a sphere of #cbj many feet in diameter1 and a plane circular surface of the diameter of a quarter of an inch4' ,it is easy to deduce these and greater absurdities1 if we proceed on his strange and baseless supposition that the object and the image on the retina are both perceived4 ,but who is conscious of the image on the retina in any other way than as he sees the object by means of it8 ,note #aid3 ,lectures1 vol4 ii4 p4 #eg4 ,note #bjd3 ,ib4 vol4 ii4 p4 #hi4 ,brown seems to have imagined that he was analysing the perception of figure 'in the same manner in which ,berkeley had analyzed the perception of distance4 ,he ought to have recollected that such an undertaking1 to be successful1 required him to show what elements he analyzed it into4 ,berkeley analyzed the perception of real figure into the interpretation of visible figure according to certain rules which he distinctly stated4 ,brown analyzes the perception of visible figure into no elements4 ,berkeley says1 that we do not directly perceive distance1 but that we perceive something else1 from which we infer distance1 namely1 visible figure and colour1 and our own efforts in seeing2 ,brown says1 that we do not see figure1 but infer it2 what then do we see1 which we infer it from8 ,to this he offers no answer4 ,he asserts the seeming perception of visible figure to be a result of 'association2'--of 'suggestion4' ,but what meaning can we attach to this8 ,suggestion requires something which suggests2 and not a hint is given what it is which suggests position4 ,association implies two things associated2 what is the sensation which we associate with form8 ,what is that visual perception which is not figure1 and which we mistake for figure8 ,what perception is it that suggests a square to the eye8 ,what impressions are those which have been associated with a visible triangle1 so that the revival of the impressions revives the notion of the triangle8 ,brown has nowhere pointed out such perceptions and impressions2 nor indeed was it possible for him to do so2 for the only visual perceptions which he allows to remain1 those of colour1 most assuredly do not suggest visible figures by their differences2 red is not associated with square rather than with round1 or with round rather than square4 ,on the contrary1 the #cba eye1 constructed in a very complex and wonderful manner in order that it may give to us directly the perception of position as well as of colour1 has it for one of its prerogatives to give us this information2 and the perception of the relative position of each part of the visible boundary of an object constitutes the perception of its apparent figure2 which faculty we cannot deny to the eye without rejecting the plain and constant evidence of our senses1 making the mechanism of the eye unmeaning1 confounding the object with the means of vision1 and rendering the mental process of vision utterly unintelligible4 ,having sufficiently discussed the processes of perception1 ,i now return to the consideration of the ,ideas which these processes assume4 #cbb ,,chapter ,,iii4 ,,successive ,,attempts ,,at ,,the ,,scientific ,,application ,,of ,,the ,,idea ,,of ,a ,,medium4 #a4 ,,in what precedes1 we have shown by various considerations that we necessarily and universally assume the perception of secondary qualities to take place by means of a medium interjacent between the object and the person perceiving4 ,perception is affected by various peculiarities1 according to the nature of the quality perceived3 but in all cases a medium is equally essential to the process4 ,this principle1 which1 as we have seen1 is accepted as evident by the common understanding of mankind1 is confirmed by all additional reflection and discipline of the mind1 and is the foundation of all the theories which have been proposed concerning the processes by which the perception takes place1 and concerning the modifications of the qualities thus perceived4 ,the medium1 and the mode in which the impression is conveyed through the medium1 seem to be different for different qualities2 but the existence of the medium leads to certain necessary conditions or alternatives1 which have successively made their appearance in science1 in the course of the attempts of men to theorize concerning the principal secondary qualities1 sound1 light1 and heat4 ,we must now point out some of the ways1 at first imperfect and erroneous1 in which the consequences of the fundamental assumption were traced4 #b4 ,sound4--,in all cases the medium of sensation1 whatever it is1 is supposed to produce the effect of conveying secondary qualities to our perception by means of its primary qualities4 ,it was conceived to operate #cbc by the size1 form1 and motion of its parts4 ,this is a fundamental principle of the class of sciences of which we have at present to speak4 ,it was assumed from the first1 as we have seen in the passage lately quoted from ,aristotle#bad1 that in the conveyance of sound1 the medium of communication was the air4 ,but although the first theorists were right so far1 that circumstance did not prevent their going entirely wrong when they had further to determine the nature of the process4 ,it was conceived by ,aristotle that the air acted after the manner of a rigid body2--like a staff1 which1 receiving an impulse at one end1 transmits it to the other4 ,now this is altogether an erroneous view of the manner in which the air conveys the impulse by which sound is perceived4 ,an approach was made to the true view of this process1 by assimilating it to the diffusion of the little circular waves which are produced on the surface of still water when a stone is dropt into it4 ,these little waves begin from the point thus disturbed1 and run outwards1 expanding on every side1 in concentric circles1 till they are lost4 ,the propagation of sound through the air from the point where it is produced1 was compared by ,vitruvius to this diffusion of circular waves in water2 and thus the notion of a propagation of impulse by the waves of a fluid was introduced1 in the place of the former notion of the impulse of an unyielding body4 ,note #bad3 ,supr4 p4 #big4 ,but though1 taking an enlarged view of the nature of the progress of a wave1 this is a just representation of the motion of air in conveying sound1 we cannot suppose that the process was1 at the period of which we speak1 rightly understood4 ,for the waves of water were contemplated only as affecting the surface of the water2 and as the air has no surface1 the communication must take place by means of an internal motion1 which can bear only a remote and obscure resemblance to the waves which we see4 ,and even with regard to the waves of water1 the mechanism by which they are #cbd produced and transferred was not at all understood2 so that the comparison employed by ,vitruvius must be considered rather as a loose analogy than as an exact scientific explanation4 ,no correct account of such motions was given1 till the formation of the science of ,mechanics in modern times had enabled philosophers to understand more distinctly the mode in which motion is propagated through a fluid1 and to discern the forces which the process calls into play1 so as to continue the motion once begun4 ,newton introduced into this subject the exact and rigorous conception of an ,undulation1 which is the true key to the explanation of impulses conveyed through a fluid4 ,even at the present day1 the right apprehension of the nature of an ,undulation transmitted through a fluid is found to be very difficult for all persons except those whose minds have been duly disciplined by mathematical studies4 ,when we see a wave run along the surface of water1 we are apt to imagine at first that a portion of the fluid is transferred bodily from one place to another4 ,but with a little consideration we may easily satisfy ourselves that this is not so3 for if we look at a field of standing corn1 when a breeze blows over it1 we see waves like those of water run along its surface4 ,yet it is clear that in this case the separate stalks of corn only bend backwards and forwards1 and no portion of the grain is really conveyed from one part of the field to the other4 ,this is obvious even to popular apprehension4 ,the poet speaks of 4 4 4 4 ,the rye1 ,that stoops its head when whirlwinds rave ,and springs again in eddying wave ,as each wild gust sweeps by4 ,each particle of the mass in succession has a small motion backwards and forwards2 and by this means a large ridge made by many such particles runs along the mass to any distance4 ,this is the true conception of an undulation in general4 ,thus1 when an ,undulation is propagated in a fluid1 it is not matter1 but form1 which is transmitted from #cbe one place to another4 ,the particles along the line of each wave assume a certain arrangement1 and this arrangement passes from one part to another1 the particles changing their places only within narrow limits1 so as to lend themselves successively to the arrangements by which the successive waves1 and the intervals between the waves1 are formed4 ,when such an ,undulation is propagated through air1 the wave is composed1 not1 as in water1 of particles which are higher than the rest1 but of particles which are closer to each other than the rest4 ,the wave is not a ridge of elevation1 but a line of condensation2 and as in water we have alternately elevated and depressed lines1 we have in air lines alternately condensed and rarefied4 ,and the motion of the particles is not1 as in water1 up and down1 in a direction transverse to that of the wave which runs forwards2 in the motion of an undulation through air the motion of each particle is alternately forwards and backwards1 while the motion of the undulation is constantly forwards4 ,this precise and detailed account of the ,undulatory ,motion of air by which sound is transmitted was first given by ,newton4 ,he further attempted to determine the motions of the separate particles1 and to point out the force by which each particle affects the next1 so as to continue the progress of the undulation once begun4 ,the motions of each particle must be oscillatory2 he assumed the oscillations to be governed by the simplest law of oscillation which had come under the notice of mathematicians1 7that of small vibrations of a pendulum27 and he proved that in this manner the forces which are called into play by the contraction and expansion of the parts of the elastic fluid are such as the continuance of the motion requires4 ,newton's proof of the exact law of ,oscillatory ,motion of the arial particles was not considered satisfactory by succeeding mathematicians2 for it was found that the same result1 the development of forces adequate to continue the motion1 would follow if any other law of the motion were assumed4 ,cramer proved this by a sort of parody on ,newton's proof1 in which1 by the #cbf alteration of a few phrases in this formula of demonstration1 it was made to establish an entirely different conclusion4 ,but the general conception of an ,undulation as presented by ,newton was1 as from its manifest mechanical truth it could not fail to be1 accepted by all mathematicians2 and in proportion as the methods of calculating the motions of fluids were further improved1 the necessary consequences of this conception1 in the communication of sound through air1 were traced by unexceptionable reasoning4 ,this was especially done by ,euler and ,lagrange1 whose memoirs on such motions of fluids are some of the most admirable examples which exist1 of refined mathematical methods applied to the solution of difficult mechanical problems4 ,but the great step in the formation of the theory of sound was undoubtedly that which we have noticed1 the introduction of the ,conception of an ,undulation such as we have attempted to describe it3--a state1 condition1 or arrangement of the particles of a fluid1 which is transferred from one part of space to another by means of small motions of the particles1 altogether distinct from the movement of the ,undulation itself4 ,this is a conception which is not obvious to common apprehension4 ,it appears paradoxical at first sight to speak of a large wave 7as the tide-wave7 running up a river at the rate of twenty miles an hour1 while the stream of the river is all the while flowing downwards4 ,yet this is a very common fact4 ,and the conception of such a motion must be fully mastered by all who would reason rightly concerning the mechanical transmission of impressions through a medium4 ,we have described the motion of sound as produced by small motions of the particle forwards and backwards1 while the waves1 or condensed and rarefied lines1 move constantly forwards4 ,it may be asked what right we have to suppose the motion to be of this kind1 since when sound is heard1 no such motions of the particles of air can be observed1 even by refined methods of observation4 ,thus ,bacon declares himself against the hypothesis of such a vibration1 since1 as he remarks1 it #cbg cannot be perceived in any visible impression upon the flame of a candle4 ,and to this we reply1 that the supposition of this ,vibration is made in virtue of a principle which is involved in the original assumption of a medium2 namely1 ,that a ,medium1 in conveying ,secondary qualities1 operates by means of its ,primary qualities1 the bulk1 figure1 motion1 and other mechanical properties of its parts4 ,this is an ,axiom belonging to the ,idea of a ,medium4 ,in virtue of this axiom it is demonstrable that the motion of the air1 when any how disturbed1 must be such as is supposed in our acoustical reasonings4 ,for the elasticity of the parts of the air1 called into play by its expansion and contraction1 lead1 by a mechanical necessity1 to such a motion as we have described4 ,we may add that1 by proper contrivances1 this motion may be made perceptible in its visible effects4 ,thus the theory of sound1 as an impression conveyed through air1 is established upon evident general principles1 although the mathematical calculations which are requisite to investigate its consequences are1 some of them1 of a very recondite kind4 #c4 ,light4--,the early attempts to explain ,vision represented it as performed by means of material rays proceeding from the eye1 by the help of which the eye felt out the form and other visible qualities of an object1 as a blind man might do with his staff4 ,but this opinion could not keep its ground long3 for it did not even explain the fact that light is necessary to vision4 ,light1 as a peculiar medium1 was next assumed as the machinery of vision2 but the mode in which the impression was conveyed through the medium was left undetermined1 and no advance was made towards sound theory1 on that subject1 by the ancients4 ,in modern times1 when the prevalent philosophy began to assume a mechanical turn 7as in the theories of ,descartes71 light was conceived to be a material substance which is emitted from luminous bodies1 and which is also conveyed from all bodies to the eye1 so as to render them visible4 ,the various changes of direction by which the rays of light are affected1 7reflection1 #cbh refraction1 c417 ,descartes explained1 by considering the particles of light as small globules1 which change their direction when they impinge upon other bodies1 according to the laws of ,mechanics4 ,newton1 with a much more profound knowledge of ,mechanics than ,descartes possessed1 adopted1 in the most mature of his speculations1 nearly the same view of the nature of light2 and endeavoured to show that reflection1 refraction1 and other properties of light1 might be explained as the effects which certain forces1 emanating from the particles of bodies1 produce upon the luminiferous globules4 ,but though some of the properties of light could thus be accounted for by the assumption of particles emitted from luminous bodies1 and reflected or refracted by forces1 other properties came into view which would not admit of the same explanation4 ,the phenomena of diffraction 7the fringes which accompany shadows7 could never be truly represented by such an hypothesis1 in spite of many attempts which were made4 ,and the colours of thin plates1 which show the rays of light to be affected by an alternation of two different conditions at small intervals along their length1 led ,newton himself to incline1 often and strongly1 to some hypothesis of undulation4 ,the double refraction of ,iceland spar1 a phenomenon in itself very complex1 could1 it was found by ,huyghens1 be expressed with great simplicity by a certain hypothesis of undulations4 ,two hypotheses of the nature of the luminiferous medium were thus brought under consideration2 the one representing ,light as ,matter emitted from the luminous object1 the other1 as ,undulations propagated through a fluid4 ,these two hypotheses remained in presence of each other during the whole of the last century1 neither of them gaining any material advantage over the other1 though the greater part of mathematicians1 following ,newton1 embraced the emission theory4 ,but at the beginning of the present century1 an additional class of phenomena1 those of the interference of two rays of light1 were brought under #cbi consideration by ,dr4 ,young2 and these phenomena were strongly in favour of the undulatory theory1 while they were irreconcilable with the hypothesis of emission4 ,if it had not been for the original bias of ,newton and his school to the other side1 there can be little doubt that from this period light as well as sound would have been supposed to be propagated by undulations2 although in this case it was necessary to assume as the vehicle of such undulations a special medium or ether4 ,several points of the phenomena of vision no doubt remained unexplained by the undulatory theory1 as absorption1 and the natural colours of bodies2 but such facts1 though they did not confirm1 did not evidently contradict the theory of a ,luminiferous ,ether2 and the facts which such a theory did explain1 it explained with singular happiness and accuracy4 ,but before this ,undulatory ,theory could be generally accepted1 it was presented in an entirely new point of view by being combined with the facts of polarization4 ,the general idea of polarization must be illustrated hereafter2 but we may here remark that ,young and ,fresnel1 who had adopted the undulatory theory1 after being embarrassed for some time by the new facts which were thus presented to their notice1 at last saw that these facts might be explained by conceiving the vibrations to be transverse to the ray1 the motions of the particles being not backwards and forwards in the line in which the impulse travels1 but to the right and left of that line4 ,this conception of transverse vibrations1 though quite unforeseen1 had nothing in it which was at all difficult to reconcile with the general notion of an undulation4 ,we have described an undulation1 or wave1 as a certain condition or arrangement of the particles of the fluid successively transferred from one part of space to another3 and it is easily conceivable that this arrangement or wave may be produced by a lateral transfer of the particles from their quiescent positions4 ,this conception of transverse vibrations being accepted1 it was found that the explanation of the phenomena of polarization and of those of interference led to the same theory #ccj with a correspondence truly wonderful2 and this coincidence in the views1 collected from two quite distinct classes of phenomena1 was justly considered as an almost demonstrative evidence of the truth of this undulatory theory4 ,it remained to be considered whether the doctrine of transverse vibrations in a fluid could be reconciled with the principles of ,mechanics4 ,and it was found that by making certain suppositions1 in which no inherent improbability existed1 the hypothesis of transverse vibrations would explain the laws1 both of interference and of polarization of light1 in air and in crystals of all kinds1 with a surprizing fertility and fidelity4 ,thus the ,undulatory ,theory of ,light1 like the ,undulatory ,theory of ,sound1 is recommended by its conformity to the fundamental principle of the ,secondary ,mechanical ,sciences1 that the medium must be supposed to transmit its peculiar impulses according to the laws of ,mechanics4 ,although no one had previously dreamt of qualities being conveyed through a medium by such a process1 yet when it is once suggested as the only mode of explaining some of the phenomena1 there is nothing to prevent our accepting it entirely1 as a satisfactory theory for all the known laws of ,light4 #d4 ,heat4--,with regard to ,heat as with regard to ,light1 a fluid medium was necessarily assumed as the vehicle of the property4 ,during the last century1 this medium was supposed to be an emitted fluid4 ,and many of the ascertained ,laws of ,heat1 those which prevail with regard to its radiation more especially1 were well explained by this hypothesis#bbd4 ,other effects of heat1 however1 as for instance latent heat#bcd1 and the change of consistence of bodies#bdd1 were not satisfactorily brought into connexion with the hypothesis2 while #cca conduction#bed1 which at first did not appear to result from the fundamental assumption1 was to a certain extent explained as internal radiation4 ,note #bbd3 ,see the ,account of the ,theory of ,exchanges1 ,hist4 ,ind4 ,sc4 b4 x4 c4 i4 sect4 #b4 ,note #bcd3 ,ib4 c4 ii4 sect4 #c4 ,note #bdd3 ,ib4 c4 ii4 sect4 #b4 ,note #bed3 ,ib4 c4 i4 sect4 #g4 ,but it was by no means clear that an ,undulatory ,theory of ,heat might not be made to explain these phenomena equally well4 ,several philosophers inclined to such a theory2 and finally1 ,ampre showed that the doctrine that the heat of a body consists in the undulations of its particles propagated by means of the undulations of a medium1 might be so adjusted as to explain all which the theory of emission could explain1 and moreover to account for facts and laws which were out of the reach of that theory4 ,about the same time it was discovered by ,prof4 ,forbes and ,m4 ,nobili that radiant heat is1 under certain circumstances1 polarized4 ,now polarization had been most satisfactorily explained by means of transverse undulations in the case of light2 while all attempts to modify the emission theory so as to include polarization in it1 had been found ineffectual4 ,hence this discovery was justly considered as lending great countenance to the opinion that ,heat consists in the vibrations of its proper medium4 ,but what is this medium8 ,is it the same by which the impressions of ,light are conveyed8 ,this is a difficult question2 or rather it is one which we cannot at present hope to answer with certainty4 ,no doubt the connexion between ,light and ,heat is so intimate and constant1 that we can hardly refrain from considering them as affections of the same medium4 ,but instead of attempting to erect our systems on such loose and general views of connexion1 it is rather the business of the philosophers of the present day to determine the laws of the operation of heat1 and its real relation to light1 in order that we may afterwards be able to connect the theories of the two qualities4 ,perhaps in a more advanced state of our knowledge we may be able to state it as an ,axiom1 that two ,secondary ,qualities1 which are intimately connected in their causes and effects1 must be affections of the same ,medium4 #ccb ,but at present it does not appear safe to proceed upon such a principle1 although many writers1 in their speculations both concerning ,light and ,heat1 and concerning other properties1 have not hesitated to do so4 ,some other consequences follow from the ,idea of a ,medium which must be the subject of another chapter4 #ccc ,,chapter ,,iv4 ,,of ,,the ,,measure ,,of ,,secondary ,,qualities4 ,,sect4 ,i4--,scales of ,qualities in general4 ,,the ultimate object of our investigation in each of the ,secondary ,mechanical ,sciences1 is the nature of the processes by which the special impressions of sound1 light1 and heat1 are conveyed1 and the modifications of which these processes are susceptible4 ,and of this investigation1 as we have seen1 the necessary basis is the principle1 that these impressions are transmitted by means of a medium4 ,but before we arrive at this ultimate object1 we may find it necessary to occupy ourselves with several intermediate objects3 before we discover the cause1 it may be necessary to determine the laws of the phenomena4 ,even if we cannot immediately ascertain the mechanism of light or heat1 it may still be interesting and important to arrange and measure the effects which we observe4 ,the idea of a ,medium affects our proceeding in this research also4 ,we cannot measure ,secondary qualities in the same manner in which we measure ,primary qualities1 by a mere addition of parts4 ,there is this leading and remarkable difference1 that while both classes of qualities are susceptible of changes of magnitude1 primary qualities increase by addition of extension1 secondary1 by augmentation of intensity4 ,a space is doubled when another equal space is placed by its side2 one weight joined to another makes up the sum of the two4 ,but when one degree of warmth is combined with another1 or one shade of red colour with another1 we cannot in like manner talk of the sum4 ,the component parts do not evidently retain their #ccd separate existence2 we cannot separate a strong green colour into two weaker ones1 as we can separate a large force into two smaller4 ,the increase is absorbed into the previous amount1 and is no longer in evidence as a part of the whole4 ,and this is the difference which has given birth to the two words extended1 and intense4 ,that is extended which has 'partes extra partes1' parts outside of parts3 that is intense which becomes stronger by some indirect and unapparent increase of agency1 like the stretching of the internal springs of a machine1 as the term intense implies4 ,extended magnitudes can at will be resolved into the parts of which they were originally composed1 or any other which the nature of their extension admits2 their proportion is apparent2 they are directly and at once subject to the relations of number4 ,intensive magnitudes cannot be resolved into smaller magnitudes2 we can see that they differ1 but we cannot tell in what proportion2 we have no direct measure of their quantity4 ,how many times hotter than blood is boiling water8 ,the answer cannot be given by the aid of our feelings of heat alone4 ,the difference1 as we have said1 is connected with the fundamental principle that we do not perceive ,secondary qualities directly1 but through a ,medium4 ,we have no natural apprehension of light1 or sound1 or heat1 as they exist in the bodies from which they proceed1 but only as they affect our organs4 ,we can only measure them1 therefore1 by some ,scale supplied by their effects4 ,and thus while extended magnitudes1 as space1 time1 are measurable directly and of themselves2 intensive magnitudes1 as brightness1 loudness1 heat1 are measurable only by artificial means and conventional scales4 ,space1 time1 measure themselves3 the repetition of a smaller space1 or time1 while it composes a larger one1 measures it4 ,but for light and heat we must have ,photometers and ,thermometers1 which measure something which is assumed to be an indication of the quality in question4 ,in the one case1 the mode of applying the measure1 and the meaning of the number resulting1 are seen by intuition2 in the #cce other1 they are consequences of assumption and reasoning4 ,in the one case1 they are ,units1 of which the extension is made up2 in the other1 they are ,degrees by which the intensity ascends4 #b4 ,when we discover any property in a sensible quality1 which at once refers us to number or space1 we readily take this property as a measure2 and thus we make a transition from quality to quantity4 ,thus ,ptolemy in the third chapter of the ,first ,book of his ,harmonics begins thus3 ',as to the differences which exist in sounds both in quality and in quantity1 if we consider that difference which refers to the acuteness and graveness1 we cannot at once tell to which of the above two classes it belongs1 till we have considered the causes of such symptoms4' ,but at the end of the chapter1 having satisfied himself that grave sounds result from the magnitude of the string or pipe1 other things being equal1 he infers1 ',thus the difference of acute and grave appears to be a difference of quantity4' ,in the same manner1 in order to form ,secondary ,mechanical ,sciences respecting any of the other properties of bodies1 we must reduce these properties to a dependence upon quantity1 and thus make them subject to measurement4 ,we cannot obtain any sciential truths respecting the comparison of sensible qualities1 till we have discovered measures and scales of the qualities which we have to consider2 and accordingly1 some of the most important steps in such sciences have been the establishment of such measures and scales1 and the invention of the requisite instruments4 ,the formation of the mathematical sciences which rest upon the measures of the intensity of sensible qualities took place mainly in the course of the last century4 ,perhaps we may consider ,lambert1 a mathematician who resided in ,switzerland1 and published about #agej1 as the person who first clearly felt the importance of establishing such sciences4 ,his ,photometry1 ,pyrometry1 and ,hygrometry1 are examples of the systematic reduction of sensible qualities 7light1 heat1 moisture7 to modes of numerical measurement4 #ccf ,we now proceed to speak of such modes of measurement with regard to the most obvious properties of bodies4 ,,sect4 ,,ii4--,the ,musical ,scale4 #c4 ,,the establishment of the ,harmonic ,canon1 that is1 of a ,scale and ,measure of the musical place of notes1 in the relation of high and low1 was the first step in the science of ,harmonics4 ,the perception of the differences and relations of musical sounds is the office of the sense of hearing2 but these relations are fixed1 and rendered accurately recognizable by artificial means4 ',indeed1 in all the senses1' as ,ptolemy truly says in the opening of his ,harmonics1 'the sense discovers what is approximately true1 and receives accuracy from another quarter3 the reason receives the approximately-true from another quarter1 and discovers the accurate truth4' ,we can have no measures of sensible qualities which do not ultimately refer to the sense2--whether they do this immediately1 as when we refer ,colours to an assumed ,standard2 or mediately1 as when we measure ,heat by ,expansion1 having previously found by an appeal to sense that the expansion increases with the heat4 ,such relations of sensible qualities cannot be described in words1 and can only be apprehended by their appropriate faculty4 ,the faculty by which the relations of sounds are apprehended is a musical ear in the largest acceptation of the term4 ,in this signification the faculty is nearly universal among men2 for all persons have musical ears sufficiently delicate to understand and to imitate the modulations corresponding to various emotions in speaking2 which modulations depend upon the succession of acuter and graver tones4 ,these are the relations now spoken of1 and these are plainly perceived by persons who have very imperfect musical ears1 according to the common use of the phrase4 ,but the relations of tones which occur in speaking are somewhat indefinite2 and in forming that musical scale which is the basis of our science upon the subject1 we #ccg take the most definite and marked of such relations of notes2 such as occur1 not in speaking but in singing4 ,those musical relations of two sounds which we call the octave1 the fifth1 the fourth1 the third1 are recognized after a short familiarity with them4 ,these chords or intervals are perceived to have each a peculiar character1 which separates them from the relations of two sounds taken at random1 and makes it easy to know them when sung or played on an instrument2 and for most persons1 not difficult to sing the sounds in succession exactly1 or nearly correct4 ,these musical relations1 or concords1 then1 are the groundwork of our musical series of sounds4 ,but how are we to name these indescribable sensible characters8 how to refer1 with unerring accuracy1 to a type which exists only in our own perceptions8 ,we must have for this purpose a ,scale and a ,standard4 ,the ,musical ,scale is a series of eight notes1 ascending by certain steps from the first or key-note to the octave above it1 each of the notes being fixed by such distinguishable musical relations as we have spoken of above4 ,we may call these notes ,c1 ,d1 ,e1 ,f1 ,g1 ,a1 ,b1 c2 and we may then say that ,g is determined by its being a fifth above ,c2 ,d by its being a fourth below ,g2 ,e by its being a third above ,c2 and similarly of the rest4 ,it will be recollected that the terms a fifth1 a fourth1 a third1 have hitherto been introduced as expressing certain simple and indescribable musical relations among sounds1 which might have been indicated by any other names4 ,thus we might call the fifth the dominant1 and the fourth the subdominant1 as is done in one part of musical science4 ,but the names we have used1 which are the common ones1 are in fact derived from the number of notes which these intervals include in the scale obtained in the above manner4 ,the notes1 ,c1 ,d1 ,e1 ,f1 ,g1 being five1 the interval from ,c to ,g is a fifth1 and so of the rest4 ,the fixation of this scale gave the means of describing exactly any note which occurs in the scale1 and the method is easily applicable to notes above and below this range2 for in a series of sounds higher or lower by an octave than #cch this standard series1 the ear discovers a recurrence of the same relations so exact1 that a person may sometimes imagine he is producing the same notes as another when he is singing the same air an octave higher4 ,hence the next eight notes may be conveniently denoted by a repetition of the same letters1 as the first2 thus1 ,c1 ,d1 ,e1 ,f1 ,g1 ,a1 ,b1 c1 d1 e1 f1 g1 a1 b2 and it is easy to devise a continuation of such cycles4 ,and other admissible notes are designated by a further modification of the standard ones1 as by making each note flat or sharp2 which modification it is not necessary here to consider1 since our object is only to show how a standard is attainable1 and how it serves the ends of science4 ,we may observe1 however1 that the above is not an exact account of the first1 or early ,greek scale2 for that scale was founded on a primary division of the interval of two octaves 7the extreme range which it admitted7 into five tetrachords1 each tetrachord including the interval of a fourth4 ,all the notes of this series had different names borrowed from this division#bfd2 thus mese was the middle or key-note2 the note below it was lichanos mesn1 the next below was parypate mesn1 the next lower1 hypate mesn4 ,the fifth above mese was nete diazeugmenn1 the octave was nete hyperboln4 ,note #bfd3 ,burney's ,history of ,music1 vol4 i4 p4 #bh4 #d4 ,but supposing a complete system of such denominations established1 how could it be with certainty and rigour applied8 ,the human ear is fallible1 the organs of voice imperfectly obedient2 if this were not so1 there would be no such thing as a good ear or a good voice4 ,what means can be devised of finding at will a perfect concord1 a fifth or a fourth8 ,or supposing such concords fixed by an acknowledged authority1 how can they be referred to1 and the authority adduced8 ,how can we enact a ,standard of sounds8 ,a ,standard was discovered in the ,monochord4 ,a musical string properly stretched1 may be made to produce different notes1 in proportion as we intercept a longer or shorter portion1 and make this portion #cci vibrate4 ,the relation of the length of the strings which thus sound the two notes ,g and ,c is fixed and constant1 and the same is true of all other notes4 ,hence the musical interval of any notes of which we know the places in the musical scale1 may be reproduced by measuring the lengths of string which are known to give them4 ,if ,c be of the length #ahj1 ,d is #afj1 ,e is #add1 ,f is #ace1 ,g is #abj2 and thus the musical relations are reduced to numerical relations1 and the monochord is a complete and perfect ,tonometer4 ,we have here taken the length of the string as the measure of the tone3 but we may observe that there is in us a necessary tendency to assume that the ground of this measure is to be sought in some ulterior cause2 and when we consider the matter further1 we find this cause in the frequency of these vibrations of the string4 ,the truth that the same note must result from the same frequency of vibration is readily assented to on a slight suggestion of experience4 ,thus ,mersenne#bgd1 when he undertakes to determine the frequency of vibrations of a given sound1 says ',supponendum est quoscunque nervos et quaslibet chordas unisonum facientes eundem efficere numerum recursuum eodem vel equali tempore1 quod perpetu constat experienti4' ,and he proceeds to apply it to cases where experience could not verify this assertion1 or at least had not verified it1 as to that of pipes4 ,note #bgd3 ,harmonia1 lib4 ii4 prop4 #ai4 ,the pursuit of these numerical relations of tones forms the science of ,harmonics2 of which here we do not pretend to give an account1 but only to show1 how the invention of a ,scale and ,nomenclature1 a ,standard and ,measure of the tone of sounds1 is its necessary basis4 ,we will therefore now proceed to speak of another subject2 colour4 ,,sect4 ,,iii4--,scales of ,colour4 #e4 ,the ,prismatic ,scale of ,colour4--,a ,,scale of ,colour must depend originally upon differences #cdj discernible by the eye1 as a scale of notes depends on differences perceived by the ear4 ,in one respect the difficulty is greater in the case of the visible qualities1 for there are no relations of colour which the eye peculiarly singles out and distinguishes1 as the ear selects and distinguishes an octave or a fifth4 ,hence we are compelled to take an arbitrary scale2 and we have to find one which is fixed1 and which includes a proper collection of colours4 ,the prismatic spectrum1 or coloured image produced when a small beam of light passes obliquely through any transparent surface 7as the surface of a prism of glass17 offers an obvious ,standard as far as it is applicable4 ,accordingly colours have1 for various purposes1 been designated by their place in the spectrum1 ever since the time of ,newton2 and we have thus a means of referring to such colours as are included in the series red1 orange1 yellow1 green1 blue1 violet1 indigo1 and the intermediate tints4 ,but this scale is not capable of numerical precision4 ,if the spectrum could be exactly defined as to its extremities1 and if these colours occupied always the same proportional part of it1 we might describe any colour in the above series by the measure of its position4 ,but the fact is otherwise4 ,the spectrum is too indefinite in its boundaries to afford any distinct point from which we may commence our measures2 and moreover the spectra produced by different transparent bodies differ from each other4 ,newton had supposed that the spectrum and its parts were the same1 so long as the refraction was the same2 but his successors discovered that1 with the same amount of refraction in different kinds of glass1 there are different magnitudes of the spectrum2 and what is still worse with reference to our present purpose1 that the spectra from different glasses have the colours distributed in different proportions4 ,in order1 therefore1 to make the spectrum the scale of colour1 we must assume some fixed substance2 for instance1 we may take water1 and thus a series approaching to the colours of the rainbow will be our standard4 ,but we should still have an extreme difficulty in applying such a rule4 ,the distinctions of #cda colour which the terms of common language express1 are not used with perfect unanimity or with rigorous precision4 ,what one person calls bluish green another calls greenish blue4 ,nobody can say what is the precise boundary between red and orange4 ,thus the prismatic scale of colour was incapable of mathematical exactness1 and this inconvenience was felt up to our own times4 ,but this difficulty was removed by a curious discovery of ,wollaston and ,fraunhofer2 who found that there are1 in the solar spectrum1 certain fine black ,lines which occupy a definite place in the series of colours1 and can be observed with perfect precision4 ,we have now no uncertainty as to what coloured light we are speaking of1 when we describe it as that part of the spectrum in which ,fraunhofer's ,line ,c or ,d occurs4 ,and thus1 by this discovery1 the prismatic spectrum of sunlight became1 for certain purposes1 an exact ,chromatometer4 #f4 ,newton's ,scale of ,colours4--,still1 such a standard1 though definite1 is arbitrary and seemingly anomalous4 ,the lines ,a1 ,b1 ,c1 ,d1 c41 of ,fraunhofer's spectrum are distributed without any apparent order or law2 and we do not1 in this way1 obtain numerical measures1 which is what1 in all cases1 we desire to have4 ,another discovery of ,newton1 however1 gives us a spectrum containing the same colours as the prismatic spectrum1 but produced in another way1 so that the colours have a numerical relation4 ,i speak of the laws of the ,colours of ,thin ,plates4 ,the little rainbows which we sometimes see in the cracks of broken glass are governed by fixed and simple laws4 ,the kind of colour produced at any point depends on the thickness of the thin plate of air included in the fissure4 ,if the thickness be eight-millionths of an inch1 the colour is orange1 if fifteen-millionths of an inch1 we have green1 and so on2 and thus these numbers1 which succeed each other in a regular order from red to indigo1 give a numerical measure of each colour2 which measure1 when we pursue the subject1 we find is one of the bases of all optical theory4 ,the series of colours obtained from plates of air of gradually increasing thickness is called #cdb ,newton's ,scale of ,colours2 but we may observe that this is not precisely what we are here speaking of1 a scale of simple colours2 it is a series produced by certain combinations1 resulting from the repetition of the first spectrum1 and is mainly useful as a standard for similar phenomena1 and not for colour in general4 ,the real scale of colour is to be found1 as we have said1 in the numbers which express the thickness of the producing film2--in the length of a fit in ,newton's phraseology1 or the length of an undulation in the modern theory4 #g4 ,scales of ,impure ,colours4--,the standards just spoken of include 7mainly at least7 only pure and simple colours2 and however complete these standards may be for certain objects of the science of optics1 they are insufficient for other purposes4 ,they do not enable us to put in their place mixed and impure colours4 ,and there is1 in the case of colour1 a difficulty already noticed1 which does not occur in the case of sound2 two notes1 when sounded together1 are not necessarily heard as one2 they are recognized as still two1 and as forming a concord or a discord4 ,but two colours form a single colour2 and the eye cannot1 in any way1 distinguish between a green compound of blue and yellow1 and the simple1 undecomposable green of the spectrum4 ,by composition of three or more colours1 innumerable new colours may be generated which form no part of the prismatic series2 and by such compositions is woven the infinitely varied web of colour which forms the clothing of nature4 ,how are we to classify and arrange all the possible colours of objects1 so that each shall have a place and name8 ,how shall we find a chromatometer for impure as well as for pure colour8 ,though no optical investigations have depended on a scale of impure colours1 such a scale has been wanted and invented for other purposes2 for instance1 in order to identify and describe objects of natural history4 ,not to speak of earlier essays1 we may notice ,werner's ,nomenclature of ,colours1 devised for the purpose of describing minerals4 ,this scale of colour was far superior to any which had previously been promulgated4 #cdc ,it was1 indeed1 arbitrary in the selection of its degrees1 and in a great measure in their arrangement2 and the colours were described by the usual terms1 though generally with some added distinction2 as blackish green1 bluish green1 apple-green1 emerald-green4 ,but the great merit of the scale was its giving a fixed conventional meaning to these terms1 so that they lost much of their usual vagueness4 ,thus apple-green did not mean the colour of any green apple casually taken2 but a certain definite colour which the student was to bear in mind1 whether or not he had ever seen an apple of that exact hue4 ,the words were not a description1 but a record of the colour3 the memory was to retain a sensation1 not a name4 ,the imperfection of the system 7arising from its arbitrary form7 was its incompleteness3 however well it served for the reference of the colours which it did contain1 it was applicable to no others2 and thus though ,werner's enumeration extended to more than a hundred colours1 there occur in nature a still greater number which cannot be exactly described by means of it4 ,in such cases the unclassed colour is1 by the ,wernerians1 defined by stating it as intermediate between two others3 thus we have an object described as between emerald-green and grass-green4 ,the eye is capable of perceiving a gradation from one colour to another2 such as may be produced by a gradual mixture in various ways4 ,and if we image to ourselves such a mixture1 we can compare with it a given colour4 ,but in employing this method we have nothing to tell us in what part of the scale we must seek for an approximation to our unclassed colour4 ,we have no rule for discovering where we are to look for the boundaries of the definition of a colour which the ,wernerian series does not supply4 ,for it is not always between contiguous members of the series that the undescribed colour is found4 ,if we place emerald-green between apple-green and grass-green1 we may yet have a colour intermediate between emerald-green and leek-green2 and1 in fact1 the ,wernerian series of colours is destitute #cdd of a principle of self-arrangement and gradation2 and is thus necessarily and incurably imperfect4 #h4 ,we should have a complete ,scale of ,colours1 if we could form a series including all colours1 and arranged so that each colour was intermediate in its tint between the adjacent terms of the series2 for then1 whether we took many or few of the steps of the series for our standard terms1 the rest could be supplied by the law of continuity2 and any given colour would either correspond to one of the steps of our scale or fall between two intermediate ones4 ,the invention of a ,chromatometer for ,impure ,colours1 therefore1 requires that we should be able to form all possible colours by such intermediation in a systematic manner2 that is1 by the mixture or combination of certain elementary colours according to a simple rule3 and we are led to ask whether such a process has been shown to be possible4 ,the colours of the prismatic spectrum obviously do form a continuous series2 green is intermediate between its neighbours yellow and blue1 orange between red and yellow2 and if we suppose the two ends of the spectrum bent round to meet each other1 so that the arrangement of the colours may be circular1 the violet and indigo will find their appropriate place between the blue and red4 ,and all the interjacent tints of the spectrum1 as well as the ones just named1 will result from such an arrangement4 ,thus all the pure colours are produced by combinations two and two of three primary colours1 ,red1 ,yellow1 and ,blue3 and the question suggests itself whether these three are not really the only ,primary ,colours1 and whether all the impure colours do not arise from mixtures of the three in various proportions4 ,there are various modes in which this suggestion may be applied to the construction of a scale of colours2 but the simplest1 and the one which appears really to verify the conjecture that all possible colours may be so exhibited1 is the following4 ,a certain combination of red1 yellow1 and blue1 will produce black1 or pure grey1 and when diluted1 will give all the shades of grey which intervene between #cde black and white4 ,by adding various shades of grey1 then1 to pure colours1 we may obtain all the possible ternary combinations of red1 yellow1 and blue2 and in this way it is found that we exhaust the range of colours4 ,thus the circle of pure colours of which we have spoken may be accompanied by several other circles1 in which these colours are tinged with a less or greater shade of grey2 and in this manner it is found that we have a perfect chromatometer2 every possible colour being exhibited either exactly or by means of approximate and contiguous limits4 ,the arrangement of colours has been brought into this final and complete form by ,m4 ,merime1 whose ,chromatic ,scale is published by ,m4 ,mirbel in his ,elements of ,botany4 ,we may observe that such a standard affords us a numerical exponent for every colour by means of the proportions of the three primary colours which compose it2 or1 expressing the same result otherwise1 by means of the pure colour which is involved1 and the proportion of grey by which it is rendered impure4 ,in such a scale the fundamental elements would be the precise tints of red1 yellow1 and blue which are found or assumed to be primary2 the numerical exponents of each colour would depend upon the arbitrary number of degrees which we interpose between each two primary colours2 and between each pure colour and absolute blackness4 ,no such numerical scale has1 however1 as yet1 obtained general acceptation#bhd4 ,note #bhd3 ,the reference to ,fraunhofer's ,lines1 as a means of determining the place of a colour in the prismatic series1 has been objected to1 because1 as is asserted1 the colours which are in the neighbourhood of each line vary with the position of the sun1 state of the atmosphere and the like4 ,it is very evident that coloured light refracted by the prism will not give the same spectrum as white light4 ,the spectrum given by white light is of course the one here meant4 ,it is an usual practice of optical experimenters to refer to the colours of such a spectrum1 defining them by ,fraunhofer's ,lines4 ,i do not know whether it needs explanation that the 'first spectrum' in ,newton's rings is a ring of the prismatic colours4 ,i have not had an opportunity of consulting ,lambert's ,photometria1 sive de mensura et gradibus luminis1 colorum1 et umbr1 published in #agfj1 nor ,mayer's ,commentatio de ,affinitate ,colorum1 7#ageh71 in which1 ,i believe1 he describes a chromatometer4 ,the present work is not intended to be complete as a history2 and ,i hope ,i have given sufficient historical detail to answer its philosophical purpose4 #cdf ,,sect4 ,,iv4--,scales of ,light4 #i4 ,photometer4--,,another instrument much needed in optical researches is a ,photometer1 a measure of the intensity of light4 ,in this case1 also1 the organ of sense1 the eye1 is the ultimate judge2 nor has any effect of light1 as light1 yet been discovered which we can substitute for such a judgment4 ,all instruments1 such as that of ,leslie1 which employ the heating effect of light1 or at least all that have hitherto been proposed1 are inadmissible as photometers4 ,but though the eye can judge of two surfaces illuminated by light of the same colour1 and can determine when they are equally bright1 or which is the brighter1 the eye can by no means decide at sight the proportion of illumination4 ,how much in such judgments we are affected by contrast1 is easily seen when we consider how different is the apparent brightness of the moon at mid-day and at midnight1 though the light which we receive from her is1 in fact1 the same at both periods4 ,in order to apply a scale in this case1 we must take advantage of the known numerical relations of light4 ,we are certain that if all other illumination be excluded1 two equal luminaries1 under the same circumstances1 will produce an illumination twice as great as one does2 and we can easily prove1 from mathematical considerations1 that if light be not enfeebled by the medium through which it passes1 the illumination on a given surface will diminish as the square of the distance of the luminary increases4 ,if1 therefore1 we can by taking a fraction thus known of the illuminating effect of one luminary1 make it equal to the total effect of another1 of which equality the eye is a competent judge1 we compare the effects of the two luminaries4 ,in order to make this comparison we may1 with ,rumford1 look at the shadows of the same object made by the two lights1 #cdg or with ,ritchie1 we may view the brightness produced on two contiguous surfaces1 framing an apparatus so that the equality may be brought about by proper adjustment2 and thus a measure will become practicable4 ,or we may employ other methods as was done by ,wollaston#bid1 who reduced the light of the sun by observing it as reflected from a bright globule1 and thus found the light of the sun to be #aj1jjj1jjj1jjj times that of ,sirius1 the brightest fixed star4 ,all these methods are inaccurate1 even as methods of comparison2 and do not offer any fixed or convenient numerical standard2 but none better have yet been devised#cjd4 ,note #bid3 ,phil4 ,trans4 #ahbj1 p4 #ai4 ,note #cjd3 ,improved ,photometers have been devised by ,professor ,wheatstone1 ,professor ,potter1 and ,professor ,steinheil2 but they depend upon principles similar to those mentioned in the text4 #aj4 ,cyanometer4--,as we thus measure the brightness of a colourless light1 we may measure the intensity of any particular colour in the same way2 that is1 by applying a standard exhibiting the gradations of the colour in question till we find a shade which is seen to agree with the proposed object4 ,such an instrument we have in the ,cyanometer1 which was invented by ,saussure for the purpose of measuring the intensity of the blue colour of the sky4 ,we may introduce into such an instrument a numerical scale1 but the numbers in such a scale will be altogether arbitrary4 ,,sect4 ,v4--,scales of ,heat4 #aa4 ,thermometers4--,,when we proceed to the sensation of heat1 and seek a measure of that quality1 we find1 at first sight1 new difficulties4 ,our sensations of this kind are more fluctuating than those of vision2 for we know that the same object may feel warm to one hand and cold to another at the same instant1 if the hands have been previously cooled and warmed respectively4 ,nor can we obtain here1 as in the case of light1 self-evident numerical relations of the heat communicated in given circumstances2 for we know that the #cdh effect so produced will depend on the warmth of the body to be heated1 as well as on that of the source of heat2 the summer sun1 which warms our bodies1 will not augment the heat of a red-hot iron4 ,the cause of the difference of these cases is1 that bodies do not receive the whole of their heat1 as they receive the whole of their light1 from the immediate influence of obvious external agents4 ,there is no readily-discovered absolute cold1 corresponding to the absolute darkness which we can easily produce or imagine4 ,hence we should be greatly at a loss to devise a ,thermometer1 if we did not find an indirect effect of heat sufficiently constant and measurable to answer this purpose4 ,we discover1 however1 such an effect in the expansion of bodies by the effect of heat4 #ab4 ,many obvious phenomena show that air1 under given circumstances1 expands by the effect of heat2 the same is seen to be true of liquids1 as of water1 and spirit of wine2 and the property is found to belong also to the metallic fluid1 quicksilver4 ,a more careful examination showed that the increase of bulk in some of these bodies by increase of ,heat was a fact of a nature sufficiently constant and regular to afford a means of measuring that previously intangible quality2 and the ,thermometer was invented4 ,there were1 however1 many difficulties to overcome1 and many points to settle1 before this instrument was fit for the purposes of science4 ,an explanation of the way in which this was done necessarily includes an important chapter of the history of ,thermotics4 ,we must now1 therefore1 briefly notice historically the progress of the ,thermometer4 ,the leading steps of this progress1 after the first invention of the instrument1 were--,the establishment of fixed points in the thermometric scale--,the comparison of the scales of different substances--,and the reconcilement of these differences by some method of interpreting them as indications of the absolute quantity of heat4 #ac4 ,it would occupy too much space to give in detail the history of the successive attempts by which #cdi these steps were effected4 ,a thermometer is described by ,bacon under the title ,vitrum ,calendare2 this was an air thermometer4 ,newton used a thermometer of linseed oil1 and he perceived that the first step requisite to give value to such an instrument was to fix its scale2 accordingly he proposed his ,scala ,graduum ,caloris#cad4 ,but when thermometers of different liquids were compared1 it appeared1 from their discrepancies1 that this fixation of the scale of heat was more difficult than had been supposed4 ,it was1 however1 effected4 ,newton had taken freezing water1 or rather thawing snow1 as the zero of his scale1 which is really a fixed point2 ,halley and ,amontons discovered 7in #afic and #agjb7 that the heat of boiling water is another fixed point2 and ,daniel ,gabriel ,fahrenheit1 of ,dantzig1 by carefully applying these two standard points1 produced1 about #agad1 thermometers1 which were constantly consistent with each other4 ,this result was much admired at the time1 and was1 in fact1 the solution of the problem just stated1 the fixation of the scale of heat4 ,note #cad3 ,phil4 ,trans4 #agja4 #ad4 ,but the scale thus obtained is a conventional not a natural scale4 ,it depends upon the fluid employed for the thermometer4 ,the progress of expansion from the heat of freezing to that of boiling water is different for mercury1 oil1 water1 spirit of wine1 air4 ,a degree of heat which is half-way between these two standard points according to a mercurial thermometer1 will be below the half-way point in a spirit thermometer1 and above it in an air thermometer4 ,each liquid has its own march in the course of its expansion4 ,deluc and others compared the marches of various liquids1 and thus made what we may call a concordance of thermometers of various kinds4 #ae4 ,here the question further occurs3 ,is there not some natural measure of the degrees of heat8 ,it appears certain that there must be such a measure1 and that by means of it all the scales of different liquids must be reconciled4 ,yet this does not seem to have occurred at once to men's minds4 ,deluc1 in speaking #cej of the researches which we have just mentioned1 says#cbd1 ',when ,i undertook these experiments1 it never once came into my thoughts that they could conduct me with any probability to a table of real degrees of heat4 ,but hope grows with success1 and desire with hope4' ,accordingly he pursued this inquiry for a long course of years4 ,note #cbd3 ,modif4 de l',atmosph4 #aghb1 p4 #cjc4 ,what are the principles by which we are to be guided to the true measure of heat8 ,here1 as in all the sciences of this class1 we have the general principle1 that the secondary quality1 ,heat1 must be supposed to be perceived in some way by a material ,medium or ,fluid4 ,if we take that which is1 perhaps1 the simplest form of this hypothesis1 that the heat depends upon the quantity of this fluid1 or ,caloric1 which is present1 we shall find that we are led to propositions which may serve as a foundation for a natural measure of heat4 ,the ,method of ,mixtures is one example of such a result4 ,if we mix together two pints of water1 one hot and one cold1 is it not manifest that the temperature of the mixture must be midway between the two8 ,each of the two portions brings with it its own heat4 ,the whole heat1 or caloric1 of the mixture is the sum of the two2 and the heat of each half must be the half of this sum1 and therefore its temperature must be intermediate between the temperatures of the equal portions which were mixed4 ,deluc made experiments founded upon this principle1 and was led by them to conclude that 'the dilatations of mercury follow an accelerated march for successive equal augmentations of heat4' ,but there are various circumstances which prevent this method of mixtures from being so satisfactory as at first sight it seems to promise to be4 ,the different capacities for heat of different substances1 and even of the same substance at different temperatures1 introduce much difficulty into the experiments2 and this path of inquiry has not yet led to a satisfactory result4 #cea #af4 ,another mode of inquiring into the natural measure of heat is to seek it by researches on the law of cooling of hot bodies4 ,if we assume that the process of cooling of hot bodies consists in a certain material heat flying off1 we may1 by means of certain probable hypotheses1 determine mathematically the law according to which the temperature decreases as time goes on2 and we may assume that to be the true measure of temperature which gives to the experimental law of cooling the most simple and probable form4 ,it appears evident from the most obvious conceptions which we can form of the manner in which a body parts with its superabundant heat1 that the hotter a body is1 the faster it cools2 though it is not clear without experiment1 by what law the rate of cooling will depend upon the heat of the body4 ,newton took for granted the most simple and seemingly natural law of this dependence3 he supposed the rate of cooling to be proportional to the temperature1 and from this supposition he could deduce the temperature of a hot iron1 calculating from the original temperature and the time during which it had been cooling4 ,by calculation founded on such a basis1 he graduated his thermometer4 #ag4 ,but a little further consideration showed that the rate of cooling of a hot body depended upon the temperature of the surrounding bodies1 as well as upon its own temperature4 ,prevost's ,theory of ,exchanges#ccd was propounded with a view of explaining this dependence1 and was generally accepted4 ,according to this theory1 all bodies radiate heat to one another1 and are thus constantly giving and receiving heat2 and a body which is hotter than surrounding bodies1 cools itself1 and warms the surrounding1 bodies1 by an exchange of heat for heat1 in which they are the gainers4 ,hence if be the temperature of the bodies1 or of the space1 by which the hot body is surrounded1 and t the temperature of the hot body1 the rate of cooling will depend #ceb upon the excess of the radiation for a temperature t1 above the radiation for a temperature 4 ,note #ccd3 ,recherches sur la ,chaleur1 #agia4 ,hist4 ,ind4 ,sc4 b4 x4 c4 i4 sect4 #b4 ,accordingly1 in the admirable researches of ,,mm4 ,dulong and ,petit upon the cooling of bodies1 it was assumed that the rate of cooling of the hot body was represented by the excess of ,f7 t7 above ,f772 where ,f represented some mathematical function1 that is1 some expression obtained by arithmetical operations from the temperatures t and 2 although what these operations are to be1 was left undecided1 and was in fact determined by the experiments4 ,and the result of their investigations was1 that the function is of this kind3 when the temperature increases by equal intervals1 the function increases in a continued geometric proportion#cdd4 ,this was1 in fact1 the same law which had been assumed by ,newton and others1 with this difference1 that they had neglected the term which depends upon the temperature of the surrounding space4 ,note #cdd3 ,the formula for the rate of cooling is ma7 t7 - ma1 where the quantity m depends upon the nature of the body1 the state of its surface1 and other circumstances4--,ann4 ,chim4 vii4 #aej4 #ah4 ,this law falls in so well with the best conceptions we can form of the mechanism of cooling upon the supposition of a radiant fluid caloric1 that it gives great probability to the scale of temperature on which the simplicity of the result depends4 ,now the temperatures in the formul just referred to were expressed by means of the air thermometer4 ,hence ,,mm4 ,dulong and ,petit justly state1 that while all different substances employed as thermometers give different laws of thermotical phenomena1 their own success in obtaining simple and general laws by means of the air thermometer1 is a strong recommendation of that as the natural scale of heat4 ,they add#ced1 ',the well-known uniformity of the principal physical properties of all gases1 and especially the perfect identity of their laws of dilatation by heat1 a very important discovery of #cec ,dalton and ,gay ,lussac#cfd1 make it very probable that in this class of bodies the disturbing causes have not the same influence as in solids and liquids2 and consequently that the changes of bulk produced by the action of heat are here in a more immediate dependence on the force which produces them4' ,note #ced3 ,annales de ,chimie1 vii4 #aec4 ,note #cfd3 ,hist4 ,ind4 ,sc4 b4 x4 c4 ii4 sect4 #a4 #ai4 ,still we cannot consider this point as settled till we obtain a more complete theoretical insight into the nature of heat itself4 ,if it be true that heat consists in the vibrations of a fluid1 then1 although1 as ,ampre has shown#cgd1 the laws of radiation will1 on mathematical grounds1 be the same as they are on the hypothesis of emission1 we cannot consider the natural scale of heat as determined1 till we have discovered some means of measuring the caloriferous vibrations as we measure luminiferous vibrations4 ,we shall only know what the quantity of heat is when we know what heat itself is2--when we have obtained a theory which satisfactorily explains the manner in which the substance or medium of heat produces its effects4 ,when we see how radiation and conduction1 dilatation and liquefaction1 are all produced by mechanical changes of the same fluid1 we shall then see what the nature of that change is which dilatation really measures1 and what relation it bears to any more proper standard of heat4 ,note #cgd3 ,ib4 c4 iv4 ,we may add1 that while our thermotical theory is still so imperfect as it is1 all attempts to divine the true nature of the relation between light and heat are premature1 and must be in the highest degree insecure and visionary4 ,speculations in which1 from the general assumption of a caloriferous and luminiferous medium1 and from a few facts arbitrarily selected and loosely analysed1 a general theory of light and heat is asserted1 are entirely foreign to the course of inductive science1 and cannot lead to any stable and substantial truth4 #bj4 ,other ,instruments for measuring ,heat4--,it does not belong to our present purpose to speak of #ced instruments of which the object is to measure1 not sensible qualities1 but some effect or modification of the cause by which such qualities are produced3 such1 for instance1 are the ,calorimeter1 employed by ,lavoisier and ,laplace1 in order to compare the ,specific ,heat of different substances2 and the ,actinometer1 invented by ,sir ,john ,herschel1 in order to determine the effect of the ,sun's ,rays by means of the heat which they communicate in a given time2 which effect is1 as may readily be supposed1 very different under different circumstances of atmosphere and position4 ,the laws of such effects may be valuable contributions to our knowledge of heat1 but the interpretation of them must depend on a previous knowledge of the relations which temperature bears to heat1 according to the views just explained4 ,,sect4 ,,vi4--,scales of other ,qualities4 #ba4 ,,before quitting the subject of the measures of sensible qualities1 we may observe that there are several other such qualities for which it would be necessary to have scales and means of measuring1 in order to make any approach to science on such subjects4 ,this is true1 for instance1 of ,tastes and ,smells4 ,indeed some attempts have been made towards a classification of the ,tastes of sapid substances1 but these have not yet assumed any satisfactory or systematic character2 and ,i am not aware that any instrument has been suggested for measuring either the ,flavour or the ,odour of bodies which possess such qualities4 #bb4 ,quality of ,sounds4--,the same is true of that kind of difference in sounds which is peculiarly termed their ,quality2 that character by which1 for instance1 the sound of a flute differs from that of a hautbois1 when the note is the same2 or a woman's voice from a boy's4 #bc4 ,articulate ,sounds4--,there is also in sounds another difference1 of which the nature is still obscure1 but in reducing which to rule1 and consequently to measure1 some progress has nevertheless been made4 #cee ,i speak of the differences of sound considered as articulate4 ,classifications of the sounds of the usual alphabets have been frequently proposed2 for instance1 that which arranges the ,consonants in the following groups13 ,sharp4 ,flat4 ,sharp ,aspirate4 ,flat ,aspirate4 ,nasal4 p b ph 7f7 bh 7v7 m k g 7hard7 kh gh ng t d th 7sharp7 th 7flat7 n s z sh zh ,it is easily perceived that the relations of the sounds in each of these horizontal lines are analogous2 and accordingly the rules of derivation and modification of words in several languages proceed upon such analogies4 ,in the same manner the ,vowels may be arranged in an order depending on their sound4 ,but to make such arrangements fixed and indisputable1 we ought to know the mechanism by which such modifications are caused4 ,instruments have been invented by which some of these sounds can be imitated2 and if such instruments could be made to produce the above series of articulate sounds1 by connected and regular processes1 we should find1 in the process1 a measure of the sound produced4 ,this has been in a great degree effected for the ,vowels by ,professor ,willis's artificial mode of imitating them4 ,for he finds that if a musical reed be made to sound through a cylindrical pipe1 we obtain by gradually lengthening the cylindrical pipe1 the series of vowels ,i1 ,e1 ,a1 ,o1 ,u1 with intermediate sounds#chd4 ,in this instrument1 then1 the length of the pipe would determine the vowel1 and might be used numerically to express it4 ,such an instrument so employed would be a measure of vowel quality1 and might be called a ,phthongometer4 ,note #chd3 ,camb4 ,trans4 vol4 iii4 p4 #bci4 ,our business at present1 however1 is not with instruments which might be devised for measuring sensible qualities1 but with those which have been so used1 and have thus been the basis of the sciences in which #cef such qualities are treated of2 and this we have now done sufficiently for our present purpose4 #bd4 ,there is another ,idea which1 though hitherto very vaguely entertained1 has had considerable influence in the formation1 both of the sciences spoken of in the present ,book1 and on others which will hereafter come under our notice3 namely1 the ,idea of ,polarity4 ,this ,idea will be the subject of the ensuing ,book4 ,and although this ,idea forms a part of the basis of various other extensive portions of science1 as ,optics and ,chemistry1 it occupies so peculiarly conspicuous a place in speculations belonging to what ,i have termed the ,mechanico-,chemical ,sciences1 7,magnetism and ,electricity17 that ,i shall designate the discussion of the ,idea of ,polarity as the ,philosophy of those ,sciences4 #ceg ,,book ,v4 ,,the ,,philosophy ,,of ,,the ,,mechanico-,,chemical ,,sciences4 ,en donnant ces cts le nom de poles1 j'appelerai polarisation la modification qui donne la lumire des proprits relatives ces poles4 ,j'ai tard jusqu' prsent admettre ce terme dans la description des phnomnes physiques dont il est question2 je n'ai pas os l'introduire dans les mmoires o j'ai publi mes dernires expriences2 mais les varits qu'offre ce nouveau phnomne1 et la difficult de les dcrire1 me forcent admettre cette nouvelle expression1 qui signifie simplement la modification que la lumire a subie en acqurant de nouvelles proprits qui ne sont pas relatives la direction du rayon1 mais seulement ses cts considrs angles droits et dans un plan perpendiculaire sa direction4 ,malus 7#ahaa71 ,mm4 de ,inst4 tom4 xi4 p4 #ajf4 #cei ,,book ,v4 ,,the ,,philosophy ,,of ,,the ,,mechanico-,,chemical ,,sciences4 ,,chapter ,i4 ,,attempts ,,at ,,the ,,scientific ,,application ,,of ,,the ,,idea ,,of ,,polarity4 #a4 ,,in some of the mechanical sciences1 as ,magnetism and ,optics1 the phenomena are found to depend upon position 7the position of the magnet1 or of the ray of light17 in a peculiar alternate manner4 ,this dependence1 as it was first apprehended1 was represented by means of certain conceptions of space and force1 as for instance by considering the two ,poles of a magnet4 ,but in all such modes of representing these alternations by the conceptions borrowed from other ideas1 a closer examination detected something superfluous and something defective2 and in proportion as the view which philosophers took of this relation was gradually purified from these incongruous elements1 and was rendered more general and abstract by the discovery of analogous properties in new cases1 it was perceived that the relation could not be adequately apprehended without considering it as involving a peculiar and independent ,idea1 which we may designate by the term ,polarity4 ,we shall trace some of the forms in which this ,idea has manifested itself in the history of science4 ,in doing so we shall not begin1 as in other ,books of this work we have done1 by speaking of the notion as it is #cfj employed in common use3 for the relation of ,polarity is of so abstract and technical a nature1 that it is not employed1 at least in any distinct and obvious manner1 on any ordinary or practical occasions4 ,the idea belongs peculiarly to the region of speculation3 in persons of common habits of thought it is probably almost or quite undeveloped2 and even most of those whose minds have been long occupied by science1 find a difficulty in apprehending it in its full generality and abstraction1 and stript of all irrelevant hypothesis4 #b4 ,magnetism4--,the name and the notion of ,poles were first adopted in the case of a magnet4 ,if we have two magnets1 their extremities attract and repel each other alternatively4 ,if the first end of the one attract the first end of the other1 it repels the second end1 and conversely4 ,in order to express this rule conveniently1 the two ends of each magnet are called the north pole and the south pole respectively1 the denominations being borrowed from the poles of the earth and heavens4 ',these poles1' as ,gilbert says#ae1 'regulate the motions of the celestial spheres and of the earth4 ,in like manner the magnet has its poles1 a northern and a southern one2 certain and determined points constituted by nature in the stone1 the primary terms of its motions and effects1 the limits and governors of many actions and virtues4' ,note #ae3 ,de ,magn4 lib4 i4 c4 iii4 ,the nature of the opposition of properties of which we speak may be stated thus3 ,the ,north pole of one magnet attracts the ,south pole of another magnet4 ,the ,north pole of one magnet repels the ,north pole of another magnet4 ,the ,south pole of one magnet repels the ,south pole of another magnet4 ,the ,south pole of one magnet attracts the ,north pole of another magnet4 ,it will be observed that the contrariety of position which is indicated by putting the ,south pole for the ,north pole in either magnet1 is accompanied by the #cfa opposition of mechanical effect which is expressed by changing attraction into repulsion and repulsion into attraction3 and thus we have the general feature of ,polarity1--,a contrast of properties corresponding to a contrast of positions4 #c4 ,electricity4--,when the phenomena of ,electricity came to be studied1 it appeared that they involved relations in some respects ,analogous to those of magnetism4 ,two kinds of electricity were distinguished1 the positive and the negative2 and it appeared that two bodies electrized positively1 or two electrized negatively1 repelled each other1 like two north or two south magnetic poles2 while a positively and a negatively electrized body attracted each other1 like the north and south poles of two magnets4 ,in conductors of an oblong form1 the electricity could easily be made to distribute itself so that one end should be positively and one end negatively electrized2 and then such conductors acted on each other exactly as magnets would do4 ,but in conductors1 however electrized1 there is no peculiar point which can permanently be considered as the pole4 ,the distribution of electricity in the conductor depends upon external circumstances3 and thus1 although the phenomena offer the general character of polarity--alternative results corresponding to alternative positions1--they cannot be referred to poles4 ,some other mode of representing the forces must be adopted than that which makes them emanate from permanent points as in a magnet4 ,the phenomena of attraction and repulsion in electrized bodies were conveniently represented by means of the hypothesis of two electric fluids1 a positive and a negative one1 which were supposed to be distributed in the bodies4 ,of these fluids1 it was supposed that each repelled its own parts and attracted those of the opposite fluid3 and it was found that this hypothesis explained all the obvious laws of electric action4 ,here then we have the phenomena of polarization explained by a new kind of machinery3--two opposite fluids #cfb distributed in bodies1 and supplying them1 so to speak1 with their polar forces4 ,this hypothesis not only explains electrical attraction1 but also the electrical spark3 namely1 thus3 when two bodies1 of which the neighbouring surfaces are charged with the two opposite fluids1 approach near to each other1 the mutual attraction of the fluids becomes more and more intense1 till at last the excess of fluid on the one body breaks through the air and rushes to the other body1 in a form accompanied by light and noise4 ,when this transfer has taken place1 the attraction ceases1 the positive and the negative fluid having neutralized each other4 ,their effort was to unite2 and this union being effected1 there is no longer any force in action4 ,bodies in their natural unexcited condition may be considered as occupied by a combination of the two fluids3 and hence we see how the production of either kind of electricity is necessarily accompanied with the production of an equivalent amount of the opposite kind4 #d4 ,voltaic ,electricity4--,such is the case in ,franklinic electricity1--that which is excited by the common electrical machine4 ,in studying ,voltaic electricity1 we are led to the conviction that the fluid which is in a condition of momentary equilibrium in electrized conductors1 exists in the state of a ,current in the voltaic circuit4 ,and here we find polar relations of a new kind existing among the forces4 ,two voltaic ,currents attract each other when they are moving in the same1 and repel each other when they are moving in opposite1 directions4 ,but we find1 in addition to these1 other polar relations of a more abstruse kind1 and which the supposition of two fluids does not so readily explain4 ,for instance1 if such fluids existed1 distinct from each other1 it might be expected that it would be possible to exhibit one of them separate from the other4 ,yet in all the phenomena of electromotive currents1 we attempt in vain to obtain one kind of electricity separately4 ',i have not1' says ,mr4 ,faraday#be1 'been able to find a #cfc single fact which could be adduced to prove the theory of two electricities rather than one1 in electric currents2 or1 admitting the hypothesis of two electricities1 have ,i been able to perceive the slightest grounds that one electricity can be more powerful than the other1 or that it can be present without the other1 or that it can be varied or in the slightest degree affected without a corresponding variation in the other4' ',thus1' he adds1 'the polar character of the powers is rigorous and complete4' ,thus1 we too may remark1 all the superfluous and precarious parts gradually drop off from the hypothesis which we devise in order to represent polar phenomena2 and the abstract notion of ,polarity--of equal and opposite powers called into existence by a common condition--remains unincumbered with extraneous machinery4 ,note #be3 ,researches1 #eaf4 #e4 ,light4--,another very important example of the application of the ,idea of ,polarity is that supplied by the discovery of the polarization of light4 ,a ray of light may1 by various processes1 be modified1 so that it has different properties according to its different sides1 although this difference is not perceptible by any common effects4 ,if1 for instance1 a ray thus modified1 pass perpendicularly through a circular glass1 and fall upon the eye1 we may turn the glass round and round in its frame1 and we shall make no difference in the brightness of the spot which we see4 ,but if1 instead of a glass1 we look through a longitudinal slice of tourmaline1 the spot is alternately dark and bright as we turn the crystal through successive quadrants4 ,here we have a contrast of ,properties 7dark and bright7 corresponding to a contrast of positions1 7the position of a line east and west being contrasted with the position north and south17 which1 as we have said1 is the general character of ,polarity4 ,it was with a view of expressing this character that the term ,polarization was originally introduced4 ,malus was forced by his discoveries into the use of this expression4 ',we find1' he says1 in #ahaa1 'that light acquires properties which are relative only to the sides of the ray1--which are the same for the north and south sides of the ray1 7using #cfd the points of the compass for description's sake only17 and which are different when we go from the north and south to the east or to the west sides of the ray4 ,i shall give the name of poles to these sides of the ray1 and shall call polarization the modification which gives to light these properties relative to these poles4 ,i have put off hitherto the admission of this term into the description of the physical phenomena with which we have to do3 ,i did not dare to introduce it into the ,memoirs in which ,i published my last observations3 but the variety of forms in which this new phenomenon appears1 and the difficulty of describing them1 compel me to admit this new expression2 which signifies simply the modification which light has undergone in acquiring new properties which are not relative to the direction of the ray1 but only to its sides considered at right angles to each other1 and in a plane perpendicular to its direction4' ,the theory which represents light as an emission of particles was in vogue at the time when ,malus published his discoveries2 and some of his followers in optical research conceived that the phenomena which he thus described rendered it necessary to ascribe poles and an axis to each particle of light4 ,on this hypothesis1 light would be polarized when the axes of all the particles were in the same direction3 and1 making such a supposition1 it may easily be conceived capable of transmission through a crystal whose axis is parallel to that of the luminous particles1 and intransmissible when the axis of the crystal is in a position transverse to that of the particles4 ,the hypothesis of particles possessing poles is a rude and arbitrary assumption1 in this as in other cases2 but it serves to convey the general notion of polarity1 which is the essential feature of the phenomena4 ,the term 'polarization of light has sometimes been complained of in modern times as hypothetical and obscure4 ,but the real cause of obscurity was1 that the ,idea of ,polarity was1 till lately1 very imperfectly developed in men's minds4 ,as we have seen1 the general notion of ,polarity1--opposite properties in opposite #cfe directions1--exactly describes the character of the optical phenomena to which the term is applied4 ,it is to be recollected that in optics we never speak of the poles1 but of the plane of polarization of a ray4 ,the word sides1 which ,newton and ,malus have used1 neither of them appears to have been satisfied with2 ,newton1 in employing it1 had recourse to the strange ,gallicism of speaking of the coast of usual and of unusual refraction of a crystal4 ,the modern theory of optics represents the plane of polarization of light as depending1 not on the position in which the axes of the luminiferous particles lie1 but on the direction of those transverse vibrations in which light consists4 ,this theory is1 as we have stated in the ,history1 recommended by an extraordinary series of successes in accounting for the phenomena4 ,and this hypothesis of transverse vibrations shows us another mechanical mode1 7besides the hypothesis of particles with axes17 by which we may represent the polarity of a ray4 ,but we may remark that the general notion of ,polarity1 as applied to light in such cases1 would subsist1 even if the undulatory theory were rejected4 ,the idea is1 as we have before said1 independent of all hypothetical machinery4 ,i need not here refer to the various ways in which light may be polarized2 as1 for instance1 by being reflected from the surface of water1 or of glass1 at certain angles1 by being transmitted1 through crystals1 and in other ways4 ,in all cases the modification produced1 the polarization1 is identically the same property4 ,nor need ,i mention the various kinds of phenomena which appear as contrasts in the result2 for these are not merely light and dark1 or white and black1 but red and green1 and generally1 a colour and its complementary colour1 exhibited in many complex and varied configurations4 ,these multiplied modes in which polarized light presents itself add nothing to the original conception of ,polarization3 and ,i shall therefore pass on to another subject4 #f4 ,crystallization4--,bodies which are perfectly crystallized exhibit the most complete regularity and #cff symmetry of form2 and this regularity not only appears in their outward shape1 but pervades their whole texture1 and manifests itself in their cleavage1 their transparency1 and in the uniform and determinate optical properties which exist in every part1 even in the smallest fragment of the mass4 ,if we conceive crystals as composed of particles1 we must suppose these particles to be arranged in the most regular manner2 for example1 if we suppose each particle to have an axis1 we must suppose all these axes to be parallel2 for the direction of the axis of the particles is indicated by the physical and optical properties of the crystal1 and therefore this direction must be the same for every portion of the crystal4 ,this parallelism of the axes of the particles may be conceived to result from the circumstance of each particle having poles1 the opposite poles attracting each other4 ,in virtue of forces acting as this hypothesis assumes1 a collection of small magnetic particles would arrange themselves in parallel positions2 and such a collection of magnetic particles offers a sort of image of a crystal4 ,thus we are led to conceive the particles of crystals as polarized1 and as determined in their crystalline positions by polar forces4 ,this mode of apprehending the constitution of crystals has been adopted by some of our most eminent philosophers4 ,thus ,berzelius says#ce1 ',it is demonstrated1 that the regular forms of bodies presuppose an effort of their atoms to touch each other by preference in certain points2 that is1 they are founded upon a ,polarity2'--he adds1 'a polarity which can be no other than an electric or magnetic polarity4' ,in this latter clause we have the identity of different kinds of polarity asserted2 a principle which we shall speak of in the next chapter4 ,but we may remark1 that even without dwelling upon this connexion1 any notion which we can form of the structure of ,crystals necessarily involves the idea of ,polarity4 ,whether this polarity necessarily requires us to believe crystals to be composed of ,atoms which exert an effort to touch #cfg each other in certain points by preference1 is another question4 ,and1 in agreement with what has been said respecting other kinds of polarity1 we shall probably find1 on a more profound examination of the subject1 that while the ,idea of ,polarity is essential1 the machinery by which it is thus expressed is precarious and superfluous4 ,note #ce3 ,essay on the ,theory of ,chemical ,properties1 #ahbj1 p4 #aac4 #g4 ,chemical ,affinity4--,we shall have1 in the next ,book1 to speak of ,chemical ,affinity at some length2 but since the ultimate views to which philosophers have been led1 induce them to consider the forces of ,affinity as ,polar ,forces1 we must enumerate these among the examples of ,polarity4 ,in chemical processes1 opposites tend to unite1 and to neutralize each other by their union4 ,thus an acid or an alkali combine with vehemence1 and form a compound1 a neutral salt1 which is neither acid nor alkaline4 ,this conception of contrariety and mutual neutralization1 involves the ,idea of ,polarity4 ,in the conception as entertained by the earlier chemists1 the ,idea enters very obscurely3 but in the attempts which have more recently been made to connect this relation 7of acid and base71 with other relations1 the chemical elements have been conceived as composed of particles which possess poles2 like poles repelling1 and unlike attracting each other1 as they do in magnetic and electric phenomena4 ,this is1 however1 a rude and arbitrary way of expressing ,polarity1 and1 as may be easily shown1 involves many difficulties which do not belong to the ,idea itself4 ,mr4 ,faraday1 who has been led by his researches to a conviction of the polar nature of the forces of chemical affinity1 has expressed their character in a more general manner1 and without any of the machinery of particles indued with poles4 ,according to his view1 chemical synthesis and analysis must always be conceived as taking place in virtue of equal and opposite forces1 by which the particles are united or separated4 ,these forces1 by the very circumstance of their being polar1 may be transferred from point to point4 ,for if we conceive a string of particles1 and if the positive force of the first particle #cfh be liberated and brought into action1 its negative force also must be set free3 this negative force neutralizes the positive force of the next particle1 and therefore the negative force of this particle 7before employed in neutralizing its positive force7 is set free3 this is in the same way transferred to the next particle1 and so on4 ,and thus we have a positive force active at one extremity of a line of particles1 corresponding to a negative force at the other extremity1 all the intermediate particles reciprocally neutralizing each other's action4 ,this conception of the transfer of chemical action was indeed at an earlier period introduced by ,grotthus#de1 and confirmed by ,davy4 ,but in ,mr4 ,faraday's hands we see it divested of all that is superfluous1 and spoken of1 not as a line of particles1 but as 'an axis of power1 having at every point contrary forces1 exactly equal1 in opposite directions4' ,note #de3 ,,dumas1 ,leons sur la ,philosophie ,chimique1 p4 #dja4 #h4 ,general ,remarks4--,thus1 as we see1 the notion of ,polarity is applicable to many large classes of phenomena4 ,yet the ,idea in a distinct and general form is only of late growth among philosophers4 ,it has gradually been abstracted and refined from many extraneous hypotheses which were at first supposed to be essential to it4 ,we have noticed some of these hypotheses2--as the poles of a body2 the poles of the particles of a fluid2 two opposite fluids2 a single fluid in excess and defect2 transverse vibrations4 ,to these others might be added4 ,thus ,dr4 ,prout#ee assumes that the polarity of molecules results from their rotation on their axes1 the opposite motions of contiguous molecules being the cause of opposite 7positive and negative7 polarities4 ,note #ee3 ,bridgewater ,treatise1 p4 #eei4 ,but none of these hypotheses can be proved by the fact of ,polarity alone2 and they have been in succession rejected when they had been assumed on that ground4 ,thus ,davy1 in #ahbf1 speaking of chemical forces says#fe1 ',in assuming the idea of two ethereal1 subtile1 elastic #cfi fluids1 attractive of the particles of each other1 and repulsive as to their own particles1 capable of combining in different proportions with bodies1 and according to their proportions giving them their specific qualities and rendering them equivalent masses1 it would be natural to refer the action of the poles to the repulsions of the substances combined with the excess of one fluid1 and the attractions of those united to the excess of the other fluid2 and a history of the phenomena1 not unsatisfactory to the reason1 might in this way be made out4 ,but as it is possible likewise to take an entirely different view of the subject1 on the idea of the dependence of the results upon the primary attractive powers of the parts of the combination on a single subtile fluid1 ,i shall not enter into any discussion on this obscure part of the theory4' ,which of these theories will best represent the case1 will depend upon the consideration of other facts1 in combination with the polar phenomena1 as we see in the history of optical theory4 ,in like manner ,mr4 ,faraday proved by experiment#ge the errour of all theories which ascribe electro-chemical decomposition to the attraction of the poles of the voltaic battery4 ,note #fe3 ,phil4 ,tr4 #ahbf1 p4 #dae4 ,note #ge3 ,researches1 p4 #die1 c4 ,in order that they may distinctly image to themselves the ,idea of ,polarity1 men clothe it in some of the forms of machinery above spoken of2 yet every new attempt shows them the unnecessary difficulties in which they thus involve themselves4 ,but on the other hand it is difficult to apprehend this ,idea divested of all machinery2 and to entertain it in such a form that it shall apply at the same time to magnetism and electricity1 galvanism and chemistry1 crystalline structure and light4 ,the ,idea of ,polarity becomes most pure and genuine1 when we entirely reject the conception of ,poles1 as ,faraday has taught us to do in considering electro-chemical decomposition2 but it is only by degrees and by effort that we can reach this point of abstraction and generality4 #cgj #i4 ,there is one other remark which we may here make4 ,it was a maxim commonly received in the ancient schools of philosophy1 that ',like attracts ,like3' but as we have seen1 the universal maxim of ,polar ,phenomena is1 that ,like repels ,like1 and attracts ,unlike4 ,the north pole attracts the south pole1 the positive fluid attracts the negative fluid2 opposite elements rush together2 opposite motions reduce each other to rest4 ,the permanent and stable course of things is that which results from the balance and neutralization of contrary tendencies4 ,nature is constantly labouring after repose by the effect of such tendencies2 and so far as ,polar ,forces enter into her economy1 she seeks harmony by means of discord1 and unity by opposition4 ,although the ,idea of ,polarity is as yet somewhat vague and obscure1 even in the minds of the cultivators of physical science1 it has nevertheless given birth to some general principles which have been accepted as evident1 and have had great influence on the progress of science4 ,these we shall now consider4 #cga ,,chapter ,,ii4 ,,of ,,the ,,connexion ,,of ,,polarities4 #a4 ,,it has appeared in the preceding chapter that in cases in which the phenomena suggest to us the idea of ,polarity1 we are also led to assume some material machinery as the mode in which the polar forces are exerted4 ,we assume1 for instance1 globular particles which possess poles1 or the vibrations of a fluid1 or two fluids attracting each other2 in every case1 in short1 some hypothesis by which the existence and operation of the ,polarity is embodied in geometrical and mechanical properties of a medium2 nor is it possible for us to avoid proceeding upon the conviction that some such hypothesis must be true2 although the nature of the connexion between the mechanism and the phenomena must still be indefinite and arbitrary4 ,but since each class of ,polar ,phenomena is thus referred to an ulterior cause1 of which we know no more than that it has a polar character1 it follows that different ,polarities may result from the same cause manifesting its polar character under different aspects4 ,taking1 for example1 the hypothesis of globular particles1 if electricity result from an action dependent upon the poles of each globule1 magnetism may depend upon an action in the equator of each globule2 or taking the supposition of transverse vibrations1 if polarized light result directly from such vibrations1 crystallization may have reference to the axes of the elasticity of the medium by which the vibrations are rendered transverse1--so far as the polar character only of the phenomena is to be accounted for4 ,i say this may be so1 in so far only as the polar character of the phenomena is concerned2 for whether the relation of #cgb electricity to magnetism1 or of crystalline forces to light1 can really be explained by such hypotheses1 remains to be determined by the facts themselves4 ,but since the first necessary feature of the hypothesis is1 that it shall give polarity1 and since an hypothesis which does this1 may1 by its mathematical relations1 give polarities of different kinds and in different directions1 any two co-existent kinds of polarity may result from the same cause1 manifesting itself in various manners4 ,the conclusion to which we are led by these general considerations is1 that two co-existing classes of polar phenomena may be effects of the same cause4 ,but those who have studied such phenomena more deeply and attentively have1 in most or in all cases1 arrived at the conviction that the various kinds of ,polarity in such cases must be connected and fundamentally identical4 ,as this conviction has exercised a great influence1 both upon the discoveries of new facts and upon the theoretical speculations of modern philosophers1 and has been put forward by some writers as a universal principle of science1 ,i will consider some of the cases in which it has been thus applied4 #b4 ,connexion of ,magnetic and ,electric ,polarity4--,the polar phenomena of electricity and magnetism are clearly analogous in their laws3 and obvious facts showed at an early period that there was some connexion between the two agencies4 ,attempts were made to establish an evident and definite relation between the two kinds of force1 which attempts proceeded upon the principle now under consideration2--namely1 that in such cases1 the two kinds of ,polarity must be connected4 ,professor rsted1 of ,copenhagen1 was one of those who made many trials founded upon this conviction3 yet all these were long unsuccessful4 ,at length1 in #ahbj1 he discovered that a galvanic current1 passing at right angles near to a magnetic needle1 exercises upon it a powerful deflecting force4 ,the connexion once detected between magnetism and galvanism was soon recognized as constant and universal4 ,it was represented in different hypothetical modes by different persons2 some considering the galvanic #cgc current as the primitive axis1 and the magnet as constituted of galvanic currents passing round it at right angles to the magnetic axis2 while others conceived the magnetic axis as the primitive one1 and the electric current as implying a magnetic current round the wire4 ,so far as many of the general relations of these two kinds of force were concerned1 either mode of representation served to express them2 and thus the assumption that the two ,polarities1 the magnetic and the electric1 were fundamentally identical1 was verified1 so far as the phenomena of magnetic attraction1 and the like1 were concerned4 ,i need not here mention how this was further confirmed by the experiments in which1 by means of the forces thus brought into view1 a galvanic wire was made to revolve round a magnet1 and a magnet round a galvanic wire2--in which artificial magnets were constructed of coils of galvanic wire2--and finally1 in which the galvanic spark was obtained from the magnet4 ,the identity which sagacious speculators had divined even before it was discovered1 and which they had seen to be universal as soon as it was brought to light1 was completely manifested in every imaginable form4 ,the relation of the electric and magnetic ,polarities was found to be1 that they were transverse to each other1 and this relation exhibited under various conditions of form and position of the apparatus1 gave rise to very curious and unexpected perplexities4 ,the degree of complication which this relation may occasion1 may be judged of from the number of constructions and modes of conception offered by rsted1 ,wollaston1 ,faraday1 and others1 for the purpose of framing a technical memory of the results4 ,the magnetic polarity gives us the north and south poles of the needle2 the electric polarity makes the current positive and negative2 and these pairs of opposites are connected by relations of situation1 as above and below1 right and left2 and give rise to the resulting motion of the needle one way or the other4 #cgd #c4 ,ampre1 by framing his hypotheses of the action of voltaic currents and the constitution of magnets1 reduced all these technical rules to rigorous deductions from one general principle4 ,and thus the vague and obscure persuasion that there must be some connexion between ,electricity and ,magnetism1 so long an idle and barren conjecture1 was unfolded into a complete theory1 according to which magnetic and electromotive actions are only two different manifestations of the same forces2 and all the above-mentioned complex relations of polarities are reduced to one single polarity1 that of the electro-dynamic current4 #d4 ,as the ,idea of ,polarity was thus firmly established and clearly developed1 it became an instrument of reasoning4 ,thus it led ,ampre to maintain that the original or elementary forces in electro-dynamic action could not be as ,m4 ,biot thought they were1 a statical couple1 but must be directly opposite to each other4 ,the same idea enabled ,mr4 ,faraday to carry on with confidence such reasonings as the following#he3 ',no other known power has like direction with that exerted between an electric current and a magnetic pole2 it is tangential1 while all other forces acting at a distance are direct4 ,hence if a magnetic pole on one side of a revolving plate follow its course by reason of its obedience to the tangential force exerted upon it by the very current of electricity which it has itself caused2 a similar pole on the other side of the plate should immediately set it free from this force2 for the currents which have to be formed by the two poles are in contrary directions4' ,and in ,article #aaad of his ,researches1 the same eminent philosopher infers that if electricity and magnetism are considered as the results of a peculiar agent or condition1 exerted in determinate directions perpendicular to each other1 one must be by some means convertible into the other2 and this he was afterwards able to prove to be the case in fact4 ,note #he3 ,researches1 #bdd4 #cge ,thus the principle that the ,co-existent ,polarities of magnetism and electricity are connected and fundamentally identical1 is not only true1 but is far from being either vague or barren4 ,it has been a fertile source both of theories which have1 at present1 a very great probability1 and of the discovery of new and striking facts4 ,we proceed to consider other similar cases4 #e4 ,connexion of ,electrical and ,chemical ,polarities4--,the doctrine that the chemical forces by which the elements of bodies are held together or separated1 are identical with the polar forces of electricity1 is a great discovery of modern times2 so great and so recent1 indeed1 that probably men of science in general have hardly yet obtained a clear view and firm hold of this truth4 ,this doctrine is now1 however1 entirely established in the minds of the most profound and philosophical chemists of our time4 ,the complete development and confirmation of this as of other great truths1 was preceded by more vague and confused opinions gradually tending to this point2 and the progress of thought and of research was impelled and guided1 in this as in similar cases1 by the persuasion that these co-existent polarities could not fail to be closely connected with each other4 ,while the ultimate and exact theory to which previous incomplete and transitory theories tended is still so new and so unfamiliar1 it must needs be a matter of difficulty and responsibility for a common reader to describe the steps by which truth has advanced from point to point4 ,i shall1 therefore1 in doing this1 guide myself mainly by the historical sketches of the progress of this great theory1 which1 fortunately for us1 have been given us by the two philosophers who have played by far the most important parts in the discovery1 ,davy and ,faraday4 ,it will be observed that we are concerned here with the progress of theory1 and not of experiment1 except so far as it is confirmatory of theory4 ,in ,davy's ,memoir#ie of #ahbf1 on the ,relations of ,electrical and #cgf ,chemical ,changes1 he gives the historical details to which ,i have alluded4 ,already in #ahjb he had conjectured that all chemical decompositions might be polar4 ,in #ahjf he attempted to confirm this conjecture1 and succeeded1 to his own satisfaction1 in establishing#aje that the combinations and decompositions by electricity were referable to the law of electrical attractions and repulsions2 and advanced the hypothesis 7as he calls it71 that chemical and electrical attractions were produced by the same cause1 acting in one case on particles1 in the other on masses4 ,this hypothesis was most strikingly confirmed by the author's being able to use electrical agency as a more powerful means of chemical decomposition than any which had yet been applied4 ',believing1' he adds1 'that our philosophical systems are exceedingly imperfect1 ,i never attached much importance to this hypothesis2 but having formed it after a copious induction of facts1 and having gained by the application of it a number of practical results1 and considering myself as much the author of it as ,i was of the decomposition of the alkalies1 and having developed it in an elementary work as far as the present state of chemistry seemed to allow1 ,i have never1' he says1 'criticised or examined the manner in which different authors have adopted or explained it1 contented1 if in the hands of others1 it assisted the arrangements of chemistry or mineralogy1 or became an instrument of discovery4' ,when the doctrine had found an extensive acceptance among chemists1 attempts were made to show that it had been asserted by earlier writers3 and though ,davy justly denies all value to these pretended anticipations1 they serve to show1 however dimly1 the working of that conviction of the ,connexion of ,co-existent ,properties which all along presided in men's minds during this course of investigation4 ',ritter and ,winterl have been quoted1' ,davy says#aae1 'among other persons1 as having imagined or anticipated the relation between electrical powers and chemical affinities before the discovery of the pile #cgg of ,volta4 ,but whoever will read with attention ,ritter's ,evidence that ,galvanic action exists in organised nature1 and 9999,winterl's ,prolusiones ad ,chemiam sculi decimi noni1 will find nothing to justify this opinion4' ,he then refers to the ,queries of ,newton at the end of his ,optics4 ',these1' he says1 'contain more grand and speculative views that might be brought to bear upon this question than any found in the works of modern electricians2 but it is very unjust to the experimentalists who by the laborious application of new instruments1 have discovered novel facts and analogies1 to refer them to any such suppositions as that all attractions1 chemical1 electrical1 magnetical1 and gravitative1 may depend upon the same cause4' ,it is perfectly true1 that such vague opinions1 though arising from that tendency to generalize which is the essence of science1 are of no value except so far as they are both rendered intelligible1 and confirmed by experimental research4 ,note #ie3 ,phil4 ,trans4 #ahbf1 p4 #chc4 ,note #aje3 ,phil4 ,trans4 #ahbf1 p4 #chi4 ,note #aae3 ,ibid4 p4 #chd4 ,the phenomena of chemical decomposition by means of the voltaic pile1 however1 led other persons to views very similar to those of ,davy4 ,thus ,grotthus in #ahjeabe published an hypothesis of the same kind4 ',the pile of ,volta1' he says1 'is an electrical magnet1 of which each element1 that is1 each pair of plates1 has a positive and a negative pole4 ,the consideration of this polarity suggested to me the idea that a similar polarity may come into play between the elementary particles of water when acted upon by the same electrical agent2 and ,i avow that this thought was for me a flash of light4' ,note #abe3 ,ann4 ,chim4 lxviii4 #ed4 #f4 ,the thought1 however1 though thus brought into being1 was very far from being as yet freed from vagueness1 superfluities1 and errours4 ,i have elsewhere noticed#ace ,faraday's remark on ,davy's celebrated ,memoir of #ahjf2 that 'the mode of action by which the effects take place is stated very generally1 so generally1 indeed1 that probably a dozen precise schemes of electro-chemical action might be drawn up1 differing #cgh essentially from each other1 yet all agreeing with the statement there given4' ,when ,davy and others proceeded to give a little more definiteness and precision to the statement of their views1 they soon introduced into the theory features which it was afterwards found necessary to abandon4 ,thus#ade both ,davy1 ,grotthus1 ,riffault1 and ,chompr1 ascribed electrical decomposition to the action of the poles1 and some of them even pretended to assign the proportion in which the force of the pole diminishes as the distance from it increases4 ,faraday1 as ,i have already stated1 showed that the polarity must be considered as residing not only in what had till then been called the poles1 but at every point of the circuit4 ,he ascribed#aee electro-chemical decomposition to internal forces1 residing in the particles of the matter under decomposition1 not to external forces1 exerted by the poles4 ,hence he shortly afterwards#afe proposed to reject the word poles altogether1 and to employ instead1 the term electrode1 meaning the doors or passages 7of whatever surface formed7 by which the decomposed elements pass out4 ,what have been called the positive and negative poles he further termed the ,anode and ,cathode2 and he introduced some other changes in nomenclature connected with these4 ,he then1 as ,i have related in the ,history#age1 invented the ,volta-electrometer1 which enabled him to measure the quantity of voltaic action1 and this he found to be identical with the quantity of chemical affinity2 and he was thus led to the clearest view of the truth towards which he and his predecessors had so long been travelling1 that electrical and chemical forces are identical#ahe4 ,note #ace3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 ix4 sect4 #a4 ,note #ade3 ,see ,faraday's ,historical ,sketch1 ,researches1 #dha-dib4 ,note #aee3 ,art4 #ebd4 ,note #afe3 ,in #ahcd4 ,eleventh ,series of ,researches4 ,art4 #ffb4 ,note #age3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 ix4 sect4 #b4 ,note #ahe3 ,arts4 #iae1 #iaf1 #iag4 #g4 ,it will1 perhaps1 be said that this beautiful train of discovery was entirely due to experiment1 and not to any priori conviction that co-existent polarities #cgi must be connected4 ,i trust ,i have sufficiently stated that such an priori principle could not be proved1 nor even understood1 without a most laborious and enlightened use of experiment2 but yet ,i think that the doctrine1 when once fully unfolded1 exhibited clearly1 and established as true1 takes possession of the mind with a more entire conviction of its certainty and universality1 in virtue of the principle we are now considering4 ,when the theory has assumed so simple a form1 it appears to derive immense probability 7to say the least7 from its simplicity4 ,like the laws of motion1 when stated in its most general form1 it appears to carry with it its own evidence4 ,and thus this great theory borrows something of its character from the ,ideas which it involves1 as well as from the ,experiments by which it was established4 #h4 ,we may find in many of ,mr4 ,faraday's subsequent reasonings1 clear evidence that this idea of the ,connexion of ,polarities1 as now developed1 is not limited in its application to facts already known experimentally1 but1 like other ideas1 determines the philosopher's researches into the unknown1 and gives us the form of knowledge even before we possess the matter4 ,thus1 he says1 in his ,thirteenth ,series#aie1 ',i have long sought1 and still seek1 for an effect or condition which shall be to statical electricity what magnetic force is to current electricity2 for as the lines of discharge are associated with a certain transverse effect1 so it appeared to me impossible but that the lines of tension or of inductive action1 which of necessity precede the discharge1 should also have their correspondent transverse condition or effect4' ,other similar passages might be found4 ,note #aie3 ,art4 #afeh4 ,i will now consider another case to which we may apply the ,principle of ,connected ,polarities4 #i4 ,connexion of ,chemical and ,crystalline ,polarities4--,the close connexion between the ,chemical ,affinity and the ,crystalline ,attraction of elements cannot be overlooked4 ,bodies never crystallize but when their elements combine chemically2 and solid bodies which #chj combine1 when they do it most completely and exactly1 also crystallize4 ,the forces which hold together the elements of a crystal of alum are the same forces which make it a crystal4 ,there is no distinguishing between the two sets of forces4 ,both chemical and crystalline forces are polar1 as we stated in the last chapter2 but the polarity in the two cases is of a different kind4 ,the polarity of chemical forces is then put in the most distinct form1 when it is identified with electrical polarity2 the polarity of the particles of crystals has reference to their geometrical form4 ,and it is clear that these two kinds of polarity must be connected4 ,accordingly1 ,berzelius expressly asserts#bje the necessary identity of these two polarities4 ',the regular forms of bodies suppose a polarity which can be no other than an electric or magnetic polarity4' ,this being so seemingly inevitable1 we might expect to find the electric forces manifesting some relation to the definite directions of crystalline forms4 ,mr4 ,faraday tried1 but in vain1 to detect some such relation4 ,he attempted to ascertain#bae whether a cube of rock crystal transmitted the electrical force of tension with different intensity along and across the axis of the crystal4 ,in the first specimen there seemed to be some difference2 but in other experiments1 made both with rock crystal and with calc spar1 this difference disappeared4 ,although therefore we may venture to assert that there must be some very close connexion between electrical and crystalline forces1 we are1 as yet1 quite ignorant what the nature of the connexion is1 and in what kind of phenomena it will manifest itself4 ,note #bje3 ,essay on ,chemical ,prop4 #aac4 ,note #bae3 ,researches4 ,art4 #afhi4 #aj4 ,connexion of ,crystalline and ,optical ,polarities4--,crystals present to us optical phenomena which have a manifestly polar character4 ,the double refraction1 both of uniaxal and of biaxal crystals1 is always accompanied with opposite polarization of the two rays2 and in this and in other ways light is polarized in directions dependent upon the axes of the crystalline form1 that is1 on the directions of the polarities of the #cha crystalline particles4 ,the identity of these two kinds of polarity 7crystalline and optical7 is too obvious to need insisting on2 and it is not necessary for us here to decide by what hypothesis this identity may most properly be represented4 ,we may hereafter perhaps find ourselves justified in considering the crystalline forces as determining the elasticity of the luminiferous ether to be different in different directions within the crystal1 and thus as determining the refraction and polarization of the light which the crystal transmits4 ,but at present we merely note this case as an additional example of the manifest connexion and fundamental identity of two co-existent polarities4 #aa4 ,connexion of ,polarities in general4--,thus we find that the ,connexion of different kinds of ,polarities1 magnetic1 electric1 chemical1 crystalline1 and optical1 is certain as a truth of experimental science4 ,we have attempted to show further that in the minds of several of the most eminent discoverers and philosophers1 such a conviction is something more than a mere empirical result3 it is a principle which has regulated their researches while it was still but obscurely seen and imperfectly unfolded1 and has given to their theories a character of generality and self-evidence which experience alone cannot bestow4 ,it will1 perhaps1 be said that these doctrines1--that scientific researches may usefully be directed by principles in themselves vague and obscure2--that theories may have an evidence superior to and anterior to experience2--are doctrines in the highest degree dangerous1 and utterly at variance with the soundest maxims of modern times respecting the cultivation of science4 ,in the justice and wisdom of this caution ,i entirely agree3 and although ,i have shown that this principle of the ,connexion of ,polarities1 rightly interpreted and established in each case by experiment1 involves profound and comprehensive truths2 ,i think it no less important to remark that1 at least in the present stage of our knowledge1 we can make no use of this principle without taking care1 at every step1 to determine by #chb clear and decisive experiments1 its proper meaning and application4 ,all endeavours to proceed otherwise have led1 and must lead1 to ignorance and confusion4 ,attempts to deduce from our bare ,idea of ,polarity1 and our fundamental convictions respecting the connexion of polarities1 theories concerning the forces which really exist in nature1 can hardly have any other result than to bewilder men's minds1 and to misdirect their efforts4 ,so far1 indeed1 as this persuasion of a connexion among apparently different kinds of agencies1 impels men1 engaged in the pursuit of knowledge1 to collect observations1 to multiply1 repeat1 and vary experiments1 and to contemplate the result of these in all aspects and relations1 it may be an occasion of the most important discoveries4 ,accordingly we find that the great laws of phenomena which govern the motions of the planets about the sun1 were first discovered by ,kepler1 in consequence of his scrutinizing the recorded observations with an intense conviction of the existence of geometrical and arithmetical harmonies in the solar system4 ,perhaps we may consider the discovery of the connexion of magnetism and electricity by ,professor rsted in #ahbj1 as an example somewhat of the same kind2 for he also was a believer in certain comprehensive but undefined relations among the properties of bodies2 and in consequence of such views entertained great admiration for the ,prologue to the ,chemistry of the ,nineteenth ,century1 of ,winterl1 already mentioned4 ,m4 rsted1 in #ahjc1 published a summary of this work2 and in so doing1 praised the views of ,winterl as far more profound and comprehensive than those of ,lavoisier4 ,soon afterwards a ,review of this publication appeared in ,france#bbe1 in which it was spoken of as a work only fit for the dark ages1 and as the indication of a sect which had for some time 'ravaged ,germany1' and inundated that country with extravagant and unintelligible mysticism4 ,it was1 therefore1 a kind of triumph to ,m4 rsted to be1 after #chc some years' labour1 the author of one of the most remarkable and fertile physical discoveries of his time4 ,note #bbe3 ,ann4 ,chim41 ,tom4 #a4 7#ahjd71 p4 #aia4 #ab4 ,it was not indeed without some reason that certain of the ,german philosophers were accused of dealing in doctrines vast and profound in their aspect1 but1 in reality1 indefinite1 ambiguous1 and inapplicable4 ,and the most prominent of such doctrines had reference to the principle now under our consideration2 they represented the properties of bodies as consisting in certain polarities1 and professed to deduce1 from the very nature of things1 with little or no reference to experiment1 the existence and connexion of these polarities4 ,thus ,schelling1 in his ,ideas towards a ,philosophy of ,nature1 published in #ahjc1 says#bce1 ',magnetism is the universal act of investing ,multiplicity with ,unity2 but the universal form of the reduction of ,multiplicity to ,unity is the ,line1 pure ,longitudinal ,extension3 hence ,magnetism is determination of pure ,longitudinal ,extension2 and as this manifests itself by absolute ,cohesion1 ,magnetism is the determination of absolute ,cohesion4' ,and as ,magnetism was1 by such reasoning1 conceived to be proved as a universal property of matter1 ,schelling asserted it to be a confirmation of his views when it was discovered that other bodies besides iron are magnetic4 ,in like manner he used such expressions as the following#bde3 ',the threefold character of the ,universal1 the ,particular1 and the ,indifference of the two1--as expressed in their ,identity1 is ,magnetism1 as expressed in their ,difference1 is ,electricity1 and as expressed in the ,totality1 is ,chemical ,process4 ,thus these forms are only one form2 and the ,chemical ,process is a mere transfer of the three ,points of ,magnetism into the ,triangle of ,chemistry4' ,note #bce3 ,p4 #bbc4 ,note #bde3 ,p4 #dhf4 ,it was very natural that the chemists should refuse to acknowledge1 in this fanciful and vague language1 7delivered1 however1 it is to be recollected1 in #ahjc17 an anticipation of ,davy's doctrine of the identity of electrical and chemical forces1 or of rsted's #chd electro-magnetic agency4 ,yet it was perhaps no less natural that the author of such assertions should look upon every great step in the electro-chemical theory as an illustration of his own doctrines4 ,accordingly we find ,schelling welcoming1 with a due sense of their importance1 the discoveries of ,faraday4 ,when he heard of the experiment in which electricity was produced from common magnetism1 he fastened with enthusiasm upon the discovery1 even before he knew any of its details1 and proclaimed it at a public meeting of a scientific body#bee as one of the most important advances of modern science4 ,we have 7he thus reasoned7 three effects of polar forces2--,electro-chemical ,decomposition1 ,electrical ,action1 ,magnetism4 ,volta and ,davy had confirmed experimentally the identity of the two former agencies3 rsted showed that a closed voltaic circuit acquired magnetic properties3 but in order to exhibit the identity of electric and magnetic action it was requisite that electric forces should be extricated from magnetic4 ,this great step ,faraday1 he remarked1 had made1 in producing the electric spark by means of magnets4 ,note #bee3 ,ueber ,faraday's ,neueste ,entdeckung4 ,mnchen4 #ahcb4 #ac4 ,although conjectures and assertions of the kind thus put forth by ,schelling involve a persuasion of the pervading influence and connexion of polarities1 which persuasion has already been confirmed in many instances1 they involve this principle in a manner so vague and ambiguous that it can rarely1 in such a form1 be of any use or value4 ,such views of polarity can never teach us in what cases we are and in what we are not expected to find polar relations2 and indeed tend rather to diffuse error and confusion1 than to promote knowledge4 ,accordingly we cannot be surprized to find such doctrines put forward by their authors as an evidence of the small value and small necessity of experimental science4 ,this is done by the celebrated metaphysician ,hegel1 in his ,encyclopdia#bfe4 ',since1' #che says he1 'the plane of incidence and of reflection in simple reflection is the same plane1 when a second reflector is introduced which further distributes the illumination reflected from the first1 the position of the first plane with respect to the second plane1 containing the direction of the first reflection and of the second1 has its influence upon the position1 illumination or darkening of the object as it appears by the second reflection4 ,this influence must be the strongest when the two planes are what we must call negatively related to each other3--that is1 when they are at right angles4' ',but1' he adds1 'when men infer 7as ,malus has done7 from the modification which is produced by this situation1 in the illumination of the reflection1 that the molecules of light in themselves1 that is1 on their different sides1 possess different physical energies2 and when on this foundation1 along with the phenomena of entoptical colours therewith connected1 a wide labyrinth of the most complex theory is erected2 we have then one of the most remarkable examples of the inferences of physics from experiment4' ,if ,hegel's reasoning prove anything1 it must prove that polarization always accompanies reflection under such circumstances as he describes3 yet all physical philosophers know that in the case of metals1 in which the reflection is most complete1 light is not completely polarized at any angle2 and that in other substances the polarization depends upon various circumstances which show how idle and inapplicable is the account which he thus gives of the property4 ,his self-complacent remark about the inferences of physics from experiment1 is intended to recommend by comparison his own method of considering the nature of 'things in themselves2' a mode of obtaining physical truth which had been more than exhausted by ,aristotle1 and out of which no new attempts have extracted anything of value since his time4 ,note #bfe3 ,sec4 #bgh4 #ad4 ,thus the general conclusion to which we are led on this subject1 is1 that the persuasion of the existence and ,connexion or ,identity of various ,polarities in nature1 although very naturally admitted1 and in many #chf cases interpreted and confirmed by observed facts1 is of itself1 so far as we at present possess it1 a very insecure guide to scientific doctrines4 ,when it is allowed to dictate our theories1 instead of animating and extending our experimental researches1 it leads only to errour1 confusion1 obscurity1 and mysticism4 ,this ,fifth ,book1 on the subject of ,polarities1 is a short one compared with most of the others4 ,this arises in a great measure from the circumstance that the ,idea of ,polarity has only recently been apprehended and applied1 with any great degree of clearness1 among physical philosophers2 and is even yet probably entertained in an obscure and ambiguous manner by most experimental inquirers4 ,i have been desirous of not attempting to bring forward any doctrines upon the subject1 except such as have been fully illustrated and exemplified by the acknowledged progress of the physical sciences4 ,if ,i had been willing to discuss the various speculations which have been published respecting the universal prevalence of ,polarities in the universe1 and their results in every province of nature1 ,i might easily have presented this subject in a more extended form2 but this would not have been consistent with my plan of tracing the influence of scientific ,ideas only so far as they have really aided in disclosing and developing scientific truths4 ,and as the influence of this ,idea is clearly distinguishable both from those which precede and those which follow1 in the character of the sciences to which it gives rise1 and as it appears likely to be hereafter of great extent and consequence1 it seemed better to treat of it in a separate ,book1 although of a brevity disproportioned to the rest4 ,,end ,,of ,,vol4 ,i4 ,cambridge3 ,printed at the ,university ,press4 ,,history ,,of ,,scientific ,,ideas4 ,,volume ,,ii4 ,cambridge2 ,,printed ,,by ,c4 ,j4 ,,clay1 ,m4,a4 ,,at ,,the ,,university ,,press4 ,,history ,,of ,,scientific ,,ideas4 ,,by ,,william ,,whewell1 ,d4,d41 ,,master ,,of ,,trinity ,,college1 ,,cambridge1 ,,and ,,corresponding ,,member ,,of ,,the ,,institute ,,of ,,france4 ,,being ,,the ,,first ,,part ,,of ,,the ,,philosophy ,,of ,,the ,,inductive ,,sciences4 ,,the ,,third ,,edition4 ,,in ,,two ,,volumes4 ,i ,i,i ,i ,,volume ,,ii4 ,,london3 ,,john ,w4 ,,parker ,,and ,,son1 ,,west ,,strand4 #aheh4 ,,contents ,,of ,,the ,,second ,,volume4 ,,book ,,vi4 ,,the ,,philosophy ,,of ,,chemistry4 ,,page ,,chap4 ,i4 ,,attempts ,,to ,,conceive ,,elementary ,,composition #c ,art4 #a4 ,fundamental ,ideas of ,chemistry4 #b4 ,elements4 #c4 ,do ,compounds resemble their ,elements8 #d4 ,the ,three ,principles4 #e4 ,a ,modern ,errour4 #f4 ,are ,compounds determined by the ,figure of ,elements8 #g4 ,crystalline ,form depends on ,figure of ,elements4 #h4 ,are ,compounds determined by ,mechanical ,attraction of ,elements8 #i4 ,newton's followers4 #aj4 ,imperfection of their ,hypotheses4 ,,chap4 ,,ii4 ,,establishment ,,and ,,development ,,of ,,the ,,idea ,,of ,,chemical ,,affinity #ae ,art4 #a4 ,early ,chemists4 #b4 ,chemical ,affinity4 #c4 ,affinity or ,attraction8 #d4 ,affinity preferable4 #e4 ,analysis is possible4 vi #f4 ,affinity is ,elective4 #g4 ,controversy on this4 #h4 ,affinity is ,definite4 #i4 ,are these ,principles necessarily true8 #aj4 ,composition determines ,properties4 #aa4 ,comparison on this subject4 #ab4 ,composition determines ,crystalline ,form4 ,,chap4 ,,iii4 ,,of ,,the ,,idea ,,of ,,substance #bi ,art4 #a4 ,indestructibility of ,substance4 #b4 ,the ,idea of ,substance4 #c4 ,locke's ,denial of ,substance4 #d4 ,is all ,substance heavy8 ,note on ,sir ,w4 ,hamilton's objections #cg ,,chap4 ,,iv4 ,,application ,,of ,,the ,,idea ,,of ,,substance ,,in ,,chemistry #ci ,art4 #a4 ,a ,body is ,equal to its ,elements4 #b4 ,lavoisier4 #c4 ,are there ,imponderable ,elements8 #d4 ,faraday's views4 #e4 ,composition of ,water4 #f4 ,heat in ,chemistry4 ,,chap4 ,v4 ,,the ,,atomic ,,theory #dh ,art4 #a4 ,the ,theory on ,chemical ,grounds4 #b4 ,hypothesis of ,atoms4 #c4 ,its ,chemical ,difficulties4 #d4 ,grounds of the ,atomic ,doctrine4 #e4 ,ancient ,atomists4 #f4 ,francis ,bacon4 #g4 ,modern ,atomists4 #h4 ,arguments for and against4 #i4 ,boscovich's ,theory4 #aj4 ,molecular ,hypothesis4 #aa4 ,poisson's ,inference4 #ab4 ,wollaston's ,argument4 #ac4 ,properties are ,permanent4 vii ,,book ,,vii4 ,,the ,,philosophy ,,of ,,morphology1 ,,including ,,crystallography4 ,,chap4 ,i4 ,,explication ,,of ,,the ,,idea ,,of ,,symmetry #fg ,art4 #a4 ,symmetry1 what4 #b4 ,kinds of ,symmetry4 #c4 ,examples in ,nature4 #d4 ,vegetables and ,animals4 #e4 ,symmetry a ,fundamental ,idea4 #f4 ,result of ,symmetry4 ,,chap4 ,,ii4 ,,application ,,of ,,the ,,idea ,,of ,,symmetry ,,to ,,crystals #ge ,art4 #a4 ',fundamental ,forms4' #b4 ,their use4 #c4 ',systems of ,crystallization4' #d4 ,cleavage4 #e4 ,other ,properties4 ,,chap4 ,,iii4 ,,speculations ,,founded ,,upon ,,the ,,symmetry ,,of ,,crystals #hj ,art4 #a4 ,integrant ,molecules4 #b4 ,difficulties of the ,theory4 #c4 ,merit of the ,theory4 #d4 ,wollaston's ,hypothesis4 #e4 ,maxim for such ,hypotheses4 #f4 ,dalton's ,hypothesis4 #g4 ,ampre's ,hypothesis4 #h4 ,difficulty of such ,hypotheses4 #i4 ,isomorphism4 viii ,,book ,,viii4 ,,philosophy ,,of ,,the ,,classificatory ,,sciences4 ,,chap4 ,i4 ,,the ,,idea ,,of ,,likeness ,,as ,,governing ,,the ,,use ,,of ,,common ,,names #ie ,art4 #a4 ,object of the ,chapter4 #b4 ,unity of the ,individual4 #c4 ,condition of ,unity4 #d4 ,kinds4 #e4 ,not made by ,definitions4 #f4 ,condition of the ,use of ,terms4 #g4 ,terms may have different ,uses4 #h4 ,gradation of ,kinds4 #i4 ,characters of ,kinds4 #aj4 ,difficulty of ,definitions4 #aa4 ',the ,five ,words4' ,,chap4 ,,ii4 ,,the ,,methods ,,of ,,natural ,,history1 ,,as ,,regulated ,,by ,,the ,,idea ,,of ,,likeness #ajh ,sect4 ,i4 ,natural ,history in ,general4 ,art4 #a4 ,idea of ,likeness in ,natural ,history4 #b4 ,condition of its ,use4 ,sect4 ,,ii4 ,terminology4 ,art4 #c4 ,meaning of the word4 ,sect4 ,,iii4 ,the ,plan of the ,system4 ,art4 #d4 ,its ,meaning4 #e4 ,latent ,reference to ,natural ,affinity4 #f4 ,natural ,classes4 #g4 ,artificial ,classes4 #h4 ,are ,genera ,natural8 #i4 ,natural ,history and ,mathematics4 #aj4 ,natural ,groups given by ,type1 not by ,definition4 #aa4 ,physiography4 #ab4 ,artificial and ,natural ,systems4 ix ,sect4 ,,iv4 ,methods of framing ,natural ,systems4 ,art4 #ac4 ,method of ,blind ,trial4 #ad4 ,method of ,general ,comparison4 ,sect4 ,v4 ,gradation of ,groups4 ,art4 #ae4 ,series of ,subdivisions4 #af4 ,what is a ,species8 #ag4 ,the words ',species' and ',genus4' #ah4 ,varieties4 ,races4 ,sect4 ,,vi4 ,nomenclature4 ,art4 #ai4 ,binary ,nomenclature4 ,sect4 ,,vii4 ,diagnosis4 ,art4 #bj4 ,characteristick and ,systematick4 ,,chap4 ,,iii4 ,,application ,,of ,,the ,,natural ,,history ,,method ,,to ,,mineralogy #ach ,art4 #a4 ,mohs's ,system4 #b4 ,his ',characteristick4' #c4 ,mineral ,species not yet well fixed4 #d4 ,orders of ,minerals4 #e4 ,nomenclature of ,minerals4 #f4 ,m4 ,necker's ',rgne ,mineral4' #g4 ,inconvenience of taking a ,chemical ,basis of ,mineral ,systems4 #h4 ,relation of ,natural ,history and ,chemistry4 #i4 ,what is a ,mineralogical ,individual8 #aj4 ,a well-formed ,crystal is an ,individual4 #aa4 ,not the ,integrant ,molecules1 #ab4 ,nor the ,cleavage ,forms4 #ac4 ,compound ,crystals are not ,individuals4 #ad4 ,crystalline ,forms are sufficiently complete for this4 #ae4 ,including aggregate ,masses4 #af4 ,do ,artificial ,crystals belong to ,mineralogy8 #ag4 ,the ,mineralogical ,individual extends as far as the same ,crystalline ,axes extend4 #ah4 ,artificial ,crystals do belong to ,mineralogy3 x #ai4 ,cannot be excluded4 #bj4 ,species to be determined by the ,crystalline ,power4 #ba4 ,secondary ,derivative ,forms are ,varieties3 #bb4 ,are not ,species1 as ,m4 ,necker holds4 ,,chap4 ,,iv4 ,,of ,,the ,,idea ,,of ,,natural ,,affinity #aei ,art4 #a4 ,the ,idea of ,affinity #b4 ,is not to be made out by ,arbitrary ,rules4 #c4 ,functions of ,living things are many1 #d4 ,but all lead to the same arrangement4 #e4 ,this is ,cuvier's principle3 #f4 ,and ,decandolle's4 #g4 ,is this applicable to ,inorganic ,bodies8 #h4 ,yes2 by the agreement of ,physical and ,chemical ,arrangement4 ,,book ,,ix4 ,,the ,,philosophy ,,of ,,biology4 ,,chap4 #a4 ,,analogy ,,of ,,biology ,,with ,,other ,,sciences4 #afi ,art4 #a4 ,biology involves the ,idea of ,life4 #b4 ,this ,idea to be historically traced4 #c4 ,the ,idea at first expressed by means of other ,ideas4 #d4 ,mystical1 ,mechanical1 ,chemical1 and ,vital ,fluid ,hypotheses4 ,,chap4 ,,ii4 ,,successive ,,biological ,,hypotheses #agd ,sect4 ,i4 ,the ,mystical ,school4 ,sect4 ,,ii4 ,the ,iatrochemical ,school4 ,sect4 ,,iii4 ,the ,iatromathematical ,school4 ,sect4 ,,iv4 ,the ,vital ,fluid ,school4 ,sect4 ,v4 ,the ,psychical ,school4 xi ,,chap4 ,,iii4 ,,attempts ,,to ,,analyse ,,the ,,idea ,,of ,,life #aie ,art4 #a4 ,definitions of ,life1 #b4 ,by ,stahl1 ,humboldt1 ,kant4 #c4 ,definition of ,organization by ,kant4 #d4 ,life is a ,system of ,functions4 #e4 ,bichat4 ,sum of ,functions4 #f4 ,use of ,definition4 #g4 ,cuvier's view4 #h4 ,classifications of ,functions4 #i4 ,vital1 ,natural1 and ,animal ,functions4 #aj4 ,bichat4 ,organic and ,animal ,life4 #aa4 ,use of this ,classification4 ,,chap4 ,,iv4 ,,attempts ,,to ,,form ,,ideas ,,of ,,separate ,,vital ,,forces1 ,,and ,,first1 ,,of ,,assimilation ,,and ,,secretion #bjc ,sect4 ,i4 ,course of ,biological ,research4 ,art4 #a4 ,observation and ,new ,conceptions4 ,sect4 ,,ii4 ,attempts to form a distinct ,conception of ,assimilation and ,secretion4 ,art4 #b4 ,the ,ancients4 #c4 ,buffon4 ,interior ,mould4 #d4 ,defect of this view4 #e4 ,cuvier4 ,life a ,vortex4 #f4 ,defect of this view4 #g4 ,schelling4 ,matter and ,form4 #h4 ,life a constant ,form of circulating ,matter1 c4 ,sect4 ,,iii4 ,attempts to conceive the ,forces of ,assimilation and ,secretion4 ,art4 #i4 ,assimilation is a ,vital ,force4 #aj4 ,the name ',assimilation4' #aa4 ,several processes involved in ,assimilation4 #ab4 ,absorption4 ,endosmose4 #ac4 ,absorption involves a ,vital ,force4 #ad4 ,secretion4 ,glands4 #ae4 ,motions of ,vital ,fluids4 xii ,sect4 ,,iv4 ,attempts to conceive the ,process of ,generation4 ,art4 #af4 ',reproduction' figuratively used for ,generation4 #ag4 ,nutrition different from #ah4 ,generation4 #ai4 ,generations successively included4 #bj4 ,pre-existence of ,germs4 #ba4 ,difficulty of this view4 #bb4 ,communication of ,vital ,forces4 #bc4 ,close similarity of ,nutrition and ,generation4 #bd4 ,the ,identity of the two ,processes exemplified4 ,,chap4 ,v4 ,,attempts ,,to ,,form ,,ideas ,,of ,,separate ,,vital ,,forces1 continued4--,,voluntary ,,motion4 #bbb ,art4 #a4 ,voluntary ,motion one of the animal ,functions4 #b4 ,progressive knowledge of it4 #c4 ,nervous ,fluid not electric4 #d4 ,irritability4 ,glisson4 #e4 ,haller4 #f4 ,contractility4 #g4 ,organic ,sensibility and ,contractility not separable4 #h4 ,improperly described by ,bichat4 #i4 ,brown4 #aj4 ,contractility a peculiar ,power4 #aa4 ,cuvier's view4 #ab4 ,elementary contractile ,action4 #ac4 ,strength of ,muscular ,fibre4 #ad4 ,sensations become ,perceptions #ae4 ,by means of ,ideas2 #af4 ,and lead to ,muscular ,actions4 #ag4 ,volition comes between ,perception and ,action4 #ah4 ,transition to ,psychology1 #ai4 ,a center is introduced4 #bj4 ,the central consciousness may be obscure4 #ba4 ,reflex ,muscular ,action4 #bb4 ,instinct4 #bc4 ,difficulty of conceiving ,instinct4 #bd4 ,instinct opposed to ,insight4 xiii ,,chap4 ,,vi4 ,,of ,,the ,,idea ,,of ,,final ,,causes #bci ,art4 #a4 ,organization4 ,parts are ,ends and ,means4 #b4 ,not merely mutually dependent4 #c4 ,not merely mutually ,cause and ,effect4 #d4 ,notion of ,end not derived from ,facts4 #e4 ,this notion has regulated ,physiology4 #f4 ,notion of ,design comes from within4 #g4 ,design not understood by ,savages4 #h4 ,design opposed to ,morphology4 #i4 ,impression of ,design when fresh4 #aj4 ,acknowledgement of an ,end by adverse ,physiologists4 #aa4 ,this included in the ,notion of ,disease4 #ab4 ,it belongs to organized ,creatures only4 #ac4 ,the term ,final ,cause4 #ad4 ,law and ,design4 #ae4 ,final ,causes and ,morphology4 #af4 ,expressions of physiological ,ends4 #ag4 ,the ,conditions of ,existence4 #ah4 ,the asserted presumption of ,teleology4 #ai4 ,final ,causes in other subjects4 #bj4 ,transition to ,paltiology4 ,,book ,x4 ,,the ,,philosophy ,,of ,,pal,,tiology4 ,,chap4 ,i4 ,,of ,,pal,,tiological ,,sciences ,,in ,,general4 #beg ,art4 #a4 ,description of ,paltiology4 #b4 ,its ,members4 #c4 ,other ,members4 #d4 ,connexion of the whole subject4 #e4 ,we shall take ,material ,sciences only2 #f4 ,but these are connected with others4 ,,chap4 ,,ii4 ,,of ,,the ,,three ,,members ,,of ,a ,,pal,,tiological ,,science #bfc ,art4 #a4 ,divisions of such ,sciences4 #b4 ,the ,study of ,causes4 #c4 tiology4 xiv #d4 ,phenomenology requires ,classification4 ,phenomenal ,geology4 #e4 ,phenomenal ,uranology4 #f4 ,phenomenal ,geography of ,plants and ,animals4 #g4 ,phenomenal ,glossology4 #h4 ,the ,study of ,phenomena leads to ,theory4 #i4 ,no sound ,theory without tiology4 #aj4 ,causes in ,paltiology4 #aa4 ,various kinds of ,cause4 #ab4 ,hypothetical ,order of ,paltiological ,causes4 #ac4 ,mode of ,cultivating tiology3--,in ,geology3 #ad4 ,in the ,geography of ,plants and ,animals3 #ae4 ,in ,languages4 #af4 ,construction of ,theories4 #ag4 ,no sound ,paltiological ,theory yet extant4 ,,chap4 ,,iii4 ,,of ,,the ,,doctrine ,,of ,,catastrophes ,,and ,,the ,,doctrine ,,of ,,uniformity #bhd ,art4 #a4 ,doctrine of ,catastrophes4 #b4 ,doctrine of ,uniformity4 #c4 ,is ,uniformity probable a priori8 #d4 ,cycle of ,uniformity indefinite4 #e4 ,uniformitarian ,arguments are ,negative only4 #f4 ,uniformity in the ,organic ,world4 #g4 ,origin of the present ,organic ,world4 #h4 ,nebular ,origin of the ,solar ,system4 #i4 ,origin of ,languages4 #aj4 ,no ,natural ,origin discoverable4 ,,chap4 ,,iv4 ,,of ,,the ,,relation ,,of ,,tradition ,,to ,,pal,,tiology #big ,art4 #a4 ,importance of ,tradition4 #b4 ,connexion of ,tradition and ,science4 #c4 ,natural and ,providential ,history of the ,world4 #d4 ,the ,sacred ,narrative4 #e4 ,difficulties in interpreting the ,sacred ,narrative4 #f4 ,such ,difficulties inevitable4 #g4 ,science tells us nothing concerning ,creation4 xv #h4 ,scientific views1 when familiar1 do not disturb the authority of ,scripture4 #i4 ,when should ,old ,interpretations be given up8 #aj4 ,in what ,spirit should the ,change be accepted8 #aa4 ,in what ,spirit should the ,change be urged8 #ab4 ,duty of ,mutual forbearance4 #ac4 ,case of ,galileo4 ,,chap4 ,v4 ,,of ,,the ,,conception ,,of ,a ,,first ,,cause #caf ,art4 #a4 ,the ,origin of things is not naturally discoverable2 #b4 ,yet has always been sought after4 #c4 ,there must be a ,first ,cause4 #d4 ,this is an ,axiom4 #e4 ,involved in the proof of a ,deity4 #f4 ,the mind is not satisfied without it4 #g4 ,the ,whole ,course of ,nature must have a ,cause4 #h4 ,necessary ,existence of ,god4 #i4 ,forms of the ,proof4 #aj4 ,idea of a ,first ,cause is ,necessary4 #aa4 ,conception of a ,first ,cause4 #ab4 ,the ,first ,cause in all ,sciences is the same4 #ac4 ,we are thus led to ,moral ,subjects4 ,conclusion of this ,history4 #a ,,book ,,vi4 ,,the ,,philosophy ,,of ,,chemistry4 ,a ,,philosopher was asked3--,how much does smoke weigh8 ,he answered3 ,subtract from the weight of the fuel the weight of the ashes1 and thou hast the weight of the smoke4 ,thus he assumed as incontrovertible that1 even in the fire1 the ,substance does not perish1 only its ,form undergoes a change4 ,in like manner the proposition1 ,nothing can come of ,nothing was only another consequence of the ,principle of ,permanence1 or rather of the ,principle of the ,enduring ,existence of the same subject with different appearances4 ,kant1 ,kritik d4 r4 ,vern4 #c ,,book ,,vi4 ,,the ,,philosophy ,,of ,,chemistry4 ,,chapter ,i4 ,,attempts ,,to ,,conceive ,,elementary ,,composition4 #a4 ,,we have now to bring into view1 if possible1 the ,ideas and ,general ,principles which are involved in ,chemistry1--the science of the composition of bodies4 ,for in this as in other parts of human knowledge1 we shall find that there are certain ,ideas1 deeply seated in the mind1 though shaped and unfolded by external observation1 which are necessary conditions of the existence of such a science4 ,these ,ideas it is1 which impel man to such a knowledge of the ,composition of bodies1 which give meaning to facts exhibiting this composition1 and universality to special truths discovered by experience4 ,these are the ,ideas of ,element and of ,substance4 ,unlike the ,idea of ,polarity1 of which we treated in the last ,book1 these ,ideas have been current in men's minds from very early times1 and formed the subject of some of the first speculations of philosophers4 ,it happened however1 as might have been expected1 that in the first attempts they were not clearly distinguished from other notions1 and were apprehended and applied in an obscure and confused manner4 ,we cannot better exhibit the peculiar character and meaning of these ,ideas than by tracing the form which they have assumed #d and the efficacy which they have exerted in these successive essays4 ,this1 therefore1 ,i shall endeavour to do1 beginning with the ,idea of ,element4 #b4 ,that bodies are composed or made up of certain parts1 elements1 or principles1 is a conception which has existed in men's minds from the beginning of the first attempts at speculative knowledge4 ,the doctrine of the ,four ,elements1 ,earth1 ,air1 ,fire and ,water1 of which all things in the universe were supposed to be constituted1 is one of the earliest forms in which this conception was systematized2 and this doctrine is stated by various authors to have existed as early as the times of the ancient ,egyptians#af4 ,the words usually employed by ,greek writers to express these elements are a principle or beginning1 and 1 which probably meant a letter 7of a word7 before it meant an element of a compound4 ,for the resolution of a word into its letters is undoubtedly a remarkable instance of a successful analysis performed at an early stage of man's history2 and might very naturally supply a metaphor to denote the analysis of substances into their intimate parts1 when men began to contemplate such an analysis as a subject of speculation4 ,the ,latin word elementum itself1 though by its form it appears to be a derivative abstract term1 comes from some root now obsolete2 probably#bf from a word signifying to grow or spring up4 ,note #af3 ,gilbert's ,phys4 #a4 i4 c4 iii4 ,note #bf3 ,vossius in voce4 ,conjecto esse ab antiqua voco eleo pro oleo1 id est cresco3 a qua signiflcatione proles1 suboles1 adolescens3 ut ab juratum1 juramentum2 ab adjutum1 adjumentum3 sic ab eletum1 elementum3 quia inde omnia crescunt ac nascuntur4 ,the mode in which elements form the compound bodies and determine their properties was at first1 as might be expected1 vaguely and variously conceived4 ,it will1 ,i trust1 hereafter be made clear to the reader that the relation of the elements to the compound involves a peculiar and appropriate ,fundamental ,idea1 not susceptible of being correctly represented by any comparison or combination of other ideas1 and guiding us to clear and definite results only when it is illustrated #e and nourished by an abundant supply of experimental facts4 ,but at first the peculiar and special notion which is required in a just conception of the constitution of bodies was neither discerned nor suspected2 and up to a very late period in the history of chemistry1 men went on attempting to apprehend the constitution of bodies more clearly by substituting for this obscure and recondite idea of ,elementary ,composition1 some other idea more obvious1 more luminous1 and more familiar1 such as the ideas of ,resemblance1 ,position1 and mechanical ,force4 ,we shall briefly speak of some of these attempts1 and of the errours which were thus introduced into speculations on the relations of elements and compounds4 #c4 ,compounds assumed to resemble their ,elements4--,the first notion was that compounds derive their qualities from their elements by resemblance3--they are hot in virtue of a hot element1 heavy in virtue of a heavy element1 and so on4 ,in this way the doctrine of the four elements was framed2 for every body is either hot or cold1 moist or dry2 and by combining these qualities in all possible ways1 men devised four elementary substances1 as has been stated in the ,history#cf4 ,note #cf3 ,hist4 ,ind4 ,sc4 b4 i4 c4 ii4 sec4 #b4 ,this assumption of the derivation of the qualities of bodies from similar qualities in the elements was1 as we shall see1 altogether baseless and unphilosophical1 yet it prevailed long and universally4 ,it was the foundation of medicine for a long period1 both in ,europe and ,asia2 disorders being divided into hot1 cold1 and the like2 and remedies being arranged according to similar distinctions4 ,many readers will recollect1 perhaps1 the story#df of the indignation which the ,persian physicians felt towards the ,european1 when he undertook to cure the ill effects of cucumber upon the patient1 by means of mercurial medicine3 for cucumber1 which is cold1 could not be counteracted1 they maintained1 by mercury1 which in their classification is cold also4 ,similar views of the operation of medicines might #f easily be traced in our own country4 ,a moment's reflection may convince us that when drugs of any kind are subjected to the chemistry of the human stomach and thus made to operate on the human frame1 it is utterly impossible to form the most remote conjecture what the result will be1 from any such vague notions of their qualities as the common use of our senses can give4 ,and in like manner the common operations of chemistry give rise1 in almost every instance1 to products which bear no resemblance to the materials employed4 ,the results of the furnace1 the alembic1 the mixture1 frequently have no visible likeness to the ingredients operated upon4 ,iron becomes steel by the addition of a little charcoal2 but what visible trace of the charcoal is presented by the metal thus modified8 ,the most beautiful colours are given to glass and earthenware by minute portions of the ores of black or dingy metals1 as iron and manganese4 ,the worker in metal1 the painter1 the dyer1 the vintner1 the brewer1 all the artisans in short who deal with practical chemistry1 are able to teach the speculative chemist that it is an utter mistake to expect that the qualities of the elements shall be still discoverable1 in an unaltered form1 in the compound4 ,this first rude notion of an element1 that it determines the properties of bodies by resemblance1 must be utterly rejected and abandoned before we can make any advance towards a true apprehension of the constitution of bodies4 ,note #df3 ,see ,hadji ,baba4 #d4 ,this step accordingly was made1 when the hypothesis of the four elements was given up1 and the doctrine of the three ,principles1 ,salt1 ,sulphur1 and ,mercury1 was substituted in its place4 ,for in making this change1 as ,i have remarked in the ,history#ef1 the real advance was the acknowledgment of the changes1 produced by the chemist's operations1 as results to be accounted for by the union and separation of substantial elements1 however great the changes1 and however unlike the product might be to the materials4 ,and this step once made1 chemists went on constantly #g advancing towards a truer view of the nature of an element1 and consequently1 towards a more satisfactory theory of chemical operations4 ,note #ef3 ,hist4 ,ind4 ,sc4 b4 iv4 c4 #a4 #e4 ,yet we may1 ,i think1 note one instance1 even in the works of eminent modern chemists1 in which this maxim1 that we have no right to expect any resemblance between the elements and the compound1 is lost sight of4 ,i speak of certain classifications of mineral substances4 ,berzelius1 in his ,system of ,mineral ,arrangement1 places sulphur next to the sulphurets4 ,but surely this is an errour1 involving the ancient assumption of the resemblance of elements and compounds2 as if we were to expect the sulphurets to bear a resemblance to sulphur4 ,all classifications are intended to bring together things resembling each other3 the sulphurets of metals have certain general resemblances to each other which make them a tolerably distinct1 well determined1 class of bodies4 ,but sulphur has no resemblances with these1 and no analogies with them1 either in physical or even in chemical properties4 ,it is a simple body2 and both its resemblances and its analogies direct us to place it along with other simple bodies1 7selenium1 and phosphorus17 which1 united with metals1 produce compounds not very different from the sulphurets4 ,sulphur cannot be1 nor approach to being1 a sulphuret2 we must not confound what it is with what it makes4 ,sulphur has its proper influence in determining the properties of the compound into which it enters2 but it does not do this according to resemblance of qualities1 or according to any principle which properly leads to propinquity in classification4 #f4 ,compounds assumed to be determined by the ,figure of ,elements4--,i pass over the fanciful modes of representing chemical changes which were employed by the ,alchemists2 for these strange inventions did little in leading men towards a juster view of the relations of elements to compounds4 ,i proceed for an instant to the attempt to substitute another obvious conception for the still obscure notion of elementary composition4 ,it was imagined that all the properties of bodies and their mutual operations might be #h accounted for by supposing them constituted of particles of various forms1 round or angular1 pointed or hooked1 straight or spiral4 ,this is a very ancient hypothesis1 and a favourite one with many casual speculators in all ages4 ,thus ,lucretius undertakes to explain why wine passes rapidly through a sieve and oil slowly1 by telling us that the latter substance has its particles either larger than those of the other1 or more hooked and interwoven together4 ,and he accounts for the difference of sweet and bitter by supposing the particles in the former case to be round and smooth1 in the latter sharp and jagged#ff4 ,similar assumptions prevailed in modern times on the revival of the mechanical philosophy1 and constitute a large part of the physical schemes of ,descartes and ,gassendi4 ,they were also adopted to a considerable extent by the chemists4 ,acids were without hesitation assumed to consist of sharp pointed particles2 which1 ',i hope1' ,lemery says#gf1 'no one will dispute1 seeing every one's experience does demonstrate it3 he needs but taste an acid to be satisfied of it1 for it pricks the tongue like anything keen and finely cut4' ,such an assumption is not only altogether gratuitous and useless1 but appears to be founded in some degree upon a confusion in the metaphorical and literal use of such words as keen and sharp4 ,the assumption once made1 it was easy to accommodate it1 in a manner equally arbitrary1 to other facts4 ',a demonstrative and convincing proof that an acid does consist of pointed parts is1 that not only all acid salts do crystallize into edges1 but all dissolutions of different things1 caused by acid liquors1 do assume this figure in their crystallization4 ,these crystals consist of points differing both in length and bigness one from another1 and this diversity must be attributed to the keener or blunter edges of the different sorts of acids3 and so likewise this difference of the points in subtilty is the cause that one acid can penetrate and dissolve with one sort of mixt1 that another can't rarify at all3 ,thus vinegar dissolves lead1 #i which aqua fortis can't3 aqua fortis dissolves quicksilver1 which vinegar will not touch2 aqua regalis dissolves gold1 whenas aqua fortis cannot meddle with it2 on the contrary1 aqua fortis dissolves silver1 but can do nothing with gold1 and so of the rest4' ,note #ff3 ,de ,rerum ,natura1 ii4 #cij sqq4 ,note #gf3 ,chemistry1 p4 #be4 ,the leading fact of the vehement combination and complete union of acid and alkali readily suggested a fit form for the particles of the latter class of substances4 ',this effect1' ,lemery adds1 'may make us reasonably conjecture that an alkali is a terrestrious and solid matter whose forms are figured after such a manner that the acid points entering in do strike and divide whatever opposes their motion4' ,and in a like spirit are the speculations in ,dr4 ,mead's ,mechanical ,account of ,poisons 7#agde74 ,thus he explains the poisonous effect of corrosive sublimate of mercury by saying#hf that the particles of the salt are a kind of lamell or blades to which the mercury gives an additional weight4 ,if resublimed with three-fourths the quantity of mercury1 it loses its corrosiveness1 7becoming calomel17 which arises from this1 that in sublimation 'the crystalline blades are divided every time more and more by the force of the fire3' and 'the broken pieces of the crystals uniting into little masses of differing figures from their former make1 those cutting points are now so much smaller that they cannot make wounds deep enough to be equally mischievous and deadly3 and therefore do only vellicate and twitch the sensible membranes of the stomach4' ,note #hf3 ,p4 #aii4 #g4 ,among all this very fanciful and gratuitous assumption we may notice one true principle clearly introduced1 namely1 that the suppositions which we make respecting the forms of the elementary particles of bodies and their mode of combination must be such as to explain the facts of crystallization1 as well as of mere chemical change4 ,this principle we shall hereafter have occasion to insist upon further4 ,i now proceed to consider a more refined form of assumption respecting the constitution of bodies1 yet #aj still one in which a vain attempt is made to substitute for the peculiar idea of chemical composition a more familiar mechanical conception4 #h4 ,compounds assumed to be determined by the ,mechanical ,attraction of the ,elements4--,when1 in consequence of the investigations and discoveries of ,newton and his predecessors1 the conception of mechanical force had become clear and familiar1 so far as the action of external forces upon a body was concerned1 it was very natural that the mathematicians who had pursued this train of speculation should attempt to apply the same conception to that mutual action of the internal parts of a body by which they are held together4 ,newton himself had pointed the way to this attempt4 ,in the ,preface to the ,principia1 after speaking of what he has done in calculating the effects of forces upon the planets1 satellites1 e41 he adds1 ',would it were permitted us to deduce the other phenomena of nature from mechanical principles by the same kind of reasoning4 ,for many things move me to suspect that all these phenomena depend upon certain forces1 by which the particles of bodies1 through causes not yet known1 are either urged towards each other1 and cohere according to regular figures1 or are repelled and recede from each other2 which forces being unknown1 philosophers have hitherto made their attempts upon nature in vain4' ,the same thought is at a later period followed out further in one of the ,queries at the end of the ,opticks#if4 ',have not the small particles of bodies certain ,powers1 ,virtues1 or ,forces1 by which they act at a distance1 not only upon the rays of light for reflecting1 refracting and inflecting them1 but also upon one another for producing a great part of the phenomena of nature8' ,and a little further on he proceeds to apply this expressly to chemical changes4 ',when ,salt of ,tartar runs per deliquium or as we now express it1 deliquesces is not this done by an attraction between the particles of the ,salt of ,tartar and the particles of the water which float in the air in #aa the form of vapours8 ,and why does not common salt1 or saltpetre1 or vitriol1 run per deliquium1 but for want of such an attraction8 or why does not ,salt of ,tartar draw more water out of the air than in a certain proportion to its quantity1 but for want of an attractive force after it is saturated with water8' ,he goes on to put a great number of similar cases1 all tending to the same point1 that chemical combinations cannot be conceived in any other way than as an attraction of particles4 ,note #if3 ,query #ca4 #i4 ,succeeding speculators in his school attempted to follow out this view4 ,dr4 ,frend1 of ,christ ,church1 in #agaj1 published his ,prlectiones ,chymic1 in quibus omne fere ,operationes ,chymic ad vera ,principia ex ipsius ,natur ,legibus rediguntur4 ,oxonii habit4 ,this book is dedicated to ,newton1 and in the dedication1 the promise of advantage to chemistry from the influence of the ,newtonian discoveries is spoken of somewhat largely1--much more largely1 indeed1 than has yet been justified by the sequel4 ,after declaring in strong terms that the only prospect of improving science consists in following the footsteps of ,newton1 the author adds1 ',that force of attraction1 of which you first so successfully traced the influence in the heavenly bodies1 operates in the most minute corpuscles1 as you long ago hinted in your ,principia1 and have lately plainly shown in your ,opticks2 and this force we are only just beginning to perceive and to study4 ,under these circumstances ,i have been desirous of trying what is the result of this view in chemistry4' ,the work opens formally enough1 with a statement of general mechanical principles1 of which the most peculiar are these3--',that there exists an attractive force by which particles when at very small distances from each other1 are drawn together2--that this force is different1 according to the different figure and density of the particles2--that the force may be greater on one side of a particle than on the other2--that the force by which particles cohere together arises from attraction1 and is variously modified according to the quantity of contacts4' ,but these principles are not #ab applied in any definite manner to the explanation of specific phenomena4 ,he attempts1 indeed1 the question of special solvents#ajf4 ,why does aqua fortis dissolve silver and not gold1 while aqua regia dissolves gold and not silver8 which1 he says1 is the most difficult question in chemistry1 and which is certainly a fundamental question in the formation of chemical theory4 ,he solves it by certain assumptions respecting the forces of attraction of the particles1 and also the diameter of the particles of the acids and the pores of the metals1 all which suppositions are gratuitous4 ,note #ajf3 ,p4 #ed4 #aj4 ,we may observe further1 that by speaking1 as ,i have stated that he does1 of the figure of particles1 he mixes together the assumption of the last section with the one which we are considering in this4 ,this combination is very unphilosophical1 or1 to say the least1 very insufficient1 since it makes a new hypothesis necessary4 ,if a body be composed of cubical particles1 held together by their mutual attraction1 by what force are the parts of each cube held together8 ,in order to understand their structure1 we are obliged again to assume a cohesive force of the second order1 binding together the particles of each particle4 ,and therefore ,newton himself says#aaf1 very justly1 ',the parts of all homogeneal hard bodies which fully touch each other1 stick together very strongly3 and for explaining how this is1 some have invented hooked atoms1 which is begging the question4' ,for 7he means to imply17 how do the parts of the hook stick together8 ,note #aaf3 ,opticks1 p4 #cfd4 ,the same remark is applicable to all hypotheses in which particles of a complex structure are assumed as the constituents of bodies3 for while we suppose bodies and their known properties to result from the mutual actions of these particles1 we are compelled to suppose the parts of each particle to be held together by forces still more difficult to conceive1 since they are disclosed only by the properties of these particles1 which as yet are unknown4 ,yet ,newton himself has not abstained from such hypotheses3 thus he says#abf1 ',a particle of #ac a salt may be compared to a chaos1 being dense1 hard1 dry1 and earthy in the center1 and moist and watery in the circumference4' ,note #abf3 ,opticks1 p4 #cfb4 ,since ,newton's time the use of the term attraction1 as expressing the cause of the union of the chemical elements of bodies1 has been familiarly continued2 and has1 no doubt1 been accompanied in the minds of many persons with an obscure notion that chemical attraction is1 in some way1 a kind of mechanical attraction of the particles of bodies4 ,yet the doctrine that chemical 'attraction' and mechanical attraction are forces of the same kind has never1 so far as ,i am aware1 been worked out into a system of chemical theory2 nor even applied with any distinctness as an explanation of any particular chemical phenomena4 ,any such attempt1 indeed1 could only tend to bring more clearly into view the entire inadequacy of such a mode of explanation4 ,for the leading phenomena of chemistry are all of such a nature that no mechanical combination can serve to express them1 without an immense accumulation of additional hypotheses4 ,if we take as our problem the changes of colour1 transparency1 texture1 taste1 odour1 produced by small changes in the ingredients1 how can we expect to give a mechanical account of these1 till we can give a mechanical account of colour1 transparency1 texture1 taste1 odour1 themselves8 ,and if our mechanical hypothesis of the elementary constitution of bodies does not explain such phenomena as those changes1 what can it explain1 or what can be the value of it8 ,i do not here insist upon a remark which will afterwards come before us1 that even crystalline form1 a phenomenon of a far more obviously mechanical nature than those just alluded to1 has never yet been in any degree explained by such assumptions as this1 that bodies consist of elementary particles exerting forces of the same nature as the central forces which we contemplate in ,mechanics4 ,when therefore ,newton asks1 ',when some stones1 as spar of lead1 dissolved in proper menstruums1 become salts1 do not these things show that salts are dry earth and watery acid united by attraction8' we may #ad answer1 that this mode of expression appears to be intended to identify chemical combination with mechanical attraction2--that there would be no objection to any such identification1 if we could1 in that way1 explain1 or even classify well1 a collection of chemical facts2 but that this has never yet been done by the help of such expressions4 ,till some advance of this kind can be pointed out1 we must necessarily consider the power which produces chemical combination as a peculiar principle1 a special relation of the elements1 not rightly expressed in mechanical terms4 ,and we now proceed to consider this relation under the name by which it is most familiarly known4 #ae ,,chapter ,,ii4 ,,establishment ,,and ,,development ,,of ,,the ,,idea ,,of ,,chemical ,,affinity4 #a4 ,,the earlier chemists did not commonly involve themselves in the confusion into which the mechanical philosophers ran1 of comparing chemical to mechanical forces4 ,their attention was engaged1 and their ideas were moulded1 by their own pursuits4 ,they saw that the connexion of elements and compounds with which they had to deal1 was a peculiar relation which must be studied directly2 and which must be understood1 if understood at all1 in itself1 and not by comparison with a different class of relations4 ,at different periods of the progress of chemistry1 the conception of this relation1 still vague and obscure1 was expressed in various manners2 and at last this conception was clothed in tolerably consistent phraseology1 and the principles which it involved were1 by the united force of thought and experiment1 brought into view4 #b4 ,the power by which the elements of bodies combine chemically1 being1 as we have seen1 a peculiar agency1 different from mere mechanical connexion or attraction1 it is desirable to have it designated by a distinct and peculiar name2 and the term ,affinity has been employed for that purpose by most modern chemists4 ,the word 'affinity' in common language means1 sometimes resemblance1 and sometimes relationship and ties of family4 ,it is from the latter sense that the metaphor is borrowed when we speak of 'chemical affinity4' ,by the employment of this term we do not indicate a resemblance1 but a disposition to unite4 ,using the word in a common unscientific manner1 we might say that chlorine1 bromine1 and iodine1 have a great #af natural affinity with each other1 for there are considerable resemblances and analogies among them2 but these bodies have very little chemical ,affinity for each other4 ,the use of the word in the former sense1 of resemblance1 can be traced in earlier chemists2 but the word does not appear to have acquired its peculiar chemical meaning till after ,boerhaave's time4 ,boerhaave1 however1 is the writer in whom we first find a due apprehension of the peculiarity and importance of the ,idea which it now expresses4 ,when we make a chemical solution#acf1 he says1 not only are the particles of the dissolved body separated from each other1 but they are closely united to the particles of the solvent4 ,when aqua regia dissolves gold1 do you not see1 he says to his hearers1 that there must be between each particle of the solvent and of the metal1 a mutual virtue by which each loves1 unites with1 and holds the other 7amat1 unit1 retinet78 ,the opinion previously prevalent had been that the solvent merely separates the parts of the body dissolved3 and most philosophers had conceived this separation as performed by mechanical operations of the particles1 resembling1 for instance1 the operation of wedges breaking up a block of timber4 ,but ,boerhaave forcibly and earnestly points out the insufficiency of the conception4 ,this1 he says1 does not account for what we see4 ,we have not only a separation1 but a new combination4 ,there is a force by which the particles of the solvent associate to themselves the parts dissolved1 not a force by which they repel and dissever them4 ,we are here to imagine not mechanical action1 not violent impulse1 not antipathy1 but love1 at least if love be the desire of uniting4 7,non igitur hic etiam actiones mechanic1 non propulsiones violent1 non inimiciti cogitand1 sed amiciti1 si amor dicendus copul cupido47 ,the novelty of this view is evidenced by the mode in which he apologizes for introducing it4 ',fateor1 paradoxa hc assertio4' ,to ,boerhaave1 therefore1 7especially considering his great influence as a teacher of chemistry17 we may #ag assign the merit of first diffusing a proper view of ,chemical ,affinity as a peculiar force1 the origin of almost all chemical changes and operations4 ,note #acf3 ,elementa ,chemi1 ,lugd4 ,bat4 #agcb1 p4 #fgg4 #c4 ,to ,boerhaave is usually assigned also the credit of introducing the word ',affinity' among chemists2 but ,i do not find that the word is often used by him in this sense2 perhaps not at all#adf4 ,but however this may be1 the term is1 on many accounts1 well worthy to be preserved1 as ,i shall endeavour to show4 ,other terms were used in the same sense during the early part of the eighteenth century4 ,thus when ,geoffroy1 in #agah1 laid before the ,academy of ,paris his ,tables of ,affinities1 which perhaps did more than any other event to fix the ,idea of ,affinity1 he termed them ',tables of the ,relations of ,bodies2' ',tables des ,rapports3' speaking however1 also1 of their 'disposition to unite1' and using other phrases of the same import4 ,note #adf3 ,see ,dumas1 ,leons de ,phil4 ,chim4 p4 #cfd4 ,rees' ,cyclopdia1 ,art4 ,chemistry4 ,in the passage of ,boerhaave to which ,i refer above1 affinitas is rather opposed to1 than identified with1 chemical combination4 ,when1 he says1 the parts of the body to be dissolved are dissevered by the solvent1 why do they remain united to the particles of the solvent1 and why do not rather both the particles of the solvent and of the dissolved body collect into homogeneous bodies by their affinity8 'denuo se affinitate su natur colligant in corpora homogenea8' ,and the answer is1 because they possess another force which counteracts this affinity of homogeneous particles1 and makes compounds of different elements4 ,affinity1 in chemistry1 now means the tendency of different kinds of matter to unite3 but it appears1 as ,i have said1 to have acquired this sense since ,boerhaave's time4 ,the term attraction1 having been recommended by ,newton as a fit word to designate the force which produces chemical combination1 continued in great favour in ,england1 where the ,newtonian philosophy was looked upon as applicable to every branch of science4 ,in ,france1 on the contrary1 where ,descartes still reigned triumphant1 'attraction1' the watch-word of the enemy1 was a sound never uttered but with dislike and suspicion4 ,in #agah 7in the notice of ,geoffroy's ,table17 the ,secretary of the ,academy1 after pointing out some of the peculiar circumstances of chemical #ah combinations1 says1 ',sympathies and attractions would suit well here1 if there were such things1' ',les sympathies1 les attractions conviendroient bien ici1 si elles taient quelque chose4' ,and at a later period1 in #agca1 having to write the loge of ,geoffroy after his death1 he says1 ',he gave1 in #agah1 a singular system1 and a ,table of ,affinities1 or ,relations of the different substances in chemistry4 ,these affinities gave an easiness to some persons1 who feared that they were attractions in disguise1 and all the more dangerous in consequence of the seductive forms which clever people have contrived to give them4 ,it was found in the sequel that this scruple might be got over4' ,this is the earliest published instance1 so far as ,i am aware1 in which the word ',affinity' is distinctly used for the cause of chemical composition2 and taking into account the circumstances1 the word appears to have been adopted in ,france in order to avoid the word attraction1 which had the taint of ,newtonianism4 ,accordingly we find the word affinit employed in the works of ,french chemists from this time4 ,thus1 in the ,transactions of the ,french ,academy for #agdf1 in a paper of ,macquer's upon ,arsenic1 he says#aef1 ',on peut facilement rendre raison de ces phenomnes par le moyen des affinits que les diffrens substances qui entrent dans ces combinaisons1 ont les uns avec les autres3' and he proceeds to explain the facts by reference to ,geoffroy's ,table4 ,and in ,macquer's ,elements of ,chemistry1 which appeared a few years later1 the ',affinity of ,composition' is treated of as a leading part of the subject1 much in the same way as has been practised in such books up to the present time4 ,from this period1 the word appears to have become familiar to all ,european chemists in the sense of which we are now speaking4 ,thus1 in the year #ageh1 the ,academy of ,sciences at ,rouen offered a prize for the best dissertation on ,affinity4 ,the prize was shared between ,m4 ,limbourg of ,theux1 near ,liege1 and ,m4 ,le ,sage #ai of ,geneva#aff4 ,about the same time other persons 7,manherr#agf1 ,nicolai#ahf1 and others7 wrote on the same subject1 employing the same name4 ,note #aef3 ,a4 ,p4 #agdf1 p4 #bja4 ,note #aff3 ,thomson's ,chemistry1 iii4 #aj4 ,limbourg's ,dissertation was published at ,liege1 in #agfa2 and ,le ,sage's at ,geneva4 ,note #agf3 ,dissertatio de ,affinitate ,corporum4 ,vindob4 #agfb4 ,note #ahf3 ,progr4 ,i4 ,,ii4 de ,affinitate ,corporum ,chimica4 ,jen4 #agge1 #aggf4 ,nevertheless1 in #agge1 the ,swedish chemist ,bergman1 pursuing still further this subject of ,chemical ,affinities1 and the expression of them by means of ,tables1 returned again to the old ,newtonian term2 and designated the disposition of a body to combine with one rather than another of two others as ,elective ,attraction4 ,and as his work on ,elective ,attractions had great circulation and great influence1 this phrase has obtained a footing by the side of ,affinity1 and both one and the other are now in common use among chemists4 #d4 ,i have said above that the term ,affinity is worthy of being retained as a technical term4 ,if we use the word attraction in this case1 we identify or compare chemical with mechanical attraction2 from which identification and comparison1 as ,i have already remarked1 no one has yet been able to extract the means of expressing any single scientific truth4 ,if such an identification or comparison be not intended1 the use of the same word in two different senses can only lead to confusion2 and the proper course1 recommended by all the best analogies of scientific history1 is to adopt a peculiar term for that peculiar relation on which chemical composition depends4 ,the word ,affinity1 even if it were not rigorously proper according to its common meaning1 still1 being simple1 familiar1 and well established in this very usage1 is much to be preferred before any other4 ,but further1 there are some analogies drawn from the common meaning of this word1 which appear to recommend it as suitable for the office which it has to discharge4 ,for common mechanical attractions and #bj repulsions1 the forces by which one body considered as a whole acts upon another external to it1 are1 as we have said1 to be distinguished from those more intimate ties by which the parts of each body are held together4 ,now this difference is implied1 if we compare the former relations1 the attractions and repulsions1 to alliances and wars between ,states1 and the latter1 the internal union of particles1 to those bonds of affinity which connect the citizens of the same state with one another1 and especially to the ties of ,family4 ,we have seen that ,boerhaave compares the union of two elements of a compound to their marriage2 'we must allow1' says an eminent chemist of our own time#aif1 'that there is some truth in this poetical comparison4' ,it contains this truth1--that the two become one to most intents and purposes1 and that the ,unit thus formed 7the ,family7 is not a mere juxtaposition of the component parts4 ,and thus the ,idea of ,affinity as the peculiar principle of chemical composition1 is established among chemists1 and designated by a familiar and appropriate name4 ,note #aif3 ,dumas1 ,leons de ,phil4 ,chim4 p4 #cfc4 #e4 ,analysis is possible4--,we must1 however1 endeavour to obtain a further insight into this ,idea1 thus fixed and named4 ,we must endeavour to extricate1 if not from the ,idea itself1 from the processes by which it has obtained acceptation and currency among chemists1 some principles which may define its application1 some additional specialities in the relations which it implies4 ,this we shall proceed to do4 ,the ,idea of ,affinity1 as already explained1 implies a disposition to combine4 ,but this combination is to be understood as admitting also of a possibility of separation4 ,synthesis implies ,analysis as conceivable3 or to recur to the image which we have already used1 ,divorce is possible when the ,marriage has taken place4 ,that there is this possibility1 is a conviction implied in all the researches of chemists1 ever since the true notion of composition began to predominate in their investigations4 ,one of the first persons who clearly #ba expressed this conviction was ,mayow1 an ,english physician1 who published his ,medico-,physical ,tracts in #afgd4 ,the first of them ,de ,sale-,nitro et ,spiritu ,nitro-,aerio1 contains a clear enunciation of this principle4 ,after showing how1 in the combinations of opposite elements1 as acid and alkali1 their properties entirely disappear1 and a new substance is formed not at all resembling either of the ingredients1 he adds#bjf1 ',although these salts thus mixed appear to be destroyed it is still possible for them to be separated from each other1 with their powers still entire4' ,he proceeds to exemplify this1 and illustrates it by the same image which ,i have already alluded to3 ',salia acida a salibus volatilibus discedunt1 ut cum sale fixo tartari1 tanquam sponso magis idoneo1 conjugium strictius ineunt4' ,this idea of a synthesis which left a complete analysis still possible1 was opposed to a notion previously current1 that when two heterogeneous bodies united together and formed a third body1 the two constituents were entirely destroyed1 and the result formed out of their ruins#baf4 ,and this conception of ,synthesis and ,analysis1 as processes which are possible successively and alternately1 and each of which supposes the possibility of the other1 has been the fundamental and regulative principle of the operations and speculations of analytical chemistry from the time of ,mayow to the present day4 ,note #bjf3 ,cap4 xiv4 p4 #bcc4 ,note #baf3 ,thomson's ,chemistry1 iii4 #h4 #f4 ,affinity is ,elective4--,when the idea of chemical affinity1 or disposition to unite1 was brought into view by the experiments and reasonings of chemists1 they found it necessary to consider this disposition as elective2--each element chose one rather than another of the elements which were presented to it1 and quitted its union with one to unite with another which it preferred4 ,this has already appeared in the passage just quoted from ,mayow4 ,he adds in the same strain1 ',i have no doubt that fixed salts choose one acid rather than another1 in order that they may coalesce with it #bb in a more intimate union4'--',nullus dubito salia fixa acidum unum pr aliis eligere1 ut cum eodem arctiore unione coalescant4' ,the same thought is expressed and exemplified by other chemists3 they notice innumerable cases in which1 when an ingredient is combined with a liquid1 if a new substance be immersed which has a greater affinity for the liquid1 the liquid combines with the new substance by election1 and the former 9999ingredient is precipitated4 ,thus ,stahl says#bbf1 ',in spirit of nitre dissolve silver2 put in copper and the silver is thrown down2 put in iron and the copper goes down2 put in zinc1 the iron precipitates2 put in volatile alkali1 the zinc is separated2 put in fixed alkali1 the volatile quits its hold4'--,as may be seen in this example1 we have in such cases1 not only a preference1 but a long gradation of preferences4 ,the spirit of nitre will combine with silver1 but it prefers copper2 prefers iron more2 zinc still more2 volatile alkali yet more2 fixed alkali the most4 ,note #bbf3 ,zymotechnia1 #afig1 p4 #aag4 ,the same thing was proved to obtain with regard to each element2 and when this was ascertained1 it became the object of chemists to express these degrees of preference1 by lists in which substances were arranged according to their disposition to unite with another substance4 ,in this manner was formed ,geoffroy's ,table of ,affinities 7#agah71 which we have already mentioned4 ,this ,table was further improved by other writers1 as ,gellert 7#agea7 and ,limbourg 7#agfa74 ,finally ,bergman improved these ,tables still further1 taking into account not only the order of affinities of each element for others1 but the sum of the tendencies to unite of each two elements1 which sum1 he held1 determined the resulting combination when several elements were in contact with each other4 #g4 ,as we have stated in the ,history#bcf1 when the doctrine of elective affinities had assumed this very definite and systematic form1 it was assailed by ,berthollet1 who maintained1 in his ,essai de ,statique #bc ,chimique1 7#ahjc17 that chemical affinities are not elective3--that1 when various elements are brought together1 their combinations do not depend upon the kind of elements alone1 but upon the quantity of each which is present1 that which is most abundant always entering most largely into the resulting compounds4 ,it may seem strange that it should be possible1 at so late a period of the science1 to throw doubt upon a doctrine which had presided over and directed its progress so long4 ,proust answered ,berthollet1 and again maintained that chemical affinity is elective4 ,i have1 in the ,history1 given the judgment of ,berzelius upon this controversy4 ',berthollet1' he says1 'defended himself with an acuteness which makes the reader hesitate in his judgment2 but the great mass of facts finally decided the point in favour of ,proust4' ,i may here add the opinion pronounced upon this subject by ,dr4 ,turner#bdf3 ',bergman erred in supposing the result of the chemical action to be in every case owing to elective affinity for this power is modified in its effects by various circumstances3 but ,berthollet ran into the opposite extreme in declaring that the effects formerly ascribed to that power are never produced by it4 ,that chemical attraction is exerted between different bodies with different degrees of energy1 is1 ,i apprehend1 indisputable4' ,and he then proceeds to give many instances of differences in affinity which cannot be accounted for by the operation of any modifying causes4 ,still more recently1 ,m4 ,dumas has taken a review of this controversy2 and1 speaking with enthusiasm of the work of ,berthollet1 as one which had been of inestimable service to himself in his early study of chemistry1 he appears at first disposed to award to him the victory in this dispute4 ,but his final verdict leaves undamaged the general principle now under our consideration1 that chemical affinity is elective4 ',for my own part1' he says#bef1 ',i willingly admit the notions of ,berthollet when we have to do with acids or #bd with bases1 of which the energy is nearly equal3 but when bodies endued with very energetic affinities are in presence of other bodies of which the affinities are very feeble1 ,i propose to adopt the following rule3 ,in a solution1 everything remaining dissolved1 the strong affinities satisfy themselves1 leaving the weak affinities to arrange matters with one another4 ,the strong acids take the strong bases1 and the weak acids can only unite with the weak bases4 ,the known facts are perfectly in accordance with this practical rule4' ,it is obvious that this recognition of a distinction between strong and weak affinities1 which operates to such an extent as to determine entirely the result1 is a complete acknowledgement of the ,elective nature of ,affinity1 as far as any person acquainted with chemical operations could contend for it4 ,for it must be allowed by all1 that solubility1 and other collateral circumstances1 influence the course of chemical combinations1 since they determine whether or not there shall take place that contact of elements without which affinity cannot possibly operate4 ,note #bcf3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 iii4 ,note #bdf3 ,chemistry1 p4 #aii4 #fth edition4 ,note #bef3 ,leons de ,philosophie ,chimique1 p4 #chf4 #h4 ,affinity is ,definite as to quantity4--,in proportion as chemists obtained a clearer view of the products of the laboratory as results of the composition of elements1 they saw more and more clearly that these results were definite2 that one element not only preferred to combine with another of a certain kind1 but also would combine with it to a certain extent and no further1 thus giving to the result not an accidental and variable1 but a fixed and constant character4 ,thus salts being considered as the result of the combination of two opposite principles1 acid and alkali1 and being termed neutral when these principles exactly balanced each other1 ,rouelle 7who was ,royal ,professor at ,paris in #agdb7 admits of neutral salts with excess of acid1 neutral salts with excess of base1 and perfect neutral salts4 ,beaume maintained#bff against him that there were no salts except those perfectly neutral1 the other classes being the results of mixture and imperfect #be combination4 ,but this question was not adequately treated till chemists made every experiment with the balance in their hands4 ,when this was done1 they soon discovered that1 in each neutral salt1 the proportional weights of the ingredients which composed it were always the same4 ,this was ascertained by ,wenzel1 whose ,doctrine of the ,affinities of ,bodies appeared in #aggg4 ,he not only ascertained that the proportions of elements in neutral chemical compounds are definite1 but also that they are reciprocal2 that is1 7to express his results in a manner now employed by chemists71 that if ,a1 a certain weight of a certain acid1 neutralize m1 a certain weight of a certain base1 and ,b1 a certain weight of a certain other acid1 neutralize n1 a certain weight of a certain other base2 the compound of ,a and n will also be neutral2 as also that of ,b and m4 ,the same views were again presented by ,richter in #agib1 in his ,principles of the ,measure of ,chemical ,elements4 ,and along with these facts1 that of the combination of elements in multiple proportions being also taken into account1 the foundations of the ,atomic ,theory were laid2 and that ,theory was propounded in #ahjc by ,mr4 ,dalton4 ,that theory1 however1 rests upon the ,idea of ,substance1 as well as upon that ,idea of ,chemical ,affinity which we are here considering2 and the discussion of its evidence and truth must be for the present deferred4 ,note #bff3 ,dumas1 ,phil4 ,chim4 p4 #aih4 #i4 ,the two principles just explained1--that ,affinity is ,definite as to the ,kind1 and as to the ,quantity of the elements which it unites1--have here been stated as results of experimental investigation4 ,that they could never have been clearly understood1 and therefore never firmly established1 without laborious and exact experiments1 is certain2 but yet we may venture to say that being once fully known1 they may seem to thoughtful men to possess an evidence beyond that of mere experiment4 ,for how1 in fact1 can we conceive combinations1 otherwise than as definite in kind and quantity8 ,if we were to suppose each element ready to combine with any other indifferently1 and indifferently in any quantity1 we should have a world in #bf which all would be confusion and indefiniteness4 ,there would be no fixed kinds of bodies4 ,salts1 and stones1 and ores1 would approach to and graduate into each other by insensible degrees4 ,instead of this1 we know that the world consists of bodies distinguishable from each other by definite differences1 capable of being classified and named1 and of having general propositions asserted concerning them4 ,and as we cannot conceive a world in which this should not be the case1 it would appear that we cannot conceive a state of things in which the laws of the combination of elements should not be of that definite and measured kind which we have above asserted4 ,this will1 perhaps1 appear more clearly by stating our fundamental convictions respecting chemical composition in another form1 which ,i shall1 therefore1 proceed to do4 #aj4 ,chemical ,composition determines ,physical ,properties4--,however obscure and incomplete may be our conception of the internal powers by which the ultimate particles of bodies are held together1 it involves1 at least1 this conviction3--that these powers are what determine bodies to be bodies1 and therefore contain the reason of all the properties which1 as bodies1 they possess4 ,the forces by which the particles of a body are held together1 also cause it to be hard or soft1 heavy or light1 opake or transparent1 black or red2 for if these forces are not the cause of these peculiarities1 what can be the cause8 ,by the very supposition which we make respecting these forces1 they include all the relations by which the parts are combined into a whole1 and therefore they1 and they only1 must determine all the attributes of the whole4 ,the foundation of all our speculations respecting the intimate constitution of bodies must be this principle1 that their composition determines their properties4 ,accordingly we find our chemists reasoning from this principle with great confidence1 even in doubtful cases4 ,thus ,davy1 in his researches concerning the diamond1 says3 ',that some chemical difference must exist between the hardest and most beautiful of the #bg gems and charcoal1 between a non-conductor and a conductor of electricity1 it is scarcely possible to doubt3 and it seems reasonable to expect that a very refined or perfect chemistry will confirm the analogies of nature2 and show that bodies cannot be the same in their composition or chemical nature1 and yet totally different in their chemical properties4' ,it is obvious that the principle here assumed is so far from being a mere result of experience1 that it is here appealed to to prove that all previous results of experience on this subject must be incomplete and inaccurate2 and that there must be some chemical difference between charcoal and diamond1 though none had hitherto been detected4 #aa4 ,in what manner1 according to what rule1 the chemical composition shall determine the kind of the substance1 we cannot reasonably expect to determine by mere conjecture or assumption1 without a studious examination of natural bodies and artificial compounds4 ,yet even in the most recent times1 and among men of science1 we find that an assumption of the most arbitrary character has in one case been mixed up with this indisputable principle1 that the elementary composition determines the kind of the substance4 ,in the classification of minerals1 one school of mineralogists have rightly taken it as their fundamental principle that the chemical composition shall decide the position of the mineral in the system4 ,but they have appended to this principle1 arbitrarily and unjustifiably1 the maxim that the element which is largest in quantity shall fix the class of the substance4 ,to make such an assumption is to renounce1 at once1 all hope of framing a system which shall be governed by the resemblances of the things classified2 for how can we possibly know beforehand that fifty-five per cent1 of iron shall give a substance its predominant properties1 and that forty-five per cent1 shall not8 ,accordingly1 the systems of mineralogical arrangement which have been attempted in this way1 7those of ,hay1 ,phillips1 and others17 have been found inconsistent with themselves1 ambiguous1 and incapable of leading to any general truths4 #bh #ab4 ,chemical ,composition and ,crystalline ,form correspond4--,thus the physical properties of bodies depend upon their chemical composition1 but in a manner which a general examination of bodies with reference to their properties and their composition can alone determine4 ,we may1 however1 venture to assert further1 that the more definite the properties are1 the more distinct may we expect to find this dependence4 ,now the most definite of the properties of bodies are those constant properties which involve relations of space2 that is1 their figure4 ,we speak not1 however1 of that external figure1 derived from external circumstances1 which1 so far from being constant and definite1 is altogether casual and arbitrary2 but of that figure which arises from their internal texture1 and which shows itself not only in the regular forms which they spontaneously assume1 but in the disposition of the parts to separate in definite directions1 and no others4 ,in short1 the most definite of the properties of perfect chemical compounds is their crystalline structure2 and therefore it is evident that the crystalline structure of each body1 and the forms which it affects1 must be in a most intimate dependence upon its chemical composition4 ,here again we are led to the brink of another theory2--that of crystalline structure1 which has excited great interest among philosophers ever since the time of ,hay4 ,but this theory involves1 besides that idea of chemical composition with which we are here concerned1 other conceptions1 which enter into the relations of figure4 ,these conceptions1 governed principally by the ,idea of ,symmetry1 must be unfolded and examined before we can venture to discuss any theory of crystallization3 and we shall proceed to do this as soon as we have first duly considered the ,idea of ,substance and its consequences4 #bi ,,chapter ,,iii4 ,,of ,,the ,,idea ,,of ,,substance4 #a4 ,axiom of the ,indestructibility of ,substance4--,,we now come to an ,idea of which the history is very different from those of which we have lately been speaking4 ,instead of being gradually and recently brought into a clear light1 as has been the case with the ,ideas of ,polarity and ,affinity1 the ,idea of ,substance has been entertained in a distinct form from the first periods of ,european speculation4 ,that this is so1 is proved by our finding a principle depending upon this ,idea current as an axiom among the early philosophers of ,greece3--namely1 that nothing can be produced out of nothing4 ,such an axiom1 more fully stated1 amounts to this3 that the substance of which a body consists is incapable of being diminished 7and consequently incapable of being augmented7 in quantity1 whatever apparent changes it may undergo4 ,its forms1 its distribution1 its qualities1 may vary1 but the substance itself is identically the same under all these variations4 ,the axiom just spoken of was the great principle of the physical philosophy of the ,epicurean school1 as it must be of every merely material philosophy4 ,the reader of ,lucretius will recollect the emphasis with which it is repeatedly asserted in his poem3 ,e nilo nil gigni1 in nilum nil posse reverti2 ,nought comes of nought1 nor ought returns to nought4 ,those who engaged in these early attempts at physical speculation were naturally much pleased with the clearness which was given to their notions of change1 composition1 and decomposition1 by keeping steadily hold of the ,idea of ,substance1 as marked by this #cj fundamental axiom4 ,nor has its authority ever ceased to be acknowledged4 ,a philosopher was asked#bgf1 ,what is the weight of smoke8 ,he answered1 ',subtract the weight of the ashes from the weight of the wood which is burnt1 and you have the weight of the smoke4' ,this reply would be assented to by all2 and it assumes as incontestable that even under the action of fire1 the material1 the substance1 does not perish1 but only changes its form4 ,note #bgf3 ,kant1 ,kritik der ,r4 ,v4 p4 #afg4 ,this principle of the indestructibility of substance might easily be traced in many reasonings and researches1 ancient and modern4 ,for instance1 when the chemist works with the retort1 he places the body on which he operates in one part of an inclosed cavity1 which1 by its bendings and communications1 separates at the same time that it confines1 the products which result from the action of fire3 and he assumes that this process is an analysis of the body into its ingredients1 not a creation of anything which did not exist before1 or a destruction of anything which previously existed4 ,and he assumes further1 that the total quantity of the substance thus analysed is the sum of the quantities of its ingredients4 ,this principle is the very basis of chemical speculation1 as we shall hereafter explain more fully4 #b4 ,the ,idea of ,substance4--,the axiom above spoken of depends upon the ,idea of ,substance1 which is involved in all our views of external objects4 ,we unavoidably assume that the qualities and properties which we observe are properties of things2--that the adjective implies a substantive2--that there is1 besides the external characters of things1 something of which they are the characters4 ,an apple which is red1 and round1 and hard1 is not merely redness1 and roundness1 and hardness3 these circumstances may all alter while the apple remains the same apple4 ,behind or under the appearances which we see1 we conceive something of which we think2 or1 to use the metaphor which obtained currency among the ancient philosophers1 the #ca attributes and qualities which we observe are supported by and inherent in something3 and this something is hence called a substratum or substance1--that which stands beneath the apparent qualities and supports them4 ,that we have such an ,idea1 using the term ',idea' in the sense in which ,i have employed it throughout these disquisitions1 is evident from what has been already said4 ,the ,axiom of the ,indestructibility of ,substance proves the existence of the ,idea of ,substance1 just as the ,axioms of ,geometry and ,arithmetic prove the existence of the ,ideas of ,space and ,number4 ,in the case of ,substance1 as of space or number1 the ideas cannot be said to be borrowed from experience1 for the axioms have an authority of a far more comprehensive and demonstrative character than any which experience can bestow4 ,the axiom that nothing can be produced from nothing and nothing destroyed1 is so far from being a result of experience1 that it is apparently contradicted by the most obvious observation4 ,it has1 at first1 the air of a paradox2 and by those who refer to it1 it is familiarly employed to show how fallacious common observation is4 ,the assertion is usually made in this form2--that nothing is created and nothing annihilated1 notwithstanding that the common course of our experience appears to show the contrary4 ,the principle is not an empirical1 but a necessary and universal truth2--is collected1 not from the evidence of our senses1 but from the operation of our ideas4 ,and thus the universal and undisputed authority of the axiom proves the existence of the ,idea of ,substance4 #c4 ,locke's ,denial of the ,idea of ,substance4--,i shall not attempt to review the various opinions which have been promulgated respecting this ,idea3 but it may be worth our while to notice briefly the part which it played in the great controversy concerning the origin of our ideas which ,locke's ,essay occasioned4 ,locke's object was to disprove the existence of all ideas not derived from ,sensation or ,reflection3 and since the idea of substance as distinct from external qualities1 is #cb manifestly not derived directly from sensation1 nor by any very obvious or distinct process from reflection1 ,locke was disposed to exclude the idea as much as possible4 ,accordingly1 in his argumentation against ,innate ,ideas#bhf1 he says plainly1 'the idea of substance1 which we neither have nor can have by sensation or reflection4' ,and the inference which he draws is1 'that we have no such clear idea at all4' ,what then1 it may be asked1 do we mean by the word substance8 ,this also he answers1 though somewhat strangely1 ',we signify nothing by the word substance1 but only an uncertain supposition of we know not what1 i4 e4 of something whereof we have no particular distinct positive idea1 which we take to be the substratum1 or support1 of those ideas we know4' ,that while he indulged in this tautological assertion of our ignorance and uncertainty1 he should still have been compelled to acknowledge that the word substance had some meaning1 and should have been driven to explain it by the identical metaphors of 'substratum' and 'support1' is a curious proof how impossible it is entirely to reject this idea4 ,note #bhf3 ,essay1 b4 i4 c4 iv4 s4 #ah4 ,but as we have already seen1 the supposition of the existence of substance is so far from being uncertain1 that it carries with it irresistible conviction1 and substance is necessarily conceived as something which cannot be produced or destroyed4 ,it may be easily supposed1 therefore1 that when the controversy between ,locke and his assailants came to this point1 he would be in some difficulty4 ,and1 indeed1 though with his accustomed skill in controversy1 he managed to retain a triumphant tone1 he was driven from his main points4 ,thus he repels the charge that he took the being of substance to be doubtful#bif4 ,he says1 ',having everywhere affirmed and built upon it that man is a substance1 ,i cannot be supposed to question or doubt of the being of substance1 till ,i can question or doubt of my own being4' ,he attempts to make a stand by saying that being of things does not depend upon our #cc ideas2 but if he had been asked how1 without having an idea of substance1 he knew substance to be1 it is difficult to conceive what answer he could have made4 ,again1 he had said that our idea of substance arises from our 'accustoming ourselves to suppose' a substratum of qualities4 ,upon this his adversary1 ,bishop ,stillingfleet1 very properly asks1 ,is this custom grounded upon true reason or no8 ,to which ,locke replies1 that it is grounded upon this3 ,that we cannot conceive how simple ideas of sensible qualities should subsist alone2 and therefore we suppose them to exist in1 and to be supported by some common subject1 which support we denote by the name substance4 ,thus he allows1 not only that we necessarily assume the reality of substance1 but that we cannot conceive qualities without substance2 which are concessions so ample as almost to include all that any advocate for the ,idea of ,substance need desire4 ,note #bif3 ,essay1 b4 ii4 c4 ii4 and ,first ,letter to the ,bishop of ,worcester4 ,perhaps ,locke1 and the adherents of ,locke1 in denying that we have an idea of substance in general1 were latently influenced by finding that they could not1 by any effort of mind1 call up any image which could be considered as an image of substance in general4 ,that in this sense we have no idea of substance1 is plain enough2 but in the same sense we have no idea of space in general1 or of time1 or number1 or cause1 or resemblance4 ,yet we certainly have such a power of representing to our minds space1 time1 number1 cause1 resemblance1 as to arrive at numerous truths by means of such representations4 ,these general representations ,i have all along called ,ideas1 nor can ,i discover any more appropriate word2 and in this sense1 we have also1 as has now been shown1 an ,idea of ,substance4 #d4 ,is all ,material ,substance heavy8--,the principle that the quantity of the substance of any body remains unchanged by our operations upon it1 is1 as we have said1 of universal validity4 ,but then the question occurs1 how are we to ascertain the quantity of substance1 and thus1 to apply the principle in particular cases4 ,in the case above mentioned1 where #cd smoke was to be weighed1 it was manifestly assumed that the quantity of the substance might be known by its weight2 and that the total quantity being unchanged1 the total weight also would remain the same4 ,now on what grounds do we make this assumption8 ,is all material substance heavy8 and if we can assert this to be so1 on what grounds does the truth of the assertion rest8 ,these are not idle questions of barren curiosity2 for in the history of that science 7,chemistry7 to which the ,idea of ,substance is principally applicable1 nothing less than the fate of a comprehensive and long established theory 7the ,phlogiston theory7 depended upon the decision of this question4 ,when it was urged that the reduction of a metal from a calcined to a metallic form could not consist in the addition of phlogiston1 because the metal was lighter than the calx had been2 it was replied by some1 that this was not conclusive1 for that phlogiston was a principle of levity1 diminishing the weight of the body to which it was added4 ,this reply was1 however1 rejected by all the sounder philosophers1 and the force of the argument finally acknowledged4 ,but why was this suggestion of a substance having no weight1 or having absolute levity1 repudiated by the most reflective reasoners8 ,it is assumed1 it appears1 that all matter must be heavy2 what is the ground of this assumption8 ,the ground of such an assumption appears to be the following4 ,our idea of substance includes in it this3--that substance is a quantity capable of addition2 and thus capable of making up1 by composition1 a sum equal to all its parts4 ,but substance1 and the quantity of substance1 can be known to us only by its attributes and qualities4 ,and the qualities which are capable constantly and indefinitely of increase and diminution by increase and diminution of the parts1 must be conceived inseparable from the substance4 ,for the qualities1 if removable from the substance at all1 must be removable by some operation performed upon the substance2 and by the idea of substance1 all such operations are only equivalent to separation1 junction1 and union of parts4 ,hence those characters #ce which thus universally increase and diminish by addition and subtraction of the things themselves1 belong to the substance of the things4 ,they are measures of its quantity1 and are not merely its separable qualities4 ,the weight of bodies is such a character4 ,however we compound or divide bodies1 we compound and divide their weight in the same manner4 ,we may dismember a body into the minutest parts2 but the sum of the weights of the parts is always equal to the whole weight of the body4 ,the weight of a body can be in no way increased or diminished1 except by adding something to it or taking something from it4 ,if we bake a brick1 we do not conceive that the change of colour or of hardness1 implies that anything has been created or destroyed4 ,it may easily be that the parts have only assumed a new arrangement2 but if the brick have lost weight1 we suppose that something 7moisture for instance7 has been removed elsewhere4 ,thus weight is apprehended as essential to matter4 ,in considering the dismemberment or analysis of bodies1 we assume that there must be some criterion of the quantity of substance2 and this criterion can possess no other properties than their weight possesses4 ,if we assume an element which has no weight1 or the weight of which is negative1 as some of the defenders of phlogiston attempted to do1 we put an end to all speculation on such subjects4 ,for if weight is not the criterion of the quantity of one element1 phlogiston for instance1 why is weight the criterion of the quantity of any other element8 ,we may1 by the same right1 assume any other real or imaginary element to have levity instead of gravity2 or to have a peculiar intensity of gravity which makes its weight no index of its quantity4 ,in short1 if we do this1 we deprive of all possibility of application our notions of element1 analysis1 and composition2 and violate the postulates on which the questions are propounded which we thus attempt to decide4 ,we must1 then1 take a constant and quantitative property of matter1 such as weight is1 to be an index #cf of the quantity of matter or of substance to which it belongs4 ,i do not here speak of the question which has sometimes been proposed1 whether the weight or the inertia of bodies be the more proper measure of the quantity of matter4 ,for the measure of inertia is regulated by the same assumption as that of substance3--that the quantity of the whole must be equal to the quantity of all the parts3 and inertia is measured by weight1 for the same reason that substance is so4 ,having thus established the certainty1 and ascertained the interpretation of the fundamental principle which the ,idea of ,substance involves1 we are prepared to consider its application in the science upon which it has a peculiar bearing4 #cg ,,note ,,to ,,chapter ,,iii4 #crd ,ed4--,,the doctrine here propounded1 that ,all ,matter is ,heavy1 has been opposed by ,sir ,william ,hamilton of ,edinburgh4 7,works of ,reid1 note1 p4 #hec47 ,this writer is a man of unquestionable acuteness and of very extensive reading2 but his acuteness shows itself in barren ontological distinctions1 which appear to me to be of the same character as the speculations of the eminent ,schoolmen of the most sterile periods of the dark ages4 ,that he should have no conception of progressive or inductive science is not wonderful1 when we recollect that he holds1 as an important part of his philosophy1 that the study of mathematics perverts and obscures the mind4 ,but it may be of some interest to consider his objections to the doctrine here maintained4 ,he says1 #ast1 that our reasoning assumes that we must necessarily have it in our power to ascertain the ,quantity of ,matter2 whereas this may be a problem out of the reach of human determination4 ,to this ,i reply1 that my reasoning does assume that there is a science1 or sciences1 which make assertions concerning the ,quantity of ,matter3 ,mechanics and ,chemistry are such sciences4 ,my assertion is1 that to make such sciences possible1 ,quantity of ,matter must be proportional to ,weight4 ,if my opponent deny that ,mechanics and ,chemistry can exist as sciences1 he may invalidate my proof2 but not otherwise4 #b4 ,he says that there are two conceivable ways of estimating the ,quantity of ,matter3 by the ,space occupied1 and by the ,weight or ,inertia2 and that ,i assume the second measure gratuitously4 ,to which ,i reply1 that the most elementary steps in ,mechanics and in ,chemistry contradict the notion that #ch the ,quantity of ,matter is proportionate to the ,space4 ,they proceed necessarily on a distinction between ,space and ,matter3--between mere ,extension and material ,substance4 #c4 ,he allows that we cannot make the ,extension of a body the measure of the ,quantity of ,matter1 because1 he says1 we do not know if 'the compressing force' is such as to produce 'the closest compression4' ,that is1 he assumes a compressing force1 assumes a closest compression1 assumes a peculiar 7and very improbable7 atomic hypothesis2 and all this to supply a reason why we are not to believe the first simple principle of ,mechanics and ,chemistry4 #d4 ,he speaks of 'a series of apparent fluids 7as ,light or its vehicle1 the ,calorific1 the ,electro-galvanic1 and ,magnetic agents7 which we can neither denude of their character of substance1 nor clothe with the attribute of weight4' ,to which my reply is1 that precisely because ,i cannot 'clothe' these agents with the attribute of ,weight1 ,i do 'denude them of the character of ,substance4' ,they are not substances1 but agencies4 ,these ,imponderable ,agents are not properly called ',imponderable ,fluids4' ,this ,i conceive that ,i have proved2 and the proof is not shaken by denying the conclusion without showing any defect in the reasoning4 #e4 ,finally1 my critic speaks about 'a logical canon1' and about 'a criterion of truth1 subjectively necessary and objectively certain2' which matters ,i shall not waste the reader's time by discussing4 #ci ,,chapter ,,iv4 ,,application ,,of ,,the ,,idea ,,of ,,substance ,,in ,,chemistry4 #a4 ,a ,body is ,equal to the ,sum of its ,elements4--,,from the earliest periods of chemistry the balance has been familiarly used to determine the proportions of the ingredients and of the compound2 and soon after the middle of the last century1 this practice was so studiously followed1 that ,wenzel and ,richter were thereby led to the doctrine of ,definite ,proportions4 ,but yet the full value and significance of the balance1 as an indispensable instrument in chemical researches1 was not understood till the gaseous1 as well as solid and fluid ingredients were taken into the account4 ,when this was done1 it was found that the principle1 that the whole is equal to the sum of its parts1 of which1 as we have seen1 the necessary truth1 in such cases1 flows from the idea of substance1 could be applied in the most rigorous manner4 ,and conversely1 it was found that by the use of the balance1 the chemist could decide1 in doubtful cases1 which was a whole1 and which were parts4 ,for chemistry considers all the changes which belong to her province as compositions and decompositions of elements2 but still the question may occur1 whether an observed change be the one or the other4 ,how can we distinguish whether the process which we contemplate be composition or decomposition8--whether the new body be formed by addition of a new1 or subtraction of an old element8 ,again2 in the case of decomposition1 we may inquire1 ,what are the ultimate limits of our analysis8 ,if we decompound bodies into others more and more simple1 how far can we carry this succession #dj of processes8 ,how far can we proceed in the road of analysis8 ,and in our actual course1 what evidence have we that our progress1 as far as it has gone1 has carried us from the more complex to the more simple8 ,to this we reply1 that the criterion which enables us to distinguish1 decidedly and finally1 whether our process have been a mere analysis of the proposed body into its ingredients1 or a synthesis of some of them with some new element1 is the principle stated above1 that the weight of the whole is equal to the weight of all the parts4 ,and no process of chemical analysis or synthesis can be considered complete till it has been verified by this fact2--by finding that the weight of the compound is the weight of its supposed ingredients2 or1 that if there be an element which we think we have detached from the whole1 its loss is betrayed by a corresponding diminution of weight4 ,i have already noticed what an important part this principle has played in the great chemical controversy which ended in the establishment of the oxygen theory4 ,the calcination of a metal was decided to be the union of oxygen with the metal1 and not the separation of phlogiston from it1 because it was found that in the process of calcination1 the weight of the metal increased1 and increased exactly as much as the weight of ambient air diminished4 ,when oxygen and hydrogen were exploded together1 and a small quantity of water was produced1 it was held that this was really a synthesis of water1 because1 when very great care was taken with the process1 the weight of the water which resulted was equal to the weight of the gases which disappeared4 #b4 ,lavoisier4--,it was when gases came to be considered as entering largely into the composition of liquid and solid bodies1 that extreme accuracy in weighing was seen to be so necessary to the true understanding of chemical processes4 ,it was in this manner discovered by ,lavoisier and his contemporaries that oxygen constitutes a large ingredient of calcined metals1 of acids1 and of water4 ,a countryman of ,lavoisier#cjf #da has not only given most just praise to that great philosopher for having constantly tested all his processes by a careful and skilful use of the balance1 but has also claimed for him the merit of having introduced the maxim1 that in chemical operations nothing is created and nothing lost4 ,but ,i think it is impossible to deny that this maxim is assumed in all the attempts at analysis made by his contemporaries1 as well as by him4 ,this maxim is indeed included in any clear notion of analysis3 it could not be the result of the researches of any one chemist1 but was the governing principle of the reasonings of all4 ,lavoisier1 however1 employed this principle with peculiar assiduity and skill4 ,in applying it1 he does not confine himself to mere additions and subtractions of the quantities of ingredients2 but often obtains his results by more complex processes4 ,in one of his investigations he says1 ',i may consider the ingredients which are brought together1 and the result which is obtained as an algebraical equation2 and if ,i successively suppose each of the quantities of this equation to be unknown1 ,i can obtain its value from the rest3 and thus ,i can rectify the experiment by the calculation1 and the calculation by the experiment4 ,i have often taken advantage of this method1 in order to correct the first results of my experiments1 and to direct me in repeating them with proper precautions4' ,note #cjf3 ,m4 ,dumas1 ,leons de la ,philosophie ,chimique4 #ahcg4 p4 #aeg4 ,the maxim1 that the whole is equal to the sum of all its parts1 is thus capable of most important and varied employment in chemistry4 ,but it may be applied in another form to the exclusion of a class of speculations which are often put forwards4 #c4 ,maxim respecting ,imponderable ,elements4--,several of the phenomena which belong to bodies1 as heat1 light1 electricity1 magnetism1 have been explained hypothetically by assuming the existence of certain fluids2 but these fluids have never been shown to have weight4 ,hence such hypothetical fluids have been termed imponderable elements4 ,it is however plain1 that so long as these fluids appear to be without weight1 they are not elements of bodies in the same #db sense as those elements of which we have hitherto been speaking4 ,indeed we may with good reason doubt whether those phenomena depend upon transferable fluids at all4 ,we have seen strong reason to believe that light is not matter1 but only motion2 and the same thing appears to be probable with regard to heat4 ,nor is it at all inconceivable that a similar hypothesis respecting electricity and magnetism should hereafter be found tenable4 ,now if heat1 light1 and those other agents1 be not matter1 they are not elements in such a sense as to be included in the principle referred to above1 ,that the body is equal to the sum of its elements4 ,consequently the maxim just stated1 that in chemical operations nothing is created1 nothing annihilated1 does not apply to ,light and ,heat4 ,they are not things4 ,and whether heat can be produced where there was no heat before1 and light struck out from darkness1 the ideas of which we are at present treating do not enable us to say4 ,in reasoning respecting chemical synthesis and analysis therefore1 we shall only make confusion by attempting to include in our conception the ,light and ,heat which are produced and destroyed4 ,such phenomena may be very proper subjects of study1 as indeed they undoubtedly are2 but they cannot be studied to advantage by considering them as sharing the nature of composition and decomposition4 ,again3 in all attempts to explain the processes of nature1 the proper course is1 first to measure the facts with precision1 and then to endeavour to understand their cause4 ,now the facts of chemical composition and decomposition1 the weights of the ingredients and of the compounds1 are facts measurable with the utmost precision and certainty4 ,but it is far otherwise with the light and heat which accompany chemical processes4 ,when combustion1 deflagration1 explosion1 takes place1 how can we measure the light or the heat8 ,even in cases of more tranquil action1 though we can apply the thermometer1 what does the thermometer tell us respecting the quantity of the heat8 ,since then we have no measure which is of any value as #dc regards such circumstances in chemical changes1 if we attempt to account for these phenomena on chemical principles1 we introduce1 into investigations in themselves perfectly precise and mathematically rigorous1 another class of reasonings1 vague and insecure1 of which the only possible effect is to vitiate the whole reasoning1 and to make our conclusions inevitably erroneous4 ,we are led then to this maxim3 that imponderable fluids are not to be admitted as chemical elements of bodies#caf4 ,note #caf3 ,see the answer to ,sir ,william ,hamilton's objections1 at the end of the last chapter4 ,since we are thus warned by a sound view of the nature of science1 from considering chemical affinity as having any hold upon imponderable elements1 we are manifestly still more decisively prohibited from supposing mechanical impulse or pressure to have any effect upon such elements4 ,to make this supposition1 is to connect the most subtle and incorporeal objects which we know in nature by the most gross material ties4 ,this remark seems to be applicable to ,m4 ,poisson's hypothesis that the electric fluid is retained at the surface of bodies by the pressure of the atmosphere4 #d4 ,it appears1 ,i think1 that our best and most philosophical chemists have proceeded upon this principle in their investigations4 ,in reasoning concerning the constitution of bodies and the interpretation of chemical changes1 the attempts to include in these interpretations the heat or cold produced1 by the addition or subtraction of a certain hypothetical 'caloric1' have become more and more rare among men of science4 ,such statements1 and the explanations often put forwards of the light and heat which appear under various circumstances in the form of fire1 must be considered as unessential parts of any sound theory4 ,accordingly we find ,mr4 ,faraday gradually relinquishing such views4 ,in ,january1 #ahcd1 he speaks generally of an hypothesis of this kind#cbf3 ',i cannot refrain from recalling here the beautiful idea put forth1 ,i believe by ,berzelius1 in his development of his views of the electro-chemical theory of affinity1 that the heat and light evolved during cases of powerful combination #dd are the consequence of the electric discharge which is at that moment taking place4' ,but in ,april of the same year#ccf1 he observes1 that in the combination of oxygen and hydrogen to produce water1 electric powers to a most enormous amount are for the time active1 but that the flame which is produced gives but feeble traces of such powers4 ',such phenomena1' therefore1 he adds1 'may not1 cannot1 be taken as evidences of the nature of the action2 but are merely incidental results1 incomparably small in relation to the forces concerned1 and supplying no information of the way in which the particles are active on each other1 or in which their forces are finally arranged4' ,note #cbf3 ,researches1 #hgj4 ,note #ccf3 ,researches1 #ifj4 ,in pursuance of this maxim1 we must consider as an unessential part of the oxygen theory that portion of it1 much insisted upon by its author at the time1 in which when sulphur1 for instance1 combined with oxygen to produce sulphuric acid1 the combustion was accounted for by means of the caloric which was supposed to be liberated from its combination with oxygen4 #e4 ,controversy of the ,composition of ,water4--,there is another controversy of our times to which we may with great propriety apply the maxim now before us4 ,after the glory of having first given a true view of the composition of water had long rested tranquilly upon the names of ,cavendish and ,lavoisier1 a claim was made in favour of ,james ,watt as the real author of this discovery by his son1 7,mr ,j4 ,watt17 and his eulogist1 7,m4 ,arago#cdf74 ,it is not to our purpose here to discuss the various questions which have arisen on this subject respecting priority of publication1 and respecting the translation of opinions published at one time into the language of another period4 ,but if we look at ,watt's own statement of his views1 given soon after those of ,cavendish had been published1 we shall perceive that it is marked by a violation of this maxim3 we shall find that he does admit imponderable fluids #de as chemical elements2 and thus shows a vagueness and confusion in his idea of chemical composition4 ,with such imperfection in his views1 it is not surprising that ,watt1 not only did not anticipate1 but did not apprehend quite precisely the discovery of ,cavendish and ,lavoisier4 ,watt's statement of his views is as follows#cef3--';,are we not authorized to conclude that water is composed of dephlogisticated air and phlogiston deprived of part of their latent or elementary heat2 that dephlogisticated or pure air is composed of water deprived of its phlogiston and united to elementary heat and light2 and that the latter are contained in it in a latent state1 so as not to be sensible to the thermometer or to the eye2 and if light be only a modification of heat1 or a circumstance attending it1 or a component part of the inflammable air1 then pure or dephlogisticated air is composed of water deprived of its phlogiston and united to elementary heat8' ,note #cdf3 loge de ,james ,watt1 ,annuaire du ,bur4 des ,long4 #ahci4 ,note #cef3 ,phil4 ,trans4 #aghd1 p4 #ccb4 ,when we compare this doubtful and hypothetical statement1 involving so much that is extraneous and heterogeneous1 with the conclusion of ,cavendish1 in which there is nothing hypothetical or superfluous1 we may confidently assent to the decision which has been pronounced by one#cff of our own time in favour of ,cavendish4 ,and we may with pleasure recognize1 in this enlightened umpire1 a due appreciation of the value of the maxim on which we are now insisting4 ',cavendish1' says ,mr4 ,vernon ,harcourt1 'pared off #df from the hypotheses their theories of combustion1 and affinities of imponderable for ponderable matter1 as complicating chemical with physical considerations4' ,note #cff3 ,the ,rev4 ,w4 ,vernon ,harcourt1 ,address to the ,british ,association1 #ahci4--,since the first edition of this work was published1 and also since the second edition of the ,history of the ,inductive ,sciences1 ,mr4 ,watt's correspondence bearing upon the question of the ,composition of ,water has been published by ,mr4 ,muirhead4 ,i do not find1 in this publication1 any reason for withdrawing what ,i have stated in the text above3 but with reference to the statement in the ,history1 it appears that ,mr4 ,cavendish's claim to the discovery was not uncontested in his own time4 ,mr4 ,watt had looked at the composition of water1 as a problem to be solved1 perhaps more distinctly than ,mr4 ,cavendish had done2 and he conceived himself wronged by ,mr4 ,cavendish's putting forwards his experiment as the first solution of this problem4 #f4 ,relation of ,heat to ,chemistry4--,but while we thus condemn the attempts to explain the thermotical phenomena of chemical processes by means of chemical considerations1 it may be asked if we are altogether to renounce the hope of understanding such phenomena8 ,it is plain1 it may be said1 that heat generated in chemical changes is always a very important circumstance1 and can sometimes be measured1 and perhaps reduced to laws2 are we prohibited from speculating concerning the causes of such circumstances and such laws8 ,and to this we reply1 that we may properly attempt to connect chemical with thermotical processes1 so far as we have obtained a clear and probable view of the nature of the thermotical processes4 ,when our theory of ,thermotics is tolerably complete and certain1 we may with propriety undertake to connect it with our theory of ,chemistry4 ,but at present we are not far enough advanced in our knowledge of heat to make this attempt with any hope of success4 ,we can hardly expect to understand the part which heat plays in the union of two bodies1 when we cannot as yet comprehend in what manner it produces the liquefaction or vaporization of one body4 ,we cannot look to account for ,gay ,lussac and ,dalton's ,law1 that all gases expand equally by heat1 till we learn how heat causes a gas to expand4 ,we cannot hope to see the grounds of ,dulong and ,petit's ,law1 that the specific heat of all atoms is the same1 till we know much more1 not only about atoms1 but about specific heat4 ,we have as yet no thermotical theory which even professes to account for all the prominent facts of the subject#cgf3 and the theories which have been proposed are of the most diverse kind4 ,laplace assumes particles of bodies surrounded by atmospheres of caloric#chf2 ,cauchy makes heat consist in longitudinal vibrations of the ether of which transverse vibrations #dg produce light3 in ,ampre's theory#cif1 heat consists in the vibrations of the particles of bodies4 ,and so long as we have nothing more certain in our conceptions of heat than the alternative of these and other precarious hypotheses1 how can we expect to arrive at any real knowledge1 by connecting the results of such hypotheses with the speculations of ,chemistry1 of which science the theory is at least equally obscure8 ,note #cgf3 ,hist4 ,ind4 ,sci4 b4 x4 c4 #d4 ,note #chf3 ,ib4 ,note #cif3 ,hist4 ,ind4 ,sci4 b4 x4 c4 #d4 ,the largest attempts at chemical theory have been made in the form of the ,atomic ,theory1 to which ,i have just had occasion to allude4 ,i must1 therefore1 before quitting the subject1 say a few words respecting this theory4 #dh ,,chapter ,v4 ,,the ,,atomic ,,theory4 #a4 ,the ,atomic ,theory considered on ,chemical ,grounds4--,,we have already seen that the combinations which result from chemical affinity are definite1 a certain quantity of one ingredient uniting1 not with an uncertain1 but with a certain quantity of another ingredient4 ,but it was found1 in addition to this principle1 that one ingredient would often unite with another in different proportions1 and that1 in such cases1 these proportions are multiples one of another4 ,in the three salts formed by potassa with oxalic acid1 the quantities of acid which combine with the same quantity of alkali are exactly in the proportion of the numbers #a1 #b1 #d4 ,and the same rule of the existence of multiple proportions is found to obtain in other cases4 ,it is obvious that such results will be accounted for1 if we suppose that the base and the acid consist each of numerous definite equal particles1 and that the formation of the salts above mentioned consists in the combination of one particle of the base with one particle of acid1 with two particles of acid1 and with four particles of acid1 respectively4 ,but further2 as we have already stated1 chemical affinity is not only definite1 but reciprocal4 ,the proportions of potassa and soda which form neutral salts being #eij and #cia in one case1 they are so in all cases4 ,these numbers represent proportions of weight in which the two bases1 potassa and soda1 enter into analogous combinations2 #eij of potassa is equivalent to #cia of soda4 ,these facts with regard to combination are still expressed by the above supposition of equal particles1 assuming that the weights of a #di particle of potassa and of soda are in the proportion of #eij to #cia4 ,but we pursue our analysis further4 ,we find that potassa is a compound of a metallic base1 potassium1 and of oxygen1 in the proportion of #dij to #ajj2 we suppose1 then1 that the particle of potassa consists of a particle of potassium and a particle of oxygen2 and these latter particles1 since we see no present need to suppose them divided1 potassium and oxygen being simple bodies1 we may call atoms1 and assume to be indivisible4 ,and by supposing all simple bodies to consist of such atoms1 and compounds to be formed by the union of two1 or three1 or more of such atoms1 we explain the occurrence of definite and multiple proportions1 and we construct the ,atomic ,theory4 #b4 ,hypothesis of ,atoms4--,so far as the assumption of such atoms as we have spoken of serves to express those laws of chemical composition which we have referred to1 it is a clear and useful generalization4 ,but if the ,atomic ,theory be put forwards 7and its author1 ,dr4 ,dalton1 appears to have put it forwards with such an intention17 as asserting that chemical elements are really composed of atoms1 that is1 of such particles not further divisible1 we cannot avoid remarking1 that for such a conclusion1 chemical research has not afforded1 nor can afford1 any satisfactory evidence whatever4 ,the smallest observable quantities of ingredients1 as well as the largest1 combine according to the laws of proportions and equivalence which have been cited above4 ,how are we to deduce from such facts any inference with regard to the existence of certain smallest possible particles8 ,the ,theory1 when dogmatically taught as a physical truth1 asserts that all observable quantities of elements are composed of proportional numbers of particles which can no further be subdivided2 but all which observation teaches us is1 that if there be such particles1 they are smaller than the smallest observable quantities4 ,in chemical experiment1 at least1 there is not the slightest positive evidence for the existence of such atoms4 ,the assumption of indivisible particles1 smaller than the smallest #ej observable1 which combine1 particle with particle1 will explain the phenomena2 but the assumption of particles bearing this proportion1 but not possessing the property of indivisibility1 will explain the phenomena at least equally well4 ,the decision of the question1 therefore1 whether the ,atomic ,hypothesis be the proper way of conceiving the chemical combinations of substances1 must depend1 not upon chemical facts1 but upon our conception of ,substance4 ,in this sense the question is an ancient and curious controversy1 and we shall hereafter have to make some remarks upon it4 #c4 ,chemical ,difficulties of the ,hypothesis4--,but before doing this1 we may observe that there is no small difficulty in reconciling this hypothesis with the facts of chemistry4 ,according to the theory1 all salts1 compounded of an acid and a base1 are analogous in their atomic constitution2 and the number of atoms in one such compound being known or assumed1 the number of atoms in other salts may be determined4 ,but when we proceed in this course of reasoning to other bodies1 as metals1 we find ourselves involved in difficulties4 ,the protoxide of iron is a base which1 according to all analogy1 must consist of one atom of iron and one of oxygen3 but the peroxide of iron is also a base1 and it appears by the analysis of this substance that it must consist of two-thirds of an atom of iron and one atom of oxygen4 ,here1 then1 our indivisible atoms must be divisible1 even upon chemical grounds4 ,and if we attempt to evade this difficulty by making the peroxide of iron consist of two atoms of iron and three of oxygen1 we have to make a corresponding alteration in the theoretical constitution of all bodies analogous to the protoxide2 and thus we overturn the very foundation of the theory4 ,chemical facts1 therefore1 not only do not prove the ,atomic ,theory as a physical truth1 but they are not1 according to any modification yet devised of the theory1 reconcileable with its scheme4 ,nearly the same conclusions result from the attempts to employ the ,atomic ,hypothesis in expressing another important chemical law2--the law of the #ea combinations of gases according to definite proportions of their volumes1 experimentally established by ,gay ,lussac#djf4 ,in order to account for this law1 it has been very plausibly suggested that all gases1 under the same pressure1 contain an equal number of atoms in the same space2 and that when they combine1 they unite atom to atom4 ,thus one volume of chlorine unites with one volume of hydrogen1 and forms hydrochloric acid#daf4 ,but then this hydrochloric acid occupies the space of the two volumes2 and therefore the proper number of particles cannot be supplied1 and the uniform distribution of atoms in all gases maintained1 without dividing into two each of the compound particles1 constituted of an atom of chlorine and an atom of hydrogen4 ,and thus in this case1 also1 the ,atomic ,theory becomes untenable if it be understood to imply the indivisibility of the atoms4 ,note #djf3 ,hist4 ,ind4 ,sc4 b4 xiv4 c4 #h4 ,note #daf3 ,dumas1 ,phil4 ,chim4 #bfc4 ,in all these attempts to obtain distinct physical conception of chemical union by the aid of the ,atomic ,hypothesis1 the atoms are conceived to be associated by certain forces of the nature of mechanical attractions4 ,but we have already seen#dbf that no such mode of conception can at all explain or express the facts of chemical combination2 and therefore it is not wonderful that when the ,atomic ,theory attempts to give an account of chemical relations by contemplating them under such an aspect1 the facts on which it grounds itself should be found not to authorize its positive doctrines2 and that when these doctrines are tried upon the general range of chemical observation1 they should prove incapable of even expressing1 without self-contradiction1 the laws of phenomena4 ,note #dbf3 ,see ,chapter ,i4 of this book4 #d4 ,grounds of the ,atomic ,doctrine4--,yet the doctrine of atoms1 or of substance as composed of indivisible particles1 has in all ages had great hold upon the minds of physical speculators2 nor would this doctrine ever have suggested itself so readily1 or have been maintained so tenaciously1 as the true mode of #eb conceiving chemical combinations1 if it had not been already familiar to the minds of those who endeavour to obtain a general view of the constitution of nature4 ,the grounds of the assumption of the atomic structure of substance are to be found rather in the idea of substance itself1 than in the experimental laws of chemical affinity4 ,and the question of the existence of atoms1 thus depending upon an idea which has been the subject of contemplation from the very infancy of philosophy1 has been discussed in all ages with interest and ingenuity4 ,on this very account it is unlikely that the question1 so far as it bears upon chemistry1 should admit of any clear and final solution4 ,still it will be instructive to look back at some of the opinions which have been delivered respecting this doctrine4 #e4 ,ancient ,prevalence of the ,atomic ,doctrine4--,the doctrine that matter consists of minute1 simple1 indivisible1 indestructible particles as its ultimate elements1 has been current in all ages and countries1 whenever the tendency of man to wide and subtle speculations has been active4 ,i need not attempt to trace the history of this opinion in the schools of ,greece and ,italy4 ,it was the leading feature in the physical tenets of the ,epicureans1 and was adopted by their ,roman disciples1 as the poem of ,lucretius copiously shows us4 ,the same tenet had been held at still earlier periods1 in forms more or less definite1 by other philosophers4 ,it is ascribed to ,democritus1 and is said to have been by him derived from ,leucippus4 ,but this doctrine is found also1 we are told#dcf1 among the speculations of another intellectual and acute race1 the ,hindoos4 ,according to some of their philosophical writers1 the ultimate elements of matter are atoms1 of which it is proved by certain reasonings1 that they are each one-sixth of one of the motes that float in the sunbeam4 ,note #dcf3 ,by ,mr4 ,colebrook4 ,asiatic ,res4 #ahbd4 ,this early prevalence of controversies of the widest and deepest kind1 which even in our day remain undecided1 has in it nothing which need surprize us2 or1 at least1 it has in it nothing which is not in conformity #ec with the general course of the history of philosophy4 ,as soon as any ideas are clearly possessed by the human mind1 its activity and acuteness in reasoning upon them are such1 that the fundamental antitheses and ultimate difficulties which belong to them are soon brought into view4 ,the ,greek and ,indian philosophers had mastered completely the ,idea of ,space1 and possessed the ,idea of ,substance in tolerable distinctness4 ,they were1 therefore1 quite ready1 with their lively and subtle minds1 to discuss the question of the finite and infinite divisibility of matter1 so far as it involved only the ideas of space and of substance1 and this accordingly they did with great ingenuity and perseverance4 ,but the ideas of ,space and of ,substance are far from being sufficient to enable men to form a complete general view of the constitution of matter4 ,we must add to these ideas1 that of mechanical ,force with its antagonist ,resistance1 and that of the ,affinity of one kind of matter for another4 ,now the former of these ideas the ancients possessed in a very obscure and confused manner2 and of the latter they had no apprehension whatever4 ,they made vague assumptions respecting the impact and pressure of atoms on each other2 but of their mutual attraction and repulsion they never had any conception1 except of the most dim and wavering kind2 and of an affinity different from mere local union they did not even dream4 ,their speculations concerning atoms1 therefore1 can have no value for us1 except as a part of the history of science4 ,if their doctrines appear to us to approach near to the conclusions of our modern philosophy1 it must be because our modern philosophy is that philosophy which has not fully profited by the additional light which the experiments and meditations of later times have thrown upon the constitution of matter4 #f4 ,bacon4--,still1 when modern philosophers look upon the ,atomic ,theory of the ancients in a general point of view merely1 without considering the special conditions which such a theory must fulfil1 in order to represent the discoveries of modern times1 they are #ed disposed to regard it with admiration4 ,accordingly we find ,francis ,bacon strongly expressing such a feeling4 ,the ,atomic ,theory is selected and dwelt upon by him as the chain which connects the best parts of the physical philosophy of the ancient and the modern world4 ,among his works is a remarkable dissertation ,on the ,philosophy of ,democritus1 ,parmenides1 and ,telesius3 the last mentioned of whom was one of the revivers of physical science in modern times4 ,in this work he speaks of the atomic doctrine of ,democritus as a favourable example of the exertions of the undisciplined intellect4 ',hc ipsa placita1 quamvis paulo emendatiora1 talia sunt qualia esse possunt illa qu ab intellectu sibi permisso1 nec continenter et gradatim sublevato1 profecta videntur4'--',these doctrines1 thus in an ancient fable presented in a better form1 are such glimpses of truth as can be obtained by the intellect left to its own natural impulses1 and not ascending by successive and connected steps1' as the ,baconian philosophy directs4 ',accordingly1' he adds1 'the doctrine of ,atoms1 from its going a step beyond the period in which it was advanced1 was ridiculed by the vulgar1 and severely handled in the disputations of the learned1 notwithstanding the profound acquaintance with physical science by which its author was allowed to be distinguished1 and from which he acquired the character of a magician4' ',however1' he continues1 'neither the hostility of ,aristotle1 with all his skill and vigour in disputation1 7though1 like the ,ottoman sultans1 he laboured to destroy all his brother philosophers that he might rest undisputed master of the throne of science17 nor the majestic and lofty authority of ,plato1 could effect the subversion of the doctrine of ,democritus4 ,and while the opinions of ,plato and ,aristotle were rehearsed with loud declamation and professorial pomp in the schools1 this of ,democritus was always held in high honour by those of a deeper wisdom1 who followed in silence a severer path of contemplation4 ,in the days of ,roman speculation it kept its ground and its favour2 ,cicero everywhere speaks of its author with the #ee greatest praise2 and ,juvenal1 who1 like poets in general1 probably expressed the prevailing judgment of his time1 proclaims his merit as a noble exception to the general stupidity of his countrymen4 4 4 4 4 ,cujus prudentia monstrat ,magnos posse viros et magna exempla daturos ,vervecum in patri crassoque sub aere nasci4 ',the destruction of this philosophy was not effected by ,aristotle and ,plato1 but by ,genseric and ,attila1 and their barbarians4 ,for then1 when human knowledge had suffered shipwreck1 those fragments of the ,aristotelian and ,platonic philosophy floated on the surface like things of some lighter and emptier sort1 and so were preserved2 while more solid matters went to the bottom1 and were almost lost in oblivion4' #g4 ,modern ,prevalence of the ,atomic ,doctrine4--,it is our business here to consider the doctrine of ,atoms only in its bearing upon existing physical sciences1 and ,i must therefore abstain from tracing the various manifestations of it in the schemes of hypothetical cosmologists2--its place among the vortices of ,descartes1 its exhibition in the monads of ,leibnitz4 ,i will1 however1 quote a passage from ,newton to show the hold it had upon his mind4 ,at the close of his ,opticks he says1 ',all these things being considered1 it seems probable to me that ,god1 in the beginning1 formed matter in solid1 massy1 hard1 impenetrable1 moveable particles1 of such sizes and figures1 and with such other properties1 and in such proportions to space1 as most conduced to the end for which ,he formed them2 and that the primitive particles1 being solids1 are incomparably harder than any porous bodies compounded of them1 even so very hard as never to wear or break in pieces2 no ordinary power being able to divide what ,god had made one in the first creation4 ,while the particles continue entire1 they may compose bodies of one and the same nature and texture in all ages3 but should they wear away or break in pieces1 the nature of things depending on them would be changed4 ,water and earth composed #ef of old worn particles and fragments of particles would not be of the same nature and texture now with water and earth composed of entire particles in the beginning4 ,and therefore that nature may be lasting1 the changes of corporeal things are to be placed only in the various separations and new associations and motions of these permanent particles2 compounded bodies being apt to break1 not in the midst of solid particles1 but where those particles are laid together and only touch in a few points4' ,we shall hereafter see how extensively the atomic doctrine has prevailed among still more recent philosophers4 ,not only have the chemists assumed it as the fittest form for exhibiting the principles of multiple proportions2 but the physical mathematicians1 as ,laplace and ,poisson1 have made it the basis of their theories of heat1 electricity1 capillary action2 and the crystallographers have been supposed to have established both the existence and the arrangement of such ultimate molecules4 ,in the way in which it has been employed by such writers1 the hypothesis of ultimate particles has been of great use1 and is undoubtedly permissible4 ,but when we would assert this theory1 not as a convenient hypothesis for the expression or calculation of the laws of nature1 but as a philosophical truth respecting the constitution of the universe1 we find ourselves checked by difficulties of reasoning which we cannot overcome1 as well as by conflicting phenomena which we cannot reconcile4 ,i will attempt to state briefly the opposing arguments on this question4 #h4 ,arguments for and against ,atoms4--,the leading arguments on the two sides of the question1 in their most general form1 may be stated as follows3 ,for the ,atomic ,doctrine4--,the appearances which nature presents are compounded of many parts1 but if we go on resolving the larger parts into smaller1 and so on successively1 we must at last come to something simple4 ,for that which is compound can be so no otherwise than by composition of what is simple2 and if we suppose all composition to be removed1 which #eg hypothetically we may do1 there can remain nothing but a number of simple substances1 capable of composition1 but themselves not compounded4 ,that is1 matter being dissolved1 resolves itself into atoms4 ,against the ,atomic ,doctrine4--,space is divisible without limit1 as may be proved by ,geometry2 and matter occupies space1 therefore matter is divisible without limit1 and no portion of matter is indivisible1 or an atom4 ,and to the argument on the other side just stated1 it is replied that we cannot even hypothetically divest a body of composition1 if by composition we mean the relation of point to point in space4 ,however small be a particle1 it is compounded of parts having relation in space4 ,the ,atomists urge again1 that if matter be infinitely divisible1 a finite body consists of an infinite number of parts1 which is a contradiction4 ,to this it is replied1 that the finite body consists of an infinite number of parts in the same sense in which the parts are infinitely small1 which is no contradiction4 ,but the opponents of the ,atomists not only rebut1 but retort this argument drawn from the notion of infinity4 ,your atoms1 they say1 are indivisible by any finite force2 therefore they are infinitely hard2 and thus your finite particles possess infinite properties4 ,to this the ,atomists are wont to reply1 that they do not mean the hardness of their particles to be infinite1 but only so great as to resist all usual natural forces4 ,but here it is plain that their position becomes untenable2 for1 in the first place1 their assumption of this precise degree of hardness in the particles is altogether gratuitous2 and in the next place1 if it were granted1 such particles are not atoms1 since in the next moment the forces of nature may be augmented so as to divide the particle1 though hitherto undivided4 ,such are the arguments for and against the ,atomic ,theory in its original form4 ,but when these atoms are conceived1 as they have been by ,newton1 and commonly by his followers1 to be solid1 hard particles exerting attractive and repulsive forces1 a new set of #eh arguments come into play4 ,of these1 the principal one may be thus stated3 ,according to the ,atomic ,theory thus modified1 the properties of bodies depend upon the attractions and repulsions of the particles4 ,therefore1 among other properties of bodies1 their hardness depends upon such forces4 ,but if the hardness of the bodies depends upon the forces1 the repulsion1 for instance1 of the particles1 upon what does the hardness of the particles depend8 what progress do we make in explaining the properties of bodies1 when we assume the same properties in our explanation8 and to what purpose do we assume that the particles are hard8 #i4 ,transition to ,boscovich's ,theory4--,to this difficulty it does not appear easy to offer any reply4 ,but if the hardness and solidity of the particles be given up as an incongruous and untenable appendage to the ,newtonian view of the ,atomic ,theory1 we are led to the theory of ,boscovich1 according to which matter consists not of solid particles1 but of mere mathematical centers of force4 ,according to this theory1 each body is composed of a number of geometrical points from which emanate forces1 following certain mathematical laws in virtue of which the forces become1 at certain small distances attractive1 at certain other distances repulsive1 and at greater distances attractive again4 ,from these forces of the points arise the cohesion of the parts of the same body1 the resistance which it exerts against the pressure of another body1 and finally the attraction of gravitation which it exerts upon bodies at a distance4 ,this theory is at least a homogeneous and consistent theory1 and it is probable that it may be used as an instrument for investigating and expressing true laws of nature2 although1 as we have already said1 the attempt to identify the forces by which the particles of bodies are bound together with mechanical attraction1 appears to be a confusion of two separate ideas#ddf4 ,note #ddf3 ',boscovich's ,theory1' that all bodies may be considered as consisting of a mere collection of centers of forces1 may be so conceived as possibly to involve an explanation of all the powers which their parts exert1 7such powers1 namely1 as those which produce optical1 thermotical and chemical phenomena27 but this theory cannot supply an explanation of the mechanical properties of a body as a whole1 especially of its inertia4 ,a collection of mere centers of force can have no inertia4 ,if two bodies are considered as two collections of centers of force1 the one attracting the other1 there is in this view nothing to limit or determine the velocity with which the one body will approach the other4 ,a world composed of such bodies is not a material world3 for matter 7as we have already seen in book iii4 chapter v47 implies not only force1 but something which resists the action of force4 #ei #aj4 ,use of the ,molecular ,hypothesis4--,in this form1 representing matter as a collection of molecules or centers of force1 the ,atomic ,theory has been abundantly employed in modern times as an hypothesis on which calculations respecting the elementary forces of bodies might be conducted4 ,when thus employed it is to be considered as expressing the principle that the properties of bodies depend upon forces emanating from immovable points of their mass4 ,this view of the way in which the properties of bodies are to be treated by the mechanical philosopher was introduced by ,newton1 and was a natural sequel to the success which he had obtained by reasoning concerning central forces on a large scale4 ,i have already quoted his ,preface to the ,principia1 in which he says1 ',many things induce me to believe that the rest of the phenomena of nature1 as well as those of astronomy1 may depend upon certain forces by which the particles of bodies1 in virtue of causes not yet known1 are urged towards each other and cohere in regular figures1 or are mutually repelled and recede2 and philosophers1 knowing nothing of these forces1 have hitherto failed in their examination of nature4' ,since the time of ,newton1 this line of speculation has been followed with great assiduity1 and by some mathematicians with great success4 ,in particular ,laplace has shown that the hypothesis may1 in many instances1 be made a much closer representation of nature1 if we suppose the forces exerted by the particles to decrease so rapidly with the increasing distance from them1 that #fj the force is finite only at distances imperceptible to our senses1 and vanishes at all remoter points4 ,he has taught the method of expressing and calculating such forces1 and he and other mathematicians of his school have applied this method to many of the most important questions of physics2 as capillary action1 the elasticity of solids1 the conduction and radiation of heat4 ,the explanation of many apparently unconnected and curious observed facts by these mathematical theories gives a strong assurance that its essential principles are true4 ,but it must be observed that the actual constitution of bodies as composed of distinct and separate particles is by no means proved by these coincidences4 ,the assumption1 in the reasoning1 of certain centers of force acting at a distance1 is to be considered as nothing more than a method of reducing to calculation that view of the constitution of bodies which supposes that they exert force at every point4 ,it is a mathematical artifice of the same kind as the hypothetical division of a body into infinitesimal parts1 in order to find its center of gravity2 and no more implies a physical reality than that hypothesis does4 #aa4 ,poisson's ,inference4--,when1 therefore1 ,m4 ,poisson1 in his views of ,capillary ,action1 treats this hypothetical distribution of centers of force as if it were a physical fact1 and blames ,laplace for not taking account of their different distribution at the surface of the fluid and below it#def1 he appears to push the claims of the molecular hypothesis too far4 ,the only ground for the assumption of separate centers1 is that we can thus explain the action of the whole mass4 ,the intervals between the centers nowhere enter into this explanation3 and therefore we can have no reason for assuming these intervals different in one part of the fluid and in the other4 ,m4 ,poisson asserts that the density of the fluid diminishes when we approach very near the surface2 but he allows that this diminution is not detected by experiment1 and that the formul on #fa his supposition1 so far as the results go1 are identical with those of ,laplace4 ,it is clear1 then1 that his doctrine consists merely in the assertion of the necessary truth of a part of the hypothesis which cannot be put to the test of experiment4 ,it is true1 that so long as we have before us the hypothesis of separate centers1 the particles very near the surface are not in a condition symmetrical with that of the others3 but it is also true that this hypothesis is only a step of calculation4 ,there results1 at one period of the process of deduction1 a stratum of smaller density at the surface of the fluid2 but at a succeeding point of the reasoning the thickness of this stratum vanishes2 it has no physical existence4 ,note #def3 ,poisson1 ,thorie de l',action ,capillaire4 ,thus the molecular hypothesis1 as used in such cases1 does not differ from the doctrine of forces acting at every point of the mass2 and this principle1 which is common to both the opposite views1 is the true part of each4 #ab4 ,wollaston's ,argument4--,an attempt has been made in another case1 but depending on nearly the same arguments1 to bring the doctrine of ultimate atoms to the test of observation4 ,in the case of the air1 we know that there is a diminution of density in approaching the upper surface of the atmosphere1 if it have a surface3 but it is held by some that except we allow the doctrine of ultimate molecules1 it will not be bounded by any surface1 but will extend to an infinite distance4 ,this is the reasoning of ,wollaston#dff4 ',if air consists of any ultimate particles no longer divisible1 then must the expansion of the medium composed of them cease at that distance where the force of gravity downwards is equal to the resistance arising from the repulsive force of the medium4' ,but if there be no such ultimate particles1 every stratum will require a stratum beyond it to prevent by its weight a further expansion1 and thus the atmosphere #fb must extend to an infinite distance4 ,and ,wollaston conceived that he could learn from observation whether the atmosphere was thus diffused through all space2 for if so1 it must1 he argued1 be accumulated about the larger bodies of the system1 as ,jupiter and the ,sun1 by the law of universal gravitation2 and the existence of an atmosphere about these bodies1 might1 he remarked1 be detected by its effects in producing refraction4 ,his result is1 that 'all the phenomena accord entirely with the supposition that the earth's atmosphere is of finite extent1 limited by the weight of ultimate atoms of definite magnitude1 no longer divisible by repulsion of their parts4' ,note #dff3 ,phil4 ,trans4 #ahbb1 p4 #hi4 ,a very little reflection will show us that such a line of reasoning cannot lead to any result4 ,for we know nothing of the law which connects the density with the compressing force1 in air so extremely rare as we must suppose it to be near the boundary of the atmosphere4 ,now there are possible laws of dependence of the density upon the compressing force such that the atmosphere would terminate in virtue of the law without any assumption of atoms4 ,this may be proved by mathematical reasoning4 ,if we suppose the density of air to be as the square root of the compressing force1 it will follow that at the very limits of the atmosphere1 the strata of equal thickness may observe in their densities such a law of proportion as is expressed by the numbers #g1 #e1 #c1 #adgf4 ,note #dgf3 ,for the compressing force on each being as the whole weight beyond it1 it will be for the four highest strata1 #af1 #i1 #d and #a1 of which the square roots are as #d1 #c1 #b1 #a1 or1 as #h1 #f1 #d1 #b2 and though these numbers are not exactly as the densities #g1 #e1 #c1 #a1 those who are a little acquainted with mathematical reasoning1 will see that the difference arises from taking so small a number of strata4 ,if we were to make the strata indefinitely thin1 as to avoid error we ought to do1 the coincidence would be exact2 and thus1 according to this law1 the series of strata terminates as we ascend1 without any consideration of atoms4 ,if it be asked how1 on this hypothesis1 the density of the highest stratum can be as #a1 since there is #fc nothing to compress it1 we answer that the upper part of the highest stratum compresses the lower1 and that the density diminishes continually to the surface1 so that the need of compression and the compressing weight vanish together4 ,the fallacy of concluding that because the height of the atmosphere is finite1 the weight of the highest stratum must be finite1 is just the same as the fallacy of those who conclude that when we project a body vertically upwards1 because it occupies only a finite time in ascending to the highest point1 the velocity at the last instant of the ascent must be finite4 ,for it might be said1 if the last velocity of ascent be not finite1 how can the body describe the last particle of space in a finite time8 and the answer is1 that there is no last finite particle of space1 and therefore no last finite velocity4 #ac4 ,permanence of ,properties of ,bodies4--,we have already seen that1 in explaining the properties of matter as we find them in nature1 the assumption of solid1 hard1 indestructible particles is of no use or value4 ,but we may remark1 before quitting the subject1 that ,newton appears to have had another reason for assuming such particles1 and one well worthy of notice4 ,he wished to express1 by means of this hypothesis1 the doctrine that the laws of nature do not alter with the course of time4 ,this we have already seen in the quotation from ,newton4 ',the ultimate particles of matter are indestructible1 unalterable1 impenetrable2 for if they could break or wear1 the structure of material bodies now would be different from that which it was when the particles were new4' ,no philosopher will deny the truth which is thus conveyed by the assertion of atoms2 but it is obviously equally easy for a person who rejects the atomic view1 to state this truth by saying that the forces which matter exerts do not vary with time1 but however modified by the new modifications of its form1 are always unimpaired in quantity1 and capable of being restored to their former mode of action4 #fd ,we now proceed to speculations in which the fundamental conceptions may1 perhaps1 be expressed1 at least in some cases1 by means of the arrangement of atoms2 but in which the philosophy of the subject appears to require a reference to a new ,fundamental ,idea4 #fe ,,book ,,vii4 ,,the ,,philosophy ,,of ,,morphology1 ,,including ,,crystallography4 ,,crystallization exhibits to us the effects of the natural arrangement of the ultimate particles of various compound bodies2 but we are scarcely yet sufficiently acquainted with chemical synthesis and analysis to understand the rationale of this process4 ,the rhomboidal form may arise from the proper position of #d1 #f1 #h or #i globular particles1 the cubic form from #h particles1 the triangular form from #c1 #f or #aj particles1 the hexahedral prism from #g particles1 c4 ,perhaps1 in due time we may be enabled to ascertain the number and order of elementary particles1 constituting any given compound element1 and from that determine the figure which it will prefer on crystallization1 and vice vers4 ,,john ,,dalton1 ,chemical ,philosophy 7#ahjh71 p4 #baj4 #fg ,,book ,,vii4 ,,the ,,philosophy ,,of ,,morphology1 ,,including ,,crystallography4 ,,chapter ,i4 ,,explication ,,of ,,the ,,idea ,,of ,,symmetry4 #a4 ,,we have seen in the ,history of the ,sciences1 that the principle which ,i have there termed#ag the ,principle of ,developed and ,metamorphosed ,symmetry1 has been extensively applied in botany and physiology1 and has given rise to a province of science termed ,morphology4 ,in order to understand clearly this principle1 it is necessary to obtain a clear idea of the ,symmetry of which we thus speak4 ,but this ,idea of ,symmetry is applicable in the inorganic1 as well as in the organic kingdoms of nature2 it is presented to our eyes in the forms of minerals1 as well as of flowers and animals2 we must1 therefore1 take it under our consideration here1 in order that we may complete our view of ,mineralogy1 which1 as ,i have repeatedly said1 is an essential part of ,chemical science4 ,i shall accordingly endeavour to unfold the ,idea of ,symmetry with which we here have to do4 ,note #ag3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 vi4 ,it will of course be understood that by the term ,symmetry ,i here intend1 not that more indefinite attribute of form which belongs to the domain of the fine arts1 as when we speak of the 'symmetry' of an edifice #fh or of a sculptured figure1 but a certain definite relation or property1 no less rigorous and precise than other relations of number and position1 which is thus one of the sure guides of the scientific faculty1 and one of the bases of our exact science4 #b4 ,in order to explain what ,symmetry is in this sense1 let the reader recollect that the bodies of animals consist of two equal and similar sets of members1 the right and the left side2--that some flowers consist of three or of five equal sets of organs1 similarly and regularly disposed1 as the iris has three straight petals1 and three reflexed ones1 alternately disposed1 the rose has five equal and similar sepals of the calyx1 and alternate with these1 as many petals of the corolla4 ,this orderly and exactly similar distribution of two1 or three1 or five1 or any other number of parts1 is ,symmetry2 and according to its various modifications1 the forms thus determined are said to be symmetrical with various numbers of members4 ,the classification of these different kinds of symmetry has been most attended to in ,crystallography1 in which science it is the highest and most general principle by which the classes of forms are governed4 ,without entering far into the technicalities of the subject1 we may point out some of the features of such classes4 ,illustration ,the first of the figures 7#a7 in the margin may represent the summit of a crystal as it appears to an eye looking directly down upon it2 the center of the figure represents the summit of a pyramid1 and the spaces of various forms which diverge from this point represent sloping sides of the pyramid4 ,now it will be observed that the figure consists of three portions exactly similar to one another1 and that each part or member is repeated in each of these portions4 ,the faces1 or pairs of faces1 are repeated in threes1 with exactly similar forms and angles4 ,this figure is said to be three-membered1 or to have triangular symmetry4 ,the same kind of #fi symmetry may exist in a flower1 as presented in the accompanying figure1 and does1 in fact1 occur in a large class of flowers1 as for example1 all the lily tribe4 ,the next pair of figures 7#b7 have four equal and similar portions1 and have their members or pairs of members four times repeated4 ,such figures are termed four-membered1 and are said to have square or tetragonal symmetry4 ,the pentagonal symmetry1 formed by five similar members1 is represented in the next figures 7#c74 ,it occurs abundantly in the vegetable world1 but never among crystals2 for the pentagonal figures which crystals sometimes assume1 are never exactly regular4 ,but there is still another kind of symmetry 7#d7 in which the opposite ends are exactly similar to each other and also the opposite sides2 this is oblong1 or two-and-two-membered symmetry4 ,and finally1 we have the case of simple symmetry 7#e7 in which the two sides of the object are exactly alike 7in opposite positions7 without any further repetition4 ,illustration #c4 ,these different kinds of symmetry occur in various ways in the animal1 vegetable1 and mineral kingdom4 ,vertebrate animals have a right and a #gj left side exactly alike1 and thus possess simple symmetry4 ,the same kind of symmetry 7simple symmetry7 occurs very largely in the forms of vegetables1 as in most leaves1 in papilionaceous1 personate1 and labiate flowers4 ,among minerals1 crystals which possess this symmetry are called oblique-prismatic1 and are of very frequent occurrence4 ,the oblong1 or two-and-two-membered symmetry belongs to right-prismatic crystals2 and may be seen in cruciferous flowers1 for though these are cross-shaped1 the cross has two longer and two shorter arms1 or pairs of arms4 ,the square or tetragonal symmetry occurs in crystals abundantly2 to the vegetable world it appears to be less congenial2 for though there are flowers with four exactly similar and regularly-disposed petals1 as the herb ,paris 7,paris quadrifolia71 these flowers appear1 from various circumstances1 to be deviations from the usual type of vegetable forms4 ,the trigonal1 or three-membered symmetry is found abundantly both in plants and in crystals1 while the pentagonal symmetry1 on the other hand1 though by far the most common among flowers1 nowhere occurs in minerals1 and does not appear to be a possible form of crystals4 ,this pentagonal form further occurs in the animal kingdom1 which the oblong1 triangular1 and square forms do not4 ,many of ,cuvier's radiate animals appear in this pentagonal form1 as echini and pentacrinites1 which latter have hence their name4 #d4 ,the regular1 or as they may be called1 the normal types of the vegetable world appear to be the forms which possess triangular and pentagonal symmetry2 from these the others may be conceived to be derived1 by transformations resulting from the expansion of one or more parts4 ,thus it is manifest that if in a three-membered or five-membered flower1 one of the petals be expanded more than the other1 it is immediately reduced from pentagonal or trigonal1 to simple symmetry4 ,and the oblong or two-and-two-membered symmetry of the flowers of cruciferous plants1 7in which the stamens are four large and two small ones1 arranged in regular opposition17 is held by botanists to result #ga from a normal form with ten stamens2 ,meinecke explaining this by adhesion1 and ,sprengel by the metamorphosis of the stamens into petals#bg4 ,note #bg3 ,sprengel1 ,gesch4 d4 ,bot4 ii4 #cjd4 ,it is easy to see that these various kinds of symmetry include relations both of form and of number1 but more especially of the latter kind2 and as this symmetry is often an important character in various classes of natural objects1 such classes have often curious numerical properties4 ,one of the most remarkable and extensive of these is the distinction which prevails between monocotyledonous and dicotyledonous plants2 the number three being the ground of the symmetry of the former1 and the number five1 of the latter4 ,thus liliaceous and bulbous plants1 and the like1 have flowers of three or six petals1 and the other organs follow the same numbers3 while the vast majority of plants are pentandrous1 and with their five stamens have also their other parts in fives4 ,this great numerical distinction corresponding to a leading difference of physiological structure cannot but be considered as a highly curious fact in phytology4 ,such properties of numbers1 thus connected in an incomprehensible manner with fundamental and extensive laws of nature1 give to numbers an appearance of mysterious importance and efficacy4 ,we learn from history how strongly the study of such properties1 as they are exhibited by the phenomena of the heavens1 took possession of the mind of ,kepler2 perhaps it was this which1 at an earlier period1 contributed in no small degree to the numerical mysticism of the ,pythagoreans in antiquity1 and of the ,arabians and others in the middle ages4 ,in crystallography1 numbers are the primary characters in which the properties of substances are expressed2--they appear1 first1 in that classification of forms which depends on the degree of symmetry1 that is1 upon the number of correspondencies2 and next1 in the laws of derivation1 which1 for the most part1 appear to be common in their occurrence in proportion to the numerical simplicity of their expression4 ,but the manifestation #gb of a governing numerical relation in the organic world strikes us as more unexpected2 and the selection of the number five as the index of the symmetry of dicotyledonous plants and radiated animals1 7a number which is nowhere symmetrically produced in inorganic bodies17 makes this a new and remarkable illustration of the constancy of numerical relations4 ,we may observe1 however1 that the moment one of these radiate animals has one of its five members expanded1 or in any way peculiarly modified1 7as happens among the echini71 it is reduced to the common type of animals simply symmetrical1 with a right and left side4 #e4 ,it is not necessary to attempt to enumerate all the kinds of ,symmetry1 since our object is only to explain what ,symmetry is1 and for this purpose enough has probably been said already4 ,it will be seen1 as soon as the notion of ,symmetry in general is well apprehended1 that it is or includes a peculiar ,fundamental ,idea1 not capable of being resolved into any of the ideas hitherto examined4 ,it may be said1 perhaps1 that the ,idea of ,symmetry is a modification or derivative of our ideas of space and number2--that a symmetrical shape is one which consists of parts exactly similar1 repeated a certain number of times1 and placed so as to correspond with each other4 ,but on further reflection it will be seen that this repetition and correspondence of parts in symmetrical figures are something peculiar2 for it is not any repetition or any correspondence of parts to which we should give the name of symmetry1 in the manner in which we are now using the term4 ,symmetrical arrangements may1 no doubt1 be concerned with space and position1 time and number2 but there appears to be implied in them a ,fundamental ,idea of regularity1 of completeness1 of complex simplicity1 which is not a mere modification of other ideas4 #f4 ,it is1 however1 not necessary1 in this and in similar cases1 to determine whether the idea which we have before us be a peculiar and independent ,fundamental ,idea or a modification of other ideas1 provided we clearly perceive the evidence of those ,axioms by #gc means of which the ,idea is applied in scientific reasonings4 ,now in the application of the ,idea of ,symmetry to crystallography1 phytology and zoology1 we must have this idea embodied in some principle which asserts more than a mere geometrical or numerical accordance of members4 ,we must have it involved in some vital or productive action1 in order that it may connect and explain the facts of the organic world4 ,nor is it difficult to enunciate such a principle4 ,we may state it in this manner4 ,all the symmetrical members of a natural product are1 under like circumstances1 alike affected by the natural formative power4 ,the parts which we have termed symmetrical1 resemble each other1 not only in their form and position1 but also in the manner in which they are produced and modified by natural causes4 ,and this principle we assume to be necessarily true1 however unknown and inconceivable may be the causes which determine the phenomena4 ,thus it has not yet been found possible to discover or represent to ourselves1 in any intelligible manner1 the forces by which the various faces of a crystal are consequent upon its primary form3 for the hypothesis of their being built up of integrant molecules1 as ,hay held1 cannot be made satisfactory4 ,but though the mechanism of crystals is still obscure1 there is no doubt as to the principle which regulates their modifications4 ,the whole of crystallography rests upon this principle1 that if one of the primary planes or axes be modified in any manner1 all the symmetrical planes and axes must be modified in the same manner4 ,and though accidental mechanical or other causes may interfere with the actual exhibition of such faces1 we do not the less assume their crystallographical reality1 as inevitably implied in the law of symmetry of the crystal#cg4 ,and we apply similar considerations to organized beings4 ,we assume that in a regular flower1 each of the similar #gd members has the same organization and similar powers of developement2 and hence if among these similar parts some are much less developed than others1 we consider them as abortive2 and if we wish to remove doubts as to what are symmetrical members in such a case1 we make the inquiry by tracing the anatomy of these members1 or by following them in their earlier states of developement1 or in cases where their capabilities are magnified by monstrosity or otherwise4 ,the power of developement may be modified by external causes1 and thus we may pass from one kind of symmetry to another2 as we have already remarked4 ,thus a regular flower with pentagonal symmetry1 growing on a lateral branch1 has one petal nearest to the axis of the plant3 if this petal be more or less expanded than the others1 the pentagonal symmetry is interfered with1 and the flower may change to a symmetry of another kind4 ,but it is easy to see that all such conceptions of expansion1 abortion1 and any other kind of metamorphosis1 go upon the supposition of identical faculties and tendencies in each similar member1 in so far as such tendencies have any relation to the symmetry4 ,and thus the principle we have stated above is the basis of that which1 in the ,history1 we termed the ,principle of ,developed and ,metamorphosed ,symmetry4 ,note #cg3 ,some crystalline forms1 instead of being holohedral 7provided with their whole number of faces71 are hemihedral 7provided with only half their number of faces74 ,but in these hemihedral forms the half of the faces are still symmetrically suppressed4 ,we shall not at present pursue the other applications of this ,idea of ,symmetry1 but we shall consider some of the results of its introduction into ,crystallography4 #ge ,,chapter ,,ii4 ,,application ,,of ,,the ,,idea ,,of ,,symmetry ,,to ,,crystals4 #a4 ,,minerals and other bodies of definite chemical composition often exhibit that marked regularity of form and structure which we designate by terming them ,crystals2 and in such crystals1 when we duly study them1 we perceive the various kinds of symmetry of which we have spoken in the previous chapter4 ,and the different kinds of symmetry which we have there described are now usually distinguished from each other1 by writers on crystallography4 ,indeed it is mainly to such writers that we are indebted for a sound and consistent classification of the kinds and degrees of symmetry of which forms are capable4 ,but this classification was by no means invented as soon as mineralogists applied themselves to the study of crystals4 ,these first attempts to arrange crystalline forms were very imperfect2 those1 for example1 of ,linnus1 ,werner1 ,rom de ,lisle1 and ,hay4 ,the essays of these writers implied a classification at once defective and superfluous4 ,they reduced all crystals to one or other of certain fundamental forms2 and this procedure might have been a perfectly good method of dividing crystalline forms into classes1 if the fundamental forms had been selected so as to exemplify the different kinds of symmetry4 ,but this was not the case4 ,hay's fundamental or 'primitive' forms1 were1 for instance1 the following3 the parallelepiped1 the octahedron1 the tetrahedron1 the regular hexagonal prism1 the rhombic dodecahedron1 and the double hexagonal pyramid4 ,of these1 the octahedron1 the tetrahedron1 the rhombic dodecahedron1 all belong to the #gf same kind of symmetry 7the ,,tessular systems72 also the hexagonal prism and the hexagonal pyramid both belong to the ,,rhombic system2 while the parallelepiped is so employed as to include all kinds of symmetry4 ,it is1 however1 to be recollected that ,hay1 in his selection of primitive forms1 not only had an eye to the external form of the crystal and to its degree and kind of regularity1 but also made his classification with an especial reference to the cleavage of the mineral1 which he considered as a primary element in crystalline analysis4 ,there can be no doubt that the cleavage of a crystal is one of its most important characters3 it is a relation of form belonging to the interior1 which is to be attended to no less than the form of the exterior4 ,but still1 the cleavage is to be regarded only as determining the degree of geometrical symmetry of the body1 and not as defining a special geometrical figure to which the body must be referred4 ,to have looked upon it in the latter light1 was a mistake of the earlier crystallographic speculators1 on which we shall shortly have to remark4 #b4 ,i have said that the reference of crystals to ,primitive ,forms might have been well employed as a mode of expressing a just classification of them4 ,this follows as a consequence from the application of the ,principle stated in the last chapter1 that all symmetrical members are alike affected4 ,thus we may take an upright triangular prism as the representative of the rhombic system1 and if we then suppose one of the upper edges to be cut off1 or truncated1 we must1 by the ,principle of ,symmetry1 suppose the other two upper edges to be truncated in precisely the same manner4 ,by this truncation we may obtain the upper part of a rhombohedron2 and by truncations of the same kind1 symmetrically affecting all the analogous parts of the figure1 we may obtain any other form possessing three-membered symmetry4 ,and the same is true of any of the other kinds of symmetry1 provided we make a proper selection of a fundamental form4 ,and this was really the method employed by ,demeste1 ,werner1 and ,rom de ,lisle4 ,they #gg assumed a ,primitive ,form1 and then conceived other forms1 such as they found in nature1 to be derived from the ,primitive ,form by truncation of the edges1 acumination of the corners1 and the like processes4 ,this mode of conception was a perfectly just and legitimate expression of the general ,idea of ,symmetry4 #c4 ,the true view of the degrees of symmetry was1 as ,i have already said1 impeded by the attempts which ,hay and others made to arrive at primitive forms by the light which cleavage was supposed to throw upon the structure of minerals4 ,at last1 however1 in ,germany1 as ,i have narrated in the ,history of ,mineralogy#dg1 ,weiss and ,mohs introduced a classification of forms implying a more philosophical principle1 dividing the forms into ,systems2 which1 employing the terms of the latter writer1 we shall call the tessular1 the pyramidal or square pyramidal1 the prismatic or oblong1 and the rhombohedral systems4 ,note #dg3 ,hist4 ,ind4 ,sc4 b4 xv4 c4 iv4 ,of these forms1 the three latter may be at once referred to those kinds of symmetry of which we have spoken in the last chapter4 ,the rhombohedral system has triangular symmetry1 or is three-membered3 the pyramidal has square symmetry1 or is four-membered3 the prismatic has oblong symmetry1 and is two-and-two-membered4 ,but the kinds of symmetry which were spoken of in the former chapter1 do not exhaust the idea when applied to minerals4 ,for the symmetry which was there explained was such only as can be exhibited on a surface1 whereas the forms of crystals are solid4 ,not only have the right and left parts of the upper surface of a crystal relations to each other2 but the upper surface and the lateral faces of the crystal have also their relations2 they may be different1 or they may be alike4 ,if we take a cube1 and hold it so that four of its faces are vertical1 not only are all these four sides exactly similar1 so as to give square symmetry2 but also we may turn the cube1 so that any one of these four sides shall become the top1 and still the four sides which are thus made vertical1 though #gh not the same which were vertical before1 are still perfectly symmetrical4 ,thus this cubical figure possesses more than square symmetry4 ,it possesses square symmetry in a vertical as well as in a horizontal sense4 ,it possesses a symmetry which has the same relation to a cube which four-membered symmetry has to a square4 ,and this kind of symmetry is termed the cubical or tessular symmetry4 ,all the other kinds of symmetry have reference to an axis1 about which the corresponding parts are disposed2 but in tessular symmetry the horizontal and vertical axes are also symmetrical1 or interchangeable2 and thus the figure may be said to have no axis at all4 #d4 ,it has already been repeatedly stated that1 by the very idea of symmetry1 all the incidents of form must affect alike all the corresponding parts4 ,now in crystals we have1 among these incidents1 not only external figure1 but cleavage1 which may be considered as internal figure4 ,cleavage1 then1 must conform to the degree of symmetry of the figure4 ,accordingly cleavage1 no less than form1 is to be attended to in determining to what system a mineral belongs4 ,if a crystal were to occur as a square prism or pyramid1 it would not on that account necessarily belong to the square pyramidal system4 ,if it were found that it was cleavable parallel to one side of the prism1 but not in the transverse direction1 it has only oblong symmetry2 and the equality of the sides which makes it square is only accidental4 ,thus no cleavage is admissible in any system of crystallization which does not agree with the degree of symmetry of the system4 ,on the other hand1 any cleavage which is consistent with the symmetry of the system1 is 7hypothetically at least7 allowable4 ,thus in the oblong prismatic system we may have a cleavage parallel to one side only of the prism2 or parallel to both1 but of different distinctness2 or parallel to the two diagonals of the prism but of the same distinctness2 or we may have both these cleavages together4 ,in the rhombohedral system1 the cleavage may be parallel to the sides of the rhombohedron1 as in ,calc #gi ,spar3 or1 in the same system1 the cleavage1 instead of being thus oblique to the axis1 may be along the axis in those directions which make equal angles with each other3 this cleavage easily gives either a triangular or a hexagonal prism4 ,again1 in the tessular system1 the cleavage may be parallel to the surface of the cube1 which is thus readily separable into other cubes1 as in ,galena2 or the cleavage may be such as to cut off the solid angle of the cube1 and since there are eight of these1 such cleavage gives us an octahedron1 which1 however1 may be reduced to a tetrahedron1 by rejecting all parallel faces1 as being mere repetitions of the same cleavage2 this is the case with ,fluor ,spar3 or the cube of the tessular system may be cleavable in planes which truncate all the edges of the cube2 and as these are twelve1 we thus obtain the dodecahedron with rhombic faces3 this occurs in ,zinc ,blende4 ,and thus we see the origin of ,hay's various primitive forms1 the tetrahedron1 octahedron1 and rhombic dodecahedron1 all belonging to the tessular system3--they are1 in fact1 different cleavage forms of that system4 #e4 ,i do not dwell upon other incidents of crystals which have reference to form1 nor upon the lustre1 smoothness1 and striation of the surfaces4 ,to all such incidents the general principle applies1 that similar parts are similarly affected2 and hence1 if any parts are found to be constantly and definitely different from other parts of the same sort1 they are not similar parts2 and the symmetry is to be interpreted with reference to this difference4 ,we have now to consider the inferences which have been drawn from these incidents of crystallization1 with regard to the intimate structure of bodies4 #hj ,,chapter ,,iii4 ,,speculations ,,founded ,,upon ,,the ,,symmetry ,,of ,,crystals4 #a4 ,,when a crystal1 as1 for instance1 a crystal of ,galena1 7sulphuret of lead17 is readily divisible into smaller cubes1 and these into smaller ones1 and so on without limit1 it is very natural to represent to ourselves the original cube as really consisting of small cubical elements2 and to imagine that it is a philosophical account of the physical structure of such a substance to say that it is made up of cubical molecules4 ,and when the ,galena crystal has externally the form of a cube1 there is no difficulty in such a conception2 for the surface of the crystal is also conceived as made up of the surfaces of its cubical molecules4 ,we conceive the crystal so constituted1 as we conceive a wall built of bricks4 ,but if1 as often happens1 the ,galena crystal be an octahedron1 a further consideration is requisite in order to understand its structure1 pursuing still the same hypothesis4 ,the mineral is still1 as in the other case1 readily cleavable into small cubes1 having their corners turned to the faces of the octahedron4 ,therefore these faces can no longer be conceived as made up of the faces of cubical elements of which the whole is constituted4 ,if we suppose a pile of such small cubes to be closely built together1 but with decreasing width above1 so as to form a pyramid1 the face of such a pyramid will no longer be plane2 it will consist of a great number of the corners or edges of the small elementary cubes4 ,it would appear at first sight1 therefore1 that such a face cannot represent the smooth polished surface of a crystal4 #ha ,but when we come to look more closely1 this difficulty disappears4 ,for how large are these elementary cubes8 ,we cannot tell1 even supposing they really have any size4 ,but we know that they must be1 at any rate1 very small2 so small as to be inappreciable by our senses1 for our senses find no limit to the divisibility of minerals by cleavage4 ,hence the surface of the pyramid above described would not consist of visible corners or edges1 but would be roughened by specks of imperceptible size2 or rather1 by supposing these specks to become still smaller1 the roughness becomes smoothness4 ,and thus we may have a crystal with a smooth surface1 made up of small cubes in such a manner that their surfaces are all oblique to the surface of the crystal4 ,hay1 struck by some instances in which the supposition of such a structure of crystals appeared to account happily for several of their relations and properties1 adopted and propounded it as a general theory4 ,the small elements1 of which he supposed crystals to be thus built up1 he termed integrant molecules4 ,the form of these molecules might or might not be the same as the primitive form with which his construction was supposed to begin2 but there was1 at any rate1 a close connexion between these forms1 since both of them were founded on the cleavage of the mineral4 ,the tenet that crystals are constituted in the manner which ,i have been describing1 ,i shall call the ,theory of ,integrant ,molecules1 and ,i have now to make some remarks on the grounds of this theory4 #b4 ,in the case of which ,i have spoken1 the mineral used as the example1 ,galena1 readily splits into cubes1 and cubes are easily placed together so as to fit each other1 and fill the space which they occupy4 ,the same is the case in the mineral which suggested to ,hay his theory1 namely1 ,calc ,spar4 ,the crystals of this substance are readily divisible into rhombohedrons1 a form like a brick with oblique angles2 and such bricks can be built together so as to produce crystals of all the immense varieties of form which ,calc ,spar presents4 ,this kind of masonry is equally possible in many other #hb minerals2 but as we go through the mineral kingdom in our survey1 we soon find cases which offer difficulties4 ,some minerals cleave only in two directions1 some in one only2 in such cases we cannot by cleavage obtain an integrant molecule of definite form2 one of its dimensions1 at least1 must remain indeterminate and arbitrary4 ,again1 in some instances1 we have more than three different planes of cleavage1 as in ,fluor ,spar1 where we have four4 ,the solid1 bounded by four planes1 is a tetrahedron2 or if we take four pairs of parallel faces1 an octahedron4 ,but if we attempt to take either of these forms for our integrant molecule1 we are met by this difficulty3 that a collection of such forms will not fill space4 ,perhaps this difficulty will be more readily conceived by the general reader if it be contemplated with reference to plane figures4 ,it will readily be seen that a number of equal squares may be put together so as to fill the space which they occupy2 but if we take a number of equal regular octagons1 we may easily convince ourselves that no possible arrangement can make them cover a flat space without leaving blank spots between4 ,in like manner octahedrons or tetrahedrons cannot be arranged in solid space so as to fill it4 ,they necessarily leave vacancies4 ,hence the structure of ,fluor ,spar1 and similar crystals1 was a serious obstacle in the way of the theory of integrant molecules4 ,that theory had been adopted in the first instance because portions of the crystal1 obtained by cleavage1 could be built up into a solid mass2 but this ground of the theory failed altogether in such instances as ,i have described1 and hence the theory1 even upon the representations of its adherents1 had no longer any claim to assent4 ,the doctrine of ,integral ,molecules1 however1 was by no means given up at once1 even in such instances4 ,in this and in other subjects1 we may observe that a theory1 once constructed and carried into detail1 has such a hold upon the minds of those who have been in the habit of applying it1 that they will attempt to uphold it by introducing suppositions inconsistent with #hc the original foundations of the theory4 ,thus those who assert the ,atomic ,theory1 reconcile it with facts by taking the halves of atoms2 and thus the ,theory of ,integrant ,molecules was maintained for ,fluor ,spar1 by representing the elementary octahedrons of which crystals are built up1 as touching each other only by the edges4 ,the contact of surface with surface amongst integrant molecules had been the first basis of the theory2 but this supposition being here inapplicable1 was replaced by one which made the theory no longer a representation of the facts 7the cleavages71 but a mere geometrical construction4 ,although1 however1 the inapplicability of the theory to such cases was thus1 in some degree1 disguised to the disciples of ,hay1 it was plain that1 in the face of such difficulties1 the ,theory of ,integrant ,molecules could not hold its place as a philosophical truth4 ,but it still answered the purpose 7a very valuable one1 and one to which crystallography is much indebted17 of an instrument for calculating the geometrical relations of the parts of crystals to each other3 for the integrant molecules were supposed to be placed layer above layer1 each layer as we ascend1 decreasing by a certain number of molecules and rows of molecules2 and the calculation of these laws of decrement was1 in fact1 the best mode then known of determining the positions of the faces4 ,the ,theory of ,decrements served to express and to determine1 in a great number of the most obvious cases1 the laws of phenomena in crystalline forms1 though the ,theory of ,integrant ,molecules could not be maintained as a just view of the structure of crystals4 #c4 ,the ,theory of ,integrant ,molecules1 however1 involved this just and important principle3 that a true view of the intimate structure of crystals must include and explain the facts of crystallization1 that is1 crystalline form and cleavage2 and that it must take these into account1 according to their degree of ,symmetry4 ,so far all theories concerning the elements of crystals must agree4 ,and it was soon seen that this was1 in reality1 all that had been established by the investigations of ,hay and his school4 ,i have already1 in the #hd ,history1 quoted ,weiss's reflections on making this step4 ',when in #ahji1' he says#eg1 ',i published my ,dissertation1 ,i shared the common opinion as to the necessity of the assumption1 and the reality of the existence of a primitive form1 at least in a sense not very different from the usual sense of the expression4' ,he then proceeds to relate that he sought a ground for such an opinion1 independent of the doctrine of ,atoms1 which he1 in common with a great number of philosophers of that time in his own country1 was disposed to reject1 inclining to believe that the properties of bodies were determined by ,forces which acted in them1 and not by ,molecules of which they were composed4 ,he adds1 that in pursuing this train of thought1 he found1 'that out of his ,primitive ,forms there was gradually unfolded to his hands that which really governs them1 and is not affected by their casual fluctuations2 namely1 the ,fundamental ,relations of their ,dimensions1' or as we now may call them1 ,axes of ,symmetry4 ,with reference to these ,axes1 he found1 as he goes on to say1 that 'a multiplicity of internal ,oppositions1 necessarily and mutually interdependent1 are developed in the crystalline mass1 each ,relation having its own ,polarity2 so that the ,crystalline ,character is co-extensive with these ,polarities4' ,the character of these polarities1 whether manifested in crystalline faces1 cleavage1 or any other incidents of crystallization1 is necessarily displayed in the degree and kind of ,symmetry which the crystal possesses3 and thus this ,symmetry1 in all our speculations concerning the structure of crystals1 necessarily takes the place of that enumeration of ,primitive ,forms which were rejected as inconsistent with observed facts1 and destitute of sound scientific principle4 ,note #eg3 ,acad4 ,berlin4 #ahaf1 p4 #cjg4 ,i may just notice here what ,i have stated in the ,history of ,mineralogy#fg1 that the distinction of systems of crystallization1 as introduced by ,weiss and ,mohs1 was strikingly confirmed by ,sir ,david ,brewster's discoveries respecting the optical properties of minerals4 #he ,the splendid phenomena which were produced by passing polarized light through crystals1 were found to vary according as the crystals were of the ,rhombohedral1 ,square ,pyramidal1 ,oblong ,prismatic1 or ,tessular ,system4 ,the ,optical ,symmetry exactly corresponded with the ,geometrical ,symmetry4 ,in the two former ,systems were crystals uniaxal in respect of their optical properties2 the oblong prismatic1 was biaxal2 while in the tessular1 the want of a predominant axis prevented the phenomena here spoken of from occurring at all4 ,the optical experiments must have led1 and would have led1 to a classification of crystals into the above systems or something nearly equivalent1 even had they not been already so arranged by attention to their forms4 ,note #fg3 ,hist4 ,ind4 ,sc4 b4 xv4 c4 v4 #d4 ,while in ,germany ,weiss and ,mohs with their disciples1 were gradually rejecting what was superfluous in the previous crystallographical hypotheses1 philosophers in ,england were also trying to represent to themselves the constitution of crystals in a manner which should be free from the obviously arbitrary and untenable fictions of the ,hayian school4 ,these attempts1 however1 were not crowned with much success4 ,one mode of representing the structure of crystals which suggested itself1 was to reject the polyhedral forms which ,hay gave to his integrant molecules1 and to conceive the elements of crystals as spheres1 the properties of the crystal being determined not by the surfaces1 but by the position of the elements4 ,this was done by ,wollaston1 in the ,philosophical ,transactions for #ahac4 ,he applied this view to the tessular system1 in which1 indeed1 the application is not difficult2 and he showed that octahedral and tetrahedral figures may be deduced from symmetrical arrangements of equal spherules4 ,but though in doing this1 he manifested a perception of the conditions of the problem1 he appeared to lose his hold on the real question when he tried to pass on to other systems of crystallization4 ,for he accounted for the rhombohedral system by supposing the spheres changed into spheroids4 ,such a procedure involved him in a gratuitous and useless hypothesis3 for to what purpose do we introduce the #hf arrangement of atoms 7instead of their figure17 as a mode of explaining the symmetry of the crystallization1 when at the next step we ascribe to the atom1 by an arbitrary fiction1 a symmetry of figure of the same kind as that which we have to explain8 ,it is just as easy1 and as allowable1 to assume an elementary rhombohedron1 as to assume elementary spheroids1 of which the rhombohedrons are constructed4 #e4 ,many hypotheses of the same kind might be adduced1 devised both by mineralogists and chemists4 ,but almost all such speculations have been pursued with a most surprising neglect of the principle which obviously is the only sound basis on which they can proceed4 ,the principle is this3--that ,all hypotheses concerning the arrangement of the elementary atoms of bodies in space must be constructed with reference to the general facts of crystallization4 ,the truth and importance of this principle can admit of no doubt4 ,for if we make any hypothesis concerning the mode of connexion of the elementary particles of bodies1 this must be done with the view of representing to ourselves the forces which connect them1 and the results of these forces as manifested in the properties of the bodies4 ,now the forces which connect the particles of bodies so as to make them crystalline1 are manifestly chemical forces4 ,it is only definite chemical compounds which crystallize2 and in crystals the force of cohesion by which the particles are held together cannot in any way be distinguished or separated from the chemical force by which their elements are combined4 ,the elements are understood to be combined1 precisely because the result is a definite1 apparently homogeneous substance4 ,the properties of the compound bodies depend upon the elements and their mode of combination2 for1 in fact1 these include everything on which they can depend4 ,there are no other circumstances than these which can affect the properties of a body4 ,therefore all those properties which have reference to space1 namely1 the crystalline properties1 cannot depend upon anything else than the arrangement of the elementary molecules in space4 ,these #hg properties are the facts which any hypothesis of the arrangement of molecules must explain1 or at least render conceivable2 and all such hypotheses1 all constructions of bodies by supposed arrangements of molecules1 can have no other philosophical object than to account for facts of this kind4 ,if they do not do this1 they are mere arbitrary geometrical fictions1 which cannot be in any degree confirmed or authorised by an examination of nature1 and are therefore not deserving of any regard4 #f4 ,those philosophers who have endeavoured to represent the mode in which bodies are constructed by the combination of their chemical atoms1 have often undertaken to show1 not only that the atoms are combined1 but also in what positions and configurations they are combined4 ,and it is truly remarkable1 as ,i have already said1 that they have done this1 almost in every instance1 without any consideration of the crystalline character of the resulting combinations2 from which alone we receive any light as to the relation of their elements in space4 ,thus ,dr4 ,dalton1 in his ,elements of ,chemistry1 in which he gave to the world the ,atomic ,theory as a representation of the doctrine of definite and multiple proportions1 also published a large collection of ,diagrams1 exhibiting what he conceived to be the configuration of the atoms in a great number of the most common combinations of chemical elements4 ,now these hypothetical diagrams do not in any way correspond1 as to the nature of their symmetry1 with the compounds1 as we find them displaying their symmetry when they occur crystallized4 ,carbonate of lime has in reality a triangular symmetry1 since it belongs to the rhombohedral system2 ,dr4 ,dalton's carbonate of lime would be an oblique rhombic prism or pyramid4 ,sulphate of baryta is really two-and-two membered2 ,dr4 ,dalton's diagram makes it two-and-one membered4 ,alum is really octahedral or tessular2 but according to the diagram it could not be so1 since the two ends of the atom are not symmetrical4 ,and the same want of correspondence between the facts and the hypothesis runs through the whole #hh system4 ,it need not surprise us that the theoretical arrangement of atoms does not explain the facts of crystallization2 for to produce such an explanation would be a second step in science quite as great as the first1 the discovery of the atomic theory in its chemical sense4 ,but we may allow ourselves to be surprised that an utter discrepance between all the facts of crystallization and the figures assumed in the theory1 did not suggest any doubt as to the soundness of the mode of philosophizing by which this part of the theory was constructed4 #g4 ,some little accordance between the hypothetical arrangements of chemical atoms and the facts of crystallization1 does appear to have been arrived at by some of the theorists to whom we here refer1 although by no means enough to show a due conviction of the importance of the principle stated above4 ,thus ,wollaston1 in the ,essay above noticed1 after showing that a symmetrical arrangement of equal spherules would give rise to octahedral and other tessular figures1 remarks1 very properly1 that the metals1 which are simple bodies1 crystallize in such forms4 ,m4 ,ampre#gg also1 in #ahad1 published a brief account of an hypothesis of a somewhat similar nature1 and stated himself to have developed this speculation in a ,memoir which has not yet1 so far as ,i am aware1 been published4 ,in this notice he conceives bodies to be compounded of molecules1 which1 arranged in a polyhedral form1 constitute particles4 ,these representative forms of the particles depend on chemical laws4 ,thus the particles of oxygen1 of hydrogen1 and of azote1 are composed each of four molecules4 ,hence it is collected that the particles of nitrous gas are composed of two molecules of oxygen and two of azote2 and similar conclusions are drawn respecting other substances4 ,these conclusions1 though expressed by means of the polyhedrons thus introduced1 are supported by chemical1 rather than by crystallographical comparisons4 ,the author does1 indeed1 appeal to the crystallization of sal #hi ammoniac as an argument#hg2 but as all the forms which he introduces appear to belong to the tessular system of crystallization1 there is1 in his reasonings1 nothing distinctive2 and therefore nothing1 crystallographically speaking1 of any weight on the side of this theory4 ,note #gg3 ,ann4 de ,chimie1 tom4 xc4 p4 #dc4 ,note #hg3 ,ann4 de ,chimie1 tom4 xc4 p4 #hc4 #h4 ,any hypothesis which should introduce any principle of chemical order among the actual forms of minerals1 would well deserve attention4 ,at first sight1 nothing can appear more anomalous than the forms which occur4 ,we have1 indeed1 one broad fact1 which has an encouraging aspect1 the tessular forms in which the pure metals crystallize4 ,the highest degree of chemical and of geometrical simplicity coincide3 irregularity disappears precisely where it is excluded by the consideration above stated1 that the symmetry of chemical composition must determine the symmetry of crystalline form#ig4 ,note #ig3 ,inasmuch as this law1 that the simple metals crystallize in tessular forms1 is the most signal example of that connexion between the chemical nature of a body and its crystalline form1 ,i in the former ,edition stated it with as much generality as ,i could find any ground for1 and ,i should have been glad if ,i could have added confirmation of the law1 derived from later observations4 ,but the most recent investigations of crystallographers appear to have afforded exceptions rather than examples of the rule4 ,arsenic and ,tellurium are said to be rhombohedral4 ,antimony1 stated by ,hay to be octahedral 7and therefore tessular71 has been found by more modern observers to be rhombohedral4 ,tin has been obtained by ,professor ,miller in beautiful crystals belonging to the pyramidal system4 ,professor ,nggerath has observed in ,zinc1 after cooling from fusion1 hexagonal cleavage1 rendering it probable that the mineral crystallized in rhombohedrons having their axes vertical1 like ice4 ,g4 ,rose conceives it highly probable that ,osmium and ,iridium are rhombohedral4 7,poggendorf4 ,bd4 liv47 ,but all the more perfect metals are tessular2 namely1 ,gold1 ,silver1 ,mercury1 ,platinum1 ,iron1 ,copper2 also ,bismuth 8 ,perhaps the observation in which the crystallization of ,zinc is affected by its position is1 on that very account1 no sufficient evidence of its free crystallization4 ,we can hardly conceive a collection of perfectly simple1 similar particles to crystallize so as to have one pre-eminent axis1 without some extraneous action affecting them4 ,but if we go on to any other class of crystalline forms1 we soon find ourselves lost in our attempts to #ij follow any thread of order4 ,we have indeed many large groups connected by obvious analogies2 as the rhombohedral carbonates of lime1 magnesia1 iron1 manganese2--the prismatic carbonates and sulphates of lime1 baryta1 strontia1 lead4 ,but even in these1 we cannot form any plausible hypothesis of the arrangement of the elements2 and in other cases to which we naturally turn1 we can find nothing but confusion4 ,for instance1 if we examine the oxides of metals3--those of iron are rhombohedral and tessular2 those of copper1 tessular2 those of tin1 of titanium1 of manganese1 square pyramidal2 those of antimony1 prismatic2 and we have other forms for other substances4 ,it may be added1 that if we take account of the optical properties which1 as we have already stated1 have constant relations to the crystalline forms1 the confusion is still further increased2 for the optical dimensions vary in amount1 though not in symmetry1 where chemistry can trace no difference of composition4 #i4 ,we will not quit the subject1 however1 without noticing the much more promising aspect which it has assumed by the detection of such groups as are referred to in the last article2 or in other words1 by ,mitscherlich's discovery of ,isomorphism4 ,according to that discovery1 there are various elements which may take the place of each other in crystalline bodies1 either without any alteration of the crystalline form1 or at most with only a slight alteration of its dimensions4 ,such a group of elements we have in the earths lime and magnesia1 the protoxides of iron and manganese3 for the carbonates of all these bases occur crystallized in forms of the rhombohedral system1 the characteristic angle being nearly the same in all4 ,now lime and magnesia1 by the discoveries of modern chemistry1 are really oxides of metals2 and therefore all these carbonates have a similar chemical constitution1 while they have also a similar crystalline form4 ,whether or no we can devise any arrangement of molecules by which this connexion of the chemical and the geometrical property can be represented1 we cannot help #ia considering the connexion as an extremely important fact in the constitution of bodies2 and such facts are more likely than any other to give us some intelligible view of the relations of the ultimate parts of bodies4 ,the same may be said of all the other isomorphous or plesiomorphous groups#ajg4 ,for instance1 we have a number of minerals which belong to the same system of crystallization1 but in which the chemical composition appears at first sight to be very various3 namely1 spinelle1 pleonaste1 gahnite1 franklinite1 chromic iron oxide1 magnetic iron oxide3 but ,abich has shown that all these may be reduced to a common chemical formula2--they are bioxides of one set of bases1 combined with trioxides of another set4 ,perhaps some mathematician may be able to devise some geometrical arrangement of such a group of elements which may possess the properties of the tessular system4 ,hypothetical arrangements of atoms1 thus expressing both the chemical and the crystalline symmetry which we know to belong to the substance1 would be valuable steps in analytical science2 and when they had been duly verified1 the hypotheses might easily be divested of their atomic character4 ,note #ajg3 ,see ,hist4 ,ind4 ,sc4 b4 xv4 c4 vi4 ,thus1 as we have already said1 mineralogy1 understood in its wider sense1 as the counterpart of chemistry1 has for one of its main objects to discover those ,relations of the ,elements of bodies which have reference to ,space4 ,in this research1 the foundation of all sound speculation is the kind and degree of ,symmetry of form which we find in definite chemical compounds3 and the problem at present before the inquirer is1 to devise such arrangements of molecules as shall answer the conditions alike of ,chemistry and of ,crystallography4 ,we now proceed to the ,classificatory ,sciences1 of which ,mineralogy is one1 though hitherto by far the least successful4 #ic ,,book ,,viii4 ,,the ,,philosophy ,,of ,,the ,,classificatory ,,sciences4 ,,where a certain apparent difference between things 7although perhaps in itself of little moment7 answers to we know not what number of other differences1 pervading not only their known properties but properties yet undiscovered1 it is not optional but imperative to recognise this difference as the foundation of a specific distinction4 ,,john ,s4 ,,mill1 ,system of ,logic1 b4 #a1 ch4 vii4 #d4 #ie ,,book ,,viii4 ,,the ,,philosophy ,,of ,,the ,,classificatory ,,sciences4 ,,chapter ,i4 ,,the ,,idea ,,of ,,likeness ,,as ,,governing ,,the ,,use ,,of ,,common ,,names4 #a4 ,object of the ,chapter4--,,not only the ,classificatory ,sciences1 but the application of names to things in the rudest and most unscientific manner1 depends upon our apprehending them as like each other4 ,we must therefore endeavour to trace the influence and operation of the ,idea of ,likeness in the common use of language1 before we speak of the conditions under which it acquires its utmost exactness and efficacy4 ,it will be my object to show in this1 as in previous cases1 that the impressions of sense are apprehended by acts of the mind2 and that these mental acts necessarily imply certain relations which may be made the subjects of speculative reasoning4 ,we shall have1 if we can1 to seize and bring into clear view the principles which the relation of like and unlike involves1 and the mode in which these principles have been developed4 #b4 ,unity of the ,individual4--,but before we can attend to several things as like or unlike1 we must be able to apprehend each of these by itself as one thing4 #if ,it may at first sight perhaps appear that this apprehension results immediately from the impressions on our senses1 without any act of our thoughts4 ,a very little attention1 however1 enables us to see that thus to single out special objects requires a mental operation as well as a sensation4 ,how1 for example1 without an exertion of mental activity1 can we see one tree1 in a forest where there are many8 ,we have1 spread before us1 a collection of colours and forms1 green and brown1 dark and light1 irregular and straight3 this is all that sensation gives or can give4 ,but we associate one brown trunk with one portion of the green mass1 excluding the rest1 although the neighbouring leaves are both nearer in contiguity and more similar in appearance than is the stem4 ,we thus have before us one tree2 but this unity is given by the mind itself4 ,we see the green and the brown1 but we must make the tree before we can see it4 ,that this composition of our sensations so as to form one thing implies an act of our own1 will perhaps be more readily allowed1 if we once more turn our attention to the manner in which we sometimes attempt to imitate and record the objects of sight1 by drawing4 ,when we do this1 as we have already observed1 we mark this unity of each object1 by drawing a line to separate the parts which we include from those which we exclude2--an ,outline4 ,this line corresponds to nothing which we see2 the beginner in drawing has great difficulty in discerning it2 he has in fact to make it4 ,it is1 as has been said by a painter of our own time#ah1 a fiction3 but it is a fiction employed to mark a real act of the mind2 to designate the singleness of the object in our conception4 ,as we have said elsewhere1 we see lines1 but especially outlines1 by mentally drawing them ourselves4 ,note #ah3 ,phillips ,on ,painting1--,design4 ,the same act of conception which the outline thus represents and commemorates in visible objects1--the same combination of sensible impressions into a unit1--is exercised also with regard to the objects of all #ig our senses3 and the singleness thus given to each object1 is a necessary preliminary to its being named or represented in any other way4 ,but it may be said1 ,is it then by an arbitrary act of our own that we put together the branches of the same tree1 or the limbs of the same animal8 ,have we equally the power and the right to make the branch of the fir a part of the neighbouring oak8 ,can we include in the outline of a man any object with which he happens to be in contact8 ,such suppositions are manifestly absurd4 ,and the answer is1 that though we give unity to objects by an act of thought1 it is not by an arbitrary act2 but by a process subject to certain conditions2--to conditions which exclude such incongruous combinations as have just been spoken of4 ,what are these conditions which regulate our apprehension of an object as one8--which determine what portion of our impressions does1 and what portion does not belong to the same thing8 #c4 ,condition of ,unity4--,i reply1 that the primary and fundamental condition is1 that we must be able to make intelligible assertions respecting the object1 and to entertain that belief of which assertions are the exposition4 ,a tree grows1 sheds its leaves in autumn1 and buds again in the spring1 waves in the wind1 or falls before the storm4 ,and to the tree belong all those parts which must be included in order that such declarations1 and the thought which they convey1 shall have a coherent and permanent meaning4 ,those are its branches which wave and fall with its trunk2 those are its leaves which grow on its branches4 ,the permanent connexions which we observe1--permanent1 among unconnected changes which affect the surrounding appearances1--are what we bind together as belonging to one object4 ,this permanence is the condition of our conceiving the object as one4 ,the connected changes may always be described by means of assertions2 and the connexion is seen in the identity of the subject of successive predications2 in the possibility of applying many verbs to one substantive4 ,we may #ih therefore express the condition of the unity of an object to be this3 that assertions concerning the object shall be possible3 or rather we should say1 that the acts of belief which such assertions enunciate shall be possible4 ,it may seem to be superfluous to put in a form so abstract and remote1 the grounds of a process apparently so simple as our conceiving an object to be one4 ,but the same condition to which we have thus been led1 as the essential principle of the unity of objects1 namely1 that propositions shall be possible1 will repeatedly occur in the present chapter2 and it may serve to illustrate our views1 to show that this condition pervades even the simplest cases4 #d4 ,kinds4--,the mental synthesis of which we have thus spoken1 gives us our knowledge of individual things2 it enables me to apprehend that particular tree or man which ,i now see1 or1 by the help of memory1 the tree or the man ,i saw yesterday4 ,but the knowledge with which we have mainly here to do is not a knowledge of individuals but of kinds2 of such classes as are indicated by common names4 ,we have to make assertions concerning a tree or a man in general1 without regarding what is peculiar to this man or that tree4 ,now it is clear that certain individual objects are all called man1 or all called tree1 in virtue of some resemblance which they have4 ,if we had not the power of perceiving in the appearances around us1 likeness and unlikeness1 we could not consider objects as distributed into kinds at all4 ,the impressions of sense would throng upon us1 but being uncompared with each other1 they would flow away like the waves of the sea1 and each vanish from our contemplation when the sensation faded4 ,that we do apprehend surrounding objects as belonging to permanent kinds1 as being men and horses1 oaks and roses1 arises from our having the idea of likeness1 and from our applying it habitually1 and so far as such a classification requires4 ,not only can we employ the idea of likeness in this manner1 but we apply it incessantly and universally to #ii the whole mass and train of our sensations4 ,for we have no external sensations to which we cannot apply some language or other2 and all language necessarily implies recognition of resemblances4 ,we cannot call an object green or round without comparing in our thoughts its colour or its shape1 with a shape and a colour seen in other objects4 ,all our sensations1 therefore1 without any exception of kind or time1 are subject to this constant process of classification2 and the idea of likeness is perpetually operating to distribute them into kinds1 at least so far as the use of language requires4 ,we come then again to the question1 ,upon what principle1 under what conditions1 is the ,idea of ,likeness thus operative8 ,what are the limits of the classes thus formed8 ,where does that similarity end1 which induces and entitles us to call a thing a tree8 ,what universal rule is there for the application of common names1 so that we may not apply them wrongly8 #e4 ,not made by ,definitions4--,perhaps some one might expect in answer to these inquiries a definition or a series of definitions2--might imagine that some description of a tree might be given which might show when the term was applicable and when it was not2 and that we might construct a body of rules to which such descriptions must conform4 ,but on consideration it will be clear that the real solution of our difficulty cannot be obtained in such a manner4 ,for first2 such descriptions must be given in words1 and must therefore suppose that we have already satisfied ourselves how words are to be used4 ,if we define a tree to be 'a living thing without the power of voluntary motion1' we shall be called upon to define 'a living thing2' and it is manifest that this renewal of the demand for definition might be repeated indefinitely2 and1 therefore1 we cannot in this way come to a final principle4 ,and in the next place1 most of those who use language1 even with great precision and consistency1 would find it difficult or impossible to give good definitions even of a few of the general names which they use2 and therefore their practice cannot be regulated by any #ajj tacit reference to such definitions4 ,that definitions of terms are of great use and importance in their right place1 we shall soon see2 but their place is not to regulate the use of common language4 ,what then1 once more1 is this regulative principle8 ,what rules do men follow in the use of words1 so as commonly to avoid confusion and ambiguity8 ,how do they come to understand each other so well as they ordinarily do1 respecting the limits of classes never defined1 and which they cannot define8 ,what is the common ,convention1 or ,condition to which they conform8 #f4 ,condition of the ,use of ,terms4--,to this we reply1 that the ,condition which regulates the use of language1 is1 that it shall be capable of being used2--that is1 that general assertions shall be possible4 ,the term tree is applicable as far as it is useful in expressing our knowledge concerning trees3--thus we know that trees are fixed in the ground1 have a solid stem1 branches1 leaves1 and many other properties4 ,with regard to all the objects which surround us1 we have an immense store of knowledge of such properties1 and we employ the names of the objects in such a manner as enables us to express these properties4 ,but the connexion of such properties is variable and indefinite4 ,some properties are constantly combined1 others occasionally only4 ,the leaves of different oaks resemble each other1 the branches resemble far less1 and may differ very widely4 ,the term oak does not enable us to say that all oaks have straight branches or all crooked4 ,terms can only express properties as far as they are constant4 ,not only1 therefore1 the accumulation of a vast mass of knowledge of the properties and attributes of objects1 but also an observation of the habitual connexion of such properties is needed1 to direct us to the consistent application of terms3--to enable us to apply them so as to express truths4 ,but here again we are largely provided with the requisite knowledge and observation by the common course of our existence4 ,the unintermitting stream of experience supplies us with an incalculable #aja amount of such observed connexions4 ,all men have observed that the associations of the same form of leaves are more constant than of the same form of branches2--that though persons walk in different attitudes1 none go on all fours2 and thus the term oak is so applied as to include those cases in which the leaves are alike in form though the branches be unlike2 and though we should refuse to apply the term man to a class of creatures which habitually and without compulsion used four legs1 we make no scruple of affixing it to persons of very different figures4 ,the whole of human experience being composed of such observed connexions1 we have thus materials even for the immense multiplicity of names which human language contains2 all which names are1 as we have said1 regulated in their application by the condition of their expressing such experience4 ,thus amid the countless combinations of properties and divisions of classes which the structure of language implies1 scarcely any are arbitrary or capricious4 ,a word which expressed a mere wanton collection of unconnected attributes could hardly be called a word2 for of such a collection of properties no truth could be asserted1 and the word would disappear1 for want of some occasion on which it could be used4 ,though much of the fabric of language appears1 not unnaturally1 fantastical and purely conventional1 it is in fact otherwise4 ,the associations and distinctions of phraseology are not more fanciful than is requisite to make them correspond to the apparent caprices of nature or of thought2 and though much in language may be called conventional1 the conventions exist for the sake of expressing some truth or opinion1 and not for their own sake4 ,the principle1 that the condition of the use of terms is the possibility of general1 intelligible1 consistent assertions1 is true in the most complete and extensive sense4 #g4 ,terms may have different ,uses4--,the ,terms with which we are here most concerned are ,names of ,classes of natural objects2 and when we say that the principle and the limit of such ,names are their use in expressing propositions concerning the classes1 it is #ajb clear that much will depend on the kind of propositions which we mainly have to express3 and that the same name may have different limits1 according to the purpose we have in view4 ,for example1 is the whale properly included in the general term fish8 ,when men are concerned in catching marine animals1 the main features of the process are the same however the animals may differ2 hence whales are classed with fishes1 and we speak of the whale-fishery4 ,but if we look at the analogies of organization1 we find that1 according to these1 the whale is clearly not a fish1 but a beast1 7confining this term1 for the sake of distinctness1 to suckling beasts or mammals74 ,in ,natural ,history1 therefore1 the whale is not included among fish4 ,the indefinite and miscellaneous propositions which language is employed to enunciate in the course of common practical life1 are replaced by a more coherent and systematic collection of properties1 when we come to aim at scientific knowledge4 ,but we shall hereafter consider the principle of the classifications of ,natural ,history2 our present subject is the application of the ,idea of ,likeness in common practice and common language4 #h4 ,gradation of ,kinds4--,common names1 then1 include many individuals associated in virtue of resemblances1 and of permanently connected properties2 and such names are applicable as far as they serve to express such properties4 ,these collections of individuals are termed ,kinds1 ,sorts1 ,classes4 ,but this association of particulars is capable of degrees4 ,as individuals by their resemblances form ,kinds1 so kinds of things1 though different1 may resemble each other so as to be again associated in a higher ,class2 and there may be several successive steps of such classification4 ,man1 horse1 tree1 stone1 are each a name of a ,kind2 but animal includes the two first and excludes the others2 living thing is a term which includes animal and tree but not stone2 body includes all the four4 ,and such a subordination of kinds may be traced very widely in the arrangements of language4 #ajc ,the condition of the use of the wider is the same as that of the narrower ,names of ,classes2--they are good as far as they serve to express true propositions4 ,in common language1 though such an order of generality may in a variety of instances be easily discerned1 it is not systematically and extensively referred to2 but this subordination and graduated comprehensiveness is the essence of the methods and nomenclatures of ,natural ,history1 as we shall soon have to show4 ,but such subordination is not without its use1 even in common cases1 and when it is expressed in the terms of common language4 ,thus organized body is a term which includes plants and animals2 animal includes beasts1 birds1 fishes2 beast includes horses and dogs2 dogs1 again1 are greyhounds1 spaniels1 terriers4 #i4 ,characters of ,kinds4--,now when we have such a ,series of ,names and ,classes1 we find that we take for granted irresistibly that each class has some ,character which distinguishes it from other classes included in the superior division4 ,we ask what kind of beast a dog is2 what kind of animal a beast is2 and we assume that such questions admit of answer2--that each kind has some mark or marks by which it may be described4 ,and such descriptions may be given3 an animal is an organized body having sensation and volition2 man is a reasonable animal4 ,whether or no we assent to the exactness of these definitions1 we allow the propriety of their form4 ,if we maintain these definitions to be wrong1 we must believe some others to be right1 however difficult it may be to hit upon them4 ,we entertain a conviction that there must be1 among things so classed and named1 a possibility of defining each4 ,now what is the foundation of this postulate8 ,what is the ground of this assumption1 that there must exist a definition which we have never seen1 and which perhaps no one has seen in a satisfactory form8 ,the knowledge of this definition is by no means necessary to our using the word with propriety2 for any one can make true assertions about dogs1 but who can define a #ajd dog8 ,and yet if the definition be not necessary to enable us to use the word1 why is it necessary at all8 ,i allow that we possess an indestructible conviction that there must be such a character of each kind as will supply a definition2 but ,i ask1 on what this conviction rests4 ,i reply1 that our persuasion that there must needs be characteristic marks by which things can be defined in words1 is founded on the assumption of the necessary possibility of reasoning4 ,the reference of any object or conception to its class without definition1 may give us a persuasion that it shares the properties of its class1 but such classing does not enable us to reason upon those properties4 ,when we consider man as an animal1 we ascribe to him in thought the appetites1 desires1 affections1 which we habitually include in our notion of animal3 but except we have expressed these in some definition or acknowledged description of the term animal1 we can make no use of the persuasion in ratiocination4 ,but if we have described animals as 'being impelled to action by appetites and passions1' we can not only think1 but say1 'man is an animal1 and therefore he is impelled to act by appetites and passions4' ,and if we add a further definition1 that 'man is a reasonable animal1' and if it appear that 'reason implies conformity to a rule of action1' we can then further infer that man's nature is to conform the results of animal appetite and passion to a rule of action4 ,the possibility of pursuing any such train of reasoning as this1 depends on the definitions1 of animal and of man1 which we have introduced2 and the possibility of reasoning concerning the objects around us being inevitably assumed by us from the constitution of our nature1 we assume consequently the possibility of such definitions as may thus form part of our deduction1 and the existence of such defining characters4 #aj4 ,difficulty of ,definitions4--,but though men are1 on such grounds1 led to make constant and importunate demands for definitions of the terms which they employ in their speculations1 they are1 in fact1 far #aje from being able to carry into complete effect the postulate on which they proceed1 that they must be able to find definitions which by logical consequence shall lead to the truths they seek4 ,the postulate overlooks the process by which our classes of things are formed and our names applied4 ,this process consisting1 as we have already said1 in observing permanent connexions of properties1 and in fixing them by the attribution of names1 is of the nature of the process of ,induction1 of which we shall afterwards have to speak4 ,and the postulate is so far true1 that this process of induction being once performed1 its result may usually be expressed by means of a few definitions1 and may thus lead by a deduction to a train of real truths4 ,but in the subjects where we principally find such a subordination of classes as we have spoken of1 this process of deduction is rarely of much prominence3 for example1 in the branches of natural history4 ,yet it is in these subjects that the existence and importance of these characteristic marks1 which we have spoken of1 principally comes into view4 ,in treating of these marks1 however1 we enter upon methods which are technical and scientific1 not popular and common4 ,and before we make this transition1 we have a remark to make on the manner in which writers1 without reference to physics or natural history1 have spoken of kinds1 their subordination1 and their marks4 #aa4 ',the ,five ,words4'--,these things1--the ,nature and ,relations of ,classes1--were1 in fact1 the subjects of minute and technical treatment by the logicians of the school of ,aristotle4 ,porphyry wrote an ,introduction to the ,categories of that philosopher1 which is entitled ,on the ,five ,words4 ,the ',five ,words' are ,genus1 ,species1 ,difference1 ,property1 ,accident4 ,genus and ,species are superior and inferior classes1 and are stated#bh to be capable of repeated subordination4 ,the 'most #ajf general ,genus' is the widest class2 the 'most special ,species' the narrowest4 ,between these are intermediate classes1 which are ,genera with regard to those below1 and ,species with regard to those above them4 ,thus ,being is the most general ,genus2 under this is ,body2 under ,body is ,living ,body2 under this again ,animal2 under ,animal is ,rational ,animal1 or ,man2 under ,man are ,socrates and ,plato1 and other individual men4 ,note #bh3 ,porphyr4 ,isagog4 c4 #bc4 ,the ,difference is that which is added to the genus to make the species2 thus ,rational is the ,difference by which the genus ,animal is made the species ,man2 the ,difference in this ,technical sense is the ',specific1' or species-making ,difference#ch4 ,it forms the ,definition for the purposes of logic1 and corresponds to the ',character' 7specific or generic7 of the ,natural ,historians4 ,indeed several of them1 as1 for instance1 ,linnus1 in his ,philosophia ,botanica1 always call these ,characters the ,difference1 by a traditional application of the ,peripatetic terms of art4 ,note #ch3 4 ,of the other two words1 the ,property is that which though not employed in defining the class1 belongs to every part of it#dh3 it is1 ',what happens to all the class1 to it alone1 and at all times2 as to be capable of laughing is a ,property of man4' ,note #dh3 ,isagog4 c4 #d ,the ,accident is that which may be present and absent without the destruction of the subject1 as to sleep is an ,accident 7a thing which happens7 to man4 ,i need not dwell further on this system of technicalities4 ,the most remarkable points in it are those which ,i have already noticed2 the doctrine of the successive ,subordination of genera1 and the fixing attention upon the ,specific ,difference4 ,these doctrines1 though invented in order to make reasoning more systematic1 and at a period anterior to the existence of any ,classificatory ,science1 have1 by a curious contrast with the intentions of their founders1 been of scarcely #ajg any use in sciences of ,reasoning1 but have been amply applied and developed in the ,natural ,history which arose in later times4 ,we must now treat of the principles on which this science 7,natural ,history7 proceeds1 and explain what peculiar and technical processes it employs in addition to those of common thought and common language4 #ajh ,,chapter ,,ii4 ,,the ,,methods ,,of ,,natural ,,history1 ,,as ,,regulated ,,by ,,the ,,idea ,,of ,,likeness4 ,,sect4 ,i4--,natural ,history in general4 #a4 ,idea of ,likeness in ,natural ,history4--,,the various branches of ,natural ,history1 in so far as they are classificatory sciences merely1 and do not depend upon physiological views1 rest upon the same ,idea of ,likeness which is the ground of the application of the names1 more or less general1 of common language4 ,but the nature of science requires that1 for her purposes1 this ,idea should be applied in a more exact and rigourous manner than in its common and popular employment2 just as occurs with regard to the other ,ideas on which science is founded2--for instance1 as the idea of space gives rise1 in popular use1 to the relations implied in the prepositions and adjectives which refer to position and form1 and in its scientific development gives rise to the more precise relations of geometry4 ,the way in which the ,idea of ,likeness has been applied1 so as to lead to the construction of a science1 is best seen in ,botany3 for1 in the ,classification of ,animals1 we are inevitably guided by a consideration of the function of parts2 that is1 by an idea of purpose1 and not of likeness merely3 and in ,mineralogy1 the attempts at classification on the principles of ,natural ,history have been hitherto very imperfectly successful4 ,but in ,botany we have an example of a branch of knowledge in which systematic classification has been effected with great beauty and advantage2 and in which the peculiarities and principles on which such #aji classification must depend have been carefully studied4 ,many of the principal botanists1 as ,linnus1 ,adanson1 ,decandolle1 have not only practically applied1 but have theoretically enunciated1 what they held to be the sound maxims of classificatory science3 and have thus enabled us to place before the reader with confidence the philosophy of this kind of science4 #b4 ,condition of its ,use4--,we may begin by remarking that the ,idea of ,likeness1 in its systematic employment1 is governed by the same principle which we have already spoken of as regulating the distribution of things into kinds1 and the assignment of names in unsystematic thought and speech2 namely1 the condition that general propositions shall be possible4 ,but as in this case the propositions are to be of a scientific form and exactness1 the likeness must be treated with a corresponding precision2 and its consequences traced by steady and distinct processes4 ,naturalists must1 for their purposes1 employ the resemblances of objects in a technical manner4 ,this technical process may be considered as consisting of three steps2--,the fixation of the resemblances2 ,the use of them in making a classification2 ,the means of applying the classification4 ,these three steps may be spoken of as the ,terminology1 the ,plan of the ,system1 and the ,scheme of the ,characters4 ,,sect4 ,,ii4--,terminology4#eh ,note #eh3 ,decandolle and others use the term ,glossology instead of ,terminology1 to avoid the blemish of a word compounded of two parts taken from different languages4 ,the convenience of treating the termination ology 7and a few other parts of compounds7 as not restricted to ,greek combinations1 is so great1 that ,i shall venture1 in these cases1 to disregard this philological scruple4 #c4 ,terminology signifies the collection of terms1 or technical words1 which belong to the science4 ,but in fixing the meaning of the terms1 at least of the descriptive terms1 we necessarily fix1 at the same time1 the perceptions and notions which the terms are to #aaj convey2 and thus the ,terminology of a classificatory science exhibits the elements of its substance as well as of its language4 ,a large but indispensable part of the study of botany 7and of mineralogy and zoology also17 consists in the acquisition of the peculiar vocabulary of the science4 ,the meaning of technical terms can be fixed in the first instance only by convention1 and can be made intelligible only by presenting to the senses that which the terms are to signify4 ,the knowledge of a colour by its name can only be taught through the eye4 ,no description can convey to a hearer what we mean by apple-green or ,french grey4 ,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 ,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 #aaa 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 ,decandolle#fh1 '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 #fh3 ,theor4 ,elem4 p4 #cbg4 ,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 #aab 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#gh4 ,sometimes terms of greater generality were devised2 as perianth to include the calyx and corolla1 whether one or both of these were present#hh2 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#ih1 pinnatipartite1 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#ajh 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#aah 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 conveyed by the following phrase3 'fronds rigid pinnate1 pinn recurved subunilateral pinnatifid1 the segments linear undivided or bifid spinuloso-serrate#abh4' ,note #gh3 ,decandolle1 #cbi ,note #hh3 ,for this ,erhart and ,decandolle use ,perigone4 ,note #ih3 ,dec4 #cah4 ,note #ajh3 ,ib4 #dic4 ,note #aah3 ,ib4 #dbb4 ,note #abh3 ,hooker1 ,brit4 ,flo4 p4 #deg4 ,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 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 #aac 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 gypsum #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 ,cesalpinus 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 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 #aad enable us to convey them in words4 ,we have now to speak of the mode in which such resemblances have been employed in the construction of a ,systematic ,classification4 ,,sect4 ,,iii4 ,the ,plan of the ,system4 #d4 ,the collection of sound views and maxims by which the resemblances of natural objects are applied so as to form a scientific classification1 is a department of the philosophy of natural history which has been termed by some writers 7as ,decandolle71 ,taxonomy1 as containing the ,laws of the ,taxis 7arrangement74 ,by some ,germans this has been denominated ,systematik2 if we could now form a new substantive after the analogy of the words ,logick1 ,rhetorick1 and the like1 we might call it ,systematick4 ,but though our ,english writers commonly use the expression ,systematical ,botany for the ,botany of ,classification1 they appear to prefer the term ,diataxis for the method of constructing the classification4 ,the rules of such a branch of science are curious and instructive4 ,in framing a ,classification of objects we must attend to their resemblances and differences4 ,but here the question occurs1 to what resemblances and differences8 for a different selection of the points of resemblance would give different results3 a plant frequently agrees in leaves with one group of plants1 in flowers with another4 ,which set of characters are we to take as our guide8 ,the view already given of the regulative principle of all classification1 namely1 that it must enable us to assert true and general propositions1 will obviously occur as applicable here4 ,the object of a scientific ,classification is to enable us to enunciate scientific truths3 we must therefore classify according to those resemblances of objects 7plants or any others7 which bring to light such truths4 ,but this reply to the inquiry1 ',on what characters of resemblance we are to found our system1' is still too general and vague to be satisfactory4 ,it carries us1 #aae however1 as far as this2--that since the truths we are to attend to are scientific truths1 governed by precise and homogeneous relations1 we must not found our scientific ,classification on casual1 indefinite1 and unconnected considerations4 ,we must not1 for instance1 be satisfied with dividing plants1 as ,dioscorides does1 into aromatic1 esculent1 medicinal and vinous2 or even with the long prevalent distribution into trees1 shrubs1 and herbs2 since in these subdivisions there is no consistent principle4 #e4 ,latent ,reference to ,natural ,affinity4--,but there may be several kinds of truths1 all exact and coherent1 which may be discovered concerning plants or any other natural objects2 and if this should be the case1 our rule leaves us still at a loss in what manner our classification is to be constructed4 ,and1 historically speaking1 a much more serious inconvenience has been this2--that the task of classification of plants was necessarily performed when the general laws of their form and nature were very little known2 or rather1 when the existence of such laws was only just beginning to be discerned4 ,even up to the present day1 the general propositions which botanists are able to assert concerning the structure and properties of plants1 are extremely imperfect and obscure4 ,we are thus led to this conclusion3--that the ,idea of ,likeness could not be applied so as to give rise to a scientific ,classification of plants1 till considerable progress was made in studying the general relations of vegetable form and life2 and that the selection of the resemblances which should be taken into account1 must depend upon the nature of the relations which were then brought into view4 ,but this amounts to saying that1 in the consideration of the ,classification of vegetables1 other ,ideas must be called into action as well as the ,idea of ,likeness4 ,the additional general views to which the more intimate study of plants leads1 must depend1 like all general truths1 upon some regulating ,idea which gives unity to scattered facts4 ,no progress could be made in botanical knowledge without the #aaf operation of such principles3 and such additional ,ideas must be employed1 besides those of mere likeness and unlikeness1 in order to point out that ,classification which has a real scientific value4 ,accordingly1 in the classificatory sciences1 ,ideas other than ,likeness do make their appearance4 ,such ,ideas in botany have influenced the progress of the science1 even before they have been clearly brought into view4 ,we have especially the ,idea of ,affinity1 which is the basis of all ,natural ,systems of ,classification1 and which we shall consider in a succeeding chapter4 ,the assumption that there is a ,natural ,system1 an assumption made by all philosophical botanists1 implies a belief in the existence of ,natural ,affinity1 and is carried into effect by means of principles which are involved in that ,idea4 ,but as the formation of all systems of classification must involve1 in a great degree1 the ,idea of ,resemblance and ,difference1 ,i shall first consider the effect of that ,idea1 before ,i treat specially of ,natural ,affinity4 #f4 ,natural ,classes4--,many attempts were made to classify vegetables before the rules which govern a natural system were clearly apprehended4 ,botanists agree in esteeming some characters as of more value than others1 before they had agreed upon any general rules or principles for estimating the relative importance of the characters4 ,they were convinced of the necessity of adding other considerations to that of ,resemblance1 without seeing clearly what these others ought to be4 ,they aimed at a ,natural ,classification1 without knowing distinctly in what manner it was to be ,natural4 ,the attempts to form ,natural ,classes1 therefore1 in the first part of their history1 belong to the ,idea of ,likeness1 though obscurely modified1 even from an early period1 by the ,ideas of ,affinity1 and even of ,function and of ,development4 ,hence ,natural ,classes may1 to a certain extent1 be treated of in this place4 ,natural ,classes are opposed to ,artificial ,classes which are understood to be regulated by an assumed #aag character4 ,yet no classes can be so absolutely ,artificial in this sense1 as to be framed upon characters arbitrarily assumed2 for instance1 no one would speak of a class of shrubs defined by the circumstance of each having a hundred leaves3 for of such a class no assertion could be made1 and therefore the class could never come under our notice4 ,in what sense then are ,artificial ,classes to be understood1 as opposed to ,natural8 #g4 ,artificial ,classes4--,to this question1 the following is the answer4 ,when ,natural ,classes of a certain small extent have been formed1 a system may be devised which shall be regulated by a few selected characters1 and which shall not dissever these small ,natural ,classes1 but conform to them as far as they go4 ,if these selected characters be then made absolute and imperative1 and if we abandon all attempt to obtain ,natural ,classes of any higher order and wider extent1 we form an ,artificial ,system4 ,thus in the ,linnan ,system of ,botanical ,classification1 it is assumed that certain natural groups1 namely1 ,species and ,genera1 are established2 it is conceived1 moreover1 that the division of ,classes according to the number of stamens and of pistils does not violate the natural connexions of ,species and ,genera4 ,this arrangement1 according to the number of stamens and pistils1 7further modified in certain cases by other considerations17 is then made the ground of all the higher divisions of plants1 and thus we have an ,artificial ,system4 ,it has been objected to this view1 that the ,linnan ,artificial ,system does not in all cases respect the boundaries of genera1 but would1 if rigorously applied1 distribute the species of the same genus into different artificial classes2 it would divide1 for instance1 the genera ,valeriana1 ,geranium#ach1 c4 ,to this we must reply1 that so far as the ,linnan ,system does this1 it is an imperfect ,artificial ,system4 ,its great merit is in its making such a disjunction in comparatively so #aah few cases2 and in the artificial characters being1 for the most part1 obvious and easily applied4 ,note #ach3 ,decand4 ,theor4 ,elem4 p4 #de4 #h4 ,are ,genera ,natural8--,it has been objected also that ,genera are not ,natural groups4 ,linnus asserts in the most positive manner that they are#adh4 ,on which ,adanson observes#aeh1 ',i know not how any ,botanist can maintain such a thesis3 that which is certain is1 that up to the present time no one has been able to prove it1 nor to give an exact definition of a natural genus1 but only of an artificial4' ,he then brings several arguments to confirm this view4 ,note #adh3 ,phil4 ,bot4 ,art4 #afe4 ,note #aeh3 ,famille de ,ph4 ,pref4 cv4 ,but we are to observe1 in answer to this1 that ,adanson improperly confounds the recognition of the existence of a natural group with the invention of a technical mark or definition of it4 ,genera are groups of species associated in virtue of natural affinity1 of general resemblance1 of real propinquity3 of such groups1 certain selected characters1 one or few1 may usually be discovered1 by which the species may be referred to their groups4 ,these ,artificial characters do not constitute1 but indicate the genus3 they are the ,diagnosis1 not the basis of the ,diataxis3 and they are always subject to be rejected1 and to have others substituted for them1 when they violate the natural connexion of species which a minute and enlarged study discovers4 ,it is1 therefore1 no proof that ,genera are not ,natural1 to say that their artificial characters are different in different systems4 ,such characters are only different attempts to confine the variety of nature within the limits of definition4 ,nor is it sufficient to say that these groups themselves are different in different writers2 that some botanists make genera what others make only species2 as ,pedicularis1 ,rhinanthus1 ,euphrasia1 ,antirrhinum#afh4 ,this discrepancy shows only that the natural arrangement is not yet completely known1 even in the smaller groups2 a conclusion to which we need not refuse our assent4 ,but in #aai opposition to these negatives1 the manner in which ,genera have been established proves that they are regulated by the principle of being natural1 and by that alone4 ,for they are not formed according to any priori rule4 ,the ,botanist does not take any selected or arbitrary part or parts of the plants1 and marshal his genera according to the differences of this part4 ,on the contrary1 the divisions of genera are sometimes made by means of the flower2 sometimes by means of the fruit3 the anthers1 the stamens1 the seeds1 the pericarp1 and the most varied features of these parts1 are used in the most miscellaneous and unsystematic manner4 ,linnus has indeed laid down a maxim that the characteristic differences of genera must reside in the fructification#agh3 but ,adanson has justly remarked#ahh1 that an arbitrary restriction like this makes the groups artificial3 and that in some families other characters are more essential than those of the fructification2 as the leaves in the families of ,aparine and ,leguminos1 and the disposition of the flowers in ,labiat4 ,and ,naturalists are so far from thinking it sufficient to distribute species into genera by arbitrary marks1 that we find them in many cases lamenting the absence of good natural marks3 as in the families of ,umbellifer1 where ,linnus declared that any one who could find good characters of genera would deserve great admiration1 and where it is only of late that good characters have been discovered and the arrangement settled#aih by means principally of the ribs of the fruit#bjh4 ,note #afh3 ,adanson1 p4 cvi4 ,note #agh3 ,phil4 ,bot4 ,art4 #afb4 ,note #ahh3 ,adanson1 ,pref4 p4 cxx4 ,note #aih3 ,lindley1 ,nat4 ,syst4 p4 #e4 ,note #bjh3 ,in like manner we find ,cuvier saying of ,rondelet that he has 'un sentiment trs vrai des genres4' ,hist4 ,ichth4 p4 #ci4 ,it is thus clear that ,genera are not established on any assumed or preconceived basis4 ,what1 then1 is the principle which regulates botanists when they try to fix genera8 ,what is the arrangement which they thus wish for1 without being able to hit upon it8 ,what is the tendency which thus drives them from the corolla to the anthers1 from the flower to the fruit1 #abj from the fructification to the leaves8 ,it is plain that they seek something1 not of their own devising and creating2--not anything merely conventional and systematic2 but something which they conceive to exist in the relations of the plants themselves2--something which is without the mind1 not within2--in nature1 not in art2--in short1 a ,natural ,order4 ,thus the regulative principle of a ,genus1 or of any other natural group is1 that it is1 or is supposed to be1 natural4 ,and by reference to this principle as our guide1 we shall be able to understand the meaning of that indefiniteness and indecision which we frequently find in the descriptions of such groups1 and which must appear so strange and inconsistent to any one who does not suppose these descriptions to assume any deeper ground of connexion than an arbitrary choice of the botanist4 ,thus in the family of the ,rose-tree1 we are told that the ovules are very rarely erect#bah1 the stigmata are usually simple4 ,of what use1 it might be asked1 can such loose accounts be8 ,to which the answer is1 that they are not inserted in order to distinguish the species1 but in order to describe the family1 and the total relations of the ovules and of the stigmata of the family are better known by this general statement4 ,a similar observation may be made with regard to the ,anomalies of each group1 which occur so commonly1 that ,mr4 ,lindley1 in his ,introduction to the ,natural ,system of ,botany1 makes the ',anomalies' an article in each ,family4 ,thus1 part of the character of the ,rosace is that they have alternate stipulate leaves1 and that the albumen is obliterated3 but yet in ,lowea1 one of the genera of this family1 the stipul are absent2 and the albumen is present in another1 ,neillia4 ,this implies1 as we have already seen1 that the artificial character 7or diagnosis as ,mr4 ,lindley calls it7 is imperfect4 ,it is1 though very nearly1 yet not exactly1 commensurate with the natural group3 and hence1 in certain cases1 this character is made to yield to the general weight of natural affinities4 ,note #bah3 ,lindley1 ,nat4 ,syst4 p4 #ha4 #aba #i4 ,difference of ,natural ,history and ,mathematics4--,these views1--of classes determined by characters which cannot be expressed in words1--of propositions which state1 not what happens in all cases1 but only usually1--of particulars which are included in a class though they transgress the definition of it1 may very probably surprise the reader4 ,they are so contrary to many of the received opinions respecting the use of definitions and the nature of scientific propositions1 that they will probably appear to many persons highly illogical and unphilosophical4 ,but a disposition to such a judgment arises in a great measure from this2--that the mathematical and mathematico-physical sciences have1 in a great degree1 determined men's views of the general nature and form of scientific truth2 while ,natural ,history has not yet had time or opportunity to exert its due influence upon the current habits of philosophizing4 ,the apparent indefiniteness and inconsistency of the classifications and definitions of ,natural ,history belongs1 in a far higher degree1 to all other except mathematical speculations3 and the modes in which approximations to exact distinctions and general truths have been made in ,natural ,history1 may be worthy our attention1 even for the light they throw upon the best modes of pursuing truth of all kinds4 #aj4 ,natural ,groups given by ,type not by ,definition4--,the further development of this suggestion must be considered hereafter4 ,but we may here observe1 that though in a ,natural ,group of objects a definition can no longer be of any use as a regulative principle1 classes are not1 therefore1 left quite loose1 without any certain standard or guide4 ,the class is steadily fixed1 though not precisely limited2 it is given1 though not circumscribed2 it is determined1 not by a boundary line without1 but by a central point within2 not by what it strictly excludes1 but by what it eminently includes2 by an example1 not by a precept2 in short1 instead of ,definition we have a ,type for our director4 ,a ,type is an example of any class1 for instance1 a species of a genus1 which is considered as eminently #abb possessing the characters of the class4 ,all the species which have a greater affinity with this ,type-species than with any others1 form the genus1 and are ranged about it1 deviating from it in various directions and different degrees4 ,thus a genus may consist of several species1 which approach very near the type1 and of which the claim to a place with it is obvious2 while there may be other species which straggle further from this central knot1 and which yet are clearly more connected with it than with any other4 ,and even if there should be some species of which the place is dubious1 and which appear to be equally bound by two generic types1 it is easily seen that this would not destroy the reality of the generic groups1 any more than the scattered trees of the intervening plain prevent our speaking intelligibly of the distinct forests of two separate hills4 ,the ,type-species of every genus1 the ,type-genus of every family1 is1 then1 one which possesses all the characters and properties of the genus in a marked and prominent manner4 ,the ,type of the ,rose family has alternate stipulate leaves1 wants the albumen1 has the ovules not erect1 has the stigmata simple1 and besides these features1 which distinguish it from the exceptions or varieties of its class1 it has the features which make it prominent in its class4 ,it is one of those which possess clearly several leading attributes2 and thus1 though we cannot say of any one genus that it must be the ,type of the family1 or of any one species that it must be the ,type of the genus1 we are still not wholly to seek3 the ,type must be connected by many affinities with most of the others of its group2 it must be near the center of the crowd1 and not one of the stragglers4 #aa4 ,it has already been repeatedly stated1 as the great rule of all classification1 that the classification must serve to assert general propositions4 ,it may be asked what propositions we are able to enunciate by means of such classifications as we are now treating of4 ,and the answer is1 that the collected knowledge of the characters1 habits1 properties1 organization1 and #abc functions of these groups and families1 as it is found in the best botanical works1 and as it exists in the minds of the best botanists1 exhibits to us the propositions which constitute the science1 and to the expression of which the classification is to serve4 ,all that is not strictly definition1 that is1 all that is not artificial character1 in the descriptions of such classes1 is a statement of truths1 more or less general1 more or less precise1 but making up1 together1 the positive knowledge which constitutes the science4 ,as we have said1 the consideration of the properties of plants in order to form a system of classification1 has been termed ,taxonomy1 or the ,systematick of ,botany2 all the parts of the descriptions1 which1 taking the system for granted1 convey additional information1 are termed the ,physiography of the science2 and the same terms may be applied in the other branches of ,natural ,history4 #ab4 ,artificial and ,natural ,systems4--,if ,i have succeeded in making it apparent that an artificial system of characters necessarily implies natural classes which are not severed by the artificial marks1 we shall now be able to compare the nature and objects of the ,artificial and ,natural ,systems2 points on which much has been written in recent times4 ,the ,artificial ,system is one which is1 or professes to be1 entirely founded upon marks selected according to the condition which has been stated1 of not violating certain narrow natural groups2 namely in the ,linnan system1 the natural genera of plants4 ,the marks which form the basis of the system1 being thus selected1 are applied rigorously and universally without any further regard to any other characters or indications of affinity4 ,thus in the ,linnan system1 which depends mainly on the number of male organs or stamens1 and on the number of female organs or styles1 the largest divisions1 or the ,classes1 are arranged according to the number of the stamens1 and are monandria1 diandria1 triandria1 tetrandria1 pentandria1 hexandria1 and so on3 the names being formed of the ,greek numerical words1 and of the word which implies male4 ,and the ,orders of each of these ,classes are #abd distinguished by the number of styles1 and are called monogynia1 digynia1 trigynia1 and so on1 the termination of these words meaning female4 ,and so far as this numerical division and subdivision go on1 the system is a rigorous system1 and strictly artificial4 ,but the condition that the artificial system shall leave certain natural affinities untouched1 makes it impossible to go through the vegetable kingdom by a method of mere numeration of stamens and styles4 ,the distinction of flowers with twenty and with thirty stamens is not a fixed distinction3 flowers of one and the same kind1 as roses1 have1 some fewer than the former1 some more than the latter number4 ,the ,artificial ,system1 therefore1 must be modified4 ,and there are various relations of connexion and proportion among the stamina which are more permanent and important than their mere number4 ,thus flowers with two longer and two shorter stamens are not placed in the class tetrandria1 but are made a separate class didynamia2 those with four longer and two shorter are in like manner tetradynamia1 not hexandria2 those in 9999which the filaments are bound into two bundles are diadelphia4 ,all these and other classes are deviations from the plan of the earlier ,classes1 and are so far defects of the artificial system2 but they are deviations requisite in order that the system may leave a basis of natural groups1 without which it would not be a ,system of ,vegetables4 ,and as the division is still founded on some properties of the stamens1 it combines not ill with that part of the system which depends on the number of them4 ,the ,classes framed in virtue of these various considerations make up an ,artificial ,system which is tolerably coherent4 ',but since the ,artificial ,system thus regards natural groups1 in what does it differ from a ,natural ,system8' ,it differs in this3--,that though it allows certain subordinate natural groups1 it merely allows these1 and does not endeavour to ascend to any wider natural groups4 ,it takes all the higher divisions of its scheme from its artificial characters1 its stamens and pistils1 without looking to any natural affinities4 ,it #abe accepts natural ,genera1 but it does not seek natural ,families1 or ,orders1 or ,classes4 ,it assumes natural groups1 but does not investigate any2 it forms wider and higher groups1 but professes to frame them arbitrarily4 ,but then1 on the other hand1 the question occurs1 ',this being the case1 what can be the use of the ,artificial ,system8' ,if its characters1 in the higher stages of classification1 be arbitrary1 how can it lead us to the natural relations of plants8 ,and the answer is1 that it does so in virtue of the original condition1 that there shall be certain natural relations which the artificial system shall not transgress2 and that its use arises from the facility with which we can follow the artificial arrangement as far as it goes4 ,we can count the stamens and pistils1 and thus we know the ,class and ,order of our plant2 and we have then to discover its ,genus and ,species by means less symmetrical but more natural4 ,the ,artificial ,system1 though arbitrary in a certain degree1 brings us to a ,class in which the whole of each ,genus is contained1 and there we can find the proper ,genus by a suitable method of seeking4 ,no ,artificial ,system can conduct us into the extreme of detail1 but it can place us in a situation where the detail is within our reach4 ,we cannot find the house of a foreign friend by its latitude and longitude2 but we may be enabled1 by a knowledge of the latitude and longitude1 to find the city in which he dwells1 or at least the island2 and we then can reach his abode by following the road or exploring the locality4 ,the ,artificial ,system is such a method of travelling by latitude and longitude2 the ,natural ,system is that which is guided by a knowledge of the country4 ,the ,natural ,system1 then1 is that which endeavours to arrange by the natural affinities of objects2 and more especially1 which attempts to ascend from the lower natural groups to the higher2 as for example from genera to natural families1 orders1 and classes4 ,but as we have already hinted1 these expressions of natural affinities1 natural groups1 and the like1 when #abf considered in reference to the idea of resemblance alone1 without studying analogy or function1 are very vague and obscure4 ,we must notice some of the attempts which were made under the operation of this imperfect view of the subject4 ,,sect4 ,,iv4--,modes of framing ,natural ,systems4 #ac4 ,decandolle#bbh distinguishes the attempts at ,natural ,classifications into three sorts3 those of blind trial 7ttonnement71 those of general comparison1 and those of subordination of characters4 ,the two former do not depend distinctly upon any principle1 except resemblance2 the third refers us to other views1 and must be considered in a future chapter4 ,note #bbh3 ,theor4 ,elem4 art #da4 ,method of ,blind ,trial4--,the notion of the existence of natural classes dependent on the general resemblance of plants1--of an affinity showing itself in different parts and various ways1--though necessarily somewhat vague and obscure1 was acted upon at an early period1 as we have seen in the formation of genera2 and was enunciated in general terms soon after4 ,thus ,magnolius#bch says that he discerns in plants an affinity1 by means of which they may be arranged in families3 ',yet it is impossible to obtain from the fructification alone the ,characters of these families2 and ,i have therefore chosen those parts of plants in which the principal characteristic marks are found1 as the root1 the stem1 the flower1 the seed4 ,in some plants there is even a certain resemblance2 an affinity which does not consist in the parts considered separately1 but in their totality2 an affinity which may be felt but not expressed2 as we see in the families of agrimonies and cinquefoils1 which every botanist will judge to be related1 though they differ by their roots1 their leaves1 their flowers1 and their seeds4' ,note #bch3 ,dec4 ,theor4 ,elem4 art4 #db4 ,petri ,magnoli1 ,prodromus ,hist4 ,gen4 ,plant4 #afhi4 #abg ,this obscure feeling of a resemblance on the whole1 an affinity of an indefinite kind1 appears fifty years later in ,linnus's attempts4 ',in the ,natural ,classification1' he says#bdh1 'no priori rule can be admitted1 no part of the fructification can be taken exclusively into consideration2 but only the simple symmetry of all its parts4' ,hence though he proposed ,natural ,families1 and even stated the formation of such ,families to be the first and last object of all ,methods1 he never gave the ,characters of those groups1 or connected them by any method4 ,he even declared it to be impossible to lay down such a system of characters4 ,this persuasion was the result of his having refused to admit into his mind any ,idea more profound than that notion of ,resemblance of which he had made so much and such successful use2 he would not attempt to unravel the ,ideas of ,symmetry and of ,function on which the clear establishment of natural relations must depend4 ,he even despised the study of the inner organization of plants2 and reckoned#beh the ,anatomici1 who studied the anatomy and physiology of plants and the laws of vegetation1 among the ,botanophili1 the mere amateurs of his science4 ,note #bdh3 ,dec4 ,theor4 ,elem4 art #db4 ,note #beh3 ,phil4 ,bot4 s4 #dd4 ,the same notion of general resemblance and affinity1 accompanied with the same vagueness1 is to be found in the writer who least participated in the general admiration of ,linnus1 ,buffon4 ,though it was in a great measure his love of higher views which made him dislike what he considered the pedantry of the ,swedish school1 he does not seem to have obtained a clearer sight of the principle of the natural method than his rival1 except that he did not restrict his ,characters to the fructification4 ,things must be arranged by their resemblances and differences1 7he says in #agejbfh17 'but the resemblances and differences must be taken not from one part but from the whole2 and we must attend to the form1 the size1 the habit1 the number and position of the parts1 even the substance #abh of the part2 and we must make use of these elements in greater or smaller number1 as we have need4' ,note #bfh3 ,adanson1 p4 clvi4 ,buffon1 ,hist4 ,nat4 t4 i4 p4 #ba4 #ad4 ,method of ,general ,comparison4--,a countryman of ,buffon1 who shared with him his depreciating estimate of the ,linnan system1 and his wish to found a natural system upon a broader basis1 was ,adanson2 and he invented an ingenious method of apparently avoiding the vagueness of the practice of following the general feeling of resemblance4 ,this method consisted in making many ,artificial ,systems1 in each of which plants were arranged by some one part2 and then collecting those plants which came near each other in the greatest number of those ,artificial ,systems1 as plants naturally the most related4 ,adanson gives an account#bgh of the manner in which this system arose in his mind4 ,he had gone to ,senegal1 animated by an intense zeal for natural history2 and there1 amid the luxuriant vegetation of the torrid zone1 he found that the methods of ,linnus and ,tournefort failed him altogether as means of arranging his new botanical treasures4 ,he was driven to seek a new system4 ',for this purpose1' he says1 ',i examined plants in all their parts1 without omitting any1 from the roots to the embryo1 the folding of the leaves in the bud1 their mode of sheathing#bhh1 the situation and folding of the embryo and of its radicle in the seed1 relatively to the fruit2 in short1 a number of particulars which few botanists notice4 ,i made in the first place a complete description of each plant1 putting each of its parts in separate articles1 in all its details2 when new species occurred ,i put down the points in which they differed1 omitting those in which they agreed4 ,by means of the aggregate of these comparative descriptions1 ,i perceived that plants arranged themselves into classes or families which could not be artificial or arbitrary1 not being founded upon one or two parts1 which might change at certain limits1 but on all the parts2 so that the disproportion of one of these parts was corrected and balanced by the introduction of another4' ,thus the principle of ,resemblance #abi was to suffice for the general arrangement1 not by means of a new principle1 as ,symmetry or ,organization1 which should regulate its application1 but by a numeration of the peculiarities in which the resemblance consisted4 ,note #bgh3 ,pref4 p4 clvii4 ,note #bhh3 ',leur manire de s'engainer4' ,the labour which ,adanson underwent in the execution of this thought was immense4 ,by taking each ,organ1 and considering its situation1 figure1 number1 c41 he framed sixty-five ,artificial ,systems2 and collected his ,natural ,families by a numerical combination of these4 ,for example1 his sixty-fifth ,artificial ,system#bih is that which depends upon the situation of the ,ovary with regard to the ,flower2 according to this system he frames ten ,artificial ,classes1 including ninety-three ,sections3 and of these ,sections the resulting ,natural ,arrangement retains thirty-five1 above one-third3 the same estimate is applied in other cases4 ,note #bih3 ,adanson1 ,pref4 p4 cccxii4 ,but this attempt to make ,number supply the defects which the vague notion of ,resemblance introduces1 however ingenious1 must end in failure4 ,for1 as ,decandolle observes#cjh1 it supposes that we know1 not only all the ,organs of plants1 but all the points of view in which it is possible to consider them2 and even if this assumption were true1 which it is not1 and must long be very far from being1 the principle is altogether vicious2 for it supposes that all these points of view1 and all the resulting artificial systems are of equal importance3--a supposition manifestly erroneous4 ,we are thus led back to the consideration of the ,relative ,importance of ,organs and their qualities1 as a basis for the classification of plants1 which no ,artificial ,method can supersede2 and thus we find the necessity of attending to something besides mere external and detached ,resemblance4 ,the method of ,general ,comparison cannot1 any more than the method of ,blind ,trial1 lead us1 with any certainty or clearness1 to the ,natural ,method4 ,adanson's ,families are held by the best botanists to be1 for the greater part1 ,natural2 but his hypotheses are unfounded2 and his success is #acj probably more due to the dim feeling of ,affinity1 by which he was unconsciously guided1 than to the help he derived from his numerical processes4 ,note #cjh3 ,dec4 ,theor4 ,elem4 p4 #fg4 ,in a succeeding chapter ,i shall treat of that ,natural ,affinity on which a ,natural ,system must really be founded4 ,but before proceeding to this higher subject1 we must say a few words on some of the other parts of the philosophy of ,natural ,history1--the ,gradation of ,groups1 the ,nomenclature1 the ,diagnosis1 and the application of the methods to other subjects4 ,,sect4 ,v4--,gradation of ,groups4 #ae4 ,it has been already noticed 7last chapter17 that even that vague application of the idea of resemblance which gives rise to the terms of common language1 introduces a subordination of classes1 as man1 animal1 body1 substance4 ,such a subordination appears in a more precise form when we employ this idea in a scientific manner as we do in ,natural ,history4 ,we have then a series of divisions1 each inclusive of the lower ones1 which are expressed by various metaphors in different writers4 ,thus some have gone as far as eight terms of the series#cah1 and have taken1 for the most part1 military names for them2 as ,hosts1 ,legions1 ,phalanxes1 ,centuries1 ,cohorts1 ,sections1 ,genera1 ,species4 ,but the most received series is ,classes1 ,orders1 ,genera1 and ,species2 in which1 however1 we often have other terms interpolated1 as ,sub-genera1 or ,sections of genera4 ,the expressions ,family and ,tribe1 are commonly appropriated to natural groups2 and we speak of the ,vegetable1 ,animal1 ,mineral ,kingdom2 but the other metaphors of ,provinces1 ,districts1 c41 which this suggests1 have not been commonly used#cbh4 ,note #cah3 ,adanson1 p4 cvi4 ,note #cbh3 ,sub-,kingdom has recently been employed by some naturalists4 ,it will of course be understood that each ascending step of classification is deduced by the same process from the one below4 ,a ,genus is a collection of ,species which resemble each other more than they #aca resemble other species2 an ,order is a collection of ,genera having1 in like manner1 the first degree of resemblance1 and so on4 ,how close or how wide the ,degrees of ,resemblance are1 must depend upon the nature of the objects compared1 and cannot possibly be prescribed beforehand4 ,hence the same term1 ,class and ,order for instance1 may imply1 in different provinces of nature1 very different degrees of resemblance4 ,the ,classes of ,animals are ,insects1 ,birds1 ,fish1 ,beasts1 c4 ,the ,orders of ,beasts are ,ruminants1 ,tardigrades1 ,plantigrades1 c4 ,the two ,classes of ,plants 7according to the ,natural ,order#cch7 are ,vascular and ,cellular1 the latter having neither sexes1 flowers1 nor spiral vessels4 ,the ,vascular ,plants are divided into ,orders1 as ,umbellifer1 ,ranunculace1 c42 but between this ,class and its ,orders are interposed two other steps3--two ,sub-classes1 ,dicotyledonous and ,monocotyledonous1 and two ,tribes of each3 ,angiospermi1 ,gymnospermi of the first2 and ,petaloide1 ,glumaci of the second4 ,such interpolations are modifications of the general formula of subordination1 for the purpose of accommodating it to the most prominent natural affinities4 ,note #cch3 ,lindley4 #af4 ,species4--,as we have already seen in tracing the principles of the ,natural ,method1 when by the intimate study of plants we seek to give fixity and definiteness to the notion of resemblance and affinity on which all these divisions depend1 we are led to the study of ,organization and ,analogy4 ,but we make a reference to physiological conditions even from the first1 with regard to the lowest step of our arrangement1 the ,species2 for we consider it a proof of the impropriety of separating two ,species1 if it be shown that they can by any course of propagation1 culture1 and treatment1 the one pass into the other4 ,it is in this way1 for example1 that it has been supposed to be established that the common ,primrose1 ,oxlip1 ,polyanthus1 and ,cowslip1 are all the same species4 ,plants which thus1 in virtue of external circumstances1 as soil1 #acb exposure1 climate1 exhibit differences which may disappear by changing the circumstances1 are called ,varieties of the species4 ,and thus we cannot say that a ,species is a collection of individuals which possess the ,first ,degree of ,resemblance2 for it is clear that a primrose resembles another primrose more than it does a cowslip2 but this resemblance only constitutes a ,variety4 ,and we find that we must necessarily include in our conception of ,species1 the notion of propagation from the same stock4 ,and thus a ,species has been well defined#cdh3 ',the collection of the individuals descended from one another1 or from common parents1 and of those which resemble these as much as these resemble each other4' ,and thus the sexual doctrine of plants1 or rather the consideration of them as things which propagate their kind1 7whether by seed1 shoot1 or in any other way17 is at the basis of our classifications4 ,note #cdh3 ,cuv4 ,rgne ,animal1 p4 #ai4 #ag4 ,the ,first permanent ,degree of ,resemblance among organized beings is thus that which depends on this relation of generation1 and we might expect that the groups which are connected by this relation would derive their names from the notion of generation4 ,it is curious that both in ,greek and ,latin languages and in our own1 the words which have this origin 71 genus1 kind17 do not1 in the phraseology of science at least1 denote the nearest degree of relationship1 but have other terms subordinate to them1 which appear etymologically to indicate a mere resemblance of appearance 71 species1 sort72 and these latter terms are appropriated to the groups resulting from propagation4 ,probably the reason of this is1 that the former terms 7genus1 c47 had been applied so widely and loosely before the scientific fixation of terms1 that to confine them to what we call species would have been to restrict them in a manner too unusual to be convenient4 #ah4 ,varieties4 ,races4--,the ,species1 as we have said1 is the collection of individuals which resemble each other as much as do the offspring of a common #acc stock4 ,but within the limits of this boundary1 there are often observable differences permanent enough to attract our notice1 though capable of being obliterated by mixture in the course of generation4 ,such different groups are called ,varieties4 ,thus the ,primrose and ,cowslip1 as has been stated above1 are found to be varieties of the same plant2 the ,poodle and the ,greyhound are well marked varieties of the species dog4 ,such differences are hereditary1 and it may be long doubtful whether such hereditary differences are varieties only1 or different species4 ,in such cases the term ,race has been applied4 ,,sect4 ,,vi4--,nomenclature4 #ai4 ,the ,nomenclature of any branch of ,natural ,history is the collection of names of all its species2 which1 when they become extremely numerous1 requires some artifice to make it possible to recollect or apply them4 ,the known species of plants1 for example1 were #aj1jjj at 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 to avoid this inconvenience is to name a ,species 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 convenient that it has been universally adopted in every other department of the ,natural ,history of organized beings4 ,many other modes of ,nomenclature have been tried1 but no other has at all taken root4 ,linnus himself #acd appears at first to have intended marking each species by the ,generic ,name 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 has1 however1 become universal1 as we have said1 and is by many persons considered the greatest improvement introduced at the ,linnan reform4 ,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 adopted2 though many of them were objected to by his contemporaries 7,adanson and others#ceh71 as capricious or unnecessary innovations4 ,many of the names1 introduced by ,linnus1 certainly appear fanciful enough3 thus he gives the name of ,bauhinia to a plant with leaves in pairs1 because the ,bauhins were a pair of brothers2 ,banisteria is the name of a climbing plant1 in honour of ,banister1 who travelled among mountains4 ,but such names1 once established by adequate authority1 lose all their inconvenience1 and easily become permanent2 and hence the reasonableness of the ,linnan rule#cfh1 that as such a perpetuation of the names of persons by the names of plants is the only honour botanists have to bestow1 it ought to be used with care and caution4 ,note #ceh3 ,pp4 cxxix4 clxxii4 ,note #cfh3 ,phil ,bot4 s4 #bci4 ,the generic name must1 as ,linnus says1 be fixed#cgh 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 established1 the species may be marked by adding to it 'a single word taken at will from any quarter2' that is1 not involving a description or any essential property of the plant1 but a casual or arbitrary appellation#chh4 ,thus the #ace various species of ,hieracium#cih are ,hieracium ,alpinum1 ,h4 ,halleri1 ,h4 ,pilosella1 ,h4 dubium1 ,h4 murorum1 c4 where we see how different may be the kind of origin of the words4 ,note #cgh3 ,ib4 s4 #bbb4 ,note #chh3 ,ib4 s4 #bfj4 ,note #cih3 ,hooker1 ,fl4 ,scot4 #bbh4 ,attempts have been made at various times to form the name of species from those of genera in some more symmetrical manner4 ,thus some have numbered the species of genus1 #a1 #b1 #c1 c42 but this method is liable to the inconveniences1 first1 that it offers nothing for the memory to take hold of2 and second1 that if a new species intermediate between #a and #b1 #b and #c1 c41 be discovered1 it cannot be put in its place4 ,it has also been proposed to mark the species by altering the termination of the genus4 ,thus ,adanson#djh1 denoting a genus by the name ,fonna 7,lychnidea71 conceived he might mark five of its species by altering the last vowel1 ,fonna1 ,fonna-e1 ,fonna-i1 ,fonna-o1 ,fonna-u2 then others by ,fonna-ha1 ,fonna-ka1 and so on4 ,this course would be liable to the same evils which have been noticed as belonging to the numerical method4 ,note #djh3 ,pref4 clxxvi4 ,the names 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 ,order have not been admitted to form part of the appellation of the species4 ,indeed it is easy to see that a name which must be identical in so many instances as that of an ,order would be1 would be felt as superfluous and burdensome4 ,accordingly1 ,linnus makes it a precept#dah1 that the name of the ,class and the ,order must not be expressed but understood3 and hence1 he says1 ,royen1 who took ,lilium for the name of a ,class1 rightly rejected it as a generic name1 and substituted ,lirium1 with the ,greek termination4 ,note #dah3 ,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 genus and #acf species1 in designating minerals1 as is done in ,mohs's nomenclature2 for example1 ,rhombohedral ,calc ,haloide1 ,paratomous ,hal ,baryte4 ,it is possible also that it may be found useful in the same science 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 ,,sect4 ,,vii4--,diagnosis4 #bj4 ,german ,naturalists speak of a part of the general method which they call the ,characteristik of ,natural ,history1 and which is distinguished from the ,systematik of the science4 ,the ,systematick arranges the objects by means of all their resemblances1 the ,characteristick enables us to detect their place in the arrangement by means of a few of their characters4 ,what these characters are to be1 must be discovered by observation of the groups and divisions of the system when they are formed4 ,to construct a collection of such characters as shall be clear and fixed1 is a useful1 and generally a difficult task2 for there is usually no apparent connexion between the marks which are used in discriminating the groups1 and the nature of the groups themselves4 ,they are assumed only because the naturalist1 extensively and exactly acquainted with the groups and the properties of the objects which compose them1 sees1 by a survey of the field1 that these marks divide it properly4 ,the ,characteristick has been termed by some ,english ,botanists the ,diagnosis of plants2 a word which we may conveniently adopt4 ,the ,diagnosis of any genus or species is different according to the system we follow4 ,thus in the ,linnan ,system the ,diagnosis of the ,rose is in the first place given by its ,class and ,order3 it is #acg ,icosandrous1 and ,polygynous2 and then the ,generic ,distinction is that the calyx is five-cleft1 the tube urceolate1 including many hairy achenia1 the receptacle villous#dbh4 ,in the ,natural ,system the ,rose-,tribe are distinguished as being#dch ',polypetalous dicotyledons1 with lateral styles1 superior simple ovaria1 regular perigynous stamens1 exalbuminous definite seeds1 and alternate stipulate leaves4' ,and the true ,roses are further distinguished by having ',nuts1 numerous1 hairy1 terminated by the persistent lateral style and inclosed within the fleshy tube of the calyx1' c4 ,note #dbh3 ,lindley1 ,nat4 ,syst4 p4 #adi4 ,note #dch3 ,ib4 pp4 #ha1 #c4 ,it will be observed that in a rigorous ,artificial ,system the ,systematick coincides with the ,characteristick2 the ,diataxis with the ,diagnosis2 the reason why a plant is put in a division is identical with the mode by which it is known to be in the division4 ,the ,rose is in the class icosandria1 because it has many stamens inserted in the calyx2 and when we see such a set of stamens we immediately know the class4 ,but this is not the case with the ,diagnosis of ,natural ,families4 ,thus the genera ,lamium and ,galeopsis 7,dead ,nettle and ,hemp ,nettle7 are each formed into a separate group in virtue of their general resemblances and differences1 and not because the former has one tooth on each side of the lower lip1 and the latter a notch in its upper lip1 though they are distinguished by these marks4 ,thus so far as our ,systems are natural1 7which1 as we have shown1 all systems to a certain extent must be71 the ,characteristick is distinct both from a ,natural and an ,artificial ,system2 and is1 in fact1 an ,artificial ,key to a ,natural ,system4 ,as being ,artificial1 it takes as few characters as possible2 as being ,natural1 its characters are not selected by any general or prescribed rule1 but follow the natural affinities4 ,the ,botanists who have made any steps in the formation of a natural method of plants since ,linnus1 have all attempted to give a ,diagnosis corresponding to the ,diataxis of their method4 #ach ,,chapter ,,iii4 ,,application ,,of ,,the ,,natural ,,history ,,method ,,to ,,mineralogy4 #a4 ,,the philosophy of the ,sciences of ,classification has had great light thrown upon it by discussions concerning the methods which are used in ,botany3 for that science is one of the most complete examples which can be conceived of the consistent and successful application of the principles and ideas of ,classification2 and this application has been made in general without giving rise to any very startling paradoxes1 or disclosing any insurmountable difficulties4 ,but the discussions concerning methods of ,mineralogical ,classification have been instructive for quite a different reason3 they have brought into view the boundaries and the difficulties of the process of ,classification2 and have presented examples in which every possible mode of classifying appeared to involve inextricable contradictions4 ,i will notice some of the points of this kind which demand our attention1 referring to the works published recently by several mineralogists4 ,in the ,history of ,mineralogy we noticed the attempt made by ,mohs and other ,germans to apply to minerals a method of arrangement similar to that which has been so successfully employed for plants4 ,the survey which we have now taken of the grounds of that method will point out some of the reasons of the very imperfect success of this attempt4 ,we have already said that the ,terminology of ,mineralogy was materially reformed by ,werner2 and including in this branch of the subject 7as we must do7 the ,crystallography of later writers1 it may be considered as to a great extent complete4 ,of the attempts at a ,natural arrangement1 that of ,mohs appears to proceed by the #aci method of blind trial1 the undefinable perception of relationship1 by which the earliest attempts at a ,natural ,arrangement of plants were made4 ,breithaupt however1 has made 7though ,i do not know that he has published7 an essay in a mode which corresponds very nearly to ,adanson's process of multiplied comparisons4 ,having ascertained the specific gravity and hardness of all the species of minerals1 he arranged them in a table1 representing by two lines at right angles to each other these two numerical quantities4 ,thus all minerals were distributed according to two co-ordinates representing specific gravity and hardness4 ,he conceived that the groups which were thus brought together were natural groups4 ,on both these methods1 and on all similar ones1 we might observe1 that in minerals as in plants1 the mere general notion of ,likeness cannot lead us to a real arrangement3 this notion requires to have precision and aim given it by some other relation2--by the relation of ,chemical ,composition in minerals1 as by the relation of ,organic ,function in vegetables4 ,the physical and crystallographical properties of minerals must be studied with reference to their constitution2 and they must be arranged into ,groups which have some common ,chemical ,character1 before we can consider any advance as made towards a ,natural ,arrangement4 ,in reality1 it happens in ,mineralogy as it happened in ,botany1 that those speculators are regulated by an obscure perception of this ulterior relation1 who do not profess to be regulated by it4 ,several of the ,orders of ,mohs have really great unity of chemical character1 and thus have good evidence of their being really ,natural ,orders4 #b4 ,supposing the ,diataxis of minerals thus obtained1 ,mohs attempted the ,diagnosis2 and his ,characteristick of the ,mineral ,kingdom1 published in ,dresden1 in #ahbj1 was the first public indication of his having constructed a system4 ,from the nature of a ,characteristick1 it is necessarily brief1 and without any ostensible principle2 but its importance was duly appreciated by the author's countrymen4 ,since that #adj time1 many attempts have been made at improved arrangements of minerals1 but none1 ,i think1 7except perhaps that of ,breithaupt17 professing to proceed rigorously on the principles of ,natural ,history2--to arrange by means of external characters1 neglecting altogether1 or rather postponing1 the consideration of chemical properties4 ,by relaxing from this rigour1 however1 and by combining physical and chemical considerations1 arrangements have been obtained 7for example1 that of ,naumann17 which appear more likely than the one of ,mohs to be approximations to an ultimate really natural system4 ,naumann's ,classes are ,hydrolytes1 ,haloides1 ,silicides1 ,metal ,oxides1 ,metals1 ,sulphurides1 ,anthracides1 with subdivisions of ,orders1 as ,anhydrous unmetallic ,silicides4 ,it may be remarked that the designations of these are mostly chemical4 ,as we have observed already1 ,chemistry1 and ,mineralogy in its largest sense1 are each the necessary supplement of the other4 ,if ,chemistry furnish the ,nomenclature1 ,mineralogy must supply the ,physiography3 if the ,arrangement be founded on ,external ,characters and the ,names be independent of ,chemistry1 the chemical composition of each species is an important scientific ,truth respecting it4 #c4 ,the inquiry may actually occur1 whether any subordination of groups in the mineral kingdom has really been made out4 ,the ancient chemical arrangements1 for instance1 that of ,hay1 though professing to distribute minerals according to ,classes1 ,orders1 ,genera1 and ,species1 were not only arbitrary1 but inapplicable2 for the first postulate of any method1 that the species should have constant characters of unity and difference1 was not satisfied4 ,it was not ascertained that carbonate of lime was really distinguishable in all cases from carbonate of magnesia1 or of iron2 yet these species were placed in remote parts of the system3 and the above carbonates made just so many species2 although1 if they were distinct from one another at all1 they were further distinguishable into additional species4 ,even now1 we may1 perhaps1 say that the limits of mineralogical species1 and their laws of fixity1 are #ada not yet clearly seen4 ,for the discoveries of the isomorphous relations and of the optical properties of minerals have rather shown us in what direction the object lies1 than led us to the goal4 ,it is clear that1 in the mineral kingdom1 the ,definition of ,species1 borrowed from the laws of the continuation of the kind1 which holds throughout the organic world1 fails us altogether1 and must be replaced by some other condition3 nor is it difficult to see that the definite atomic relations of the chemical constituents1 and the definite crystalline angle1 must supply the principles of the ,specific ,identity for minerals4 ,yet the exact limits of definiteness in both these cases 7when we admit the effect of mechanical mixtures1 c47 have not yet been completely disentangled4 ,moreover1 any arbitrary assumption 7as the allowance of a certain per-centage of mixture1 or a certain small deviation in the angle17 is altogether contrary to the philosophy of the ,natural ,system1 and can lead to no stable views4 ,it is only by laborious1 extensive1 and minute research1 that we can hope to attain to any solid basis of arrangement4 #d4 ,still1 though there are many doubts respecting mineralogical species1 a large number of such species are so far fixed that they may be supposed capable of being united under the higher divisions of a system with approximate truth4 ,of these higher divisions1 those which have been termed ,orders appear to tend to something like a fixed chemical character4 ,thus the ,haloids of ,naumann1 and mostly those of ,mohs1 are combinations of an oxide with an acid1 and thus resemble ,salts1 whence their name4 ,the ,silicides contain most of ,mohs's ,spaths3 and the ,orders ,pyrites1 ,glance1 and ,blende1 are common to ,naumann and ,mohs2 being established by the latter on a difference of external character1 which difference is1 indeed1 very manifest2 and being included by the former in one chemical ,class1 ,sulphurides4 ,the distinctions of ,hydrous and ,anhydrous1 ,metallic and ,unmetallic1 are1 of course1 chemical distinctions1 but occur as the differences of ,orders in ,naumann's mixed system4 #adb ,we may observe that some ,french writers1 following ,hay's last edition1 use1 instead of metallic and unmetallic1 autopside metallic and heteropside metallic2 meaning by this phraseology to acknowledge the discovery that earths1 etc41 are metallic1 though they do not appear to be so1 while metals both are and appear metallic4 ,but this seems to be a refinement not only useless but absurd4 ,for what is gained by adding the word metallic1 which is common to all1 and therefore makes no distinction8 ,if certain metals are distinguished by their appearing to be metals1 this appearance is a reason for giving them the peculiar name1 metals4 ,nothing is gained by first bringing earths and metals together1 and then immediately separating them again by new and inconvenient names4 ,no proposition can be expressed better by calling earths1 heteropside metallic substances1 and therefore such nomenclature is to be rejected4 ,granting1 then1 that the ,orders of the best recent mineralogical systems approximate to natural groups1 we are led to ask whether the same can be said of the ,genera of the ,natural ,history systems1 such as those of ,mohs and ,breithaupt4 ,and here ,i must confess that ,i see no principle in these ,genera2 ,i have failed to apprehend the conceptions by the application of which they have been constructed3 ,i shall therefore not pass any further judgment upon them4 ,the subordination of ,mineralogical ,species to ,orders is a manifest gain to science3 in the interposition of ,genera ,i see nothing but a source of confusion4 #e4 ,in ,mineralogy1 as in other branches of natural history1 a reformed arrangement ought to give rise to a reformed ,nomenclature2 and for this1 there is more occasion at present in ,mineralogy than there was in ,botany at the worst period1 at least as far as the extent of the subject allows4 ,the characters of minerals are much more dimly and unfrequently developed than those of plants2 hence arbitrary chemical arrangements1 which could not lead to any natural groups1 and therefore not to any good names1 prevailed till recently2 and this state of things produced an anarchy #adc in which every man did what seemed right in his own eyes1--proposed species without any ascertained distinction1 and without a thought of subordination1 and gave them arbitrary names2 and thus with only about two or three hundred known species1 we have thousands upon thousands of names1 of anomalous form and uncertain application4 ,mohs has attempted to reform the ,nomenclature of the subject in a mode consistent with his attempt to reform the ,system4 ,in doing this1 he has fatally transgressed a rule always insisted upon by the legislators of ,botany1 of altering usual names as little as possible2 and his names are both so novel and so cumbrous1 that they appear to have little chance of permanent currency4 ,they are1 perhaps1 more unwieldy than they need to be1 by referring1 as we have said1 to three of the steps of his classification1 the ,species1 ,genus1 and ,order4 ,we may1 however1 assert confidently1 from the whole analogy of natural history1 that no good names can be found which do not refer to at least two terms of the arrangement4 ,this rule has been practically adopted to a great extent by ,naumann1 who gives to most of his ,haloids the name ,spar1 as ,calc spar1 ,iron spar1 c42 to all his ,oxides the terminal word ,erz 7,ore72 and to the species of the orders ,kies 7,pyrites71 ,glance1 and ,blende1 these names4 ,it has also been theoretically assented to by ,beudant1 who proposes that we should say silicate stilbite1 silicate chabasie2 carbonate calcaire1 carbonate witherite2 sulphate couperose1 c4 ,one great difficulty in this case would arise from the great number of silicides2 it is not likely that any names would obtain a footing which tacked the term silicide to another word for each of these species4 ,the artifice which ,i have proposed1 in order to obviate this difficulty1 is that we should make the names of the silicides1 and those alone1 end in ite or lite1 which a large proportion of them do already4 ,by this and a few similar contrivances1 we might1 ,i conceive1 without any inconvenient change1 introduce into ,mineralogy a systematic nomenclature4 #add #f4 ,i shall now proceed to make a few remarks on a work on ,mineralogy more recent than those which ,i have above noticed1 and written with express reference to such difficulties as ,i have been discussing4 ,i allude to the treatise of ,m4 ,necker1 ,le ,rgne ,mineral ramen aux ,methods d',histoire ,naturelle#ddh1 which also contains various dissertations on the ,philosophy of ,classification in general1 and its application to ,mineralogy in particular4 ,note #ddh3 ,paris1 #ahce4 ,m4 ,necker remarks very justly1 that ,mineralogy1 as it has hitherto been treated1 differs from all other branches of ,natural ,history in this3--that while it is invested with all the forms of the sciences of classification1--,classes1 ,divisions1 ,genera1 and the like1--the properties of those bodies to which the mineralogical student's attention is directed have no bearing whatever on the classification4 ,a person1 he remarks#deh1 might be perfectly well acquainted with all the characters of minerals which ,werner or ,hay examined so carefully1 and might yet be quite unable to assign to any mineral its place in the divisions of their methods4 ,there is#dfh a complete separation between the study of mineralogical characters and the recognition of the name and systematic place of a mineral4 ,those who know mineralogy well1 may know minerals ill1 or hardly at all2 the systematist may be in such knowledge vastly inferior to the mineral-dealer or the miner4 ,in this respect there is a complete contrast between this science and other classificatory sciences4 ,note #deh3 ,rgne ,mineral1 p4 #c4 ,note #dfh3 ,ib4 p4 #h4 ,again1 in the best-known systems of ,mineralogy1 7as those of ,werner and ,hay174 the bodies which are grouped together as belonging to the same division1 have not1 as they have in other classificatory sciences1 any resemblance4 ,the different members of the larger classes are united by the common possession of some abstract property1--as1 that they all contain iron4 ,this is a property to which no common circumstance in the bodies themselves corresponds4 ,what is there common to the minerals named oxidulous iron1 sulphuret #ade of iron1 carbonate of iron1 sulphate of iron1 except that they all contain iron8 ,and when we have classed these bodies together1 what general assertion can we make concerning them1 except that which is the ground of our classification1 that they contain iron8 ,they have nothing in common with iron or with each other in any other way4 ,again1 as these classes have no general properties1 all the properties are particular to the species2 and the descriptions of these necessarily become both tediously long1 and inconveniently insulated4 #g4 ,these inconveniences arise from making ,chemical ,composition the basis of ,mineralogical ,classification without giving ,chemical ,analysis the first place among ,mineral ,properties4 ,shall we1 then1 correct this omission1 so far as it has affected mineralogical systems8 ,shall we teach the student the chemical analysis of minerals1 and then direct him to classify them according to the results of his analysis#dgh8 ,note #dgh3 ,rgne ,mineral1 p4 #ah4 ,but why should we do this8 ,to what purpose1 or on what ground1 do we arrange the results of chemical analysis according to the forms and subordination of natural history8 ,is not ,chemistry a science distinct from ,natural ,history8 ,are not the sciences opposed8 ,is not natural history confined to organic bodies8 ,can mere chemical elements and their combinations be1 with any propriety or consistency1 arranged into ,species1 ,genera1 and ,families8 ,what is the principle on which genera and species depend8 ,do not ,species imply ,individuals8 ,what is an ,individual in the case of a chemical substance8 #h4 ,we thus find some of the widest and deepest questions of the philosophy of classification brought under our consideration when we would provide a method for the classification of minerals4 ,the answers to these questions are given by ,m4 ,necker2 and ,i shall state some of his opinions2 taking the liberty of adding such remarks as are suggested by referring the subject #adf to those principles which have already been established in this work4 ,m4 ,necker asserts#dhh that the distinctions of different ,sciences depend1 not on the objects they consider1 but on the different and independent points of view on which they proceed4 ,each science has its logic1 that is1 its mode of applying the general rules of human reason to its own special case4 ,it has been said by some#dih1 that in minerals1 natural history and chemistry contemplate common objects1 and thus form a single science4 ,but do chemistry and natural history consider minerals in the same point of view8 ,note #dhh3 ,rgne ,mineral1 p4 #bc4 ,note #dih3 ,ib4 p4 #bg4 ,the answer is1 that they do not4 ,physics and ,chemistry consider the properties of bodies in an abstract manner2 as1 their composition1 their elements1 their mutual actions1 with the laws of these2 their forces1 as attraction1 affinity2 all which objects are abstract ideas4 ,in these cases we have nothing to do with bodies themselves1 but as the vehicles of the powers and properties which we contemplate4 ,natural ,history1 on the other hand1 has to do with natural bodies3 their properties are not considered abstractedly1 but only as characters4 ,if the properties are abstracted1 it is but for a moment4 ,natural history has to describe and class bodies as they are4 ,all which cannot be perceived by the senses1 belongs not to its domain1 as molecules1 atoms1 elements4 ,natural history#ejh may have recourse to physics or chemistry in order to recognize those properties of bodies which serve as characters2 but natural history is not1 on that account1 physics or chemistry4 ,classification is the essential business of the natural historian#eah1 to which task chemistry and physics are only instrumental1 and the further account of properties only complementary4 ,note #ejh3 ,ib4 p4 #cg4 ,note #eah3 ,ib4 p4 #da4 ,it has been said1 in support of the doctrine that chemistry and mineralogy are identical1 that chemistry does not neglect external characters4 ',the chemist in #adg describing sulphur1 mentions its colour1 taste1 odour1 hardness1 transparence1 crystalline form1 specific gravity2 how does he then differ from the mineralogist8' ,but to this it is replied1 that these notices of the external characters of this or any substance are introduced in chemistry merely as convenient marks of recognition2 whereas they are essential in mineralogy4 ,if we had taken the account given of several substances instead of one1 we should have seen that the chemist and the naturalist consider them in ways altogether different4 ,the chemist will make it his business to discover the mutual action of the substances2 he will combine them1 form new products1 determine the proportions of the elements4 ,the mineralogist will divide the substances into groups according to their properties1 and then subdivide these groups1 till he refers each substance to its species4 ,exterior and physical characters are merely accessory and subordinate for the chemist2 chemistry is merely instrumental for the mineralogist4 ,this view agrees with that to which we have been led by our previous reasonings2 and may1 according to our principles1 be expressed briefly by saying1 that the ,idea which ,chemistry has to apply is the ,idea of ,elementary ,composition1 while ,natural ,history applies the ,idea of ,graduated ,resemblances1 and thus performs the task of classification4 #i4 ,the question occurs#ebh1 whether ,natural ,history can be applied to ,inorganic ,substances8 ,and the answer to this question is1 that it can be applied1 if there are such things as inorganic individuals1 since the resemblances and differences with which natural history has to do are the resemblances and differences of individuals4 ,note #ebh3 ,rgne ,mineral1 p4 #df4 ,what is an ,individual8 ,it certainly is not that which is so simple that it cannot be divided4 ,individual animals are composed of many parts4 ,but if we examine1 we shall find that our ,idea of an ,individual is1 that it is a whole composed of parts1 which #adh are not similar to the whole1 and have not an independent existence1 while the whole has an independent existence and a definite form#ech4 ,note #ech3 ,rgne ,mineral1 p4 #eb4 ,what then is the ,mineralogical ,individual8 ,at first1 while minerals were studied for their use1 the most precious of the substances which they contained was looked upon as the characteristic of the mineral4 ,the smallest trace of silver made a mineral an ore of silver4 ,thus forms and properties were disregarded1 and substance was considered as identical with mineral4 ,and hence#edh ,daubenton refused to recognize species in the mineral kingdom1 because he recognized no individuals4 ,he proposed to call sorts what we call species4 ,in this way of considering minerals1 there are no individuals4 ,note #edh3 ,ib4 p4 #ed4 #aj4 ,but still this is not satisfactory3 for if we take a well-formed and distinct crystal1 this clearly is an individual#eeh4 ,note #eeh3 ,ib4 p4 #ef4 ,it may be objected1 that the crystal is divisible 7according to the theory of crystallography7 into smaller solids2 that these small solids are really the simple objects2 and that actual crystals are formed by combinations of these molecules according to certain laws4 ,but1 as we have already said1 an individual is such1 not because it cannot be divided1 but because it cannot be divided into parts similar to the whole4 ,as to the division of the form into its component laws1 this is an abstract proceeding1 foreign to natural history#efh4 ,therefore there is so far nothing to prevent a crystal from being an individual4 ,note #efh3 ,ib4 p4 #eh4 #aa4 ,we cannot 7,m4 ,necker goes on to remark7 consider the ,integrant ,molecules as individuals4 ,these are useful abstractions1 but abstractions only1 which we must not deal with as real objects4 ,hay himself warns us#egh that his doctrine of increments is a purely abstract conception1 and that nature1 in fact1 follows a different process4 ,accordingly1 ,weiss and ,mohs express laws identical with those of ,hay1 without even #adi speaking of molecules2 and ,wollaston and ,davy have deemed it probable that the molecules are not polyhedrons1 but spheres or spheroids4 ,such mere creations of the mind can never be treated as individuals4 ,if the maxim of natural history1--that the ,species is a collection of ,individuals--be applied so as to make those individuals mere abstractions2 or if1 instead of ,individuals1 we take such an abstraction as ,substance or ,matter1 the course of natural history is altogether violated4 ,and yet this errour has hitherto generally prevailed2 and mineralogists have classified1 not things1 but abstract ideas#ehh4 ,note #egh3 ,ib4 p4 #fa4 ,note #ehh3 ,rgne ,mineral1 p4 #fg4 #ab4 ,but it may be said#eih1 will not the small solids obtained by ,cleavage better answer the idea of individuals8 ,to this it is replied1 that these small solids have no independent existence4 ,they are only the result of a mode of division4 ,they are never found separate and independent4 ,the secondary forms which they compose are determined by various circumstances 7the nature of the solution1 c472 and the cleavage which produces these small solids is only one result among many1 from the crystalline forces#fjh4 ,note #eih3 ,ib4 p4 #fi4 ,note #fjh3 ,ib4 p4 #ga4 ,thus neither ,integrant ,molecules1 nor ,solids obtained by ,cleavage1 can be such mineralogical ,individuals as the spirit of natural history requires4 ,hence it appears that we must take the real ,crystals for ,individuals#fah4 ,note #fah3 ,ib4 p4 #gc4 #ac4 ,we must1 however1 reject crystals 7generally large ones7 which are obviously formed of several smaller ones of a similar form 7as occurs so often in quartz and calc spar74 ,we must also distinguish cases in which a large regular form is composed of smaller but different regular forms 7as octahedrons of fluor spar made up of cubes74 ,here the small component forms are the individuals4 ,also we must notice the cases#fbh in which we have a natural crystal1 similar to the primary form4 ,here the face will show whether #aej the body is a result obtained by cleavage or a natural individual4 ,note #fbh3 ,ib4 p4 #ge4 #ad4 ,it will be objected#fch1 that the crystalline form ought not to be made the dominant character in mineralogy1 since it rarely occurs perfect4 ,to this it is replied1 that even if the application of the principle be difficult1 still it has been shown to be the only true principle1 and therefore we have no alternative4 ,but further#fdh1 it is not true that amorphous substances are more numerous than crystals4 ,in ,leonhard's ,manual of ,oryctognosy1 there are #cgg mineral substances4 ,of these1 #bha have a crystalline structure1 and #if only have not been found in a regular form4 ,note #fch3 ,rgne ,mineral1 p4 #gi4 ,note #fdh3 ,ib4 p4 #hb4 ,again1 the #bha crystalline forms have each its varieties1 some of which are crystalline1 and some are not so4 ,now the crystalline varieties amount to #adec1 and the uncrystalline to #ahf only4 ,thus mineralogy1 according to the view of it here presented1 has a sufficiently wide field#feh4 ,note #feh3 ,ib4 p4 #hd4 #ae4 ,it will be objected#ffh1 that according to this mode of proceeding1 we must reject from our system all non-crystalline minerals4 ,but we reply1 that if the mass be composed of crystals1 the size of the crystals makes no difference4 ,now lamellar and other compact masses are very generally groups of crystals in various positions4 ,individuals mutilated and mixed together are not the less individuals2 and therefore such masses may be treated as objects of natural history4 ,note #ffh3 ,ib4 p4 #hf4 ,if we cannot refer all rocks to crystalline species1 those which elude our method may appear as an appendix1 corresponding to those plants which botanists call genera incert sedis#fgh4 ,note #fgh3 ,ib4 p4 #ia4 ,but these genera and species will often be afterwards removed into the crystalline part of the system1 by being identified with crystalline species4 ,thus pyrope1 c41 have been referred to garnet1 and basalt1 #aea wacke1 c41 to compound rocks4 ,thus veins of ,dolerite1 visibly composed of two or three elements1 pass to an apparently simple state by becoming fine-grained#fhh4 ,note #fhh3 ,rgne ,mineral1 p4 #ic4 #af4 ,finally#fih1 we have to ask1 are artificial crystals to enter into our classification8 ,m4 ,necker answers1 ,no2 because they are the result of art1 like mules1 mestizos1 hybrids1 and the like4 ,note #fih3 ,ib4 p4 #ie4 #ag4 ,upon these opinions1 we may observe1 that they appear to be1 in the main1 consistent with the soundest philosophy4 ,that each natural crystal is an individual1 is a doctrine which is the only basis of ,mineralogy as a ,natural ,historical ,science2 yet the imperfections and confused unions of crystals make this principle difficult to apply4 ,perhaps it may be expressed in a more precise manner by referring to the crystalline forces1 and to the axes by which their operation is determined1 rather than to the external form4 ,that portion of a mineral substance is a mineralogical individual which is determined by crystalline forces acting to the same axes4 ,in this way we avoid the difficulty arising from the absence of faces1 and enable ourselves to use either cleavage1 or optical properties1 or any others1 as indications of the identity of the individual4 ,the individual extends so far as the polar forces extend by which crystalline form is determined1 whether or not those forces produce their full effect1 namely1 a perfectly circumscribed polyhedron4 #ah4 ,there is only one material point on which our principles lead us to differ from ,m4 ,necker2--the propriety of including artificial crystals in our mineralogical classification4 ,to exclude them1 as he does1 is a conclusion so entirely at variance with the whole course of his own reasonings1 that it is difficult to conceive that he would persist in his conclusion1 if his attention were drawn to the question more steadily4 ,for1 as he justly says#gjh1 each science has its appropriate domain1 determined by its peculiar point of view4 ,now artificial and natural crystals are considered in the same point of view1 7namely1 with reference to #aeb crystalline1 physical1 and optical properties1 as subservient to classification17 and ought1 therefore1 to belong to the same science4 ,again1 he says#gah1 that ,chemistry would reject as useless all notice of the physical properties and external characters of substances1 if a special science were to take charge of the description and classification of these products4 ,but such a special science must be ,mineralogy2 for we cannot well make one science of the classification of natural1 and another of that of artificial substances3 or if we do1 the two sciences will be identical in method and principles1 and will extend over each other's boundaries1 so that it will be neither useful nor possible to distinguish them4 ,again1 ,m4 ,necker's own reasonings on the selection of the individual in mineralogy are supported by well chosen examples#gbh2 but these examples are taken from artificial salts2 as1 for instance1 common salt crystallizing in different mixtures4 ,again1 the analogy of mules and mestizos1 as products of art1 with chemical compounds1 is not just4 ,chemical compounds correspond rather to natural species1 propagated by man under the most natural circumstances1 in order that he may study the laws of their production#gch4 ,note #gjh3 ,ib4 p4 #bc4 ,note #gah3 ,rgne ,mineral1 p4 #cf4 ,note #gbh3 ,ib4 p4 #ga4 ,note #gch3 ,we may remark that ,m4 ,necker1 in his own arrangement of minerals1 inserts among his species ,iron and ,lead1 which do not occur ,native4 #ai4 ,but the decisive argument against the separation of natural and artificial crystals in our schemes of classification is1 that we cannot make such a separation4 ,substances which were long known only as the products of the laboratory1 are often discovered1 after a time1 in natural deposits4 ,are the crystals which are found in a forgotten retort or solution to be considered as belonging to a different science from those which occur in a deserted mine8 ,and are the crystals which are produced where man has turned a stream of water or air out of its course1 to be separated from natural crystals1 when the composition1 growth1 and properties1 are exactly the same in both8 ,and again3 ,how many natural crystals can we already produce by #aec synthesis6 ,how many more may we hope to imitate hereafter6 ,m4 ,necker himself states#gdh1 that ,mitscherlich found1 in the scori of the mines of ,sweden and ,germany1 artificial minerals having the same composition and the same crystalline form with natural minerals3 as silicates of iron1 lime1 and magnesia1 agreeing with ,peridot2 bisilicate of iron1 lime1 and magnesia1 agreeing with ,pyroxene2 red oxide of copper2 oxide of zinc2 protoxide of iron 7fer oxydul72 sulphurets of iron1 zinc1 lead2 arseniuret of nickel2 black mica4 ,these were accidental results of fusion4 ,but ,m4 ,berthier1 by bringing together the elements in proper quantities1 has succeeded in composing similar minerals1 and has thus obtained artificial silicates1 with the same forms and the same characters as natural silicates4 ,other chemists 7,m4 ,haldat1 ,m4 ,becquerel7 have1 in like manner1 obtained1 by artificial processes1 other crystals1 known previously as occurring naturally4 ,how are these crystals1 thus identical with natural minerals1 to be removed out of the domain of mineralogy1 and transferred to a science which shall classify artificial crystals only8 ,if this be done1 the mineralogist will not be able to classify any specimen till he has human testimony whether it was found naturally occurring or produced by chemical art4 ,or is the other alternative to be taken1 and are these crystals to be given up to mineralogy because they occur naturally also8 ,but what can be more unphilosophical than to refer to separate sciences the results of chemical processes closely allied1 and all but identical8 ,the chemist constructs bisilicates1 and these are classified by the mineralogist3 but if he constructs a trisilicate1 it belongs to another science4 ,all these intolerable incongruities are avoided by acknowledging that artificial1 as well as natural1 crystals belong to the domain of mineralogy4 ,it is1 in fact1 the name only of ,mineralogy which appears to discover any inconsistency in this mode of proceeding4 ,mineralogy is the #aed representative of a science which has a wider office than mineralogists first contemplated2 but which must exist1 in order that the body of science may be complete4 ,there must1 as we have already said1 be a ,science1 the object of which is to classify bodies by their physical characters1 in order that we may have some means of asserting chemical truths concerning bodies2 some language in which we may express the propositions which chemical analysis discovers4 ,and this ,science will have its object prescribed1 not by any accidental or arbitrary difference of the story belonging to each specimen2--not by knowing whether the specimen was found in the mine or in the laboratory2 produced by attempting to imitate nature1 or to do violence to her3--but will have its course determined by its own character4 ,the range and boundaries of this ,science will be regulated by the ,ideas with which it deals4 ,like all other sciences1 it must extend to everything to which its principles apply4 ,the limits of the province which it includes are fixed by the consideration that it must be a connected whole4 ,no previous definition1 no historical accident1 no casual phrase1 can at all stand in the way of philosophical consistency2--can make this ,science exclude what that includes1 or oblige it to admit what that rejects4 ,and thus1 whatever we call our ,science2--whether we term it ,external ,chemistry1 ,mineralogy1 the ,natural ,history of ,inorganic ,bodies2--since it can be nothing but the ,science of the ,classification of ,inorganic ,bodies of definite forms and properties1 it must classify all such bodies1 whether or not they be minerals1 and whether or not they be natural4 ,note #gdh3 ,rgne ,mineral1 p4 #aea4 #bj4 ,in the application of the principles of classification to minerals1 the question occurs1 ,what are to be considered as mineral ,species8 ,by ,species we are to understand1 according to the usage of other parts of natural history1 the lowest step of our subordinate divisions2--the most limited of the groups which have definite distinctions4 ,what definite distinctions of groups of objects of any kind really occur in nature1 is to be learnt from an examination of nature3 and the #aee result of our inquiries will be some general principle which connects the members of each group1 and distinguishes the members of groups which1 though contiguous1 are different4 ,in the classification of organized bodies1 the rule which thus presides over the formation of ,species is the principle of reproduction4 ,those animals and those plants are of the same ,species which are produced from a common stock1 or which resemble each other as much as the progeny of a common stock4 ,accordingly in practice1 if any questions arise whether two varieties of form in organic things be of the same or different species1 it is settled by reference to the fact of reproduction2 and when it is ascertained that the two forms come within the habitual and regular limits of a common circle of reproduction1 they are held to be of the same species4 ,now in crystals1 this principle of reproduction disappears altogether1 and the basis of the formation of species must be sought elsewhere4 ,we must have some other principle to replace the reproduction which belongs only to organic life4 ,this principle will be1 we may expect1 one which secures the permanence and regularity of mineral forms1 as the reproductive power does of animal and vegetable4 ,such a principle is the ,power of ,crystallization4 ,the forces of which solidity1 cohesion1 and crystallization are the result1 are those which give to minerals their permanent existence and their physical properties2 and ever since the discovery of the distinctions of ,crystalline ,forms and ,crystalline ,systems1 it is certain that this force distinguishes groups of crystals in the most precise and definite manner4 ,the rhombohedral carbonates of lime and of iron1 for instance1 are distinguished exactly by the angles of their rhombohedrons4 ,and if1 in the case of any proposed crystal1 we should doubt to which kind the specimen belongs1 the measurement of the angles of cleavage would at once decide the question4 ,the principle of ,crystallization therefore appears1 from analogy1 to be exactly fitted to take the place of the principle of organic ,generation4 ,the forces which make the individual permanent and its properties definite1 here stand in the place of the forces #aef which preserve the race1 while individuals are generated and die4 #ba4 ,according to this view1 the different ,modifications of the same crystalline form would be ,varieties only of the same ,species4 ,all the various solids1 for example1 which are produced by the different laws of derivation of rhombohedral carbonate of lime1 would fall within the same ,species4 ,and this appears to be required by the general analogy of ,natural ,history4 ,for these differences of form1 produced by the laws of crystalline derivation1 are not definite4 ,the faces which are added to one form in order to produce another1 may be of any size1 small or large1 and thus the crystal which represents one modification passes by insensible degrees to another4 ,the forms of calc spar1 which we call dog-tooth spar1 cannon spar1 nail-head spar1 and the like1 appear at first1 no doubt1 distinct enough2 but so do the races of dogs4 ,and we find1 in the mineral as in the animal1 that the distinction is obliterated by taking such intermediate steps as really occur4 ,and if a fragment of any of these crystals is given us1 we can determine that it is rhombohedral carbonate of lime2 but it is not possible1 in general1 to determine to which of the kinds of crystals it has belonged4 #bb4 ,notwithstanding these considerations1 ,m4 ,necker has taken for his basis of mineral species#geh the ,secondary ,modifications1 and not the ,primary ,forms4 ,thus cubical galena1 octahedral galena1 and triform galena1 are1 with him1 three species of crystals4 ,note #geh3 ,rgne ,mineral1 p4 #cif4 ,on this ,i have to observe1 as ,i have already done1 that on this principle we have no definite distinction of species2 for these forms may and do pass into each other3 among cubo-octahedrons of galena occur cubes and octahedrons1 as one face or another vanishes1 and the transition is insensible4 ,we shall1 on this principle1 find almost always three or four species in the same tuft of crystals2 for almost every individual in such assemblages may exhibit a different combination of #aeg secondary faces4 ,again1 in cases where the secondary laws are numerous1 it would be impracticable to enumerate all their combinations1 and impossible therefore to give a list of species4 ,accordingly ,m4 ,necker#gfh gives seventy-one ,species of spath calcaire1 and then says1 ',nous n'avons pas numer la dixime partie des espces connues de ce genre1 qui se montent plus de huit cents4' ,again1 in many substances1 of which few crystals are found1 every new specimen would be a new species2 if indeed it were perfect enough to be referred to a species at all4 ,but from a specimen without perfect external form1 however perfect in crystalline character1 although everything else might be known1--angles1 optical properties1 physical properties1 and chemical constitution1--the species could not be determined4 ,thus ,m4 ,necker says#ggh of the micas1 ',quant aux espces propre chaque genre1 la lacune sera presque complte2 car jusqu'ici les cristaux entiers de ,mica et de ,talc n'ont pas t fort communs4' ,note #gfh3 ,rgne ,mineral1 p4 #cfd4 ,note #ggh3 ,ib4 ii4 #dad4 ,these inconveniences arise from neglecting the leading rule of natural history1 that the predominant principle of the existence of an object must determine the ,species2 whether this principle be ,reproduction operating for ,development1 or ,crystallization operating for ,permanence of form4 ,we may add to the above statement of inconveniences this2--that if ,m4 ,necker's view of mineralogical species be adopted1 the distinction of ,species is vague and indefinite1 while that of ,genera is perfectly precise and rigorous2--an aspect of the system entirely at variance with other parts of ,natural ,history2 for in all these the ,species is a more definite group than the ,genus4 ,this result follows1 as has already been said1 from ,m4 ,necker's wish to have individuals marked by external form4 ,if1 instead of this1 we are contented to take for an individual that portion of a mass1 of whatever form1 which is connected by the continuous influence of the same crystalline forces1 by whatever incidents these forces may be manifested1 7as cleavage1 #aeh physical and optical properties1 and the like17 our mode of proceeding avoids all the above inconveniences1 applies alike to the most perfect and most imperfect specimens1 and gives a result agreeable to the general analogy of natural history1 and the rules of its methods#ghh4 ,note #ghh3 ,i will not again enter into the subject of ,nomenclature2 but ,i may remark that ,m4 ,necker has adopted 7i4 #dae7 the ,nomenclature of ,beudant1 latinizing the names1 and thus converting each into a single word4 ,he has also introduced1 besides the names of ,genera1 names of ,families taken from the typical ,genus4 ,thus the ,family of ,carbonidiens contains the following genera3 ,calcispathum1 ,magnesispathum1 ,dolomispathum1 ,ferrispathum1 c41 ,malachita1 ,azuria1 ,gaylusacia4 ,i now quit the subject of mere ,resemblance1 and proceed to treat of that natural affinity which ,natural ,systems of ,classification for organic bodies must involve4 #aei ,,chapter ,,iv4 ,,of ,,the ,,idea ,,of ,,natural ,,affinity4 #a4 ,,in the ,second ,chapter of this ,book it was shown that although the ,classificatory ,sciences proceed ostensibly upon the ,idea of ,resemblance as their main foundation1 they necessarily take for granted in the course of their progress a further ,idea of ,natural ,affinity4 ,this appeared#gih by a general consideration of the nature of ,science1 by the recognition of natural species and genera1 even in ,artificial ,systems of ,classification#hjh1 and by the 9999attempts of botanists to form a ,natural ,system4 ,it further appeared that among the processes by which endeavours have been made to frame a ,natural ,system1 some1 as the method of ,blind ,trial and the method of ,general ,comparison1 have been altogether unsuccessful1 being founded only upon a collection of resemblances1 casual in the one case and arbitrary in the other4 ,in neither of these processes is there employed any general principle by which we may be definitely directed as to what resemblances we should employ1 or by which the result at which we arrive may be verified and confirmed4 ,our object in the present chapter is to show that the ,idea of ,natural ,affinity supplies us with a principle which may answer such purposes4 ,note #gih3 ,art4 #e4 ,note #hjh3 ,art4 #g4 ,i shall first consider the ,idea of ,affinity as exemplified in organized beings4 ,in doing this1 we may appear to take for granted ,ideas which have not yet come under our discussion1 as the ,ideas of ,organization1 and ,vital ,function2 but it will be found that the principle to which we are led is independent of these additional ,ideas4 #afj #b4 ,we have already seen that the attempts to discover the divisions which result from this ,natural ,affinity have led to the consideration of the ,subordination of ,characters4 ,it is easy to see that some organs are more essential than others to the existence of an organized being2 the organs of nutrition1 for example1 more essential than those of locomotion4 ,but at the same time it is clear that any arbitrary assumption of a certain scale of relative values of different kinds of characters will lead only to an ,artificial ,system4 ,this will happen1 if1 for example1 we begin by declaring the nutritive to be superior in importance to the reproductive functions4 ,it is clear that this relation of importance of organs and functions must be collected by the study of the organized beings2 and cannot be determined priori1 without depriving us of all right to expect a general accordance between our system and the arrangement of nature4 ,we see1 therefore1 that our notion of ,natural ,affinity involves in it this consequence2--that it is not to be made out by an arbitrary subordination of characters4 #c4 ,the functions and actions of living things which we separate from each other in our consideration1 cannot be severed in nature4 ,each function is essential2 ,life implies a collection of movements1 and ceases when any of these movements is stopped4 ,a change in the organization subservient to one set of functions may lead necessarily to a change in the organization belonging to others4 ,we can often see this necessary connexion2 and from a comparison of the forms of organized beings1--from the way in which their structure changes in passing from one class to another1 we are led to the conviction that there is some general principle which connects and graduates all such changes4 ,when the circulatory system changes1 the nervous system changes also3 when the mode of locomotion changes1 the respiration is also modified4 #d4 ,these corresponding changes may be considered as ways in which the living thing is fitted to its mode of life2 as marks of adaptation to a purpose2 or1 as it has been otherwise expressed1 as results of the #afa conditions of existence4 ,but at the present moment1 we put forward these correspondencies in a different light4 ,we adduce them as illustrations of what we mean by ,affinity1 and what we consider as the tendency of a ,natural ,classification4 ,it has sometimes been asserted that if we were to classify any of the departments of organized nature by means of one function1 and then by means of another1 the two classifications1 if each strictly consistent with itself1 would be consistent with each other4 ,such an assertion is perhaps more than we are entitled to make with confidence2 but it shows very well what is meant by ,affinity4 ,the disposition to believe such a general identity of all partial natural classifications1 shows how readily we fix upon the notion of ,affinity1 as a general result of the causes which determine the forms of living things4 ,when these causes or principles1 of whatever nature they are conceived to be1 vary so as to modify one part of the organization of the being1 they also modify another3 and thus the groups which exhibit this variation of the fundamental principles of form1 are the same1 whether the manifestation of the change be sought in one part or in another of the organized structure4 ,the groups thus formed are related by ,affinity2 and in proportion as we find the evidence of more functions and more organs to the propriety of our groups1 we are more and more satisfied that they are ,natural ,classes4 ,it appears1 then1 that our ,idea of ,affinity involves the conviction of the ,coincidence of natural arrangements formed on different functions2 and this1 rather than the principle of the ,subordination of some characters to others1 is the true ground of the natural method of ,classification4 #e4 ,for example1 ,cuvier1 after speaking of the ,subordination of ,characters as the guide which he intends to follow in his arrangement of animals1 interprets this principle in such a manner#hah as to make it agree nearly with the one just stated3 ',in pursuance of what has been said on methods in general1 we now require to #afb know what characters in animals are the most influential1 and therefore those which must be made the grounds of the primary divisions4' ',these1' he says1 'it is clear must be those which are taken from the animal functions2--sensation and motion3'--,but how does he confirm this8 ,not by showing that the animal functions are independent of1 or predominant over1 the vegetative1 but by observing that they follow the same gradations4 ',observation1' he continues1 'confirms this view1 by showing that the degrees of development and complication of the animal functions agree with those of the vegetative4 ,the heart and the organs of the circulation are a sort of center for the vegetative functions1 as the brain and the trunk of the nervous system are for the animal functions4 ,now we see these two systems descend in the scale1 and disappear the one with the other4 ,in the lowest animals1 when there are no longer any distinct nerves1 there are also no longer distinct fibres1 and the organs of digestion are simply hollowed out in the homogeneous mass of the body4 ,the muscular system disappears even before the nervous1 in insects2 but in general the distribution of the medullary masses corresponds to that of the muscular instruments2 a spinal cord1 on which knots or ganglions represent so many brains1 corresponds to a body divided into numerous rings and supported on pairs of members placed at different points of the length1 and so on4 ,note #hah3 ,rgne ,animal1 p4 #ee4 ',this correspondence of the general forms which result from the arrangement of the motive organs1 from the distribution of the nervous masses1 and from the energy of the circulatory system1 must therefore form the ground of the first great sections by which we divide the animal kingdom4' #f4 ,decandolle takes the same view4 ,there must be1 he says1 an equilibrium of the different functions#hbh4 ,and he exemplifies this by the case of the distinction of monocotyledonous and dicotyledonous plants1 which being at first established by means of the organs of #afc reproduction1 was afterwards found to coincide with the distinction of endogenous and exogenous1 which depends on the process of nutrition4 ',thus1' he adds1 'the natural classes founded on one of the great functions of the vegetable are necessarily the same as those which are founded upon the other function2 and ,i find here a very useful criterion to ascertain whether a class is natural3 namely1 in order to announce that it is so1 it must be arrived at by the two roads which vegetable organization presents4 ,thus ,i affirm1' he says1 'that the division of monocotyledons from dicotyledons1 and the distinction of ,gramine from ,cyperace1 are real1 because in these cases1 ,i arrive at the same result by the reproductive and the nutritive organs2 while the distinction of monopetalous and polypetalous1 of ,rhodorace and ,ericine1 appears to me artificial1 because ,i can arrive at it only by the reproductive organs4' ,note #hbh3 ,theor4 ,elem4 p4 #gi4 ,thus the ,correspondence of the indications of different functions is the criterion of ,natural ,classes2 and this correspondence may be considered as one of the best and most characteristic marks of the fundamental ,idea of ,affinity4 ,and the ,maxim by which all ,systems professing to be natural must be tested is this3--that the arrangement obtained from one set of characters coincides with the arrangement obtained from another set4 ,this ,idea of ,affinity1 as a natural connexion among various species1 of which connexion all particular resemblances are indications1 has principally influenced the attempts at classifying the animal kingdom4 ,the reason why the classification in this branch of ,natural ,history has been more easy and certain than that of the vegetable world is1 as ,decandolle says#hch1 that besides the functions of nutrition and reproduction1 which animals have in common with plants1 they have also in addition the function of sensation2 and thus have a new means of verification and concordance4 ,but we may add1 as a further reason1 that the functions of #afd animals are necessarily much more obvious and intelligible to us than those of vegetables1 from their clear resemblance to the operations which take place in our own bodies1 to which our attention has necessarily been strongly directed4 ,note #hch3 ,theor4 ,elem4 p4 #hj4 #g4 ,the question here offers itself1 whether this ,idea of ,natural ,affinity is applicable to inorganic as well as to organic bodies2--whether there be ,natural ,affinities among ,minerals4 ,and to this we are now enabled to reply by considering whether or not the principle just stated is applicable in such cases4 ,and the conclusion to which our principle leads us is1--that there are such ,natural ,affinities among ,minerals1 since there are different sets of characters which may be taken1 7and have by different writers been taken17 as the basis of classification4 ,the hardness1 specific gravity1 colour1 lustre1 crystallization1 and other external characters1 as they are termed1 form one body of properties according to which minerals may be classified2 as has in fact been done by ,mohs1 ,breithaupt1 and others4 ,the chemical constitution of the substances1 on the other hand1 may be made the principle of their arrangement1 as was done by ,hay1 and more recently1 and on a different scheme1 by ,berzelius4 ,which of these is the true and natural classification8 ,to this we answer1 that each of these arrangements is true and natural1 then1 and then only1 when it coincides with the other4 ,an arrangement by external characters which gives us classes possessing a common chemical character2--a chemical order which brings together like and separates unlike minerals2--such classifications have the evidence of truth in their agreement with one another4 ,every classification of minerals which does not aim at and tend to such a result1 is so far merely arbitrary2 and cannot be subservient to the expression of general chemical and mineralogical truths1 which is the proper purpose of such a classification4 #h4 ,in the ,history of ,mineralogy ,i have related the advances which have been made among mineralogists and chemists in modern times towards a ,system #afe possessing this character of truth4 ,i have there described the mixed systems of ,werner and ,hay2--the attempt made by ,mohs to form a pure ,natural ,history system2--the first and second attempt of ,berzelius to form a pure chemical system2 and the failure of both these attempts4 ,but the distinct separation of the two elements of which science requires the coincidence threw a very useful light upon the subject2 and the succeeding mixed systems1 such as that of ,naumann1 approached much nearer to the true conditions of the problem than any of the preceding ones had done4 ,thus1 as ,i have stated1 several of ,naumann's groups have both a common chemical character and great external resemblances4 ,such are his ,anhydrous ,unmetallic ,haloids--his ,anhydrous ,metallic ,haloids--,hydrous ,metallic ,haloids--,oxides of metals--,pyrites--,glances-- ,blendes4 ,the existence of such groups shows that we may hope ultimately to obtain a classification of minerals which shall be both chemically significant1 and agreeable to the methods of ,natural ,history3 although when we consider how very imperfect as yet our knowledge of the chemical composition of minerals is1 we can hardly flatter ourselves that we shall arrive at such a result very soon4 ,we have thus seen that in ,mineralogy1 as well as in the sciences which treat of organized bodies1 we may apply the ,idea of ,natural ,affinity2 of which the fundamental maxim is1 that arrangements obtained from different sets of characters must coincide4 ,since the notion of ,affinity is thus applicable to inorganic as well as to organic bodies1 it is plain that it is not a mere modification of the ,idea of ,organization or ,function1 although it may in some of its aspects appear to approach near to these other ,ideas4 ,but these ,ideas1 or others which are the foundation of them1 necessarily enter in a very prominent and fundamental manner into all the other parts of ,natural ,history4 ,to the consideration of these1 therefore1 we shall now proceed4 #afg ,,book ,,ix4 ,,the ,,philosophy ,,of ,,biology4 ,,la vie est donc un ,,tourbillon plus ou moins rapide1 plus ou moins compliqu1 dont la direction est constante1 et qui entraine toujours des molecules de mmes sorts1 mais o les molecules individuelles entrent et d'o elles sortent continuellement1 de manire que la ,forme du corps vivant lui est plus essentielle que sa ,matire4 ,tant que ce mouvement subsiste1 le corps o il s'exerce est vivant2 il vit4 ,lorsque le mouvement s'arrte sans retour1 le corps meurt4 ,,cuvier1 ,rgne ,animal1 s4 #ab4 ,i ,,remember1 upon asking our famous ,harvey1 what induced him to think of a circulation of the blood1 he said1 that observing the valves in the veins of many parts of the body1 so placed as to give a free passage to the blood towards the heart1 but to oppose the passage of the venal blood the contrary way1 he imagined that so provident a cause as nature had not thus placed so many valves without design2 and as no design seemed more probable than that the blood could not well1 because of the interposing valves1 be sent by the veins to the limbs1 it should be sent through the arteries and return through the veins when valves did not oppose its course that way4 ,,boyle1 ,on the ,final ,causes of ,natural ,things4 ,on the ,proposition3 ',tis often allowable for a naturalist1 from the manifest and apposite uses of the parts of animal bodies1 to collect some of the particular ends for which the ,creator designed them3 and in some cases we may1 from the known nature and structure of the parts1 draw particular conjectures about the particular offices of them4 #afi ,,book ,,ix4 ,,the ,,philosophy ,,of ,,biology4 ,,chapter ,i4 ,,analogy ,,of ,,biology ,,with ,,other ,,sciences4 #a4 ,,in the ,history of the ,sciences1 after treating of the ,sciences of ,classification1 we proceeded to what are there termed the ,organical ,sciences1 including in this term ,physiology and ,comparative ,anatomy4 ,a peculiar feature in this group of sciences is that they involve the notion of living things4 ,the notion of ,life1 however vague and obscure it may be in men's minds1 is apprehended as a peculiar ,idea1 not resolvable into any other ,ideas1 such1 for instance1 as ,matter and ,motion4 ,the separation between living creatures and inert matter1 between organized and unorganized beings1 is conceived as a positive and insurmountable barrier4 ,the two classes of objects are considered as of a distinct kind1 produced and preserved by different forces4 ,whether the ,idea of ,life is really thus original and fundamental1 and whether1 if so1 it be one ,idea only1 or involve several1 it must be the province of true philosophy to determine4 ,what we shall here offer may be considered as an attempt to contribute something to the determination of these questions2 but we shall perhaps be able to make it appear that science is at present only in the course of its progress towards a complete solution of such problems4 ,since the main feature of those sciences of which we have now to examine the philosophy is1 that they #agj involve the ,idea of ,life1 it would be desirable to have them designated by a name expressive of that circumstance4 ,the word ,physiology1 by which they have most commonly been described1 means the ,science of ,nature2 and though it would be easy to explain1 by reference to history1 the train of thought by which the word was latterly restricted to ,living ,nature1 it is plain that the name is1 etymologically speaking1 loose and improper4 ,the term ,biology1 which means exactly what we wish to express1 the ,science of ,life1 has often been used1 and has of late become not uncommon among good winters4 ,i shall therefore venture to employ it1 in most cases1 rather than the word ,physiology4 #b4 ,as ,i have already intimated1 one main inquiry belonging to the ,philosophy of ,biology1 is concerning the ,fundamental ,idea or ,ideas which the science involves4 ,if we look back at the course and the results of our disquisitions respecting other sciences in this work1 and assume1 as we may philosophically do1 that there will be some general analogy between those sciences and this1 in their development and progress1 we shall be enabled to anticipate in some measure the nature of the view which we shall now have to take4 ,we have seen that in other subjects the ,fundamental ,ideas on which science depended1 and the ,conceptions derived from these1 were at first vague1 obscure1 and confused2--that by gradual steps1 by a constant union of thought and observation1 these conceptions become more and more clear1 more and more definite2--and that when they approached complete distinctness and precision1 there were made great positive discoveries into which these conceptions entered2 and thus the new precision of thought was fixed and perpetuated in some conspicuous and lasting truths4 ,thus we have seen how the first confused mechanical conceptions 7,force1 and the like17 were1 from time to time1 growing clearer1 down to the epoch of ,newton2--how true conceptions of ,genera and of wider classes1 gradually unfolded themselves among the botanists of the sixteenth and seventeenth centuries2--how the idea of ,substance became steady enough to govern the #aga theories of chemists only at the epoch of ,lavoisier2--how the ,idea of ,polarity1 although often used by physicists and chemists1 is even now somewhat vague and indistinct in the minds of the greater part of speculators4 ,in like manner we may expect to find that the ,idea of ,life1 if indeed that be the governing ,idea of the ,science which treats of ,living ,things1 will be found to have been gradually approaching towards a distinct and definite form among the physiologists of all ages up to the present day4 ,and if this be the case1 it may not be considered superfluous1 with reference to so interesting a subject1 if we employ some space in tracing historically the steps of this progress2--the changes by which the originally loose notion of ,life1 or of ,vital ,powers1 became more nearly an ,idea suited to the purposes of science4 #c4 ,but we may safely carry this analogy between ,biology and other sciences somewhat further4 ,we have seen1 in other sciences1 that while men in their speculations were thus tending towards a certain peculiar ,idea1 but before they as yet saw clearly that it was peculiar and independent1 they naturally and inevitably clothed their speculations in conceptions borrowed from some other extraneous idea4 ,and the unsatisfactoriness of all such attempts1 and the necessary consequence of this1 a constant alteration and succession of such inappropriate hypotheses1 were indications and aids of the progress which was going on towards a more genuine form of the science4 ,for instance1 we have seen that in chemistry1 so long as men refused to recognize a peculiar and distinct kind of power in the ,affinity which binds together the elements of bodies1 they framed to themselves a series of hypotheses1 each constructed according to the prevalent ideas of the time1 by which they tried to represent the relation of the compound to the ingredients3--first1 supposing that the elements bestowed upon the whole qualities resembling their own3--then giving up this supposition1 and imagining that the properties of the body depended upon the shape of the component particles2--then1 as their view expanded1 assuming that it was #agb not the shape1 but the mechanical forces of the particles which gave the body its attributes2--and finally acquiescing in1 or rather reluctantly admitting1 the idea of ,affinity1 conceived as a peculiar power1 different not only from material contact1 but from any mechanical or dynamical attraction4 ,now we cannot but think it very natural1 if we find that the history of ,biology offers a series of occurrences of the same nature4 ,the notions of ,life in general1 or of any ,vital ,functions or ,vital ,forces in particular1 are obviously very loose and vague as they exist in the minds of most men4 ,the discrepancies and controversies respecting the definitions of all such terms1 which are found in all works on physiology1 afford us abundant evidence that these notions are not1 at least not generally1 apprehended with complete clearness and steadiness4 ,we shall therefore find approaches and advances1 intermediate steps1 gradually leading up to the greatest degree of distinctness which has yet been attained4 ,and in those stages of imperfect apprehension in which the notions of ,life and of ,vital ,powers are still too loose and unformed to be applied independently1 we may expect to find them supported and embodied by means of hypotheses borrowed from other subjects1 and thus1 made so distinct and substantial as to supply at least a temporary possibility of scientific reasoning upon the laws of life4 #d4 ,for example1 if we suppose that men begin to speculate upon the properties of living things1 not acknowledging a peculiar ,vital ,power1 but making use successively of the knowledge supplied by the study of other subjects1 we may easily imagine a series of hypotheses along which they would pass4 ,they would probably1 first1 in this as in other sciences1 have their thoughts occupied by vague and mystical notions in which material and spiritual agency1 natural and supernatural events1 were mixed together without discrimination1 and without any clear notion at all4 ,but as they acquired a more genuine perception of the nature of 9999knowledge1 they would naturally try to explain vital motions and processes by means of #agc such forces as they had learnt the existence of from other sciences4 ,they might first have a mechanical hypothesis1 in which the mechanical ,forces of the solids and fluids which compose organized bodies should be referred to1 as the most important influences in the process of life4 ,they might then attend to the actions which the fluids exercise in virtue of their ,affinity1 and might thus form a chemical theory4 ,when they had proved the insufficience of these hypotheses1 borrowed from the powers which matter exhibits in other cases1 they might think themselves authorized to assume some peculiar power or agency1 still material1 and thus they would have the hypothesis of a ,vital ,fluid4 ,and if they were driven to reject this1 they might think that there was no resource but to assume an immaterial principle of life1 and thus they would arrive at the doctrine of an ,animal ,soul4 ,now1 through the cycle of hypotheses which we have thus supposed1 physiology has actually passed4 ,the conclusions to which the most philosophical minds have been led by a survey of this progress is1 that by the failure of all these theories1 men have exhausted this path of inquiry1 and shown that scientific truth is to be sought in some other manner4 ,but before ,i proceed further to illustrate this result1 it will be proper1 as ,i have already stated1 to exhibit historically the various hypotheses which ,i have described4 ,in doing this ,i shall principally follow the ,history of ,medicine of ,sprengel4 ,it is only by taking for my guide a physiologist of acknowledged science and judgment1 that ,i can hope1 on such a subject1 to avoid errours of detail4 ,i proceed now to give in succession an account of the ,mystical1 the ,iatrochemical1 the ,iatromathematical1 and the ,vital-,fluid ,schools2 and finally of the ,psychical ,school1 who hold the ,vital ,powers to be derived from the ,soul 7,psyche74 #agd ,,chapter ,,ii4 ,,successive ,,biological ,,hypotheses4 ,,sect4 ,i4--,the ,mystical ,school4 ,,in order to abbreviate as much as can conveniently be done the historical view which ,i have now to take1 ,i shall altogether pass over the physiological speculations of the ancients1 and begin my survey with the general revival of science in modern times4 ,we need not dwell long on the fantastical and unsubstantial doctrines concerning physiology which prevailed in the sixteenth century1 and which flowed in a great measure from the fertile but ill-regulated imaginations of the cultivators of ,alchemy and ,magic4 ,one of the prominent doctors of this school is the celebrated ,paracelsus1 whose doctrines contained a combination of biblical interpretations1 visionary religious notions1 fanciful analogies1 and bold experiments in practical medicine4 ,the opinion of a close but mystical resemblance of parts between the universe and the human body1--the ,macrocosm and the ,microcosm1--as these two things1 thus compared1 were termed1 had probably come down from the ,neoplatonists2 it was adopted by the ,paracelsists#ai1 and connected with various astrological dreams and cabbalistic riddles4 ,a succession of later ,paracelsists#bi1 ,rosicrucians1 and other fanatics of the same kind1 continued into the seventeenth century4 ,upon their notions was founded the pretension of curing wounds by a sympathetic powder1 which ,sir ,kenelm ,digby1 among others1 asserted2 while animal magnetism1 and the transfer of diseases from one person to another#ci1 were maintained by others of this #age school4 ,they held1 too1 the doctrines of astral bodies corresponding to each terrestrial body2 and of the signatures of plants1 that is1 certain features in their external form by which their virtues might be known4 ,how little advantage or progress real physiology could derive from speculations of this kind may be seen from this1 that their tendency was to obliterate the distinction between living and lifeless things3 according to ,paracelsus1 all things are alive1 eat1 drink1 and excrete2 even minerals and fluids#di4 ,according to him and his school1 besides material and immaterial beings1 there are elementary ,spirits which hold an intermediate place1 ,sylvans1 ,nymphs1 ,gnomes1 ,salamanders1 c4 by whose agency various processes of enchantment may be achieved1 and things apparently supernatural explained4 ,thus this spiritualist scheme dealt with a world of its own by means of fanciful inventions and mystical visions1 instead of making any step in the study of nature4 ,note #ai3 ,spr4 iii4 #def4 ,note #bi3 ,ib4 iv4 #bgj4 ,note #ci3 ,ib4 iv4 #bgf4 ,note #di3 ,spr4 iii4 #deh4 ,parac4 ,de ,vita ,rerum ,naturalium1 p4 #hhi4 ,perhaps1 however1 one of the most fantastical of the inventions of ,paracelsus may be considered as indicating a perception of a peculiar character in the vital powers4 ,according to him1 the business of digestion is performed by a certain demon whom he calls ,archus1 who has his abode in the stomach1 and who1 by means of his alchemical processes1 separates the nutritive from the harmful part of our food1 and makes it capable of assimilation#ei4 ,this fanciful notion was afterwards adopted and expanded by ,van ,helmont#fi4 ,according to him the stomach and spleen are both under the direction of this ,master-spirit1 and these two organs form a sort of ,duumvirate in the body4 ,note #ei3 ,ib4 iii4 #dfh4 ,note #fi3 ,ib4 iv4 #cjb4 ,but though we may see in such writers occasional gleams of physiological thought1 the absence of definite physical relations in the speculations thus promulgated was necessarily intolerable to men of sound understanding and scientific tendencies4 ,such men naturally took hold of that part of the phenomena of life which could be most distinctly conceived1 and #agf which could be apparently explained by means of the sciences then cultivated2 and this was the part which appeared to be reducible to chemical conceptions and doctrines4 ,it will readily be supposed that the processes of chemistry have a considerable bearing upon physiological processes1 and might1 till their range was limited by a sound investigation1 be supposed to have still more than they really had2 and thus a ,physiology was formed which depended mainly upon ,chemistry1 and the school which held this doctrine has been called the ,iatrochemical ,school4 ,,sect4 ,,ii4--,the ,iatrochemical ,school4 ,that all physical properties1 and therefore chemical relations1 have a material influence on physiological results1 was already recognized1 though dimly1 in the ,galenic doctrine of the 'four elementary qualities4' ,but at the time of ,paracelsus1 chemical action was more distinctly than before separated from other kinds of physical action2 and therefore a physiological doctrine1 founded upon chemistry1 and freed from the extravagance and mysticism of the ,paracelsists1 was a very promising path of speculation4 ,andrew ,libavius#gi of ,halle1 in ,saxony1 ,physician and ,teacher in the ,gymnasium at ,koberg1 is pointed out by ,sprengel as the person who began to cultivate chemistry1 as distinct from the theosophic fantasies of his predecessors2 and ,angelus ,sala of ,vienna#hi1 as his successor4 ,the latter has the laudable distinction of having rejected the prevalent conceits about a potable gold1 a universal medicine1 and the like#ii4 ,in ,germany already at the beginning of the seventeenth century a peculiar chair of ,chymiatria was already created at ,marpurg3 and many in various places pursued the same studies1 till1 in the middle of the seventeenth century1 we come to ,lemery#aji1 the principal reformer of pharmaceutical chemistry4 ,but we are not here so much concerned #agg with the practical as with the theoretical parts of ,iatrochemistry2 and hence we pass on to ,sylvius#aai and his system4 ,note #gi3 ,spr4 iii4 #eej4 ,note #hi3 ,ib4 iv4 #bha4 ,note #ii3 ,ib4 iv4 #bhc4 ,note #aji3 ,ib4 iv4 #bia4 ,note #aai3 ,spr4 iv4 #ccf4 ,the opinion that chemistry had an important bearing upon physiology did not1 however1 begin with ,sylvius4 ,paracelsus1 among his extravagant absurdities1 did some service to medicine by drawing attention to this important truth4 ,he used#abi chemical principles for the explanation of particular diseases3 most or all diseases according to him1 arise from the effervescence of salts1 from the combustion of sulphur1 or from the coagulation of mercury4 ,his medicines were chemical preparations2 and it was#aci an undeniable advantage of the ,paracelsian doctrine that chemistry thus became indispensable to the physician4 ,we still retain a remnant of the chemical nomenclature of ,paracelsus in the term tartar1 denoting the stony concretion which forms on the teeth#adi4 ,according to him there is a certain substance1 the basis of all diseases which arise from a thickening of the juices and a collection of earthy matter2 and this substance he calls ,tartarus1 because 'it burns like the fire of hell4' ,helmont1 the successor of ,paracelsus in many absurdities1 also followed him in the attempt to give a chemical account1 however loose and wild1 of the functions of the human body2 and is by ,sprengel considered1 with all his extravagancies1 as a meritorious and important discoverer4 ,the notion of the fermentation of fluids#aei1 and of the arial product thence resulting1 to which he gave the name of ,gas1 forms an important part of his doctrines2 and of the six digestions which he assumes1 the first prepares an acid1 which is neutralized by the gall when it reaches the duodenum1 and this constitutes the second digestion4 ,note #abi3 ,ib4 iii4 #dgb4 ,note #aci3 ,ib4 iii4 #dhb4 ,note #adi3 ,ib4 iii4 #dge4 ,note #aei3 ,vol4 v4 #cae4 ,i have already1 in the ,history of ,chemistry#afi1 stated1 that the doctrine of the opposition of acid and alkali1 the great step which theoretical chemistry owes to ,sylvius1 was first brought into view as a physiological #agh tenet1 although we had then to trace its consequences in another science4 ,the explanation of all the functions of the animal system1 both healthy and morbid1 by means of this and other chemical doctrines1 and the prescription of methods of cure founded upon such explanations1 form the scheme of the iatrochemical school2 a school which almost engrossed the favour of ,european physicians during the greater part of the seventeenth century4 ,note #afi3 ,hist4 ,ind4 ,sc4 b4 xiii4 c4 #b4 ,sylvius taught medicine at ,leyden1 from the year #afeh1 with so much success1 that ,boerhaave alone surpassed him#agi4 ,his notions1 although he piqued himself on their originality1 were manifestly suggested in no small degree 7as all such supposed novelties are7 by the speculations of his predecessors1 and the spirit of the times4 ,like ,helmont#ahi1 he considers digestion as consisting in a fermentation2 but he states it more definitely as the effervescence of an acid1 supplied by the saliva and the pancreatic juice1 with the alkali of the gall4 ,by various other hypothetical processes1 all of a chemical nature1 the blood becomes a collection of various juices1 which are the subjects of the speculations of the iatrochemists1 to the entire neglect of the solid parts of the body4 ,diseases were accounted for by a supposed prevalence of one or the other of the acrid principles1 the acid or the alkaline3 and ,sylvius#aii was bold enough to found upon these hypotheses practical methods of cure1 which were in the highest degree mischievous4 ,note #agi3 ,spr4 iv4 #ccf4 ,note #ahi3 ,ib4 #cch4 ,note #aii3 ,ib4 iv4 #cde4 ,the ,sylvian doctrine was often combined with some of the notions of the ,cartesian system of philosophy2 but this mixture ,i shall not notice1 since my present object is to trace the history of a mere chemical physiology as one of the unsuccessful attempts at a philosophy of life4 ,with various modifications1 this doctrine was diffused over ,europe4 ,it gave rise to several controversies1 which turned upon the questions of the novelty of the doctrine1 and the use of chemical remedies to which it pointed1 as well as upon its #agi theoretical truth4 ,we need not dwell long upon these controversies1 although they were carried on with no small vehemence in their time4 ,thus the school of ,paris opposed all innovation1 remained true to the ,galenic dogmatism1 and declared itself earnestly against all combination of chemistry with medicine2 and even against the chemical preparation of medicaments4 ,guy ,patin1 a celebrated and learned professor of that day1 declares#bji that the chemists are no better than forgers1 and ought to be punished as such4 ,the use of antimonial medicines was a main point of dispute between the iatrochemists and their opponents2 ,patin maintained that more men had been destroyed by antimony than by the thirty years' war of ,germany2 and endeavoured to substantiate this assertion by collecting all such cases in his ,martyrologium ,antimonii4 ,it must have been a severe blow to ,patin when#bai in #afff1 the ,doctors of the ,faculty of ,paris1 assembled by command of the parliament1 declared1 by a majority of ninety-two voices1 that the use of antimonial medicines was allowable and laudable1 and when all attempts to set aside this decision failed4 ,note #bji3 ,spr4 #cdi4 ,note #bai3 ,ib4 iv4 #cej4 ,florentius ,schuyl of ,leyden sought to recommend the iatrochemical doctrines1 by maintaining that they were to be found in the ,hippocratic writings2 nor was it difficult to give a chemical interpretation of the humoral pathology of the ancients4 ,the ,italian#bbi physicians also1 for the most part1 took this line1 and attempted to show the agreement of the principles of the ancient school of medicine with the new chemical notions4 ,this1 indeed1 is the usual manner in which the diffusion of new theoretical ideas becomes universal4 ,note #bbi3 ,ib4 #cfh4 ,the progress of the chemical school of medicine in ,england#bci requires our more especial notice4 ,willis was the most celebrated champion of this sect4 ,he assumed1 but with modifications of his own1 the three ,paracelsian principles1 ,salt1 ,sulphur1 and ,mercury2 considered digestion as the effect of an acid1 and #ahj explained other parts of the animal economy by distillation1 fermentation1 and the like4 ,all diseases arise from the want of the requisite ferment2 and the physician1 he says#bdi1 may be compared to a vintner1 since both the one and the other have to take care that the necessary fermentations go on1 that no foreign matter mixes itself with the wine of life1 to interrupt or derange those operations4 ,in the middle of the seventeenth century1 medicine had reached a point in which the life of the animal body was considered as merely a chemical process2 the wish to explain everything on known principles left no recognized difference between organized and unorganized bodies1 and diseases were treated according to this delusive notion4 ,the condition of chemistry itself during this period1 though not one of brilliant progress1 was sufficiently stable and flourishing to give a plausibility to any speculation which was founded on chemical principles2 and the real influence of these principles in the animal frame could not be denied4 ,note #bci3 ,ib4 #cec4 ,note #bdi3 ,spr4 #ced4 ,the iatrochemists were at first resisted1 as we have seen1 by the adherents of the ancient schools2 they were attacked on various grounds1 and finally deposed from them ascendancy by another sect1 which we have to speak of1 as the iatromathematical1 or mechanical school4 ,this sect was no less unsatisfactory and erroneous in its positive doctrines than the chemists had been2 for the animal frame is no more a mere machine than a mere laboratory3 but it promoted the cause of truth1 by detecting and exposing the insufficient explanations and unproved assertions of the reigning theory4 ,boyle was one of the persons who first raised doubts against the current chemical doctrines of his time1 as we have elsewhere noted2 but his objections had no peculiar physiological import4 ,herman ,coming#bei1 the most learned physician of his time1 a contemporary with ,sylvius1 took a view more pertinent to our present object2 for he not only rejected the alchemical #aha and hermetical medicines1 but taught expressly that chemistry1 in its then existing condition1 was better fitted to be of use in the practice of pharmacy1 than in the theories of physiology and pathology4 ,he made the important assertion1 also1 that chemical principles do not pre-exist as such in the animal body2 and that there are higher powers which operate in the organic world1 and which do not depend on the form and mixture of matter4 ,note #bei3 ,ib4 iv4 #cfa4 ,attempts were made to prove the acid and alkaline nature of the fluids of the human body by means of experiments1 as by ,john ,viridet of ,geneva#bfi1 and by ,raimond ,vieussens#bgi1 the latter of whom maintained that he had extracted an acid from the blood1 and detected a ferment in the stomach4 ,in opposition to him1 ,hecquet1 a disciple of the iatromathematical school1 endeavoured to prove that digestion was performed1 not by means of fermentation1 but by trituration4 ,hecquet's own opinions cannot be defended2 but his objections to the chemical doctrines1 and his assertion of the difference of chemical and organical processes1 are evidences of just thought#bhi4 ,note #bfi3 ,spr4 iv4 #cbi4 ,note #bgi3 ,ib4 #cej1 7#agae74 ,note #bhi3 ,ib4 #dja4 ,the most important opponents of the iatrochemical school were ,pitcairn in ,england1 ,bohn and ,hoffman in ,germany1 and ,boerhaave in ,holland4 ,these eminent physicians1 about the end of the seventeenth century1 argued on the same grounds of observation1 that digestion is not fermentation1 and that the ,sylvian accounts of the origin of diseases by means of acid and alkali are false4 ,the arguments and authority of these and other persons finally gained an ascendancy in the medical world1 and soon after this period we may consider the reign of the chemical school of physiology as past4 ,in fact1 the attempts to prove its assertions experimentally were of the feeblest kind1 and it had no solid basis on which it could rest1 so as to resist the shock of the next hypothesis which the progress of the physical sciences might impel against it4 ,we may1 therefore1 now consider the opinion of the mere #ahb chemical nature of the vital processes as disproved1 and we proceed next to notice the history of another unsuccessful essay to reduce vital actions to known actions of another kind4 ,,sect4 ,,iii4--,the ,iatromathematical ,school4 ,in the first ,section of this chapter1 we enumerated the biological hypotheses which at first present themselves1 as the mystical1 the mechanical1 the chemical4 ,we might have expected that they should occur to men's minds in the order thus stated3 and in fact they did so2 for the physiology of the ancient materialists1 as ,democritus and ,lucretius1 is mechanical so far as it is at all distinct in its views1 and thus the mechanical preceded the chemical doctrine4 ,but in modern times1 the fluid or chemical physiology was developed before the solid or mechanical3 of which the reason appears to have been this2--that ,mechanics and ,chemistry began to assume a scientific character about the same time2 and that of the two1 ,chemistry not only appeared at first sight more applicable to the functions of the body1 because all the more rapid changes appear to be connected with modifications of the fluids of the animal system1 but also1 by its wider range of facts and more indefinite principles1 afforded a better temporary refuge for the mind when perplexed by the difficulties and mysteries which spring out of the speculations concerning life4 ,but if ,chemistry was thus at first a more inviting field for the physiologist1 ,mechanics soon became more attractive in virtue of the splendid results obtained by the schools of ,galileo and ,newton4 ,and when the insufficiency of chemical physiology was discovered by trial1 as we have seen it was1 the hope naturally arose1 that the mechanical principles which had explained so many of the phenomena of the external universe might also be found1 applicable to the smaller world of material life2--that the microcosm as well as the macrocosm might have its mechanical principles4 ,from this hope sprung the #ahc ,iatromathematical ,school1 or school of ,mechanical ,physiologists4 ,we may1 however1 divide this school into two parts1 the ,italian1 and the ,cartesio-,newtonian sect4 ,the former employed themselves in calculating and analysing a number of the properties of the animal frame which are undoubtedly mechanical2 the latter1 somewhat intoxicated by the supposed triumphs of the corpuscular philosophy1 endeavoured to extend these to physiology1 and for this purpose introduced into the subject many arbitrary and baseless hypotheses4 ,i will very briefly mention some of the writers of both these sects4 ,the main points to which the ,italian or genuine ,mechanical ,physiologists attended1 were the application of mechanical calculations to the force of the muscles1 and of hydraulical reasonings to the motion of the fluids of the animal system4 ,the success with which ,galileo and his disciples had pursued these branches of mechanical philosophy1 and the ascendancy which they had obtained1 first in ,italy1 and then in other lands1 made such speculations highly interesting4 ,borelli may be considered as the first great name in his line1 and his book1 ,de ,motu ,animalium1 7,opus ,posthumum1 ,rom1 #afhj17 is even now a very instructive treatise on the forces and action of the bones and muscles4 ,this1 certainly one of the most valuable portions of mechanical physiology1 has not even yet been so fully developed as it deserves1 although ,john ,bernoulli#bii and his son ,daniel#cji applied to it the resources of analysis1 and ,pemberton#cai in ,england1 pursued the same subject4 ,other of these mechanico-physiological problems consisted in referring the pressure of the blood and of the breath to hydrostatical principles4 ,in this manner ,borelli was led to assert that the muscles of the heart exert a force of #ahj1jjj pounds#cbi4 ,but a little later1 ,keill reduced this force #ahd to a few ounces#cci4 ,keill and others attempted to determine1 on similar principles1 the velocity of the blood2 we need not notice the controversies which thus arose1 since there is not involved in them any peculiar physiological principle4 ,note #bii3 ,de ,motu ,musculorum4 ,note #cji3 ,act4 ,acad4 ,petrop4 ,note #cai3 ,course of ,physiology1 #aggc4 ,note #cbi3 ,spr4 iv4 #aaj4 ,note #cci3 ,spr4 iv4 #ddc4 ,the peculiar character of the iatromathematical school1 as an attempt at physiological theory1 is more manifest in its other section1 which we have called the ,cartesio-,newtonian4 ,the ,cartesian system pretended to account for the appearances and changes of bodies by means of the size1 figure1 and motion of their minute particles4 ,and though this system in its progress towards the intellectual empire of ,europe was suddenly overturned by the rise of the ,newtonian philosophy1 these corpuscular doctrines rather gained than lost by the revolution2 for the ,newtonian philosophy enlarged the powers of the corpuscular hypothesis1 by adding the effects of the attractive and repulsive forces of particles to those of their form and motion4 ,by this means1 although ,newton's discoveries did not in fact augment the probability of the corpuscular hypothesis1 they so far increased its plausibility1 that this hypothesis found favour both with ,newton himself and his contemporaries1 no less than it had done with the ,cartesians4 ,the attempt to apply this corpuscular hypothesis to physiology was made by ,des ,cartes himself4 ,the general character of such speculations may easily be guessed#cdi4 ,the secretions are effected by the organs operating after the manner of sieves4 ,bound particles pass through cylindrical tubes1 pyramidal ones through triangular pores1 cubical particles through square apertures1 and thus different kinds of matter are separated4 ,similar speculations were pursued by other mathematicians3 the various diameter of the vessels#cei1 their curvatures1 folds1 and angles1 were made subjects of calculation4 ,bellini1 ,donzellini1 ,gulielmini1 in ,italy2 ,perrault1 ,dodart1 in ,france2 ,cole1 ,keill1 ,jurin1 in ,england1 were the principal cultivators of such studies4 #ahe ,in the earlier part of the eighteenth century1 physiological theorists considered it as almost self-evident that their science required them to reason concerning the size and shape of the particles of the fluids1 the diameter and form of the invisible vessels4 ,such was1 for instance1 the opinion of ,cheyne#cfi1 who held that acute fevers arise from the obstruction of the glands1 which occasions a more vehement motion of the blood4 ,mead1 the physician of the ,king1 and the friend of ,newton1 in like manner explained the effects of poisons by hypotheses concerning the form of their particles#cgi1 as we have already seen in speaking of chemistry4 ,note #cdi3 ,ib4 #cbi4 ,note #cei3 ,ib4 #dcb4 ,note #cfi3 ,spr4 iv4 #bbc4 ,note #cgi3 ,mechanical ,account of ,poisons1 #agjb4 ,it is not necessary for us to dwell longer on this subject1 or to point out the total insufficiency of the mere mechanical physiology4 ,the iatrochemists had neglected the effect of the solids of the living frame2 the iatromathematicians attended only to these#chi4 ,and even these were considered only as canals1 as cords1 as levers1 as lifeless machines4 ,these reasoners never looked for any powers of a higher order than the cohesion1 the resistance1 the gravity1 the attraction1 which operate in inert matter4 ,if the chemical school assimilated the physician to a vintner or brewer1 the mechanical physiologists made him an hydraulic engineer2 and1 in fact1 several of the iatromathematicians were at the same time teachers of engineering and of medicine4 ,note #chi3 ,spr4 iv4 #dai4 ,several of the reasoners of this school combined chemical with their mechanical principles2 but it would throw no additional light upon the subject to give any account of these1 and ,i shall therefore go on to speak of the next form of the attempt to explain the processes of life4 ,,sect4 ,,iv4--,the ,vital-,fluid ,school4 ,i speak here1 not of that opinion which assumes some kind of fluid or ether as the means of #ahf communication along the nerves in particular1 but of the hypothesis that all the peculiar functions of life depend upon some subtile ethereal substance diffused through the frame2--not of a ,nervous ,fluid1 but of a ,vital ,fluid4 ,again1 ,i distinguish this opinion from the doctrine of an immaterial vital power or principle1 an ,animal ,soul1 which will be the subject of the next ,section3 nor is this distinction insignificant2 for a material element1 however subtile1 however much spiritualized1 must still act everywhere according to the same laws2 whereas we do not conceive an immaterial spirit or soul to be subject to this necessity4 ,the iatromathematical school could explain to their own satisfaction how motions1 once begun1 were transferred and modified2 but in many organs of the living frame there seemed to be a power of beginning motion1 which is beyond all mere mechanical action4 ,this led to the assumption of a ,principle of a higher kind1 though still material4 ,such a ,principle was asserted by ,frederick ,hoffmann1 who was born at ,halle1 in #affjcii1 and became ,professor of ,medicine at the newly established ,university there in #afid4 ,according to him#dji1 the reason of the greater activity of organized bodies lies in the influence of a material substance of extreme subtilty1 volatility1 and energy4 ,this is1 he holds1 no other than the ,ether1 which1 diffused through all nature1 produces in plants the bud1 the secretion and motion of the juices1 and is separated from the blood and lodged in the brain of animals#dai4 ,from this1 acting through the nerves1 must be derived all the actions of the organs in the animal frame2 for when the influence of the nerve upon the muscle ceases1 muscular motion ceases also4 ,note #cii3 ,spr4 v4 #bed4 ,note #dji3 ,ib4 v4 #beg4 ,note #dai3 ,de ,differenti ,organismi et ,mechanismi1 pp4 #dh1 #fg4 ,the mode of operation of this vital fluid was1 however1 by no means steadily apprehended by ,hoffmann and his followers4 ,its operations are so far mechanical#dbi that all effects are reduced to motion1 yet they #ahg cannot be explained according to known mechanical laws4 ,at one time the effects are said to take place according to laws of a ,higher ,mechanics which are still to be discovered#dci4 ,at another time1 in complete contradiction of the general spirit of the system1 metaphysical conceptions are introduced3 each particle of the vital fluid is said to have a determined idea of the whole mechanism and organism#ddi1 and according to this1 it forms the body and preserves it by its motion4 ,by means of this fluid the soul operates upon the body1 and the instincts and the passions have their source in this material sensitive soul4 ,this attribution of ideas to the particles of the fluid is less unaccountable when we recollect that something of the same kind is admitted into ,leibnitz's system1 whose ,monads have also ideas4 ,note #dbi3 ,spr4 v4 #bfb1 #c4 ,note #dci3 ,hoffmann1 ,opp4 ,vol4 v4 p4 #abc4 ,note #ddi3 ,de ,diff4 ,organ4 et ,mechan4 p4 #ha4 ,notwithstanding its inconsistencies1 ,hoffmann's system was received with very general favour both in ,germany and in the rest of ,europe2 the more so1 inasmuch as it fell in very well with the philosophy both of ,leibnitz and of ,newton4 ,the ,newtonians were generally inclined to identify the ,vital ,fluid with the ,ether1 of which their master was so strongly disposed to assume the existence3 and indeed he himself suggested this identification4 ,when the discoveries made respecting ,electricity in the course of the eighteenth century had familiarized men with the notion of a pervading subtile agent1 invisible1 intangible1 yet producing very powerful effects in every part of nature1 physiologists also caught at the suggestion of such an agent1 and tried1 by borrowing or imitating it1 to aid the imperfection of their notions of the vital powers4 ,the ,vital ,principle#dei was imagined to be a substance of the same kind1 by some to be the same substance1 with the ,electric ,fluid4 ,by its agency all these processes in organized bodies were accounted for which cannot be #ahh explained by mechanical or chemical laws1 as the secretion of various matters 7tears1 milk1 bile1 c47 from an homogeneous fluid1 the blood2 the production of animal heat1 digestion1 and the like4 ,according to ,john ,hunter1 this attenuated substance pervaded the blood itself1 as well as the solid organic frame2 and the changes which take place in the blood which has flowed out of the veins into a basin are explained by saying that it is1 for a time1 till this vital fluid evaporates1 truly alive4 ,note #dei3 ,prichard1 ,on the ,doctrine of a ,vital ,principle1 p4 #ab4 ,the notion of a ,vital ,fluid appears also to be favourably looked upon by ,cuvier2 although with him this doctrine is mainly put forwards in the form of a ,nervous ,fluid4 ,yet in the following passage he extends the operation of such an agent to all the vital functions#dfi3 ',we have only to suppose that all the medullary and nervous parts produce the ,nervous ,agent1 and that they alone conduct it2 that is1 that it can only be transmitted by them1 and that it is changed or consumed by their actions4 ,then everything appears simple4 ,a detached portion of muscle preserves for some time its irritability1 on account of the portion of nerve which always adheres to it4 ,the sensibility and the irritability reciprocally exhaust each other by their exercise1 because they change or consume the same agent4 ,all the interior motions of digestion1 secretion1 excretion1 participate in this exhaustion1 or may produce it4 ,all local excitation of the nerves brings thither more blood by augmenting the irritability of the arteries1 and the afflux of blood augments the real sensibility by augmenting the production of the nervous agent4 ,hence the pleasures of titillations1 the pains of inflammation4 ,the particular sensations increase in the same manner and by the same causes2 and the imagination exercises1 7still by means of the nerves17 upon the internal fibres of the arteries or other parts1 and through them on the sensations1 an action analogous to that of the will upon the voluntary motions4 ,as each exterior sense is exclusively disposed #ahi to admit the substances which it is to perceive1 so each interior organ1 secretory or other1 is also more excitable by some one agent than by another3 and hence arises what has been called the proper sensibility or proper life of the organs2 and the influence of specifics which1 introduced into the general circulation1 affect only certain parts4 ,in fine1 if the nervous agent cannot become sensible to us1 the reason is that all sensation requires that this agent should be altered in some way or other2 and it cannot alter itself4 ,note #dfi3 ,hist4 ,sc4 ,nat4 depuis #aghi1 i4 #bad4 ',such is the summary idea which we may at present form of the mutual and general working of the vital powers in animals4' ,against the doctrine of a ,vital ,fluid as one uniform material agent pervading the organic frame1 an argument has been stated which points out extremely well the philosophical objection to such an hypothesis#dgi4 ,if the ,vital ,principle be the same in all parts of the body1 how does it happen1 it is asked1 that the secretions are so different8 ,how do the particles in the blood1 separated from their old compounds and united into new ones1 under the same influence1 give origin to all the different fluids which are produced by the glands8 ,the liver secretes bile1 the lacrymal gland1 tears1 and so on4 ,is the ,vital ,principle different in all these organs8 ,to assert this1 is to multiply nominal principles without limit1 and without any advance in the explanation of facts4 ,is the ,vital ,principle the same1 but its operation modified by the structure of the organ8 ,we have then two unknown causes1 the ,vital ,principle and the ,organic ,structure1 to account1 for the effect4 ,by such a multiplication of hypotheses nothing is gained4 ,we may as well say at once1 that the structure of the organ1 acting by laws yet unknown1 is the cause of the peculiar secretion4 ,it is as easy to imagine this structure acting to produce the whole effect1 as it is to imagine it modifying the activity of another agent4 ,thus the hypothesis of the ,vital ,fluid in this form explains nothing1 and does not in any #aij way help onwards the progress of real biological knowledge4 ,note #dgi3 ,prichard1 ,on a ,vital ,principle1 p4 #ih4 ,the hypothesis of an immaterial vital principle must now be considered4 ,,sect4 ,v4--,the ,psychical ,school4 ,the doctrine of an ,animal ,soul as the principle which makes the operations of organic different from those of inorganic matter1 is quite distinct from1 and we may say independent of1 the doctrine of the soul as the intelligent1 moral1 responsible part of man's nature4 ,it is the former doctrine alone of which we have here to speak1 and those who thus hold the existence of an immaterial agent as the cause of the phenomena of life1 ,i term the ,psychical ,school4 ,such a view of the constitution of living things is very ancient4 ,for instance1 ,aristotle's ,treatise ',on the ,soul1' goes entirely upon the supposition that the ,soul is the cause of motion1 and he arrives at the conclusion that there are different parts in the ,soul2 the nutritive or vegetative1 the sensitive1 and the rational#dhi4 ,note #dhi3 ,aristotle4 1 ii4 #b4 ,but this doctrine is more instructive to us1 when it appears as the antagonist of other opinions concerning the nature of life4 ,in this form it comes before us as promulgated by ,stahl1 whom we have already noticed as one of the great discoverers in chemistry4 ,born in the same year as ,hoffmann1 and appointed at his suggestion professor at the same time in the same new university of ,halle1 he soon published a rival physiological theory4 ,in a letter to ,lucas ,schrck1 the president of the ,academy of ,naturalists1 he describes the manner in which he was led to form a system for himself#dii4 ,educated in the tenets of ,sylvius and ,willis1 according to which all diseases are derived from the acidity of the fluids1 ,stahl1 when a young student1 often wondered how these fluids1 so liable to be polluted and corrupted1 are so wonderfully preserved through innumerable external influences1 and seem to #aia be far less affected by these than by age1 constitution1 passion4 ,no material cause could1 he thought1 produce such effects4 ,no attention to mechanism or chemistry alone could teach us the true nature and laws of organization4 ,note #dii3 ,spr4 v4 #cjc4 ,so far as ,stahl recognized the influence1 in living bodies1 of something beyond the range of mechanics and chemistry1 there can be no doubt of the sound philosophy of his views2 but when he proceeds to found a positive system of physiology1 his tenets become more precarious4 ,the basis of his theory is this#eji3 the body has1 as body1 no power to move itself1 and must always be put in motion by immaterial substances4 ,all motion is a spiritual act#eai4 ,the source of all activity in the organic body1 from which its preservation1 the permanency of its composition1 and all its other functions proceed1 is an immaterial being1 which ,stahl calls the ,soul2 because1 as he says1 when the effects are so similar1 he will not multiply powers without necessity4 ,of this principle1 he says1 as the ,hippocratians said of ,nature1 that 'it does without teaching what it ought to do#ebi1' and does it 'without consideration#eci4' ,these ancient tenets ,stahl interprets in such a manner that even the involuntary motions proceed from the soul1 though without reflection or clear consciousness4 ,it is indeed evident1 that there are many customary motions and sensations which are perfectly rational1 yet not the objects of distinct consciousness3 and thus instinctive motions1 and those of which we are quite unconscious1 may still be connected with reason4 ,the questions which in this view offer themselves1 as1 how the soul passes from the mother to the child1 he dismisses as unprofitable#edi4 ,he considers nutrition and secretion as the work of the soul4 ,the corpuscular theory and the doctrine of animal spirits #aib are1 he rightly observes1 mere hypotheses1 which are arbitrary in their character1 and only shift the difficulty4 ,for1 if the animal spirits are not matter1 how can they explain the action of an immaterial substance on the body2 and if they are matter1 how are they themselves acted on8 ,note #eji3 ,spr4 v4 #cjh ,note #eai3 ,ib4 v4 #cad4 ,note #ebi3 ,stahl1 4 ,note #eci3 4 ,note #edi3 ,this was of course an obvious problem4 ,harvey1 ,on ,generation ,exercise #bg1 p4 #adh1 teaches1 ',that the egg is not the production of the womb1 but of the soul4' ,this doctrine of the action of the soul on the body1 was accepted by many persons1 especially by the iatromathematicians1 who could not but feel the insufficiency of their system without some such supplement3 such were ,cheyne and ,mead4 ,in ,germany1 ,stahl's disciples in physiology were for the most part inconsiderable persons#eei4 ,several ,englishmen who speculated concerning the metaphysics as well as the physiology of ,sensation and ,motion1 inclined to this psychical view1 as ,porterfield and ,whytt4 ,among the ,french1 ,boissier de ,sauvages was the most zealous defender of the ,stahlian system4 ,actions1 he says#efi1 which belong to the preservation of life are determined by a moral not a mechanical necessity4 ,they proceed from the soul1 but cannot be controlled by it1 as the starting from fear1 or the trembling at danger4 ,unzer1 a physician at ,altona#egi1 was also a philosophical ,stahlian#ehi4 ,note #eei3 ,spr4 v4 #cci1 c4 ,note #efi3 ,ib4 #ceh4 ,note #egi3 ,a4,d4 #agii ,note #ehi3 ,spr4 v4 #cfj4 ,we need not dwell on the opposition which was offered to this theory1 first by ,hoffmann1 and afterwards by ,haller4 ,the former of these had promulgated1 as we have seen1 the rival theory of a ,nervous ,fluid1 the latter was the principal assertor of the doctrine of ,irritability1 an important theory on which we may afterwards have to touch4 ,haller's animosity against the ,stahlian hypothesis is a remarkable feature in one who is in general so tolerant in his judgment of opinions4 ,his arguments are taken from the absence of the control of the will over the vital actions1 from the want of consciousness accompanying these actions1 from the uniformity of them in different conditions of the mind1 and from the small sensibility of #aic the heart which is the source of the vital actions4 ,these objections1 and the too decided distinction which ,haller made between voluntary and involuntary muscles1 were very satisfactorily answered by ,whytt and ,platner4 ,in particular it was urged that the instinctive actions of brutes are inexplicable by means of mechanism1 and may be compared with the necessary vital actions of the human body4 ,neither kind are accidental1 neither kind are voluntary1 both are performed without reflection4 ,without tracing further the progress of the ,psychical ,doctrine1 ,i shall borrow a few reflections upon it from ,sprengel#eii3-- ',when the opponents of the ,stahlian system repeat incessantly that the assumption of a psychical cause in corporeal effects is a metaphysical speculation which does not belong to medicine1 they talk to no purpose4 ,the states of the soul are objects of our internal experience1 and interest the physician too nearly to allow him to neglect them4 ,the innumerable unconscious efforts of the soul1 the powerful and daily effects of the passions upon the body1 too often put to confusion those who would expel into the region of metaphysics the dispositions of the mind4 ,the connexion of our knowledge of the soul1 as gathered from experience1 with our knowledge of the human body1 is far closer than the mechanical and chemical physiologists suspect4 ,note #eii3 ,spr4 v4 #chc4 ',the strongest objection against the psychical system1 and one which has never been sufficiently answered by any of its advocates1 is the universality of organic effects in the vegetable kingdom4 ,the comparison of the physiology of plants with the physiology of animals puts the latter in its true light4 ,without absolutely trifling with the word soul1 we cannot possibly derive from a soul the organic operations of vegetables4 ,but just as little can we1 as some ,stahlians have done1 draw a sharp line between plants and animals1 and ascribe the processes of the former to mere mechanism1 while #aid we derive the operations of the latter from an intellectual principle4 ,not to mention that such a line is not possible1 the rise of the sap and the alteration of the fluids of plants cannot be derived entirely from material causes as their highest origin4' ,thus1 ,i may add1 this psychical theory1 however difficult to defend in its detail1 does in its generalities express some important truths respecting the vital powers4 ,it not only1 like the last theory1 gives unity to the living body1 but it marks1 more clearly than any other theory1 the wide interval which separates mechanical and chemical from vital action1 and fixes our attention upon the new powers which the consideration of life compels us to assume4 ,it not only reminds us that these powers are elevated above the known laws of the material world1 but also that they are closely connected with the world of thought and feeling1 of will and reason2 and thus it carries us1 in a manner in which none of the preceding theories have done1 to a true conception of a living1 conscious1 sentient1 active individual4 ,at the same time we cannot but allow that the life of plants and of the lower orders of animals shows us very clearly that1 in order to arrive at any sound and consistent knowledge respecting life1 we must form some conception of it from which all the higher attributes which the term 'soul' involves1 are utterly and carefully excluded2 and therefore we cannot but come to the conclusion that the psychical school are right mainly in this2 that in ascribing the functions of life to a soul1 they mark strongly and justly the impossibility of ascribing them to any known attributes of body4 #aie ,,chapter ,,iii4 ,,attempts ,,to ,,analyse ,,the ,,idea ,,of ,,life4 #a4 ,definitions of ,life4--,,we have seen in the preceding chapter that all attempts to obtain a distinct conception of the nature of ,life in general have ended in failure1 and produced nothing beyond a negative result4 ,and the conjecture may now naturally occur1 that the cause of this failure resides in an erroneous mode of propounding to ourselves the problem4 ,instead of contemplating ,life as a single ,idea1 it may perhaps be proper to separate it into several component notions3 instead of seeking for one cause of all vital operations1 it may be well to look at the separate vital functions1 and to seek their causes4 ,when the view of this possibility opens upon us1 how shall we endeavour to verify it1 and to take advantage of it8 ,let us1 as one obvious course1 take some of the attempts which have been made to define ,life1 and let us see whether they appear to offer to us any analysis of the idea into component parts4 ,such definitions1 when they proceed from men of philosophical minds1 are the ultimate result of a long course of thought and observation2 and by no means deserve to be slighted as arbitrary selections of conditions1 or empty forms of words4 #b4 ,life has been defined by ,stahl#fji1 ',the condition by which a body resists a natural tendency to chemical changes1 such as putrefaction4' ,in like manner1 ,m4 von ,humboldt#fai defines living bodies to be 'those which1 notwithstanding the constant operation #aif of causes tending to change their form1 are hindered by a certain inward power from undergoing such change4' ,the first of these definitions amounts only to the assertion1 that vital processes are not chemical2 a negative result1 which we may accept as true1 but which is1 as we have seen1 a barren truth4 ,the second appears to be1 in its import1 identical with the first4 ,an inward principle can only be understood as distinguished from known external powers1 such as mechanical and chemical agencies4 ,or if1 by an internal principle1 we mean such a principle as that of which we are conscious within ourselves1 we ascribe a soul to all living things3 an hypothesis which we have seen is not more effective than the former in promoting the progress of biological science4 ,nearly the same criticism applies to such definitions as that of ,kant3 that ',life is an internal faculty producing change1 motion1 and action4' ,note #fji3 ,treviranus1 ,biologie1 p4 #ai4 ,stahlii1 9999,theor4 ,med4 p4 #bed4 ,note #fai3 ,aphorismen aus d4 ,chem4 ,physiol4 der ,pflanzen1 s4 #a4 ,other definitions refer us1 not to some property residing in the whole of an organized mass1 but to the connexion and relation of its parts4 ,thus ,m4 von ,humboldt#fbi has given another definition of a living body3 that 'it is a whole whose parts1 arbitrarily separated1 no longer resist chemical changes4' ,but this additional assertion concerning the parts1 adds nothing of any value to the definition of the whole4 ,and in some of the lower kinds of plants and animals it is hardly true as a fact4 ,note #fbi3 ,versuche ber die gereitzte ,muskel und ,nervenfser1 b4 ii4 p4 #dcc4 #c4 ,another definition#fci places the character of ,life in 'motions serviceable to the body moved4' ,to this it has been objected#fdi1 that1 on this definition1 the earth and the planets are living bodies4 ,perhaps it would be more philosophical to object to the introduction of so loose a notion as that of a property being serviceable to a body4 ,we might also add1 that if we speak of all vital functions as motions1 we make an assumption quite unauthorized1 and probably false4 ,note #fci3 ,erhard1 ,rschlaub's ,magazin der ,heilkunde1 b4 i4 st4 #a4 p4 #fi4 ,note #fdi3 ,treviranus1 ,biologie1 p4 #da4 #aig ,other definitions refer the idea of ,life to the idea of ,organization4 ',life is the activity of matter according to laws of organization#fei4' ,we are then naturally led to ask1 ,what is ,organization8 ,in reply to this is given us the ,kantian definition of ,organization1 which ,i have already quoted elsewhere#ffi1 ',an organized product of nature is that in which all the parts are mutually ends and means#fgi4' ,that this definition involves exact fundamental ideas1 and is capable of being made the basis of sound knowledge1 ,i shall hereafter endeavour to show4 ,but ,i may observe that such a definition leads us somewhat further4 ,if the parts of organized bodies are known to be means to certain ends1 this must be known because they fulfil these ends1 and produce certain effects by the operation of a certain cause or causes4 ,the question then recurs1 what is the cause which produces such effects as take place in organized or living bodies8 and this is identical with the problem of which in the last chapter we traced the history1 and related the failure of physiologists in all attempts at its solution4 ,note #fei3 ,schmid1 ,physiologie1 b4 ii4 p4 #bgd4 ,note #ffi3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 viii4 s4 #b4 ,note #fgi3 ,kant1 ,urtheilskraft1 p4 #bif4 #d4 ,but what has been just said suggests to us that it may be an improvement to put our problem in another shape3--not to take for granted that the cause of all vital processes is one1 but to suppose that there may be several separate causes at work in a living body4 ,if this be so1 life is no longer one kind of activity1 but several4 ,we have a number of operations which are somehow bound together1 and life is the totality of all these3 in short1 life is not one ,function1 but a ,system of ,functions4 #e4 ,we are thus brought very near to the celebrated definition of life given by ,bichat#fhi3 ',life is the sum of the functions by which death is resisted4' ,but upon the definition thus stated1 we may venture to observe2--first1 that the introduction of the notion of #aih death in order to define the notion of life appears to be unphilosophical4 ,we may more naturally define death with reference to life1 as the cessation of life2 or at least we may consider life and death as correlative and interdependent notions4 ,again1 the word 'sum1' used in the way in which it here occurs1 appears to be likely to convey an erroneous conception1 as if the functions here spoken of were simply added to each other1 and connected by co-existence4 ,it is plain that our idea of life involves more than this3 the functions are all clearly connected1 and mutually depend on each other2 nutrition1 circulation1 locomotion1 reproduction1--each has its influence upon all the others4 ,these functions not merely co-exist1 but exist with many mutual relations and connexions2 they are continued so as to form1 not merely a sum1 but a system4 ,and thus we are led to modify ,bichat's definition1 and to say that ,life is the system of vital functions4 ,note #fhi3 ,physiological ,researches on ,life and ,death4 #f4 ,but it will be objected that by such a definition we explain nothing3 the notion of vital functions1 it may be said1 involves the idea of life1 and thus brings us round again to our starting-point4 ,or if not1 at least it is as necessary to define ,vital ,functions as to define ,life itself1 so that we have made little progress in our task4 ,to this we reply1 that if any one seeks1 upon such subjects1 some ultimate and independent definition from which he can1 by mere reasoning1 deduce a series of conclusions1 he seeks that which cannot be found4 ,in the ,inductive ,sciences1 a ,definition does not form the basis of reasoning1 but points out the course of investigation4 ,the definition must include words2 and the meaning of these words must be sought in the progress and results of observations1 as ,i have elsewhere said#fii4 ',the meaning of words is to be sought in the progress of thought2 the history of science is our dictionary2 the steps of scientific induction are our definitions4' ,it will appear1 ,i think1 that it is more easy for us to form an idea of a separate ,function of the #aii animal frame1 as ,nutrition or ,reproduction1 than to comprehend ,life in general under any single idea4 ,and when we say that ,life is a system of ,vital ,functions1 we are of course directed to study these functions separately1 and 7as in all other subjects of scientific research7 to endeavour to form of them such clear and definite ideas as may enable us to discover their laws4 ,note #fii3 ,hist4 ,ind4 ,sc4 b4 xiii4 c4 ix4 #g4 ,the view to which we are thus led1 of the most promising mode of conducting the researches of ,biology1 is one which the greatest and most philosophical physiologists of modern times have adopted4 ,thus ,cuvier considers this as the true office of physiology at present4 ',it belongs to modern times1' he says1 'to form a just classification of the vital phenomena2 the task of the present time is to analyse the forces which belong to each organic element1 and upon the zeal and activity which are given to this task1 depends1 according to my judgment1 the fortune of physiology#gji4' ,this classification of the phenomena of life involves1 of course1 a distinction and arrangement of the vital functions2 and the investigation of the powers by which these functions are carried on1 is a natural sequel to such a classification4 ,note #gji3 ,hist4 ,sc4 ,nat4 dep4 #aghi1 i4 #bah4 #h4 ,classification of ,functions4--,attempts to classify the ,vital ,functions of man were made at an early period1 and have been repeated in great number up to modern times4 ,the task of classification is exposed to the same difficulties1 and governed by the same conditions1 in this as in other subjects4 ,here1 as in the case of other things1 there may be many classifications which are moderately good and natural1 but there is only one which is the best and the true natural system4 ,here1 as in other cases1 one classification brings into view one set of relations2 another1 another2 and each may be valuable for its special purpose4 ,here1 as in other cases1 the classes may be well constituted1 though the boundary lines which divide them be somewhat indistinct1 and the order doubtful4 ,here1 #bjj as in other cases1 we may have approached to the natural classification without having attained it2 and here1 as in other cases1 to define our classes is the last and hardest of our problems4 #i4 ,the most ancient classification of the ,functions of living things#gai1 is the division of them into ,vital1 ,natural1 and ,animal4 ,the ,vital ,functions are those which cannot be interrupted without loss of life1 as ,circulation1 ,respiration1 and ,nervous ,communication4 ,the ,natural ,functions are those which without the intervention of the will operate on their proper occasions to preserve the bodies of animals2 they are ,digestion1 ,absorption1 ,nutrition2 to which was added ,generation4 ,the ,animal ,functions are those which involve perception and will1 by which the animal is distinguished from the vegetable2 they are ,sensibility1 ,locomotion1 and ,voice4 ,note #gai3 ,dict4 des ,sciences ,nat4 art4 ,fonctions4 ,the two great grounds of this division1 the distinction of functions which operate continually1 and those which operate occasionally2 and again1 the distinction of functions which involve sensation and voluntary motion from those which do not2 are truly of fundamental importance1 and gave a real value to this classification4 ,it was1 however1 liable to obvious objections3 namely1 ,first1 that the names of the classes were ill chosen2 for all the functions are natural1 all are vital3 ,second1 that the lines of demarcation between the classes are indefinite and ambiguous2 ,respiration is a vital function1 as being continually necessary to life2 but it is also a natural function1 since it occurs in the formation of the nutritive fluid1 and an animal function1 since it depends in part on the will4 ,but these objections were not fatal1 for a classification may be really sound and philosophical1 though its boundary lines are vague1 and its nomenclature ill selected4 ,the division of the functions we have mentioned kept its ground long2 or was employed with a subdivision of one class1 so as to make them four2 the vital1 natural1 animal and sexual functions4 #bja #aj4 ,i pass over many intermediate attempts to classify the functions1 and proceed to that of ,bichat as that which is1 ,i believe1 the one most generally assented to in modern times4 ,the leading principle in the scheme of this celebrated physiologist is the distinction between organic and animal life4 ,this separation is nearly identical with the one just noticed between the vital and animal functions2 but ,bichat1 by the contrasts which he pointed out between these classes of functions1 gave a decided prominence and permanence to the distinction4 ,the ,organic ,life1 which in animals is analogous to the life of vegetables1 and the ,animal ,life1 which implies sensation and voluntary motion1 have each its system of organs4 ,the center of the animal life is the brain1 of the organic life1 the heart4 ,the former is carried on by a symmetrical1 the latter1 by an unsymmetrical system of organs3 the former produces intermitting1 the latter continuous actions3 and1 in addition to these1 other differences are pointed out4 ,this distinction of the two lives1 being thus established1 each is subdivided into two orders of ,functions4 ,the ,animal ,functions are passive1 as ,sensation3 or active1 as ,locomotion and ,voice2 again1 the ,organic ,functions are those of ,composition1 which are concerned in taking matter into the system2 ,digestion1 ,absorption1 ,respiration1 ,circulation1 ,assimilation2 and those of ,decomposition1 which reject the materials when they have discharged their office in the system2 and these are again1 ,absorption1 ,circulation1 and ,secretion4 ,to these are added ,calorification1 or the production of animal heat4 ,it appears1 from what has been said1 that ,absorption and ,circulation 7and we may add ,assimilation and ,secretion1 which are difficult to separate17 belong alike to the processes of composition and decomposition2 nor in truth1 can we1 with any rigour1 separate the centripetal and centrifugal movements in that vortex which1 as we shall see1 is an apt image of organic life4 ,several objections have been made to this classification3 and in particular1 to the terms thus employed4 ,it has been asserted to be a perversion of language to #bjb ascribe to animals two lives1 and to call the higher faculties in man1 perception and volition1 the animal functions4 ,but1 as we have already said1 when a classification is really good1 such objections1 which bear only upon the mode in which it is presented1 are by no means fatal3 and it is generally acknowledged by all the most philosophical cultivators of biology1 that this arrangement of the functions is better suited to the purposes of the science than those which preceded it4 #aa4 ,but according to the principles which we have already laid down1 the solidity of such a classification is to be verified by its serving as a useful guide in biological researches4 ,if the arrangement which we have explained be really founded in natural relations1 it will be found that in proportion as physiologists have studied the separate functions above enumerated1 their ideas of these functions1 and of the powers by which they are carried on1 have become more and more clear2--have tended more and more to the character of exact and rigorous science4 ,to examine how far this has been the case with regard to all the separate functions1 would be to attempt to estimate the value of all the principal physiological speculations of modern times2 a task far too vast and too arduous for any one to undertake who has not devoted his life to such studies4 ,but it may properly come within the compass of our present plan to show how1 with regard to the broader lines of the above classification1 there has been such a progress as we have above described1 from more loose and inaccurate notions of some of the vital functions to more definite and precise ideas4 ,this ,i shall attempt to point out in one or two instances4 #bjc ,,chapter ,,iv4 ,,attempts ,,to ,,form ,,ideas ,,of ,,separate ,,vital ,,forces1 ,,and ,,first ,,of ,,assimilation ,,and ,,secretion4 ,,sect4 ,i4--,course of ,biological ,research4 #a4 ,,it is to be observed that at present ,i do not speak of the progress of our knowledge with regard to the detail of the processes which take place in the human body1 but of the approach made to some distinct ,idea of the specially vital part of each process4 ,in the ,history of ,physiology1 it has been seen#gbi that all the great discoveries made respecting the organs and motions of the animal frame have been followed by speculations and hypotheses connected with such discoveries4 ,the discovery of the circulation of the blood led to theories of animal heat2 the discovery of the motion of the chyle led to theories of digestion2 the close examination of the process of reproduction in plants and animals led to theories of generation4 ,in all these cases1 the discovery brought to light some portion of the process which was mechanical or chemical1 but it also1 in each instance1 served to show that the process was something more than mechanical or chemical4 ,the theory attempted to explain the process by the application of known causes2 but there always remained some part of it which must unavoidably be referred to an unknown cause4 ,but though unknown1 such a cause was not a hopeless object of study4 ,as the vital functions became better and better understood1 it was seen more and more clearly at what precise points of the process it was necessary to assume a peculiar vital energy1 and what sort of properties #bjd this energy must be conceived to possess4 ,it was perceived where1 in what manner1 in what degree1 mechanical and chemical agencies were modified1 over-ruled1 or counteracted1 by agencies which must be hypermechanical and hyperchemical4 ,and thus the discoveries made in anatomy by a laborious examination of facts1 pointed out the necessity of introducing new ideas1 in order that the facts might be intelligible4 ,observation taught much2 and among other things1 she taught that there was something which could not be observed1 but which must1 if possible1 be conceived4 ,i shall notice a few instances of this4 ,note #gbi3 ,hist4 ,ind4 ,sc4 b4 xvii4 ,,sect4 ,,ii4--,attempts to form a distinct ,conception of ,assimilation and ,secretion4 #b4 ,the ,ancients4--,that plants and animals grow by taking into their substance matter previously extraneous1 is obvious to all3 but as soon as we attempt to conceive this process distinctly in detail1 we find that it involves no inconsiderable mystery4 ,how does the same food become blood and flesh1 bone and hair8 ,perhaps the earliest attempt to explain this mystery1 is that recorded by ,lucretius#gci as the opinion of ,anaxagoras1 that food contains some bony1 some fleshy particles1 some of blood1 and so on4 ,we might1 on this supposition1 conceive that the mechanism of the body appropriates each kind of particle to its suitable place4 ,note #gci3 ,lucr4 i4 #hee4 ,nunc et ,anaxagor scrutemur 4 ,but it is easy to refute this essay at philosophizing 7as ,lucretius refutes it7 by remarking that we do not find milk in grass1 or blood in fruit1 though such food gives such products in cattle and in men4 ,in opposition to this ',homoiomereia1' the opinion that is forced upon us by the facts is1 that the process of nutrition is not a selection merely1 but an assimilation2 the organized system does not find1 but make1 the additions to its structure4 #bje #c4 ,buffon4--,this notion of assimilation may be variously expressed and illustrated2 and all that we can do here1 in order to show the progress of thought1 is to adduce the speculations of those writers who have been most successful in seizing and marking its peculiar character4 ,buffon may be taken as an example of the philosophy of his time on this subject4 ',the body of the animal1' says he#gdi1 'is a kind of interior mould1 in which the matter subservient to its increase is modelled and assimilated to the whole1 in such a way that1 without occasioning any change in the order and proportion of the parts1 there results an augmentation in each part taken separately4 ,this increase1 this development1 if we would have a clear idea of it1 how can we obtain it1 except by considering the body of the animal1 and each of the parts which is to be developed1 as so many interior moulds which only receive the accessory matter in the order which results from the position of all their parts8 ,this development cannot take place1 as persons sometimes persuade themselves1 by an addition to the outside2 on the contrary1 it goes on by an intimate susception which penetrates the mass2 for1 in the part thus developed1 the size increases in all parts proportionally1 so that the new matter must penetrate it in all its dimensions3 and it is quite necessary that this penetration of substance must take place in a certain order1 and according to a certain measure2 for if this were not so1 some parts would develope themselves more than others4 ,now what can there be which shall prescribe such a rule to the accessory matter except the interior mould8' ,note #gdi3 ,hist4 ,nat4 b4 i4 c4 iii4 ,to speak of a mould simply1 would convey a coarse mechanical notion1 which could not be received as any useful contribution to physiological speculation4 ,but this interior mould is1 of course1 to be understood figuratively1 not as an assemblage of cavities1 but as a collection of laws1 shaping1 directing1 and modifying the new matter2 giving it not only form1 but motion #bjf and activity1 such as belong to the parts of an organic being4 #d4 ,it must be allowed1 however1 that even with this explanation1 the comparison is very loose and insufficient4 ,a mould may be permitted to mean a collection of laws1 but still it can convey no conception except that of laws regulated by relations of space2 and such a conception is very plainly quite inadequate to the purpose4 ,what can we conceive of the interior mould by which chyle is separated from the aliments at the pores of the lacteals1 or tears secreted in the lacrymatory gland8 ,an additional objection to this mode of expression of ,buffon is1 that it suggests to us only a single marked change in the assimilated matter1 not a continuous series of changes4 ,yet the animal fluids and other substances are1 in fact1 undergoing a constant series of changes4 ,food becomes chyme1 and chyme becomes chyle2 chyle is poured into the blood2 from the blood secretions take place1 as the bile2 the bile is poured into the digestive canal1 and a portion of the matter previously introduced is rejected out of the system4 ,here we must have a series of 'interior moulds2' and these must impress matter at its ejection from the organic system as well as at its reception4 ,but1 moreover1 it is probable that none of the above transformations are quite abrupt4 ,change is going on between the beginning and the end of each stage of the nutritive circulation4 ,to express the laws of this continuous change1 the image of an interior mould is quite unsuited4 ,we must seek a better mode of conception4 #e4 ,vegetable and animal nutrition is1 as we have said1 a constant circulation4 ,the matter so assumed is not all retained3 a perpetual subtraction accompanies a perpetual addition4 ,there is an excretion as well as an intussusception4 ,the matter which is assumed by the living creature is retained only for a while1 and is then parted with4 ,the individual is the same1 but its parts are in a perpetual flux3 they come and go4 ,for a time the matter which belongs to the organic body is bound to it by certain laws3 but before it is thus bound1 and #bjg after it is loose1 this matter may circulate about the universe in any other form4 ,life consists in a permanent influence over a perpetually changing set of particles4 ,cuvier4--,this condition also has been happily expressed1 by means of a comparison1 by another great naturalist4 ',if1' says ,cuvier#gei1 'if1 in order to obtain a just idea of the essence of life1 we consider it in the beings where its effects are most simple1 we shall soon perceive that it consists in the faculty which belongs to certain bodily combinations to continue during a determinate time under a determinate form2 constantly attracting into their composition a part of the surrounding substances1 and giving up in return some part of their own substance4 ,note #gei3 ,rgne ,animal1 i4 #aa4 ',life is thus a vortex1 more or less rapid1 more or less complex1 which has a constant direction1 and which always carries along its stream particles of the same kinds2 but in which the individual particles are constantly entering in and departing out2 so that the form of the living body is more essential to it than its matter4 ',so long as this motion subsists1 the body in which it takes place is alive2 it lives4 ,when the motion stops finally1 the body dies4 ,after death1 the elements which compose the body1 given up to the ordinary chemical affinities1 soon separate1 and the body which was alive is dissolved4' ,this notion of a vortex#gfi which is permanent while the matter which composes it constantly changes1--of peculiar forces which act in this vortex so long as it exists1 and which give place to chemical forces when #bjh the circulatory motion ceases1--appears to express some of the leading conditions of the assimilative power of living things in a simple and general manner1 and thus tends to give distinctness to the notion of this vital function4 ,note #gfi3 ,the definition of life given by ,m4 de ,blainville appears to me not to differ essentially from that of ,cuvier3 ',un corps vivant est une sorte de foyer chimique o il-y-a tous momens apport de nouvelles molecules et dpart de molecules anciennes2 o la composition n'est jamais fixe 7si ce n'est d'un certain nombre de parties veritablement mortes ou en dept71 mais toujours pour ainsi dire in nisu1 d'o mouvement plus ou moins lent et quelquefois chaleur4'--,principes d',anat4 #ahbb1 t4 i4 p4 #af4 #f4 ,but we may observe that this notion of a ,vortex is still insufficient4 ,particles are not only taken into the system and circulated through it for a time1 but1 as we have seen1 they are altered in character in a manner to us unintelligible1 both at their first admission into the system and at every period of their progress through it4 ,in the vortex each particle is constantly transformed while it whirls4 ,it may be said1 perhaps1 that this transformation of the kinds of matter may be conceived to be merely a new arrangement of their particles1 and that thus all the changes which take place in the circulating substances are merely so many additional windings in the course of the whirling current4 ,but to say this1 is to take for granted the atomic hypothesis in its rudest form4 ,what right have we to assume that blood and tears1 bile and milk1 consist of like particles of matter differently arranged8 ,what can arrangement1 a mere relation of space1 do towards explaining such differences8 ,is not the insufficiency1 the absurdity of such an assumption proved by the whole course of science8 ,are not even chemical changes1 according to the best views hitherto obtained1 something more than a mere new arrangement of particles8 ,and are not vital as much beyond chemical1 as chemical are beyond geometrical modifications8 ,it is not enough1 then1 to conceive life as a vortex4 ,the particles which are taken into the organic frame do more than circulate there4 ,they are1 at every point of their circulation1 acted upon by laws of an unknown kind1 changing the nature of the substance which they compose4 ,life is a vortex in which vital forces act at every point of the stream3 it is not only a current of whirling matter1 but a cycle of recurring powers4 #g4 ,matter and ,form4--,this image of a vortex is closely connected with the representation of life offered #bji us by writers of a very different school4 ,in ,schelling's ,lectures on ,academic ,study1 he takes a survey of the various branches of human knowledge1 determining according to his own principles the shape which each science must necessarily assume4 ,the peculiar character of organization1 according to him#ggi1 is that the matter is only an accident of the thing itself1 and the organization consists in ,form alone4 ,but this ,form1 by its very opposition to ,matter1 ceases to be independent of it1 and is only ideally separable4 ,in organization1 therefore1 substance and accident1 matter and form1 are completely identical#ghi4 ,this notion1 that in organization the ,form is essential and the ,matter accidental1 or1 in other words1 that the ,form is permanent and the ,matter fluctuating and transitory1 agrees1 if taken in the grossest sense of matter and form1 with ,cuvier's image of a ,vortex4 ,in a whirlpool1 or in a waterfall1 the form remains1 the matter constantly passes away and is renewed4 ,but we have already seen#gii that in metaphysical speculations in which matter and form are opposed1 the word form is used in a far more extensive sense than that which denotes a relation of space4 ,it may indeed designate any change which matter can undergo2 and we may very allowably say that food and blood are the same matter under different forms4 ,hence if we assert that ,life is a constant ,form of a circulating ,matter1 we express ,cuvier's notion in a mode free from the false suggestion which ',vortex' conveys4 ,note #ggi3 ,lect4 xiii4 p4 #bhh4 ,note #ghi3 ,i have not translated ,schelling's words1 but given their import as far as ,i could4 ,note #gii3 ,book i4 #h4 ,we may1 however1 still add something to this account of life4 ,the circulating parts of the system not only circulate1 but they form the non-circulating parts4 ,or rather1 there are no non-circulating parts3 all portions of the frame circulate more or less rapidly4 ,the food which we take circulates rapidly in the fluids1 more slowly in the flesh1 still more slowly in the bones2 but in all these parts it is taken into the system1 #baj retained there for some time1 and finally replaced by other matter4 ,but while it remains in the body1 it exercises upon the other circulating parts the powers by which their motion is produced4 ,nutriment forms and supports the organs1 and the organs carry fresh nutriment to its destination4 ,the peculiar forces of the living body1 and its peculiar structure1 are thus connected in an indescribable manner4 ,the forces produce the structure2 the structure1 again1 is requisite for the exertion of the forces4 ,the ,idea of an ,organic or ,living ,being includes this peculiar condition--that its construction and powers are such1 that it constantly appropriates to itself new portions of substance which1 so appropriated1 become indistinguishable parts of the whole1 and serve to carry on subsequently the same functions by which they were assimilated4 ,and thus ,organic ,life is a constant ,form of a circulating ,matter1 in which the ,matter and the ,form determine each other by peculiar laws 7that is1 by ,vital ,forces74 ,,sect4 ,,iii4--,attempts to conceive the forces of ,assimilation and ,secretion4 #i4 ,i have already stated that in our attempts to obtain clear and scientific ,ideas of ,vital ,forces1 we have1 in the first place1 to seek to understand the course of change and motion in each function1 so as to see at what points of the process peculiar causes come into play2 and next1 to endeavour to obtain some insight into the peculiar character and attributes of these causes4 ,having spoken of the first part of this mode of investigation in regard to the general nutrition of organic bodies1 ,i must now say a few words on the second part4 ,the ,forces here spoken of are ,vital ,forces4 ,from what has been said1 we may see in some measure the distinction between forces of this kind and mechanical or chemical forces2 the latter tend constantly to produce a final condition1 after which there is no further cause of change3 mechanical forces tend to produce equilibrium2 chemical forces tend to produce #baa composition or decomposition2 and this point once reached1 the matter in which these forces reside is altogether inert4 ,but an organic body tends to a constant motion1 and the highest activity of organic forces shows itself in continuous change4 ,again1 in mechanical and chemical forces1 the force of any aggregate is the sum of the forces of all the parts3 the sum of the forces corresponds to the sum of the matter4 ,but in organic bodies1 the amount of effect does not depend on the matter1 but on the form3 the particles lose their separate energy1 in order to share in that of the system2 they are not added1 they are assimilated4 #aj4 ,it is difficult to say whether anything has been gained to science by the various attempts to assign a fixed name to the vital force which is thus the immediate cause of ,assimilation4 ,it has been called ,organic ,attraction or ,vital ,attraction1 ,organic ,affinity or ,vital ,affinity1 being thus compared with mechanical ,attraction or chemical ,affinity4 ,but1 perhaps1 as the process is certainly neither mechanical nor chemical1 it is desirable to appropriate to it a peculiar name2 and the name ,assimilation1 or ,organic ,assimilation1 by the usage of good biological writers1 is generally employed for this purpose1 and may be taken as the standard name of this ,vital ,force4 ,to illustrate this1 ,i will quote a passage from the excellent ,elements of ,physiology of ,professor ,mller4 ',in the process of nutrition is exemplified the fundamental principle of organic assimilation4 ,each elementary particle of an organ attracts similar particles from the blood1 and by the changes it produces in them1 causes them to participate in the vital principle of the organ itself4 ,nerves take up nervous substance1 muscles1 muscular substance3 even morbid structures have the assimilating power2 warts in the skin grow with their own peculiar structure2 in an ulcer1 the base and border are nourished in a way conformable to the mode of action and secretion determined by the disease4' #aa4 ,the ,force of ,organic ,assimilation spoken of in the last paragraph denotes peculiarly the force by which each organ appropriates to itself a part of the #bab nutriment received into the system1 and thus is maintained and augmented with the growth of the whole4 ,but the growth of the solid parts is only one portion of the function of nutrition2 besides this1 we must consider the motion and changes of the fluids1 and must ask what kind of forces may be conceived to produce these4 ,what are the powers by which chyle is absorbed from the food1 by which bile is secreted from the blood1 by which the circulating motion of these and all other fluids of the body are constantly maintained8 ,to the questions1--,what are the forces by which absorption1 secretion1 and the vital motions1 of fluids are produced8--no satisfactory answer has been returned4 ,yet still some steps have been made1 which it may be instructive to point out4 #ab4 ,in ,absorption it would appear that a part of the agency is inorganic2 for not only dead membranes1 but inorganic substances1 absorb fluids1 and even absorb them with elective forces1 according to the ingredients1 of the fluid4 ,a force which is of this kind1 and which has been termed ,endosmose1 has been found to produce very curious effects4 ,when a membrane separates two fluids1 holding in solution different ingredients1 the fluids pass through the membrane in an imperceptible manner1 and mix or exchange their elements4 ,the force which produces these effects is capable of balancing a very considerable pressure4 ,it appears1 moreover1 to depend1 at least among other causes1 upon attractions operating between the elements of the solids and the fluids1 as well as between the different fluids2 and this force1 though thus apparently of a mechanical and chemical nature1 probably has considerable influence in vital phenomena4 #ac4 ,but still1 though ,endosmose may account in part for absorption in some cases1 it is certain that there is some other vital force at work in this process4 ,there must be1 as ,mller says#hji1 'an organic attraction of a kind hitherto unknown4' ',if absorption1' he adds#hai1 is to be explained in a manner analogous to #bac the laws of endosmose1 it must be supposed that a chemical affinity1 resulting from the vital process itself1 is exerted between the chyme in the intestines and the chyle in the lacteals1 by which the chyle is enabled to attract the chyme without being itself attracted by it4 ,but such affinity or attraction would be of a vital nature1 since it does not exist after death4' ,note #hji3 ,physiology1 p4 #bii4 ,note #hai3 ,ib4 p4 #cja4 #ad4 ,if the force of absorption be thus mysterious in its nature1 the force of ,secretion is still more so4 ,in this case we have an organ filled with a fine net-work of blood-vessels1 and in the cavities of some gland1 or open part1 we have a new fluid formed1 of a kind altogether different from the blood itself4 ,it is easily shown that this cannot be explained by any action of pores or capillary tubes4 ,but what conception can we form of the forces by which such a change is produced8 ,here1 again1 ,i shall borrow the expressions of ,mller1 as presenting the last result of modern physiology4 ,he says#hbi1 ',the more probable supposition is1 that by virtue of imbibition1 or the general organic porosity1 the fluid portion of the blood becomes diffused through the tissue of the secreting organ2 that the external surface of the glandular canals exerts a chemical attraction on the elements of the fluid1 infusing into them at the same time a tendency to unite in new combinations2 and then repels them in a manner which is certainly quite inexplicable1 towards the inner surface of the secreting membrane1 or glandular canals4' ',although quite unsupported by facts1' he adds1 'this theory of attraction and repulsion is not without its analogy in physical phenomena2 and it would appear that very similar powers effect the elimination of the fluid in secretion1 and cause it to be taken up by the lymphatics in absorption4' ,he elsewhere says#hci1 ',absorption seems to depend on an attraction the nature of which is unknown1 but of which the very counterpart1 as it were1 takes place in secretion2 the fluids altered by the secreting action being repelled towards the free side or open surface only of the #bad secreting membranes1 and then pressed forwards by the successive portions of the fluids secreted4' ,note #hbi3 ,physiology1 p4 #dfd4 ,note #hci3 ,ib4 p4 #cja4 #ae4 ,with regard to the forces which produce the ,motion of absorbed or secreted fluids along their destined course1 it may be seen1 from the last quoted sentence1 that the same vital force which changes the nature1 also produces the movement of the substance4 ,the fluids are pressed forwards by the successive portions absorbed or secreted4 ,that this is the sole cause1 or at least a very powerful cause1 of the motion of the nutritive fluids in organic bodies1 is easily shown by experience4 ,it is found#hdi that the organs which effect the ascent of the sap in trees during the spring are the terminal parts of the roots2 that the whole force by which the sap is impelled upwards is the vis a tergo1 as it has been called1 the force pushing from behind1 exerted in the roots4 ,and thus the force which produces this motion is exerted exactly at those points where the organic body selects from the contiguous mass those particles which it absorbs and appropriates4 ,and the same may most probably be taken for the cause of the motion of the lymph and chyle2 at least1 ,mller says#hei that no other motive power has been detected which impels those fluids in their course4 ,note #hdi3 ,mller1 p4 #cjj4 ,note #hei3 ,ib4 p4 #bed4 ,thus1 though we must confess the ,vital ,force concerned in ,assimilation and ,secretion to be unknown in its nature1 we still obtain a view of some of the attributes which it involves4 ,it has mechanical efficacy1 producing motions1 often such as would require great mechanical force4 ,but it exerts at the same point both an attraction and a repulsion1 attracting matter on one side1 and repelling it on the other2 and in this circumstance it differs entirely from mechanical forces4 ,again1 it is not only mechanical but chemical1 producing a complete change in the nature of the substance on which it acts2 to which we must add that the changes produced by the vital forces are such as1 for the most part1 our artificial chemistry #bae cannot imitate4 ,but1 again1 by the action of the vital force at any point of an organ1 not only are fluids made to pass1 and changed as they pass1 but the organ itself is maintained and strengthened1 so as to continue or to increase its operation3 and thus the vital energy supports its activity by its action1 and is augmented by being exerted4 ,we have thus endeavoured to obtain a view of some of the peculiar characters which belong to the ,force of ,organic ,assimilation2--the ,force by which life is kept up1 conceived in the most elementary form to which we can reduce it by observation and contemplation4 ,it appears that it is a force which not only produces motion and chemical change1 but also vitalizes the matter on which it acts1 giving to it the power of producing like changes on other matter1 and so on indefinitely4 ,it not only circulates the particles of matter1 but puts them in a stream of which the flow is development as well as movement4 ,the force of ,organic ,assimilation being thus conceived1 it becomes instructive to compare it with the force concerned in ,generation1 which we shall therefore endeavour to do4 ,,sect4 ,,iv4--,attempts to conceive the ,process of ,generation4 #af4 ,at first sight the function of ,nutrition appears very different from the function of ,generation4 ,in the former case we have merely the existing organs maintained or enlarged1 and their action continued2 in the latter1 we have a new individual produced and extricated from the parent4 ,the term ,reproduction has1 no doubt1 been applied1 by different writers1 to both these functions2--to the processes by which an organ when mutilated1 is restored by the forces of the living body1 and to the process by which a new generation of individuals is produced which may be considered as taking the place of the old generation1 as these are gradually removed by death4 ,but these are obviously different senses of the word4 ,in the latter case1 the #baf term ,reproduction is figuratively used2 for the same individuals are not reproduced2 but the species is kept up by the propagation of new individuals1 as in nutrition the organ is kept up by the assimilation of new matter4 ,to escape ambiguity1 ,i shall avoid using the term ,reproduction in the sense of ,propagation4 #ag4 ,in ,nutrition1 as we have seen1 the matter1 which from being at first extraneous1 is appropriated by the living system1 and directed to the sustentation of the organs1 undergoes a series of changes of which the detail eludes our observation and apprehension4 ,the nutriment which we receive contributes to the growth of flesh and bone1 viscera and organs of sense4 ,but we cannot trace in its gradual changes a visible preparation for its final office4 ,the portion of matter which is destined to repair the waste of the eye or the skin1 is not found assuming a likeness to the parts of the eye or the structure of the skin1 as it comes near the place where it is moulded into its ultimate form4 ,the new parts are insinuated among the old ones1 in an obscure and imperceptible matter4 ,we can trace their progress only by their effects4 ,the organs are nourished1 and that is almost all we can learn3 we cannot discover how this is done4 ,we cannot follow nature through a series of manifest preparations and processes to this result4 #ah4 ,in ,generation the case is quite different4 ,the young being is formed gradually and by a series of distinguishable processes4 ,it is included within the parent before it is extruded1 and approaches more or less to the likeness of the parent before it is detached4 ,while it is still an embryo1 it shares in the nutriment which circulates through the system of the mother2 but its destination is already clear4 ,while the new and the old parts1 in every other portion of the mother1 are undistinguishably mixed together1 this new part1 the ftus1 is clearly distinct from the rest of the system1 and becomes rapidly more and more so1 as the time goes on4 ,and thus there is formed1 not a new part1 but a new whole2 it is not an organ which is kept up1 but an offspring which is prepared4 ,the progeny is #bag included in the parent1 and is gradually fitted to be separated from it4 ,the young is at first only the development of a part of the organization of the mother2--of a germ1 an ovule4 ,but it is not developed like other organs1 retaining its general form4 ,it does not become merely a larger bud1 a larger ovule2 it is entirely changed2 it becomes--from a bud--a blossom1 a flower1 a fruit1 a seed2 from an ovule it becomes an egg1 a chick1 a bird2 or it may be1 a ftus1 a child4 ,the original rudiment is not merely nourished1 but unfolded and transformed through the most marked and remote changes1 gradually tending to the form of the new individual4 #ai4 ,but this is not all4 ,the ftus is1 as we have said1 a development of a portion of the mother's organization4 ,but the ftus 7supposing it female7 is a likeness of the mother4 ,the mother1 even before conception1 contains within herself the germs of her progeny2 the female ftus1 therefore1 at a certain stage of development1 will contain also the germs of possible progeny2 and thus we may have the germs of future generations1 pre-existing and included successively within one another4 ,and this state of things1 which thus suggests itself to us as possible1 is found to be the case in facts which observation supplies4 ,anatomists have traced ovules in the unborn ftus1 and thus we have three generations included one within another4 #bj4 ,supposing we were to stop here1 the process of propagation might appear to be altogether different from that of nutrition4 ,the latter1 as we have seen1 may be in some measure illustrated by the image of a vortex2 the former has been represented by the image of a series of germs1 sheathed one within another successively1 and this without any limit4 ,this view of the subject has been termed the doctrine of the ,pre-existence of germs2 and has been designated by ,german writers by a term ',einschachtelungs-theorie' descriptive of the successive sheathing of which ,i have spoken4 ,imitating this term1 we may call it the ,theory of successive inclusion4 ,it has always had many #bah adherents2 and has been1 perhaps1 up to the present time1 the most current opinion on the subject of generation4 ,cuvier inclines to this opinion#hfi4 ',fixed forms perpetuating themselves by generation distinguish the species of living things4 ,these forms do not produce themselves1 do not change themselves4 ,life supposes them to exist already2 its flame can be lighted only in organization previously prepared2 and the most profound meditations and the most delicate researches terminate alike in the mystery of the pre-existence of germs4' ,note #hfi3 ,rgne ,animal1 p4 #bj4 #ba4 ,yet this doctrine is full of difficulty4 ,it is1 as ,cuvier says1 a mysterious view of the subject2--so mysterious1 that it can hardly be accepted by us1 who seek distinct conceptions as the basis of our philosophy4 ,can it be true1 not only that the germ of the offspring is originally included in the parent1 but also the germs of its progeny1 and so on without limit3--so that each fruitful individual contains in itself an infinite collection of future possible individuals2--a reserve of infinite succeeding generations8 ,this is hard to admit4 ,have we no alternative8 ,what is the opposite doctrine8 #bb4 ,the opposite doctrine deserves at least some notice4 ,it extends1 to the production of a new individual1 the conception of growth by nutrition4 ,according to this view1 we suppose propagation to take place1 not as in the view just spoken of1 by inclusion and extrusion1 but by assimilation and development2--not by the material pre-existence of germs1 but by the communication of vital forces to new matter4 ,this opinion appears to be entertained by some of the most eminent physiologists of the present time4 ,thus1 ,mller says1 ',the organic force is also creative4 ,the organic force which resides in the whole1 and on which the existence of each part depends1 has also the property of generating1 from organic matter1 the parts necessary to the whole4' ,life1 he adds1 is not merely a harmony of the #bai parts4 ,on the contrary1 the harmonious action of the parts subsists only by the influence of a force pervading all parts of the body4 ',this force exists before the harmonizing parts1 which are in fact formed by it during the development of the embryo4' ,and again2 ',the creative force exists in the germ1 and creates in it the essential force of the future animal4 ,the germ is potentially the whole animal3 during the development of the germ the parts which constitute the actual whole are produced4' #bc4 ,in this view1 we extend to the reproduction of an individual the same conception of organic assimilation which we have already arrived at1 as the best notion we can form of the force by which the reproduction and sustentation of parts takes place4 ,and is not such an extension really very consistent8 ,if a living thing can appropriate to itself extraneous matter1 invest it with its own functions1 and thus put it in the stream of constant development1 may we not conceive the development of a new whole to take place in this way as well as of a part8 ,if the organized being can infuse into new matter its vital forces1 is there any contradiction in supposing this infusion to take place in the full measure which is requisite for the production of a new individual8 ,the force of organic assimilation is transferred to the very matter on which it acts2 it may be transferred so that the operation of the forces produces not only an organ1 but a system of organs4 #bd4 ,this identification of the forces which operate in ,nutrition and ,generation may at first seem forced and obscure1 in consequence of the very strong apparent differences of the two processes which we have already noticed4 ,but this defect in the doctrine is remedied by the consideration of what may be considered as intermediate cases4 ,it is not true that1 in the nutrition of special organs1 the matter is always conveyed to its ultimate destination without being on its way moulded into the form which it is finally to bear1 as the embryo is moulded into the form of the #bbj future individual4 ,on the contrary1 there are cases in which the waste of the organs is supplied by the growth of new ones1 which are prepared and formed before they are used1 just as the offspring is prepared and formed before it is separated from the parent4 ,this is the case with the teeth of many animals1 and especially with the teeth of animals of the crocodile kind4 ,young teeth grow near the root of the old ones1 like buds on the stem of a plant2 and as these become fully developed1 they take the place of the parent tooth when that dies and is cast away4 ,and these new teeth in their turn are succeeded by others which germinate from them4 ,several generations of such teeth1 it is said as many as four1 have been detected by anatomists1 visibly existing at the same time2 just as several generations of germs of individuals have been1 as we already stated1 observed included in one another4 ,but this case of the teeth appears to show very strikingly how insufficient such observations are to establish the doctrine of successive inclusion1 or of the pre-existence of germs4 ,are we to suppose that every crocodile's tooth includes in itself the germs of an infinite number of possible teeth1 as in the theory of pre-existing germs every individual includes an infinite number of individuals8 ,if this be true of teeth1 we must suppose that organ to follow laws entirely different from almost every other organ2 for no one would apply to the other organs in general such a theory of reproduction4 ,but if such a theory be not maintained respecting the teeth1 how can we maintain the theory of the pre-existing germs of individuals1 which has no recommendation except that of accounting for exactly the same phenomena8 ,it would seem1 then1 that we are1 by the closest consideration of the subject1 led to conceive the forces by which generation is produced1 as forces which vitalize certain portions of matter1 and thus prepare them for development according to organic forms2 and thus the conception of this ,generative ,force is identified with the conception of the ,force of ,organic ,assimilation1 to #bba which we were led by the consideration of the process of nutrition4 ,i shall not attempt to give further distinctness and fixity to this conception of one of the vital forces2 but ,i shall proceed to exemplify the same analysis of life by some remarks upon another ,vital ,process1 and the ,forces of which it exhibits the operation4 #bbb ,,chapter ,v4 ,,attempts ,,to ,,form ,,ideas ,,of ,,separate ,,vital ,,forces1 continued4--,,voluntary ,,motion4 #a4 ,,we formerly noticed the distinctions of organic and animal functions1 organic and animal forces1 as one of the most marked distinctions to which physiologists have been led in their analysis of the vital powers4 ,i have now taken one of the former1 the organic class of functions1 namely1 ,nutrition2 and have endeavoured to point out in some measure the peculiar nature of the vital forces by which this function is carried on4 ,it may serve to show the extent and the difficulty of this subject1 if1 before quitting it1 ,i offer a few remarks suggested by a function belonging to the other class1 the animal functions4 ,this ,i shall briefly do with respect to ,voluntary ,motion4 #b4 ,in the ,history of ,physiology1 ,i have already related the progress of the researches by which the organs employed in voluntary motion became known to anatomists4 ,it was ascertained to the satisfaction of all physiologists1 that the immediate agents in such motion are the muscles2 that the muscles are in some way contracted1 when the nerves convey to them the agency of the will2 and that thus the limbs are moved4 ,it was ascertained1 also1 that the nerves convey sensations from the organs of sense inwards1 so as to make these sensations the object of the animal's consciousness4 ,in man and the higher animals1 these impressions upon the nerves are all conveyed to one internal organ1 the brain2 and from this organ all impressions of the will appear to proceed2 and thus the brain is #bbc the center of animal life1 towards which sensations converge1 and from which volitions diverge4 ,but this being the process1 we are led to inquire how far we can obtain any knowledge1 or form any conception1 of the vital forces by means of which the process is carried on4 ,and here ,i have further stated in the ,history#hgi1 that the transfer of sensations and volitions along the nerves was often represented as consisting in the motion of a ,nervous ,fluid4 ,i have related that the hypothesis of such a fluid1 conveying its impressions either by motions of translation or of vibration1 was countenanced by many great names1 as ,newton1 ,haller1 and even ,cuvier4 ,but ,i have ventured to express my doubt whether this hypothesis can have much value3 'for1' ,i have said1 'this principle cannot be mechanical1 chemical1 or physical1 and therefore cannot be better understood by embodying it in a fluid4 ,the difficulty we have in conceiving what the force is1 is not got rid of by explaining the machinery by which it is transferred4' ,note #hgi3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 v4 s4 #b4 #c4 ,i may add1 that no succeeding biological researches appear to have diminished the force of these considerations4 ,in modern times1 attempts have repeatedly been made to identify the nervous fluid with electricity or galvanism4 ,but these attempts have not been satisfactory or conclusive of the truth of such an identity3 and ,professor ,mller probably speaks the judgment of the most judicious physiologists1 when he states it as his opinion1 after examining the evidence#hhi1 ',that the vital actions of the nerves are not attended with the development of any galvanic currents which our instruments can detect2 and that the laws of action of the nervous principle are totally different from those of electricity4' ,note #hhi3 ,elem4 ,phys4 p4 #fdj4 ,that the powers by which the nerves are the instruments of sensation1 and the muscles of motion1 are vital endowments1 incapable of being expressed or explained by any comparison with mechanical1 chemical1 and electrical forces1 is the result which we should #bbd expect to find1 judging from the whole analogy of science2 and which thus is confirmed by the history of physiology up to the present time4 ,we naturally1 then1 turn to inquire whether such peculiar vital powers have been brought into view with any distinctness and clearness4 #d4 ,the property by which muscles1 under proper stimulation1 contract and produce motion1 has been termed ,irritability or ,contractility2 the property by which nerves are susceptible of their appropriate impressions has been termed ,sensibility4 ,a very few words on each of these subjects must suffice4 ,irritability4--,i have1 in the ,history of ,physiology#hii1 noticed that ,glisson1 a ,cambridge professor1 distinguished the ,irritation of muscles as a peculiar property1 different from any merely mechanical or physical action4 ,i have mentioned1 also1 that he divides ,irritation into natural1 vital1 and animal2 and points out1 though briefly1 the graduated differences of ,irritability in different organs4 ,although these opinions did not at first attract much notice1 about seventy years afterwards attention was powerfully called to this vital force1 ,irritability1 by ,haller4 ,i shall borrow ,sprengel's reflections on this subject4 ,note #hii3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 v4 ',hitherto men had been led to see more and more clearly that the cause of the bodily functions1 the fundamental power of the animal frame1 is not to be sought in the mechanism1 and still less in the mixture of the parts4 ,in this conviction1 they had had recourse partly to the quite supersensuous principle of the ,soul1 partly to the half-material principle of the ,animal ,spirits1 in order to explain the bodily motions4 ,glisson alone saw the necessity of assuming an ,original ,power in the fibres1 which1 independent of the influence of the animal spirits1 should produce contraction in them4 ,and ,gorter first held that this ,original ,power was not to be confined to the muscles1 but to be extended to all parts of the living body4 #bbe ',but as yet the laws of this ,power were not known1 nor had men come to an understanding whether it were fully distinct from the elasticity of the parts1 or by what causes it was put in action4 ,they had neither instituted observations nor experiments which established its relation to other assumed forces of the body4 ,there was still wanting a determination of the peculiar seat of this power1 and experiments to trace its gradual differences in different parts of the body4 ,in addition to other causes1 the necessity of the assumption of such a power was felt the more1 in consequence of the prevalence of ,leibnitz's doctrine of the activity of matter2 but it was an occult quality1 and remained so till ,haller1 by numerous experiments and solid observations1 placed in a clear light the peculiarities of the powers of the animal body4' #e4 ,perhaps1 however1 ,haller did more in the way of determining experimentally the limits and details of the application of this idea of ,irritability as a peculiar attribute1 than in developing the ,idea itself4 ,in that way his merits were great4 ,as early as the year #agci1 he published his opinion upon ,irritability as the cause of muscular motion1 which he promulgated again in #agdc4 ,but from the year #agdg he was more attentive to the peculiarities of ,irritability1 and its difference from the effect of the nerves4 ,in the first edition of his ,physiology1 which appeared in #agdg1 he distinguished three kinds of ,force in muscles1--the ,dead ,force1 the ,innate ,force1 and the ,nervous ,power4 ,the first is identical with the elastic force of dead matter1 and remains even after death4 ,the innate force continues only a short time after death1 and discloses itself especially by alternate oscillations2 the motions which arise from this are much more lively than those which arise from mere elasticity3 they are not excited by tension1 nor by pressure1 nor by any mechanical alteration1 but only by irritation4 ,the nervous force of the muscle is imparted to it from without by the nerves2 it preserves the irritability1 which cannot long subsist without the influence of the nervous force1 but is not identical with it4 #bbf ,in the year #ageb1 ,haller laid before the ,society of ,gttingen the result of one hundred and ninety experiments2 from which it appears to what parts of the animal system ,irritability and ,nervous ,power belong4 ,these ,i need not enumerate4 ,he also investigated with care its gradations in those parts which do possess it4 ,thus the heart possesses it in the highest degree1 and other organs follow in their order4 #f4 ,haller's doctrine was1 that there resides in the muscles a peculiar vital power by which they contract1 and that this power is distinct from the attributes of the nerves4 ,and this doctrine has been accepted by the best physiologists of modern times4 ,but this distinction of the irritability of the muscles from the sensibility of the nerves became somewhat clearer by giving to the former attribute the name of ,contractility4 ,this accordingly was done2 it is1 for example1 the phraseology used by ,bichat4 ,by speaking of animal sensibility and animal contractility1 the passive and the active element of the processes of animal life are clearly separated and opposed to each other4 ,the sensations which we feel1 and the muscular action which we exert1 may be closely and inseparably connected1 yet still they are clearly distinguishable4 ,we can easily in our apprehension separate the titillation felt in the nose on taking snuff1 from the action of the muscles in sneezing2 or the perception of an object falling towards the eye1 from the exertion which shuts the eye-lid2 although in these cases the passive and active part of the process are almost or quite inseparable in fact4 ,and this clear separation of the active from the passive power is something1 it would seem1 peculiar to the ,animal ,vital ,powers2 it is a character by which they differ1 not only from mechanical1 chemical1 and all other merely physical forces1 but even from ,organic ,vital ,powers4 #g4 ,but this difference between the ,animal and the ,organic ,vital ,powers requires to be further insisted upon1 for it appears to have been overlooked or denied by very eminent physiologists4 ,for instance1 ,bichat classifies the ,vital ,powers as ,animal ,sensibility1 #bbg ,animal ,contractility1 ,organic ,sensibility1 ,organic ,contractility4 ,now the view which suggests itself to us1 in agreement with what has been said1 is this3--that though ,animal ,sensibility and ,animal ,contractility are clearly and certainly distinct1 ,organic ,sensibility and ,organic ,contractility are neither separable in fact nor in our conception1 but together make up a single ,vital ,power4 ,that they are not separable in fact is1 indeed1 acknowledged by ,bichat himself4 ',the organic contractility1' he says#iji1 'can never be separated from the sensibility of the same kind2 the reaction of the excreting tubes is immediately connected with the action which the secreted fluids exercise upon them3 the contraction of the heart must necessarily succeed the influx of the blood into it4' ,it is not wonderful1 therefore1 that it should have happened1 as he complains1 that 'authors have by no means separated these two things1 either in their consideration or in language4' ,we cannot avoid asking1 ,are ,organic ,sensibility and ,organic ,contractility really anything more than two different aspects of the same thing1 like action and reaction in mechanics1 which are only two ways of considering the action which takes place at a point2 or like the positive and negative electricities1 which1 as we have seen1 always co-exist and correspond to each other8 ,note #iji3 ,life and ,death1 p4 #id4 #h4 ,but we may observe1 moreover1 that ,bichat1 by his use of the term ,contractility1 includes in it powers to which it cannot with any propriety be applied4 ,why should we suppose that the vital powers of absorption1 secretion1 assimilation1 are of such a nature that the name contractility may be employed to describe them8 ,we have seen1 in the last chapter1 that the most careful study of these powers leads us to conceive them in a manner altogether removed from any notion of contraction4 ,is it not then an abuse of language which cannot possibly lead to anything but #bbh confusion1 to write thus#iai3 ',the insensible organic contractility is that1 by virtue of which the excreting tubes react upon their respective fluids1 the secreting organs upon the blood which flows into them1 the parts where nutrition is performed upon the nutritive juices1 and the lymphatics upon the substances which excite their open extremities'8 ,in the same manner he ascribes#ibi to the peculiar sensibility of each organ the peculiarity of its products and operations4 ,an increased absorption is produced by an increased susceptibility of the 'absorbent orifices4' ,and thus1 in this view1 each organic power may be contemplated either as sensibility or as contractility1 and may be supposed to be rendered more intense by magnifying either of these its aspects2 although1 in fact1 neither can be conceived to be increased without an exactly commensurate increase of the other4 ,note #iai3 ,life and ,death1 p4 #ie4 ,note #ibi3 ,ib4 p4 #ij4 #i4 ,this opinion1 unfounded as it thus appears to be1 that all the different organic vital powers are merely different kinds of ,contractility or ,excitability1 was connected with the doctrines of ,brown and his followers1 which were so celebrated in the last century1 that all diseases arise from increase or from diminution of the ,vital ,force4 ,the considerations which have already offered themselves would lead us to assent to the judgment which ,cuvier has pronounced upon this system4 ',the theory of excitation1' he says1 'so celebrated in these later times by its influence upon pathology and therapeutick1 is at bottom only a modification of that1 in which1 including under a common name ,sensibility and ,irritability1' and we may add1 applying this name to all the ,vital ,powers1 'the speculator takes refuge in an abstraction so wide1 that if1 by it1 he simplifies medicine1 he by it annihilates all positive physiology#ici4' ,note #ici3 ,hist4 des ,sc4 ,nat4 depuis #aghi1 i4 #bai4 #aj4 ,the separation of the nervous influence and the muscular irritability1 although it has led to many highly instructive speculations1 is not without its #bbi difficulties1 when viewed with reference to the ,idea of ,vital ,power4 ,if the irritability of each muscle reside in the muscle itself1 how does it differ from a mere mechanical force1 as elasticity8 ,but1 in point of fact1 it is certain that the muscular irritability of the animal body is not an attribute of the muscle itself independent of its connexion with the system4 ,no muscle1 or other part1 removed from the body1 long preserves its irritability4 ,this power cannot subsist permanently1 except in connexion with an organic whole4 ,this condition peculiarly constitutes irritability a living force3 and this condition would be satisfied by considering the force as derived from the nervous system2 but it appears that though the nervous system has the most important influence upon all vital actions1 the muscular irritability must needs be considered as something distinct4 ,and thus the ,irritability or ,contractility of the muscle is a peculiar endowment of the texture1 but it is at the same time an endowment which can only co-exist with life2 it is1 in short1 a peculiar ,vital ,power4 #aa4 ,this necessity of the union of the muscle with the whole nervous system1 in order that it may possess irritability1 was the meaning of the true part of ,stahl's psychical doctrine2 and the reason why he and his adherents persisted in asserting the power of the soul even over involuntary motions4 ,this doctrine was the source of much controversy in later times4 ',but1' says ,cuvier#idi1 'this opposition of opinion may be reconciled by the intimate union of the nervous substance with the fibre and the other contractile organic elements1 and by their reciprocal action2--doctrines which had been presented with so much probability by physiologists of the ,scotch school1 but which were elevated above the rank of hypotheses only by the observations of more recent times4 ,note #idi3 ,hist4 des ,sc4 ,nat4 depuis #aghi1 i4 #bac4 ',the fibre does not contract by itself1 but by the influence of the nervous filaments1 which are always united with it4 ,the change which produces the #bcj contraction cannot take place without the concurrence of both these substances2 and it is further necessary that it should be occasioned each time by an exterior cause1 by a stimulant4 ',the ,will is one of these stimulants2 but it only excites the ,irritability1 it does not constitute it2 for in the case of persons paralytic from apoplexy1 the ,irritability remains1 though the power of the ,will over it is gone4 ,thus irritability depends in part on the nerve1 but not on the sensibility3 this last is another property1 still more admirable and occult than the irritability2 but it is only one among several functions of the nervous system4 ,it would be an abuse of words to extend this denomination to functions unaccompanied by perception4' #ab4 ,supposing1 then1 that ,contractility is established as a peculiar ,vital ,power residing in the muscles1 we may ask whether we can trace with any further exactness the seat and nature of this power4 ,it would be unsuitable to the nature of the present work to dwell upon the anatomical discussions bearing upon this point4 ,i will only remark that some anatomists maintain#iei that muscles are contracted by those fibres assuming a zigzag form1 which at first were straight4 ,others 7,professor ,owen and ,dr4 ,a4 ,thompson7 doubt the accuracy of this observation2 and conceive that the muscular fibre becomes shorter and thicker1 but does not deviate from a right line4 ,we may remark that the latter kind of action appears to be more elementary in its nature4 ,we can1 as a matter of geometry1 conceive a straight line thrown into a zigzag shape by muscular contractions taking place between remote parts of it2 but it is difficult to conceive by what elementary mode of action a straight fibre could bend itself at certain points1 and at certain points only2 since the elementary force must act at every point of the fibre1 and not at certain selected points4 ,note #iei3 ,mller1 ,elem4 ,phys4 p4 #hhg4 #ac4 ,a circumstance which remarkably marks the difference between the vital force of ,contractility1 #bca inherent in muscles1 and any merely dead or mechanical force1 is this2 that in assuming their contractile state1 muscles exert a tension which they could not themselves support or convey if not strengthened by their vital irritability4 ,they are capable of raising weights by their exertion1 which will tear them asunder when the power of contraction is lost by death4 ,this has induced ,cuvier and other physiologists#ifi to believe 'that in the moment of action1 the particles that compose a fibre1 not only approach towards each other longitudinally1 but that their cohesive attraction becomes instantaneously much greater than it was before3 for without such an increase of cohesive force1 the tendency to shorten could not1 as it would appear1 prevent the fibre from being torn4' ,we see here the difficulty1 or rather the impossibility1 of conceiving muscular contractility as a mere mechanical force2 and perhaps there is little hope of any advantage by calling in the aid of chemical hypothesis to solve the mechanical difficulty4 ,cuvier conjectures that a sudden change in the chemical composition may thus so quickly and powerfully augment the cohesion4 ,but we may ask1 are not a chemical synthesis and analysis1 suddenly performed by a mere act of the will1 as difficult to conceive as a sudden increase and decrease of mechanical power directly produced by the same cause8 ,note #ifi3 ,prichard1 ,vital ,prin4 p4 #abf4 #ad4 ,sensibility4 ,the nerves are the organs and channels of ,sensibility4 ,by means of them we receive our sensations1 whether of mere pleasure and pain1 or of qualities which we ascribe to external objects1 as a bitter taste1 a sweet odour1 a shrill sound1 a red colour1 a hard or a hot feeling of touch4 ,some of these sensations are but obscurely the objects of our consciousness2 as for example the feeling which our feet have of the ground1 or the sight which our eyes have of neighbouring objects1 when we walk in a reverie4 ,in these cases the sensations1 though obscure1 exist2 for they #bcb serve to balance and guide us as we walk4 ,in other cases1 our sensations are distinctly and directly the objects of our attention4 ,but our ,sensations1 as we have already said1 we ascribe as ,qualities to external objects4 ,by our senses we perceive objects1 and thus our sensations become perceptions4 ,we have not only the sensation of round1 purple1 and green1 repeated and varied1 but the perception of a bunch of grapes partly ripe and partly unripe4 ,we have not only sensations of noise and of variously-coloured specks rapidly changing their places1 but we have perceptions1 by sound and sight1 of a stone rolling down the hill and crushing the shrubs in its path4 ,we scarcely ever dwell upon our ,sensations2 our thoughts are employed upon ,objects4 ,we regard the impressions upon our nerves1 not for what they are1 but for what they tell us4 ,but in what ,language do the impressions upon the nerves thus speak to us of an external world1--of the forms and qualities and actions of objects8 ,how is it that by the aid of our nervous system we become acquainted not only with impressions but with things2 that we learn not only the relation of objects to us1 but to one another8 #ae4 ,it has been shown at some length in the previous ,books1 that the mode in which ,sensations are connected in our minds so as to convey to us the knowledge of ,objects and their ,relations1 is by being contemplated with reference to ,ideas4 ,our ,sensations1 connected by the ,idea of ,space1 become ,figures2 connected by the ,idea of ,time1 they become ,causes and ,effects2 connected by the ,idea of ,resemblance1 they become ,individuals and ,kinds2 connected by the ,idea of ,organization1 they become ,living ,things4 ,it has been shown that without these ,ideas there can be no connexion among our sensations1 and therefore no perception of ,figure1 ,action1 ,kind1 or in short1 of bodies under any aspect whatever4 ,sensations are the rude ,matter of our perceptions2 and are nothing1 except so far as they have ,form given them by ,ideas4 #bcc ,but thus moulded by our ,ideas1 ,sensation becomes the source of an endless store of important ,knowledge of every possible kind4 #af4 ,but one of the most obvious uses of our perceptions and our knowledge is to direct our ,actions4 ,it is suitable to the condition of our being that when we perceive a bunch of grapes1 we should be able to pluck and eat the ripe ones2 that when we perceive a stone rushing down the side of a hill1 we should be able to move so as to avoid it4 ,and this must be done by moving our limbs2 in short1 by the use of our muscles4 ,and thus ,sensation leads1 not directly1 but through the medium of ,ideas1 to muscular ,contraction4 ,i say that sensation and ,muscular action are in such cases connected through the medium of ,ideas4 ,for when we proceed to pluck the grape which we see1 the sensation does not determine the motion of the hand by any necessary geometrical or mechanical conditions1 as an impression made upon a machine determines its motions2 but the perception leads us to stretch forth the hand to that part of space1 wherever it is1 where we know that the grape is2 and this1 not in any determinate path1 but1 it may be1 avoiding or removing intervening obstacles1 which we also perceive4 ,there is in every such case a connexion between the sensation and the resulting action1 not of a material but of a mental kind4 ,the cause and the effect are bound together1 not by physical but by intellectual ties4 #ag4 ,and thus in such cases1 between the two vital operations1 ,sensation and ,muscular ,action1 there intervenes1 as an intermediate step1 ,perception or ,knowledge1 which is not merely vital but ideal4 ,but this is not all2 there is still another mental part of the process which may be readily distinguished from that which we have described4 ,an act of the ,will1 a ,volition1 is that1 in the ,mind1 which immediately determines the action of the ,muscles of the ,body4 ,and thus ,will intervenes between ,knowledge and ,action2 and the cycle of operations which take place when animals act with reference to external objects is #bcd this3--,sensation1 ,perception1 ,volition1 ,muscular ,contraction4 #ah4 ,to attempt further to analyse the mental part of this cycle does not belong to the present part of our work4 ,but we may remark here1 as we have already remarked in the ,history#igi1 how irresistibly we are led by physiological researches into the domain of thought and mind4 ,we pass from the body to the soul1 from physics to metaphysics2 from biology to psychology2 from things to persons2 from nouns to pronouns4 ,i have there noticed the manner in which ,cuvier expresses this transition by the introduction of the pronoun3 ',the impression of external objects upon the ,,me1 the production of a sensation1 of an image1 is a mystery impenetrable to our thoughts4' ,note #igi3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 v4 s4 #b4 #ai4 ,but to return to the merely biological part of our speculations4 ,we have arrived1 it will be perceived1 at this result3 that in animal actions there intervenes between the two terms of ,sensation and ,muscular ,contraction1 an intermediate process2 which may be described as a communication to and from a ,center4 ,the ,center is the seat of the sentient and volent faculties1 and is of a hyperphysical nature4 ,but the existence of such a ,center as a necessary element in the functions of the animal life is a truth which is important in biology4 ,this indeed may be taken as the peculiar character of animal1 as distinguished from merely organic powers4 ,accordingly1 it is so stated by ,bichat4 ,for although he superfluously1 as ,i have tried to show1 introduces into his list of vital powers an organic sensibility1 he still draws the distinction of which ,i have spoken2 'in the animal life1 ,sensibility is the faculty of receiving an ,impression plus that of referring it to a common ,center#ihi4' ,note #ihi3 ,life and ,death1 p4 #hd4 #bj4 ,but since ,sensibility and ,contractility are thus connected by reference to a common ,center1 we may ask1 before quitting the subject1 what are the different forms which this reference assumes8 ,is the connexion #bce always attended by the distinct steps of ,knowledge and ,will1--by a clear act of consciousness1 as in the case which we have taken1 of plucking a grape2 or may these steps become obscure1 or vanish altogether8 ,we need not further illustrate the conscious connexion4 ,such actions as we have described are called voluntary actions4 ,in extreme cases1 the mental part of the process is obvious enough4 ,but we may gradually pass from these to cases in which the mental operation is more and more obscure4 ,in walking1 in speaking1 in eating1 in breathing1 our muscular exertions are directed by our sensations and perceptions3 yet in such processes1 how dimly are we conscious of perceptive and directive power6 ,how the mind should be able to exercise such a power1 and yet should be scarcely or not at all conscious of its exercise1 is a very curious problem4 ,but in all or in most of the instances just mentioned1 the solution of this problem appears to depend upon psychological rather than biological principles1 and therefore does not belong to this place4 #ba4 ,but in cases at the other extreme 7unconscious actions7 the mental part of the operation vanishes altogether4 ,in many animals1 even after decapitation1 the limbs shrink when irritated4 ,the motions of the iris are determined by the influence of light on our eyes1 without our being aware of the motions4 ,here ,sensations produce ,motions1 but with no trace of intervening ,perception or ,will4 ,the ,sensation appears to be reflected back from the central element of animal life1 in the form of a ,muscular ,contraction2 but in this case the ,sensation is not modified or regulated by any ,idea4 ,these reflected motions have no reference to relations of space or force among surrounding objects4 ,they are blind and involuntary1 like the movements of convulsion1 depending for direction and amount only on the position and circumstances of the limb itself with its muscles4 ,here the ,centre from which the reflection takes place is merely animal1 not intellectual4 ,in this case some physiologists have doubted whether the reflection of the sensation in the form of a muscular #bcf contraction does really take place from the ,center2 and have conceived that sensorial impressions might affect motor nerves without any communication with the nervous ,center4 ,but on this subject we may1 ,i conceive1 with safety adopt the decision of ,professor ,mller1 deliberately given after a careful examination of the subject3 ',when impressions made by the action of external stimuli on sensitive nerves give rise to motions in other parts1 these motions are never the result of the direct reaction of the sensitive and motor fibres of the nerves on each other2 the irritation is conveyed by the sensitive fibres to the brain and spinal cord1 and is by these communicated to the motor fibres4' #bb4 ,thus we have two extreme cases of the connexion of sensation with muscular action2 in one of which the connexion clearly is1 and in the other it as clearly is not1 determined by relations of ,ideas1 in its transit through the nervous ,center4 ,there is another highly curious case standing intermediate between these two1 and extremely difficult to refer to either4 ,i speak of the case of ,instinct4 ,instinct leads to actions which are such as if they were determined by ,ideas4 ,the lamb follows its mother by instinct2 but the motions by which it does this1 the special muscular exertions1 depend entirely upon the geometrical and mechanical relations of external bodies1 as the form of the ground1 and the force of the wind4 ,the contractions of the muscles which are requisite in order that the creature may obey its instinct1 vary with every variation of these external conditions2--are not determined by any rule or necessity1 but by properties of ,space and ,force4 ,thus the action is not governed by ,sensations directly1 but by sensations moulded by ,ideas4 ,and the same is the case with other cases of instinct4 ,the dog hunts by instinct2 but he hunts certain kinds of animals merely1 thus showing that his instinct acts according to ,resemblances and ,differences2 he crosses the field repeatedly to find the track of his prey by scent2 thus recognizing the relations of ,space with reference to the track2 he leaps1 adjusting his ,force to #bcg the distance and height of the leap with mechanical precision2 and thus he practically recognizes the ,ideas of ,resemblance1 ,space1 and ,force4 ,but have animals such ,ideas8 ,in any proper sense in which we can speak of possessing ,ideas1 it appears plain that they have not4 ,animals cannot1 at any time1 be said properly to possess ideas1 for ideas imply the possibility of speculative knowledge4 #bc4 ,but even if we allow to animals only the practical possession of ,ideas1 we have still a great difficulty remaining4 ,in the case of man1 his ideas are unfolded gradually by his intercourse with the external world4 ,the child learns to distinguish forms and positions by a repeated and incessant use of his hands and eyes2 he learns to walk1 to run1 to leap1 by slow and laborious degrees2 he distinguishes one man from another1 and one animal from another1 only after repeated mistakes4 ,nor can we conceive this to be otherwise4 ,how should the child know at once what muscles he is to exert in order to touch with his hand a certain visible object8 ,how should he know what muscles to exert that he may stand and not fall1 till he has tried often8 ,how should he learn to direct his attention to the differences of different faces and persons1 till he is roused by some memory1 or hope which implies memory8 ,it seems to us as if the sensations could not1 without considerable practice1 be rightly referred to ,ideas of ,space1 ,force1 ,resemblance1 and the like4 ,yet that which thus appears impossible1 is in fact done by animals4 ,the lamb almost immediately after its birth follows its mother1 accommodating the actions of its muscles to the form of the ground4 ,the chick1 just escaped from the shell1 picks up a minute insect1 directing its beak with the greatest accuracy4 ,even the human infant seeks the breast and exerts its muscles in sucking1 almost as soon as it is born4 ,hence1 then1 we see that ,instinct produces at once actions regulated by ,ideas1 or1 at least1 which take place as if they were regulated by ,ideas2 although the ,ideas cannot have been developed by exercise1 and only appear to exist so far as such actions are concerned4 #bch #bd4 ,the term ,instinct may properly be opposed to ,insight4 ,the former implies an inward principle of action1 implanted within a creature and practically impelling it1 but not capable of being developed into a subject of contemplation4 ,while the instinctive actions of animals are directed by such a principle1 the deliberate actions of man are governed by insight3 he can contemplate the ideal relations on which the result of his action depends4 ,he can in his mind map the path he will follow1 and estimate the force he will exert1 and class the objects he has to deal with1 and determine his actions by the relations which he thus has present to his mind4 ,he thus possesses ,ideas not only practically1 but speculatively4 ,and knowing that the ,ideas by which he commonly directs his actions1 ,space1 ,cause1 ,resemblance1 and the like1 have been developed to that degree of clearness in which he possesses them by the assiduous exercise of the senses and the mind from the earliest stage of infancy1 and that these ,ideas are capable of being still further unfolded into long trains of speculative truth1 he is unable to conceive the manner in which animals possess such ,ideas as their instinctive actions disclose3--,ideas which neither require to be unfolded nor admit of unfolding2 which are adequate for practical purposes without any previous exercise1 and inadequate for speculative purposes with whatever labour cultivated4 ,i have ventured to make these few remarks on ,instinct since it may1 perhaps1 justly be considered as the last province of ,biology1 where we reach the boundary line of ,psychology4 ,i have now1 before quitting this subject1 only one other principle to speak of4 #bci ,,chapter ,,vi4 ,,of ,,the ,,idea ,,of ,,final ,,causes4 #a4 ,,by an examination of those notions which enter into all our reasonings and judgments on living things1 it appeared that we conceive animal life as a vortex or cycle of moving matter in which the form of the vortex determines the motions1 and these motions again support the form of the vortex3 the stationary parts circulate the fluids1 and the fluids nourish the permanent parts4 ,each portion ministers to the others1 each depends upon the other4 ,the parts make up the whole1 but the existence of the whole is essential to the preservation of the parts4 ,but parts existing under such conditions are organs1 and the whole is organized4 ,this is the fundamental conception of organization4 ',organized beings1' says the physiologist#iii1 'are composed of a number of essential and mutually dependent parts4' ',an organized product of nature1' says the great metaphysician#ajji1 'is that in which all the parts are mutually ends and means4' ,note #iii3 ,mller1 ,elem4 p4 #ah4 ,note #ajji3 ,kant1 ,urtheilskraft1 p4 #bif4 #b4 ,it will be observed that we do not content ourselves with saying that in such a whole1 all the parts are mutually dependent4 ,this might be true even of a mechanical structure2 it would be easy to imagine a framework in which each part should be necessary to the support of each of the others2 for example1 an arch of several stones4 ,but in such a structure1 the parts have no properties which they derive from the whole4 ,they are beams or stones when separate2 they are no more when joined4 ,but the same is not the case in an organized whole4 ,the limb of an animal separated #bdj from the body1 loses the properties of a limb1 and soon ceases to retain even its form4 #c4 ,nor do we content ourselves with saying that the parts are mutually causes and effects4 ,this is the case in machinery4 ,in a clock1 the pendulum by means of the escapement causes the descent of the weight1 the weight by the same escapement keeps up the motion of the pendulum4 ,but things of this kind may happen by accident4 ,stones slide from a rock down the side of a hill and cause it to be smooth2 the smoothness of the slope causes stones still to slide4 ,yet no one would call such a slide an organized system4 ,the system is organized1 when the effects which take place among the parts are essential to our conception of the whole2 when the whole would not be a whole1 nor the parts1 parts1 except these effects were produced2 when the effects not only happen in fact1 but are included in the idea of the object2 when they are not only seen1 but foreseen2 not only expected1 but intended3 in short when1 instead of being causes and effects1 they are ends and means1 as they are termed in the above definition4 ,thus we necessarily include1 in our ,idea of ,organization1 the notion of an ,end1 a ,purpose1 a ,design2 or1 to use another phrase which has been peculiarly appropriated in this case1 a ,final ,cause4 ,this idea of a ,final ,cause is an essential condition in order to the pursuing our researches respecting organized bodies4 #d4 ,this ,idea of ,final ,cause is not deduced from the phenomena by reasoning1 but is assumed as the only condition under which we can reason on such subjects at all4 ,we do not deduce the ,idea of ,space1 or ,time1 or efficient ,cause from the phenomena about us1 but necessarily look at phenomena as subordinate to these ,ideas from the beginning of our reasoning4 ,it is true1 our ideas of relations of ,space1 and ,time1 and ,force1 may become much more clear by our familiarizing ourselves with particular phenomena3 but still1 the ,fundamental ,ideas are not generated1 but unfolded2 not extracted from the external world1 but evolved from the world within4 ,in like manner1 in the contemplation of organic structures1 we consider #bda each part as subservient to some use1 and we cannot study the structure as organic without such a conception4 ,this notion of adaptation1--this ,idea of an ,end1--may become much more clear and impressive by seeing it exemplified in particular cases4 ,but still1 though suggested and evoked by special cases1 it is not furnished by them4 ,if it be not supplied by the mind itself1 it can never be logically deduced from the phenomena4 ,it is not a portion of the facts which we study1 but it is a principle which connects1 includes1 and renders them intelligible2 as our other ,fundamental ,ideas do the classes of facts to which they respectively apply4 #e4 ,this has already been confirmed by reference to fact2 in the ,history of ,physiology1 ,i have shown that those who studied the structure of animals were irresistibly led to the conviction that the parts of this structure have each its end or purpose2--that each member and organ not merely produces a certain effect or answers a certain use1 but is so framed as to impress us with the persuasion that it was constructed for that use3--that it was intended to produce the effect4 ,it was there seen that this persuasion was repeatedly expressed in the most emphatic manner by ,galen2--that it directed the researches and led to the discoveries of ,harvey2--that it has always been dwelt upon as a favourite contemplation1 and followed as a certain guide1 by the best anatomists2--and that it is inculcated by the physiologists of the profoundest views and most extensive knowledge of our own time4 ,all these persons have deemed it a most certain and important principle of physiology1 that in every organized structure1 plant or animal1 each intelligible part has its allotted office3--each organ is designed for its appropriate function3--that nature1 in these cases1 produces nothing in vain3 that1 in short1 each portion of the whole arrangement has its final cause2 an ,end to which it is adapted1 and in this ,end1 the reason that it is where and what it is4 #f4 ,this ,notion of ,design in organized bodies must1 ,i say1 be supplied by the student of organization out of his own mind3 a truth which will become clearer if #bdb we attend to the most conspicuous and acknowledged instances of design4 ,the structure of the ,eye1 in which the parts are curiously adjusted so as to produce a distinct image on the retina1 as in an optical instrument2--the ,trochlear ,muscle of the eye1 in which the tendon passes round a support and turns back1 like a rope round a pulley2--the prospective contrivances for the preservation of animals1 provided long before they are wanted1 as the ,milk of the mother1 the ,teeth of the child1 the ,eyes and ,lungs of the ftus3--these arrangements1 and innumerable others1 call up in us a persuasion that ,design has entered into the plan of animal form and progress4 ,and if we bring in our minds this conception of ,design1 nothing can more fully square with and fit it1 than such instances as these4 ,but if we did not already possess the ,idea of ,design2--if we had not had our notion of mechanical contrivance awakened by inspection of optical instruments1 or pulleys1 or in some other way3--if we had never been conscious ourselves of providing for the future2--if this were the case1 we could not recognize contrivance and prospectiveness in such instances as we have referred to4 ,the facts are1 indeed1 admirably in accordance with these conceptions1 when the two are brought together3 but the facts and the conceptions come together from different quarters--from without and from within4 #g4 ,we may further illustrate this point by referring to the relations of travellers who tell us that when consummate examples of human mechanical contrivance have been set before savages1 they have appeared incapable of apprehending them as proofs of design4 ,this shows that in such cases the ,idea of ,design had not been developed in the minds of the people who were thus unintelligent3 but it no more proves that such an idea does not naturally and necessarily arise1 in the progress of men's minds1 than the confused manner in which the same savages apprehend the relations of space1 or number1 or cause1 proves that these ideas do not naturally belong to their intellects4 ,all men have these ideas2 and it is because they #bdc cannot help referring their sensations to such ideas1 that they apprehend the world as existing in time and space1 and as a series of causes and effects4 ,it would be very erroneous to say that the belief of such truths is obtained by logical reasoning from facts4 ,and in like manner we cannot logically deduce design from the contemplation of organic structures2 although it is impossible for us1 when the facts are clearly before us1 not to find a reference to design operating in our minds4 #h4 ,again2 the evidence of the doctrine of ,final ,causes as a fundamental principle of ,biology may be obscured and weakened in some minds by the constant habit of viewing this doctrine with suspicion as unphilosophical and at variance with ,morphology4 ,by cherishing such views1 it is probable that many persons1 physiologists and others1 have gradually brought themselves to suppose that many or most of the arrangements which are familiarly adduced as instances of design may be accounted for1 or explained away2--that there is a certain degree of prejudice and narrowness of comprehension in that lively admiration of the adaptation of means to ends which common minds derive from the spectacle of organic arrangements4 ,and yet1 even in persons accustomed to these views1 the strong and natural influence of the ,idea of a ,final ,cause1 the spontaneous recognition of the relation of ,means to an ,end as the assumption which makes organic arrangements intelligible1 breaks forth when we bring before them a new case1 with regard to which their genuine convictions have not yet been modified by their intellectual habits4 ,i will offer1 as an example which may serve to illustrate this1 the discoveries recently made with regard to the process of ,suckling in the ,kangaroo4 ,in the case of this1 as of other pouched animals1 the young animal is removed1 while very small and imperfectly formed1 from the womb to the pouch1 in which the teats are1 and is there placed with its lips against one of the nipples4 ,but the young animal taken altogether is not so large as the nipple1 and is therefore incapable of sucking after the manner of common mammals4 ,here is a difficulty3 #bdd how is it overcome8--,by an appropriate contrivance3 the nipple1 which in common mammals is not furnished with any muscle1 is in the kangaroo provided with a powerful extrusory muscle by which the mother can inject the milk into the mouth of her offspring4 ,and again2 in order to give attachment to this muscle there is a bone which is not found in animals of other kinds4 ,but this mode of solving the problem of suckling so small a creature introduces another difficulty4 ,if the milk is injected into the mouth of the young one1 without any action of its own muscles1 what is to prevent the fluid entering the windpipe and producing suffocation8 ,how is this danger avoided8--,by another appropriate contrivance3 there is a funnel in the back of the throat by which the air passage is completely separated from the passage for nutriment1 and the injected milk passes in a divided stream on each side of the larynx to the sophagus#ajai4 ,and as if to show that this apparatus is really formed with a view to the wants of the young one1 the structure alters in the course of the animal's growth2 and the funnel1 no longer needed1 is modified and disappears4 ,note #ajai3 ,mr4 ,owen1 in ,phil4 ,trans4 #ahcd1 p4 #cdh4 ,with regard to this and similar examples1 the remark which ,i would urge is this3--that no one1 however prejudiced or unphilosophical he may in general deem the reference to ,final ,causes1 can1 at the first impression1 help regarding this curious system of arrangement as the ,means to an ,end4 ,so contemplated1 it becomes significant1 intelligible1 admirable3 without such a principle1 it is an unmeaning complexity1 a collection of contradictions1 producing an almost impossible result by a portentous conflict of chances4 ,the parts of this apparatus cannot have produced one another3 one part is in the mother2 another part in the young one3 without their harmony they could not be effective2 but nothing except design can operate to make them harmonious4 ,they are intended to work together2 and we cannot resist the conviction of this intention when the facts first come before us4 ,perhaps #bde there may hereafter be physiologists who1 tracing the gradual development of the parts of which we have spoken1 and the analogies which connect them with the structures of other animals1 may think that this development1 these analogies1 account for the conformation we have described2 and may hence think lightly of the explanation derived from the reference to ,final ,causes4 ,yet surely it is clear1 on a calm consideration of the subject1 that the latter explanation is not disturbed by the former2 and that the observer's first impression1 that this is 'an irrefragable evidence of creative foresight#ajbi1' can never be obliterated2 however much it may be obscured in the minds of those who confuse this view by mixing it with others which are utterly heterogeneous to it1 and therefore cannot be contradictory4 ,note #ajbi3 ,mr4 ,owen1 in ,phil4 ,trans4 #ahcd1 p4 #cdi4 #i4 ,i have elsewhere#ajci remarked how physiologists1 who thus look with suspicion and dislike upon the introduction of ,final ,causes into physiology1 have still been unable to exclude from their speculations causes of this kind4 ,thus ,cabanis says#ajdi1 ',i regard with the great ,bacon1 the philosophy of ,final ,causes as sterile2 but ,i have elsewhere acknowledged that it was very difficult for the most cautious man never to have recourse to them in his explanations4' ,accordingly1 he says1 ',the partisans of ,final ,causes nowhere find arguments so strong in favour of their way of looking at nature as in the laws which preside and the circumstances of all kinds which concur in the reproduction of living races4 ,in no case do the means employed appear so clearly relative to the end4' ,and it would be easy to find similar acknowledgments1 express or virtual1 in other writers of the same kind4 ,thus ,bichat1 after noting the difference between the organic sensibility by which the organs are made to perform their offices1 and the animal sensibility of which the #bdf nervous center is the seat1 says#ajei1 ',no doubt it will be asked1 why'--that is1 as we shall see1 for what end--'the organs of internal life have received from nature an inferior degree of sensibility only1 and why they do not transmit to the brain the impressions which they receive1 while all the acts of the animal life imply this transmission8 ,the reason is simply this1 that all the phenomena which establish our connexions with surrounding objects ought to be1 and are in fact1 under the influence of the ,will2 while all those which serve for the purpose of assimilation only1 escape1 and ought indeed to escape1 such influence4' ,the reason here assigned is the ,final ,cause2 which1 as ,bichat justly says1 we cannot help asking for4 ,note #ajci3 ,bridgewater ,treatise1 p4 #ceb4 ,note #ajdi3 ,rapports du ,physique et du ,moral1 i4 #bii4 ,note #ajei3 ,life and ,death1 7trans47 p4 #cb4 #aj4 ,again2 ,i may quote from the writer last mentioned another remark1 which shows that in the organical sciences1 and in them alone1 the ,idea of forces as ,means acting to an ,end1 is inevitably assumed and acknowledged as of supreme authority4 ,in ,biology alone1 observes ,bichat#ajfi1 have we to contemplate the state of ,disease4 ',physiology is to the movements of living bodies1 what astronomy1 dynamics1 hydraulics1 e41 are to those of inert matter3 but these latter sciences have no branches which correspond to them as ,pathology corresponds to ,physiology4 ,for the same reason all notion of a ,medicament is repugnant to the physical sciences4 ,a ,medicament has for its object to bring the properties of the system back to their ,natural ,type2 but the physical properties never depart from this ,type1 and have no need to be brought back to it3 and thus there is nothing in the physical sciences which holds the place of ,therapeutick in ,physiology4' ,or1 as we might express it otherwise1 of inert forces we have no conception of what they ought to do1 except what they do4 ,the forces of gravity1 elasticity1 affinity1 never act in a diseased manner2 we never conceive them as failing in their purpose2 for we do not conceive them as having any purpose which is answered by one mode of their action rather than #bdg another4 ,but with organical forces the case is different2 they are necessarily conceived as acting for the preservation and development of the system in which they reside4 ,if they do not do this1 they fail1 they are deranged1 diseased4 ,they have for their object to conform the living being to a certain type2 and if they cause or allow it to deviate from this type1 their action is distorted1 morbid1 contrary to the ends of nature4 ,and thus this conception of organized beings as susceptible of disease1 implies the recognition of a state of health1 and of the organs and the vital forces as means for preserving this normal condition4 ,the state of health1 and of perpetual development1 is necessarily contemplated as the ,final ,cause of the processes and powers with which the different parts of plants and animals are endowed4 ,note #ajfi3 ,anatomie ,gnrale1 i4 liii4 #aa4 ,this ,idea of a ,final ,cause is applicable as a fundamental and regulative idea to our speculations concerning organized creatures only4 ,that there is a purpose in many other parts of the creation1 we find abundant reason to believe1 from the arrangements and laws which prevail around us4 ,but this persuasion is not to be allowed to regulate and direct our reasonings with regard to inorganic matter1 of which conception the relation of means and end forms no essential part4 ,in mere ,physics1 ,final ,causes1 as ,bacon has observed1 are not to be admitted as a principle of reasoning4 ,but in the organical sciences1 the assumption of design and purpose in every part of every whole1 that is1 the pervading idea of ,final ,cause1 is the basis of sound reasoning and the source of true doctrine4 #ab4 ,the ,idea of ,final ,cause1 of end1 purpose1 design1 intention1 is altogether different from the ,idea of ,cause1 as ,efficient ,cause1 which we formerly had to consider2 and on this account the use of the word ,cause in this phrase has been objected to4 ,if the idea be clearly entertained and steadily applied1 the word is a question of subordinate importance4 ,the term ,final ,cause has been long familiarly used1 and appears not likely to lead to confusion4 #bdh #ac4 ,the consideration of ,final ,causes1 both in physiology and in other subjects1 has at all times attracted much attention1 in consequence of its bearing upon the belief of an ,intelligent ,author of the ,universe4 ,i do not intend1 in this place1 to pursue the subject far in this view3 but there is one antithesis of opinion1 already noticed in the ,history of ,physiology1 on which ,i will again make a few remarks#ajgi4 ,note #ajgi3 ,hist4 ,ind4 ,sc4 b4 xvii4 c4 viii4 ,on the ,doctrine of ,final ,causes in ,physiology4 ,it has appeared to some persons that the mere aspect of order and symmetry in the works of nature--the contemplation of comprehensive and consistent law--is sufficient to lead us to the conception of a design and intelligence producing the order and carrying into effect the law4 ,without here attempting to decide whether this is true1 we may discern1 after what has been said1 that the conception of ,design1 arrived at in this manner1 is altogether different from that ,idea of ,design which is suggested to us by organized bodies1 and which we describe as the doctrine of ,final ,causes4 ,the regular form of a crystal1 whatever beautiful symmetry it may exhibit1 whatever general laws it may exemplify1 does not prove design in the same manner in which design is proved by the provisions for the preservation and growth of the seeds of plants1 and of the young of animals4 ,the law of universal gravitation1 however wide and simple1 does not impress us with the belief of a purpose1 as does that propensity by which the two sexes of each animal are brought together4 ,if it could be shown that the symmetrical structure of a flower results from laws of the same kind as those which determine the regular forms of crystals1 or the motions of the planets1 the discovery might be very striking and important1 but it would not at all come under our idea of ,final ,cause4 #ad4 ,accordingly1 there have been1 in modern times1 two different schools of physiologists1 the one proceeding upon the idea of ,final ,causes1 the other school #bdi seeking in the realm of organized bodies wide laws and analogies from which that idea is excluded4 ,all the great biologists of preceding times1 and some of the greatest of modern times1 have belonged to the former school2 and especially ,cuvier1 who may be considered as the head of it4 ,it was solely by the assiduous application of this principle of ,final ,cause1 as he himself constantly declared1 that he was enabled to make the discoveries which have rendered his name so illustrious1 and which contain a far larger portion of important anatomical and biological truth than it ever before fell to the lot of one man to contribute to the science4 ,the opinions which have been put in opposition to the principle of ,final ,causes have1 for the most part1 been stated vaguely and ambiguously4 ,among the most definite of such principles1 is that which1 in the ,history of the subject1 ,i have termed the ,principle of ,metamorphosed and ,developed ,symmetry1 upon which has been founded the science of ,morphology4 ,the reality and importance of this principle are not to be denied by us3 we have shown how they are proved by its application in various sciences1 and especially in botany4 ,but those advocates of this principle who have placed it in antithesis to the doctrine of ,final ,causes1 have1 by this means1 done far more injustice to their own favourite doctrine than damage to the one which they opposed4 ,the adaptation of the bones of the skeleton to the muscles1 the provision of fulcrums1 projecting processes1 channels1 so that the motions and forces shall be such as the needs of life require1 cannot possibly become less striking and convincing1 from any discovery of general analogies of one animal frame with another1 or of laws connecting the development of different parts4 ,whenever such laws are discovered1 we can only consider them as the means of producing that adaptation which we so much admire4 ,our conviction that the ,artist works intelligently1 is not destroyed1 though it may be modified and transferred1 when we obtain a sight of his tools4 ,our discovery of laws cannot contradict our persuasion of ends2 our ,morphology cannot prejudice our ,teleology4 #bej #ae4 ,the irresistible and constant apprehension of a purpose in the forms and functions of animals has introduced into the writings of speculators on these subjects various forms of expression1 more or less precise1 more or less figurative2 as1 that 'animals are framed with a view to the part which they have to play2'--that 'nature does nothing in vain2' that 'she employs the best means for her ends2' and the like4 ,however metaphorical or inexact any of these phrases may be in particular1 yet taken altogether1 they convey1 clearly and definitely enough to preclude any serious errour1 a principle of the most profound reality and of the highest importance in the organical sciences4 ,but some adherents of the morphological school of which #a have spoken reject1 and even ridicule1 all such modes of expression4 ',i know nothing1' says ,m4 ,geoffroy ,saint ,hilaire1 'of animals which have to play a part in nature4 ,i cannot make of nature an intelligent being who does nothing in vain2 who acts by the shortest mode2 who does all for the best4' ,the philosophers of this school1 therefore1 do not1 it would seem1 feel any of the admiration which is irresistibly excited in all the rest of mankind at the contemplation of the various and wonderful adaptations for the preservation1 the enjoyment1 the continuation of the creatures which people the globe2--at the survey of the mechanical contrivances1 the chemical agencies1 the prospective arrangements1 the compensations1 the minute adaptations1 the comprehensive interdependencies1 which zoology and physiology have brought into view1 more and more1 the further their researches have been carried4 ,yet the clear and deep-seated conviction of the reality of these provisions1 which the study of anatomy produces in its most profound and accurate cultivators1 cannot be shaken by any objections to the metaphors or terms in which this conviction is clothed4 ,in regard to the ,idea of a ,purpose in organization1 as in regard to any other idea1 we cannot fully express our meaning by phrases borrowed from any extraneous source2 but that impossibility arises precisely from the circumstance of its being a ,fundamental ,idea which is inevitably assumed in our #bea representation of each special fact4 ,the same objection has been made to the idea of mechanical force1 on account of its being often expressed in metaphorical language2 for writers have spoken of an energy1 effort1 or solicitation to motion2 and bodies have been said to be animated by a force4 ,such language1 it has been urged1 implies volition1 and the act of animated beings4 ,but the idea of ,force as distinct from mere motion1--as the ,cause of motion1 or of tendency to motion1--is not on that account less real4 ,we endeavour in vain to conduct our mechanical reasonings without the aid of this idea1 and must express it as we can4 ,just as little can we reason concerning organized beings without assuming that each part has its function1 each function its purpose2 and so far as our phrases imply this1 they will not mislead us1 however inexact1 or however figurative they be4 #af4 ,the doctrine of a purpose in ,organization has been sometimes called the doctrine of the ,conditions of ,existence2 and has been stated as teaching that each animal must be so framed as to contain in its structure the ,conditions which its existence requires4 ,when expressed in this manner1 it has given rise to the objection1 that it merely offers an identical proposition2 since no animal can exist without such conditions4 ,but in reality1 such expressions as those just quoted give an inadequate statement of the ,principle of a ,final ,cause4 ,for we discover in innumerable cases1 arrangements in an animal1 of which we see1 indeed1 that they are subservient to its well being2 but the nature of which we never should have been able at all to conjecture1 from considering what was necessary to its existence1 and which strike us1 no less by their unexpectedness than by their adaptation3 so far are they from being presented by any perceptible necessity4 ,who would venture to say that the trochlear muscle1 or the power of articulate speech1 must occur in man1 because they are the necessary conditions of his existence8 ,when1 indeed1 the general scheme and mode of being of an animal are known1 the expert and profound anatomist can reason concerning the proportions and #beb form of its various parts and organs1 and prove in some measure what their relations must be4 ,we can assert1 with ,cuvier1 that certain forms of the viscera require certain forms of the teeth1 certain forms of the limbs1 certain powers of the senses4 ,but in all this1 the functions of self-nutrition and digestion are supposed already existing as ends3 and it being taken for granted1 as the only conceivable basis of reasoning1 that the organs are means to these ends1 we may discover what modifications of these organs are necessarily related to and connected with each other4 ,instead of terming this rule of speculation merely 'the ,principle of the ,conditions of ,existence1' we might term it 'the ,principle of the conditions of organs as ,means adapted to animal existence as their ,end4' ,and how far this principle is from being a mere barren truism1 the extraordinary discoveries made by the great assertor of the principle1 and universally assented to by naturalists1 abundantly prove4 ,the vast extinct creation which is recalled to life in ,cuvier's great work1 the ,ossemens ,fossiles1 cannot be the consequence of a mere identical proposition4 #ag4 ,it has been objected1 also1 that the doctrine of ,final ,causes supposes us to be acquainted with the intentions of the ,creator2 which1 it is insinuated1 is a most presumptuous and irrational basis for our reasonings4 ,but there can be nothing presumptuous or irrational in reasoning on that basis1 which if we reject1 we cannot reason at all4 ,if men really can discern1 and cannot help discerning1 a design in certain portions of the works of creation1 this perception is the soundest and most satisfactory ground for the convictions to which it leads4 ,the ,ideas which we necessarily employ in the contemplation of the world around us1 afford us the only natural means of forming any conception of the ,creator and ,governor of the ,universe2 and if we are by such means enabled to elevate our thoughts1 however inadequately1 towards ,him1 where is the presumption of doing so8 or rather1 where is the wisdom of refusing to open our minds to contemplations so animating and elevating1 and yet #bec so entirely convincing8 ,we possess the ideas of ,time and ,space1 under which all the objects of the universe present themselves to us2 and in virtue of these ideas thus possessed1 we believe the ,creator to be eternal and omnipotent4 ,when we find that we1 in like manner1 possess the idea of a ,design in ,creation1 and that with regard to ourselves1 and creatures more or less resembling ourselves1 we cannot but contemplate their constitution under this idea1 we cannot abstain from ascribing to the ,creator the infinite profundity and extent of design to which all these special instances belong as parts of a whole4 #ah4 ,i have here considered ,design as manifest in organization only3 for in that field of speculation it is forced upon us as contained in all the phenomena1 and as the only mode of our understanding them4 ,the existence of ,final ,causes has often been pointed out in other portions of the creation2--for instance1 in the apparent adaptations of the various parts of the earth and of the solar system to each other and to organized beings4 ,in these provinces of speculation1 however1 the principle of ,final ,causes is no longer the basis and guide1 but the sequel and result of our physical reasonings4 ,if in looking at the universe1 we follow the widest analogies of which we obtain a view1 we see1 however dimly1 reason to believe that all its laws are adapted to each other1 and intended to work together for the benefit of its organic population1 and for the general welfare of its rational tenants4 ,on this subject1 however1 not immediately included in the principle of ,final ,causes as here stated1 ,i shall not dwell4 ,i will only make this remark2 that the assertion appears to be quite unfounded1 that as science advances from point to point1 ,final ,causes recede before it1 and disappear one after the other4 ,the principle of design changes its mode of application indeed1 but it loses none of its force4 ,we no longer consider particular facts as produced by special interpositions1 but we consider design as exhibited in the establishment and adjustment of the laws by which particular facts are produced4 ,we do not look upon each particular #bed cloud as brought near us that it may drop fatness on our fields2 but the general adaptation of the laws of heat1 and air1 and moisture1 to the promotion of vegetation1 does not become doubtful4 ,we do not consider the sun as less intended to warm and vivify the tribes of plants and animals1 because we find that1 instead of revolving round the earth as an attendant1 the earth along with other planets revolves round him4 ,we are rather1 by the discovery of the general laws of nature1 led into a scene of wider design1 of deeper contrivance1 of more comprehensive adjustments4 ,final causes1 if they appear driven further from us by such an extension of our views1 embrace us only with a vaster and more majestic circuit3 instead of a few threads' connecting some detached objects1 they become a stupendous net-work1 which is wound round and round the universal frame of things4 #ai4 ,i now quit the subject of ,biology1 and with it the circle of sciences depending upon separate original ,ideas and permanent relations4 ,if from the general relations which permanently prevail and constantly recur among the objects around us1 we turn to the inquiry of what has actually happened1--if from ,science we turn to ,history1--we find ourselves in a new field4 ,in this region of speculation we can rarely obtain a complete and scientific view of the connexion between objects and events4 ,the past ,history of ,man1 of the ,arts1 of ,languages1 of the ,earth1 of the ,solar ,system1 offers a vast series of problems1 of which perhaps not one has been rigorously solved4 ,still1 man1 as his speculative powers unfold themselves1 cannot but feel prompted and invited to employ his thoughts even on these problems4 ,he cannot but wish and endeavour to understand the connexion between the successive links of such chains of events4 ,he attempts to form a ,science which shall be applicable to each of these ,histories2 and thus he begins to construct the class of sciences to which ,i now1 in the last place1 proceed4 #bee ,,book ,x4 ,,the ,,philosophy ,,of ,,pal,,tiology4 4 1 1 1 1 4 ,,strabo1 ,geogr4 #a4 p4 #ed4 ,,it is therefore1 not so much what these forms of the earth actually are1 as what they are continually becoming1 that we have to observe2 nor is it possible thus to observe them without an instinctive reference to the first state out of which they have been brought4444 ,yet to such questions continually suggesting themselves1 it is never possible to give a complete answer4 ,for a certain distance1 the past work of existing forces can be traced2 but then gradually the mist gathers1 and the footsteps of more gigantic agencies are traceable in the darkness2 and still as we endeavour to penetrate further and further into departed time1 the thunder of the ,almighty power sounds louder and louder1 and the clouds gather broader and more fearfully1 until at last the ,sinai of the world is seen altogether upon a smoke1 and the fence of its foot is reached1 where none can break through4 ,,ruskin1 ,modern ,painters1 ,vol4 ,,iv4 p4 #adc4 #beg ,,book ,x4 ,,the ,,philosophy ,,of ,,pal,,tiology4 ,,chapter ,i4 ,,of ,,pal,,tiological ,,sciences ,,in ,,general4 #a4 ,i ,,have already stated in the ,history of the ,sciences#aaj1 that the class of ,sciences which ,i designate as ,paltiological are those in which the object is to ascend from the present state of things to a more ancient condition1 from which the present is derived by intelligible causes4 ,as conspicuous examples of this class we may take ,geology1 ,glossology or ,comparative ,philology1 and ,comparative ,archology4 ,these provinces of knowledge might perhaps be intelligibly described as ,histories2 the ,history of the ,earth1--the ,history of ,languages1--the ,history of ,arts4 ,but these phrases would not fully describe the sciences we have in view2 for the object to which we now suppose their investigations to be directed is1 not merely to ascertain what the series of events has been1 as in the common forms of ,history1 but also how it has been brought about4 ,these sciences are to treat of causes as well as of effects4 ,such researches might be termed ,philosophical ,history2 or1 in order to mark more distinctly that the causes of events are the leading object of attention1 tiological ,history4 ,but since #beh it will be more convenient to describe this class of sciences by a single appellation1 ,i have taken the liberty of proposing to call them#baj the ,paltiological ,sciences4 ,note #aaj3 ,b4 xviii4 ,introd4 ,note #baj3 ,a philological writer1 in a very interesting work 7,mr4 ,donaldson1 in his ,new ,cratylus1 p4 #ab71 expresses his dislike of this word1 and suggests that ,i must mean pal-tiological4 ,i think the word is more likely to obtain currency in the more compact and euphonious form in which ,i have used it4 ,it has been adopted by ,mr4 ,winning1 in his ,manual of ,comparative ,philology1 and more recently1 by other writers4 ,while ,palontology describes the beings which have lived in former ages without investigating their causes1 and tiology treats of causes without distinguishing historical from mechanical causation2 ,paltiology is a combination of the two sciences2 exploring1 by means of the second1 the phenomena presented by the first4 ,the portions of knowledge which ,i include in this term are palontological tiological sciences4 #b4 ,all these sciences are connected by this bond2--that they all endeavour to ascend to a past state1 by considering what is the present state of things1 and what are the causes of change4 ,geology examines the existing appearance of the materials which form the earth1 infers from them previous conditions1 and speculates concerning the forces by which one condition has been made to succeed another4 ,another science1 cultivated with great zeal and success in modern times1 compares the languages of different countries and nations1 and by an examination of their materials and structure1 endeavours to determine their descent from one another3 this science has been termed ,comparative ,philology1 or ,ethnography2 and by the ,french1 ,linguistique1 a word which we might imitate in order to have a single name for the science1 but the ,greek derivative ,glossology appears to be more convenient in its form4 ,the progress of the ,arts 7,architecture and the like72--how one stage of the culture produced another2 and how far we can trace their maturest and most complete condition to their earliest form in various nations2--are problems of great interest belonging to another subject1 which we may for the present term #bei ,comparative ,archology4 ,i have already noticed1 in the ,history#caj how the researches into the origin of natural objects1 and those relating to works of art1 pass by slight gradations into each other2 how the examination of the changes which have affected an ancient temple or fortress1 harbour or river1 may concern alike the geologist and the antiquary4 ,cuvier's assertion that the geologist is an antiquary of a new order1 is perfectly correct1 for both are paltiologists4 ,note #caj3 ,b4 xviii4 ,introd4 #c4 ,we are very far from having exhausted1 by this enumeration1 the class of sciences which are thus connected4 ,we may easily point out many other subjects of speculation of the same kind4 ,as we may look back towards the first condition of our planet1 we may in like manner turn our thoughts towards the first condition of the solar system1 and try whether we can discern any traces of an order of things antecedent to that which is now established2 and if we find1 as some great mathematicians have conceived1 indications of an earlier state in which the planets were not yet gathered into their present forms1 we have1 in the pursuit of this train of research1 a paltiological portion of ,astronomy4 ,again1 as we may inquire how languages1 and how man1 have been diffused over the earth's surface from place to place1 we may make the like inquiry with regard to the races of plants and animals1 founding our inferences upon the existing geographical distribution of the animal and vegetable kingdoms3 and thus the ,geography of ,plants and of ,animals also becomes a portion of ,paltiology4 ,again1 as we can in some measure trace the progress of ,arts from nation to nation and from age to age1 we can also pursue a similar investigation with respect to the progress of ,mythology1 of ,poetry1 of ,government1 of ,law4 ,thus the philosophical history of the human race1 viewed with reference to these subjects1 if it can give rise to knowledge so exact as to be properly called ,science1 will supply ,sciences belonging to the class ,i am now to consider4 #bfj #d4 ,it is not an arbitrary and useless proceeding to construct such a ,class of ,sciences4 ,for wide and various as their subjects are1 it will be found that they have all certain principles1 maxims1 and rules of procedure in common2 and thus may reflect light upon each other by being treated of together4 ,indeed it will1 ,i trust1 appear1 that we may by such a juxtaposition of different speculations1 obtain most salutary lessons4 ,and questions1 which1 when viewed as they first present themselves under the aspect of a special science1 disturb and alarm men's minds1 may perhaps be contemplated more calmly1 as well as more clearly1 when they are considered as general problems of paltiology4 #e4 ,it will at once occur to the reader that1 if we include in the circuit of our classification such subjects as have been mentioned1--politics and law1 mythology and poetry1--we are travelling very far beyond the material sciences within whose limits we at the outset proposed to confine our discussion of principles4 ,but we shall remain faithful to our original plan2 and for that purpose shall confine ourselves1 in this work1 to those paltiological sciences which deal with material things4 ,it is true1 that the general principles and maxims which regulate these sciences apply also to investigations of a parallel kind respecting the products which result from man's imaginative and social endowments4 ,but although there may be a similarity in the general form of such portions of knowledge1 their materials are so different from those with which we have been hitherto dealing1 that we cannot hope to take them into our present account with any profit4 ,language1 ,government1 ,law1 ,poetry1 ,art1 embrace a number of peculiar ,fundamental ,ideas1 hitherto not touched upon in the disquisitions in which we have been engaged2 and most of them involved in far greater perplexity and ambiguity1 the subject of controversies far more vehement1 than the ,ideas we have hitherto been examining4 ,we must therefore avoid resting any part of our philosophy upon sciences1 or supposed sciences1 which treat of such subjects4 ,to attend to this caution1 #bfa is the only way in which we can secure the advantage we proposed to ourselves at the outset1 of taking1 as the basis of our speculations1 none but systems of undisputed truths1 clearly understood and expressed#daj4 ,we have already said that we must1 knowingly and voluntarily1 resign that livelier and warmer interest which doctrines on subjects of ,polity or ,art possess1 and content ourselves with the cold truths of the material sciences1 in order that we may avoid having the very foundations of our philosophy involved in controversy1 doubt1 and obscurity4 ,note #daj3 ,see ,introd4 p4 #i4 #f4 ,we may remark1 however1 that the necessity of rejecting from our survey a large portion of the researches which the general notion of ,paltiology includes1 suggests one consideration which adds to the interest of our task4 ,we began our inquiry with the trust that any sound views which we should be able to obtain respecting the nature of ,truth in the physical sciences1 and the mode of discovering it1 must also tend to throw light upon the nature and prospects of knowledge of all other kinds2--must be useful to us in moral1 political1 and philological researches4 ,we stated this as a confident anticipation2 and the evidence of the justice of our belief already begins to appear4 ,we have seen1 in the last ,book1 that biology leads us to psychology1 if we choose to follow the path2 and thus the passage from the material to the immaterial has already unfolded itself at one point2 and we now perceive that there are several large provinces of speculation which concern subjects belonging to man's immaterial nature1 and which are governed by the same laws as sciences altogether physical4 ,it is not our business here to dwell on the prospects which our philosophy thus opens to our contemplation2 but we may allow ourselves1 in this last stage of our pilgrimage among the foundations of the physical sciences1 to be cheered and animated by the ray #bfb that thus beams upon us1 however dimly1 from a higher and brighter region4 ,but in our reasonings and examples we shall mainly confine ourselves to the physical sciences2 and for the most part to ,geology1 which in the ,history ,i have put forwards as the best representative of the ,paltiological ,sciences4 #bfc ,,chapter ,,ii4 ,,of ,,the ,,three ,,members ,,of ,a ,,pal,,tiological ,,science4 #a4 ,divisions of such ,sciences4--,,in each of the ,sciences of this class we consider some particular order of phenomena now existing3--from our knowledge of the causes of change among such phenomena1 we endeavour to infer the causes which have made this order of things what it is3--we ascend in this manner to some previous stage of such phenomena2--and from that1 by a similar course of inference1 to a still earlier stage1 and to its causes4 ,hence it will be seen that each such science will consist of two parts1--the knowledge of the ,phenomena1 and the knowledge of their ,causes4 ,and such a division is1 in fact1 generally recognized in such sciences3 thus we have ,history1 and the ,philosophy of ,history2 we have ,comparison of ,languages1 and the ,theories of the ,origin and ,progress of ,language2 we have ,descriptive ,geology1 and ,theoretical or ,physical ,geology4 ,in all these cases1 the relation between the two parts in these several provinces of knowledge is nearly the same2 and it may1 on some occasions at least1 be useful to express the distinction in a uniform or general manner4 ,the investigation of ,causes has been termed tiology by philosophical writers1 and this term we may use1 in contradistinction to the mere ,phenomenology of each such department of knowledge4 ,and thus we should have ,phenomenal ,geology and tiological ,geology1 for the two divisions of the science which we have above termed ,descriptive and ,theoretical ,geology4 #b4 ,the ,study of ,causes4--,but our knowledge respecting the causes which actually have produced any #bfd order of phenomena must be arrived at by ascertaining what the causes of change in such matters can do4 ,in order to learn1 for example1 what share earthquakes1 and volcanoes1 and the beating of the ocean against its shores1 ought to have in our ,theory of ,geology1 we must make out what effects these agents of change are able to produce4 ,and this must be done1 not hastily1 or unsystematically1 but in a careful and connected manner2 in short1 this study of the causes of change in each order of phenomena must become a distinct body of ,science1 which must include a large amount of knowledge1 both comprehensive and precise1 before it can be applied to the construction of a theory4 ,we must have an tiology corresponding to each order of phenomena4 #c4 tiology4--,in the ,history of ,geology1 ,i have spoken of the necessity for such an tiology with regard to geological phenomena3 this necessity ,i have compared with that which1 at the time of ,kepler1 required the formation of a separate science of ,dynamics 7the doctrine of the ,causes of ,motion71 before ,physical ,astronomy could grow out of ,phenomenal ,astronomy4 ,in pursuance of this analogy1 ,i have there given the name of ,geological ,dynamics to the science which treats of the causes of geological change in general4 ,but1 as ,i have there intimated1 in a large portion of the subject the changes are so utterly different in their nature from any modification of motion1 that the term ,dynamics1 so applied1 sounds harsh and strange4 ,for in this science we have to treat1 not only of the subterraneous forces by which parts of the earth's crust are shaken1 elevated1 or ruptured1 but also of the causes which may change the climate of a portion of the earth's surface1 making a country hotter or colder than in former ages2 again1 we have to treat of the causes which modify the forms and habits of animals and vegetables1 and of the extent to which the effects of such causes can proceed2 whether1 for instance1 they can extinguish old species and produce new4 ,these and other similar investigations would not be naturally included in the notion of ,dynamics2 and therefore it #bfe might perhaps be better to use the term tiology when we wish to group together all those researches which have it for their object to determine the laws of such changes4 ,in the same manner the ,comparison and ,history of ,languages1 if it is to lead to any stable and exact knowledge1 must have appended to it an tiology1 which aims at determining the nature and the amount of the causes which really do produce changes in language2 as colonization1 conquest1 the mixture of races1 civilization1 literature1 and the like4 ,and the same rule applies to all sciences of this class4 ,we shall now make a few remarks on the characteristics of such branches of science as those to which we are led by the above considerations4 #d4 ,phenomenology requires ,classification4 ,phenomenal ,geology4--,the ,phenomenal portions of each science imply ,classification1 for no description of a large and varied mass of phenomena can be useful or intelligible without classification4 ,a representation of phenomena1 in order to answer the purposes of science1 must be systematic4 ,accordingly1 in giving the ,history of ,descriptive or ,phenomenal ,geology1 ,i have called it ,systematic ,geology1 just as ,classificatory ,botany is termed ,systematic ,botany4 ,moreover1 as we have already seen1 ,classification can never be an arbitrary process1 but always implies some natural connexion among the objects of the same ,class2 for if this connexion did not exist1 the ,classes could not be made the subjects of any true assertion4 ,yet though the classes of phenomena which our system acknowledges must be such as already exist in nature1 the discovery of these classes is1 for the most part1 very far from obvious or easy4 ,to detect the true principles of ,natural ,classes1 and to select marks by which these may be recognized1 are steps which require genius and good fortune1 and which fall to the lot only of the most eminent persons in each science4 ,in the ,history1 ,i have pointed out ,werner1 ,william ,smith1 and ,cuvier1 as the three great authors of ,systematic ,geology of ,europe4 ,the mode of classifying the materials of the earth's surface which was found1 by these philosophers1 fitted to #bff enunciate such general facts as came under their notice1 was to consider the rocks and other materials as divided into successive layers or strata1 superimposed one on another1 and variously inclined and broken4 ,the ,german geologist distinguished his strata for the most part by their mineralogical character2 the other two1 by the remains of animals and plants which the rocks contained4 ,after a beginning had thus been made in giving a genuine scientific form to phenomenal geology1 other steps followed in rapid succession1 as has already been related in the ,history#eaj4 ,the ,classification of the ,strata was fixed by a suitable ,nomenclature4 ,attempts were made to apply to other countries the order of strata which had been found to prevail in that first studied3 and in this manner it was ascertained what rocks in distant regions are the synonyms1 or ,equivalents#faj1--of each other4 ,the knowledge thus collected and systematized was exhibited in the form of ,geological ,maps4 ,note #eaj3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 iii4 ,note #faj3 ,ib4 sect4 #d4 ,moreover1 among the phenomena of geology we have ,laws of ,nature as well as ,classes4 ,the general form of mountain-chains2 the relations of the direction and inclination of different chains to each other2 the general features of mineral veins1 faults1 and fissures2 the prevalent characters of slaty cleavage2--were the subjects of laws established1 or supposed to be established1 by extensive observation of facts4 ,in like manner the organic fossils discovered in the strata were found to follow certain laws with reference to the climate which they appeared to have lived in2 and the evidence which they gave of a regular zoological development4 ,and thus1 by the assiduous labours of many accomplished and active philosophers1 ,descriptive or ,phenomenal ,geology was carried towards a state of completeness4 #e4 ,phenomenal ,uranography4--,in like manner in other paltiological researches1 as soon as they approach to an exact and scientific form1 we find the necessity of constructing in the first place a science of #bfg classification and exact description1 by means of which the phenomena may be correctly represented and compared2 and of obtaining by this step a solid basis for an inquiry into the causes which have produced them4 ,thus the ,paltiology of the ,solar ,system has1 in recent times1 drawn the attention of speculators2 and a hypothesis has been started1 that our sun and his attendant planets have been produced by the condensation of a mass of diffused matter1 such as that which constitutes the nebulous patches which we observe in the starry heavens4 ,but the sagest and most enlightened astronomers have not failed to acknowledge1 that to verify or to disprove this conjecture1 must be the work of many ages of observation and thought4 ,they have perceived also that the first step of the labour requisite for the advancement of this portion of science must be to obtain and to record the most exact knowledge at present within our reach1 respecting the phenomena of these nebul1 with which we thus compare our own system2 and1 as a necessary element of such knowledge1 they have seen the importance of a classification of these objects1 and of others1 such as ,double ,stars1 of the same kind4 ,sir ,william ,herschel1 who first perceived the bearing of the phenomena of nebul upon the history of the solar system1 made the observation of such objects his business1 with truly admirable zeal and skill2 and in the account of the results of his labours1 gave a classification of ,nebul2 separating them into1 first1 ,clusters of ,stars2 second1 ,resolvable ,nebul2 third1 ,proper ,nebul2 fourth1 ,planetary ,nebul2 fifth1 ,stellar ,nebul2 sixth1 ,nebulous ,stars#gaj4 ,and since1 in order to obtain from these remote appearances1 any probable knowledge respecting our own system1 we must discover whether they undergo any changes in the course of ages1 he devoted himself to the task of forming a record of their number and appearance in his own time1 that thus the astronomers of succeeding generations might have a #bfh definite and exact standard with which to compare their observations4 ,still1 this task would have been executed only for that part of the heavens which is visible in this country1 if this ,hipparchus of the ,nebul and ,double ,stars had not left behind him a son who inherited all his father's zeal and more than his father's knowledge4 ,sir ,john ,herschel in #ahcc went to the ,cape of ,good ,hope to complete what ,sir ,william ,herschel left wanting2 and in the course of five years observed with care all the nebul and double stars of the ,southern hemisphere4 ,this great ,herschelian ,survey of the ,heavens1 the completion of which is the noblest monument ever erected by a son to a father1 must necessarily be1 to all ages1 the basis of all speculations concerning the history and origin of the solar system2 and has completed1 so far as at present it can be completed1 the phenomenal portion of ,astronomical ,paltiology4 ,note #gaj3 ,phil4 ,trans4 #aghf and #aghi1 and ,sir ,j4 ,herschel's ,astronomy1 ,art4 #faf4 #f4 ,phenomenal ,geography of ,plants and ,animals4--,again1 there is another ,paltiological ,science1 closely connected with the speculations forced upon the geologist by the organic fossils which he discovers imbedded in the strata of the earth2--namely1 the ,science which has for its object the ,causes of the ,diffusion and ,distribution of the various kinds of ,plants and ,animals4 ,and the science also has for its first portion and indispensable foundation a description and classification of the existing phenomena4 ,such portions of science have recently been cultivated with great zeal and success1 under the titles of the ,geography of ,plants1 and the ,geography of ,animals4 ,and the results of the inquiries thus undertaken have assumed a definite and scientific form by leading to a division of the earth's surface into a certain number of botanical and zoological ,provinces1 each province occupied by its own peculiar vegetable and animal population4 ,we find1 too1 in the course of these investigations1 various general laws of the phenomena offered to our notice2 such1 for instance1 as this3--that the difference of the animals originally occupying each province1 which is clear and entire for the higher orders of #bfi animals and plants1 becomes more doubtful and indistinct when we descend to the lower kinds of organizations2 as ,infusoria and ,zoophytes#haj in the animal kingdom1 ,grasses and ,mosses among vegetables4 ,again1 other laws discovered by those who have studied the geography of plants are these3--that countries separated from each other by wide tracts of sea1 as the opposite shores of the ,mediterranean1 the islands of the ,indian and ,pacific ,oceans1 have usually much that is common in their vegetation3--and again1 that in parallel climates1 analogous tribes replace each other4 ,it would be easy to adduce other laws1 but those already stated may serve to show the great extent of the portions of knowledge which have just been mentioned1 even considered as merely ,sciences of ,phenomena4 ,note #haj3 ,prichard1 ,researches into the ,physical ,history of ,mankind1 i4 #ee1 #bh4 #g4 ,phenomenal ,glossology4--,it is not my purpose in the present work to borrow my leading illustrations from any portions of knowledge but those which are concerned with the study of material nature2 and ,i shall1 therefore1 not dwell upon a branch of research1 singularly interesting1 and closely connected with the one just mentioned1 but dealing with relations of thought rather than of things2--,i mean the ,paltiology of ,language2--the theory1 so far as the facts enable us to form a theory1 of the causes which have led to the resemblances and differences of human speech in various regions and various ages4 ,this1 indeed1 would be only a portion of the study of the history and origin of the diffusion of animals1 if we were to include man among the animals whose dispersion we thus investigate2 for language is one of the most clear and imperishable records of the early events in the career of the human race4 ,but the peculiar nature of the faculty of speech1 and the ideas which the use of it involves1 make it proper to treat ,glossology as a distinct science4 ,and of this science1 the first part must necessarily be1 as in the other sciences of this order1 a #bgj classification and comparison of languages governed in many respects by the same rules1 and presenting the same 9999difficulties1 as other sciences of classification4 ,such1 accordingly1 has been the procedure of the most philosophical glossologists4 ,they have been led to throw the languages of the earth into certain large classes or ,families1 according to various kinds of resemblance2 as the ,semitic ,family1 to which belong ,hebrew1 ,arabic1 ,chaldean1 ,syrian1 ,phoenician1 ,ethiopian1 and the like2 the ,indo-,european1 which includes ,sanskrit1 ,persian1 ,greek1 ,latin1 and ,german2 the ,monosyllabic languages1 ,chinese1 ,tibetan1 ,birman1 ,siamese2 the ,polysynthetic languages1 a class including most of the ,north-,american ,indian dialects2 and others4 ,and this work of classification has been the result of the labour and study of many very profound linguists1 and has advanced gradually from step to step4 ,thus the ,indo-,european ,family was first formed on an observation of the coincidences between ,sanskrit1 ,greek1 and ,latin2 but it was soon found to include the ,teutonic languages1 and more recently ,dr4 ,prichard#iaj has shown beyond doubt that the ,celtic must be included in the same ,family4 ,other general resemblances and differences of languages have been marked by appropriate terms3 thus ,august von ,schlegel has denominated them synthetical and analytical1 according as they form their conjugations and declensions by auxiliary verbs and prepositions1 or by changes in the word itself3 and the polysynthetic languages are so named by ,m4 ,duponceau1 in consequence of their still more complex mode of inflexion4 ,nor are there wanting1 in this science also1 general laws of phenomena2 such1 for instance1 is the curious rule of the interchange of consonants in the cognate words of ,greek1 ,gothic1 and ,german1 which has been discovered by ,james ,grimm4 ,all these remarkable portions of knowledge1 and the great works which have appeared on ,glossology1 such1 for example1 as the ,mithridates of ,adelung and ,vater1 contain1 for their largest1 and #bga hitherto probably their most valuable part1 the phenomenal portion of the science1 the comparison of languages as they now are4 ,and beyond all doubt1 until we have brought this ,comparative ,philology to a considerable degree of completeness1 all our speculations respecting the causes which have operated to produce the languages of the earth must be idle and unsubstantial dreams4 ,note #iaj3 ,dr ,prichard1 ,on the ,eastern ,origin of the ,celtic ,nations4 #ahca4 ,thus in all ,paltiological ,sciences1 in all attempts to trace back the history and discover the origin of the present state of things1 the portion of the science which must first be formed is that which classifies the phenomena1 and discovers general laws prevailing among them4 ,when this work is performed1 and not till then1 we may begin to speculate successfully concerning causes1 and to make some progress in our attempts to go back to an origin4 ,we must have a ,phenomenal science preparatory to each tiological one4 #h4 ,the ,study of ,phenomena leads to ,theory4--,as we have just said1 we cannot1 in any subject1 speculate successfully concerning the causes of the present state of things1 till we have obtained a tolerably complete and systematic view of the phenomena4 ,yet in reality men have not in any instance waited for this completeness and system in their knowledge of facts before they have begun to form theories4 ,nor was it natural1 considering the speculative propensities of the human mind1 and how incessantly it is endeavouring to apply the ,idea of ,cause1 that it should thus restrain itself4 ,i have already noticed this in the ,history of ,geology4 ',while we have been giving an account1' it is there said1 'of the objects with which ,descriptive ,geology is occupied1 it must have been felt how difficult it is1 in contemplating such facts1 to confine ourselves to description and classification4 ,conjectures and reasonings respecting the causes of the phenomena force themselves upon us at every step2 and even influence our classification and nomenclature4 ,our ,descriptive ,geology impels us to construct a ,physical ,geology4' ,and the same is the case with regard to the other subjects which ,i have mentioned4 ,the mere #bgb consideration of the different degrees of condensation of different ,nebul led ,herschel and ,laplace to contemplate the hypothesis that our solar system is a condensed ,nebula4 ,immediately upon the division of the earth's surface into botanical and zoological provinces1 and even at an earlier period1 the opposite hypotheses of the ,origin of all the animals of each kind from a single pair1 and of their original diffusion all over the earth1 were under discussion4 ,and the consideration of the families of languages irresistibly led to speculations concerning the ,families of the earliest human inhabitants of the earth4 ,in all cases the contemplation of a very few phenomena1 the discovery of a very few steps in the history1 made men wish for and attempt to form a theory of the history from the very beginning of things4 #i4 ,no sound ,theory without tiology4--,but though man is thus impelled by the natural propensities of his intellect to trace each order of things to its causes1 he does not at first discern the only sure way of obtaining such knowledge3 he does not suspect how much labour and how much method are requisite for success in this undertaking3 he is not aware that for each order of phenomena he must construct1 by the accumulated results of multiplied observation and distinct thought1 a separate iology4 ,thus1 as ,i have elsewhere remarked#ajaj1 when men had for the first time become acquainted with some of the leading phenomena of ,geology1 and had proceeded to speculate concerning the past changes and revolutions by which such results had been produced1 they forthwith supposed themselves able to judge what would be the effects of any of the obvious agents of change1 as ,water or ,volcanic ,fire4 ,it did not at first occur to them to suspect that their common and extemporaneous judgment on such points was by no means sufficient for sound knowledge4 ,they did not foresee that1 before they could determine what share these or any other causes had had in producing the present condition of the earth1 they must create #bgc a special science whose object should be to estimate the general laws and effects of such assumed causes2--that before they could obtain any sound ,geological ,theory1 they must carefully cultivate ,geological tiology4 ,note #ajaj3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 v4 sect4 #a4 ,the same disposition to proceed immediately from the facts to the theory1 without constructing1 as an intermediate step1 a ,science of ,causes1 might be pointed out in the other sciences of this order4 ,but in all of them this errour has been corrected by the failures to which it led4 ,it soon appeared1 for instance1 that a more careful inquiry into the effects which climate1 food1 habit and circumstances can produce in animals1 was requisite in order to determine how the diversities of animals in different countries have originated4 ,the tiology of ,animal ,life 7if we may be allowed to give this name to that study of such causes of change which is at present so zealously cultivated1 and which yet has no distinctive designation1 except so far as it coincides with the ,organic ,geological ,dynamics of our ,history7 is now perceived to be a necessary portion of all attempts to construct a history of the earth and its inhabitants4 #aj4 ,cause1 in ,paltiology4--,we are thus led to contemplate a class of ,sciences which are commenced with the study of ,causes4 ,we have already considered sciences which depended mainly upon the ,idea of ,cause1 namely1 the ,mechanical ,sciences4 ,but it is obvious that the ,idea of ,cause in the researches now under our consideration must be employed in a very different way from that in which we applied it formerly4 ,force is the ,cause of motion1 because force at all times and under all circumstances1 if not counteracted1 produces motion2 but the ,cause of the present condition and elevation of the ,alps1 whatever it was1 was manifested in a series of events of which each happened but once1 and occupied its proper place in the series of time4 ,the former is mechanical1 the latter historical1 cause4 ,in our present investigations1 we consider the events which we contemplate1 of whatever order they be1 as forming a chain which is extended #bgd from the beginning of things down to the present time2 and the causes of which we now speak are those which connect the successive links of this chain4 ,every occurrence which has taken place in the history of the solar system1 or the earth1 or its vegetable and animal creation1 or man1 has been at the same time effect and cause2--the effect of what preceded1 the cause of what succeeded4 ,by being effect and cause1 it has occupied some certain portion of time2 and the times which have thus been occupied by effects and causes1 summed up and taken altogether1 make up the total of ,past ,time4 ,the ,past has been a series of events connected by this historical causation1 and the ,present is the last term of this series4 ,the problem in the ,paltiological ,sciences1 with which we are here concerned1 is1 to determine the manner in which each term is derived from the preceding1 and thus1 if possible1 to calculate backwards to the origin of the series4 #aa4 ,various kinds of ,cause4--,those modes by which one term in the natural series of events is derived from another1--the forms of historical causation1--the kinds of connexion between the links of the infinite chain of time1--are very various2 nor need we attempt to enumerate them4 ,but these kinds of causation being distinguished from each other1 and separately studied1 each becomes the subject of a separate tiology4 ,thus the causes of change in the earth's surface1 residing in the elements1 fire and water1 form the main subject of ,geological tiology4 ,the tiology of the vegetable and animal kingdoms investigates the causes by which the forms and distribution of species of plants and animals are affected4 ,the study of causes in ,glossology leads to an tiology of ,language1 which shall distinguish1 analyse1 and estimate the causes by which certain changes are produced in the languages of nations2 in like manner we may expect to have an tiology of ,art1 which shall scrutinise the influences by which the various forms of art have each given birth to its successor3 by which1 for example1 there have been brought into being those various forms of architecture which we term ,egyptian1 #bge ,doric1 ,ionic1 ,roman1 ,byzantine1 ,romanesque1 ,gothic1 ,italian1 ,elizabethan4 ,it is easily seen by this slight survey how manifold and diverse are the kinds of cause which the ,paltiological ,sciences bring under our consideration4 ,but in each of those sciences we shall obtain solid and complete systems of knowledge1 only so far as we study1 with steady thought and careful observation1 that peculiar kind of cause which is appropriate to the phenomena under our consideration4 #ab4 ,hypothetical ,order of ,paltiological ,causes4--,the various kinds of historical cause are not only connected with each other by their common bearing upon the historical sciences1 but they form a kind of progression which we may represent to ourselves as having acted in succession in the hypothetical history of the earth and its inhabitants4 ,thus assuming1 merely as a momentary hypothesis1 the origin of the ,solar ,system by the condensation of a ,nebula1 we have to contemplate1 first1 the causes by which the luminous incandescent diffused mass of which a nebula is supposed to be constituted1 is gradually condensed1 cooled1 collected into definite masses1 solidified1 and each portion made to revolve about its axis1 and the whole to travel about another body4 ,we have no difficulty in ascribing the globular form of each mass to the mutual attraction of its particles3 but when this form was once assumed1 and covered with a solid crust1 are there1 we may ask1 in the constitution of such a body1 any causes at work by which the crust might be again broken up and portions of it displaced1 and covered with other matter8 ,again1 if we can thus explain the origin of the ,earth1 can we with like success account for the presence of the ,atmosphere and the ,waters of earth and ocean8 ,supposing this done1 we have then to consider by what causes such a body could become stocked with vegetable and animal ,life2 for there have not been wanting persons1 extravagant speculators1 no doubt1 who have conceived that even this event in the history of the world might be the work of natural causes4 ,supposing an origin given to life #bgf upon our earth1 we have then1 brought before us by geological observations1 a series of different forms of vegetable and animal existence2 occurring in different strata1 and1 as the phenomena appear irresistibly to prove1 existing at successive periods3 and we are compelled to inquire what can have been the causes by which the forms of each period have passed into those of the next4 ,we find1 too1 that strata1 which must have been at first horizontal and continuous1 have undergone enormous dislocations and ruptures1 and we have to consider the possible effect of aqueous and volcanic causes to produce such changes in the earth's crust4 ,we are thus led to the causes which have produced the present state of things on the earth2 and these are causes to which we may hypothetically ascribe1 not only the form and position of the inert materials of the earth1 but also the nature and distribution of its animal and vegetable population4 ,man too1 no less than other animals1 is affected by the operation of such causes as we have referred to1 and must1 therefore1 be included in such speculations4 ,but man's history only begins1 where that of other animals ends1 with his mere existence4 ,they are stationary1 he is progressive4 ,other species of animals1 once brought into being1 continue the same through all ages2 man is changing1 from age to age1 his language1 his thoughts1 his works4 ,yet even these changes are bound together by laws of causation2 and these causes too may become objects of scientific study4 ,and such causes1 though not to be dwelt upon now1 since we permit ourselves to found our philosophy upon the material sciences only1 must still1 when treated scientifically1 fall within the principles of our philosophy1 and must be governed by the same general rules to which all science is subject4 ,and thus we are led by a close and natural connexion1 through a series of causes1 extending from those which regulate the imperceptible changes of the remotest nebul in the heavens1 to those which determine the diversities of language1 the mutations of art1 and even the progress of civilization1 polity1 and literature4 #bgg ,while ,i have been speaking of this supposed series of events1 including in its course the formation of the earth1 the introduction of animal and vegetable life1 and the revolutions by which one collection of species has succeeded another1 it must not be forgotten1 that though ,i have thus hypothetically spoken of these events as occurring by force of natural causes1 this has been done only that the true efficacy of such causes might be brought under our consideration and made the subject of scientific examination4 ,it may be found1 that such occurrences as these are quite inexplicable by the aid of any natural causes with which we are acquainted2 and thus1 the result of our investigations1 conducted with strict regard to scientific principles1 may be1 that we must either contemplate supernatural influences as part of the past series of events1 or declare ourselves altogether unable to form this series into a connected chain4 #ac4 ,mode of ,cultivating tiology3--,in ,geology4--,in what manner1 it may be asked1 is tiology1 with regard to each subject such as we have enumerated1 to be cultivated8 ,in order to answer this question1 we must1 according to our method of proceeding1 take the most successful and complete examples which we possess of such portions of science4 ,but in truth1 we can as yet refer to few examples of this kind4 ,in ,geology1 it is only very recently1 and principally through the example and influence of ,sir ,charles ,lyell1 that the tiology has been detached from the descriptive portion of the science2 and cultivated with direct attention3 in other sciences the separation has hardly yet been made4 ,but if we examine what has already been done in ,geological tiology1 or as in the ,history it is termed1 ,geological ,dynamics1 we shall find a number of different kinds of investigation which1 by the aid of our general principles respecting the formation of sciences1 may suffice to supply very useful suggestions for tiology in general4 ,in ,geological tiology1 causes have been studied1 in many instances1 by attending to their action in the phenomena of the present state of things1 and by inferring #bgh from this the nature and extent of the action which they may have exercised in former times4 ,this has been done1 for example1 by ,von ,hoff1 ,sir ,charles ,lyell1 and others1 with regard to the operations of rivers1 seas1 springs1 glaciers1 and other aqueous causes of change1 ,again1 the same course has been followed by the same philosophers with respect to volcanoes1 earthquakes1 and other violent agents4 ,sir ,charles ,lyell has attempted to show1 too1 that there take place1 in our own time1 not only violent agitations1 but slow motions of parts of the earth's crust1 of the same kind and order with those which have assisted in producing all anterior changes4 ,but while we thus seek instruction in the phenomena of the present state of things1 we are led to the question1 ,what are the limits of this 'present' period8 ,for instance1 among the currents of lava which we trace as part of the shores of ,italy and ,sicily1 which shall we select as belonging to the existing order of things8 ,in going backwards in time1 where shall we draw the line8 and why at such particular point8 ,these questions are important1 for our estimate of the efficacy of known causes will vary with the extent of the effects which we ascribe to them4 ,hence the mode in which we group together rocks is not only a step in geological classification1 but is also important to tiology4 ,thus1 when the vast masses of trap rocks in the ,western ,isles of ,scotland and in other countries1 which had been maintained by the ,wernerians to be of aqueous origin1 were1 principally by the sagacity and industry of ,macculloch1 identified as to their nature with the products of recent volcanoes1 the amount of effect which might justifiably be ascribed to volcanic agency was materially extended4 ,in other cases1 instead of observing the current effects of our geological causes1 we have to estimate the results from what we know of the causes themselves2 as when1 with ,herschel1 we calculate the alterations in the temperature of the earth which astronomical changes may possibly produce2 or when1 with ,fourier1 we try to calculate the rate of cooling of the earth's #bgi surface1 on the hypothesis of an incandescent central mass4 ,in other cases1 again1 we are not able to calculate the effects of our causes rigorously1 but estimate them as well as we can2 partly by physical reasonings1 and partly by comparison with such analogous cases as we can find in the present state of things4 ,thus ,sir ,charles ,lyell infers the change of climate which would result if land were transferred from the neighbourhood of the poles to that of the equator1 by reasonings on the power of land and water to contain and communicate heat1 supported by a reference to the different actual climates of places1 lying under the same latitude1 but under different conditions as to the distribution of land and water4 ,thus our tiology is constructed partly from calculation and reasoning1 partly from phenomena4 ,but we may observe that when we reason from phenomena to causes1 we usually do so by various steps2 often ascending from phenomena to mere laws of phenomena1 before we can venture to connect the phenomenon confidently with its cause4 ,thus the law of subterranean heat1 that it increases in descending below the surface1 is now well established1 although the doctrine which ascribes this effect to a central heat is not universally assented to4 #ad4 ,in the ,geography of ,plants and ,animals4--,we may find in other subjects also1 considerable contributions towards tiology1 though not as yet a complete ,system of ,science4 ,the tiology of ,vegetables and ,animals1 indeed1 has been studied with great zeal in modern times1 as an essential preparative to geological theory2 for how can we decide whether any assumed causes have produced the succession of species which we find in the earth's strata1 except we know what effect of this kind given causes can produce8 ,accordingly1 we find in ,sir ,charles ,lyell's ,treatise on ,geology the most complete discussion of such questions as belong to these subjects3--for example1 the question whether species can be transmuted into other species by the long-continued influence of external causes1 as climate1 food1 domestication1 combined with internal #bhj causes1 as habits1 appetencies1 progressive tendencies4 ,we may observe1 too1 that as we have brought before us1 the inquiry what change difference of climate can produce in any species1 we have also the inverse problem1 how far a different development of the species1 or a different collection of species1 proves a difference of climate4 ,in the same way1 the geologist of the present day considers the question1 whether1 in virtue of causes now in action1 species are from time to time extinguished2 and in like manner1 the geologists of an earlier period discussed the question1 now long completely decided1 whether fossil species in general are really extinct species4 #ae4 ,in ,languages4--,even with reference to the tiology of ,language1 although this branch of science has hardly been considered separately from the glossological investigations in which it is employed or assumed to be employed1 it might perhaps be possible to point out causes or conditions of change which1 being general in their nature1 must operate upon all languages alike4 ,changes made for the sake of euphony when words are modified and combined1 occur in all dialects4 ,who can doubt that such changes of consonants as those by which the ,greek roots become ,gothic1 and the ,gothic1 ,german1 have for their cause some general principle in the pronunciation of each language8 ,again1 we might attempt to decide other questions of no small interest4 ,have the terminations of verbs arisen from the accretion of pronouns2 or1 on the other hand1 does the modification of a verb imply a simpler mental process than the insulation of a pronoun1 as ,adam ,smith has maintained8 ,again1 when the language of a nation is changed by the invasion and permanent mixture of an enemy of different speech1 is it generally true that it is changed from a synthetic to an analytical structure8 ,i will mention only one more of these wide and general glossological inquiries4 ,is it true1 as ,dr4 ,prichard has suggested#aaaj1 that languages have become more permanent as we come down #bha towards later times8 ,may we justifiably suppose1 with him1 that in the very earliest times1 nations1 when they had separated from one stock1 might lose all traces of this common origin out of their languages1 though retaining strong evidences of it in their mythology1 social forms1 and arts1 as appears to be the case with the ancient ,egyptians and the ,indians#abaj4 ,note #aaaj3 ,researches1 ii4 #bba4 ,note #abaj3 ,researches1 ii4 #aib4 ,large questions of this nature cannot be treated profitably in any other way than by an assiduous study of the most varied forms of living and dead languages4 ,but on the other hand1 the study of languages should be prosecuted not only by a direct comparison of one with another1 but also with a view to the formation of a science of causes and general principles1 embracing such discussions as ,i have pointed out4 ,it is only when such a science has been formed1 that we can hope to obtain any solid and certain results in the ,paltiology of ,language2--to determine1 with any degree of substantial proof1 what is the real evidence which the wonderful faculty of speech1 under its present developments and forms1 bears to the events which have taken place in its own history1 and in the history of man since his first origin4 #af4 ,construction of ,theories4--,when we have thus obtained1 with reference to any such subject as those we have here spoken of1 these two portions of science1 a ,systematic ,description of the ,facts1 and a rigorous ,analysis of the ,causes1--the ,phenomenology and the tiology of the subject1--we are prepared for the third member which completes the science1 the ,theory of the actual facts4 ,we can then take a view of the events which really have happened1 discerning their connexion1 interpreting their evidence1 supplying from the context the parts which are unapparent4 ,we can account for known facts by intelligible causes2 we can infer latent facts from manifest effects1 so as to obtain a distinct insight into the whole history of events up to the present time1 and to see the last result of the whole in the present condition of things4 #bhb ,the term ,theory1 when rigorously employed in such sciences as those which we here consider1 bears nearly the sense which ,i have adopted3 it implies a consistent and systematic view of the actual facts1 combined with a true apprehension of their connexion and causes4 ,thus if we speak of 'a ,theory of ,mount ,etna1' or 'a ,theory of the ,paris ,basin1' we mean a connected and intelligible view of the events by which the rocks in these localities have come into their present condition4 ,undoubtedly the term ,theory has often been used in a looser sense2 and men have put forth ',theories of the ,earth1' which1 instead of including the whole mass of actual geological facts and their causes1 only assigned1 in a vague manner1 some causes by which some few phenomena might1 it was conceived1 be accounted for4 ,perhaps the portion of our ,paltiological ,sciences which we now wish to designate1 would be more generally understood if we were to describe it as ,theoretical or ,philosophical ,history2 as when we talk of 'the ,theoretical ,history of ,architecture1' or 'the ,philosophical ,history of ,language4' ,and in the same manner we might speak of the ,theoretical ,history of the ,animal and ,vegetable ,kingdoms2 meaning1 a distinct account of the events which have produced the present distribution of species and families4 ,but by whatever phrase we describe this portion of science1 it is plain that such a ,theory1 such a ,theoretical ,history1 must result from the application of causes well understood to facts well ascertained4 ,and if the term ,theory be here employed1 we must recollect that it is to be understood1 not in its narrower sense as opposed to facts1 but in its wider signification1 as including all known facts and differing from them only in introducing among them principles of intelligible connexion4 ,the ,theories of which we now speak are true ,theories1 precisely because they are identical with the total system of the ,facts4 #ag4 ,no sound ,paltiological ,theory yet extant4--,it is not to disparage unjustly the present state of science1 to say that as yet no such theory exists on any subject4 ',theories of the ,earth' have been #bhc repeatedly published2 but when we consider that even the facts of geology have been observed only on a small portion of the earth's surface1 and even within those narrow bounds very imperfectly studied1 we shall be able to judge how impossible it is that geologists should have yet obtained a well-established ,theoretical ,history of the changes which have taken place in the crust of the terrestrial globe from its first origin4 ,accordingly1 ,i have ventured in my ,history to designate the most prominent of the ,theories which have hitherto prevailed as premature geological theories#acaj3 and we shall soon see that geological theory has not advanced beyond a few conjectures1 and that its cultivators are at present mainly occupied with a controversy in which the two extreme hypotheses which first offer themselves to men's minds are opposed to each other4 ,and if we have no theoretical ,history of the ,earth which merits any confidence1 still less have we any theoretical ,history of ,language1 or of the ,arts1 which we can consider as satisfactory4 ,the ,theoretical ,history of the ,vegetable and ,animal ,kingdoms is closely connected with that of the ,earth on which they subsist1 and must follow the fortunes of ,geology4 ,and thus we may venture to say that no ,paltiological ,science1 as yet1 possesses all its three members4 ,indeed most of them are very far from having completed and systematized their ,phenomenology3 in all1 the cultivation of tiology is but just begun1 or is not begun2 in all1 the ,theory must reward the exertions of future1 probably of distant1 generations4 ,note #acaj3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 vii4 sect4 #c4 ,but in the mean time we may derive some instruction from the comparison of the two antagonist hypotheses of which ,i have spoken4 #bhd ,,chapter ,,iii4 ,,of ,,the ,,doctrine ,,of ,,catastrophes ,,and ,,the ,,doctrine ,,of ,,uniformity4 #a4 ,doctrine of ,catastrophes4--,i ,,have already shown1 in the ,history of ,geology1 that the attempts to frame a theory of the earth have brought into view two completely opposite opinions3--one1 which represents the course of nature as uniform through all ages1 the causes which produce change having had the same intensity in former times which they have at the present day2--the other opinion1 which sees1 in the present condition of things1 evidences of catastrophes2--changes of a more sweeping kind1 and produced by more powerful agencies than those which occur in recent times4 ,geologists who held the latter opinion1 maintained that the forces which have elevated the ,alps or the ,andes to their present height could not have been any forces which are now in action3 they pointed to vast masses of strata hundreds of miles long1 thousands of feet thick1 thrown into highly-inclined positions1 fractured1 dislocated1 crushed3 they remarked that upon the shattered edges of such strata they found enormous accumulations of fragments and rubbish1 rounded by the action of water1 so as to denote ages of violent aqueous action3 they conceived that they saw instances in which whole mountains of rock in a state of igneous fusion1 must have burst the earth's crust from below3 they found that in the course of the revolutions by which one stratum of rock was placed upon another1 the whole collection of animal species which tenanted the earth and the seas had been removed1 and a new set of living things introduced in its place3 finally1 they found1 above all the strata1 #bhe vast masses of sand and gravel containing bones of animals1 and apparently the work of a mighty deluge4 ,with all these proofs before their eyes1 they thought it impossible not to judge that the agents of change by which the world was urged from one condition to another till it reached its present state must have been more violent1 more powerful1 than any which we see at work around us4 ,they conceived that the evidence of 'catastrophes' was irresistible4 #b4 ,doctrine of ,uniformity4--,i need not here repeat the narrative 7given in the ,history#adaj7 of the process by which this formidable array of proofs was1 in the minds of some eminent geologists1 weakened1 and at last overcome4 ,this was done by showing that the sudden breaks in the succession of strata were apparent only1 the discontinuity of the series which occurred in one country being removed by terms interposed in another locality3--by urging that the total effect produced by existing causes1 taking into account the accumulated result of long periods1 is far greater than a casual speculator would think possible3--by making it appear that there are in many parts of the world evidences of a slow and imperceptible rising of the land since it was the habitation of now existing species3--by proving that it is not universally true that the strata separated in time by supposed catastrophes contain distinct species of animals3--by pointing out the limited fields of the supposed diluvial action3--and finally1 by remarking that though the creation of species is a mystery1 the extinction of species is going on in our own day4 ,hypotheses were suggested1 too1 by which it was conceived that the change of climate might be explained1 which1 as the consideration of the fossil remains seemed to show1 must have taken place between the ancient and the modern times4 ,in this manner the whole evidence of catastrophes was explained away3 the notion of a series of paroxysms of violence in the causes of change was represented as a delusion arising from our #bhf contemplating short periods only1 in the action of present causes3 length of time was called in to take the place of intensity of force3 and it was declared that ,geology need not despair of accounting for the revolutions of the earth1 as ,astronomy accounts for the revolutions of the heavens1 by the universal action of causes which are close at hand to us1 operating through time and space without variation or decay4 ,note #adaj3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 viii4 sect4 #b4 ,an antagonism of opinions1 somewhat of the same kind as this1 will be found to manifest itself in the other ,paltiological ,sciences as well as in ,geology2 and it will be instructive to endeavour to balance these opposite doctrines4 ,i will mention some of the considerations which bear upon the subject in its general form4 #c4 ,is ,uniformity probable priori8--,the doctrine of ,uniformity in the course of nature has sometimes been represented by its adherents as possessing a great degree of priori probability4 ,it is highly unphilosophical1 it has been urged1 to assume that the causes of the geological events of former times were of a different kind from causes now in action1 if causes of this latter kind can in any way be made to explain the facts4 ,the analogy of all other sciences compels us1 it was said1 to explain phenomena by known1 not by unknown1 causes4 ,and on these grounds the geological teacher recommended#aeaj 'an earnest and patient endeavour to reconcile the indications of former change with the evidence of gradual mutations now in progress4' ,note #aeaj3 ,lyell1 #dth ed4 b4 iv4 c4 i4 p4 #cbh4 ,but on this we may remark1 that if by known causes we mean causes acting with the same intensity which they have had during historical times1 the restriction is altogether arbitrary and groundless4 ,let it be granted1 for instance1 that many parts of the earth's surface are now undergoing an imperceptible rise4 ,it is not pretended that the rate of this elevation is rigorously uniform2 what1 then1 are the limits of its velocity8 ,why may it not increase so as to assume that character of violence which we may term a #bhg catastrophe with reference to all changes hitherto recorded8 ,why may not the rate of elevation be such that we may conceive the strata to assume suddenly a position nearly vertical8 ,and is it1 in fact1 easy to conceive a position of strata nearly vertical1 a position which occurs so frequently1 to be gradually assumed8 ,in cases where the strata are nearly vertical1 as in the ,isle of ,wight1 and hundreds of other places1 or where they are actually inverted1 as sometimes occurs1 are not the causes which have produced the effect as truly known causes1 as those which have raised the coasts where we trace the former beach in an elevated terrace8 ,if the latter case proves slow elevation1 does not the former case prove rapid elevation8 ,in neither case have we any measure of the time employed in the change2 but does not the very nature of the results enable us to discern1 that if one was gradual1 the other was comparatively sudden8 ,the causes which are now elevating a portion of ,scandinavia can be called known causes1 only because we know the effect4 ,are not the causes which have elevated the ,alps and the ,andes known causes in the same sense8 ,we know nothing in either case which confines the intensity of the force within any limit1 or prescribes to it any law of uniformity4 ,why1 then1 should we make a merit of cramping our speculations by such assumptions8 ,whether the causes of change do act uniformly2--whether they oscillate only within narrow limits2--whether their intensity in former times was nearly the same as it now is2--these are precisely the questions which we wish ,science to answer to us impartially and truly3 where is then the wisdom of 'an earnest and patient endeavour' to secure an affirmative reply8 ,thus ,i conceive that the assertion of an priori claim to probability and philosophical spirit in favour of the doctrine of uniformity1 is quite untenable4 ,we must learn from an examination of all the facts1 and not from any assumption of our own1 whether the course of nature be uniform4 ,the limit of intensity being really unknown1 catastrophes are just as probable #bhh as uniformity4 ,if a volcano may repose for a thousand years1 and then break out and destroy a city2 why may not another volcano repose for ten thousand years1 and then destroy a continent2 or if a continent1 why not the whole habitable surface of the earth8 #d4 ,cycle of ,uniformity indefinite4--,but this argument may be put in another form4 ,when it is said that the course of nature is uniform1 the assertion is not intended to exclude certain smaller variations of violence and rest1 such as we have just spoken of2--alternations of activity and repose in volcanoes2 or earthquakes1 deluges1 and storms1 interposed in a more tranquil state of things4 ,with regard to such occurrences1 terrible as they appear at the time1 they may not much affect the average rate of change2 there may be a cycle1 though an irregular one1 of rapid and slow change2 and if such cycles go on succeeding each other1 we may still call the order of nature uniform1 notwithstanding the periods of violence which it involves4 ,the maximum and minimum intensities of the forces of mutation alternate with one another2 and we may estimate the average course of nature as that which corresponds to something between the two extremes4 ,but if we thus attempt to maintain the uniformity of nature by representing it as a series of cycles1 we find that we cannot discover1 in this conception1 any solid ground for excluding catastrophes4 ,what is the length of that cycle1 the repetition of which constitutes uniformity8 ,what interval from the maximum to the minimum does it admit of8 ,we may take for our cycle a hundred or a thousand years1 but evidently such a proceeding is altogether arbitrary4 ,we may mark our cycles by the greatest known paroxysms of volcanic and terremotive agency1 but this procedure is no less indefinite and inconclusive than the other4 ,but further2 since the cycle in which violence and repose alternate is thus indefinite in its length and in its range of activity1 what ground have we for assuming more than one such cycle1 extending from the origin of things to the present time8 ,why may we not suppose the maximum force of the causes of change #bhi to have taken place at the earliest period1 and the tendency towards the minimum to have gone on ever since8 ,or instead of only one cycle1 there may have been several1 but of such length that our historical period forms a portion only of the last2--the feeblest portion of the latest cycle4 ,and thus violence and repose may alternate upon a scale of time and intensity so large1 that man's experience supplies no evidence enabling him to estimate the amount4 ,the course of things is uniform1 to an ,intelligence which can embrace the succession of several cycles1 but it is catastrophic to the contemplation of man1 whose survey can grasp a part only of one cycle4 ,and thus the hypothesis of uniformity1 since it cannot exclude degrees of change1 nor limit the range of these degrees1 nor define the interval of their recurrence1 cannot possess any essential simplicity which1 previous to inquiry1 gives it a claim upon our assent superior to that of the opposite catastrophic hypothesis4 #e4 ,uniformitarian ,arguments are ,negative only4--,there is an opposite tendency in the mode of maintaining the catastrophist and the uniformitarian opinions1 which depends upon their fundamental principles1 and shows itself in all the controversies between them4 ,the ,catastrophist is affirmative1 the ,uniformitarian is negative in his assertions3 the former is constantly attempting to construct a theory2 the latter delights in demolishing all theories4 ,the one is constantly bringing fresh evidence of some great past event1 or series of events1 of a striking and definite kind2 his antagonist is at every step explaining away the evidence1 and showing that it proves nothing4 ,one geologist adduces his proofs of a vast universal deluge2 but another endeavours to show that the proofs do not establish either the universality or the vastness of such an event4 ,the inclined broken edges of a certain formation1 covered with their own fragments1 beneath superjacent horizontal deposits1 are at one time supposed to prove a catastrophic breaking up of the earlier strata2 but this opinion is controverted by showing that the same formations1 when pursued into other countries1 #bij exhibit a uniform gradation from the lower to the upper1 with no trace of violence4 ,extensive and lofty elevations of the coast1 continents of igneous rock1 at first appear to indicate operations far more gigantic than those which now occur2 but attempts are soon made to show that time only is wanting to enable the present age to rival the past in the production of such changes4 ,each new fact adduced by the catastrophist is at first striking and apparently convincing2 but as it becomes familiar1 it strikes the imagination less powerfully2 and the uniformitarian1 constantly labouring to produce some imitation of it by the machinery which he has so well studied1 at last in every case seems to himself to succeed1 so far as to destroy the effect of his opponent's evidence4 ,this is so with regard to more remote1 as well as with regard to immediate evidences of change4 ,when it is ascertained that in every part of the earth's crust the temperature increases as we descend below the surface1 at first this fact seems to indicate a central heat3 and a central heat naturally suggests an earlier state of the mass1 in which it was incandescent1 and from which it is now cooling4 ,but this original incandescence of the globe of the earth is manifestly an entire violation of the present course of things2 it belongs to the catastrophist view1 and the advocates of uniformity have to explain it away4 ,accordingly1 one of them holds that this increase of heat in descending below the surface may very possibly not go on all the way to the center4 ,the heat which increases at first as we descend1 may1 he conceives1 afterwards decrease2 and he suggests causes which may have produced such a succession of hotter and colder shells within the mass of the earth4 ,i have mentioned this suggestion in the ,history of ,geology2 and have given my reasons for believing it altogether untenable#afaj4 ,other persons also1 desirous of reconciling this subterraneous heat with the tenet of uniformity1 have #bia offered another suggestion3--that the warmth or incandescence of the interior parts of the earth does not arise out of an originally hot condition from which it is gradually cooling1 but results from chemical action constantly going on among the materials of the earth's substance4 ,and thus new attempts are perpetually making1 to escape from the cogency of the reasonings which send us towards an original state of things different from the present4 ,those who theorize concerning an origin go on building up the fabric of their speculations1 while those who think such theories unphilosophical1 ever and anon dig away the foundation of this structure4 ,as we have already said1 the uniformitarian's doctrines are a collection of negatives4 ,note #afaj3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 v4 sect4 #e1 and note4 ,this is so entirely the case1 that the uniformitarian would for the most part shrink from maintaining as positive tenets the explanations which he so willingly uses as instruments of controversy4 ,he puts forward his suggestions as difficulties1 but he will not stand by them as doctrines4 ,and this is in accordance with his general tendency2 for any of his hypotheses1 if insisted upon as positive theories1 would be found inconsistent with the assertion of uniformity4 ,for example1 the nebular hypothesis appears to give to the history of the heavens an aspect which obliterates all special acts of creation1 for1 according to that hypothesis1 new planetary systems are constantly forming2 but when asserted as the origin of our own solar system1 it brings with it an original incandescence1 and an origin of the organic world4 ,and if1 instead of using the chemical theory of subterraneous heat to neutralize the evidence of original incandescence1 we assert it as a positive tenet1 we can no longer maintain the infinite past duration of the earth2 for chemical forces1 as well as mechanical1 tend to equilibrium2 and that condition once attained1 their efficacy ceases4 ,chemical affinities tend to form new compounds2 and though1 when many and various elements are mingled together1 the play of synthesis and analysis may go on for a long time1 it must at last end4 ,if1 for instance1 a large portion of the earth's mass were originally pure potassium1 we #bib can imagine violent igneous action to go on so long as any part remained unoxidized2 but when the oxidation of the whole has once taken place1 this action must be at an end2 for there is in the hypothesis no agency which can reproduce the deoxidized metal4 ,thus a perpetual motion is impossible in chemistry1 as it is in mechanics2 and a theory of constant change continued through infinite time1 is untenable when asserted upon chemical1 no less than upon mechanical principles4 ,and thus the ,skepticism of the uniformitarian is of force only so long as it is employed against the ,dogmatism of the catastrophist4 ,when the ,doubts are erected into ,dogmas1 they are no longer consistent with the tenet of ,uniformity4 ,when the ,negations become ,affirmations1 the ,negation of an ,origin vanishes also4 #f4 ,uniformity in the ,organic ,world4--,in speaking of the violent and sudden changes which constitute catastrophes1 our thoughts naturally turn at first to great mechanical and physical effects2--ruptures and displacements of strata2 extensive submersions and emersions of land2 rapid changes of temperature4 ,but the catastrophes which we have to consider in geology affect the organic as well as the inorganic world4 ,the sudden extinction of one collection of species1 and the introduction of another in their place1 is a ,catastrophe1 even if unaccompanied by mechanical violence4 ,accordingly1 the antagonism of the catastrophist and uniformitarian schools has shown itself in this department of the subject1 as well as in the other4 ,when geologists had first discovered that the successive strata are each distinguished by appropriate organic fossils1 they assumed at once that each of these collections of living things belonged to a separate creation4 ,but this conclusion1 as ,i have already said1 ,sir ,c4 ,lyell has attempted to invalidate1 by proving that in the existing order of things1 some species become extinct2 and by suggesting it as possible1 that in the same order1 it may be true that new species are from time to time produced1 even in the present course of nature4 ,and in this1 as in the other part of the subject1 he calls in #bic the aid of vast periods of time1 in order that the violence of the changes may be softened down3 and he appears disposed to believe that the actual extinction and creation of species may be so slow as to excite no more notice than it has hitherto obtained2 and yet may be rapid enough1 considering the immensity of geological periods1 to produce such a succession of different collections of species as we find in the strata of the earth's surface4 #g4 ,origin of the present ,organic ,world4--,the last great event in the history of the vegetable and animal kingdoms was that by which their various tribes were placed in their present seats4 ,and we may form various hypotheses with regard to the sudden or gradual manner in which we may suppose this distribution to have taken place4 ,we may assume that at the beginning of the present order of things1 a stock of each species was placed in the vegetable or animal province to which it belongs1 by some cause out of the common order of nature2 or we may take a uniformitarian view of the subject1 and suppose that the provinces of the organic world derived their population from some anterior state of things by the operation of natural causes4 ,nothing has been pointed out in the existing order of things which has any analogy or resemblance1 of any valid kind1 to that creative energy which must be exerted in the production of a new species4 ,and to assume the introduction of new species as 'a part of the order of nature1' without pointing out any natural fact with which such an event can be classed1 would be to reject creation by an arbitrary act4 ,hence1 even on natural grounds1 the most intelligible view of the history of the animal and vegetable kingdoms seems to be1 that each period which is marked by a distinct collection of species forms a cycle2 and that at the beginning of each such cycle a creative power was exerted1 of a kind to which there was nothing at all analogous in the succeeding part of the same cycle4 ,if it be urged that in some cases the same species1 or the same genus1 runs through two geological formations1 #bid which must1 on other grounds1 be referred to different cycles of creative energy1 we may reply that the creation of many new species does not imply the extinction of all the old ones4 ,thus we are led by our reasonings to this view1 that the present order of things was commenced by an act of creative power entirely different to any agency which has been exerted since4 ,none of the influences which have modified the present races of animals and plants since they were placed in their habitations on the earth's surface can have had any efficacy in producing them at first4 ,we are necessarily driven to assume1 as the beginning of the present cycle of organic nature1 an event not included in the course of nature4 ,and we may remark that this necessity is the more cogent1 precisely because other cycles have preceded the present4 #h4 ,nebular ,origin of the ,solar ,system4--,if we attempt to apply the same antithesis of opinion 7the doctrines of ,catastrophe and ,uniformity7 to the other subjects of paltiological sciences1 we shall be led to similar conclusions4 ,thus1 if we turn our attention to ,astronomical ,paltiology1 we perceive that the ,nebular ,hypothesis has a uniformitarian tendency4 ,according to this hypothesis the formation of this our system of sun1 planets1 and satellites1 was a process of the same kind as those which are still going on in the heavens4 ,one after another1 nebul condense into separate masses1 which begin to revolve about each other by mechanical necessity1 and form systems of which our solar system is a finished example4 ,but we may remark1 that the uniformitarian doctrine on this subject rests on most unstable foundations4 ,we have as yet only very vague and imperfect reasonings to show that by such condensation a material system such as ours could result2 and the introduction of organized beings into such a material system is utterly out of the reach of our philosophy4 ,here again1 therefore1 we are led to regard the present order of the world as pointing towards an origin altogether of a different kind from anything which our material science can grasp4 #bie #i4 ,origin of ,languages4--,we may venture to say that we should be led to the same conclusion once more1 if we were to take into our consideration those paltiological sciences which are beyond the domain of matter2 for instance1 the ,history of ,languages4 ,we may explain many of the differences and changes which we become acquainted with1 by referring to the action of causes of change which still operate4 ,but what glossologist will venture to declare that the efficacy of such causes has been uniform2--that the influences which mould a language1 or make one language differ from others of the same stock1 operated formerly with no more efficacy than they exercise now4 ',where1' as has elsewhere been asked1 'do we now find a language in the process of formation1 unfolding itself in inflexions1 terminations1 changes of vowels by grammatical relations1 such as characterise the oldest known languages8' ,again1 as another proof how little the history of languages suggests to the philosophical glossologist the persuasion of a uniform action of the causes of change1 ,i may refer to the conjecture of ,dr4 ,prichard1 that the varieties of language produced by the separation of one stock into several1 have been greater and greater as we go backwards in history3--that#agaj the formation of sister dialects from a common language 7as the ,scandinavian1 ,german1 and ,saxon dialects from the ,teutonic1 or the ,gaelic1 ,erse and ,welsh from the ,celtic7 belongs to the first millennium before the ,christian era2 while the formation of cognate languages of the same family1 as the ,sanskrit1 ,latin1 ,greek and ,gothic1 must be placed at least two thousand years before that era2 and at a still earlier period took place the separation of the great families themselves1 the ,indo-,european1 ,semitic1 and others1 in which it is now difficult to trace the features of a common origin4 ,no hypothesis except one of this kind will explain the existence of the families1 groups1 and dialects of languages1 which we find in existence4 ,yet this is an entirely different view from that which #bif the hypothesis of the uniform progress of change would give4 ,and thus1 in the earliest stages of man's career1 the revolutions of language must have been1 even by the evidence of the theoretical history of language itself1 of an order altogether different from any which have taken place within the recent history of man4 ,and we may add1 that as the early stages of the progress of language must have been widely different from those later ones of which we can in some measure trace the natural causes1 we cannot place the origin of language in any point of view in which it comes under the jurisdiction of natural causation at all4 ,note #agaj3 ,researches1 ii4 #bbd4 #aj4 ,no ,natural ,origin discoverable4--,we are thus led by a survey of several of the paltiological sciences to a confirmation of the principle formerly asserted#ahaj1 ,that in no paltiological science has man been able to arrive at a beginning which is homogeneous with the known course of events4 ,we can in such sciences often go very far back2--determine many of the remote circumstances of the past series of events2--ascend to a point which seems to be near the origin2--and limit the hypotheses respecting the origin itself3 but philosophers never have demonstrated1 and1 so far as we can judge1 probably never will be able to demonstrate1 what was that primitive state of things from which the progressive course of the world took its first departure4 ,in all these paths of research1 when we travel far backwards1 the aspect of the earlier portions becomes very different from that of the advanced part on which we now stand2 but in all cases the path is lost in obscurity as it is traced backwards towards its starting-point3 it becomes not only invisible1 but unimaginable2 it is not only an interruption1 but an abyss1 which interposes itself between us and any intelligible beginning of things4 ,note #ahaj3 ,hist4 ,ind4 ,sc4 b4 xviii4 c4 vi4 sect #e4 #big ,,chapter ,,iv4 ,,of ,,the ,,relation ,,of ,,tradition ,,to ,,pal,,tiology4 #a4 ,importance of ,tradition4--,,since the ,paltiological ,sciences have it for their business to study the train of past events produced by natural causes down to the present time1 the knowledge concerning such events which is supplied by the remembrance and records of man1 in whatever form1 must have an important bearing upon these sciences4 ,all changes in the condition and extent of land and sea1 which have taken place within man's observation1 all effects of deluges1 sea-waves1 rivers1 springs1 volcanoes1 earthquakes1 and the like1 which come within the reach of human history1 have a strong interest for the paltiologist4 ,nor is he less concerned in all recorded instances of the modification of the forms and habits of plants and animals1 by the operations of man1 or by transfer from one land to another4 ,and when we come to the ,paltiology of ,language1 of ,art1 of ,civilization1 we find our subject still more closely connected with history2 for in truth these are historical1 no less than paltiological investigations4 ,but1 confining ourselves at present to the material sciences1 we may observe that though the importance of the information which tradition gives us1 in the sciences now under our consideration1 as1 for instance1 geology1 has long been tacitly recognised2 yet it is only recently that geologists have employed themselves in collecting their historical facts upon such a scale and with such comprehensive views as are required by the interest and use of collections of this kind4 ,the ,essay of ,von #bih ,hoff#aiaj1 ,on the ,natural ,alterations in the ,surface of the ,earth which are proved by ,tradition1 was the work which first opened the eyes of geologists to the extent and importance of this kind of investigation4 ,since that time the same path of research has been pursued with great perseverance by others1 especially by ,sir ,c4 ,lyell2 and is now justly considered as an essential portion of ,geology4 ,note #aiaj3 ,vol4 i4 #ahbb2 vol4 ii4 #ahbd4 #b4 ,connexion of ,tradition and ,science4--,events which we might naturally expect to have some bearing on geology1 are narrated in the historical writings which1 even on mere human grounds1 have the strongest claim to our respect as records of the early history of the world1 and are confirmed by the traditions of various nations all over the globe2 namely1 the formation of the earth and of its population1 and a subsequent deluge4 ,it has been made a matter of controversy how the narrative of these events is to be understood1 so as to make it agree with the facts which an examination of the earth's surface and of its vegetable and animal population discloses to us4 ,such controversies1 when they are considered as merely archological1 may occur in any of the paltiological sciences4 ,we may have to compare and to reconcile the evidence of existing phenomena with that of historical tradition4 ,but under some circumstances this process of conciliation may assume an interest of another kind1 on which we will make a few remarks4 #c4 ,natural and ,providential ,history of the ,world4--,we may contemplate the existence of man upon the earth1 his origin and his progress1 in the same manner as we contemplate the existence of any other race of animals2 namely1 in a purely paltiological view4 ,we may consider how far our knowledge of laws of causation enables us to explain his diffusion and migration1 his differences and resemblances1 his actions and works4 ,and this is the view of man as a member of the ,natural ,course of ,things4 #bii ,but man1 at the same time the contemplator and the subject of his own contemplation1 endowed with faculties and powers which make him a being of a different nature from other animals1 cannot help regarding his own actions and enjoyments1 his recollections and his hopes1 under an aspect quite different from any that we have yet had presented to us4 ,we have been endeavouring to place in a clear light the ,fundamental ,ideas1 such as that of ,cause1 on which depends our knowledge of the natural course of things4 ,but there are other ,ideas to which man necessarily refers his actions2 he is led by his nature1 not only to consider his own actions1 and those of his fellow-men1 as springing out of this or that cause1 leading to this or that material result2 but also as good or bad1 as what they ought or ought not to be4 ,he has ,ideas of moral relations as well as those ,ideas of material relations with which we have hitherto been occupied4 ,he is a moral as well as a natural agent4 ,contemplating himself and the world around him by the light of his ,moral ,ideas1 man is led to the conviction that his moral faculties were bestowed upon him by design and for a purpose2 that he is the subject of a ,moral ,government2 that the course of the world is directed by the ,power which governs it1 to the unfolding and perfecting of man's moral nature2 that this guidance may be traced in the career of individuals and of the world2 that there is a ,providential as well as a ,natural ,course of ,things4 ,yet this view is beset by no small difficulties4 ,the full development of man's moral faculties2--the perfection of his nature up to the measure of his own ideas2--the adaptation of his moral being to an ultimate destination1 by its transit through a world full of moral evil1 in which evil each person has his share2--are effects for which the economy of the world appears to contain no adequate provision4 ,man1 though aware of his moral nature1 and ready to believe in an ultimate destination of purity and blessedness1 is too feeble to resist the temptation of evil1 and too helpless to restore his purity when once lost4 ,he cannot but look for #cjj some confirmation of that providential order which he has begun to believe2 some provision for those deficiencies in his moral condition which he has begun to feel4 ,he looks at the history of the world1 and he finds that at a certain period it offers to him the promise of what he seeks4 ,when the natural powers of man had been developed to their full extent1 and were beginning to exhibit symptoms of decay2--when the intellectual progress of the world appeared to have reached its limit1 without supplying man's moral needs2--we find the great ,epoch in the ,providential ,history of the world4 ,we find the announcement of a ,dispensation by which man's deficiencies shall be supplied and his aspirations fulfilled3 we find a provision for the purification1 the support1 and the ultimate beatification of those who use the provided means4 ,and thus the providential course of the world becomes consistent and intelligible4 #d4 ,the ,sacred ,narrative4--,but with the new ,dispensation1 we receive1 not only an account of its own scheme and history1 but also a written narrative of the providential course of the world from the earliest times1 and even from its first creation4 ,this narrative is recognized and authorized by the new dispensation1 and accredited by some of the same evidences as the dispensation itself4 ,that the existence of such a sacred narrative should be a part of the providential order of things1 cannot but appear natural2 but1 naturally also1 the study of it leads to some difficulties4 ,the ,sacred ,narrative in some of its earliest portions speaks of natural objects and occurrences respecting them4 ,in the very beginning of the course of the world1 we may readily believe 7indeed1 as we have seen in the last chapter1 our scientific researches lead us to believe7 that such occurrences were very different from anything which now takes place2--different to an extent and in a manner which we cannot estimate4 ,now the narrative must speak of objects and occurrences in the words and phrases which have derived their meaning from their application to the existing natural state of things4 ,when applied to an initial #cja supernatural state therefore1 these words and phrases cannot help being to us obscure and mysterious1 perhaps ambiguous and seemingly contradictory4 #e4 ,difficulties in interpreting the ,sacred ,narrative4--,the moral and providential relations of man's condition are so much more important to him than mere natural relations1 that at first we may well suppose he will accept the ,sacred ,narrative1 as not only unquestionable in its true import1 but also as a guide in his views even of mere natural things4 ,he will try to modify the conceptions which he entertains of objects and their properties1 so that the ,sacred ,narrative of the supernatural condition shall retain the first meaning which he had put upon it in virtue of his own habits in the usage of language4 ,but man is so constituted that he cannot persist in this procedure4 ,the powers and tendencies of his intellect are such that he cannot help trying to attain true conceptions of objects and their properties by the study of things themselves4 ,for instance1 when he at first read of a firmament dividing the waters above from the waters below1 he perhaps conceived a transparent floor in the skies1 on which the superior waters rested1 which descend in rain2 but as his observations and his reasonings satisfied him that such a floor could not exist1 he became willing to allow 7as ,st4 ,augustine allowed7 that the waters above the firmament are in a state of vapour4 ,and in like manner in other subjects1 men1 as their views of nature became more distinct and precise1 modified1 so far as it was necessary for consistency's sake1 their first rude interpretations of the ,sacred ,narrative2 so that1 without in any degree losing its import as a view of the providential course of the world1 it should be so conceived as not to contradict what they knew of the natural order of things4 ,but this accommodation was not always made without painful struggles and angry controversies4 ,when men had conceived the occurrences of the ,sacred ,narrative in a particular manner1 they could not readily and willingly adopt a new mode of conception2 and all attempts to recommend to them such novelties1 they #cjb resisted as attacks upon the sacredness of the ,narrative4 ,they had clothed their belief of the workings of ,providence in certain images2 and they clung to those images with the persuasion that1 without them1 their belief could not subsist4 ,thus they imagined to themselves that the earth was a flat floor1 solidly and broadly laid for the convenience of man2 and they felt as if the kindness of ,providence was disparaged1 when it was maintained that the earth was a globe held together only by the mutual attraction of its parts4 ,the most memorable instance of a struggle of this kind is to be found in the circumstances which attended the introduction of the ,heliocentric ,theory of ,copernicus to general acceptance4 ,on this controversy ,i have already made some remarks in the ,history of ,science#bjaj1 and have attempted to draw from it some lessons which may be useful to us when any similar conflict of opinions may occur4 ,i will here add a few reflections with a similar view4 ,note #bjaj3 ,b4 v4 c4 iii4 sect4 #d4 #f4 ,such difficulties inevitable4--,in the first place1 ,i remark that such modifications of the current interpretation of the words of ,scripture appear to be an inevitable consequence of the progressive character of ,natural ,science4 ,science is constantly teaching us to describe known facts in new language2 but the language of ,scripture is always the same4 ,and not only so1 but the language of ,scripture is necessarily adapted to the common state of man's intellectual development1 in which he is supposed not to be possessed of science4 ,hence the phrases used by ,scripture are precisely those which science soon teaches man to consider as inaccurate4 ,yet they are not1 on that account1 the less fitted for their proper purpose3 for if any terms had been used1 adapted to a more advanced state of knowledge1 they must have been unintelligible among those to whom the ,scripture was first addressed4 ,if the ,jews had been told that water existed in the clouds in small drops1 they would have marvelled that it did #cjc not constantly descend2 and to have explained the reason of this1 would have been to teach ,atmology in the sacred writings4 ,if they had read in their ,scripture that the earth was a sphere1 when it appeared to be a plain1 they would only have been disturbed in their thoughts or driven to some wild and baseless imaginations1 by a declaration to them so strange4 ,if the ,divine ,speaker1 instead of saying that he would set his bow in the clouds1 had been made to declare that he would give to water the property of refracting different colours at different angles1 how utterly unmeaning to the hearers would the words have been6 ,and in these cases1 the expressions1 being unintelligible1 startling1 and bewildering1 would have been such as tended to unfit the ,sacred ,narrative for its place in the providential dispensation of the world4 ,accordingly1 in the great controversy which took place in ,galileo's time between the defenders of the then customary interpretations of ,scripture1 and the assertors of the ,copernican system of the universe1 when the innovators were upbraided with maintaining opinions contrary to ,scripture1 they replied that ,scripture was not intended to teach men astronomy1 and that it expressed the acts of divine power in images which were suited to the ideas of unscientific men4 ,to speak of the rising and setting and travelling of the sun1 of the fixity and of the foundations of the earth1 was to use the only language which would have made the ,sacred ,narrative intelligible4 ,to extract from these and the like expressions doctrines of science1 was1 they declared1 in the highest degree unjustifiable2 and such a course could lead1 they held1 to no result but a weakening of the authority of ,scripture in proportion as its credit was identified with that of these modes of applying it4 ,and this judgment has since been generally assented to by those who most reverence and value the study of the designs of ,providence as well as that of the works of nature4 #g4 ,science tells us nothing concerning ,creation4--,other apparent difficulties arise from the accounts given in the ,scripture of the first origin of the world #cjd in which we live3 for example1 ,light is represented as created before the ,sun4 ,with regard to difficulties of this kind1 it appears that we may derive some instruction from the result to which we were led in the last chapter2--namely1 that in the sciences which trace the progress of natural occurrences1 we can in no case go back to an origin1 but in every instance appear to find ourselves separated from it by a state of things1 and an order of events1 of a kind altogether different from those which come under our experience4 ,the thread of induction respecting the natural course of the world snaps in our fingers1 when we try to ascertain where its beginning is4 ,since1 then1 science can teach us nothing positive respecting the beginning of things1 she can neither contradict nor confirm what is taught by ,scripture on that subject2 and thus1 as it is unworthy timidity in the lover of ,scripture to fear contradiction1 so is it ungrounded presumption to look for confirmation1 in such cases4 ,the providential history of the world has its own beginning1 and its own evidence2 and we can only render the system insecure1 by making it lean on our material sciences4 ,if any one were to suggest that the nebular hypothesis countenances the ,scripture history of the formation of this system1 by showing how the luminous matter of the sun might exist previous to the sun itself1 we should act wisely in rejecting such an attempt to weave together these two heterogeneous threads2--the one a part of a providential scheme1 the other a fragment of a physical speculation4 ,we shall best learn those lessons of the true philosophy of science which it is our object to collect1 by attending to portions of science which have gone through such crises as we are now considering2 nor is it requisite1 for this purpose1 to bring forwards any subjects which are still under discussion4 ,it may1 however1 be mentioned that such maxims as we are now endeavouring to establish1 and the one before us in particular1 bear with a peculiar force upon those ,paltiological ,sciences of which we have been treating in the present ,book4 #cje #h4 ,scientific views1 when familiar1 do not disturb the authority of ,scripture4--,there is another reflection which may serve to console and encourage us in the painful struggles which thus take place1 between those who maintain interpretations of ,scripture already prevalent and those who contend for such new ones as the new discoveries of science require4 ,it is this2--that though the new opinion is resisted by one party as something destructive of the credit of ,scripture and the reverence which is its due1 yet1 in fact1 when the new interpretation has been generally established and incorporated with men's current thoughts1 it ceases to disturb their views of the authority of the ,scripture or of the truth of its teaching4 ,when the language of ,scripture1 invested with its new meaning1 has become familiar to men1 it is found that the ideas which it calls up are quite as reconcileable as the former ones were1 with the most entire acceptance of the providential dispensation4 ,and when this has been found to be the case1 all cultivated persons look back with surprise at the mistake of those who thought that the essence of the revelation was involved in their own arbitrary version of some collateral circumstance in the revealed narrative4 ,at the present day1 we can hardly conceive how reasonable men could ever have imagined that religious reflections on the stability of the earth1 and the beauty and use of the luminaries which revolve round it1 would be interfered with by an acknowledgment that this rest and motion are apparent only#baaj4 ,and thus the authority of revelation is not shaken by any changes introduced by the progress of science in the mode of interpreting expressions which describe physical objects and occurrences2 provided the new interpretation is admitted at a proper season1 and in a proper spirit2 so as to soften1 as much as possible1 both the public controversies and the private scruples which almost inevitably accompany such an alteration4 ,note #baaj3 ,i have here borrowed a sentence or two from my own ,history4 #i4 ,when should old ,interpretations be given up8--,but the question then occurs1 ,what is the proper #cjf season for a religious and enlightened commentator to make such a change in the current interpretation of sacred ,scripture8 ,at what period ought the established exposition of a passage to be given up1 and a new mode of understanding the passage1 such as is1 or seems to be1 required by new discoveries respecting the laws of nature1 accepted in its place8 ,it is plain1 that to introduce such an alteration lightly and hastily would be a procedure fraught with inconvenience2 for if the change were made in such a manner1 it might be afterwards discovered that it had been adopted without sufficient reason1 and that it was necessary to reinstate the old exposition4 ,and the minds of the readers of ,scripture1 always to a certain extent and for a time disturbed by the subversion of their long-established notions1 would be distressed without any need1 and might be seriously unsettled4 ,while1 on the other hand1 a too protracted and obstinate resistance to the innovation1 on the part of the scriptural expositors1 would tend to identify1 at least in the minds of many1 the authority of the ,scripture with the truth of the exposition2 and therefore would bring discredit upon the revealed word1 when the established interpretation was finally proved to be untenable4 ,a rule on this subject1 propounded by some of the most enlightened dignitaries of the ,roman ,catholic church1 on the occasion of the great ,copernican controversy begun by ,galileo1 seems well worthy of our attention4 ,the following was the opinion given by ,cardinal ,bellarmine at the time3--',when a demonstration shall be found to establish the earth's motion1 it will be proper to interpret the sacred ,scriptures otherwise than they have hitherto been interpreted in those passages where mention is made of the stability of the earth and movement of the heavens4' ,this appears to be a judicious and reasonable maxim for such cases in general4 ,so long as the supposed scientific discovery is doubtful1 the exposition of the meaning of ,scripture given by commentators of established credit is not wantonly to be disturbed3 but when a scientific theory1 irreconcileable with this ancient #cjg interpretation1 is clearly proved1 we must give up the interpretation1 and seek some new mode of understanding the passage in question1 by means of which it may be consistent with what we know2 for if it be not1 our conception of the things so described is no longer consistent with itself4 ,it may be said that this rule is indefinite1 for who shall decide when a new theory is completely demonstrated1 and the old interpretation become untenable8 ,but to this we may reply1 that if the rule be assented to1 its application will not be very difficult4 ,for when men have admitted as a general rule1 that the current interpretations of scriptural expressions respecting natural objects and events may possibly require1 and in some cases certainly will require1 to be abandoned1 and new ones admitted1 they will hardly allow themselves to contend for such interpretations as if they were essential parts of revelation2 and will look upon the change of exposition1 whether it come sooner or later1 without alarm or anger4 ,and when men lend themselves to the progress of truth in this spirit1 it is not of any material importance at what period a new and satisfactory interpretation of the scriptural difficulty is found2 since a scientific exactness in our apprehension of the meaning of such passages as are now referred to is very far from being essential to our full acceptance of revelation4 #aj4 ,in what ,spirit should the ,change be accepted8--,still these revolutions in scriptural interpretation must always have in them something which distresses and disturbs religious communities4 ,and such uneasy feelings will take a different shape1 according as the community acknowledges or rejects a paramount interpretative authority in its religious leaders4 ,in the case in which the interpretation of the ,church is binding upon all its members1 the more placid minds rest in peace upon the ancient exposition1 till the spiritual authorities announce that the time for the adoption of a new view has arrived2 but in these circumstances1 the more stirring and inquisitive minds1 which cannot refrain from the pursuit of new truths #cjh and exact conceptions1 are led to opinions which1 being contrary to those of the ,church1 are held to be sinful4 ,on the other hand1 if the religious constitution of the community allow and encourage each man to study and interpret for himself the ,sacred ,writings1 we are met by evils of another kind4 ,in this case1 although1 by the unforced influence of admired commentators1 there may prevail a general agreement in the usual interpretation of difficult passages1 yet as each reader of the ,scripture looks upon the sense which he has adopted as being his own interpretation1 he maintains it1 not with the tranquil acquiescence of one who has deposited his judgment in the hands of his ,church1 but with the keenness and strenuousness of self-love4 ,in such a state of things1 though no judicial severities can be employed against the innovators1 there may arise more angry controversies than in the other case4 ,it is impossible to overlook the lesson which here offers itself1 that it is in the highest degree unwise in the friends of religion1 whether individuals or communities1 unnecessarily to embark their credit in expositions of ,scripture on matters which appertain to natural ,science4 ,by delivering physical doctrines as the teaching of revelation1 religion may lose much1 but cannot gain anything4 ,this maxim of practical wisdom has often been urged by ,christian writers4 ,thus ,st4 ,augustine says#bbaj3 ',in obscure matters and things far removed from our senses1 if we read anything1 even in the divine ,scripture1 which may produce diverse opinions without damaging the faith which we cherish1 let us not rush headlong by positive assertion to either the one opinion or the other2 lest1 when a more thorough discussion has shown the opinion which we had adopted to be false1 our faith may fall with it3 and we should be found contending1 not for the doctrine of the sacred ,scriptures1 but for our own2 endeavouring to make our doctrine to be that of the ,scriptures1 instead of taking the doctrine of the ,scriptures to be ours4' ,and in nearly the same spirit1 at the #cji time of the ,copernican controversy1 it was thought proper to append to the work of ,copernicus a postil1 to say that the work was written to account for the phenomena1 and that people must not run on blindly and condemn either of the opposite opinions4 ,even when the ,inquisition1 in #afaf1 thought itself compelled to pronounce a decision upon this subject1 the verdict was delivered in very moderate language2--that 'the doctrine of the earth's motion appeared to be contrary to ,scripture3' and yet1 moderate as this expression is1 it has been blamed by judicious members of the ,roman church as deciding a point such as religious authorities ought not to pretend to decide2 and has brought upon that church no ordinary weight of general condemnation4 ,kepler pointed out1 in his lively manner1 the imprudence of employing the force of religious authorities on such subjects3 ,acies dolabr in ferrum illisa1 postea nec in lignum valet amplius4 ,capiat hoc cujus interest4 ',if you will try to chop iron1 the axe becomes unable to cut even wood4 ,i warn those whom it concerns4' ,note #bbaj3 ,lib4 i4 de ,genesi1 cap4 xviii4 #aa4 ,in what ,spirit should the ,change be urged8--,but while we thus endeavour to show in what manner the interpreters of ,scripture may most safely and most properly accept the discoveries of science1 we must not forget that there may be errours committed on the other side also2 and that men of science1 in bringing forward views which may for a time disturb the minds of lovers of ,scripture1 should consider themselves as bound by strict rules of candour1 moderation1 and prudence4 ,intentionally to make their supposed discoveries a means of discrediting1 contradicting1 or slighting the sacred ,scriptures1 or the authority of religion1 is in them unpardonable4 ,as men who make the science of ,truth the business of their lives1 and are persuaded of her genuine superiority1 and certain of her ultimate triumph1 they are peculiarly bound to urge her claims in a calm and temperate spirit2 not forgetting that there are other kinds of truth besides that which they peculiarly study4 ,they may properly reject authority in matters of science2 but they are to leave #caj it its proper office in matters of religion4 ,i may here again quote ,kepler's expressions3 ',in ,theology we balance authorities1 in ,philosophy we weigh reasons4 ,a holy man was ,lactantius who denied that the earth was round2 a holy man was ,augustine1 who granted the rotundity1 but denied the antipodes2 a holy thing to me is the ,inquisition1 which allows the smallness of the earth1 but denies its motion2 but more holy to me is ,truth2 and hence ,i prove1 from philosophy1 that the earth is round1 and inhabited on every side1 of small size1 and in motion among the stars1--and this ,i do with no disrespect to the ,doctors4' ,i the more willingly quote such a passage from ,kepler1 because the entire ingenuousness and sincere piety of his character does not allow us to suspect him in anything of hypocrisy or latent irony4 ,that similar professions of respect may be made ironically1 we have a noted example in the celebrated ,introduction to ,galileo's ,dialogue on the ,copernican ,system2 probably the part which was most offensive to the authorities4 ',some years ago1' he begins1 'a wholesome edict was promulgated at ,rome1 which1 in order to check the perilous scandals of the present age1 imposed silence upon the ,pythagorean opinion of the mobility of the earth4 ,there were not wanting1' he proceeds1 'persons who rashly asserted that this decree was the result1 not of a judicious inquiry1 but of passion ill-informed2 and complaints were heard that councillors1 utterly unacquainted with astronomical observation1 ought not to be allowed1 with their sudden prohibitions1 to clip the wings of speculative intellects4 ,at the hearing of rash lamentations like these1 my zeal could not keep silence4' ,and he then goes on to say1 that he wishes1 in his ,dialogue1 to show that the subject had been fully examined at ,rome4 ,here the irony is quite transparent1 and the sarcasm glaringly obvious4 ,i think we may venture to say that this is not the temper in which scientific questions should be treated2 although by some1 perhaps1 the prohibition of public discussion may be considered as justifying any evasion which is likely to pass unpunished4 #caa #ab4 ,duty of ,mutual ,forbearance4--,we may add1 as a further reason for mutual forbearance in such cases1 that the true interests of both parties are the same4 ,the man of science is concerned1 no less than any other person1 in the truth and import of the divine dispensation2 the religious man1 no less than the man of science1 is1 by the nature of his intellect1 incapable of believing two contradictory declarations4 ,hence they have both alike a need for understanding the ,scripture in some way in which it shall be consistent with their understanding of nature4 ,it is for their common advantage to conciliate1 as ,kepler says1 the finger and the tongue of ,god1 his works and his word4 ,and they may find abundant reason to bear with each other1 even if they should adopt for this purpose different interpretations1 each finding one satisfactory to himself2 or if any one should decline employing his thoughts on such subjects at all4 ,i have elsewhere#bcaj quoted a passage from ,kepler#bdaj which appears to me written in a most suitable spirit3 ',i beseech my reader that1 not unmindful of the divine goodness bestowed upon man1 he do with me praise and celebrate the wisdom of the ,creator1 which ,i open to him from a more inward explication of the form of the world1 from a searching of causes1 from a detection of the errours of vision2 and that thus not only in the firmness and stability of the earth may we perceive with gratitude the preservation of all living things in nature as the gift of ,god3 but also that in its motion1 so recondite1 so admirable1 we may acknowledge the wisdom of the ,creator4 ,but whoever is too dull to receive this science1 or too weak to believe the ,copernican system without harm to his piety1 him1 ,i say1 ,i advise that1 leaving the school of astronomy1 and condemning1 if so he please1 any doctrines of the philosophers1 he follow his own path1 and desist from this wandering through the universe2 and that1 lifting up his natural eyes1 with which alone he can see1 #cab he pour himself out from his own heart in worship of ,god the ,creator1 being certain that he gives no less worship to ,god than the astronomer1 to whom ,god has given to see more clearly with his inward eyes1 and who1 from what he has himself discovered1 both can and will glorify ,god4' ,note #bcaj3 ,bridgewater ,tr4 p4 #cad4 ,note #bdaj3 ,com4 ,stell4 ,mart4 ,introd4 #ac4 ,case of ,galileo4--,i may perhaps venture here to make a remark or two upon this subject with reference to a charge brought against a certain portion of the ,history of the ,inductive ,sciences4 ,complaint has been made#beaj that the character of the ,roman church1 as shown in its behaviour towards ,galileo1 is misrepresented in the account given of it in the ,history of ,astronomy4 ,it is asserted that ,galileo provoked the condemnation he incurred2 first1 by pertinaciously demanding the assent of the ecclesiastical authorities to his opinion of the consistency of the ,copernican doctrine with ,scripture2 and afterwards by contumaciously1 and1 as we have seen1 contumeliously violating the silence which the ,church had enjoined upon him4 ,it is further declared that the statement which represents it as the habit of the ,roman church to dogmatize on points of natural science is unfounded2 as well as the opinion that in consequence of this habit1 new scientific truths were promulgated less boldly in ,italy than in other countries4 ,i shall reply very briefly on these subjects2 for the decision of them is by no means requisite in order to establish the doctrines to which ,i have been led in the present chapter1 nor1 ,i hope1 to satisfy my reader that my views have been collected from an impartial consideration of scientific history4 ,note #beaj3 ,dublin ,review1 ,no4 ix4 ,july1 #ahch1 p4 #gb4 ,with regard to ,galileo1 ,i do not think it can be denied that he obtruded his opinions upon the ecclesiastical authorities in an unnecessary and imprudent manner4 ,he was of an ardent character1 strongly convinced himself1 and urged on still more by the conviction which he produced among his disciples1 and #cac thus he became impatient for the triumph of truth4 ,this judgment of him has recently been delivered by various independent authorities1 and has undoubtedly considerable foundation#bfaj4 ,as to the question whether authority in matters of natural science were habitually claimed by the authorities of the ,church of ,rome1 ,i have to allow that ,i cannot produce instances which establish such a habit4 ,we1 who have been accustomed to have daily before our eyes the ,monition which the ,romish editors of ,newton thought it necessary to prefix--,cterum latis a summo ,pontifice contra telluris motum ,decretis1 nos obsequi profitemur--were not likely to conjecture that this was a solitary instance of the interposition of the ,papal authority on such subjects4 ,but although it would be easy to find declarations of heresy delivered by ,romish ,universities1 and writers of great authority1 against tenets belonging to the natural sciences1 ,i am not aware that any other case can be adduced in which the ,church or the ,pope can be shown to have pronounced such a sentence4 ,i am well contented to acknowledge this2 for ,i should be far more gratified by finding myself compelled to hold up the seventeenth century as a model for the nineteenth in this respect1 than by having to sow enmity between the admirers of the past and the present through any disparaging contrast#bgaj4 ,note #bfaj3 ,besides the ,dublin ,review1 ,i may quote the ,edinburgh ,review1 which ,i suppose will not be thought likely to have a bias in favour of the exercise of ecclesiastical authority in matters of science2 though certainly there is a puerility in the critic's phraseology which does not add to the weight of his judgment4 ',galileo contrived to surround the truth with every variety of obstruction4 ,the tide of knowledge1 which had hitherto advanced in peace1 he crested with angry breakers1 and he involved in its surf both his friends and his foes4'--,ed4 ,rev4 ,no4 cxxiii4 p4 #abf4 ,note #bgaj3 ,i may add that the most candid of the adherents of the ,church of ,rome condemn the assumption of authority in matters of science1 made1 in this one instance at least1 by the ecclesiastical tribunals4 ,the author of the ,ages of ,faith 7book viii4 p4 #bdh71 says1 ',a ,congregation1 it is to be lamented1 declared the new system to be opposed to ,scripture1 and therefore heretical4' #cad ,with respect to the attempt made in my ,history to characterize the intellectual habits of ,italy as produced by her religious condition1--certainly it would ill become any student of the history of science to speak slightingly of that country1 always the mother of sciences1 always ready to catch the dawn and hail the rising of any new light of knowledge4 ,but ,i think our admiration of this activity and acuteness of mind is by no means inconsistent with the opinion1 that new truths were promulgated more boldly beyond the ,alps1 and that the subtilty of the ,italian intellect loved to insinuate what the rough ,german bluntly asserted4 ,of the decent duplicity with which forbidden opinions were handled1 the reviewer himself gives us instances1 when he boasts of the liberality with which ,copernican professors were placed in important stations by the ecclesiastical authorities1 soon after the doctrine of the motion of the earth had been declared by the same authorities to be contrary to ,scripture4 ,and in the same spirit is the process of demanding from ,galileo a public and official recantation of opinions which he had repeatedly been told by his ecclesiastical superiors he might hold as much as he pleased4 ,i think it is easy to believe that among persons so little careful to reconcile public profession with private conviction1 official decorum was all that was demanded4 ,when ,galileo had made his renunciation of the earth's motion on his knees1 he rose and said1 as we are told1 ,e pur si muove--'and yet it does move4' ,this is sometimes represented as the heroic soliloquy of a mind cherishing its conviction of the truth1 in spite of persecution2 ,i think we may more naturally conceive it uttered as a playful epigram in the ear of a cardinal's secretary1 with a full knowledge that it would be immediately repeated to his master#bhaj4 ,note #bhaj3 ,i have somewhat further discussed the case of ,galileo in the later editions of the ,history1 book v4 chap4 iii4 sect4 #d4 ,besides the ,ideas involved in the material sciences1 #cae of which we have already examined the principal ones1 there is one ,idea or ,conception which our ,sciences do not indeed include1 but to which they not obscurely point2 and the importance of this ,idea will make it proper to speak of it1 though this must be done very briefly4 #caf ,,chapter ,v4 ,,of ,,the ,,conception ,,of ,a ,,first ,,cause4 #a4 ,,at the end of the last chapter but one1 we were led to this result1--that we cannot1 in any of the ,paltiological ,sciences1 ascend to a beginning which is of the same nature as the existing cause of events1 and which depends upon causes that are still in operation4 ,philosophers never have demonstrated1 and probably never will be able to demonstrate1 what was the original condition of the solar system1 of the earth1 of the vegetable and animal worlds1 of languages1 of arts4 ,on all these subjects the course of investigation1 followed backwards as far as our materials allow us to pursue it1 ends at last in an impenetrable gloom4 ,we strain our eyes in vain when we try1 by our natural faculties1 to discern an origin4 #b4 ,yet speculative men have been constantly employed in attempts to arrive at that which thus seems to be placed out of their reach4 ,the ,origin of ,languages1 the ,origin of the present ,distribution of ,plants and ,animals1 the ,origin of the ,earth1 have been common subjects of diligent and persevering inquiry4 ,indeed inquiries respecting such subjects have been1 at least till lately1 the usual form which ,paltiological researches have assumed4 ,cosmogony1 the ,origin of the ,world1 of which1 in such speculations1 the earth was considered as a principal part1 has been a favourite study both of ancient and of modern times3 and most of the attempts at ,geology previous to the present period have been ,cosmogonies or ,geogonies1 rather than that more genuine science which we have endeavoured to delineate4 ,again3 ,glossology1 though now an extensive body of solid knowledge1 was #cag mainly brought into being by inquiries concerning the ,original ,language spoken by men2 and the nature of the first separation and diffusion of languages1 the first peopling of the earth by man and by animals1 were long sought after with ardent curiosity1 although of course with reference to the authority of the ,scriptures1 as well as the evidence of natural phenomena4 ,indeed the interest of such inquiries even yet is far from being extinguished4 ,the disposition to explore the past in the hope of finding1 by the light of natural reasoning as well as by the aid of revelation1 the origin of the present course of things1 appears to be unconquerable4 ',what was the beginning8' is a question which the human race cannot desist from perpetually asking4 ,and no failure in obtaining a satisfactory answer can prevent inquisitive spirits from again and again repeating the inquiry1 although the blank abyss into which it is uttered does not even return an echo4 #c4 ,what1 then1 is the reason of an attempt so pertinacious yet so fruitless8 ,by what motive are we impelled thus constantly to seek what we can never find8 ,why are the errour of our conjectures1 the futility of our reasonings1 the precariousness of our interpretations1 over and over again proved to us in vain8 ,why is it impossible for us to acquiesce in our ignorance and to relinquish the inquiry8 ,why cannot we content ourselves with examining those links of the chain of causes which are nearest to us1--those in which the connexion is intelligible and clear2 instead of fixing our attention upon those remote portions where we can no longer estimate its coherence8 ,in short1 why did not men from the first take for the subject of their speculations the ,course of ,nature rather than the ,origin of ,things8 ,to this we reply1 that in doing what they have thus done1 in seeking what they have sought1 men are impelled by an intellectual necessity4 ,they cannot conceive a ,series of connected occurrences without a ,commencement2 they cannot help supposing a cause for the ,whole1 as well as a cause for each part2 they cannot be satisfied with a succession of causes without #cah assuming a ,first ,cause4 ,such an assumption is necessarily impressed upon our minds by our contemplation of a series of causes and effects2 that there must be a ,first ,cause1 is accepted by all intelligent reasoners as an ,axiom3 and like other ,axioms1 its truth is necessarily implied in the ,idea which it involves4 #d4 ,the evidence of this axiom may be illustrated in several ways4 ,in the first place1 the axiom is assumed in the argument usually offered to prove the existence of the ,deity4 ,since1 it is said1 the world now exists1 and since nothing cannot produce something1 something must have existed from eternity4 ,this ,something is the ,first ,cause3 it is ,god4 ,now what ,i have to remark here is this3--the conclusiveness of this argument1 as a proof of the existence of one independent1 immutable ,deity1 depends entirely upon the assumption of the axiom above stated4 ,the ,world1 a 9999series of causes and effects1 exists3 therefore there must be1 not only this series of causes and effects1 but also a ,first ,cause4 ,it will be easily seen1 that without the axiom1 that in every series of causes and effects there must be a ,first ,cause1 the reasoning is altogether inconclusive4 #e4 ,or to put the matter otherwise3 ,the argument for the existence of the ,deity was stated thus3 ,something exists1 therefore something must have existed from eternity4 ',granted1' the opponent might say2 'but this something which has existed from eternity1 why may it not be this very series of causes and effects which is now going on1 and which appears to contain in itself no indication of beginning or end8' ,and thus1 without the assumption of the necessity of a ,first ,cause1 the force of the argument may be resisted4 #f4 ,but1 it may be asked1 how do those who have written to prove the existence of the ,deity reply to such an objection as the one just stated8 ,it is natural to suppose that1 on a subject so interesting and so long discussed1 all the obvious arguments with their replies1 have been fully brought into view4 ,what is the result in this case8 #cai ,the principal modes of replying to the above objection1 that the series of causes and effects which now exists1 may have existed from eternity1 appear to be these4 ,in the first place1 our minds cannot be satisfied with a series of successive1 dependent1 causes and effects1 without something first and independent4 ,we pass from effect to cause1 and from that to a higher cause1 in search of something on which the mind can rest2 but if we can do nothing but repeat this process1 there is no use in it4 ,we move our limbs1 but make no advance4 ,our question is not answered1 but evaded4 ,the mind cannot acquiesce in the destiny thus presented to it1 of being referred from event to event1 from object to object1 along an interminable vista of causation and time4 ,now this mode of stating the reply1--to say that the mind cannot thus be satisfied1 appears to be equivalent to saying that the mind is conscious of a ,principle1 in virtue of which such a view as this must be rejected2--the mind takes refuge in the assumption of a ,first ,cause1 from an employment inconsistent with its own nature4 #g4 ,or again1 we may avoid the objection1 by putting the argument for the existence of a ,deity in this form3 ,the series of causes and effects which we call the world1 or the course of nature1 may be considered as a whole1 and this whole must have a cause of its existence4 ,the whole collection of objects and events may be comprehended as a single effect1 and of this effect there must be a cause4 ,this ,cause of the ,universe must be superior to1 and independent of the special events1 which1 happening in time1 make up the universe of which ,he is the cause4 ,he must exist and exercise causation1 before these events can begin3 ,he must be the ,first ,cause4 ,although the argument is here somewhat modified in form1 the substance is the same as before4 ,for the assumption that we may consider the whole series of causes and effects as a single effect1 is equivalent to the assumption that besides partial causes we must have a ,first ,cause4 ,and thus the ,idea of a ,first ,cause1 and #cbj the axiom which asserts its necessity1 are recognized in the usual argumentation on this subject4 #h4 ,this ,idea of a ,first ,cause1 and the principle involved in the ,idea1 have been the subject of discussion in another manner4 ,as we have already said1 we assume as an axiom that a ,first ,cause must exist2 and we assert that ,god1 the ,first ,cause1 exists eternal and immutable1 by the necessity which the axiom implies4 ,hence ,god is said to exist necessarily2--to be a necessarily existing being4 ,and when this necessary existence of ,god had been spoken of1 it soon began to be contemplated as a sufficient reason1 and as an absolute demonstration of ,his existence2 without any need of referring to the world as an effect1 in order to arrive at ,god as the cause4 ,and thus men conceived that they had obtained a proof of the existence of the ,deity1 priori1 from ,ideas1 as well as posteriori1 from ,effects4 #i4 ,thus1 ,thomas ,aquinas employs this reasoning to prove the eternity of ,god#biaj3 ',oportet ponere aliquod primum necessarium quod est per se ipsum necessarium2 et hoc est ,deus1 cum sit prima causa ut dictum est3 igitur ,deus ternus est1 cum omne necessarium per se sit ternum4' ,it is true that the schoolmen never professed to be able to prove the existence of the ,deity priori3 but they made use of this conception of necessary existence in a manner which approached very near to such an attempt4 ,thus ,suarez#cjaj discusses the question1 ',utrum aliquo modo possit priori demonstrari ,deum esse4' ,and resolves the question in this manner3 ',ad hunc ergo modum dicendum est3 ,demonstrato posteriori ,deum esse ens necessarium et a se1 ex hoc attributo posse priori demonstrari prter illud non posse esse aliud ens necessarium et a se1 et consequenter demonstrari ,deum esse4' ,note #biaj3 ,aquin4 ,cont4 ,gentil4 lib4 i4 c4 xiv4 p4 #ba4 ,note #cjaj3 ,metaphys4 tom4 ii4 disp4 xxix4 sect4 #c1 p4 #bh4 ,but in modern times attempts were made by ,descartes and ,samuel ,clarke1 to prove the ,divine #cba existence at once priori1 from the conception of necessary existence2 which1 it was argued1 could not subsist without actual existence4 ,this argumentation was acutely and severely criticised by ,dr4 ,waterland4 #aj4 ,without dwelling upon a subject1 the discussion of which does not enter into the design of the present work1 ,i may remark that the question whether an priori proof of the existence of a ,first ,cause be possible1 is a question concerning the nature of our ,ideas1 and the evidence of the axioms which they involve1 of the same kind as many questions which we have already had to discuss4 ,is our ,conception or ,idea of a ,first ,cause gathered from the effects we see around us8 ,it is plain that we must answer1 here as in other cases1 that the ,idea is not extracted from the phenomena1 but assumed in order that the phenomena may become intelligible to the mind2--that the ,idea is a necessary one1 inasmuch as it does not depend upon observation for its evidence2 but that it depends upon observation for its development1 since without some observation1 we cannot conceive the mind to be cognizant of the relation of causation at all4 ,in this respect1 however1 the ,idea of a ,first ,cause is no less necessary than the ideas of ,space1 or ,time1 or ,cause in general4 ,and whether we call the reasoning derived from such a necessity an argument priori or posteriori1 in either case it possesses the genuine character of demonstration1 being founded upon axioms which command universal assent4 #aa4 ,i have1 however1 spoken of our ,conception rather than of our ,idea of a ,first ,cause2 for the notion of a ,first ,cause appears to be rather a modification of the ,fundamental ,idea of ,cause1 which was formerly discussed1 than a separate and peculiar ,idea4 ,and the ,axiom1 that there must be a ,first ,cause1 is recognised by most persons as an application of the general ,axiom of ,causation1 that every effect must have a ,cause2 this latter ,axiom being applied to the ,world1 considered in its totality1 as a single ,effect4 ,this distinction1 however1 between an ,idea and a ,conception1 is of no material consequence to our argument2 provided we #cbb allow the maxim1 that there must be a ,first ,cause1 to be necessarily and evidently true2 whether it be thought better to speak of it as an independent ,axiom1 or to consider it as derived from the general ,axiom of ,causation4 #ab4 ,thus we necessarily infer a ,first ,cause1 although the ,paltiological ,sciences only point towards it1 and do not lead us to it4 ,but ,i must observe further2 that in each of the series of events which form the subject of ,paltiological research1 the ,first ,cause is the same4 ,without here resting upon reasoning founded upon our ,conception of a ,first ,cause1 ,i may remark that this identity is proved by the close connexion of all the branches of natural science1 and the way in which the causes and the events of each are interwoven with those which belong to the others4 ,we must needs believe that the ,first ,cause which produced the earth and its atmosphere is also the ,cause of the plants which clothe its surface2 that the ,first ,cause of the vegetable and of the animal world are the same2 that the ,first ,cause which produced light produced also eyes2 that the ,first ,cause which produced air and organs of articulation produced also language and the faculties by which language is rendered possible3 and if those faculties1 then also all man's other faculties2--the powers by which1 as we have said1 he discerns right and wrong1 and recognises a providential as well as a natural course of things4 ,nor can we think otherwise than that the ,being who gave these faculties1 bestowed them for some purpose2--bestowed them for that purpose which alone is compatible with their nature3--the purpose1 namely1 of guiding and elevating man in his present career1 and of preparing him for another state of being to which they irresistibly direct his hopes4 ,and thus1 although1 as we have said1 no one of the ,paltiological ,sciences can be traced continuously to an ,origin1 yet they not only each point to an ,origin1 but all to the same ,origin4 ,their lines are broken indeed1 as they run backwards into the early periods of the world1 but yet they all appear to converge to the same invisible point4 ,and #cbc this point1 thus indicated by the natural course of things1 can be no other than that which is disclosed to us as the starting-point of the providential course of the world2 for we are persuaded by such reasons as have just been hinted1 that the ,creator of the natural world can be no other than the ,author and ,governor and ,judge of the moral and spiritual world4 #ac4 ,thus we are led1 by our material ,sciences1 and especially by the ,paltiological class of them1 to the borders of a higher region1 and to a point of view from which we have a prospect of other provinces of knowledge2--to contemplations in which other faculties of man are concerned besides his intellectual1 other interests involved besides those of speculation4 ,on these it does not belong to our present plan to dwell3 but even such a brief glance as we have taken of the connexion of material with moral speculations may not be useless1 since it may serve to show that the principles of truth which we are now laboriously collecting among the results of the physical sciences1 may possibly find some application in those parts of knowledge towards which men most naturally look with deeper interest and more serious reverence4 ,we have been employed hitherto in examining the materials of knowledge1 ,facts and ,ideas2--,facts in our former ,history1 and ,ideas in the present ,history4 ,we have dwelt at length on this latter element2 inasmuch as the consideration of it is1 on various accounts1 and especially at the present time1 by far the most important1 having hitherto been least distinctly attended to as a special element of scientific knowledge4 ,there still remains an important task1 with a view to which we have undertaken this survey of the past course of human thought and discovery3--namely1 the task of determining the processes by which these materials may actually be made to constitute knowledge4 #cbd ,we have surveyed the stones which lie before us1 partly built and partly ready for building3 we have found them exactly squared1 and often curiously covered with significant imagery and important inscriptions4 ,we have now to discover how they may best be fitted into their places1 and cemented together1 so that rising stage above stage1 they may grow at last into that fair and lofty temple of ,truth1 for which we cannot doubt that they were intended by the ,great ,architect4 ,this task1 the description of the processes by which ,scientific ,truth is discovered and established1 we shall1 as has already been said1 entitle1 in reference to previous attempts of the same kind1 ,novum ,organum ,renovatum4 ,,end ,,of ,,vol4 ,,ii4 ,cambridge3 ,printed at the ,university ,press4 ,transcriber's ,note ,whewell published the first edition of the ,philosophy of the ,inductive ,sciences in #ahdj1 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#aheh - the present text1 relying upon resources kindly provided by the ,internet ,archive71 ,novum ,organon ,renovatum 7#aheh71 and ,on the ,philosophy of ,discovery3 chapters historical and critical 7#ahfj - already in ,project ,gutenberg's collection3 #eaee74 ,the present text has combined the two volumes into one continuous text4 ,footnotes are numbered by ,book and marked mn where m the number of the note within the ,book1 and n the number of the ,book4 ,in the original1 notes were numbered by chapter4 ,page numbers appear in 1 or where there is no printed number2 where a word was hyphenated across pages the number has been placed before the word4 ,superscripts are marked with 4 ,there is one significant problem to report4 ,for ,book ,,ix chapter ,,vi1 the ,table of ,contents lists #bj articles1 but the actual text has only #ai numbered paragraphs4 ,the text version leaves this inconsistency untouched2 in the htm version1 a correction has been made by numbering the paragraph beginning on p4 #bdd as #i1 and renumbering those that follow1 thereby matching the descriptions in the ,table of ,contents4 ,other corrections to the text are marked with 9999 and are listed below4 ,location ,text of printed edition ,emendation ,vol4 #a p4 #ga conlcusion conclusion p4 #hg vi4 vii4 p4 #aeg sciences science note #ac ,book #a4 chap4 xii4 ,book #c4 chap4 ii4 p4 #bca ,marriotte ,mariotte p4 #cgg ,winter's ,winterl's ,vol4 #b p4 #bb ingedient ingredient p4 #abd wich which p4 #aei attemps attempts p4 #agb knowlege knowledge note #fji ,their4 ,theor4 p4 #bgj dfficulties difficulties p4 #cah serious series