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If you are not located in the United States, you -will have to check the laws of the country where you are located before -using this eBook. - -Title: History of scientific ideas - -Author: William Whewell - -Release Date: October 4, 2022 [eBook #69093] - -Language: English - -Produced by: Ed Brandon from materials generously provided by the - Internet Archive - -*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF SCIENTIFIC -IDEAS *** - - -HISTORY -OF -SCIENTIFIC IDEAS. - - - -VOLUME I. - - - - -Cambridge; -PRINTED BY C. J. CLAY, M.A. -AT THE UNIVERSITY PRESS. - - - -HISTORY -OF -SCIENTIFIC IDEAS. - -BY WILLIAM WHEWELL, D.D., -MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND -CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE. - - - -BEING THE FIRST PART OF THE PHILOSOPHY -OF THE INDUCTIVE SCIENCES. - - - -_THE THIRD EDITION._ - -IN TWO VOLUMES. - - -ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ - - -VOLUME I. - - - -LONDON: -JOHN W. PARKER AND SON, WEST STRAND. -1858. - - - -{{v}} -PREFACE TO THIS EDITION. - - - -THE Chapters now offered to the Reader were formerly -published as a portion of _The Philosophy of the Inductive -Sciences, founded upon their History_: but the nature and -subject of these Chapters are more exactly described by the -present title, _The History of Scientific Ideas_. For this -part of the work is mainly historical, and was, in fact, -collected from the body of scientific literature, at the -same time that the _History of the Inductive Sciences_ was -so collected. The present work contains the history of -Science so far as it depends on _Ideas_; the former work -contains the same history so far as it is derived from -_Observation_. The leading features in _that_ were Theories -inferred from Facts; the leading features of _this_ are -Discussions of Theories tending to make them consistent with -the conditions of human thought. - -The Ideas of which the History is here given are mainly the -following: -_Space_, _Time_, _Number_, _Motion_, _Cause_, _Force_, -_Matter_, _Medium_, _Intensity_, _Scale_, _Polarity_, -_Element_, _Affinity_, _Substance_, _Atom_, _Symmetry_, -_Likeness_, _Natural Classes_, _Species_, _Life_, -_Function_, _Vital Forces_, _Final_ {vi} _Causes_, -_Historical Causation_, _Catastrophe and Uniformity_, _First -Cause_. - -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 Science: but they also form -an important part of the Philosophy of Science, for no -Philosophy of Science can be complete which does not solve -the difficulties, antitheses, and paradoxes on which such -controversies have turned. I have given a survey of such -controversies, generally carried from their earliest origin -to their latest aspect; and have stated what appeared to me -the best solution of each problem. This has necessarily -involved me in much thorny metaphysics; but such metaphysics -is a necessary part of the progress of Science. The human -mind deriving its knowledge of Truth from the observation of -nature, cannot evade the task of determining at every step -how Truth is consistent with itself. This is the Metaphysics -of Progressive Knowledge, and this is the matter of this -present History. - -Of the remaining part of what was formerly published as the -Philosophy of the Inductive Sciences, an additional part, -described in the Introduction to the present work, will -shortly be published. - -TRINITY LODGE, -_May_ 24, 1858. - - -ERRATUM, p. 157, l. 11 from top, _for_ sciences -_read_ science. - - - - -CONTENTS -OF -THE FIRST VOLUME. - - - PAGE -PREFACE v - -PART I. -OF IDEAS. - - -INTRODUCTION 3 - -BOOK I. - -OF IDEAS IN GENERAL. - -CHAP. I. OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY 23 - -_Sect._ 1. _Thoughts and Things_ -- - 2. _Necessary and Experiential Truths_ 25 - 3. _Deduction and Induction_ 27 - 4. _Theories and Facts_ 29 - 5. _Ideas and Sensations_ 30 - 6. _Reflexion and Sensation_ 33 - 7. _Subjective and Objective_ 35 - 8. _Matter and Form_ 38 - 9. _Man the Interpreter of Nature_ 41 - 10. _The Fundamental Antithesis is inseparable_ 43 - 11. _Successive Generalization_ 49 -{viii} - -CHAP. II. OF TECHNICAL TERMS 54 - - _Art._ 1. Examples. - 2. Use of Terms. - -CHAP. III. OF NECESSARY TRUTHS 57 - - _Art._ 1. The two Elements of Knowledge, - 2. Shown by necessary Truths. - 3. Examples of necessary Truths in numbers. - 4. The opposite cannot be distinctly conceived. - 5. Other Examples. - 6. Universal Truths. - -CHAP. IV. OF EXPERIENCE 65 - - _Art._ 1. Experience cannot prove necessary Truths, - 2. Except when aided by Ideas. - -CHAP. V. OF THE GROUNDS OF NECESSARY TRUTHS 69 - - _Art._ 1. These Grounds are Fundamental Ideas. - 2. These are to be reviewed. - 3. Definitions and Axioms. - 4. Syllogism, - 5. Produces no new Truths. - 6. Axioms needed. - 7. Axioms depend on Ideas: - 8. So do Definitions. - 9. Idea not completely expressed. - -CHAP. VI. THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE 76 - - _Art._ 1. No connexion observed. - 2. Faculties implied in observation. - 3. We are to examine our Faculties. - -CHAP. VII. OF THE PHILOSOPHY OF THE SCIENCES 81 - - Sciences arranged according to Ideas. -{ix} - -BOOK II. - -THE PHILOSOPHY OF THE PURE SCIENCES. - -CHAP. I. OF THE PURE SCIENCES 88 - - _Art._ 1. Geometry, Arithmetic, Algebra, - 2. Are not Inductive Sciences: - 3. Are Mathematical Sciences. - 4. Mixed Mathematics. - 5. Space, Time, Number. - -CHAP. II. OF THE IDEA OF SPACE 91 - - _Art._ 1. Space is an Idea, - 2. Not derived from Experience, - 3. As Geometrical Truth shows. - 4. Space is a Form of Experience. - 5. The phrase not essential. - -CHAP. III. OF SOME PECULIARITIES OF THE IDEA OF SPACE 95 - - _Art._ 1. Space is not an Abstract Notion. - 2. Space is infinite. - 3. Space is real. - 4. Space is a Form of Intuition. - 5. Figure. - 6. Three Dimensions. - -CHAP. IV. OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE 98 - - _Art._ 1. Geometry. - 2. Definitions. - 3. Axioms. - 4. Not Hypotheses. - 5. Axioms necessary. - 6. Straight Lines. - 7. Planes. - 8. Elementary Geometry. - -CHAP. V. OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE - DOCTRINES STATED IN THE PREVIOUS CHAPTER 107 - - _Art._ 1. How is Geometry hypothetical? - 2. What was Stewart's view? -{x} - 3. 'Legitimate filiations' of Definitions. - 4. Is a Definition a complete explanation? - 5. Are some Axioms Definitions? - 6. Axiom concerning Circles. - 7. Can Axioms become truisms? - 8. Use of such. - -CHAP. VI. OF THE PERCEPTION OF SPACE 117 - - _Art._ 1. Which Senses apprehend Space? - 2. Perception of solid figure. - 3. Is an interpretation. - 4. May be analysed. - 5. Outline. - 6. Reversed convexity. - 7. Do we perceive Space by Touch? - 8. Brown's Opinion. - 9. The Muscular Sense. - 10. Bell's Opinion. - 11. Perception includes Activity. - 12. Perception of the Skyey Dome. - 13. Reid's Idomenians. - 14. Motion of the Eye. - 15. Searching Motion. - 16. Sensible Spot. - 17. Expressions implying Motion. - -CHAP. VII. OF THE IDEA OF TIME 131 - - _Art._ 1. Time an Idea not derived from Experience. - 2. Time is a Form of Experience. - 3. Number. - 4. Is Time derived from Motion? - -CHAP. VIII. OF SOME PECULIARITIES IN THE IDEA OF TIME 134 - - _Art._ 1. Time is not an Abstract Notion. - 2. Time is infinite. - 3. Time is a Form of Intuition. - 4. Time is of one Dimension, - 5. And no more. - 6. Rhythm. - 7. Alternation. - 8. Arithmetic. -{xi} - -CHAP. IX. OF THE AXIOMS WHICH RELATE TO NUMBER 138 - - _Art._ 1. Grounds of Arithmetic. - 2. Intuition. - 3. Arithmetical Axioms, - 4. Are Conditions of Numerical Reasoning - 5. In all Arithmetical Operations. - 6. Higher Numbers. - -CHAP. X. OF THE PERCEPTION OF TIME AND NUMBER 141 - - _Art._ 1. Memory. - 2. Sense of Successiveness - 3. Implies Activity. - 4. Number also does so. - 5. And apprehension of Rhythm. - Note to Chapter X. 145 - -CHAP. XI. OF MATHEMATICAL REASONING 147 - - _Art._ 1. Discursive Reasoning. - 2. Technical Terms of Reasoning. - 3. Geometrical Analysis and Synthesis. - -CHAP. XII. OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS 151 - - _Art._ 1. The Idea of a Limit. - 2. The use of General Symbols. - 3. Connexion of Symbols and Analysis. - -CHAP. XIII. THE DOCTRINE OF MOTION 156 - -_Art._ 1. Pure Mechanism. - 2. Formal Astronomy. - -CHAP. XIV. OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE - SCIENCES 159 - - _Art._ 1. The Ideas of Space and Number are clear from - the first. - 2. Their application in Astronomy. - 3. Conic Sections, &c. - 4. Arabian Numerals. - 5. Newton's Lemmas. - 6. Tides. - 7. Mechanics. - 8. Optics. - 9. Conclusion. -{xii} - -BOOK III. - -THE PHILOSOPHY OF THE MECHANICAL SCIENCES. - -CHAP. I. OF THE MECHANICAL SCIENCES 171 - -CHAP. II. OF THE IDEA OF CAUSE 173 - - _Art._ 1. Not derived from Observation, - 2. As appears by its use. - 3. Cause cannot be observed. - 4. Is Cause only constant succession? - 5. Other reasons. - -CHAP. III. MODERN OPINIONS RESPECTING THE IDEA OF CAUSE 178 - - _Art._ 1. Hume's Doctrine. - 2. Stewart and Brown. - 3. Kant. - 4. Relation of Kant and Brown. - 5. Axioms flow from the Idea. - 6. The Idea implies activity in the Mind. - -CHAP. IV. OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE 184 - - _Art._ 1. Causes are Abstract Conceptions. - 2. First Axiom. - 3. Second Axiom. - 4. Limitation of the Second Axiom. - 5. Third Axiom. - 6. Extent of the Third Axiom. - -CHAP. V. OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER 205 - - _Art._ 1. Force. - 2. Matter. - 3. Solidity. - 4. Inertia. - 5. Application. -{xiii} - -CHAP. VI. OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS 212 - - _Art._ 1. Object of the Chapter. - 2. Statics and Dynamics. - 3. Equilibrium. - 4. Measure of Statical Forces. - 5. The Center of Gravity. - 6. Oblique Forces. - 7. Force acts at any point of its Direction. - 8. The Parallelogram of Forces - 9. Is a necessary Truth. - 10. Center of Gravity descends. - 11. Stevinus's Proof. - 12. Principle of Virtual Velocities. - 13. Fluids press equally. - 14. Foundation of this Axiom. - -CHAP. VII. OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS 235 - - _Art._ 1. History. - 2. The First Law of Motion. - 3. Gravity is a Uniform Force. - 4. The Second Law of Motion. - 5. The Third Law of Motion. - 6. Action and Reaction in Moving Bodies. - 7. D'Alembert's Principle. - 8. Connexion of Statics and Dynamics. - 9. Mechanical Principles grow more evident. - 10. Controversy of the Measure of Force. - -CHAP. VIII. OF THE PARADOX OF UNIVERSAL PROPOSITIONS - OBTAINED FROM EXPERIENCE 263 - - _Art._ 1. Experience cannot establish necessary Truths; - 2. But can interpret Axioms. - 3. Gives us the Matter of Truths. - 4. Exemplifies Truths. - 5. Cannot shake Axioms. - 6. Is this applicable in other cases? - -CHAP. IX. OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL - GRAVITATION 272 - - _Art._ 1. General course of the History. -{xiv} - 2. Particulars as to the Law. - 3. As to the Gravity of Matter. - 4. Universality of the Law. - 5. Is Gravity an essential quality? - 6. Newton's Rule of Philosophizing. - 7. Hypotheses respecting Gravity. - 8. Do Bodies act at a distance? - -CHAP. X. OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS 279 - - _Art._ 1. Nature of the Process - 2. Among the Ancients. - 3. Kepler, &c. - 4. Lord Monboddo, &c. - 5. Schelling, &c. - 6. Common usage. - 7. Effect of Phrases. - 8. Contempt of Predecessors. - 9. Less detail hereafter. - 10. Mechanico-Chemical Sciences. - 11. Secondary Mechanical Sciences. - - -BOOK IV. - -THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES. - -CHAP. I. OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED 293 - - _Art._ 1. Of Primary and Secondary Qualities. - 2. The Idea of Externality. - 3. Sensation by a Medium. - 4. Process of Perception of Secondary Qualities. - -CHAP. II. ON PECULIARITIES IN THE PERCEPTIONS OF THE - DIFFERENT SENSES 302 - - _Art._ 1. Difference of Senses. - -_Sect._ I. _Prerogatives of Sight._ - _Art._ 2. Position. - 3. Distance. -{xv} -_Sect._ II. _Prerogatives of Hearing._ - _Art._ 4. Musical Intervals. - 5. Chords. - 6. Rhythm. - -_Sect._ III. _The Paradoxes of Vision._ - _Art._ 7. First Paradox. - 8. Second Paradox. - 9. The same for near Objects. - 10. Objections answered. - -_Sect._ IV. _The Perception of Visible Figures._ - _Art._ 11. Brown's Opinion. - -CHAP. III. SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC - APPLICATION OF THE IDEA OF A MEDIUM 322 - - _Art._ 1. Introduction. - 2. Sound. - 3. Light. - 4. Heat. - -CHAP. IV. OF THE MEASURE OF SECONDARY QUALITIES 333 - -_Sect._ I. _Scales of Qualities in General._ - _Art._ 1. Intensity. - 2. Quantity and Quality. - -_Sect._ II. _The Musical Scale._ - _Art._ 3. Musical Relations. - 4. Musical Standard. - -_Sect._ III. _Scales of Colour._ - _Art._ 5. The Prismatic Scale. - 6. Newton's Scale. - 7. Scales of Impure Colours. - 8. Chromatometer. - -_Sect._ IV. _Scales of Light._ - _Art._ 9. Photometer. - 10. Cyanometer. - -_Sect._ V. _Scales of Heat._ - _Art._ 11. Thermometers. - 12. Their progress. - 13. Fixed Points. - 14. Concordance of Thermometers. - 15. Natural Measure. - 16. Law of Cooling. -{xvi} - 17. Theory of Exchanges. - 18. Air Thermometer. - 19. Theory of Heat. - 20. Other Instruments. - -_Sect._ VI. _Scales of other Quantities._ - _Art._ 21. Tastes and Smells. - 22. Quality of Sounds. - 23. Articulate Sounds. - 24. Transition. - - -BOOK V. - -OF THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES. - -CHAP. I. ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA - OF POLARITY 359 - - _Art._ 1. Introduction of the Idea. - 2. Magnetism. - 3. Electricity. - 4. Voltaic Electricity. - 5. Light. - 6. Crystallization. - 7. Chemical Affinity. - 8. General Remarks. - 9. Like _repels_ like. - -CHAP. II. OF THE CONNEXION OF POLARITIES 371 - - _Art._ 1. Different Polar Phenomena from one Cause. - 2. Connexion of Magnetic and Electric Polarity. - 3. Ampère's Theory. - 4. Faraday's views. - 5. Connexion of Electrical and Chemical Polarity. - 6. Davy's and Faraday's views - 7. Depend upon Ideas as well as Experiments. - 8. Faraday's Anticipations. - 9. Connexion of Chemical and Crystalline Polarities. - 10. Connexion of Crystalline and Optical Polarities. - 11. Connexion of Polarities in general. - 12. Schelling's Speculations. - 13. Hegel's vague notions. - 14. Ideas must guide Experiment. - - - - -{{1}} -THE -PHILOSOPHY -OF THE -INDUCTIVE SCIENCES. - - - -INTRODUCTION. - -{{3}} -INTRODUCTION. - - -THE PHILOSOPHY OF SCIENCE, if the phrase were to be -understood in the comprehensive sense which most naturally -offers itself to our thoughts, would imply nothing less than -a complete insight into the essence and conditions of all -real knowledge, and an exposition of the best methods for -the discovery of new truths. We must narrow and lower this -conception, 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 success; yet still it may be a rational and useful -undertaking, to endeavour to make some advance towards such -a Philosophy, even according to the most ample conception of -it which we can form. The present work has been written with -a view of contributing, in some measure, however small it -may be, towards such an undertaking. - -But in this, as in every attempt to advance beyond the -position which we at present occupy, our hope of success -must depend mainly upon our being able to profit, to the -fullest extent, by the progress already made. We may best -hope to understand the nature and conditions of real -knowledge, by studying the nature and conditions of the most -certain and stable portions of knowledge which we already -possess: and we are most likely to learn the best methods of -discovering truth, by examining how truths, now universally -recognized, have really been discovered. Now there do exist -among us doctrines of solid and acknowledged certainty, and -truths of which the discovery has been received with -universal applause. These constitute what we commonly term -_Sciences_; and of these bodies of exact and enduring -knowledge, we have within our {4} reach so large and varied -a collection, that we may examine them, and the history of -their formation, with a good prospect of deriving from the -study such instruction as we seek. We may best hope to make -some progress towards the Philosophy of Science, by -employing ourselves upon THE PHILOSOPHY OF THE SCIENCES. - -The _Sciences_ to which the name is most commonly and -unhesitatingly given, are those which are concerned about -the material world; whether they deal with the celestial -bodies, as the sun and stars, or the earth and its products, -or the elements; whether they consider the differences which -prevail among such objects, or their origin, or their mutual -operation. And in all these Sciences it is familiarly -understood and assumed, that their doctrines are obtained by -a common process of collecting general truths from -particular observed facts, which process is termed -_Induction_. It is further assumed that both in these and in -other provinces of knowledge, so long as this process is -duly and legitimately performed, the results will be real -substantial truth. And although this process, with the -conditions under which it is legitimate, and the general -laws of the formation of Sciences, will hereafter be -subjects of discussion in this work, I shall at present so -far adopt the assumption of which I speak, as to give to the -Sciences from which our lessons are to be collected the name -of _Inductive Sciences_. And thus it is that I am led to -designate my work as THE PHILOSOPHY OF THE INDUCTIVE -SCIENCES. - -The views respecting the nature and progress of knowledge, -towards which we shall be directed by such a course of -inquiry as I have pointed out, though derived from those -portions of human knowledge which are more peculiarly and -technically termed _Sciences_, will by no means be confined, -in their bearing, to the domain of such Sciences as deal -with the material world, nor even to the whole range of -Sciences now existing. On the contrary, we shall be led to -believe that the nature of truth is in all subjects the -same, and that its discovery involves, in all cases, the -like {5} conditions. On one subject of human speculation -after another, man's knowledge assumes that exact and -substantial character which leads us to term it _Science_; -and in all these cases, whether inert matter or living -bodies, whether permanent relations or successive -occurrences, be the subject of our attention, we can point -out certain universal characters which belong to truth, -certain general laws which have regulated its progress among -men. And we naturally expect that, even when we extend our -range of speculation wider still, when we contemplate the -world within us as well as the world without us, when we -consider the thoughts and actions of men as well as the -motions and operations of unintelligent bodies, we shall -still find some general analogies which belong to the -essence of truth, and run through the whole intellectual -universe. 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 -speculation. By considering what is the real import of our -acquisitions, where they are certain and definite, we may -learn something respecting the difference between true -knowledge and its precarious or illusory semblances; by -examining the steps by which such acquisitions have been -made, we may discover the conditions under which truth is to -be obtained; by tracing the boundary-line between our -knowledge and our ignorance, we may ascertain in some -measure the extent of the powers of man's understanding. - -But it may be said, in such a design there is nothing new; -these are objects at which inquiring men have often before -aimed. To determine the difference between real and -imaginary knowledge, the conditions under which we arrive at -truth, the range of the powers of the human mind, has been a -favourite employment of speculative men from the earliest to -the most recent times. To inquire into the original, -certainty, and compass of man's knowledge, the limits of his -capacity, the strength and weakness of his reason, has been -the professed purpose of many of the most conspicuous and -valued labours of the philosophers of {6} all periods up to -our own day. It may appear, therefore, that there is little -necessity to add one more to these numerous essays; and -little hope that any new attempt will make any very -important addition to the stores of thought upon such -questions, which have been accumulated by the profoundest -and acutest thinkers of all ages. - -To this I reply, 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 -knowledge, it may still be possible to add something to what -they have done. The writings of all great philosophers, up -to our own time, form a series which is not yet terminated. -The books and systems of philosophy which have, each in its -own time, won the admiration of men, and exercised a -powerful influence upon their thoughts, have had each its -own part and functions in the intellectual history of the -world; and other labours which shall succeed these may also -have their proper office and useful effect. We may not be -able to do much, and yet still it may be in our power to -effect something. Perhaps the very advances made by former -inquirers may have made it possible for us, at present, to -advance still further. In the discovery of truth, in the -development of man's mental powers and privileges, each -generation has its assigned part; and it is for us to -endeavour to perform our portion of this perpetual task of -our species. Although the terms which describe our -undertaking may be the same which have often been employed -by previous writers to express their purpose, yet our -position is different from theirs, and thus the result may -be different too. We have, as they had, to run our -appropriate course of speculation with the exertion of our -best powers; but our course lies in a more advanced part of -the great line along which Philosophy travels from age to -age. However familiar and old, therefore, be the design of -such a work as this, the execution may have, and if it be -performed in a manner suitable to the time, will have, -something that is new and not unimportant. {7} - -Indeed, it appears to be absolutely necessary, in order to -check the prevalence of grave and pernicious errour, that -the doctrines which are taught concerning the foundations of -human knowledge and the powers of the human mind, should be -from time to time revised and corrected or extended. -Erroneous and partial views are promulgated and accepted; -one portion of the truth is insisted upon to the undue -exclusion of another; or principles true in themselves are -exaggerated till they produce on men's minds the effect of -falsehood. When evils of this kind have grown to a serious -height, a _Reform_ is requisite. The faults of the existing -systems must be remedied by correcting what is wrong, and -supplying what is wanting. In such cases, 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 arrived. The new form which errour -has assumed makes it proper to endeavour to give a new and -corresponding form to truth. Thus the mere progress of time, -and the natural growth of opinion from one stage to another, -leads to the production of new systems and forms of -philosophy. It will be found, I think, 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 needed. The present age seems, by many -indications, to be called upon to seek a sounder Philosophy -of Knowledge than is now current among us. To contribute -towards such a Philosophy is the object of the present work. -The work is, therefore, like all works which take into -account the most recent forms of speculative doctrine, -invested with a certain degree of novelty in its aspect and -import, by the mere time and circumstances of its -appearance. - -But, moreover, we can point out a very important peculiarity -by which this work is, in its design, distinguished from -preceding essays on like subjects; 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 labours. The peculiarity {8} of which I speak -has already been announced;--it is this: that we purpose to -collect our doctrines concerning the nature of knowledge, -and the best mode of acquiring it, from a contemplation of -the Structure and History of those Sciences (the Material -Sciences), which are universally recognized as the clearest -and surest examples of knowledge and of discovery. It is by -surveying and studying the whole mass of such Sciences, and -the various steps of their progress, that we now hope to -approach to the true Philosophy of Science. - -Now this, I venture to say, is a new method of pursuing the -philosophy of human knowledge. Those who have hitherto -endeavoured to explain the nature of knowledge, and the -process of discovery, have, it is true, often illustrated -their views by adducing special examples of truths which -they conceived to be established, and by referring to the -mode of their establishment. But these examples have, for -the most part, been taken at random, not selected according -to any principle or system. Often they have involved -doctrines so precarious or so vague that they confused -rather than elucidated the subject; and instead of a single -difficulty,--What is the nature of Knowledge? these attempts -at illustration introduced two,--What was the true analysis -of the Doctrines thus adduced? and,--Whether they might -safely be taken as types of real Knowledge? - -This has usually been the case when there have been adduced, -as standard examples of the formation of human knowledge, -doctrines belonging to supposed sciences other than the -material sciences; doctrines, for example, of Political -Economy, or Philology, or Morals, or the Philosophy of the -Fine Arts. I am very far from thinking that, in regard to -such subjects, there are no important truths hitherto -established: but it would seem that those truths which have -been obtained in these provinces of knowledge, have not yet -been fixed by means of distinct and permanent phraseology, -and sanctioned by universal reception, and formed into a -connected system, and traced through the steps of their -gradual discovery and establishment, so as to make {9} them -instructive examples of the nature and progress of truth in -general. Hereafter we trust to be able to show that the -progress of moral, and political, and philological, and -other knowledge, is governed by the same laws as that of -physical science. But since, at present, the former class of -subjects are full of controversy, doubt, and obscurity, -while the latter consist of undisputed truths clearly -understood and expressed, it may be considered a wise -procedure to make the latter class of doctrines the basis of -our speculations. And on the having taken this course, is, -in a great measure, my hope founded, of obtaining valuable -truths which have escaped preceding inquirers. - -But it may be said that many preceding writers on the nature -and progress of knowledge have taken their examples -abundantly from the Physical Sciences. It would be easy to -point out admirable works, which have appeared during the -present and former generations, in which instances of -discovery, borrowed from the Physical Sciences, are -introduced in a manner most happily instructive. And to the -works in which this has been done, I gladly give my most -cordial admiration. But at the same time I may venture to -remark that there still remains a difference between my -design and theirs: 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 to. For the -conclusions stated in the present work, respecting knowledge -and discovery, are drawn from _a connected and systematic -survey of the whole range of Physical Science and its -History_; whereas, hitherto, philosophers have contented -themselves with adducing detached examples of scientific -doctrines, drawn from one or two departments of science. So -long as we select our examples in this arbitrary and limited -manner, we lose the best part of that philosophical -instruction, which the sciences are fitted to afford when we -consider them as all members of one series, and as governed -by rules which are the same for all. Mathematical and -chemical truths, physical and physiological doctrines, the -sciences of {10} classification and of causation, must alike -be taken into our account, in order that we may learn what -are the general characters of real knowledge. When our -conclusions assume so comprehensive a shape that they apply -to a range of subjects so vast and varied as these, we may -feel some confidence that they represent the genuine form of -universal and permanent truth. But if our exemplification is -of a narrower kind, it may easily cramp and disturb our -philosophy. We may, for instance, render our views of truth -and its evidence so rigid and confined as to be quite -worthless, by founding them too much on the contemplation of -mathematical truth. We may overlook some of the most -important steps in the general course of discovery, by -fixing our attention too exclusively upon some one -conspicuous group of discoveries, as, for instance, those of -Newton. We may misunderstand the nature of physiological -discoveries, by attempting to force an analogy between them -and discoveries of mechanical laws, and by not attending to -the intermediate sciences which fill up the vast interval -between these extreme terms in the series of material -sciences. In these and in many other ways, a partial and -arbitrary reference to the material sciences in our inquiry -into human knowledge may mislead us; or at least may fail to -give us those wider views, and that deeper insight, which -should result from a systematic study of the whole range of -sciences with this particular object. - -The design of the following work, then, is to form a -Philosophy of Science, by analyzing the substance and -examining the progress of the existing body of the sciences. -As a preliminary to this undertaking, a survey of the -history of the sciences was necessary. This, accordingly, I -have already performed; and the result of the labour thus -undertaken has been laid before the public as a _History of -the Inductive Sciences_. - -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 satisfaction. The -events which that History relates, the speculations and -controversies {11} which are there described, and -discussions of the same kind, far more extensive, which are -there omitted, must all be taken into our account at -present, as the prominent and standard examples of the -circumstances which attend the progress of knowledge. With -so much of real historical fact before us, we may hope to -avoid such views of the processes of the human mind as are -too partial and limited, or too vague and loose, or too -abstract and unsubstantial, to represent fitly the real -forms of discovery and of truth. - -Of former attempts, made with the same view of tracing the -conditions of the progress of knowledge, that of Bacon is -perhaps the most conspicuous: and his labours on this -subject were opened by his book on the _Advancement of -Learning_, which contains, among other matter, a survey of -the then existing state of knowledge. But this review was -undertaken rather with the object of ascertaining in what -quarters future advances were to be hoped for, than of -learning by what means they were to be made. His examination -of the domain of human knowledge was conducted rather with -the view of discovering what remained undone, than of -finding out how so much had been done. Bacon's survey was -made for the purpose of tracing the boundaries, rather than -of detecting the principles of knowledge. 'I will now -attempt,' he says[1\I], 'to make a general and faithful -perambulation of learning, with an inquiry what parts -thereof lie fresh and waste, and not improved and converted -by the industry of man; to the end that such a plot made and -recorded to memory, may both minister light to any public -designation, and also serve to excite voluntary endeavours.' -Nor will it be foreign to our scheme also hereafter to -examine with a like purpose the frontier-line of man's -intellectual estate. But the object of our perambulation in -the first place, is not so much to determine the extent of -the field, as the sources of its fertility. We would learn -by what plan and rules {12} of culture, conspiring with the -native forces of the bounteous soil, those rich harvests -have been produced which fill our garners. Bacon's maxims, -on the other hand, respecting the mode in which he conceived -that knowledge was thenceforth to be cultivated, have little -reference to the failures, still less to the successes, -which are recorded in his Review of the learning of his -time. His precepts are connected with his historical views -in a slight and unessential manner. His Philosophy of the -Sciences is not collected from the Sciences which are -noticed in his survey. Nor, in truth, could this, at the -time when he wrote, have easily been otherwise. At that -period, scarce any branch of physics existed as a science, -except Astronomy. The rules which Bacon gives for the -conduct of scientific researches are obtained, as it were, -by divination, from the contemplation of subjects with -regard to which no sciences as yet were. His instances of -steps rightly or wrongly made in this path, are in a great -measure cases of his own devising. He could not have -exemplified his Aphorisms by references to treatises then -extant, on the laws of nature; for the constant burden of -his exhortation is, that men up to his time had almost -universally followed an erroneous course. And however we may -admire the sagacity with which he pointed the way along a -better path, we have this great advantage over him;--that we -can interrogate the many travellers who since his time have -journeyed on this road. At the present day, when we have -under our notice so many sciences, of such wide extent, so -well established; a Philosophy of the Sciences ought, it -must seem, to be founded, not upon conjecture, but upon an -examination of many instances;--should not consist of a few -vague and unconnected maxims, difficult and doubtful in -their application, but should form a system of which every -part has been repeatedly confirmed and verified. - -[Note 1\I: _Advancement of Learning_, b. i. p. 74.] - -This accordingly it is the purpose of the present work to -attempt. But I may further observe, that as my hope of -making any progress in this undertaking is {13} founded upon -the design of keeping constantly in view the whole result of -the past history and present condition of science, I have -also been led to draw my lessons from my examples in a -manner more systematic and regular, as appears to me, than -has been done by preceding writers. Bacon, as I have just -said, was led to his maxims for the promotion of knowledge -by the sagacity of his own mind, with little or no aid from -previous examples. Succeeding philosophers may often have -gathered useful instruction from the instances of scientific -truths and discoveries which they adduced, but their -conclusions were drawn from their instances casually and -arbitrarily. They took for their moral any which the story -might suggest. But such a proceeding as this cannot suffice -for us, whose aim is to obtain a consistent body of -philosophy from a contemplation of the whole of Science and -its History. For our purpose it is necessary to resolve -scientific truths into their conditions and ingredients, in -order that we may see in what manner each of these has been -and is to be provided, in the cases which we may have to -consider. This accordingly is necessarily the first part of -our task:--_to analyse Scientific Truth into its Elements_. -This attempt will occupy the earlier portion of the present -work; and will necessarily be somewhat long, and perhaps, in -many parts, abstruse and uninviting. The risk of such an -inconvenience is inevitable; for the inquiry brings before -us many of the most dark and entangled questions in which -men have at any time busied themselves. And even if these -can now be made clearer and plainer than of yore, still they -can be made so only by means of mental discipline and mental -effort. Moreover this analysis of scientific truth into its -elements contains much, both in its principles and in its -results, different from the doctrines most generally -prevalent among us in recent times: but on that very account -this analysis is an essential part of the doctrines which I -have now to lay before the reader: and I must therefore -crave his indulgence towards any portion of it which may -appear to him obscure or repulsive. {14} - -There is another circumstance which may tend to make the -present work less pleasing than others on the same subject, -in the nature of the examples of human knowledge to which I -confine myself; all my instances being, as I have said, -taken from the material sciences. For the truths belonging -to these sciences are, for the most part, neither so -familiar nor so interesting to the bulk of readers as those -doctrines which belong to some other subjects. Every general -proposition concerning politics or morals at once stirs up -an interest in men's bosoms, which makes them listen with -curiosity to the attempts to trace it to its origin and -foundation. Every rule of art or language brings before the -mind of cultivated men subjects of familiar and agreeable -thought, and is dwelt upon with pleasure for its own sake, -as well as on account of the philosophical lessons which it -may convey. But the curiosity which regards the truths of -physics or chemistry, or even of physiology or astronomy, is -of a more limited and less animated kind. Hence, in the mode -of inquiry which I have prescribed to myself, the examples -which I have to adduce will not amuse and relieve the -reader's mind as much as they might do, if I could allow -myself to collect them from the whole field of human -knowledge. They will have in them nothing to engage his -fancy, or to warm his heart. I am compelled to detain the -listener in the chilly air of the external world, in order -that we may have the advantage of full daylight. - -But although I cannot avoid this inconvenience, so far as it -is one, I hope it will be recollected how great are the -advantages which we obtain by this restriction. We are thus -enabled to draw all our conclusions from doctrines which are -universally allowed to be eminently certain, clear, and -definite. The portions of knowledge to which I refer are -well known, and well established among men. Their names are -familiar, their assertions uncontested. Astronomy and -Geology, Mechanics and Chemistry, Optics and Acoustics, -Botany and Physiology, are each recognized as large and -substantial collections of undoubted truths. Men are {15} -wont to dwell with pride and triumph on the acquisitions of -knowledge which have been made in each of these provinces; -and to speak with confidence of the certainty of their -results. And all can easily learn in what repositories these -treasures of human knowledge are to be found. When, -therefore, we begin our inquiry from such examples, we -proceed upon a solid foundation. With such a clear ground of -confidence, we shall not be met with general assertions of -the vagueness and uncertainty of human knowledge; with the -question, What truth is, and How we are to recognize it; -with complaints concerning the hopelessness and -unprofitableness of such researches. We have, at least, a -definite problem before us. We have to examine the structure -and scheme, not of a shapeless mass of incoherent materials, -of which we doubt whether it be a ruin or a natural -wilderness, but of a fair and lofty palace, still erect and -tenanted, where hundreds of different apartments belong to a -common plan, where every generation adds something to the -extent and magnificence of the pile. The certainty and the -constant progress of science are things so unquestioned, -that we are at least engaged in an intelligible inquiry, -when we are examining the grounds and nature of that -certainty, the causes and laws of that progress. - -To this inquiry, then, we now proceed. And in entering upon -this task, however our plan or our principles may differ -from those of the eminent philosophers who have endeavoured, -in our own or in former times, to illustrate or enforce the -philosophy of science, we most willingly acknowledge them as -in many things our leaders and teachers. Each reform must -involve its own peculiar principles, and the result of our -attempts, so far as they lead to a result, must be, in some -respects, different from those of former works. But we may -still share with the great writers who have treated this -subject before us, their spirit of hope and trust, their -reverence for the dignity of the subject, their belief in -the vast powers and boundless destiny of man. And we may -once more venture to use the {16} words of hopeful -exhortation, with which the greatest of those who have -trodden this path encouraged himself and his followers when -he set out upon his way. - -'Concerning ourselves we speak not; but as touching the -matter which we have in hand, this we ask;--that men deem it -not to be the setting up an Opinion, but the performing of a -Work: and that they receive this as a certainty; that we are -not laying the foundations of any sect or doctrine, but of -the profit and dignity of mankind. Furthermore, that being -well disposed to what shall advantage themselves, and -putting off factions and prejudices, they take common -counsel with us, to the end that being by these our aids and -appliances freed and defended from wanderings and -impediments, they may lend their hands also to the labours -which remain to be performed: and yet further, that they be -of good hope; neither imagine to themselves this our Reform -as something of infinite dimension, and beyond the grasp of -mortal man, when in truth it is the end and true limit of -infinite errour; and is by no means unmindful of the -condition of mortality and humanity, not confiding that such -a thing can be carried to its perfect close in the space of -one single age, but assigning it as a task to a succession -of generations.' - -[The Philosophy of the Inductive Sciences, according to our -view, must be founded upon the History of such Sciences; -which history we have attempted in a former work. The events -of that history may be described generally as the rise of -Theories out of Facts. But besides this, which we may term -the _external_ history of Theories, there is an internal -history of Theories, namely, the series of steps by which -the human mind becomes capable of forming each Theory. Hence -to complete the History of the Sciences as derived from -Facts, we require a history of the Ideas by which such -derivation has been made possible: and thus, the _First -Part_ of our Philosophy must be a _History of Scientific -Ideas_;--a labour no less historical than our former work, -and concerned with the same events; but which has been -purposely kept separate during the {17} composition, in -order that it might be afterwards presented in a more -systematic form, which I have here attempted to do. - -Scientific Ideas are the Conditions of the derivation of -Sciences from Facts: but can any method or methods be given -by which such a Derivation can be ensured, or at least, -aided? Many such methods have been proposed; of which the -most celebrated is the _Novum Organon_ of Bacon, of which -the title was intended to imply that its scope goes much -beyond the _Organon_ of Aristotle. With the experience of -the formation of Science which the world has had since -Bacon's time, it does not appear presumptuous to suppose -that we can now improve or correct his methods; nor to term -such an attempt _Novum Organon Renovatum_. - -The Philosophy of the Inductive Sciences, then, contains -these two parts, _The History of Scientific Ideas_, and the -_Novum Organon Renovatum_.] - - - - -{{19}} -THE -PHILOSOPHY -OF THE -INDUCTIVE SCIENCES. - - -PART I. - -HISTORY OF SCIENTIFIC IDEAS. - - -[We have just spoken of _Theories_ and _Facts_, of _Ideas_ -and _Facts_, and of _Inductive_ Sciences, which imply the -opposition of _Induction_ and _Deduction_. The explanation -of these antitheses must be the starting point of our -Philosophy.] - - -[Knowledge grows, and] through the ages one increasing purpose runs, -And the thoughts of men are widen'd with the process of the Suns. - - - - -BOOK I. - - -OF IDEAS IN GENERAL. - - -Quæ adhuc inventa sunt in Scientiis, ea hujusmodi sunt ut -Notionibus Vulgaribus fere subjaceant: ut vero ad interiora -et remotiora Naturæ penetretur, necesse est ut tam NOTIONES -quam AXIOMATA magis certâ et munitâ viâ a particularibus -abstrahantur; atque omnino melior et certior intellectûs -adoperatio in usum veniat. - -BACON, _Nov. Org._, Lib. 1. Aphor. xviii. - - -{{23}} -BOOK I. - - -OF IDEAS IN GENERAL. - - -CHAPTER I. - -OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY. - - -_Sect._ 1.--_Thoughts and Things._ - -IN order that we may do something towards determining the -nature and conditions of human knowledge, (which I have -already stated as the purpose of this work,) I shall have to -refer to an antithesis or opposition, which is familiar and -generally recognized, and in which the distinction of the -things opposed to each other is commonly considered very -clear and plain. I shall have to attempt to make this -opposition sharper and stronger than it is usually -conceived, and yet to shew that the distinction is far from -being so clear and definite as it is usually assumed to be: -I shall have to point the contrast, yet shew that the things -which are contrasted cannot be separated:--I must explain -that the antithesis is constant and essential, but yet that -there is no fixed and permanent line dividing its members. I -may thus appear, in different parts of my discussion, to be -proceeding in opposite directions, 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 him. - -The antithesis or opposition of which I speak is denoted, -with various modifications, by various pairs of terms: I -shall endeavour to shew the connexion of these different -modes of expression, and I will begin with that form which -is the simplest and most idiomatic. {24} - -The simplest and most idiomatic expression of the antithesis -to which I refer is that in which we oppose to each other -THINGS and THOUGHTS. The opposition is familiar and plain. -Our thoughts are something which belongs to ourselves; -something which takes place within us; they are what we -think; they are actions of our minds. Things, on the -contrary, are something different from ourselves and -independent of us; something which is without us; they -_are_; we see them, touch them, and thus know that they -exist; but we do not make them by seeing or touching them, -as we make our _Thoughts_ by thinking them; we are passive, -and _Things_ act upon our organs of perception. - -Now what I wish especially to remark is this: that in all -human KNOWLEDGE both Thoughts and Things are concerned. In -every part of my knowledge there must be some _thing_ about -which I know, and an internal act of _me_ who know. Thus, to -take simple yet definite parts of our knowledge, if I know -that a solar year consists of 365 days, or a lunar month of -30 days, I know something about the sun or the moon; namely, -that those objects perform certain revolutions and go -through certain changes, in those numbers of days; but I -count such numbers and conceive such revolutions and changes -by acts of my own thoughts. And both these elements of my -knowledge are indispensable. 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 them. And -however regular were the motions of the sun and moon, if I -could not count their appearances and combine their changes -into a cycle, or if I could not understand this when done by -other men, I could not know anything about a year or a -month. In the former case I might be conceived as a human -being, possessing the human powers of thinking and -reckoning, but kept in a dark world with nothing to mark the -progress of existence. The latter is the case of brute -animals, which see the sun and moon, but do not know how -many days make a month or a year, because they have not -human powers of thinking and reckoning. {25} - -The two elements which are essential to our knowledge in the -above cases, are necessary to human knowledge in all cases. -In all cases, Knowledge implies a combination of Thoughts -and Things. Without this combination, it would not be -Knowledge. Without Thoughts, there could be no connexion; -without Things, there could be no reality. Thoughts and -Things are so intimately combined in our Knowledge, that we -do not look upon them as distinct. One single act of the -mind involves them both; and their contrast disappears in -their union. - -But though Knowledge requires the union of these two -elements, Philosophy requires the separation of them, in -order that the nature and structure of Knowledge may be -seen. Therefore I begin by considering this separation. And -I now proceed to speak of another way of looking at the -antithesis of which I have spoken; and which I may, for the -reasons which I have just mentioned, call the FUNDAMENTAL -ANTITHESIS OF PHILOSOPHY. - - -_Sect._ 2.--_Necessary and Experiential Truths._ - -MOST persons are familiar with the distinction of -_necessary_ and _contingent_ truths. The former kind are -Truths which cannot but be true; as that 19 and 11 make -30;--that parallelograms upon the same base and between the -same parallels are equal;--that all the angles in the same -segment of a circle are equal. The latter are Truths which -_it happens_ (_contingit_) are true; but which, for anything -which we can see, might have been otherwise; as that a lunar -month contains 30 days, or that the stars revolve in circles -round the pole. The latter kind of Truths are learnt by -experience, and hence we may call them _Truths of -Experience_, or, for the sake of convenience, _Experiential_ -Truths, in contrast with Necessary Truths. - -Geometrical propositions are the most manifest examples of -Necessary Truths. All persons who have read and understood -the elements of geometry, know that the propositions above -stated (that parallelograms {26} upon the same base and -between the same parallels are equal; that all the angles in -the same segment of a circle are equal,) are necessarily -true; not only they are true, but they _must be_ true. The -meaning of the terms being understood, and the proof being -gone through, the truth of the propositions must be assented -to. We learn these propositions to be true by demonstrations -deduced from definitions and axioms; and when we have thus -learnt them, we see that they could not be otherwise. In the -same manner, the truths which concern numbers are necessary -truths: 19 and 11 not only _do_ make 30, but _must_ make -that number, and cannot make anything else. In the same -manner, it is a necessary truth that half the sum of two -numbers added to half their difference is equal to the -greater number. - -It is easy to find examples of Experiential Truths;-- -propositions which we know to be true, but know by -experience only. We know, in this way, that salt will -dissolve in water; that plants cannot live without light;-- -in short, we know in this way all that we do know in -chemistry, physiology, and the material sciences in general. -I take the _Sciences_ as my examples of human knowledge, -rather than the common truths of daily life, or moral or -political truths; because, though the latter are more -generally interesting, the former are much more definite and -certain, and therefore better starting-points for our -speculations, as I have already said. And we may take -elementary astronomical truths as the most familiar examples -of Experiential Truths in the domain of science. - -With these examples, the distinction of Necessary and -Experiential Truths is, I hope, clear. The former kind, we -see to be true by thinking about them, and see that they -could not be otherwise. The latter kind, men could never -have discovered to be true without looking at them; and -having so discovered them, still no one will pretend to say -they might not have been otherwise. For aught we can see, -the astronomical truths which express the motions and -periods of the sun, moon and stars, might have been -otherwise. If we had been placed in another part of the -solar system, our {27} experiential truths respecting days, -years, and the motions of the heavenly bodies, would have -been other than they are, as we know from astronomy itself. - -It is evident that this distinction of Necessary and -Experiential Truths involves the same antithesis which we -have already considered;--the antithesis of Thoughts and -Things. Necessary Truths are derived from our own Thoughts: -Experiential truths are derived from our observation of -Things about us. The opposition of Necessary and -Experiential Truths is another aspect of the Fundamental -Antithesis of Philosophy. - - -_Sect._ 3.--_Deduction and Induction._ - -I HAVE already stated that geometrical truths are -established by demonstrations _deduced_ from definitions and -axioms. The term _Deduction_ is specially applied to such a -course of demonstration of truths from definitions and -axioms. In the case of the parallelograms upon the same base -and between the same parallels, we prove certain triangles -to be equal, by supposing them placed so that their two -bases have the same extremities; and hence, referring to an -Axiom respecting straight lines, we infer that the bases -coincide. We combine these equal triangles with other equal -spaces, and in this way make up both the one and the other -of the parallelograms, in such a manner as to shew that they -are equal. In this manner, going on step by step, deducing -the equality of the triangles from the axiom, and the -equality of the parallelograms from that of the triangles, -we travel to the conclusion. And this process of successive -deduction is the scheme of all geometrical proof. We begin -with Definitions of the notions which we reason about, and -with Axioms, or self-evident truths, respecting these -notions; and we get, by reasoning from these, other truths -which are demonstratively evident; and from these truths -again, others of the same kind, and so on. We begin with our -own Thoughts, which supply us with Axioms to start from; and -we reason from these, till we come to propositions {28} -which are applicable to the Things about us; as for -instance, the propositions respecting circles and spheres -applicable to the motions of the heavenly bodies. This is -_Deduction_, or _Deductive Reasoning_. - -Experiential truths are acquired in a very different way. In -order to obtain such truths, we begin with Things. In order -to learn how many days there are in a year, or in a lunar -month, we must begin by observing the sun and the moon. We -must observe their changes day by day, and try to make the -cycle of change fit into some notion of number which we -supply from our own Thoughts. We shall find that a cycle of -30 days nearly will fit the changes of phase of the -moon;--that a cycle of 365 days nearly will fit the changes -of daily motion of the sun. Or, to go on to experiential -truths of which the discovery comes within the limits of the -history of science--we shall find (as Hipparchus found) that -the unequal motion of the sun among the stars, such as -observation shews it to be, may be fitly represented by the -notion of an _eccentric_;--a circle in which the sun has an -equable annual motion, the spectator not being in the center -of the circle. Again, in the same manner, at a later period, -Kepler started from more exact observations of the sun, and -compared them with a supposed motion in a certain ellipse; -and was able to shew that, not a circle about an eccentric -point, but an ellipse, supplied the mode of conception which -truly agreed with the motion of the sun about the earth; or -rather, as Copernicus had already shewn, of the earth about -the sun. In such cases, in which truths are obtained by -beginning from observation of external things and by finding -some notion with which the Things, as observed, agree, the -truths are said to be obtained by _Induction_. The process -is an _Inductive Process_. - -The contrast of the Deductive and Inductive process is -obvious. In the former, we proceed at each step from general -truths to particular applications of them; in the latter, -from particular observations to a general truth which -includes them. In the former case we may be said to reason -_downwards_, in the latter case, {29} _upwards_; for general -notions are conceived as standing above particulars. -Necessary truths are proved, like arithmetical sums, by -adding together the portions of which they consist. An -inductive truth is proved, like the guess which answers a -riddle, by its agreeing with the facts described. -Demonstration is irresistible in its effect on the belief, -but does not produce surprize, because all the steps to the -conclusion are exhibited, before we arrive at the -conclusion. Inductive inference is not demonstrative, but it -is often more striking than demonstrative reasoning, because -the intermediate links between the particulars and the -inference are not shewn. Deductive truths are the results of -relations among our own Thoughts. Inductive truths are -relations which we discern among existing Things; and thus, -this opposition of Deduction and Induction is again an -aspect of the Fundamental Antithesis already spoken of. - - -_Sect._ 4.--_Theories and Facts._ - -GENERAL experiential Truths, such as we have just spoken of, -are called _Theories_, and the particular observations from -which they are collected, and which they include and -explain, are called _Facts_. Thus Hipparchus's doctrine, -that the sun moves in an eccentric about the earth, is _his -Theory_ of the Sun, or the _Eccentric Theory_. The doctrine -of Kepler, that the Earth moves in an Ellipse about the Sun, -is _Kepler's Theory_ of the Earth, the Elliptical Theory. -Newton's doctrine that this elliptical motion of the Earth -about the Sun is produced and governed by the Sun's -attraction upon the Earth, is the _Newtonian_ theory, the -_Theory of Attraction_. Each of these Theories was accepted, -because it included, connected and explained the _Facts_; -the Facts being, in the two former cases, the motions of the -Sun as observed; and in the other case, the elliptical -motion of the Earth as known by Kepler's Theory. This -antithesis of _Theory_ and _Fact_ is included in what has -just been said of Inductive Propositions. A Theory is an -Inductive Proposition, and the Facts {30} are the particular -observations from which, as I have said, such Propositions -are inferred by Induction. The Antithesis of Theory and Fact -implies the fundamental Antithesis of Thoughts and Things; -for a Theory (that is, a true Theory) may be described as a -Thought which is contemplated distinct from Things and seen -to agree with them; while a Fact is a combination of our -Thoughts with Things in so complete agreement that we do not -regard them as separate. - -Thus the antithesis of Theory and Fact involves the -antithesis of Thoughts and Things, but is not identical with -it. Facts involve Thoughts, for we know Facts only by -thinking about them. The Fact that the year consists of 365 -days; the Fact that the month consists of 30 days, cannot be -known to us, except we have the Thoughts of Time, Number and -Recurrence. But these Thoughts are so familiar, that we have -the fact in our mind as a simple Thing without attending to -the Thought which it involves. When we mould our Thoughts -into a Theory, we consider the thought as distinct from the -Facts; but yet, though distinct, not independent of them; -for it is a true Theory, only by including and agreeing with -the Facts. - - -_Sect._ 5.--_Ideas and Sensations._ - -WE have just seen that the antithesis of Theory and Fact, -although it involves the antithesis of Thoughts and Things, -is not identical with it. There are other modes of -expression also, which involve the same Fundamental -Antithesis, more or less modified. Of these, the pair of -words which in their relations appear to separate the -members of the antithesis most distinctly are _Ideas_ and -_Sensations_. We see and hear and touch external things, and -thus perceive them by our senses; but in perceiving them, we -connect the impressions of sense according to relations of -space, time, number, likeness, cause, &c. Now some at least -of these kinds of connexion, as space, time, number, may be -contemplated distinct from the things to which they are -applied; and so contemplated, I term them _Ideas_. And {31} -the other element, the impressions upon our senses which -they connect, are called _Sensations_. - -I term space, time, cause, &c., _Ideas_, because they are -general relations among our sensations, apprehended by an -act of the mind, not by the senses simply. These relations -involve something beyond what the senses alone could -furnish. By the sense of sight we see various shades and -colours and shapes before us, but the _outlines_ by which -they are separated into distinct objects of definite forms, -are the work of the mind itself. And again, when we conceive -visible things, not only as surfaces of a certain form, but -as _solid bodies_, placed at various distances in space, we -again exert an act of the mind upon them. When we see a body -move, we see it move in a path or _orbit_, but this orbit is -not itself seen; it is constructed by the mind. In like -manner when we see the motions of a needle towards a magnet, -we do not _see_ the attraction or force which produces the -effects; but we infer the force, by having in our minds the -Idea of Cause. Such acts of thought, such _Ideas_, enter -into our perceptions of external things. - -But though our perceptions of external things involve some -act of the mind, they must involve something else besides an -act of the mind. If we must exercise an act of thought in -order to see force exerted, or orbits described by bodies in -motion, or even in order to see bodies existing in space, -and to distinguish one kind of object from another, still -the act of thought alone does not make the Bodies. There -must be something besides, _on which_ the thought is -exerted. A colour, a form, a sound, are not produced by the -mind, however they may be moulded, combined, and interpreted -by our mental acts. A philosophical poet has spoken of - All the world - Of eye and ear, both what they half create, - And what perceive. -But it is clear, that though they _half_ create, they do not -wholly create: there must be an external world of colour and -sound to give impressions to the eye and ear, as well as internal -powers by which we perceive {32} what is offered to our organs. -The mind is in some way passive as well as active: there are -objects without as well as faculties within;--Sensations, -as well as acts of Thought. - -Indeed this is so far generally acknowledged, that according -to common apprehension, the mind is passive _rather_ than -active in acquiring the knowledge which it receives -concerning the material world. Its sensations are generally -considered more distinct than its operations. The world -without is held to be more clearly real than the faculties -within. That there is something different from ourselves, -something external to us, something independent of us, -something which no act of our minds can make or can destroy, -is held by all men to be at least as evident, as that our -minds can exert any effectual process in modifying and -appreciating the impressions made upon them. Most persons -are more likely to doubt whether the mind be always actively -applying Ideas to the objects which it perceives, than -whether it perceive them passively by means of Sensations. - -But yet a little consideration will show us that an activity -of the mind, and an activity according to certain Ideas, is -requisite in all our knowledge of external objects. We see -objects, of various solid forms, and at various distances -from us. But we do not thus perceive them by sensation -alone. Our visual impressions cannot, of themselves, convey -to us a knowledge of solid form, or of distance from us. -Such knowledge is inferred from what we see:--inferred by -conceiving the objects as existing in space, and by applying -to them the Idea of Space. Again:--day after day passes, -till they make up a year: but we do not know that the days -are 365, except we count them; and thus apply to them our -Idea of Number. Again:--we see a needle drawn to a magnet: -but, in truth, the _drawing_ is what we cannot see. We see -the needle move, and infer the attraction, by applying to -the fact our Idea of Force, as the cause of motion. -Again:--we see two trees of different kinds; but we cannot -know that they are so, except by applying to them our Idea -of the resemblance {33} and difference which makes kinds. -And thus Ideas, as well as Sensations, necessarily enter -into all our knowledge of objects: and these two words -express, perhaps more exactly than any of the pairs before -mentioned, that Fundamental Antithesis, in the union of -which, as I have said, all knowledge consists. - - -_Sect._ 6.--_Reflexion and Sensation._ - -IT will hereafter be my business to show what the Ideas are, -which thus enter into our knowledge; and how each Idea has -been, as a matter of historical fact, introduced into the -Science to which it especially belongs. But before I proceed -to do this, I will notice some other terms, besides the -phrases already noticed, which have a reference, more or -less direct, to the Fundamental Antithesis of Ideas and -Sensations. I will mention some of these, in order that if -they should come under the reader's notice, he may not be -perplexed as to their bearing upon the view here presented -to him. - -The celebrated doctrine of Locke, that all our 'Ideas,' -(that is, in his use of the word, all our objects of -thinking,) come from Sensation or Reflexion, will naturally -occur to the reader as connected with the antithesis of -which I have been speaking. But there is a great difference -between Locke's account of Sensation and Reflexion, and our -view of Sensation and Ideas. He is speaking of the origin of -our knowledge;--we, of its nature and composition. He is -content to say that all the knowledge which we do not -receive directly by Sensation, we obtain by Reflex Acts of -the mind, which make up his Reflexion. But we hold that -there is no Sensation without an act of the mind, and that -the mind's activity is not only reflexly exerted upon -itself, but directly upon objects, so as to perceive in them -connexions and relations which are not Sensations. He is -content to put together, under the name of Reflexion, -everything in our knowledge which is not Sensation: we are -to attempt to analyze all that is not Sensation; not only to -say it consists of Ideas, but {34} to point out what those -Ideas are, and to show the mode in which each of them enters -into our knowledge. His purpose was, to prove that there are -no Ideas, except the reflex acts of the mind: our endeavour -will be to show that the acts of the mind, both direct and -reflex, are governed by certain Laws, which may be -conveniently termed Ideas. His procedure was, to deny that -any knowledge could be derived from the mind alone: our -course will be, to show that in every part of our most -certain and exact knowledge, those who have added to our -knowledge in every age have referred to principles which the -mind itself supplies. I do not say that my view is contrary -to his: but it is altogether different from his. If I grant -that all our knowledge comes from Sensation and Reflexion, -still my task then is only begun; for I want further to -determine, in each science, what portion comes, not from -mere Sensation, but from those Ideas by the aid of which -either Sensation or Reflexion can lead to Science. - -Locke's use of the word 'idea' is, as the reader will -perceive, different from ours. He uses the word, as he says, -which 'serves best to stand for whatsoever is the object of -the understanding when a man thinks.' 'I have used it,' he -adds, 'to express whatever is meant by _phantasm_, _notion_, -_species_, or whatever it is to which the mind can be -employed about in thinking.' It might be shown that this -separation of the _mind itself_ from the ideal _objects_ -about which it is employed in thinking, may lead to very -erroneous results. But it may suffice to observe that we use -the word _Ideas_, in the manner already explained, to -express that element, supplied by the mind itself, which -must be combined with Sensation in order to produce -knowledge. For us, Ideas are not Objects of Thought, but -rather Laws of Thought. Ideas are not synonymous with -Notions; they are Principles which give to our Notions -whatever they contain of truth. But our use of the term -_Idea_ will be more fully explained hereafter. {35} - - -_Sect._ 7.--_Subjective and Objective._ - -THE Fundamental Antithesis of Philosophy of which I have to -speak has been brought into great prominence in the writings -of modern German philosophers, and has conspicuously formed -the basis of their systems. They have indicated this -antithesis by the terms _subjective_ and _objective_. -According to the technical language of old writers, a thing -and its qualities are described as _subject_ and -_attributes_; and thus a man's faculties and acts are -attributes of which he is the _subject_. The mind is the -_subject_ in which ideas inhere. Moreover, the man's -faculties and acts are employed upon external _objects_; and -from objects all his sensations arise. Hence the part of a -man's knowledge which belongs to his own mind, is -_subjective_: that which flows in upon him from the world -external to him, is _objective_. And as in man's -contemplation of nature, there is always some act of thought -which depends upon himself, and some matter of thought which -is independent of him, there is, in every part of his -knowledge, a subjective and an objective element. The -combination of the two elements, the subjective or ideal, -and the objective or observed, is necessary, in order to -give us any insight into the laws of nature. But different -persons, according to their mental habits and constitution, -may be inclined to dwell by preference upon the one or the -other of these two elements. It may perhaps interest the -reader to see this difference of intellectual character -illustrated in two eminent men of genius of modern times, -Göthe and Schiller. - -Göthe himself gives us the account to which I refer, in his -history of the progress of his speculations concerning the -Metamorphosis of Plants; a mode of viewing their structure -by which he explained, in a very striking and beautiful -manner, the relations of the different parts of a plant to -each other; as has been narrated in the _History of the -Inductive Sciences_. Göthe felt a delight in the passive -contemplation of nature, unmingled with the desire of -reasoning and theorizing; a delight such as naturally -belongs to those poets who {36} merely embody the images -which a fertile genius suggests, and do not mix with these -pictures, judgments and reflexions of their own. Schiller, -on the other hand, both by his own strong feeling of the -value of a moral purpose in poetry, and by his adoption of a -system of metaphysics in which the subjective element was -made very prominent, was well disposed to recognize fully -the authority of ideas over external impressions. - -Göthe for a time felt a degree of estrangement towards -Schiller, arising from this contrariety in their views and -characters. But on one occasion they fell into discussion on -the study of natural history; and Göthe endeavoured to -impress upon his companion his persuasion that nature was to -be considered, not as composed of detached and incoherent -parts, but as active and alive, and unfolding herself in -each portion, in virtue of principles which pervade the -whole. Schiller objected that no such view of the objects of -natural history had been pointed out by observation, the -only guide which the natural historians recommended; and was -disposed on this account to think the whole of their study -narrow and shallow. 'Upon this,' says Göthe, 'I expounded to -him, in as lively a way as I could, the metamorphosis of -plants, drawing on paper for him, as I proceeded, a diagram -to represent that general form of a plant which shows itself -in so many and so various transformations. Schiller attended -and understood; and, accepting the explanation, he said, -"This is not observation, but an idea." I replied,' adds -Göthe, 'with some degree of irritation; for the point which -separated us was most luminously marked by this expression: -but I smothered my vexation, and merely said, "I was happy -to find that I had got ideas without knowing it; nay, that I -saw them before my eyes."' Göthe then goes on to say, that -he had been grieved to the very soul by maxims promulgated -by Schiller, that no observed fact ever could correspond -with an idea. Since he himself loved best to wander in the -domain of external observation, he had been led to look with -repugnance and hostility upon anything which professed to -depend upon ideas. 'Yet,' he {37} observes, 'it occurred to -me that if my Observation was identical with his Idea, there -must be some common ground on which we might meet.' They -went on with their mutual explanations, and became intimate -and lasting friends. 'And thus,' adds the poet, by means of -that mighty and interminable controversy between _object_ -and _subject_, we two concluded an alliance which remained -unbroken, and produced much benefit to ourselves and others.' - -The general diagram of a plant, of which Göthe here speaks, -must have been a combination of lines and marks expressing -the relations of position and equivalence among the elements -of vegetable forms, by which so many of their resemblances -and differences may be explained. Such a symbol is not an -Idea in that general sense in which we propose to use the -term, but is a particular modification of the general Ideas -of symmetry, developement, and the like; and we shall -hereafter see, according to the phraseology which we shall -explain in the next chapter, how such a diagram might -express the _ideal conception_ of a plant. - -The antithesis of _subjective_ and _objective_ is very -familiar in the philosophical literature of Germany and -France; nor is it uncommon in any age of our own literature. -But though efforts have recently been made to give currency -among us to this phraseology, it has not been cordially -received, and has been much complained of as not of obvious -meaning. Nor is the complaint without ground: for when we -regard the mind as the _subject_ in which ideas inhere, it -becomes for us an _object_, and the antithesis vanishes. We -are not so much accustomed to use _subject_ in this sense, -as to make it a proper contrast to _object_. The combination -'_ideal_ and _objective_,' would more readily convey to a -modern reader the opposition which is intended between the -ideas of the mind itself, and the objects which it -contemplates around it. - -To the antitheses already noticed--Thoughts and Things; -Necessary and Experiential Truths; Deduction and Induction; -Theory and Fact; Ideas and Sensations; Reflexion and -Sensation; Subjective and {38} Objective; we may add others, -by which distinctions depending more or less upon the -fundamental antithesis have been denoted. Thus we speak of -the _internal_ and _external_ sources of our knowledge; of -the world _within_ and the world _without_ us; of _Man_ and -_Nature_. Some of the more recent metaphysical writers of -Germany have divided the universe into the _Me_ and _Not-me_ -(Ich and Nicht-ich). Upon such phraseology we may observe, -that to have the fundamental antithesis of which we speak -really understood, is of the highest consequence to -philosophy, but that little appears to be gained by -expressing it in any novel manner. The most weighty part of -the philosopher's task is to analyze the operations of the -mind; and in this task, it can aid us but little to call it, -instead of the _mind_, the _subject_, or the _me_. - - -_Sect._ 8.--_Matter and Form._ - -THERE are some other ways of expressing, or rather of -illustrating, the fundamental antithesis, which I may -briefly notice. The antithesis has been at different times -presented by means of various images. One of the most -ancient of these, and one which is still very instructive, -is that which speaks of Sensations as the _Matter_, and -Ideas as the _Form_, of our knowledge; just as ivory is the -matter, and a cube the form, of a die. This comparison has -the advantage of showing that two elements of an antithesis -which cannot be separated in fact, may yet be advantageously -separated in our reasonings. For Matter and Form cannot by -any means be detached from each other. All matter must have -some form; all form must be the form of some material thing. -If the ivory be not a cube, it must have a spherical or some -other form. And the cube, in order to be a cube, must be of -some material;--if not of ivory, of wood, or stone, for -instance, A figure without matter is merely a geometrical -conception;--a modification of the idea of space. Matter -without figure is a mere abstract term;--a supposed union of -certain sensible qualities which, so insulated {39} from -others, cannot exist. Yet the distinction of Matter and Form -is real; and, as a subject of contemplation, clear and -plain. Nor is the distinction by any means useless. The -speculations which treat of the two subjects, Matter and -Figure, are very different. Matter is the subject of the -sciences of Mechanics and Chemistry; Figure, of Geometry. -These two classes of Sciences have quite different sets of -principles. If we refuse to consider the Matter and the Form -of bodies separately, because we cannot exhibit Matter and -Form separately, we shut the door to all philosophy on such -subjects. In like manner, though Sensations and Ideas are -necessarily united in all our knowledge, they can be -considered as distinct; and this distinction is the basis of -all philosophy concerning knowledge. - -This illustration of the relation of Ideas and Sensations -may enable us to estimate a doctrine which has been put -forwards at various times. In a certain school of -speculators there has existed a disposition to derive all -our Ideas from our Sensations, the term _Idea_, being, in -this school, used in its wider sense, so as to include all -modifications and limitations of our Fundamental Ideas. The -doctrines of this school have been summarily expressed by -saying that 'Every Idea is a transformed Sensation.' Now, -even supposing this assertion to be exactly true, we easily -see, from what has been said, how little we are likely to -answer the ends of philosophy by putting forward such a -maxim as one of primary importance. For we might say, in -like manner, that every statue is but a transformed block of -marble, or every edifice but a collection of transformed -stones. But what would these assertions avail us, if our -object were to trace the rules of art by which beautiful -statues were formed, or great works of architecture erected? -The question naturally occurs, What is the nature, the -principle, the law of this Transformation? In what faculty -resides the transforming power? What train of ideas of -beauty, and symmetry, and stability, in the mind of the -statuary or the architect, has produced those great works -which {40} mankind look upon as among their most valuable -possessions;--the Apollo of the Belvidere, the Parthenon, -the Cathedral of Cologne? When this is what we want to know, -how are we helped by learning that the Apollo is of Parian -marble, or the Cathedral of basaltic stone? We must know -much more than this, in order to acquire any insight into -the principles of statuary or of architecture. In like -manner, in order that we may make any progress in the -philosophy of knowledge, which is our purpose, we must -endeavour to learn something further respecting ideas than -that they are transformed sensations, even if they were this. - -But, in reality, the assertion that our ideas are -transformed sensations, is erroneous as well as frivolous. -For it conveys, and is intended to convey, the opinion that -our sensations have one form which properly belongs to them; -and that, in order to become ideas, they are converted into -some other form. But the truth is, that our sensations, of -themselves, without some act of the mind, such as involves -what we have termed an Idea, have no form. We cannot see one -object without the idea of space; we cannot see two without -the idea of resemblance or difference; and space and -difference are not sensations. Thus, if we are to employ the -metaphor of Matter and Form, which is implied in the -expression to which I have referred, our sensations, from -their first reception, have their Form not _changed_, but -_given_ by our Ideas. Without the relations of thought which -we here term _Ideas_, the sensations are matter without -form. Matter without form cannot exist: and in like manner -sensations cannot become perceptions of objects, without -some formative power of the mind. By the very act of being -received as perceptions, they have a formative power -exercised upon them, the operation of which might be -expressed, by speaking of them, not as _transformed_, but -simply as _formed_;--as invested with form, instead of being -the mere formless material of perception. The word _inform_, -according to its Latin etymology, at first implied this -process by which matter is {41} invested with form. Thus -Virgil[1\1] speaks of the thunderbolt as _informed_ by the -hands of Brontes, and Steropes, and Pyracmon. And Dryden -introduces the word in another place:-- - Let others better mould the running mass - Of metals, or _inform_ the breathing brass. -Even in this use of the word, the form is something superior -to the brute manner, and gives it a new significance and -purpose. And hence the term is again used to denote the -effect produced by an intelligent principle of a still -higher kind:-- - . . . . He _informed_ - This ill-shaped body with a daring soul. -And finally even the soul itself, in its original condition, -is looked upon as matter, when viewed with reference to -education and knowledge, by which it is afterwards moulded; -and hence these are, in our language, termed _information_. -If we confine ourselves to the first of these three uses of -the term, we may correct the erroneous opinion of which we -have just been speaking, and retain the metaphor by which it -is expressed, by saying, that ideas are not _transformed_, -but _informed_ sensations. - -[Note 1\1: Ferrum exercebant vasto Cyclopes in Antro -Brontesque Steropesque et nudus membra Pyracmon; -His informatum manibus, jam parte polita -Fulmen erat.--_Æn._ viii. 424.] - - -_Sect._ 9.--_Man the Interpreter of Nature._ - -THERE is another image by which writers have represented the -acts of thought through which knowledge is obtained from the -observation of the external world. Nature is the Book, and -Man is the _Interpreter_. The facts of the external world -are marks, in which man discovers a meaning, and so reads -them. Man is the Interpreter of Nature, and Science is the -right Interpretation. And this image also is, in many -respects, {42} instructive. It exhibits to us the necessity -of both elements;--the marks which man has to look at, and -the knowledge of the alphabet and language which he must -possess and apply before he can find any meaning in what he -sees. Moreover this image presents to us, as the ideal -element, an activity of the mind of that very kind which we -wish to point out. Indeed the illustration is rather an -example than a comparison of the composition of our -knowledge. The letters and symbols which are presented to -the Interpreter are really objects of sensation: the notion -of letters as signs of words, the notion of connexions among -words by which they have meaning, really are among our -Ideas;--_Signs_ and _Meaning_ are Ideas, supplied by the -mind, and added to all that sensation can disclose in any -collection of visible marks. The Sciences are not -figuratively, but really, Interpretations of Nature. But -this image, whether taken as example or comparison, may -serve to show both the opposite character of the two -elements of knowledge, and their necessary combination, in -order that there may be knowledge. - -This illustration may also serve to explain another point in -the conditions of human knowledge which we shall have to -notice:--namely, the very different degrees in which, in -different cases, we are conscious of the mental act by which -our sensations are converted into knowledge. For the same -difference occurs in reading an inscription. If the -inscription were entire and plain, in a language with which -we were familiar, we should be unconscious of any mental act -in reading it. We should seem to collect its meaning by the -sight alone. But if we had to decipher an ancient -inscription, of which only imperfect marks remained, with a -few entire letters among them, we should probably make -several suppositions as to the mode of reading it, before we -found any mode which was quite successful; and thus, our -guesses, being separate from the observed facts, and at -first not fully in agreement with them, we should be clearly -aware that the conjectured meaning, on the one hand, and the -observed marks on the other, were distinct things, though -these {43} two things would become united as elements of one -act of knowledge when we had hit upon the right conjecture. - - -_Sect._ 10.--_The Fundamental Antithesis inseparable._ - -THE illustration just referred to, as well as other ways of -considering the subject, may help us to get over a -difficulty which at first sight appears perplexing. We have -spoken of the common opposition of _Theory_ and _Fact_ as -important, and as involving what we have called the -Fundamental Antithesis of Philosophy. But after all, it may -be asked, Is this distinction of Theory and Fact really -tenable? Is it not often difficult to say whether a special -part of our knowledge is a Fact or a Theory? Is it a Fact or -a Theory that the stars revolve round the pole? Is it a Fact -or a Theory that the earth is a globe revolving on its axis? -Is it a Fact or a Theory that the earth travels in an -ellipse round the sun? Is it a Fact or a Theory that the sun -attracts the earth? Is it a Fact or a Theory that the -loadstone attracts the needle? In all these cases, probably -some persons would answer one way, and some persons the -other. There are many persons by whom the doctrine of the -globular form of the earth, the doctrine of the earth's -elliptical orbit, the doctrine of the sun's attraction on -the earth, would be called _theories_, even if they allowed -them to be true theories. But yet if each of these -propositions be true, is it not a _fact_? And even with -regard to the simpler facts, as the motion of the stars -round the pole, although this may be a Fact to one who has -watched and measured the motions of the stars, one who has -not done this, and who has only carelessly looked at these -stars from time to time, may naturally speak of the circles -which the astronomer makes them describe as Theories. It -would seem, then, that we cannot in such cases expect -general assent, if we say, _This is a Fact and not a -Theory_, or _This is a Theory and not a Fact_. And the same -is true in a vast range of cases. It would seem, therefore, -that we cannot rest any reasoning upon this distinction of -Theory {44} and Fact; and we cannot avoid asking whether -there is any real distinction in this antithesis, and if so, -what it is. - -To this I reply: the distinction between Theory (that is, -true Theory) and Fact, is this: that in Theory the Ideas are -considered as distinct from the Facts: in Facts, though -Ideas may be involved, they are not, in our apprehension, -separated from the sensations. In a Fact, the Ideas are -applied so readily and familiarly, and incorporated with the -sensations so entirely, that we do not see _them_, we see -_through them_. A person who carefully notes the motion of a -star all night, sees the circle which it describes, as he -sees the star, though the circle is, really, a result of his -own Ideas. A person who has in his mind the measures of -different lines and countries on the earth's surface, and -who can put them, together into one conception, finds that -they can make no figure but a globular one: to him, the -earth's globular form is a Fact, as much as the square form -of his chamber. 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 country, looks upon the former event as a Fact, just as -he looks upon the latter events as Facts. And a person who, -knowing the Fact of the earth's annual motion, refers it -distinctly to its mechanical cause, conceives the sun's -attraction as a Fact, just as he conceives as a Fact, the -action of the wind which turns the sails of a mill. He -cannot _see_ the force in either case; he supplies it out of -his own Ideas. And thus, a true Theory is a Fact; a Fact is -a familiar Theory. That which is a Fact under one aspect, is -a Theory under another. The most recondite Theories when -firmly established are Facts: the simplest Facts involve -something of the nature of Theory. Theory and Fact -correspond, in a certain degree, with Ideas and Sensations, -as to the nature of their opposition. But the Facts are -Facts, so far as the Ideas have been combined with the -Sensations and absorbed in them: the Theories are Theories, -so far as the Ideas are kept distinct from the Sensations, -and so far as it is {45} considered still a question whether -those can be made to agree with these. - -We may, as I have said, illustrate this matter by -considering man as _interpreting_ the phenomena which he -sees. He often interprets without being aware that he does -so. Thus when we see the needle move towards the magnet, we -assert that the magnet exercises an attractive force on the -needle. But it is only by an interpretative act of our own -minds that we ascribe this motion to attraction. That, in -this case, a force is exerted--something of the nature of -the pull which we could apply by our own volition--is our -interpretation of the phenomena; although we may be -conscious of the act of interpretation, and may then regard -the attraction as a Fact. - -Nor is it in such cases only that we interpret phenomena in -our own way, without being conscious of what we do. We see a -tree at a distance, and judge it to be a chestnut or a lime; -yet this is only an inference from the colour or form of the -mass according to preconceived classifications of our own. -Our lives are full of such unconscious interpretations. The -farmer recognizes a good or a bad soil; the artist a picture -of a favourite master; the geologist a rock of a known -locality, as we recognize the faces and voices of our -friends; that is, by judgments formed on what we see and -hear; but judgments in which we do not analyze the steps, or -distinguish the inference from the appearance. And in these -mixtures of observation and inference, we speak of the -judgment thus formed, as a Fact directly observed. - -Even in the case in which our perceptions appear to be most -direct, and least to involve any interpretations of our -own,--in the simple process of seeing,--who does not know -how much we, by an act of the mind, add to that which our -senses receive? Does any one fancy that he sees a solid -cube? It is easy to show that the solidity of the figure, -the relative position of its faces and edges to each other, -are inferences of the spectator; no more conveyed to his -conviction by the eye alone, than they would be if he were -looking at {46} a painted representation of a cube. The -scene of nature is a picture without depth of substance, no -less than the scene of art; and in the one case as in the -other, it is the mind which, by an act of its own, discovers -that colour and shape denote distance and solidity. Most men -are unconscious of this perpetual habit of reading the -language of the external world, and translating as they -read. The draughtsman, indeed, is compelled, for his -purposes, to return back in thought from the solid bodies -which he has inferred, to the shapes of surface which he -really sees. He knows that there is a mask of theory over -the whole face of nature, if it be _theory_ to infer more -than we _see_. But other men, unaware of this masquerade, -hold it to be a fact that they see cubes and spheres, -spacious apartments and winding avenues. And these things -are facts to them, because they are unconscious of the -mental operation by which they have penetrated nature's -disguise. - -And thus, we still have an intelligible distinction of Fact -and Theory, if we consider Theory as a conscious, and Fact -as an unconscious inference, from the phenomena which are -presented to our senses. - -But still, Theory and Fact, Inference and Perception, -Reasoning and Observation, are antitheses in none of which -can we separate the two members by any fixed and definite line. - -Even the simplest terms by which the antithesis is expressed -cannot be separated. Ideas and Sensations, Thoughts and -Things, Subject and Object, cannot in any case be applied -absolutely and exclusively. Our Sensations require Ideas to -bind them together, namely, Ideas of space, time, number, -and the like. If not so bound together, Sensations do not -give us any apprehension of Things or Objects. All Things, -all Objects, must exist in space and in time--must be one or -many. Now space, time, number, are not Sensations or Things. -They are something different from, and opposed to Sensations -and Things. We have termed them Ideas. It may be said they -are _Relations_ of Things, or of Sensations. But granting -this form of expression, still a _Relation_ is not a Thing -or a {47} Sensation; and therefore we must still have -another and opposite element, along with our Sensations. And -yet, though we have thus these two elements in every act of -perception, we cannot designate any portion of the act as -absolutely and exclusively belonging to one of the elements. -Perception involves Sensation, along with Ideas of time, -space, and the like; or, if any one prefers the expression, -we may say, Perception involves Sensations along with the -apprehension of Relations. Perception is Sensation, along -with such Ideas as make Sensation into an apprehension of -Things or Objects. - -And as Perception of Objects implies Ideas,--as Observation -implies Reasoning;--so, on the other hand, Ideas cannot -exist where Sensation has not been; Reasoning cannot go on -when there has not been previous Observation. This is -evident from the necessary order of developement of the -human faculties. Sensation necessarily exists from the first -moments of our existence, and is constantly at work. -Observation begins before we can suppose the existence of -any Reasoning which is not involved in Observation. Hence, -at whatever period we consider our Ideas, we must consider -them as having been already engaged in connecting our -Sensations, and as having been modified by this employment. -By being so employed, our Ideas are unfolded and defined; -and such developement and definition cannot be separated -from the Ideas themselves. We cannot conceive space, without -boundaries or forms; now Forms involve Sensations. We cannot -conceive time, without events which mark the course of time; -but events involve Sensations. We cannot conceive number, -without conceiving things which are numbered; and Things -imply sensations. And the forms, things, events, which are -thus implied in our Ideas, having been the objects of -Sensation constantly in every part of our life, have -modified, unfolded, and fixed our Ideas, to an extent which -we cannot estimate, but which we must suppose to be -essential to the processes which at present go on in our -minds. We cannot say that Objects create Ideas; for to -perceive Objects we must already have Ideas. But we may {48} -say, that Objects and the constant Perception of Objects -have so far modified our Ideas, that we cannot, even in -thought, separate our Ideas from the perception of Objects. - -We cannot say of any Ideas, as of the Idea of space, or -time, or number, that they are absolutely and exclusively -Ideas. We cannot conceive what space, or time, or number, -would be in our minds, if we had never perceived any Thing -or Things in space or time. We cannot conceive ourselves in -such a condition as never to have perceived any Thing or -Things in space or time. But, on the other hand, just as -little can we conceive ourselves becoming acquainted with -space and time or numbers as objects of Sensation. We cannot -reason without having the operations of our minds affected -by previous Sensations; but we cannot conceive Reasoning to -be merely a series of Sensations. In order to be used in -Reasoning, Sensation must become Observation; and, as we -have seen, Observation already involves Reasoning. In order -to be connected by our Ideas, Sensations must be Things or -Objects, and Things or Objects already include Ideas. And -thus, none of the terms by which the fundamental antithesis -is expressed can be absolutely and exclusively applied. - -I will make a remark suggested by the views which have thus -been presented. Since, as we have just seen, none of the -terms which express the fundamental antithesis can be -applied absolutely and exclusively, the absolute application -of the antithesis in any particular case can never be a -conclusive or immoveable principle. This remark is the more -necessary to be borne in mind, as the terms of this -antithesis are often used in a vehement and peremptory -manner. Thus we are often told that such a thing is _a -Fact_; A FACT and not a Theory, with all the emphasis which, -in speaking or writing, tone or italics or capitals can -give. We see from what has been said, that when this is -urged, before we can estimate the truth, or the value of the -assertion, we must ask to whom is it a Fact? what habits of -thought, what previous information, what Ideas does it -imply, to conceive the Fact as a Fact? {49} Does not the -apprehension of the Fact imply assumptions which may with -equal justice be called Theory, and which are perhaps false -Theory? in which case, the Fact is no Fact. Did not the -ancients assert it as a Fact, that the earth stood still, -and the stars moved? and can any Fact have stronger apparent -evidence to justify persons in asserting it emphatically -than this had? - -These remarks are by no means urged in order to show that no -Fact can be certainly known to be true; but only, to show -that no Fact can be certainly shown to be a Fact, merely by -calling it a Fact, however emphatically. There is by no -means any ground of general skepticism with regard to truth, -involved in the doctrine of the necessary combination of two -elements in all our knowledge. On the contrary, Ideas are -requisite to the essence, and Things to the reality of our -knowledge in every case. The proportions of Geometry and -Arithmetic are examples of knowledge respecting our Ideas of -space and number, with regard to which there is no room for -doubt. The doctrines of Astronomy are examples of truths not -less certain respecting the Facts of the external world. - - -_Sect._ 11.--_Successive Generalization._ - -IN the preceding pages we have been led to the doctrine, -that though, in the Antithesis of Theory and Fact, there is -involved an essential opposition; namely the opposition of -the thoughts within us and the phenomena without us; yet -that we cannot distinguish and define the members of this -antithesis separately. Theories become Facts, by becoming -certain and familiar: and thus, as our knowledge becomes -more sure and more extensive, we are constantly transferring -to the class of facts, opinions which were at first regarded -as theories. - -Now we have further to remark, that in the progress of human -knowledge respecting any branch of speculation, there may be -several such steps in succession, each depending upon and -including the preceding. {50} The theoretical views which -one generation of discoverers establishes, become the facts -from which the next generation advances to new theories. As -men rise from the particular to the general, so, in the same -manner, they rise from what is general to what is more -general. Each induction supplies the materials of fresh -inductions; each generalization, with all that it embraces -in its circle, may be found to be but one of many circles, -comprehended within the circuit of some wider -generalization. - -This remark has already been made, and illustrated, in the -_History of the Inductive Sciences_[2\1]; and, in truth, the -whole of the history of science is full of suggestions and -exemplifications of this course of things. It may be -convenient, however, to select a few instances which may -further explain and confirm this view of the progress of -scientific knowledge. - -[Note 2\1: _Hist. Inductive Sciences_, b. vii. c. ii. sect. 5.] - -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 times, and which exhibits -by far the richest collection of successive discoveries: I -mean Astronomy. It is easy to see that each of these -successive discoveries depended on those antecedently made, -and that in each, 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 next. Thus we find, in the -days of Greek discovery, Hipparchus and Ptolemy combining -and explaining the particular _facts_ of the motion of the -sun, moon, and planets, by means of the _theory_ of -epicycles and eccentrics;--a highly important step, which -gave an intelligible connexion and rule to the motions of -each of these luminaries. When these cycles and epicycles, -thus truly representing the apparent motions of the heavenly -bodies, had accumulated to an inconvenient amount, by the -discovery of many inequalities in the observed motions, -Copernicus showed that their effects might all be more -simply included, by making the sun the center of motion of -the planets, instead of {51} the earth. But in this new -view, he still retained the epicycles and eccentrics which -governed the motion of each body. Tycho Brahe's -observations, and Kepler's calculations, showed that, -besides the vast number of facts which the epicyclical -theory could account for, there were some which it would not -exactly include, and Kepler was led to the persuasion that -the planets move in ellipses. But this view of motion was at -first conceived by Kepler as a modification of the -conception of epicycles. On one occasion he blames himself -for not sooner seeing that such a modification was possible. -'What an absurdity on my part!' he cries[3\1]; 'as if -libration in the diameter of the epicycle might not come to -the same thing as motion in the ellipse.' But again; -Kepler's _laws_ of the elliptical motion of the planets were -established; and these laws immediately became the _facts_ -on which the mathematicians had to found their mechanical -theories. From these facts, Newton, as we have related, -proved that the central force of the sun retains the planets -in their orbits, according to the law of the inverse square -of the distance. The same _law_ was shown to prevail in the -gravitation of the earth. It was shown, too, by induction -from the motions of Jupiter and Saturn, that the planets -attract each other; by calculations from the figure of the -earth, that the parts of the earth attract each other; and, -by considering the course of the tides, that the sun and -moon attract the waters of the ocean. And all these curious -discoveries being established as _facts_, the subject was -ready for another step of generalization. By an unparalleled -rapidity in the progress of discovery in this case, not only -were all the inductions which we have first mentioned made -by one individual, but the new advance, the higher flight, -the closing victory, fell to the lot of the same -extraordinary person. - -[Note 3\1: _Hist. Inductive Sciences_, b. v. c. iv. sect. 3.] - -The attraction of the sun upon the planets, of the moon upon -the earth, of the planets on each other, of the parts of the -earth on themselves, of the sun and {52} moon upon the -ocean;--all these truths, each of itself a great discovery, -were included by Newton in the higher _generalization_, of -the universal gravitation of matter, by which each particle -is drawn to every other according to the law of the inverse -square: and thus this long advance from discovery to -discovery, from truths to truths, each justly admired when -new, and then rightly used as old, was closed in a worthy -and consistent manner, by a truth which is the most worthy -admiration, because it includes all the researches of -preceding ages of Astronomy. - -We may take another example of a succession of this kind -from the history of a science, which, though it has made -wonderful advances, has not yet reached its goal, as -physical astronomy appears to have done, but seems to have -before it a long prospect of future progress. I now refer to -Chemistry, in which I shall try to point out how the -preceding discoveries afforded the materials of the -succeeding; although this subordination and connexion is, in -this case, less familiar to men's minds than in Astronomy, -and is, perhaps, more difficult to present in a clear and -definite shape. Sylvius saw, in the facts which occur, when -an acid and an alkali are brought together, the evidence -that they neutralize each other. But cases of -neutralization, and acidification, and many other effects of -mixture of the ingredients of bodies, being thus viewed as -_facts_, had an aspect of unity and law given them by -Geoffroy and Bergman[4\1], who introduced the _conception_ -of the Chemical Affinity or Elective Attraction, by which -certain elements select other elements, as if by preference. -That combustion, whether a chemical union or a chemical -separation of ingredients, is of the same nature with -acidification, was the doctrine of Beccher and Stahl, and -was soon established as a truth which must form a part of -every succeeding physical theory. That the rules of affinity -and chemical composition may include gaseous elements, was -established by Black and Cavendish. And all these truths, -thus brought to light by {53} chemical -discoverers,--affinity, the identity of acidification and -combustion, the importance of gaseous elements,--along with -all the facts respecting the weight of ingredients and -compounds which the balance disclosed,--were taken up, -connected, and included as _particulars_ in the oxygen -_theory_ of Lavoisier. Again, the results of this theory, -and the quantity of the several ingredients which entered -into each compound--(such results, for the most part, being -now no longer mere theoretical speculations, but recognized -facts)--were the _particulars_ from which Dalton derived -that wide law of chemical combination which we term the -Atomic _Theory_. And this law, soon generally accepted among -chemists, is already in its turn become one of the _facts_ -included in Faraday's _Theory_ of the identity of Chemical -Affinity and Electric Attraction. - -[Note 4\1: _Hist. Inductive Sciences_, b. xiv. c. iii.] - -It is unnecessary to give further exemplifications of this -constant ascent from one step to a higher; this perpetual -conversion of true theories into the materials of other and -wider theories. It will hereafter be our business to -exhibit, in a more full and formal manner, the mode in which -this principle determines the whole scheme and structure of -all the most exact sciences. And thus, beginning with the -facts of sense, we gradually climb to the highest forms of -human knowledge, and obtain from experience and observation -a vast collection of the most wide and elevated truths. - -There are, however, truths of a very different kind, to -which we must turn our attention, in order to pursue our -researches respecting the nature and grounds of our -knowledge. But before we do this, we must notice one more -feature in that progress of science which we have already in -part described. - - - -{{54}} -CHAPTER II. - -OF TECHNICAL TERMS. - - -1. IT has already been stated that we gather knowledge from -the external world, when we are able to apply, to the facts -which we observe, some ideal conception, which gives unity -and connexion to multiplied and separate perceptions. We -have also shown that our conceptions, thus verified by -facts, may themselves be united and connected by a new bond -of the same nature; and that man may thus have to pursue his -way from truth to truth through a long progression of -discoveries, each resting on the preceding, and rising above it. - -Each of these steps, in succession, is recorded, fixed, and -made available, by some peculiar form of words; and such -words, thus rendered precise in their meaning, and -appropriated to the service of science, we may call -_Technical Terms_. It is in a great measure by inventing -such Terms that men not only best express the discoveries -they have made, but also enable their followers to become so -familiar with these discoveries, and to possess them so -thoroughly, that they can readily use them in advancing to -ulterior generalizations. - -Most of our ideal conceptions are described by exact and -constant words or phrases, such as those of which we here -speak. We have already had occasion to employ many of these. -Thus we have had instances of technical Terms expressing -geometrical conceptions, as _Ellipsis_, _Radius Vector_, -_Axis_, _Plane_, the Proportion of the _Inverse Square_, and -the like. Other Terms have described mechanical conceptions, -as _Accelerating Force_ and _Attraction_. Again, chemistry -exhibits (as do all sciences) a series of Terms which mark -the steps of our {55} progress. The views of the first real -founders of the science are recorded by the Terms which are -still in use, _Neutral Salts_, _Affinity_, and the like. The -establishment of Dalton's theory has produced the use of the -word _Atom_ in a peculiar sense, or of some other word, as -_Proportion_, in a sense equally technical. And Mr. Faraday -has found it necessary, in order to expound his -electro-chemical theory, to introduce such terms as _Anode_ -and _Cathode_, _Anïon_ and _Cathïon_. - -2. I need not adduce any further examples, for my object at -present is only to point out the use and influence of such -language: its rules and principles I shall hereafter try, in -some measure, to fix. But what we have here to remark is, -the extraordinary degree in which the progress of science is -facilitated, by thus investing each new discovery with a -compendious and steady form of expression. These terms soon -become part of the current language of all who take an -interest in speculation. However strange they may sound at -first, they soon grow familiar in our ears, and are used -without any effort, or any recollection of the difficulty -they once involved. They become as common as the phrases -which express our most frequent feelings and interests, -while yet they have incomparably more precision than belongs -to any terms which express feelings; and they carry with -them, in their import, the results of deep and laborious -trains of research. They convey the mental treasures of one -period to the generations that follow; and laden with this, -their precious freight, they sail safely across gulfs of -time in which empires have suffered shipwreck, and the -languages of common life have sunk into oblivion. We have -still in constant circulation among us the Terms which -belong to the geometry, the astronomy, the zoology, the -medicine of the Greeks, and the algebra and chemistry of the -Arabians. And we can in an instant, by means of a few words, -call to our own recollection, or convey to the apprehension -of another person, phenomena and relations of phenomena in -optics, mineralogy, chemistry, which are so complex and -abstruse, that it might seem to require the utmost subtlety -of the human mind to {56} grasp them, even if that were made -the sole object of its efforts. By this remarkable effect of -Technical Language, we have the results of all the labours -of past times not only always accessible, but so prepared -that we may (provided we are careful in the use of our -instrument) employ what is really useful and efficacious for -the purpose of further success, without being in any way -impeded or perplexed by the length and weight of the chain -of past connexions which we drag along with us. - -By such means,--by the use of the Inductive Process, and by -the aid of Technical Terms,--man has been constantly -advancing in the path of scientific truth. In a succeeding -part of this work we shall endeavour to trace the general -rules of this advance, and to lay down the maxims by which -it may be most successfully guided and forwarded. But in -order that we may do this to the best advantage, we must -pursue still further the analysis of knowledge into its -elements; and this will be our employment in the first part -of the work. - - - -{{57}} -CHAPTER III. - -OF NECESSARY TRUTHS. - - -1. EVERY advance in human knowledge consists, as we have -seen, in adapting new ideal conceptions to ascertained -facts, and thus in superinducing the Form upon the Matter, -the active upon the passive processes of our minds. Every -such step introduces into our knowledge an additional -portion of the ideal element, and of those relations which -flow from the nature of Ideas. It is, therefore, important -for our purpose to examine more closely this element, and to -learn what the relations are which may thus come to form -part of our knowledge. An inquiry into those Ideas which -form the foundations of our sciences;--into the reality, -independence, extent, and principal heads of the knowledge -which we thus acquire; is a task on which we must now enter, -and which will employ us for several of the succeeding Books. - -In this inquiry our object will be to pass in review all the -most important Fundamental Ideas which our sciences involve; -and to prove more distinctly in reference to each, what we -have already asserted with regard to all, that there are -everywhere involved in our knowledge acts of the mind as -well as impressions of sense; and that our knowledge -derives, from these acts, a generality, certainty, and -evidence which the senses could in no degree have supplied. -But before I proceed to do this in particular cases, I will -give some account of the argument in its general form. - -We have already considered the separation of our knowledge -into its two elements,--Impressions of Sense and Ideas,--as -evidently indicated by this; that all knowledge possesses -characters which neither of these {58} elements alone could -bestow. Without our ideas, our sensations could have no -connexion; without external impressions, our ideas would -have no reality; and thus both ingredients of our knowledge -must exist. - -2. There is another mode in which the distinction of the two -elements of knowledge appears, as I have already said (c. i. -sect. 2): namely in the distinction of _necessary_, and -_contingent_ or _experiential_, truths. For of these two -classes of truths, the difference arises from this;--that -the one class derives its nature from the one, and the other -from the other, of the two elements of knowledge. I have -already stated briefly the difference of these two kinds of -truths:--namely, that the former are truths which, we see, -must be true:--the latter are true, but so far as we can -see, might be otherwise. The former are true necessarily and -universally: the latter are learnt from experience and -limited by experience. Now with regard to the former kind of -truths, I wish to show that the universality and necessity -which distinguish them can by no means be derived from -experience; that these characters do in reality flow from -the ideas which these truths involve; and that when the -necessity of the truth is exhibited in the way of logical -demonstration, it is found to depend upon certain -fundamental principles, (Definitions and Axioms,) which may -thus be considered as expressing, in some measure, the -essential characters of our ideas. These fundamental -principles I shall afterwards proceed to discuss and to -exhibit in each of the principal departments of science. - -I shall begin by considering Necessary Truths more fully -than I have yet done. As I have already said, necessary -truths are those in which we not only learn, that the -proposition _is_ true, but see that it _must be_ true; in -which the negation of the truth is not only false, but -impossible; in which we cannot, even by an effort of -imagination, or in a supposition, conceive the reverse of -that which is asserted. - -3. That there are such truths cannot be doubted. We may -take, for example, all relations of number. Three and Two -added together make Five. We cannot {59} conceive it to be -otherwise. We cannot, by any freak of thought, imagine Three -and Two to make Seven. - -It may be said that this assertion merely expresses what we -mean by our words; that it is a matter of definition; that -the proposition is an identical one. - -But this is by no means so. The definition of Five is not -Three and Two, but Four and One. How does it appear that -Three and Two is the same number as Four and One? It is -evident that it is so; but _why_ is it evident?--not because -the proposition is identical; for if that were the reason, -all numerical propositions must be evident for the same -reason. If it be a matter of definition that 3 and 2 make 5, -it must be a matter of definition that 39 and 27 make 66. -But who will say that the definition of 66 is 39 and 27? Yet -the magnitude of the numbers can make no difference in the -ground of the truth. How do we know that the product of 13 -and 17 is 4 less than the product of 15 and 15? We see that -it is so, if we perform certain operations by the rules of -arithmetic; but how do we know the truth of the rules of -arithmetic? If we divide 123375 by 987 according to the -process taught us at school, how are we assured that the -result is correct, and that the number 125 thus obtained is -really the number of times one number is contained in the -other? - -The correctness of the rule, it may be replied, can be -rigorously demonstrated. It can be shown that the process -must inevitably give the true quotient. - -Certainly this can be shown to be the case. And precisely -because it _can_ be shown that the result must be true, we -have here an example of a necessary truth; and this truth, -it appears, is not _therefore_ necessary because it is -itself evidently identical, however it may be possible to -prove it by reducing it to evidently identical propositions. -And the same is the case with all other numerical -propositions; for, as we have said, the nature of all of -them is the same. - -Here, then, we have instances of truths which are not only -true, but demonstrably and necessarily true. Now such truths -are, in this respect at least, altogether {60} different -from truths, which, however certain they may be, are learnt -to be so only by the evidence of observation, interpreted, -as observation must be interpreted, by our own mental -faculties. There is no difficulty in finding examples of -these merely observed truths. We find that sugar dissolves -in water, and forms a transparent fluid, but no one will say -that we can see any reason beforehand why the result _must_ -be so. We find that all animals which chew the cud have also -the divided hoof; but could any one have predicted that this -would be universally the case? or supposing the truth of the -rule to be known, can any one say that he cannot conceive -the facts as occurring otherwise? Water expands when it -crystallizes, some other substances contract in the same -circumstances; but can any one know that this will be so -otherwise than by observation? We have here propositions -_rigorously_ true, (we will assume,) but can any one say -they are _necessarily_ true? These, and the great mass of -the doctrines established by induction, are actual, but so -far as we can see, accidental laws; results determined by -some unknown selection, not demonstrable consequences of the -essence of things, inevitable and perceived to be -inevitable. According to the phraseology which has been -frequently used by philosophical writers, they are -_contingent_, not necessary truths. - -It is requisite to insist upon this opposition, because no -insight can be obtained into the true nature of knowledge, -and the mode of arriving at it, by any one who does not -clearly appreciate the distinction. The separation of truths -which are learnt by observation, and truths which can be -seen to be true by a pure act of thought, is one of the -first and most essential steps in our examination of the -nature of truth, and the mode of its discovery. If any one -does not clearly comprehend this distinction of necessary -and contingent truths, he will not be able to go along with -us in our researches into the foundations of human -knowledge; nor, indeed, to pursue with success any -speculation on the subject. But, in fact, this distinction -is one that can hardly fail to be at once understood. It -{61} is insisted upon by almost all the best modern, as well -as ancient, metaphysicians[5\1], as of primary importance. -And if any person does not fully apprehend, at first, the -different kinds of truth thus pointed out, let him study, to -some extent, those sciences which have necessary truth for -their subject, as geometry, or the properties of numbers, so -as to obtain a familiar acquaintance with such truth; and he -will then hardly fail to see how different the evidence of -the propositions which occur in these sciences, is from the -evidence of the facts which are merely learnt from -experience. That the year goes through its course in 365 -days, can only be known by observation of the sun or stars: -that 365 days is 52 weeks and a day, it requires no -experience, but only a little thought to perceive. That bees -build their cells in the form of hexagons, we cannot know -without looking at them; that regular hexagons may be -arranged so as to fill space, may be proved with the utmost -rigour, even if there were not in existence such a thing as -a material hexagon. - -[Note 5\1: Aristotle, Dr Whately, Dugald Stewart, &c.] - -4. As I have already said, one mode in which we may express -the difference of necessary truths and truths of experience, -is, that necessary truths are those of which we cannot -distinctly conceive the contrary. We can very readily -conceive the contrary of experiential truths. We can -conceive the stars moving about the pole or across the sky -in any kind of curves with any velocities; we can conceive -the moon always appearing during the whole month as a -luminous disk, as she might do if her light were inherent -and not borrowed. But we cannot conceive one of the -parallelograms on the same base and between the same -parallels larger than the other; for we find that, if we -attempt to do this, when we separate the parallelograms into -parts, we have to conceive one triangle larger than another, -both having all their parts equal; which we cannot conceive -at all, if we conceive the triangles distinctly. We make -this impossibility more clear by conceiving {62} the -triangles to be placed so that two sides of the one coincide -with two sides of the other; and it is then seen, that in -order to conceive the triangles unequal, we must conceive -the two bases which have the same extremities both ways, to -be different lines, though both straight lines. This it is -impossible to conceive: we assent to the impossibility as an -axiom, when it is expressed by saying, that two straight -lines cannot inclose a space; and thus we cannot distinctly -conceive the contrary of the proposition just mentioned -respecting parallelograms. - -But it is necessary, in applying this distinction, to bear -in mind the terms of it;--that we cannot _distinctly_ -conceive the contrary of a necessary truth. For in a certain -loose, indistinct way, persons conceive the contrary of -necessary geometrical truths, when they erroneously conceive -false propositions to be true. Thus, Hobbes erroneously held -that he had discovered a means of geometrically 'doubling -the cube,' as it is called, that is, finding two mean -proportionals between two given lines; a problem which -cannot be solved by plane geometry. Hobbes not only proposed -a construction for this purpose, but obstinately maintained -that it was right, when it had been proved to be wrong. But -then, the discussion showed how indistinct the geometrical -conceptions of Hobbes were; 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 supposed, but in -another point near to it; he maintained, in reply, that one -of these points was large enough to include the other, so -that they might be considered as the same point. Such a mode -of conceiving the opposite of a geometrical truth, forms no -exception to the assertion, that this opposite cannot be -distinctly conceived. - -In like manner, the indistinct conceptions of children and -of rude savages do not invalidate the distinction of -necessary and experiential truths. Children and savages make -mistakes even with regard to numbers; and might easily -happen to assert that 27 and 38 are equal to 63 or 64. But -such mistakes cannot {63} make arithmetical truths cease to -be necessary truths. When any person conceives these numbers -and their addition distinctly, by resolving them into parts, -or in any other way, he sees that their sum is necessarily -65. If, on the ground of the possibility of children and -savages conceiving something different, it be held that this -is not a necessary truth, it must be held on the same -ground, that it is not a necessary truth that 7 and 4 are -equal to 11; for children and savages might be found so -unfamiliar with numbers as not to reject the assertion that -7 and 4 are 10, or even that 4 and 3 are 6, or 8. But I -suppose that no persons would on such grounds hold that -these arithmetical truths are truths known only by -experience. - -5. I have taken examples of necessary truths from the -properties of number and space; but such truths exist no -less in other subjects, although the discipline of thought -which is requisite to perceive them distinctly, may not be -so usual among men with regard to the sciences of mechanics -and hydrostatics, as it is with regard to the sciences of -geometry and arithmetic. Yet every one may perceive that -there are such truths in mechanics. If I press the table -with my hand, the table presses my hand with an equal force: -here is a self-evident and necessary truth. In any machine, -constructed in whatever manner to increase the force which I -can exert, it is certain that what I gain in force I must -lose in the velocity which I communicate. This is not a -contingent truth, borrowed from and limited by observation; -for a man of sound mechanical views applies it with like -confidence, however novel be the construction of the -machine. When I come to speak of the ideas which are -involved in our mechanical knowledge, I may, perhaps, be -able to bring more clearly into view the necessary truth of -general propositions on such subjects. That reaction is -equal and opposite to action, is as necessarily true as that -two straight lines cannot inclose a space; it is as -impossible theoretically to make a perpetual motion by mere -mechanism as to make the diagonal of a square commensurable -with the side. {64} - -6. Necessary truths must be _universal_ truths. If any -property belong to a right-angled triangle _necessarily_, it -must belong to _all_ right-angled triangles. And it shall be -proved in the following Chapter, that truths possessing -these two characters, of Necessity and Universality, cannot -possibly be the mere results of experience. - -[Necessary truths are not considered as a portion of the -_Inductive_ Sciences. They are Deductions from our Ideas. -Thus the necessary truths which constitute the Science of -Geometry are Deductions from our Idea of Space: the -necessary truths which constitute the Science of Arithmetic -are Deductions from our notions of Number; which perhaps -involves necessarily the Idea of Time. But though we do not -call those Sciences _Inductive_ which involve properties of -Space, Number and Time alone, the properties of Space, Time -and Number enter in many very important ways into the -Inductive Sciences; and therefore the Ideas of Space, Time -and Number require to be considered in the first place. And -moreover the examination of these Ideas is an essential step -towards the examination of other Ideas: and the conditions -of the possibility and certainty of truth, which are -exemplified in Geometry and Arithmetic, open to us important -views respecting the conditions of the possibility and -certainty of all Scientific Truth. We shall therefore in the -next Book examine the Ideas on which the Pure Sciences, -Geometry and Arithmetic, are founded. But we must first say -a little more of Ideas in general.] - - - -{{65}} -CHAPTER IV. - -OF EXPERIENCE. - - -1. I HERE employ the term Experience in a more definite and -limited sense than that which it possesses in common usage; -for I restrict it to matters belonging to the domain of -science. In such cases, the knowledge which we acquire, by -means of experience, is of a clear and precise nature; and -the passions and feelings and interests, which make the -lessons of experience in practical matters so difficult to -read aright, no longer disturb and confuse us. We may, -therefore, hope, by attending to such cases, to learn what -efficacy experience really has, in the discovery of truth. - -That from _experience_ (including intentional experience, or -_observation_,) we obtain much knowledge which is highly -important, and which could not be procured from any other -source, is abundantly clear. We have already taken several -examples of such knowledge. We know by experience that -animals which ruminate are cloven-hoofed; and we know this -in no other manner. We know, in like manner, that all the -planets and their satellites revolve round the sun from west -to east. It has been found by experience that all meteoric -stones contain chrome. Many similar portions of our -knowledge might be mentioned. - -Now what we have here to remark is this;--that in no case -can experience prove a proposition to be _necessarily_ or -_universally_ true. However many instances we may have -observed of the truth of a proposition, yet if it be known -merely by observation, there is nothing to assure us that -the next case shall not be an exception to the rule. If it -be strictly true that every ruminant animal yet known has -cloven hoofs, we {66} still cannot be sure that some -creature will not hereafter be discovered which has the -first of these attributes without having the other. When the -planets and their satellites, as far as Saturn, had been all -found to move round the sun in one direction, it was still -possible that there might be other such bodies not obeying -this rule; and, accordingly, when the satellites of Uranus -were detected, they appeared to offer an exception of this -kind. Even in the mathematical sciences, we have examples of -such rules suggested by experience, and also of their -precariousness. However far they may have been tested, we -cannot depend upon their correctness, except we see some -reason for the rule. For instance, various rules have been -given, for the purpose of pointing out _prime numbers_; that -is, those which cannot be divided by any other number. We -may try, as an example of such a rule, this one--any odd -power of the number two, diminished by one. Thus the third -power of two, diminished by one, is seven; the fifth power, -diminished by one, is thirty-one; the seventh power so -diminished is one hundred and twenty-seven. All these are -prime numbers: and we might be led to suppose that the rule -is universal. But the next example shows us the -fallaciousness of such a belief. The ninth power of two, -diminished by one, is five hundred and eleven, which is not -a prime, being divisible by seven. - -Experience must always consist of a limited number of -observations. And, however numerous these may be, they can -show nothing with regard to the infinite number of cases in -which the experiment has not been made. Experience being -thus unable to prove a fact to be universal, is, as will -readily be seen, still more incapable of proving a truth to -be necessary. Experience cannot, indeed, offer the smallest -ground for the necessity of a proposition. She can observe -and record what has happened; but she cannot find, in any -case, or in any accumulation of cases, any reason for what -must happen. She may see objects side by side; but she -cannot see a reason why they must ever be side by side. She -finds certain events to occur in succession; but the -succession supplies, in its occurrence, no {67} reason for -its recurrence. She contemplates external objects; but she -cannot detect any internal bond, which indissolubly connects -the future with the past, the possible with the real. To -learn a proposition by experience, and to see it to be -necessarily true, are two altogether different processes of -thought. - -2. But it may be said, that we do learn by means of -observation and experience many universal truths; indeed, -all the general truths of which science consists. Is not the -doctrine of universal gravitation learnt by experience? Are -not the laws of motion, the properties of light, the general -principles of chemistry, so learnt? How, with these examples -before us, can we say that experience teaches no universal -truths? - -To this we reply, that these truths can only be known to be -general, not universal, if they depend upon experience -alone. Experience cannot bestow that universality which she -herself cannot have, and that necessity of which she has no -comprehension. If these doctrines _are_ universally true, -this universality flows from the _ideas_ which we apply to -our experience, and which are, as we have seen, the real -sources of necessary truth. How far these ideas can -communicate their universality and necessity to the results -of experience, it will hereafter be our business to -consider. It will then appear, that when the mind collects -from observation truths of a wide and comprehensive kind, -which approach to the simplicity and universality of the -truths of pure science; she gives them this character by -throwing upon them the light of her own Fundamental Ideas. - -But the truths which we discover by observation of the -external world, even when most strikingly simple and -universal, are not necessary truths. Is the doctrine of -universal gravitation necessarily true? It was doubted by -Clairaut (so far as it refers to the moon), when the -progression of the apogee in fact appeared to be twice as -great as the theory admitted. It has been doubted, even more -recently, with respect to the planets, their mutual -perturbations appearing to indicate a deviation from the -law. It is doubted still, by some {68} persons, with respect -to the double stars. But suppose all these doubts to be -banished, and the law to be universal; is it then proved to -be necessary? Manifestly not: the very existence of these -doubts proves that it is not so. For the doubts were -dissipated by reference to observation and calculation, not -by reasoning on the nature of the law. Clairaut's difficulty -was removed by a more exact calculation of the effect of the -sun's force on the motion of the apogee. The suggestion of -Bessel, that the intensity of gravitation might be different -for different planets, was found to be unnecessary, when -Professor Airy gave a more accurate determination of the -mass of Jupiter. And the question whether the extension of -the law of the inverse square to the double stars be true, -(one of the most remarkable questions now before the -scientific world,) must be answered, not by any speculations -concerning what the laws of attraction must necessarily be, -but by carefully determining the actual laws of the motion -of these curious objects, by means of the observations such -as those which Sir John Herschel has collected for that -purpose, by his unexampled survey of both hemispheres of the -sky. And since the extent of this truth is thus to be -determined by reference to observed facts, it is clear that -no mere accumulation of them can make its universality -certain, or its necessity apparent. - -Thus no knowledge of the necessity of any truths can result -from the observation of what really happens. This being -clearly understood, we are led to an important inquiry. - -The characters of universality and necessity in the truths -which form part of our knowledge, can never be derived from -experience, by which so large a part of our knowledge is -obtained. But since, as we have seen, we really do possess a -large body of truths which are necessary, and because -necessary, therefore universal, the question still recurs, -from what source these characters of universality and -necessity are derived. - -The answer to this question we will attempt to give in the -next chapter. - - - -{{69}} -CHAPTER V. - -OF THE GROUNDS OF NECESSARY TRUTHS. - - -1. TO the question just stated, I reply, that the necessity -and universality of the truths which form a part of our -knowledge, are derived from the _Fundamental Ideas_ which -those truths involve. These ideas entirely shape and -circumscribe our knowledge; they regulate the active -operations of our minds, without which our passive -sensations do not become knowledge. They govern these -operations, according to rules which are not only fixed and -permanent, but which may be expressed in plain and definite -terms; and these rules, when thus expressed, 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 truth. - -These enunciations of the necessary and evident conditions -imposed upon our knowledge by the Fundamental Ideas which it -involves, are termed _Axioms_. Thus the Axioms of Geometry -express the necessary conditions which result from the Idea -of Space; the Axioms of Mechanics express the necessary -conditions which flow from the Ideas of Force and Motion; -and so on. - -2. 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 terms. I shall there pass in -review many of the most important fundamental ideas on which -the existing body of our science depends; and I shall -endeavour to show, for each such idea in succession, that -knowledge involves an active as well as a passive element; -that it is not possible without an act of the mind, -regulated by certain {70} laws. I shall further attempt to -enumerate some of the principal fundamental relations which -each idea thus introduces into our thoughts, and to express -them by means of definitions and axioms, and other suitable -forms. - -I will only add a remark or two to illustrate further this -view of the ideal grounds of our knowledge. - -3. To persons familiar with any of the demonstrative -sciences, it will be apparent that if we state all the -Definitions and Axioms which are employed in the -demonstrations, we state the whole basis on which those -reasonings rest. For the whole process of demonstrative or -deductive reasoning in any science, (as in geometry, for -instance,) consists entirely in combining some of these -first principles so as to obtain the simplest propositions -of the science; then combining these so as to obtain other -propositions of greater complexity; and so on, till we -advance to the most recondite demonstrable truths; these -last, however intricate and unexpected, still involving no -principles except the original definitions and axioms. Thus, -by combining the Definition of a triangle, and the -Definitions of equal lines and equal angles, namely, that -they are such as when applied to each other, coincide, with -the Axiom respecting straight lines (that two such lines -cannot inclose a space,) we demonstrate the equality of -triangles, under certain assumed conditions. Again, by -combining this result with the Definition of parallelograms, -and with the Axiom that if equals be taken from equals the -wholes are equal, we prove the equality of parallelograms -between the same parallels and upon the same base. From this -proposition, again, we prove the equality of the square on -the hypotenuse of a triangle to the squares on the two sides -containing the right angle. But in all this there is nothing -contained which is not rigorously the result of our -geometrical Definitions and Axioms. All the rest of our -treatises of geometry consists only of terms and phrases of -reasoning, the object of which is to connect those first -principles, and to exhibit the effects of their combination -in the shape of demonstration. {71} - -4. This combination of first principles takes place -according to the forms and rules of _Logic_. 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 conclusiveness, that is, in -_Syllogisms_. Thus our geometrical reasonings might be -resolved into such steps as the following:-- -All straight lines drawn from the centre of a circle to its -circumference are equal: -But the straight lines AB, AC, are drawn from the centre of -a circle to its circumference: -Therefore the straight lines AB, AC, are equal. - -Each step of geometrical, and all other demonstrative -reasoning, may be resolved into three such clauses as these; -and these three clauses are termed respectively, the _major -premiss_, the _minor premiss_, and the _conclusion_; or, -more briefly, the _major_, the _minor_, and the -_**conclusion_. - -The principle which justifies the reasoning when exhibited -in this syllogistic form, is this:--that a truth which can -be asserted as generally, or rather as universally true, can -be asserted as true also in each particular case. The -_minor_ only asserts a certain particular case to be an -example of such conditions as are spoken of in the _major_; -and hence the conclusion, which is true of the major by -supposition, is true of the minor by consequence; and thus -we proceed from syllogism to syllogism, in each one -employing some general truth in some particular instance. -Any proof which occurs in geometry, or any other science of -demonstration, may thus be reduced to a series of processes, -in each of which we pass from some general proposition to -the narrower and more special propositions which it -includes. And this process of deriving truths by the mere -combination of general principles, applied in particular -hypothetical cases, is called _deduction_; being opposed to -_induction_, in which, as we have seen (chap. i. sect. 3), a -new general principle is introduced at every step. - -5. Now we have to remark that, this being so, however far we -follow such deductive reasoning, we can {72} never have, in -our conclusion any truth which is not virtually included in -the original principles from which the reasoning started. -For since at any step we merely take out of a general -proposition something included in it, while at the preceding -step we have taken this general proposition out of one more -general, and so on perpetually, it is manifest that our last -result was really included in the principle or principles -with which we began. I say _principles_, because, although -our logical conclusion can only exhibit the legitimate issue -of our first principles, it may, nevertheless, contain the -result of the combination of several such principles, and -may thus assume a great degree of complexity, and may appear -so far removed from the parent truths, as to betray at first -sight hardly any relationship with them. Thus the -proposition which has already been quoted respecting the -squares on the sides of a right-angled triangle, contains -the results of many elementary principles; as, the -definitions of parallels, triangle, and square; the axioms -respecting straight lines, and respecting parallels; and, -perhaps, others. The conclusion is complicated by containing -the effects of the combination of all these elements; but it -contains nothing, and can contain nothing, but such elements -and their combinations. - -This doctrine, that logical reasoning produces no new -truths, but only unfolds and brings into view those truths -which were, in effect, contained in the first principles of -the reasoning, is assented to by almost all who, in modern -times, have attended to the science of logic. Such a view is -admitted both by those who defend, and by those who -depreciate the value of logic. 'Whatever is established by -reasoning, must have been contained and virtually asserted -in the premises[6\1].' 'The only truth which such -propositions can possess consists in conformity to the -original principles.' - -[Note 6\1: Whately's _Logic_, pp. 237, 238.] - -In this manner the whole substance of our geometry is -reduced to the Definitions and Axioms which we employ in our -elementary reasonings; and in like {73} manner we reduce the -demonstrative truths of any other science to the definitions -and axioms which we there employ. - -6. But in reference to this subject, it has sometimes been -said that demonstrative sciences do in reality depend upon -Definitions only; and that no additional kind of principle, -such as we have supposed Axioms to be, is absolutely -required. It has been asserted that in geometry, for -example, the source of the necessary truth of our -propositions is this, that they depend upon definitions -alone, and consequently merely state the identity of the -same thing under different aspects. - -That in the sciences which admit of demonstration, as -geometry, mechanics, and the like, Axioms as well as -Definitions are needed, in order to express the grounds of -our necessary convictions, must be shown hereafter by an -examination of each of these sciences in particular. But -that the propositions of these sciences, those of geometry -for example, do not merely assert the identity of the same -thing, will, I think, be generally allowed, if we consider -the assertions which we are enabled to make. When we declare -that 'a straight line is the shortest distance between two -points,' is this merely an identical proposition? the -definition of a straight line in another form? Not so: the -definition of a straight line involves the notion of form -only, and does not contain anything about magnitude; -consequently, it cannot contain anything equivalent to -'shortest.' Thus the propositions of geometry are not merely -identical propositions; nor have we in their general -character anything to countenance the assertion, that they -are the results of definitions alone. And when we come to -examine this and other sciences more closely, we shall find -that axioms, such as are usually in our treatises made the -fundamental principles of our demonstrations, neither have -ever been, nor can be, dispensed with. Axioms, as well as -Definitions, are in all cases requisite, in order properly -to exhibit the grounds of necessary truth. - -7. Thus the real logical basis of every body of demonstrated -truths are the Definitions and Axioms {74} which are the -first principles of the reasonings. But when we are arrived -at this point, the question further occurs, what is the -ground of the truth of these Axioms? It is not the logical, -but the philosophical, not the formal, but the real -foundation of necessary truth, which we are seeking. Hence -this inquiry necessarily comes before us, What is the ground -of the Axioms of Geometry, of Mechanics, and of any other -demonstrable science? - -The answer which we are led to give, by the view which we -have taken of the nature of knowledge, has already been -stated. The ground of the axioms belonging to each science -is the _Idea_ which the axiom involves. The ground of the -Axioms of Geometry is the _Idea of Space_: the ground of the -Axioms of Mechanics is the _Idea of Force_, of _Action_ and -_Reaction_, and the like. And hence these Ideas are -Fundamental Ideas; and since they are thus the foundations, -not only of demonstration but of truth, an examination into -their real import and nature is of the greatest consequence -to our purpose. - -8. Not only the Axioms, but the definitions which form the -basis of our reasonings, depend upon our Fundamental Ideas. -And the Definitions are not arbitrary definitions, but are -determined by a necessity no less rigorous than the Axioms -themselves. We could not think of geometrical truths without -conceiving a circle; and we could not reason concerning such -truths without defining a circle in some mode equivalent to -that which is commonly adopted. The Definitions of -parallels, of right angles, and the like, are quite as -necessarily prescribed by the nature of the case, as the -Axioms which these Definitions bring with them. Indeed we -may substitute one of these kinds of principles for another. -We cannot always put a Definition in the place of an Axiom; -but we may always find an Axiom which shall take the place -of a Definition. If we assume a proper Axiom respecting -straight lines, we need no Definition of a straight line. -But in whatever shape the principle appear, as Definition or -as Axiom, it has about it nothing casual or {75} arbitrary, -but is determined to be what it is, as to its import, by the -most rigorous necessity, growing out of the Idea of Space. - -9. These principles,--Definitions, and Axioms,--thus -exhibiting the primary developments of a fundamental idea, -do in fact express the idea, so far as its expression in -words forms part of our science. They are different views of -the same body of truth; and though each principle, by -itself, exhibits only one aspect of this body, taken -together they convey a sufficient conception of it for our -purposes. The Idea itself cannot be fixed in words; but -these various lines of truth proceeding from it, suggest -sufficiently to a fitly-prepared mind, the place where the -idea resides, its nature, and its efficacy. - -It is true that these principles,--our elementary -Definitions and Axioms,--even taken all together, express -the Idea incompletely. Thus the Definitions and Axioms of -Geometry, as they are stated in our elementary works, do not -fully express the Idea of Space as it exists in our minds. -For, in addition to these, other Axioms, independent of -these, and no less evident, can be stated; and are in fact -stated when we come to the Higher Geometry. Such, for -instance, 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 curve. And thus the -Idea is disclosed but not fully revealed, imparted but not -transfused, by the use we make of it in science. When we -have taken from the fountain so much as serves our purpose, -there still remains behind a deep well of truth, which we -have not exhausted, and which we may easily believe to be -inexhaustible. - - - -{{76}} -CHAPTER VI. - -THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE. - - -1. BY the course of speculation contained in the last three -Chapters, we are again led to the conclusion which we have -already stated, that our knowledge contains an ideal -element, and that this element is not derived from -experience. For we have seen that there are propositions -which are known to be necessarily true; and that such -knowledge is not, and cannot be, obtained by mere -observation of actual facts. It has been shown, also, that -these necessary truths are the results of certain -fundamental ideas, such as those of space, number, and the -like. Hence it follows inevitably that these ideas and -others of the same kind are not derived from experience. For -these ideas possess a power of infusing into their -developments that very necessity which experience can in no -way bestow. This power they do not borrow from the external -world, but possess by their own nature. Thus we unfold out -of the Idea of Space the propositions of geometry, which are -plainly truths of the most rigorous necessity and -universality. But if the idea of space were merely collected -from observation of the external world, it could never -enable or entitle us to assert such propositions: it could -never authorize us to say that not merely some lines, but -_all_ lines, not only have, but _must_ have, those -properties which geometry teaches. Geometry in every -proposition speaks a language which experience never dares -to utter; and indeed of which she but half comprehends the -meaning. Experience sees that the assertions are true, but -she sees not how profound and absolute is their truth. {77} -She unhesitatingly assents to the laws which geometry -delivers, but she does not pretend to see the origin of -their obligation. She is always ready to acknowledge the -sway of pure scientific principles as a matter of fact, but -she does not dream of offering her opinion on their -authority as a matter of right; still less can she justly -claim to be herself the source of that authority. - -David Hume asserted[7\1], that we are incapable of seeing in -any of the appearances which the world presents anything of -necessary connexion; and hence he inferred that our -knowledge cannot extend to any such connexion. It will be -seen from what we have said that we assent to his remark as -to the fact, but we differ from him altogether in the -consequence to be drawn from it. Our inference from Hume's -observation is, not the truth of his conclusion, but the -falsehood of his premises;--not that, therefore, we can know -nothing of natural connexion, but that, therefore, we have -some other source of knowledge than experience:--not, that -we can have no idea of connexion or causation, because, in -his language, it cannot be the copy of an impression; but -that since we have such an idea, our ideas are not the -copies of our impressions. - -[Note 7\1: _Essays_, vol. ii. p. 70.] - -Since it thus appears that our fundamental ideas are not -acquired from the external world by our senses, but have -some separate and independent origin, it is important for us -to examine their nature and properties, as they exist in -themselves; and this it will be our business to do through a -portion of the following pages. But it may be proper first -to notice one or two objections which may possibly occur to -some readers. - -2. It may be said that without the use of our senses, of -sight and touch, for instance, we should never have any idea -of space; that this idea, therefore, may properly be said to -be derived from those senses. And to this I reply, by -referring to a parallel instance. Without light we should -have no perception of visible {78} figure; yet the power of -perceiving visible figure cannot be said to be derived from -the light, but resides in the structure of the eye. If we -had never seen objects in the light, we should be quite -unaware that we possessed a power of vision; yet we should -not possess it the less on that account. If we had never -exercised the senses of sight and touch (if we can conceive -such a state of human existence) we know not that we should -be conscious of an idea of space. But the light reveals to -us at the same time the existence of external objects and -our own power of seeing. And in a very similar manner, the -exercise of our senses discloses to us, at the same time, -the external world, and our own ideas of space, time, and -other conditions, without which the external world can -neither be observed nor conceived. That light is necessary -to vision, does not, in any degree, supersede the importance -of a separate examination of the laws of our visual powers, -if we would understand the nature of our own bodily -faculties and the extent of the information they can give -us. In like manner, the fact that intercourse with the -external world is necessary for the conscious employment of -our ideas, does not make it the less essential for us to -examine those ideas in their most intimate structure, in -order that we may understand the grounds and limits of our -knowledge. Even before we see a single object, we have a -faculty of vision; and in like manner, if we can suppose a -man who has never contemplated an object in space or time, -we must still assume him to have the faculties of -entertaining the ideas of space and time, which faculties -are called into play on the very first occasion of the use -of the senses. - -3. In answer to such remarks as the above, it has sometimes -been said that to assume separate faculties in the mind for -so many different processes of thought, is to give a mere -verbal explanation, since we learn nothing concerning our -idea of space by being told that we have a faculty of -forming such an idea. It has been said that this course of -explanation leads to an endless multiplication of elements -in man's nature, without any advantage to our knowledge of -his true {79} constitution. We may, it is said, assert man -to have a faculty of walking, of standing, of breathing, of -speaking; but what, it is asked, is gained by such -assertions? To this I reply, that we undoubtedly have such -faculties as those just named; that it is by no means -unimportant to consider them; and that the main question in -such cases is, whether they are separate and independent -faculties, or complex and derivative ones; and, if the -latter be the case, what are the simple and original -faculties by the combination of which the others are -produced. In walking, standing, breathing, for instance, a -great part of the operation can be reduced to one single -faculty; the voluntary exercise of our muscles. But in -breathing this does not appear to be the whole of the -process. The operation is, in part at least, involuntary; -and it has been held that there is a certain sympathetic -action of the nerves, in addition to the voluntary agency -which they transmit, which is essential to the function. To -determine whether or no this sympathetic faculty is real and -distinct, and if so, what are its laws and limits, is -certainly a highly philosophical inquiry, and well deserving -the attention which has been bestowed upon it by eminent -physiologists. And just of the same nature are the inquiries -with respect to man's intellectual constitution, on which we -propose to enter. For instance, man has a faculty of -apprehending time, and a faculty of reckoning numbers: are -these distinct, or is one faculty derived from the other? To -analyze the various combinations of our ideas and -observations into the original faculties which they involve; -to show that these faculties are original, and not capable -of further analysis: to point out the characters which mark -these faculties and lead to the most important features of -our knowledge;--these are the kind of researches on which we -have now to enter, and these, we trust, will be found to be -far from idle or useless parts of our plan. If we succeed in -such attempts, it will appear that it is by no means a -frivolous or superfluous step to distinguish separate -faculties in the mind. If we do not learn much by being told -that we have a faculty {80} of forming the idea of space, we -at least, by such a commencement, circumscribe a certain -portion of the field of our investigations, which, we shall -afterwards endeavour to show, requires and rewards a special -examination. And though we shall thus have to separate the -domain of our philosophy into many provinces, these are, as -we trust it will appear, neither arbitrarily assigned, nor -vague in their limits, nor infinite in number. - - - -{{81}} -CHAPTER VII. - -OF THE PHILOSOPHY OF THE SCIENCES. - - -WE proceed, in the ensuing Books, to the closer examination -of a considerable number of those Fundamental Ideas on which -the sciences, hitherto most successfully cultivated, are -founded. In this task, our objects will be to explain and -analyze such Ideas so as to bring into view the Definitions -and Axioms, or other forms, in which we may clothe the -conditions to which our speculative knowledge is subjected. -I shall also try to prove, for some of these Ideas in -particular, what has been already urged respecting them in -general, that they are not derived from observation, but -necessarily impose their conditions upon that knowledge of -which observation supplies the materials. I shall further, -in some cases, endeavour to trace the history of these Ideas -as they have successively come into notice in the progress -of science; the gradual development by which they have -arrived at their due purity and clearness; and, as a -necessary part of such a history, I shall give a view of -some of the principal controversies which have taken place -with regard to each portion of knowledge. - -An exposition and discussion of the Fundamental Ideas of -each Science may, with great propriety, be termed the -PHILOSOPHY OF such SCIENCE. These ideas contain in -themselves the elements of those truths which the science -discovers and enunciates; and in the progress of the -sciences, both in the world at large and in the mind of each -individual student, the most important steps consist in -apprehending these ideas clearly, and in bringing them into -accordance with the observed facts. I shall, therefore, in a -series of Books, {82} treat of the _Philosophy of the Pure -Sciences_, the _Philosophy of the Mechanical Sciences_, the -_Philosophy of Chemistry_, and the like, and shall analyze -and examine the ideas which these sciences respectively -involve. - -In this undertaking, inevitably somewhat long, and involving -many deep and subtle discussions, I shall take, as a chart -of the country before me, by which my course is to be -guided, the scheme of the sciences which I was led to form -by travelling over the history of each in order[8\1]. Each -of the sciences of which I then narrated the progress, -depends upon several of the Fundamental Ideas of which I -have to speak: some of these Ideas are peculiar to one field -of speculation, others are common to more. A previous -enumeration of Ideas thus collected may serve both to show -the course and limits of this part of our plan, and the -variety of interest which it offers. - -[Note 8\1: _History of the Inductive Sciences._] - -I shall, then, successively, have to speak Of the Ideas -which are the foundation of Geometry and Arithmetic, (and -which also regulate all sciences depending upon these, as -Astronomy and Mechanics;) namely, the Ideas of _Space_, -_Time_, and _Number_ (Book II.): - -Of the Ideas on which the Mechanical Sciences (as Mechanics, -Hydrostatics, Physical Astronomy) more peculiarly rest; the -ideas of _Force_ and _Matter_, or rather the idea of -_Cause_, which is the basis of these (Book III.): - -Of the Ideas which the Secondary Mechanical Sciences -(Acoustics, Optics, and Thermotics) involve; namely, the -Ideas of the _Externality_ of objects, and of the _Media_ by -which we perceive their qualities (Book IV.): - -Of the Ideas which are the basis of Mechanico-chemical and -Chemical Science; _Polarity_, _Chemical Affinity_, and -_Substance_; and the Idea of _Symmetry_, a necessary part of -the Philosophy of Crystallography (Books V. VI.): - -Of the Ideas on which the Classificatory Sciences proceed -(Mineralogy, Botany, and Zoology); namely, {83} the Ideas of -_Resemblance_, and of its gradations, and of _Natural -Affinity_ (Books VII. VIII.): - -Finally, of those Ideas on which the Physiological Sciences -are founded; the Ideas of separate Vital Powers, such as -_Assimilation_ and _Irritability_; and the Idea of _Final -Cause_ (Book IX.): - -We have, besides these, the Palætiological Sciences, which -proceed mainly on the conception of _Historical Causation_ -(Book X.): - -It is plain that when we have proceeded so far as this, we -have advanced to the verge of those speculations which have -to do with mind as well as body. The extension of our -philosophy to such a field, if it can be justly so extended, -will be one of the most important results of our researches; -but on that very account we must fully study the lessons -which we learn in those fields of speculation where our -doctrines are most secure, before we venture into a region -where our principles will appear to be more precarious, and -where they are inevitably less precise. - -We now proceed to the examination of the above Ideas, and to -such essays towards the philosophy of each Science as this -course of investigation may suggest. - - - -{{85}} -BOOK II. - - -THE -PHILOSOPHY -OF THE -PURE SCIENCES. - - - - -The way in which we are led to regard human knowledge is -like the way in which Copernicus was led to regard the -heavens. 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 spectator, he tried whether it -would not answer better if he made the spectator turn, and -left the stars at rest. We may make a similar trial in -Metaphysics, as to our way of looking at objects. If our -view of them must be governed altogether by the properties -of the objects themselves, I see not how man can know -anything about them _à priori_. But if the thing, as an -object of the senses, is regulated by the constitution of -our power of knowing, I can very readily represent to myself -this possibility. - -KANT, _Kritik d. R. V. Pref._ - - -{{87}} -BOOK II. - -THE PHILOSOPHY OF THE PURE SCIENCES. - - -[The principal question discussed in the last Book was this -(see chaps. V. and VI.): How are _necessary_ and _universal_ -truths possible? And the answer then given was: that the -necessity and universality of truths are derived from the -_Fundamental Ideas_ which they involve. And we proceed in -this Book to exemplify this doctrine in the case of the -truths of Geometry and Arithmetic, which derive their -necessity and universality from the Fundamental Ideas of -Space, and Time, or Number. - -The question thus examined is that which Kant undertook to -deal with in his celebrated work, _Kritik der reinen -Vernunft_ (_Examination of the Pure Reason_): and our -solution of the Problem, so far as the Ideas of Space and -Time are concerned, agrees in the main with his. The -arguments contained in chapters II. and **VII. of this Book, -are the leading arguments respecting Space and Time, in -Kant's _Kritik_. Kant, however, instead of calling Space and -Time _Ideas_, calls them the necessary _Forms_ of our -experience, as I have stated in the text. - -But though I have adopted Kant's arguments as to Space and -Time, all that follows in the succeeding Books, with regard -to other Ideas, has no resemblance to any doctrines of Kant -or his school (with the exception, perhaps, of some of the -views on the Idea of _Cause_). The nature and character of -the other Scientific Ideas which I have examined, in the -succeeding Books, have been established by an analysis of -the history of the several Sciences to which those Ideas are -essential, and an examination of the writings of the -principal discoverers in those Sciences.] - - - -{{88}} -CHAPTER I. - -OF THE PURE SCIENCES. - - -1. ALL external objects and events which we can contemplate -are viewed as having relations of Space, Time, and Number; -and are subject to the general conditions which these Ideas -impose, as well as to the particular laws which belong to -each class of objects and occurrences. The special laws of -nature, considered under the various aspects which -constitute the different sciences, are obtained by a mixed -reference to Experience and to the Fundamental Ideas of each -science. But besides the sciences thus formed by the aid of -special experience, the conditions which flow from those -more comprehensive ideas first mentioned, Space, Time, and -Number, constitute a body of science, applicable to objects -and changes of all kinds, and deduced without recurrence -being had to any observation in particular. These sciences, -thus unfolded out of ideas alone, unmixed with any reference -to the phenomena of matter, are hence termed _Pure_ -Sciences. The principal sciences of this class are Geometry, -Theoretical Arithmetic, and Algebra considered in its most -general sense, as the investigation of the relations of -space and number by means of general symbols. - -2. These Pure Sciences were not included in our survey of -the history of the sciences, because they are not -_inductive_ sciences. Their progress has not consisted in -collecting laws from phenomena, true theories from observed -facts, and more general from more limited laws; but in -tracing the consequences of the ideas themselves, and in -detecting the most general and intimate analogies and -connexions which prevail {89} among such conceptions as are -derivable from the ideas. These sciences have no principles -besides definitions and axioms, and no process of proof but -_deduction_; this process, however, assuming here a most -remarkable character; and exhibiting a combination of -simplicity and complexity, of rigour and generality, quite -unparalleled in other subjects. - -3. The universality of the truths, and the rigour of the -demonstrations of these pure sciences, attracted attention -in the earliest times; and it was perceived that they -offered an exercise and a discipline of the intellectual -faculties, in a form peculiarly free from admixture of -extraneous elements. They were strenuously cultivated by the -Greeks, both with a view to such a discipline, and from the -love of speculative truth which prevailed among that people: -and the name _mathematics_, by which they are designated, -indicates this their character of _disciplinal_ studies. - -4. As has already been said, the ideas which these sciences -involve extend to all the objects and changes which we -observe in the external world; 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 nature, as Astronomy, Optics, and Mechanics. Such -sciences are hence often termed _Mixed Mathematics_, the -relations of space and number being, in these branches of -knowledge, combined with principles collected from special -observation; while Geometry, Algebra, and the like subjects, -which involve no result of experience, are called _Pure -Mathematics_. - -5. Space, time, and number, may be conceived as _forms_ by -which the knowledge derived from our sensations is moulded, -and which are independent of the differences in the _matter_ -of our knowledge, arising from the sensations themselves. -Hence the sciences which have these ideas for their subject -may be termed _Formal Sciences_. In this point of view, they -are distinguished from sciences in which, besides these mere -formal laws by which appearances are corrected, we endeavour -to apply to the phenomena the idea of cause, {90} or some of -the other ideas which penetrate further into the principles -of nature. We have thus, in the History, distinguished -Formal Astronomy and Formal Optics from Physical Astronomy -and Physical Optics. - -We now proceed to our examination of the Ideas which -constitute the foundation of these formal or pure -mathematical sciences, beginning with the Idea of Space. - - - -{{91}} -CHAPTER II. - -OF THE IDEA OF SPACE. - - -1. BY speaking of space as an Idea, I intend to imply, as -has already been stated, that the apprehension of objects as -existing in space, and of the relations of position, &c., -prevailing among them, is not a consequence of experience, -but a result of a peculiar constitution and activity of the -mind, which is independent of all experience in its origin, -though constantly combined with experience in its exercise. - -That the idea of space is thus independent of experience, -has already been pointed out in speaking of ideas in -general: but it may be useful to illustrate the doctrine -further in this particular case. - -I assert, then, that space is not a notion obtained by -experience. Experience gives us information concerning -things without us: but our apprehending them _as_ without -us, takes for granted their existence in space. Experience -acquaints us what are the form, position, magnitude of -particular objects: but that they have form, position, -magnitude, presupposes that they are in space. We cannot -derive from appearances, by the way of observation, the -habit of representing things to ourselves as in space; for -no single act of observation is possible any otherwise than -by beginning with such a representation, and conceiving -objects as already existing in space. - -2. That our mode of representing space to ourselves is not -derived from experience, is clear also from this: that -through this mode of representation we arrive at -propositions which are rigorously universal and necessary. -Propositions of such a kind could not possibly be obtained -from experience; for experience can {92} only teach us by a -limited number of examples, and therefore can never securely -establish a universal proposition: and again, experience can -only inform us that anything is so, and can never prove that -it must be so. That two sides of a triangle are greater than -the third is a universal and necessary geometrical truth: it -is true of all triangles; it is true in such a way that the -contrary cannot be conceived. Experience could not prove -such a proposition. And experience has not proved it; for -perhaps no man ever made the trial as a means of removing -doubts: and no trial could, in fact, add in the smallest -degree to the certainty of this truth. To seek for proof of -geometrical propositions by an appeal to observation proves -nothing in reality, except that the person who has recourse -to such grounds has no due apprehension of the nature of -geometrical demonstration. 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 true: but these were persons whose minds had -been engrossed by practical habits, and in whom the -speculative development of the idea of space had been -stifled by other employments. The practical trial of the -rule may illustrate, but cannot prove it. The rule will of -course be confirmed by such trial, because what is true in -general is true in particular: but the rule cannot be proved -from any number of trials, for no accumulation of particular -cases makes up a universal case. To all persons who can see -the force of any proof, the geometrical rule above referred -to is as evident, and its evidence as independent of -experience, as the assertion that sixteen and nine make -twenty-five. At the same time, the truth of the geometrical -rule is quite independent of numerical truths, and results -from the relations of space alone. This could not be if our -apprehension of the relations of space were the fruit of -experience: for experience has no element from which such -truth and such proof could arise. - -3. Thus the existence of necessary truths, such as those of -geometry, proves that the idea of space from {93} which they -flow is not derived from experience. Such truths are -inconceivable on the supposition of their being collected -from observation; for the impressions of sense include no -evidence of necessity. But we can readily understand the -necessary character of such truths, if we conceive that -there are certain necessary conditions under which alone the -mind receives the impressions of sense. Since these -conditions reside in the constitution of the mind, and apply -to every perception of an object to which the mind can -attain, we easily see that their rules must include, not -only all that has been, but all that can be, matter of -experience. Our sensations can each convey no information -except about itself; each can contain no trace of another -additional sensation; and thus no relation and connexion -between two sensations can be given by the sensations -themselves. But the mode in which the mind perceives these -impressions as objects, may and will introduce necessary -relations among them: and thus by conceiving the idea of -space to be a condition of perception in the mind, we can -conceive the existence of necessary truths, which apply to -all perceived objects. - -4. If we consider the impressions of sense as the mere -materials of our experience, such materials may be -accumulated in any quantity and in any order. But if we -suppose that this matter has a certain form given it, in the -act of being accepted by the mind, we can understand how it -is that these materials are subject to inevitable -rules;--how nothing can be perceived exempt from the -relations which belong to such a form. And since there are -such truths applicable to our experience, and arising from -the nature of space, we may thus consider space as a _form_ -which the materials given by experience necessarily assume -in the mind; as an arrangement derived from the perceiving -mind, and not from the sensations alone. - -5. Thus this phrase,--that space is a _form_ belonging to -our perceptive power,--may be employed to express that we -cannot perceive objects as in space, without an operation of -the mind as well as of the senses--without active as well as -passive faculties. This phrase, however, {94} is not -necessary to the exposition of our doctrines. Whether we -call the conception of space a Condition of perception, a -Form of perception, or an Idea, or by any other term, it is -something originally inherent in the mind perceiving, and -not in the objects perceived. And it is because the -apprehension of all objects is thus subjected to certain -mental conditions, forms or ideas, that our knowledge -involves certain inviolable relations and necessary truths. -The principles of such truths, so far as they regard space, -are derived from the idea of space, and we must endeavour to -exhibit such principles in their general form. But before we -do this, we may notice some of the conditions which belong, -not to our Ideas in general, but to this Idea of Space in -particular. - - - -{{95}} -CHAPTER III. - -OF SOME PECULIARITIES OF THE IDEA OF SPACE. - - -1. SOME of the Ideas which we shall have to examine involve -conceptions of certain relations of objects, as the idea of -Cause and of Likeness; and may appear to be suggested by -experience, enabling us to _abstract_ this general relation -from particular cases. But it will be seen that Space is not -such a general conception of a relation. For we do not speak -of _Spaces_ as we speak of Causes and Likenesses, but of -Space. And when we speak of _spaces_, we understand by the -expression, parts of one and the same identical -everywhere-extended Space. We conceive a universal Space; -which is not made up of these partial spaces as its -component parts, for it would remain if these were taken -away; and these cannot be conceived without presupposing -absolute space. Absolute Space is essentially one; and the -complication which exists in it, and the conception of -various spaces, depends merely upon boundaries. Space must, -therefore, be, as we have said, not a general conception -abstracted from particulars, but a universal mode of -representation, altogether independent of experience. - -2. Space is infinite. We represent it to ourselves as an -infinitely great magnitude. Such an idea as that of Likeness -or Cause, is, no doubt, found in an infinite number of -particular cases, and so far includes these cases. But these -ideas do not include an infinite number of cases as parts of -an infinite whole. When we say that all bodies and partial -spaces exist _in_ infinite space, we use an expression which -is not applied in the same sense to any cases except those -of Space and Time. {96} - -3. What is here said may appear to be a denial of the real -existence of space. It must be observed, however, that we do -not deny, but distinctly assert, the existence of space as a -real and necessary condition of all objects perceived; and -that we not only allow that objects are seen external to us, -but we found upon the fact of their being so seen, our view -of the nature of space. If, however, it be said that we deny -the reality of space as an object or thing, this is true. -Nor does it appear easy to maintain that space exists as a -thing, when it is considered that this thing is infinite in -all its dimensions; and, moreover, that it is a thing, -which, being nothing in itself, exists only that other -things may exist in it. And those who maintain the real -existence of space, must also maintain the real existence of -time in the same sense. Now two infinite things, thus really -existing, and yet existing only as other things exist in -them, are notions so extravagant that we are driven to some -other mode of explaining the state of the matter. - -4. Thus space is not an object of which we perceive the -properties, but a form of our perception; not a thing which -affects our senses, but an idea to which we conform the -impressions of sense. And its peculiarities appear to depend -upon this, that it is not only a form of sensation, but of -_intuition_; that in reference to space, we not only -perceive but _contemplate_ objects. We see objects in space, -side by side, exterior to each other; space, and objects in -so far as they occupy space, have parts exterior to other -parts; and have the whole thus made up by the juxtaposition -of parts. This mode of apprehension belongs only to the -ideas of space and time. Space and Time are made up of -parts, but Cause and Likeness are not apprehended as made up -of parts. And the term _intuition_ (in its rigorous sense) -is applicable only to that mode of contemplation in which we -thus look at objects as made up of parts, and apprehend the -relations of those parts at the same time and by the same -act by which we apprehend the objects themselves. - -5. As we have said, space limited by _boundaries_ {97} gives -rise to various conceptions which we have often to consider. -Thus limited, space assumes _form_ or _figure_; and the -variety of conceptions thus brought under our notice is -infinite. We have every possible form of line, straight -line, and curve; and of curves an endless number;--circles, -parabolas, hyperbolas, spirals, helices. We have plane -surfaces of various shapes,--parallelograms, polygons, -ellipses; and we have solid figures,--cubes, cones, -cylinders, spheres, spheroids, and so on. All these have -their various properties, depending on the relations of -their boundaries; and the investigation of their properties -forms the business of the science of Geometry. - -6. Space has three dimensions, or directions in which it may -be measured; it cannot have more or fewer. The simplest -measurement is that of a straight line, which has length -alone. A surface has both length and breadth: and solid -space has length, breadth, and thickness or depth. The -origin of such a difference of dimensions will be seen if we -reflect that each portion of space has a boundary, and is -extended both _in_ the direction in which its boundary -extends, and also in a direction _from_ its boundary; for -otherwise it would not be a boundary. A point has no -dimensions. A line has but one dimension,--the distance from -its boundary, or its _length_. A plane, bounded by a -straight line, has the dimension which belongs to this line, -and also has another dimension arising from the distance of -its parts from this boundary line; and this may be called -_breadth_. A solid, bounded by a plane, has the dimensions -which this plane has; and has also a third dimension, which -we may call _height_ or _depth_, as we consider the solid -extended above or below the plane; or _thickness_, if we -omit all consideration of up and down. And no space can have -any dimensions which are not resoluble into these three. - -We may now proceed to consider the mode in which the idea of -space is employed in the formation of Geometry. - - - -{{98}} -CHAPTER IV. - -OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE. - - -1. THE relations of space have been apprehended with -peculiar distinctness and clearness from the very first -unfolding of man's speculative powers. This was a -consequence of the circumstance which we have just noticed, -that the simplest of these relations, and those on which the -others depend, are seen by intuition. Hence, as soon as men -were led to speculate concerning the relations of space, -they assumed just principles, and obtained true results. It -is said that the science of _geometry_ had its origin in -Egypt, before the dawn of the Greek philosophy: but the -knowledge of the early Egyptians (exclusive of their -mythology) appears to have been purely practical; and, -probably, their geometry consisted only in some maxims of -_land-measuring_, which is what the term implies. The Greeks -of the time of Plato, had, however, not only possessed -themselves of many of the most remarkable elementary -theorems of the science; but had, in several instances, -reached the boundary of the science in its elementary form; -as when they proposed to themselves the problems of doubling -the cube and squaring the circle. - -But the deduction of these theorems by a systematic process, -and the primary exhibition of the simplest principles -involved in the idea of space, which such a deduction -requires, did not take place, so far as we are aware, till a -period somewhat later. The _Elements of Geometry_ of Euclid, -in which this task was performed, are to this day the -standard work on the subject: the author of this work taught -mathematics with great applause at Alexandria, in the reign -of Ptolemy Lagus, {99} about 280 years before Christ. The -principles which Euclid makes the basis of his system have -been very little simplified since his time; and all the -essays and controversies which bear upon these principles, -have had a reference to the form in which they are stated by him. - -2. _Definitions._--The first principles of Euclid's geometry -are, as the first principles of any system of geometry must -be, definitions and axioms respecting the various ideal -conceptions which he introduces; as straight lines, parallel -lines, angles, circles, and the like. But it is to be -observed that these definitions and axioms are very far from -being arbitrary hypotheses and assumptions. They have their -origin in the idea of space, and are merely modes of -exhibiting that idea in such a manner as to make it afford -grounds of deductive reasoning. The axioms are necessary -consequences of the conceptions respecting which they are -asserted; and the definitions are no less necessary -limitations of conceptions; not requisite in order to arrive -at this or that consequence; but necessary in order that it -may be possible to draw any consequences, and to establish -any general truths. - -For example, if we rest the end of one straight staff upon -the middle of another straight staff, and move the first -staff into various positions, we, by so doing, alter the -angles which the first staff makes with the other to the -right hand and to the left. But if we place the staff in -that special position in which these two angles are equal, -each of them is a right angle, according to Euclid; and this -is the _definition_ of a right angle, except that Euclid -employs the abstract conception of straight lines, instead -of speaking, as we have done, of staves. But this selection -of the case in which the two angles are equal is not a mere -act of caprice; as it might have been if he had selected a -case in which these angles are unequal in any proportion. -For the consequences which can be drawn concerning the cases -of unequal angles, do not lead to general truths, without -some reference to that peculiar case in which the angles are -equal: and thus it becomes necessary to {100} single out and -define that special case, marking it by a special phrase. -And this definition not only gives complete and distinct -knowledge what a right angle is, to any one who can form the -conception of an angle in general; but also supplies a -principle from which all the properties of right angles may -be deduced. - -3. _Axioms._--With regard to other conceptions also, as -circles, squares, and the like, it is possible to lay down -definitions which are a sufficient basis for our reasoning, -so far as such figures are concerned. But, besides these -definitions, it has been found necessary to introduce -certain axioms among the fundamental principles of geometry. -These are of the simplest character; for instance, that two -straight lines cannot cut each other in more than one point, -and an axiom concerning parallel lines. Like the -definitions, these axioms flow from the Idea of Space, and -present that idea under various aspects. They are different -from the definitions; nor can the definitions be made to -take the place of the axioms in the reasoning by which -elementary geometrical properties are established. For -example, the definition of parallel straight lines is, that -they are such as, however far continued, can never meet: -but, in order to reason concerning such lines, we must -further adopt some axiom respecting them: for example, we -may very conveniently take this axiom; that two straight -lines which cut one another are not both of them parallel to -a third straight line[1\2]. The definition and the axiom are -seen to be inseparably connected by our intuition of the -properties of space; but the axiom cannot be proved from the -definition, by any rigorous deductive demonstration. And if -we were to take any other definition of two parallel -straight lines, (as that they are both perpendicular to a -third straight line,) we should still, at some point or -other of our progress, fall in with the same difficulty of -demonstratively establishing their properties without some -further assumption. - -[Note 1\2: This axiom is simpler and more convenient than -that of Euclid. It is employed by the late Professor -Playfair in his _Geometry_.] - -{101} 4. Thus the elementary properties of figures, which -are the basis of our geometry, are necessary results of our -Idea of Space; and are connected with each other by the -nature of that idea, and not merely by our hypotheses and -constructions. Definitions and axioms must be combined, in -order to express this idea so far as the purposes of -demonstrative reasoning require. These verbal enunciations -of the results of the idea cannot be made to depend on each -other by logical consequence; but have a mutual dependence -of a more intimate kind, which words cannot fully convey. It -is not possible to resolve these truths into certain -_hypotheses_, of which all the rest shall be the necessary -logical consequence. The necessity is not hypothetical, but -intuitive. The axioms require not to be granted, but to be -seen. If any one were to assent to them without seeing them -to be true, his assent would be of no avail for purposes of -reasoning: for he would be also unable to see in what cases -they might be applied. The clear possession of the Idea of -Space is the first requisite for all geometrical reasoning; -and this clearness of idea may be tested by examining -whether the axioms offer themselves to the mind as evident. - -5. The necessity of ideas added to sensations, in order to -produce knowledge, has often been overlooked or denied in -modern times. The ground of necessary truth which ideas -supply being thus lost, it was conceived that there still -remained a ground of necessity in definitions;--that we -might have necessary truths, by asserting especially what -the definition implicitly involved in general. It was held, -also, that this was the case in geometry:--that all the -properties of a circle, for instance, were implicitly -contained in the definition of a circle. That this alone is -not the ground of the necessity of the truths which regard -the circle,--that we could not in this way unfold a -definition into proportions, without possessing an intuition -of the relations to which the definition led,--has already -been shown. But the insufficiency of the above account of -the grounds of necessary geometrical truth appeared in -another way also. It was found impossible to lay {102} down -a system of definitions out of which alone the whole of -geometrical truth could be evolved. It was found that axioms -could not be superseded. No definition of a straight line -could be given which rendered the axiom concerning straight -lines superfluous. And thus it appeared that the source of -geometrical truths was not definition alone; and we find in -this result a confirmation of the doctrine which we are here -urging, that this source of truth is to be found in the form -or conditions of our perception;--in the idea which we -unavoidably combine with the impressions of sense;--in the -activity, and not in the passivity of the mind[2\2]. - -[Note 2\2: I formerly stated views similar to these in some -'Remarks' appended to a work which I termed _The Mechanical -Euclid_, published in 1837. These Remarks, so far as they -bear upon the question here discussed, were noticed and -controverted in No. 135 of the _Edinburgh Review_. As an -examination of the reviewer's objections may serve further -to illustrate the subject, I shall annex to this chapter an -answer to the article to which I have referred.] - -6. This will appear further when we come to consider the -mode in which we exercise our observation upon the relations -of space. But we may, in the first place, make a remark -which tends to show the connexion between our conception of -a straight line, and the axiom which is made the foundation -of our reasonings concerning space. The axiom is this;--that -two straight lines, which have both their ends joined, -cannot have the intervening parts separated so as to inclose -a space. The necessity of this axiom is of exactly the same -kind as the necessity of the definition of a right angle, of -which we have already spoken. For as the line standing on -another makes _right angles_ when it makes the angles on the -two sides of it equal; so a line is a _straight line_ when -it makes the two portions of space, on the two sides of it, -similar. And as there is only a single position of the line -first mentioned, which can make the angles equal, 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 other: and -{103} therefore there cannot be two straight lines, such as -the axiom describes, which, between the same limits, give -two different boundaries to space thus separated. And thus -we see a reason for the axiom. Perhaps this view may be -further elucidated if we take a leaf of paper, double it, -and crease the folded edge. We shall thus obtain a straight -line at the folded edge; and this line divides the surface -of the paper, as it was originally spread out, into two -similar spaces. And that these spaces are similar so far as -the fold which separates them is concerned, appears from -this;--that these two parts coincide when the paper is -doubled. And thus a fold in a sheet of paper at the same -time illustrates the definition of a straight line according -to the above view, and confirms the axiom that two such -lines cannot inclose a space. - -If the separation of the two parts of space were made by any -other than a straight line; if, for instance, the paper were -cut by a concave line; then, on turning one of the parts -over, it is easy to see that the edge of one part being -concave one way, and the edge of the other part concave the -other way, these two lines would enclose a space. And each -of them would divide the whole space into two portions which -were not similar; for one portion would have a concave edge, -and the other a convex edge. Between any two points, there -might be innumerable lines drawn, some, convex one way, and -some, convex the other way; but the straight line is the -line which is not convex either one way or the other; it is -the single medium standard from which the others may deviate -in opposite directions. - -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 space. -But yet the above conceptions of the similar form of the two -parts of space on the two sides of a line, and of the form -of a line which is intermediate among all other forms, are -of so vague a nature, that they cannot fitly be made the -basis of our elementary geometry; and they are far more -conveniently replaced, as they have been in almost all -treatises of {104} geometry, by the axiom, that two straight -lines cannot inclose a space. - -7. But we may remark that, in what precedes, we have -considered space only under one of its aspects:--as a plane. -The sheet of paper which we assumed in order to illustrate -the nature of a straight line, was supposed to be perfectly -_plane_ or _flat_: for otherwise, by folding it, we might -obtain a line not straight. Now this assumption of a plane -appears to take for granted that very conception of a -straight line which the sheet was employed to illustrate; -for the definition of a plane given in the Elements of -Geometry is, that it is a surface on which lie all straight -lines drawn from one point of the surface to another. And -thus the explanation above given of the nature of a straight -line,--that it divides a plane space into similar portions -on each side,--appears to be imperfect or nugatory. - -To this we reply, 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 line. Any portion of solid space may -be divided into two portions by surfaces passing through any -given line or boundaries. And these surfaces may be convex -either on one side or on the other, and they admit of -innumerable changes from being convex on one side to being -convex on the other in any degree. So long as the surface is -convex either way, the two portions of space which it -separates are not similar, one having a convex and the other -a concave boundary. But there is a certain intermediate -position of the surface, in which position the two portions -of space which it divides have their boundaries exactly -similar. In this position, the surface is neither convex nor -concave, but plane. 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 divided,--and of its separating -such space into two portions, of which the boundaries, -though they are the same surface in two opposite positions, -are exactly similar. {105} - -Thus a plane is the simplest and most symmetrical boundary -by which a solid can be divided; and a straight line is the -simplest and most symmetrical boundary by which a plane can -be separated. These conceptions are obtained by considering -the boundaries of an interminable space, capable of -imaginary division in every direction. And as a limited -space may be separated into two parts by a plane, and a -plane again separated into two parts by a straight line, so -a line is divided into two portions by a point, which is the -common boundary of the two portions; the end of the one and -the beginning of the other portion having itself no -magnitude, form, or parts. - -8. The geometrical properties of planes and solids are -deducible from the first principles of the Elements, without -any new axioms; the definition of a plane above -quoted,--that all straight lines joining its points lie in -the plane,--being a sufficient basis for all reasoning upon -these subjects. And thus, the views which we have presented -of the nature of space being verbally expressed by means of -certain definitions and axioms, become the groundwork of a -long series of deductive reasoning, by which is established -a very large and curious collection of truths, namely, the -whole science of Elementary Plane and Solid Geometry. - -This science is one of indispensable use and constant -reference, for every student of the laws of nature; for the -relations of space and number are the _alphabet_ in which -those laws are written. But besides the interest and -importance of this kind which geometry possesses, it has a -great and peculiar value for all who wish to understand the -foundations of human knowledge, and the methods by which it -is acquired. For the student of geometry acquires, with a -degree of insight and clearness which the unmathematical -reader can but feebly imagine, a conviction that there are -necessary truths, many of them of a very complex and -striking character; and that a few of the most simple and -self-evident truths which it is possible for the mind of man -to apprehend, may, by systematic deduction, lead to the most -remote and unexpected results. {106} - -In pursuing such philosophical researches as that in which -we are now engaged, it is of great advantage to the -speculator to have cultivated to some extent the study of -geometry; since by this study he may become fully aware of -such features in human knowledge as those which we have -mentioned. By the aid of the lesson thus learned from the -contemplation of geometrical truths, we have been -endeavouriug to establish those further doctrines;--that -these truths are but different aspects of the same -Fundamental Idea, and that the grounds of the necessity -which these truths possess reside in the Idea from which -they flow, this Idea not being a derivative result of -experience, but its primary rule. When the reader has -obtained a clear and satisfactory view of these doctrines, -so far as they are applicable to our knowledge concerning -space, he has, we may trust, overcome the main difficulty -which will occur in following the course of the speculations -now presented to him. He is then prepared to go forwards -with us; to see over how wide a field the same doctrines are -applicable: and how rich and various a harvest of knowledge -springs from these seemingly scanty principles. - -But before we quit the subject now under our consideration, -we shall endeavour to answer some objections which have been -made to the views here presented; and shall attempt to -illustrate further the active powers which we have ascribed -to the mind. - - - -{{107}} -CHAPTER V. - -OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE DOCTRINES -STATED IN THE PREVIOUS CHAPTER.[3\2] - - -[Note 3\2: In order to render the present chapter more -intelligible, it may be proper to state briefly the -arguments which gave occasion to the review. After noticing -Stewart's assertions, that the certainty of mathematical -reasoning arises from its depending upon definitions, and -that mathematical truth is hypothetical; I urged,--that no -one has yet been able to construct a system of mathematical -truths by the aid of definitions alone; that a definition -would not be admissible or applicable except it agreed with -a distinct conception in the mind; that the definitions -which we employ in mathematics are not arbitrary or -hypothetical, but necessary definitions; that if Stewart had -taken as his examples of axioms the peculiar geometrical -axioms, his assertions would have been obviously erroneous; -and that the real foundation of the truths of mathematics is -the Idea of Space, which may be expressed (for purposes of -demonstration) partly by definitions and partly by axioms.] - -THE _Edinburgh Review_, No. cxxxv., contains a critique on a -work termed _The Mechanical Euclid_, in which opinions were -delivered to nearly the same effect as some of those stated -in the last chapter, and hereafter in Chapter xi. 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 (except, perhaps, one or two remarks -which have reference to mechanical ideas), it may serve to -illustrate the subject if I reply to the objections -directly, taking them as the reviewer has stated them. - -I. I had dissented from Stewart's assertion that -mathematical truth is hypothetical, or depends upon -arbitrary definitions; since we understand by an {108} -hypothesis a supposition, not only which we may make, but -may abstain from making, or may replace by a different -supposition; whereas the definitions and hypotheses of -geometry are necessarily such as they are, and cannot be -altered or excluded. The reviewer (p. 84) informs us that he -understands Stewart, when he speaks of hypotheses and -definitions being the foundation of geometry, to speak of -the hypothesis that real objects correspond to our -geometrical definitions. '_If_ a crystal be an exact -hexahedron, the geometrical properties of the hexahedron may -be predicated of that crystal.' To this I reply,--that such -hypotheses as this are the grounds of our applications of -geometrical truths to real objects, but can in no way be -said to be the foundation of the truths themselves;--that I -do not think that the sense which the reviewer gives was -Stewart's meaning;--but that if it was, this view of the use -of mathematics does not at all affect the question which -both he and I proposed to discuss, which was, the ground of -mathematical certainty. I may add, that whether a crystal be -an exact hexahedron, is a matter of observation and -measurement, not of definition. I think the reader can have -no difficulty in seeing how little my doctrine is affected -by the connexion on which the reviewer thus insists. I have -asserted that the proposition which affirms the square on -the diagonal of a rectangle to be equal to the squares on -two sides, does not rest upon arbitrary hypotheses; the -objector answers, that the proposition that the square on -the diagonal _of this page_ is equal to the squares on the -sides, depends upon the arbitrary hypothesis that the page -is a rectangle. Even if this fact were a matter of arbitrary -hypothesis, what could it have to do with the general -geometrical proposition? How could a single fact, observed -or hypothetical, affect a universal and necessary truth, -which would be equally true if the fact were false? If there -be nothing arbitrary or hypothetical in geometry till we -come to such steps in its application, it is plain that the -truths themselves are not hypothetical; which is the -question for us to decide. {109} - -2. The reviewer then (p. 85) considers the doctrine that -axioms as well as definitions are the foundations of -geometry; and here he strangely narrows and confuses the -discussion by making himself the advocate of Stewart, -instead of arguing the question itself. I had asserted that -some axioms are necessary as the foundations of mathematical -reasoning, in addition to the definitions. If Stewart did -not intend to discuss this question, I had no concern with -what he had said about axioms. But I had every reason to -believe that this was the question which Stewart did intend -to discuss. I conceive there is no doubt that he intended to -give an opinion upon the grounds of mathematical reasoning -in general. For he begins his discussions (_Elements_, vol. -ii. p. 38) by contesting Reid's opinion on this subject, -which is stated generally; and he refers again to the same -subject, asserting in general terms, that the first -principles of mathematics are not axioms but definitions. -If, then, afterwards, he made his proof narrower than his -assertion;--if having declared that no axioms are necessary, -he afterwards limited himself to showing that seven out of -twelve of Euclid's axioms are barren truisms, it was no -concern of mine to contest this assertion, which left my -thesis untouched. I had asserted that the proper geometrical -axioms (that two straight lines cannot inclose a space, and -the axiom about parallel lines) are indispensable in -geometry. What account the reviewer gives of these axioms we -shall soon see; but if Stewart allowed them to be axioms -necessary to geometrical reasoning, he overturned his own -assertion as to the foundations of such reasoning; and if he -said nothing decisive about these axioms, which are the -points on which the battle must turn, he left his assertion -altogether unproved; nor was it necessary for me to pursue -the war into a barren and unimportant corner, when the -metropolis was surrendered. The reviewer's exultation that I -have not contested the first seven axioms is an amusing -example of the self-complacent zeal of advocacy. - -3. But let us turn to the material point,--the proper -geometrical axioms. What is the reviewer's account of {110} -these? Which side of the alternative does he adopt? Do they -depend upon the definitions, and is he prepared to show the -dependence? Or are they superfluous, and can he erect the -structure of geometry without their aid? One of these two -courses, it would seem, he must take. For we both begin by -asserting the excellence of geometry as an example of -demonstrated truth. It is precisely this attribute which -gives an interest to our present inquiry. How, then, does -the reviewer explain this excellence on his views? How does -he reckon the foundation courses of the edifice which we -agree in considering as a perfect example of intellectual -building? - -I presume I may take, as his answer to this question, his -hypothetical statement of what Stewart would have said (p. -87), on the supposition that there had been, among the -foundations of geometry, self-evident indemonstrable truths: -although it is certainly strange that the reviewer should -not venture to make up his mind as to the truth or falsehood -of this supposition. If there were such truths they would -be, he says, 'legitimate filiations' of the definitions. -They would be involved in the definitions. And again he -speaks of the foundation of the geometrical doctrine of -parallels as a flaw, and as a truth which requires, but has -not received demonstration. And yet again, he tells us that -each of these supposed axioms (Euclid's twelfth, for -instance) is 'merely an indication of the point at which -geometry fails to perform that which it undertakes to -perform' (p. 91); and that in reality her truths are not yet -demonstrated. The amount of this is, that the geometrical -axioms are to be held to be _legitimate filiations_ of the -definitions, because though certainly true, they cannot be -proved from the definitions; that they are involved in the -definitions, although they cannot be evolved out of them; -and that rather than admit that they have any other origin -than the definitions, we are to proclaim that geometry has -failed to perform what she undertakes to perform. - -To this I reply--that I cannot understand what is meant by -'legitimate filiations' of principles, if the {111} phrase -do not mean consequences of such principles established by -rigorous and formal demonstrations;--that the reviewer, if -he claims any real signification for his phrase, must -substantiate the meaning of it by such a demonstration; he -must establish his 'legitimate filiation' by a genealogical -table in a satisfactory form. When this cannot be done, to -assert, notwithstanding, that the propositions are involved -in the definitions, is a mere begging the question; and to -excuse this defect by saying that geometry fails to perform -what she has promised, is to calumniate the character of -that science which we profess to make our standard, rather -than abandon an arbitrary and unproved assertion respecting -the real grounds of her excellence. I add, further, that if -the doctrine of parallel lines, or any other geometrical -doctrine of which we see the truth, with the most perfect -insight of its necessity, have not hitherto received -demonstration to the satisfaction of any school of -reasoners, the defect must arise from their erroneous views -of the nature of demonstrations, and the grounds of -mathematical certainty. - -4. I conceive, then, 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 science. I had -asserted further that these axioms supply what the -definitions leave deficient; and that they, along with -definitions, serve to present the idea of space under such -aspects that we can reason logically concerning it. To this -the reviewer opposes (p. 96) the common opinion that a -perfect definition is a complete explanation of a name, and -that the test of its perfection is, that we may substitute -the definition for the name wherever it occurs. I reply, -that my doctrine, that a definition expresses a part, but -not the whole, of the essential characters of an idea, is -certainly at variance with an opinion sometimes maintained, -that a definition merely explains a word, and should explain -it so fully that it may always replace it. The error of this -common opinion may, I think, be shown from considerations -such as these;--that if {112} we undertake to explain one -word by several, we may be called upon, on the same ground, -to explain each of these several by others, and that in this -way we can reach no limit nor resting-place;--that in point -of fact, it is not found to lead to clearness, but to -obscurity, when in the discussion of general principles, we -thus substitute definitions for single terms;--that even if -this be done, we cannot reason without conceiving what the -terms mean;--and that, in doing this, the relations of our -conceptions, and not the arbitrary equivalence of two forms -of expression, are the foundations of our reasoning. - -5. The reviewer conceives that some of the so-called axioms -are really definitions. The axiom, that 'magnitudes which -coincide with each other, that is, which fill the same -space, are equal,' is a definition of geometrical -_equality_: the axiom, that 'the whole is greater than its -part,' is a definition of _whole_ and _part_. But surely -there are very serious objections to this view. It would -seem more natural to say, if the former axiom is a -definition of the word _equal_, that the latter is a -definition of the word _greater_. And how can one short -phrase define two terms? If I say, 'the heat of summer is -greater than the heat of winter,' does this assertion define -anything, though the proposition is perfectly intelligible -and distinct? I think, then, that this attempt to reduce -these axioms to definitions is quite untenable. - -6. I have stated that a definition can be of no use, except -we can conceive the possibility and truth of the property -connected with it; and that if we do conceive this, we may -rightly begin our reasonings by stating the property as an -axiom; which Euclid does, in the case of straight lines and -of parallels. The reviewer inquires (p. 92), whether I am -prepared to extend this doctrine to the case of circles, for -which the reasoning is usually rested upon the -definition;--whether I would replace this definition by an -axiom, asserting the possibility of such a circle. To this I -might reply, that it is not at all incumbent upon me to -assent to such a change; for I have all along stated that it -is indifferent {113} whether the fundamental properties from -which we reason be exhibited as definitions or as axioms, -provided the necessity be clearly seen. But I am ready to -declare that I think the form of our geometry would be not -at all the worse, if, instead of the usual definition of a -circle,--'that it is a figure contained by one line, which -is called the circumference, and which is such, that all -straight lines drawn from a certain point within the -circumference are equal to one another,'--we were to -substitute an axiom and a definition, as follows:-- -_Axiom_. If a line be drawn so as to be at every point -equally distant from a certain point, this line will return -into itself or will be _one_ line including a space. -_Definition_. The space is called a _circle_, the line the -_circumference_, and the point the _center_. - -And this being done, it would be true, as the reviewer -remarks, that geometry cannot stir _one_ step without -resting on an axiom. And I do not at all hesitate to say, -that the above axiom, expressed or understood, is no less -necessary than the definition, and is tacitly assumed in -every proposition into which circles enter. - -7. I have, I think, now disposed of the principal objections -which bear upon the proper axioms of geometry. The -principles which are stated as the first seven axioms of -Euclid's _Elements_, need not, as I have said, be here -discussed. They are principles which refer, not to Space in -particular, but to Quantity in general: such, for instance, -as these; 'If equals be added to equals the wholes are -equal;'--'If equals be taken from equals the remainders are -equal.' But I will make an observation or two upon them -before I proceed. - -Both Locke and Stewart have spoken of these axioms as barren -truisms: as propositions from which it is not possible to -deduce a single inference: and the reviewer asserts that -they are not first principles, but laws of thought (p. 88). -To this last expression I am {114} willing to assent; but I -would add, that not only these, but all the principles which -express the fundamental conditions of our knowledge, may -with equal propriety be termed laws of thought; for these -principles depend upon our ideas, and regulate the active -operations of the mind, by which coherence and connexion are -given to its passive impressions. But the assertion that no -conclusions can be drawn from simple axioms, or laws of -human thought, which regard quantity, is by no means true. -The whole of arithmetic,--for instance, the rules for the -multiplication and division of large numbers, the rule for -finding a common measure, and, in short, a vast body of -theory respecting numbers,--rests upon no other foundation -than such axioms as have been just noticed, that if equals -be added to equals the wholes will be equal. And even when -Locke's assertion, that from these axioms no truths can be -deduced, is modified by Stewart and the reviewer, and -limited to _geometrical_ truths, it is hardly tenable -(although, in fact, it matters little to our argument -whether it is or no). For the greater part of the Seventh -Book of Euclid's _Elements_, (on Commensurable and -Incommensurable Quantities,) and the Fifth Book, (on -Proportion,) depend upon these axioms, with the addition -only of the definition or axiom (for it may be stated either -way) which expresses the idea of proportionality in numbers. -So that the attempt to disprove the necessity and use of -axioms, as principles of reasoning, fails even when we take -those instances which the opponents consider as the more -manifestly favourable to their doctrine. - -8. But perhaps the question may have already suggested -itself to the reader's mind, of what use can it be formally -to state such principles as these, (for example, that if -equals be added to equals the wholes are equal,) since, -whether stated or no, they will be assumed in our reasoning? -And how can such principles be said to be necessary, when -our proof proceeds equally well without any reference to -them? And the answer is, that it is precisely because these -are the {115} common principles of reasoning, which we -naturally employ without specially contemplating them, that -they require to be separated from the other steps and -formally stated, when we _analyse_ the demonstrations which -we have obtained. In every mental process many principles -are combined and abbreviated, and thus in some measure -concealed and obscured. In analysing these processes, the -combination must be resolved, and the abbreviation expanded, -and thus the appearance is presented of a pedantic and -superfluous formality. But that which is superfluous for -proof, is necessary for the analysis of proof. In order to -exhibit the conditions of demonstration distinctly, they -must be exhibited formally. In the same manner, in -demonstration we do not usually express every step in the -form of a syllogism, but we see the grounds of the -conclusiveness of a demonstration, by resolving it into -syllogisms. Neither axioms nor syllogisms are necessary for -conviction; but they are necessary to display the conditions -under which conviction becomes inevitable. The application -of a single one of the axioms just spoken of is so minute a -step in the proof, that it appears pedantic to give it a -marked place; but the very essence of demonstration consists -in this, that it is composed of an indissoluble succession -of such minute steps. The admirable circumstance is, that by -the accumulation of such apparently imperceptible advances, -we can in the end make so vast and so sure a progress. The -completeness of the analysis of our knowledge appears in the -smallness of the elements into which it is thus resolved. -The minuteness of any of these elements of truth, of axioms -for instance, does not prevent their being as essential as -others which are more obvious. And any attempt to assume one -kind of element only, when the course of our analysis brings -before us two or more kinds, is altogether unphilosophical. -Axioms and definitions are the proximate constituent -principles of our demonstrations; and the intimate bond -which connects together a definition and an axiom on the -same subject is not truly expressed {116} by asserting the -latter to be derived from the former. This bond of connexion -exists in the mind of the reasoner, in his conception of -_that_ to which both definition and axiom refer, and -consequently in the general Fundamental Idea of which that -conception is a modification. - - - -{{117}} -CHAPTER VI. - -OF THE PERCEPTION OF SPACE. - - -1. ACCORDING to the views above explained, certain of the -impressions of our senses convey to us the perception of -objects as existing in space; inasmuch as by the -constitution of our minds we cannot receive those -impressions otherwise than in a certain form, involving such -a manner of existence. But the question deserves to be -asked, _What_ are the impressions of sense by which we thus -become acquainted with space and its relations? And as we -have seen that this idea of space implies an act of the mind -as well as an impression on the sense, what manifestations -do we find of this activity of the mind, in our observation -of the external world? - -It is evident that sight and touch are the senses by which -the relations of space are perceived, principally or -entirely. It does not appear that an odour, or a feeling of -warmth or cold, would, independently of experience, suggest -to us the conception of a space surrounding us. But when we -_see_ objects, we see that they are extended and occupy -space; when we _touch_ them, we feel that they are in a -space in which we also are. We have before our eyes any -object, for instance, a board covered with geometrical -diagrams; and we distinctly perceive, by vision, those lines -of which the relations are the subjects of our mathematical -reasoning. Again, we see before us a solid object, a cubical -box for instance; we see that it is within reach; we stretch -out the hand and perceive by the touch that it has sides, -edges, corners, which we had already perceived by vision. {118} - -2. Probably most persons do not generally apprehend that -there is any material difference in these two cases;--that -there are any different acts of mind concerned in perceiving -by sight a mathematical diagram upon paper, and a solid cube -lying on a table. Yet it is not difficult to show that, in -the latter case at least, the perception of the shape of the -object is not immediate. A very little attention teaches us -that there is an act of judgment as well as a mere -impression of sense requisite, in order that we may see any -solid object. For there is no visible appearance which is -inseparably connected with solidity. If a picture of a cube -be rightly drawn, in perspective and skilfully shaded, the -impression upon the sense is the same as if it were a real -cube. The picture may be mistaken for a solid object. But it -is clear that, in this case, the solidity is given to the -object by an act of mental judgment. All that is seen is -outline and shade, figures and colours on a flat board. The -solid angles and edges, the relation of the faces of the -figure by which they form a cube, are matters of inference. -This, which is evident in the case of the pictured cube, is -true in all vision whatever. We see a scene before us on -which are various figures and colours, but the eye cannot -see more. It sees length and breadth, but no third -dimension. In order to know that there are solids, we must -infer as well as see. And this we do readily and constantly; -so familiarly, indeed, that we do not perceive the -operation. Yet we may detect this latent process in many -ways; for instance, by attending to cases in which the habit -of drawing such inferences misleads us. Most persons have -experienced this delusion in looking at a scene in a -theatre, and especially that kind of scene which is called a -_diorama_, when the interior of a building is represented. -In these cases, 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 form, instead -of a flat painted canvass. Here, at least, the space is our -own creation; but yet here, it is {119} 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 us. And the act by which we thus create -space of three dimensions out of visible extent of length -and breadth, is constantly and imperceptibly going on. We -are perpetually interpreting in this manner the language of -the visible world. From the appearances of things which we -directly see, we are constantly inferring that which we -cannot directly see,--their distance from us, and the -position of their parts. - -3. The characters which we thus interpret are various. They -are, for instance, the visible forms, colours, and shades of -the parts, understood according to the maxims of -perspective; (for of perspective every one has a practical -knowledge, as every one has of grammar;) the effort by which -we fix both our eyes on the same object, and adjust each eye -to distinct vision; and the like. The right interpretation -of the information which such circumstances give us -respecting the true forms and distances of things, is -gradually learned; the lesson being begun in our earliest -infancy, and inculcated upon us every hour during which we -use our eyes. The completeness with which the lesson is -mastered is truly admirable; for we forget that our -conclusion is obtained indirectly, and mistake a judgment on -evidence for an intuitive perception. We see the breadth of -the street, as clearly and readily as we see the house on -the other side of it; and we see the house to be square, -however obliquely it be presented to us. This, however, by -no means throws any doubt or difficulty on the doctrine that -in all these cases we do interpret and infer. The rapidity -of the process, and the unconsciousness of the effort, are -not more remarkable in this case than they are when we -understand the meaning of the speech which we hear, or of -the book which we read. In these latter cases we merely hear -noises or see black marks; but we make, out of these -elements, thought and feeling, without being aware of the -act by which we do so. And by an exactly similar process we -see a variously-coloured {120} expanse, and collect from it -a space occupied by solid objects. In both cases the act of -interpretation is become so habitual that we can hardly stop -short at the mere impression of sense. - -4. But yet there are various ways in which we may satisfy -ourselves that these two parts of the process of seeing -objects are distinct. To separate these operations is -precisely the task which the artist has to execute, in -making a drawing of what he sees. He has to recover the -consciousness of his real and genuine sensations, and to -discern the lines of objects as they appear. This at first -he finds difficult; for he is tempted to draw what he knows -of the forms of visible objects, and not what he sees: but -as he improves in his art, he learns to put on paper what he -sees only, separated from what he infers, in order that thus -the inference, and with it a conception like that of the -reality, may be left to the spectator. And thus the natural -process of vision is the habit of seeing that which cannot -be seen; and the difficulty of the art of drawing consists -in learning not to see more than is visible. - -5. But again; even in the simplest drawing we exhibit -something which we do not see. However slight is our -representation of objects, it contains something which we -create for ourselves. For we draw an _outline_. Now an -outline has no existence in nature. There are no visible -lines presented to the eye by a group of figures. We -separate each figure from the rest, and the boundary by -which we do this is the outline of the figure; and the like -may be said of each member of every figure. A painter of our -own times has made this remark in a work upon his art[4\2]: -'The effect which natural objects produce upon our sense of -vision is that of a number of parts, or distinct masses of -form and colour, and not of lines. But when we endeavour to -represent by painting the objects which are before us, or -which invention supplies to our minds, {121} the first and -the simplest means we resort to is this picture, by which we -separate the form of each object from those that surround -it, marking its boundary, the extreme extent of its -dimensions in every direction, as impressed on our vision: -and this is termed drawing its outline.' - -[Note 4\2: Phillips _On Painting._] - -6. Again, 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 space, the -impressions of sense being merely subservient to this act. -If we look at a medal through a glass which inverts it, we -see the figures upon it become concave depressions instead -of projecting convexities; for the light which illuminates -the nearer side of the convexity will be transferred to the -opposite side by the apparent inversion of the medal, and -will thus imply a hollow in which the side nearest the light -gathers the shade. Here our decision as to which part is -nearest to us, has reference to the side from which the -light comes. In other cases the decision is more -spontaneous. If we draw black outlines, such as represent -the edges of a cube seen in perspective, certain of the -lines will cross each other; and we may make this cube -appear to assume two different positions, 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 cross. Here an act of the will, operating upon -the same sensible image, gives us two cubes, occupying two -entirely different positions. Again, many persons may have -observed that when a windmill in motion at a distance from -us, (so that the outline of the sails only is seen,) stands -obliquely to the eye, we may, by an effort of thought, make -the obliquity assume one or the other of two positions; and -as we do this, the sails, which in one instance appear to -turn from right to left, in the other case turn from left to -right. A person a little familiar with this mental effort, -can invert the motion as often as he pleases, so long as the -conditions of form and light do not offer a manifest -contradiction to either position. {122}. - -Thus we have these abundant and various manifestations of -the activity of the mind, in the process by which we collect -from vision the relations of solid space of three -dimensions. But we must further make some remarks on the -process by which we perceive mere visible figure; and also, -on the mode in which we perceive the relations of space by -the touch; and first, of the latter subject. - -7. The opinion above illustrated, that our sight does not -give us a direct knowledge of the relations of solid space, -and that this knowledge is acquired only by an inference of -the mind, was first clearly taught by the celebrated Bishop -Berkeley[5\2], and is a doctrine now generally assented to -by metaphysical speculators. - -[Note 5\2: _Theory of Vision._] - -But does the sense of _touch_ give us directly a knowledge -of space? This is a question which has attracted -considerable notice in recent times; and new light has been -thrown upon it in a degree which is very remarkable, when we -consider that the philosophy of perception has been a -prominent subject of inquiry from the earliest times. Two -philosophers, advancing to this inquiry from different -sides, the one a metaphysician, the other a physiologist, -have independently arrived at the conviction that the long -current opinion, according to which we acquire a knowledge -of space by the sense of touch, is erroneous. And the -doctrine which they teach instead of the ancient errour, has -a very important bearing upon the principle which we are -endeavouring to establish,--that our knowledge of space and -its properties is derived rather from the active operations -than from the passive impressions of the percipient mind. - -Undoubtedly the persuasion that we acquire a knowledge of -form by the touch is very obviously suggested by our common -habits. If we wish to know the form of any body in the dark, -or to correct the impressions conveyed by sight, when we -suspect them to be false, we have only, it seems to us, at -least at first, to stretch forth the hand and touch the -object; and we learn its {123} shape with, no chance of -errour. In these cases, form appears to be as immediate a -perception of the sense of touch, as colour is of the sense -of sight. - -8. But is this perception really the result of the passive -sense of touch merely? Against such an opinion Dr. Brown, -the metaphysician of whom I speak, urges[6\2] that the -feeling of touch alone, when any object is applied to the -hand, or any other part of the body, can no more convey the -conception of form or extension, than the sensation of an -odour or a taste can do, except we have already some -knowledge of the relative position of the parts of our -bodies; that is, except we are already in possession of an -idea of space, and have, in our minds, referred our limbs to -their positions; which is to suppose the conception of form -already acquired. - -[Note 6\2: _Lectures_, Vol. i. p. 459, (1824).] - -9. By what faculty then do we originally acquire our -conceptions of the relations of position? Brown answers by -the _muscular sense_; that is, by the conscious exertions of -the various muscles by which we move our limbs. When we feel -out the form and position of bodies by the hand, our -knowledge is acquired, not by the mere touch of the body, -but by perceiving the course the fingers must take in order -to follow the surface of the body, or to pass from one body -to another. We are conscious of the slightest of the -volitions by which we thus feel out form and place; we know -whether we move the finger to the right or left, up or down, -to us or from us, through a large or a small space; and all -these conscious acts are bound together and regulated in our -minds by an idea of an extended space in which they are -performed. That this idea of space is not borrowed from the -sight, and transferred to the muscular feelings by habit, is -evident. For a man born blind can feel out his way with his -staff, and has his conceptions of position determined by the -conditions of space, no less than one who has the use of his -eyes. And the muscular consciousness which reveals to us the -position of objects and parts of objects, {124} when we feel -them out by means of the hand, shows itself in a thousand -other ways, and in all our limbs: for our habits of -standing, walking, and all other attitudes and motions, are -regulated by our feeling of our position and that of -surrounding objects. And thus, we cannot touch any object -without learning something respecting its position; not that -the sense of touch directly conveys such knowledge; but we -have already learnt, from the muscular sense, constantly -exercised, the position of the limb which the object thus -touches. - -10. The justice of this distinction will, I think, be -assented to by all persons who attend steadily to the -process itself, and might be maintained by many forcible -reasons. Perhaps one of the most striking evidences in its -favour is that, as I have already intimated, it is the -opinion to which another distinguished philosopher, Sir -Charles Bell, has been led, reasoning entirely upon -physiological principles. From his researches it resulted -that besides the nerves which convey the impulse of the will -from the brain to the muscle, by which every motion of our -limbs is produced, there is another set of nerves which -carry back to the brain a sense of the condition of the -muscle, and thus regulate its activity; and give us the -consciousness of our position and relation to surrounding -objects. The motion of the hand and fingers, or the -consciousness of this motion, must be combined with the -sense of touch properly so called, in order to make an inlet -to the knowledge of such relations. This consciousness of -muscular exertion, which he has called a sixth sense[7\2], -is our guide, Sir C. Bell shows, in the common practical -government of our motions; and he states that having given -this explanation of perception as a physiological doctrine, -he had afterwards with satisfaction seen it confirmed by Dr. -Brown's speculations. - -[Note 7\2: _Bridgewater Treatise_, p. 195. _Phil. Trans._ -1826, Pt. ii. p. 167.] - -11. Thus it appears that our consciousness of the relations -of space is inseparably and fundamentally connected with our -own actions in space. We perceive {125} only while we act; -our sensations require to be interpreted by our volitions. -The apprehension of extension and figure is far from being a -process in which we are inert and passive. We draw lines -with our fingers; we construct surfaces by curving our -hands; we generate spaces by the motion of our arms. When -the geometer bids us form lines, or surfaces, or solids by -motion, he intends his injunction to be taken as -hypothetical only; we need only conceive such motions. But -yet this hypothesis represents truly the origin of our -knowledge; we perceive spaces by motion at first, as we -conceive spaces by motion afterwards:--or if not always by -actual motion, at least by potential. If we perceive the -length of a staff by holding its two ends in our two hands -without running the finger along it, 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 -conscious. Even in the simplest case, our perceptions are -derived not from the touch, but from the sixth sense; and -this sixth sense at least, whatever may be the case with the -other five, implies an active mind along with the passive sense. - -12. Upon attentive consideration, it will be clear that a -large portion of the perceptions respecting space which -appear at first to be obtained by sight alone, are, in fact, -acquired by means of this sixth sense. Thus we consider the -visible sky as a single surface surrounding us and returning -into itself, and thus forming a hemisphere. But such a mode -of conceiving an object of vision could never have occurred -to us, if we had not been able to turn our heads, to follow -this surface, to pursue it till we find it returning into -itself. And when we have done this, we necessarily present -it to ourselves as a concave inclosure within which we are. -The sense of sight alone, without the power of muscular -motion, could not have led us to view the sky as a vault or -hemisphere. Under such circumstances, we should have -perceived only what was presented to the eye in one -position; and if different appearances had been presented in -succession, we could {126} not have connected them as parts -of the same picture, for want of any perception of their -relative position. They would have been so many detached and -incoherent visual sensations. The muscular sense connects -their parts into a whole, making them to be only different -portions of one universal scene[8\2]. - -[Note 8\2: It has been objected to this view that we might -obtain a conception of the sky as a hemisphere, by being -ourselves turned round, (as on a music-stool, for instance,) -and thus seeing in succession all parts of the sky. But this -assertion I conceive to be erroneous. By being thus turned -round, we should see a number of pictures which we should -put together as parts of a plane picture; and when we came -round to the original point, we should have no possible -means of deciding that it was the _same_ point: it would -appear only as a _repetition_ of the picture. That sight, of -itself, can give us only a plane picture, the doctrine of -Berkeley, appears to be indisputable; and, no less so, 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 body. We can see length and breadth -with our eyes, but we must thrust out our arm towards the -flat surface, in order that we may, in our thoughts, combine -a third dimension with the other two.] - -13. These considerations point out the fallacy of a very -curious representation made by Dr. Reid, of the convictions -to which man would be led, if he possessed vision without -the sense of touch. To illustrate this subject, Reid uses -the fiction of a nation whom he terms the _Idomenians_, who -have no sense except that of sight. He describes their -notions of the relations of space as being entirely -different from ours. The axioms of their geometry are quite -contradictory to our axioms. For example, it is held to be -self-evident among them that two straight lines which -intersect each other once, must intersect a second time; -that the three angles of any triangle are _greater_ than two -right angles; and the like. These paradoxes are obtained by -tracing the relations of lines on the surface of a concave -sphere, which surrounds the spectator, and on which all -visible appearances may be supposed to be presented to him. -But from what is said above it appears that the notion of -such a sphere, and such a connexion of visible objects which -are seen in different {127} directions, cannot be arrived at -by sight alone. When the spectator combines in his -conception the relations of long-drawn lines and large -figures, as he sees them by turning his head to the right -and to the left, upwards and downwards, he ceases to be an -Idomenian. And thus our conceptions of the properties of -space, derived through the exercise of one mode of -perception, are not at variance with those obtained in -another way; but all such conceptions, however produced or -suggested, are in harmony with each other; being, as has -already been said, only different aspects of the same idea. - -14. If our perceptions of the position of objects around us -do not depend on the sense of vision alone, but on the -muscular feeling brought into play when we turn our head, it -will obviously follow that the same is true when we turn the -eye instead of the head. And thus we may learn the form of -objects, not by looking at them with a fixed gaze, but by -following the boundary of them with the eye. While the head -is held perfectly still, the eye can rove along the outlines -of visible objects, scrutinize each point in succession, and -leap from one point to another; each such act being -accompanied by a muscular consciousness which makes us aware -of the direction in which the look is travelling. And we may -thus gather information concerning the figures and places -which we trace out with the visual ray, as the blind man -learns the forms of things which he traces out with his -staff, being conscious of the motions of his hand. - -15. This view of the mode in which the eye perceives -position, which is thus supported by the analogy of other -members employed for the same purpose, is further confirmed -by Sir Charles Bell by physiological reasons. He teaches us -that[9\2] when an object is seen we employ two senses: there -is an impression on the retina; but we receive also the idea -of position or relation in space, which it is not the office -of the retina to give, by our consciousness of the efforts -of the voluntary {128} muscles of the eye: and he has traced -in detail the course of the nerves by which these muscles -convey their information. The constant _searching_ motion of -the eye, as he terms it[10\2], is the means by which we -become aware of the position of objects about us. - -[Note 9\2: _Phil. Trans._ 1823. On the Motions of the Eye.] - -[Note 10\2: _Bridgewater Treatise_, p. 282. I have adopted, -in writing the above, the views and expressions of Sir -Charles Bell. The essential part of the doctrine there -presented is, that the eye constantly makes efforts to turn, -so that the image of an object to which our attention is -drawn, shall fall upon a certain particular point of the -retina; and that when the image falls upon any other point, -the eye turns away from this oblique into the direct -position. 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_ point, but that it is -the point of _greatest distinctness_ of vision. They urge -that a small star, which disappears when the eye is turned -full upon it, may often be seen by looking a little away -from it: and hence, they infer that the parts of the retina -removed from the spot of direct vision, are more sensible -than it is. The facts are very curious, however they be -explained, but they do not disturb the doctrine delivered in -the text.] - -16. It is not to our present purpose to follow the -physiology of this subject; but we may notice that Sir C. -Bell has examined the special circumstances which belong to -this operation of the eye. 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 spot_; being that part which is _most -distinctly_ sensible to the impressions of light and colour. -This part, indeed, is not a spot of definite size and form, -for it appears that proceeding from a certain point of the -retina, the distinct sensibility diminishes on every side by -degrees. 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 directed. We are uneasy and impatient till the eye is -turned so that this is effected. And as our attention is -transferred from point to point of the scene before us, the -eye, and this point of the eye in particular, travel along -with the thoughts; and the muscular sense, which tells us of -these movements of the organ of {129} vision, conveys to us -a knowledge of the forms and places which we thus -successively survey. - -17. 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 forms. We apply to them -not merely adjectives of form, but verbs of motion. An -abrupt hill _starts_ out of the plain; a beautiful figure -has a _gliding_ outline. We have - The windy summit, wild and high, - Roughly _rushing_ on the sky. -These terms express the course of the eye as it follows the -lines by which such forms are bounded and marked. In like -manner another modern poet[11\2] says of Soracte, that it - From out the plain - _Heaves_ like a long-swept wave about to break, - And on the curl _hangs pausing_. - -[Note 11\2: Byron, _Ch. Har._ vi. st. 75.] - -Thus the muscular sense, which is inseparably connected with -an act originating in our own mind, not only gives us all -that portion of our perceptions of space in which we use the -sense of touch, but also, at least in a great measure, -another large portion of such perceptions, in which we -employ the sense of sight. 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 -act, governed by conditions depending on its own nature; so -it now appears that our _perceptions_ of visible figure are -not obtained without an act performed under the same -conditions. The sensations of touch and sight are -subordinated to an idea which is the basis of our -speculative knowledge concerning space and its relations; -and this same idea is disclosed to our consciousness by its -practically regulating our intercourse with the external world. - -By considerations such as have been adduced and referred to, -it is proved beyond doubt, that in a great {130} number of -cases our knowledge of form and position is acquired from -the muscular sense, and not from sight directly:--for -instance, 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[12\2]. - -[Note 12\2: The expression in the first edition was 'large -objects and extensive spaces.' In the text as now given, I -state a definite size and extent, within which the sight by -itself can judge of position and figure. - -The doctrine, that we require the assistance of the muscular -sense to enable us to perceive space of three dimensions, is -not at all inconsistent with this other doctrine, that -within the space which is seen by the fixed eye, we perceive -the relative positions of points directly by vision, and -that, consequently, we have a perception of _visible -figure_. - -Sir Charles Bell has said, (_Phil. Trans._ 1823, p. 181,) -'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 -objects, if the sense of muscular activity be excluded which -accompanies the motion of the eyeball.' But surely we should -have no difficulty in perceiving the relation of the sides -and angles of a small triangle, placed before the eye, even -if the muscles of the eyeball were severed. This subject is -resumed b. iv. c. ii. sect. 11.] - -We now quit the consideration of the properties of Space, -and consider the Idea of Time. - - - -{{131}} -CHAPTER VII. - -OF THE IDEA OF TIME. - - -1. RESPECTING the Idea of Time, we may make several of the -same remarks which we made concerning the idea of space, in -order to show that it is not borrowed from experience, but -is a bond of connexion among the impressions of sense, -derived from a peculiar activity of the mind, and forming a -foundation both of our experience and of our speculative -knowledge. - -Time is not a notion obtained by experience. Experience, -that is, the impressions of sense and our consciousness of -our thoughts, gives us various perceptions; and different -successive perceptions considered together exemplify the -notion of change. But this very connexion of different -perceptions,--this successiveness,--presupposes that the -perceptions exist _in time_. That things happen either -together, or one after the other, is intelligible only by -assuming time as the condition under which they are -presented to us. - -Thus time is a necessary condition in the presentation of -all occurrences to our minds. We cannot conceive this -condition to be taken away. We can conceive time to go on -while nothing happens in it; but we cannot conceive anything -to happen while time does not go on. - -It is clear from this that time is not an impression derived -from experience, in the same manner in which we derive from -experience our information concerning the objects which -exist, and the occurrences which take place in time. The -objects of experience can easily be conceived to be, or not -to be:--to be absent as well as present. Time always is, and -always is {132} present, and even in our thoughts we cannot -form the contrary supposition. - -2. Thus time is something distinct from the _matter_ or -substance of our experience, and may be considered as a -necessary _form_ which that matter (the experience of -change) must assume, in order to be an object of -contemplation to the mind. Time is one of the necessary -conditions under which we apprehend the information which -our senses and consciousness give us. By considering time as -a form which belongs to our power of apprehending -occurrences and changes, and under which alone all such -experience can be accepted by the mind, we explain the -necessity, which we find to exist, of conceiving all such -changes as happening in time; and we thus see that time is -not a property perceived as existing in objects, or as -conveyed to us by our senses; but a condition impressed upon -our knowledge by the constitution of the mind itself; -involving an act of thought as well as an impression of sense. - -3. We showed that space is an idea of the mind, or form of -our perceiving power, independent of experience, by pointing -out that we possess necessary and universal truths -concerning the relations of space, which could never be -given by means of experience; but of which the necessity is -readily conceivable, if we suppose them to have for their -basis the constitution of the mind. There exist also -respecting number, many truths absolutely necessary, -entirely independent of experience and anterior to it; and -so far as the conception of number depends upon the idea of -time, the same argument might be used to show that the idea -of time is not derived from experience, but is a result of -the native activity of the mind: but we shall defer all -views of this kind till we come to the consideration of Number. - -4. Some persons have supposed that we obtain the notion of -time from the perception of motion. But it is clear that the -perception of motion, that is, change of place, presupposes -the conception of time, and is not capable of being -presented to the mind in any other {133} way. If we -contemplate the same body as being in different places at -different times, and connect these observations, we have the -conception of motion, which thus presupposes the necessary -conditions that existence in time implies. And thus we see -that it is possible there should be necessary truths -concerning all Motion, and consequently, concerning those -motions which are the objects of experience; but that the -source of this necessity is the Ideas of Time and Space, -which, being universal conditions of knowledge residing in -the mind, afford a foundation for necessary truths. - - - -{{134}} -CHAPTER VIII. - -OF SOME PECULIARITIES OF THE IDEA OF TIME. - - -1. THE Idea of Time, like the Idea of Space, offers to our -notice some characters which do not belong to our -fundamental ideas generally, but which are deserving of -remark. These characters are, in some respects, closely -similar with regard to Time and to Space, while, in other -respects, the peculiarities of these two ideas are widely -different. We shall point out some of these characters. - -Time is not a general _abstract_ notion collected from -experience; as, for example, a certain general conception of -the relations of things. For we do not consider particular -_times_ as examples of Time in general, (as we consider -particular causes to be examples of Cause,) but we conceive -all particular times to be parts of a single and endless -Time. This continually-flowing and endless time is what -offers itself to us when we contemplate any series of -occurrences. All actual and possible times exist as Parts, -in this original and general Time. And since all particular -times are considered as derivable from time in general, it -is manifest that the notion of time in general cannot be -derived from the notions of particular times. The notion of -time in general is therefore not a general conception -gathered from experience. - -2. Time is infinite. Since all actual and possible times -exist in the general course of time, this general time must -be infinite. All limitation merely divides, and does not -terminate, the extent of absolute time. Time has no -beginning and no end; but the beginning and the end of every -other existence takes place in it. - -3. Time, like space, is not only a form of perception, but -of _intuition_. We contemplate events as {135} taking place -_in_ time. We consider its parts as added to one another, -and events as filling a larger or smaller extent of such -parts. The time which any event takes up is the sum of all -such parts, and the relation of the same to time is fully -understood when we can clearly see what portions of time it -occupies, and what it does not. Thus the relation of known -occurrences to time is perceived by intuition; and time is a -form of intuition of the external world. - -4. Time is conceived as a quantity of one dimension; it has -great analogy with a line, but none at all with a surface or -solid. Time may be considered as consisting of a series of -instants, which are before and after one another; and they -have no other relation than this, of _before_ and _after_. -Just the same would be the case with a series of points -taken along a line; each would be after those on one side of -it, and before those on another. Indeed the analogy between -time, and space of one dimension, is so close, that the same -terms are applied to both ideas, and we hardly know to which -they originally belong. Times and lines are alike called -_long_ and _short_; we speak of the _beginning_ and _end_ of -a line; of a _point_ of time, and of the _limits_ of a -portion of duration. - -5. But, as has been said, there is nothing in time which -corresponds to more than one dimension in space, and hence -nothing which has any obvious analogy with figure. Time -resembles a line indefinitely extended both ways; all -partial times are portions of this line; and no mode of -conceiving time suggests to us a line making any angle with -the original line, or any other combination which might give -rise to figures of any kind. The analogy between time and -space, which in many circumstances is so clear, here -disappears altogether. Spaces of two and of three -dimensions, planes and solids, have nothing to which we can -compare them in the conceptions arising out of time. - -6. As figure is a conception solely appropriate to space, -there is also a conception which peculiarly belongs to time, -namely, the conception of recurrence of times similarly -marked; or, as it may be termed, {136} _rhythm_, using this -word in a general sense. The term rhythm is most commonly -used to designate the recurrence of times marked by the -syllables of a verse, or the notes of a melody: 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 sense. The forms of such recurrence are innumerable. -Thus in such a line as - Quádrupedánte putrém sonitú quatit úngula cámpum, -we have alternately one long or forcible syllable, and two -short or light ones, recurring over and over. In like manner -in our own language, in the line - At the clóse of the dáy when the hámlet is still, -we have two light and one strong syllable repeated four -times over. Such repetition is the essence of versification. -The same kind of rhythm is one of the main elements of -music, with this difference only, that in music the forcible -syllables are made so for the purposes of rhythm by their -length only or principally; for example, if either of the -above lines were imitated by a melody in the most simple and -obvious manner, each strong syllable would occupy exactly -twice as much time as two of the weaker ones. Something very -analogous to such rhythm may be traced in other parts of -poetry and art, which we need not here dwell upon. But in -reference to our present subject, we may remark that by the -introduction of such rhythm, the flow of time, which appears -otherwise so perfectly simple and homogeneous, admits of an -infinite number of varied yet regular modes of progress. All -the kinds of versification which occur in all languages, and -the still more varied forms of recurrence of notes of -different lengths, which are heard in all the varied strains -of melodies, are only examples of such modifications, or -configurations as we may call them, of time. They involve -relations of various portions of time, as figures involve -relations of various portions of space. But yet the analogy -between rhythm and figure is by no means very close; for in -rhythm we have relations of quantity alone in the parts of -time, whereas in figure we have {137} relations not only of -quantity, but of a kind altogether different,--namely, of -position. On the other hand, a _repetition_ of similar -elements, which does not necessarily occur in figures, is -quite essential in order to impress upon us that measured -progress of time of which we here speak. And thus the ideas -of time and space have each its peculiar and exclusive -relations; position and figure belonging only to space, -while repetition and rhythm are appropriate to time. - -7. One of the simplest forms of recurrence is _alternation_, -as when we have alternate strong and slight syllables. For -instance,-- - Awáke, aríse, or bé for éver fáll'n. -Or without any subordination, as when we reckon numbers, and -call them in succession, _odd_, _even_, _odd_, _even_. - -8. But the simplest of all forms of recurrence is that which -has no variety;--in which a series of units, each considered -as exactly similar to the rest, succeed each other; as -_one_, _one_, _one_, and so on. In this case, however, we -are led to consider each unit with reference to all that -have preceded; and thus the series _one_, _one_, _one_, and -so forth, becomes _one_, _two_, _three_, _four_, _five_, and -so on; a series with which all are familiar, and which may -be continued without limit. - -We thus collect from that repetition of which time admits, -the conception of _Number_. - -9. The relations of position and figure are the subject of -the science of geometry; and are, as we have already said, -traced into a very remarkable and extensive body of truths, -which rests for its foundations on axioms involved in the -Idea of Space. There is, in like manner, a science of great -complexity and extent, which has its foundation in the Idea -of Time. But this science, as it is usually pursued, applies -only to the conception of Number, which is, as we have said, -the simplest result of repetition. This science is -_Theoretical Arithmetic_, or the speculative doctrine of the -properties and relations of numbers; and we must say a few -words concerning the principles which it is requisite to -assume as the basis of this science. - - - -{{138}} -CHAPTER IX. - -OF THE AXIOMS WHICH RELATE TO NUMBER. - - -1. THE foundations of our speculative knowledge of the -relations and properties of Number, as well as of Space, are -contained in the mode in which we represent to ourselves the -magnitudes which are the subjects of our reasonings. To -express these foundations in axioms in the case of number, -is a matter requiring some consideration, for the same -reason as in the case of geometry; that is, because these -axioms are principles which we assume as true, without being -aware that we have made any assumption; and we cannot, -without careful scrutiny, determine when we have stated, in -the form of axioms, all that is necessary for the formation -of the science, and no more than is necessary. We will, -however, attempt to detect the principles which really must -form the basis of theoretical arithmetic. - -2. Why is it that three and two are equal to four and one? -Because if we look at five things of any kind, we see that -it is so. The five are four and one; they are also three and -two. The truth of our assertion is involved in our being -able to conceive the number five at all. We perceive this -truth by _intuition_, for we cannot see, or imagine we see, -five things, without perceiving also that the assertion -above stated is true. - -But how do we state in words this fundamental principle of -the doctrine of numbers? Let us consider a very simple case. -If we wish to show that seven and two are equal to four and -five, we say that seven are four and three, _therefore_ -seven and two are four and three and two; and because three -and two are {139} five, this is four and five. Mathematical -reasoners justify the first inference (marked by the -conjunctive word _therefore_), by saying that "When equals -are added to equals the wholes are equal," and that thus, -since seven is equal to three and four, if we add two to -both, seven and two are equal to four and three and two. - -3. Such _axioms_ as this, that when equals are added to -equals the wholes are equal, are, in fact, expressions of -the general condition of intuition, by which a whole is -contemplated as made up of parts, and as identical with the -aggregate of the parts. And a yet more general form in which -we might more adequately express this condition of intuition -would be this; that 'Two magnitudes are equal when they can -be divided into parts which are equal, each to each.' Thus -in the above example, seven and two are equal to four and -five, because each of the two sums can be divided into the -parts, four, three, and two. - -4. In all these cases, a person who had never seen such -axioms enunciated in a verbal form would employ the same -reasoning as a practised mathematician, in order to satisfy -himself that the proposition was true. The steps of the -reasoning, being seen to be true by intuition, would carry -an entire conviction, whether or not the argument were made -verbally complete. Hence the axioms may appear superfluous, -and on this account such axioms have often been spoken -contemptuously of, as empty and barren assertions. In fact, -however, although they cannot supply the deficiency of the -clear intuition of number and space in the reasoner himself, -and although when he possesses such a faculty, he will -reason rightly if he have never heard of such axioms, they -still have their place properly at the beginning of our -treatises on the science of quantity; since they express, as -simply as words can express, those conditions of the -intuition of magnitudes on which all reasoning concerning -quantity must be based; and are necessary when we want, not -only to see the truth of the elementary reasonings on these -subjects, but to put such reasonings in a formal and logical -shape. {140} - -5. We have considered the above-mentioned axioms as the -basis of all arithmetical operations of the nature of -_addition_. But it is easily seen that the same principle -may be carried into other cases; as for instance, -_multiplication_, which is merely a repeated addition, and -admits of the same kind of evidence. Thus five times three -are equal to three times five; why is this? If we arrange -fifteen things in five rows of three, it is seen by looking, -or by imaginary looking, which is _intuition_, that they may -also be taken as three rows of five. And thus the principle -that those wholes are equal which can be resolved into the -same partial magnitudes, is immediately applicable in this -as in the other case. - -6. We may proceed to higher numbers, and may find ourselves -obliged to use artificial nomenclature and notation in order -to represent and reckon them; but the reasoning in these -cases also is still the same. And the usual artifice by -which our reasoning in such instances is assisted is, that -the number which is the root of our scale of notation (which -is _ten_ in our usual system), is alternately separated into -parts and treated as a single thing. Thus 47 and 35 are 82; -for 47 is four tens and seven; 35 is three tens and five; -whence 47 and 35 are seven tens and twelve; that is, 7 tens, -1 ten, and 2; which is 8 tens and 2, or 82. The like -reasoning is applicable in other cases. 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 -propositions, we have, in the principles just noticed, the -foundation of the whole of Theoretical Arithmetic. - - - -{{141}} -CHAPTER X. - -OF THE PERCEPTION OF TIME AND NUMBER. - - -1. OUR perception of the passage of time involves a series -of acts of memory. This is easily seen and assented to, when -large intervals of time and a complex train of occurrences -are concerned. But since memory is requisite in order to -apprehend time in such cases, we cannot doubt that the same -faculty must be concerned in the shortest and simplest cases -of succession; for it will hardly be maintained that the -process by which we contemplate the progress of time is -different, when small, and when large intervals are -concerned. If memory be absolutely requisite to connect two -events which begin and end a day, and to perceive a tract of -time between them, it must be equally indispensable to -connect the beginning and end of a minute, or a second; -though in this case the effort may be smaller, and -consequently more easily overlooked. In common cases, we are -unconscious of the act of thought by which we recollect the -preceding instant, though we perceive the effort when we -recollect some distant event. And this is analogous to what -happens in other instances. Thus, we walk without being -conscious of the volitions by which we move our muscles; -but, in order to leap, a distinct and manifest exertion of -the same muscles is necessary. Yet no one will doubt that we -walk as well as leap by an act of the will exerted through -the muscles; and in like manner, our consciousness of small -as well as large intervals of time involves something of the -nature of an act of memory. - -2. But this constant and almost imperceptible kind of -memory, by which we connect the beginning and {142} end of -each instant as it passes, may very fitly be distinguished -in common cases from manifest acts of recollection, although -it may be difficult or impossible to separate the two -operations in general. This perpetual and latent kind of -memory may be termed a _sense of successiveness_; and must -be considered as an internal sense by which we perceive -ourselves existing in time, much in the same way as by our -external and muscular sense we perceive ourselves existing -in space. And both our internal thoughts and feelings, and -the events which take place around us, are apprehended as -objects of this internal sense, and thus as taking place in -time. - -3. In the same manner in which our interpretation of the -notices of the muscular sense implies the power of moving -our limbs, and of touching at will this object or that; our -apprehension of the relations of time, by means of the -internal sense of successiveness, implies a power of -recalling what has past, and of retaining what is passing. -We are able to seize the occurrences which have just taken -place, and to hold them fast in our minds so as mentally to -measure their distance in time from occurrences now present. -And thus, this sense of successiveness, like the muscular -sense with which we have compared it, implies activity of -the mind itself, and is not a sense passively receiving -impressions. - -4. The conception of _Number_ appears to require the -exercise of the same sense of succession. At first sight, -indeed, we seem to apprehend Number without any act of -memory, or any reference to time: for example, we look at a -horse, and see that his legs are four; and this we seem to -do at once, without reckoning them. But it is not difficult -to see that this seeming instantaneousness of the perception -of small numbers is an illusion. This resembles the many -other cases in which we perform short and easy acts so -rapidly and familiarly that we are unconscious of them; as -in the acts of seeing, and of articulating our words. And -this is the more manifest, since we begin our acquaintance -with number by counting even the {143} smallest numbers. -Children and very rude savages must use an effort to reckon -even their five fingers, and find a difficulty in going -further. And persons have been known who were able by habit, -or by a peculiar natural aptitude, to count by dozens as -rapidly as common persons can by units. We may conclude, -therefore, that when we appear to catch a small number by a -single glance of the eye, we do in fact count the units of -it in a regular, though very brief succession. To count -requires an act of memory. Of this we are sensible when we -count very slowly, as when we reckon the strokes of a -church-clock; for in such a case we may forget in the -intervals of the strokes, and _miscount_. Now it will not be -doubted that the nature of the process in counting is the -same whether we count fast or slow. There is no definite -speed of reckoning at which the faculties which it requires -are changed; and therefore memory, which is requisite in -some cases, must be so in all[13\2]. - -[Note 13\2: I have considered Number as involving the -exercise of the sense of succession, because I cannot draw -any line between those cases of large numbers, in which, the -process of counting being performed, there is a manifest -apprehension of succession; and those cases of small -numbers, in which we seem to see the number at one glance. -But if any one holds Number to be apprehended by a direct -act of intuition, as Space and Time are, this view will not -disturb the other doctrines delivered in the text.] - -The act of counting, (_one_, _two_, _three_, and so on,) is -the foundation of all our knowledge of number. The intuition -of the relations of number involves this act of counting; -for, as we have just seen, the conception of number cannot -be obtained in any other way. And thus the whole of -theoretical arithmetic depends upon an act of the mind, and -upon the conditions which the exercise of that act implies. -These have been already explained in the last chapter. - -5. But if the apprehension of number be accompanied by an -act of the mind, the apprehension of _rhythm_ is so still -more clearly. All the forms of versification and the -_measures_ of melodies are the creations of man, who thus -realizes in words and sounds the {144} forms of recurrence -which rise within his own mind. When we hear in a quiet -scene any rapidly-repeated sound, as those made by the -hammer of the smith or the saw of the carpenter, every one -knows how insensibly we throw these noises into a rhythmical -form in our own apprehension. We do this even without any -suggestion from the sounds themselves. For instance, if the -beats of a clock or watch be ever so exactly alike, we still -reckon them alternately tick-_tack_, tick-_tack_. That this -is the case, may be proved by taking a watch or clock of -such a construction that the returning swing of the pendulum -is silent, and in which therefore all the beats are -rigorously alike: we shall find ourselves still reckoning -its sounds as tick-_tack_. In this instance it is manifest -that the rhythm is entirely of our own making. In melodies, -also, and in verses in which the rhythm is complex, obscure -and difficult, we perceive something is required on our -part; for we are often incapable of contributing our share, -and thus lose the sense of the measure altogether. And when -we consider such cases, and attend to what passes within us -when we catch the measure, even of the simplest and -best-known air, we shall no longer doubt that an act of our -own thoughts is requisite in such cases, as well as -impressions on the sense. And thus the conception of this -peculiar modification of time, which we have called -_rhythm_, like all the other views which we have taken of -the subject, shows that we must, in order to form such -conceptions, supply a certain idea by our own thoughts, as -well as merely receive by senses, whether external or -internal, the impressions of appearances and collections of -appearances. - - - -{{145}} -NOTE TO CHAPTER X. - - -I HAVE in the last ten chapters described Space, Time, and -Number by various expressions, all intended to point out -their office as exemplifying the Ideal Element of human -knowledge. I have called them _Fundamental Ideas_; _Forms of -Perception_; _Forms of Intuition_; and perhaps other names. -I might add yet other phrases. I might say that the -properties of Space, Time, and Number are _Laws of the -Mind's Activity_ in apprehending what is. For the mind -cannot apprehend any thing or event except conformably to -the properties of space, time, and number. It is not only -that it _does_ not, but it _can_ not: and this impossibility -shows that the law is a law of the mind, and not of objects -extraneous to the mind. - -It is usual for some of those who reject the doctrines here -presented to say that the axioms of geometry, and of other -sciences, are obtained by Induction from facts constantly -presented by experience. But I do not see how Induction can -prove that a proposition _must_ be true. The only -intelligible usage of the word _Induction_ appears to me to -be, that in which it is applied to a proposition which, -being separable from the facts in our apprehension, and -being compared with them, is seen to agree with them. But in -the cases now spoken of, the proposition is not separable -from the facts. We cannot infer by induction that two -straight lines cannot inclose a space, because we cannot -contemplate special cases of two lines inclosing a space, in -which it remains to be determined whether or not the -proposition, that both are straight, is true. - -I do not deny that the activity of the mind by which it -perceives objects and events as related according to the -laws of space, time, and number, is awakened and developed -by being constantly exercised; and that we cannot imagine a -stage of human existence in which the powers have not been -awakened and {146} developed by such exercise. In this way, -experience and observation are necessary conditions and -prerequisites of our apprehension of geometrical (and other) -axioms. We cannot see the truth of these axioms without some -experience, because we cannot see any thing, or be human -beings, without some experience. This might be expressed by -saying that such truths are acquired necessarily _in the -course of_ all experience; but I think it is very -undesirable to apply, to such a case, the word _Induction_, -of which it is so important to us to keep the scientific -meaning free from confusion. Induction cannot give -demonstrative proofs, as I have already stated in Book 1. C. -i. sect. 3, and therefore cannot be the ground of necessary -truths. - -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 -edition. 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 infinitum_.' I have already given reasons why -I cannot adopt the former expression; but I do not see why -space, time, number, cause, and the rest, may not be termed -_different forms_ of the _impulse of the mind to -generalize_. But if we put together all the Fundamental -Ideas as results of the Generalizing Impulse, we must still -separate them as different modes of action of that Impulse, -showing themselves in various characteristic ways in the -axioms and modes of reasoning which belong to different -sciences. The Generalizing Impulse in one case proceeds -according to the Idea of Space; in another, according to the -Idea of Mechanical Cause; and so in other subjects. - - - -{{147}} -CHAPTER XI. - -OF MATHEMATICAL REASONING. - - -1. _Discursive Reasoning._--WE have thus seen that our -notions of space, time, and their modifications, necessarily -involve a certain activity of the mind; and that the -conditions of this activity form the foundations of those -sciences which have the relations of space, time, and -number, for their object. Upon the fundamental principles -thus established, the various sciences which are included in -the term _Pure Mathematics_, (Geometry, Algebra, -Trigonometry, Conic Sections, and the rest of the Higher -Geometry, the Differential Calculus, and the like,) are -built up by a series of reasonings. These reasonings are -subject to the rules of Logic, as we have already remarked; -nor is it necessary here to dwell long on the nature and -rules of such processes. But we may here notice that such -processes are termed _discursive_, in opposition to the -operations by which we acquire our fundamental principles, -which are, as we have seen, _intuitive_. This opposition was -formerly very familiar to our writers; as Milton,-- - . . . Thus the soul reason receives, - Discursive or intuitive.--_Paradise Lost_, v. 438. -For in such reasonings we obtain our conclusions, not by -looking at our conceptions steadily in one view, which is -_intuition_, but by passing from one view to another, like -those who run from place to place (_discursus_). Thus a -straight line may be at the same time a side of a triangle -and a radius of a circle: and in the first proposition of -Euclid a line is considered, first in one of these -relations, and then in the other, and thus the sides of a -certain triangle are proved to be equal. And by this -'discourse of reason,' as by our older {148} writers it was -termed, we set forth from those axioms which we perceive by -intuition, travel securely over a vast and varied region, -and become possessed of a copious store of mathematical -truths. - -2. _Technical Terms of Reasoning._--The reasoning of -mathematics, thus proceeding from a few simple principles to -many truths, is conducted according to the rules of Logic. -If it be necessary, mathematical proofs may be reduced to -logical forms, and expressed in Syllogisms, consisting of -major, minor, and conclusion. But in most cases the -syllogism is of that kind which is called by logical writers -an _Enthymeme_; a word which implies something existing in -the thoughts only, and which designates a syllogism in which -one of the premises is understood, and not expressed. Thus -we say in a mathematical proof, 'because the point C is the -center of the circle AB, AC is equal to BC;' not stating the -_major_,--that all lines drawn from the center of a circle -to the circumference are equal; or introducing it only by a -transient reference to the definition of a circle. But the -enthymeme is so constantly used in all habitual forms of -reasoning, that it does not occur to us as being anything -peculiar in mathematical works. - -The propositions which are proved to be generally true are -termed _Theorems_: but when anything is required to be done, -as to draw a line or a circle under given conditions, this -proposition is a _Problem_. A theorem requires -demonstration; a problem, solution. And for both purposes -the mathematician usually makes a _Construction_. He directs -us to draw certain lines, circles, or other curves, on which -is to be founded his demonstration that his theorem is true, -or that his problem is solved. Sometimes, too, he -establishes some _Lemma_, or preparatory proposition, before -he proceeds to his main task; and often he deduces from his -demonstration some conclusion in addition to that which was -the professed object of his proposition; and this is termed -a _Corollary_. - -These technical terms are noted here, not as being very -important, but in order that they may not sound {149} -strange and unintelligible if we should have occasion to use -some of them. There is, however, one technical distinction -more peculiar, and more important. - -3. _Geometrical Analysis and Synthesis._--In geometrical -reasoning such as we have described, we introduce at every -step some new consideration; and it is by combining all -these considerations, that we arrive at the conclusion, that -is, the demonstration of the proposition. Each step tends to -the final result, by exhibiting some part of the figure -under a new relation. To what we have already proved, is -added something more; and hence this process is called -_Synthesis_, or _putting together_. The proof flows on, -receiving at every turn new contributions from different -quarters; like a river fed and augmented by many tributary -streams. And each of these tributaries flows from some -definition or axiom as its fountain, or is itself formed by -the union of smaller rivulets which have sources of this -kind. In descending along its course, the synthetical proof -gathers all these accessions into one common trunk, the -proposition finally proved. - -But we may proceed in a different manner. We may begin from -the formed river, and ascend to its sources. We may take the -proposition of which we require a proof, and may examine -what the supposition of its truth implies. If this be true, -then something else may be seen to be true; and from this, -something else, and so on. We may often, in this way, -discover of what simpler propositions our theorem or -solution is compounded, and may resolve these in succession, -till we come to some proposition which is obvious. This is -geometrical _Analysis_. Having succeeded in this analytical -process, we may invert it; and may descend again from the -simple and known propositions, to the proof of a theorem, or -the solution of a problem, which was our starting-place. - -This process resembles, as we have said, tracing a river to -its sources. As we ascend the stream, we perpetually meet -with bifurcations; and some sagacity is needed to enable us -to see which, in each case, is the main stream: but if we -proceed in our research, we {150} exhaust the unexplored -valleys, and finally obtain a clear knowledge of the place -whence the waters flow. _Analytical_ is sometimes confounded -with _symbolical_ reasoning, on which subject we shall make -a remark in the next chapter. The object of that chapter is -to notice certain other fundamental principles and ideas, -not included in those hitherto spoken of, which we find -thrown in our way as we proceed in our mathematical -speculations. It would detain us too long, and involve us in -subtle and technical disquisitions, to examine fully the -grounds of these principles; but the Mathematics hold so -important a place in relation to the inductive sciences, -that I shall briefly notice the leading ideas which the -ulterior progress of the subject involves. - - - -{{151}} -CHAPTER XII. - -OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS. - - -1. _The Idea of a Limit._--THE general truths concerning -relations of space which depend upon the axioms and -definitions contained in Euclid's _Elements_, and which -involve only properties of straight lines and circles, are -termed Elementary Geometry: all beyond this belongs to the -Higher Geometry. To this latter province appertain, for -example, all propositions respecting the lengths of any -portions of curve lines; for these cannot be obtained by -means of the principles of the Elements alone. Here then we -must ask to what other principles the geometer has recourse, -and from what source these are drawn. Is there any origin of -geometrical truth which we have not yet explored? - -The _Idea of a Limit_ supplies a new mode of establishing -mathematical truths. Thus with regard to the length of any -portion of a curve, a problem which we have just mentioned; -a curve is not made up of straight lines, and therefore we -cannot by means of any of the doctrines of elementary -geometry measure the length of any curve. But we may make up -a figure nearly resembling any curve by putting together -many short straight lines, just as a polygonal building of -very many sides may nearly resemble a circular room. And in -order to approach nearer and nearer to the curve, we may -make the sides more and more small, more and more numerous. -We may then possibly find some mode of measurement, some -relation of these small lines to other lines, which is not -disturbed by the multiplication of the sides, however far it -be carried. And thus, we may do what is equivalent to -measuring the curve itself; for by multiplying the {152} -sides we may approach more and more closely to the curve -till no appreciable difference remains. The curve line is -the _Limit_ of the polygon; and in this process we proceed -on the _Axiom_, that 'What is true up to the Limit is true -at the Limit.' - -This mode of conceiving mathematical magnitudes is of wide -extent and use; for every curve may be considered as the -limit of some polygon; every varied magnitude, as the limit -of some aggregate of simpler forms; and thus the relations -of the elementary figures enable us to advance to the -properties of the most complex cases. - -A Limit is a peculiar and fundamental conception, the use of -which in proving the propositions of the Higher Geometry -cannot be superseded by any combination of other hypotheses -and definitions[14\2]. The axiom just noticed, that what is -true up to the limit is true at the limit, is involved in -the very conception of a Limit: and this principle, with its -consequences, leads to all the results which form the -subject of the higher mathematics, whether proved by the -consideration of evanescent triangles, by the processes of -the Differential Calculus, or in any other way. - -[Note 14\2: This assertion cannot be fully proved and -illustrated without a reference to mathematical reasonings -which would not be generally intelligible. I have shown the -truth of the assertion in my _Thoughts on the Study of -Mathematics_, annexed to the _Principles of English -University Education_. The proof is of this kind:--The -ultimate equality of an arc of a curve and the corresponding -periphery of a polygon, when the sides of the polygon are -indefinitely increased in number, is _evident_. But this -truth cannot be proved from any other axiom. For if we take -the supposed axiom, that a curve is always less than the -including broken line, this is not true, except with a -condition; and in tracing the import of this condition, we -find its necessity becomes evident only when we introduce a -reference to a Limit. 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 -involved. Therefore these evident truths are _self_-evident, -_in virtue of the Idea of a Limit_.] - -The ancients did not expressly introduce this conception of -a Limit into their mathematical reasonings; although in the -application of what is termed the {153} _Method of -Exhaustions_, (in which they show how to _exhaust_ the -_difference_ between a polygon and a curve, or the like,) -they were in fact proceeding upon an obscure apprehension of -principles equivalent to those of the Method of Limits. Yet -the necessary fundamental principle not having, in their -time, been clearly developed, their reasonings were both -needlessly intricate and imperfectly satisfactory. Moreover -they were led to put in the place of axioms, assumptions -which were by no means self-evident; as when Archimedes -assumed, for the basis of his measure of the circumference -of the circle, the proposition that a circular arc is -necessarily less than two lines which inclose it, joining -its extremities. The reasonings of the older mathematicians, -which professed to proceed upon such assumptions, led to -true results in reality, only because they were guided by a -latent reference to the limiting case of such assumptions. -And this latent employment of the conception of a Limit, -reappeared in various forms during the early period of -modern mathematics; as for example, in the _Method of -Indivisibles_ of Cavalleri, and the _Characteristic -Triangle_ of Barrow; till at last, Newton distinctly -referred such reasonings to the conception of a Limit, and -established the fundamental principles and processes which -that conception introduces, with a distinctness and -exactness which required little improvement to make it as -unimpeachable as the demonstrations of geometry. And when -such processes as Newton thus deduced from the conception of -a Limit, are represented by means of general algebraical -symbols instead of geometrical diagrams, we have then before -us the _Method of Fluxions_, or the _Differential Calculus_; -a mode of treating mathematical problems justly considered -as the principal weapon by which the splendid triumphs of -modern mathematics have been achieved. - -2. _The Use of General Symbols._--The employment of -algebraical symbols, of which we have just spoken, has been -another of the main instruments to which the successes of -modern mathematics are owing. And here again the processes -by which we obtain our {154} results depend for their -evidence upon a fundamental conception,--the conception of -_arbitrary symbols_ as the _Signs_ of quantity and its -relations; and upon a corresponding axiom, that 'The -interpretation of such symbols must be perfectly general.' -In this case, as in the last, it was only by degrees that -mathematicians were led to a just apprehension of the -grounds of their reasoning. For symbols were at first used -only to represent numbers considered with regard to their -numerical properties; and thus the science of Algebra was -formed. But it was found, even in cases belonging to common -algebra, that the symbols often admitted of an -interpretation which went beyond the limits of the problem, -and which yet was not unmeaning, since it pointed out a -question closely analogous to the question proposed. This -was the case, for example, when the answer was a _negative -quantity_; for when Descartes had introduced the mode of -representing curves by means of algebraical relations among -the symbols of the _co-ordinates_, or distances of each of -their points from fixed lines, it was found that negative -quantities must be dealt with as not less truly significant -than positive ones. And as the researches of mathematicians -proceeded, other cases also were found, in which the -symbols, although destitute of meaning according to the -original conventions of their institution, still pointed out -truths which could be verified in other ways; as in the -cases in which what are called _impossible quantities_ -occur. Such processes may usually be confirmed upon other -principles, and the truth in question may be established by -means of a demonstration in which no such seeming fallacies -defeat the reasoning. But it has also been shown in many -such cases, that the process in which some of the steps -appear to be without real meaning, does in fact involve a -valid proof of the proposition. And what we have here to -remark is, that this is not true accidentally or partially -only, but that the results of systematic symbolical -reasoning must _always_ express general truths, by their -nature; and do not, for their justification, require each of -the steps of the process to represent {155} some definite -operation upon quantity. _The absolute universality of the -interpretation of symbols_ is the fundamental principle of -their use. This has been shown very ably by Dr. Peacock in -his _Algebra_. He has there illustrated, in a variety of -ways, this principle: that 'If general symbols express an -identity when they are supposed to be of any special nature, -they must also express an identity when they are general in -their nature.' And thus, this universality of symbols is a -principle in addition to those we have already noticed; and -is a principle of the greatest importance in the formation -of mathematical science, according to the wide generality -which such science has in modern times assumed. - -3. _Connexion of Symbols and Analysis._--Since in our -symbolical reasoning our symbols thus reason for us, we do -not necessarily here, as in geometrical reasoning, go on -adding carefully one known truth to another, till we reach -the desired result. On the contrary, if we have a theorem to -prove or a problem to solve which can be brought under the -domain of our symbols, we may at once state the given but -unproved truth, or the given combination of unknown -quantities, in its symbolical form. After this first -process, we may then proceed to trace, by means of our -symbols, what other truth is involved in the one just -stated, or what the unknown symbols must signify; resolving -step by step the symbolical assertion with which we began, -into others more fitted for our purpose. The former process -is a kind of _synthesis_, the latter is termed _analysis_. -And although symbolical reasoning does not necessarily imply -such analysis; yet the connexion is so familiar, that the -term _analysis_ is frequently used to designate symbolical -reasoning. - - - -{{156}} -CHAPTER XIII. - -THE DOCTRINE OF MOTION. - - -1. _Pure Mechanism._--THE doctrine of Motion, of which we -have here to speak, is that in which motion is considered -quite independently of its cause, force; for all -consideration of force belongs to a class of ideas entirely -different from those with which we are here concerned. In -this view it may be termed the _pure_ doctrine of motion, -since it has to do solely with space and time, which are the -subjects of pure mathematics. (See c. i. of this book.) -Although the doctrine of motion in connexion with force, -which is the subject of mechanics, is by far the most -important form in which the consideration of motion enters -into the formation of our sciences, the Pure Doctrine of -Motion, which treats of space, time, and velocity, might be -followed out so as to give rise to a very considerable and -curious body of science. Such a science is the science of -Mechanism, independent of force, and considered as the -solution of a problem which may be thus enunciated: 'To -communicate any given motion from a first mover to a given -body.' The science which should have for its object to solve -all the various cases into which this problem would ramify, -might be termed _Pure Mechanism_, in contradistinction to -_Mechanics Proper_, or _Machinery_, in which Force is taken -into consideration. 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 problem. We -have also important contributions to such a science in the -works of Mathematicians; for example, the various -investigations and demonstrations which have been published -respecting the form of the Teeth {157} of Wheels, and Mr. -Babbage's memoir[15\2] on the Language of Machinery. There -are also several works which contain collections of the -mechanical contrivances which have been invented for the -purpose of transmitting and modifying motion, and these -works may be considered as treatises on the science of Pure -Mechanism. But this science has not yet been reduced to the -systematic simplicity which is desirable, nor indeed -generally recognized as a separate science. It has been -confounded, under the common name of _Mechanics_, with the -other **science, Mechanics Proper, or Machinery, which -considers the effect of _force_ transmitted by Mechanism -from one part of a material combination to another. For -example, the _Mechanical Powers_, as they are usually -termed, (the Lever, the Wheel and Axle, the Inclined Plane, -the Wedge, and the Screw,) have almost always been treated -with reference to the relation between the _Power_ and the -_Weight_, and not primarily as a mode of changing the -velocity and kind of the motion. The science of pure motion -has not generally been separated from the science of motion -viewed with reference to its causes. - -[Note 15\2: _On a Method of expressing by Signs the action -of Machinery._ _Phil. Trans._ 1826, p. 250.] - -Recently, indeed, the necessity of such a separation has -been seen by those who have taken a philosophical view of -science. Thus this necessity has been urged by M. Ampère, in -his _Essai sur la Philosophie des Sciences_ (1834): 'Long,' -he says, (p. 50,) 'before I employed myself upon the present -work, I had remarked that it is usual to omit, in the -beginning of all books treating of sciences which regard -motion and force, certain considerations which, duly -developed, must constitute a special science: of which -science certain parts have been treated of, either in -memoirs or in special works; such, for example, as that of -Carnot upon Motion considered Geometrically, and the essay -of Lanz and Betancourt upon the Composition of Machines.' He -then proceeds to describe this science nearly as we have -{158} done, and proposes to term it _Kinematics_ -(_Cinématique_), from κίνημα, motion. - -2. _Formal Astronomy._--I shall not attempt here further to -develop the form which such a science must assume. But I may -notice one very large province which belongs to it. When men -had ascertained the apparent motions of the sun, moon, and -stars, to a moderate degree of regularity and accuracy, they -tried to conceive in their minds some mechanism by which -these motions might be produced; and thus they in fact -proposed to themselves a very extensive problem in -_Kinematics_. This, indeed, was the view originally -entertained of the nature of the science of astronomy. Thus -Plato in the seventh Book of his _Republic_[16\2], speaks of -astronomy as the doctrine of the motion of solids, meaning -thereby, spheres. And the same was a proper description of -the science till the time of Kepler, and even later: for -Kepler endeavoured in vain to conjoin with the knowledge of -the motions of the heavenly bodies, those true mechanical -conceptions which converted formal into physical -astronomy[17\2]. - -[Note 16\2: P. 528.] - -[Note 17\2: _Hist. Induc. Sc._ ii. 130.] - -The astronomy of the ancients admitted none but uniform -circular motions, and could therefore be completely -cultivated by the aid of their elementary geometry. But the -pure science of motion might be extended to all motions, -however varied as to the speed or the path of the moving -body. In this form it must depend upon the doctrine of -limits; and the fundamental principle of its reasonings -would be this: That velocity is measured by the Limit of the -_space_ described, considered with reference to the _time_ -in which it is described. I shall not further pursue this -subject; and in order to complete what I have to say -respecting the Pure Sciences, I have only a few words to add -respecting their bearing on Inductive Science in general. - - - -{{159}} -CHAPTER XIV. - -OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE SCIENCES. - - -1. ALL objects in the world which can be made the subjects -of our contemplation are subordinate to the conditions of -Space, Time, and Number; and on this account, the doctrines -of pure mathematics have most numerous and extensive -applications in every department of our investigations of -nature. And there is a peculiarity in these Ideas, which has -caused the mathematical sciences to be, in all cases, the -first successful efforts of the awakening speculative powers -of nations at the commencement of their intellectual -progress. Conceptions derived from these Ideas are, from the -very first, perfectly precise and clear, so as to be fit -elements of scientific truths. This is not the case with the -other conceptions which form the subjects of scientific -inquiries. The conception of _statical force_, for instance, -was never presented in a distinct form till the works of -Archimedes appeared: the conception of _accelerating force_ -was confused, in the mind of Kepler and his contemporaries, -and only became clear enough for purposes of sound -scientific reasoning in the succeeding century: the just -conception of chemical _composition_ of elements gradually, -in modern times, emerged from the erroneous and vague -notions of the ancients. If we take works published on such -subjects before the epoch when the foundations of the true -science were laid, we find the knowledge not only small, but -worthless. The writers did not see any evidence in what we -now consider as the axioms of the science; nor any -inconsistency where we now see self-contradiction. But this -was never the case with speculations concerning {160} space -and number. From their first rise, these were true as far as -they went. The Geometry and Arithmetic of the Greeks and -Indians, even in their first and most scanty form, contained -none but true propositions. Men's intuitions upon these -subjects never allowed them to slide into error and -confusion; and the truths to which they were led by the -first efforts of their faculties, so employed, form part of -the present stock of our mathematical knowledge. - -2. But we are here not so much concerned with mathematics in -their pure form, as with their application to the phenomena -and laws of nature. 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 -science. Space and time, position and motion, govern all -visible objects; but by far the most conspicuous examples of -the relations which arise out of such elements, are -displayed by the ever-moving luminaries of the sky, which -measure days, and months, and years, by their motions, and -man's place on the earth by their position. Hence the -sciences of space and number were from the first cultivated -with peculiar reference to Astronomy. I have elsewhere[18\2] -quoted Plato's remark,--that it is absurd to call the -science of the relations of space _geometry_, the measure of -the earth, since its most important office is to be found in -its application to the heavens. And on other occasions also -it appears how strongly he, who may be considered as the -representative of the scientific and speculative tendencies -of his time and country, had been impressed with the -conviction, that the formation of a science of the celestial -motions must depend entirely upon the progress of -mathematics. In the Epilogue to the Dialogue on the -Laws[19\2], he declares mathematical knowledge to be the -first and main requisite for the astronomer, and describes -the portions of it which he holds necessary for astronomical -speculators to cultivate. These seem to be, Plane Geometry, -Theoretical Arithmetic, the Application of Arithmetic {161} -to planes and to solids, and finally the doctrine of -Harmonics. Indeed the bias of Plato appears to be rather to -consider mathematics as the essence of the science of -astronomy, than as its instrument; and he seems disposed, in -this as in other things, to disparage observation, and to -aspire after a science founded upon demonstration alone. 'An -astronomer,' he says in the same place, 'must not be like -Hesiod and persons of that kind, whose astronomy consists in -noting the settings and risings of the stars; but he must be -one who understands the revolutions of the celestial -spheres, each performing its proper cycle.' - -[Note 18\2: _Hist. Ind. Sc._ b. iii. c. ii.] - -[Note 19\2: _Epinomis_, p. 990.] - -A large portion of the mathematics of the Greeks, so long as -their scientific activity continued, was directed towards -Astronomy. Besides many curious propositions of plane and -solid Geometry, to which their astronomers were led, their -Arithmetic, though very inconvenient in its fundamental -assumptions (as being sexagesimal not decimal), was -cultivated to a great extent; and the science of -Trigonometry, in which problems concerning the relations of -space were resolved by means of tables of numerical results -previously obtained, was created. Menelaus of Alexandria -wrote six Books on Chords, probably containing methods of -calculating Tables of these quantities; such Tables were -familiarly used by the later Greek astronomers. The same -author also wrote three Books on Spherical Trigonometry, -which are still extant. - -3. The Greeks, however, in the first vigour of their pursuit -of mathematical truth, at the time of Plato and soon after, -had by no means confined themselves to those propositions -which had a visible bearing on the phenomena of nature; but -had followed out many beautiful trains of research, -concerning various kinds of figures, for the sake of their -beauty alone; as for instance in their doctrine of Conic -Sections, of which curves they had discovered all the -principal properties. But it is curious to remark, that -these investigations, thus pursued at first as mere matters -of curiosity and intellectual gratification, were destined, -two thousand years later, to play a very important part in -{162} establishing that system of the celestial motions -which succeeded the Platonic scheme of cycles and epicycles. -If the properties of the conic sections had not been -demonstrated by the Greeks, and thus rendered familiar to -the mathematicians of succeeding ages, 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 -science. - -4. The Arabians, who, as I have elsewhere said, added little -of their own to the stores of science which they received -from the Greeks, did however make some very important -contributions in those portions of pure mathematics which -are subservient to astronomy. Their adoption of the Indian -mode of computation by means of the Ten Digits, 1, 2, 3, 4, -5, 6, 7, 8, 9, 0, and by the method of Local Values, instead -of the cumbrous sexagesimal arithmetic of the Greeks, was an -improvement by which the convenience and facility of -numerical calculations were immeasurably augmented. The -Arabians also rendered several of the processes of -trigonometry much more commodious, by using the Sine of an -arc instead of the Chord; an improvement which Albategnius -appears to claim for himself[20\2]; and by employing also -the Tangents of arcs, or, as they called them[21\2], -_upright shadows_. - -[Note 20\2: Delambre, _Ast., M. A._, p. 12.] - -[Note 21\2: _Ibid._ p. 17.] - -5. The constant application of mathematical knowledge to the -researches of Astronomy, and the mutual influence of each -science on the progress of the other, has been still more -conspicuous in modern times. Newton's Method of Prime and -Ultimate Ratios, which we have already noticed as the first -correct exposition of the doctrine of a Limit, is stated in -a series of Lemmas, or preparatory theorems, prefixed to his -_Treatise on the System of the World_. Both the properties -of curve lines and the doctrines concerning force and -motion, which he had to establish, required that the common -mathematical processes should be methodized and extended. If -Newton had not been a most {163} expert and inventive -mathematician, as well as a profound and philosophical -thinker, 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[22\2]. And if we see that the -great task begun by him, goes on more slowly in the hands of -his immediate successors, and lingers a little before its -full completion, we perceive that this arises, in a great -measure, from the defect of the mathematical methods then -used. Newton's synthetical modes of investigation, as we -have elsewhere observed, were an instrument[23\2], powerful -indeed in his mighty hand, but too ponderous for other -persons to employ with effect. The countrymen of Newton -clung to it the longest, out of veneration for their master; -and English cultivators of physical astronomy were, on that -very account, left behind the progress of mathematical -science in France and Germany, by a wide interval, which -they have only recently recovered. On the Continent, the -advantages offered by a familiar use of symbols, and by -attention to their symmetry and other relations, were -accepted without reserve. In this manner the Differential -Calculus of Leibnitz, which was in its origin and -signification identical with the Method of Fluxions of -Newton, soon surpassed its rival in the extent and -generality of its application to problems. This Calculus was -applied to the science of mechanics, to which it, along with -the symmetrical use of co-ordinates, gave a new form; for it -was soon seen that the most difficult problems might in -general be reduced to finding integrals, which is the -reciprocal process of that by which differentials are found; -so that all difficulties of physical astronomy were reduced -to difficulties of symbolical calculation, these, indeed, -being often sufficiently stubborn. Clairaut, Euler, and -D'Alembert employed the increased resources of mathematical -science upon the Theory of the Moon, and other questions -relative to the system of the world; and thus began to -pursue such inquiries in the course in which mathematicians -{164} are still labouring up to the present day. This course -was not without its checks and perplexities. We have -elsewhere quoted[24\2] Clairaut's expression when he had -obtained the very complex differential equations which -contain the solution of the problem of the moon's motion: -'Now integrate them who can!' But in no very long time they -were integrated, at least approximately; and the methods of -approximation have since then been improved; so that now, -with a due expenditure of labour, they may be carried to any -extent which is thought desirable. If the methods of -astronomical observation should hereafter reach a higher -degree of exactness than they now profess, so that -irregularities in the motions of the sun, moon, and planets, -shall be detected which at present escape us, 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 facts. Indeed at present -the mathematical theory is in advance of such observations. -It can venture to suggest what may afterwards be detected, -as well as to explain what has already been observed. This -has happened recently; for Professor Airy has calculated the -law and amount of an inequality depending upon the mutual -attraction of the Earth and Venus; of which inequality (so -small is it,) it remains to be determined whether its effect -can be traced in the series of astronomical observations. - -[Note 22\2: _Hist. Ind. Sc._ b. vii. c. ii.] - -[Note 23\2: _Ibid._ p. 175.] - -[Note 24\2: _Hist. Ind. Sc._ b. vi. c. vi. sect. 7.] - -6. As the influence of mathematics upon the progress of -astronomy is thus seen in the cases in which theory and -observation confirm each other, so this influence appears in -another way, in the very few cases in which the facts have -not been fully reduced to an agreement with theory. The most -conspicuous case of this kind is the state of our knowledge -of the Tides. This is a portion of astronomy: for the -Newtonian theory asserts these curious phenomena to be the -result of the attraction of the sun and moon. Nor can there -be any doubt that this is true, as a general statement; yet -the subject is up to the present time a blot {165} on the -perfection of the theory of universal gravitation; for we -are very far from being able in this, as in the other parts -of astronomy, to show that theory will exactly account for -the time, and magnitude, and all other circumstances of the -phenomenon at every place on the earth's surface. And what -is the portion of our mathematics which is connected with -this solitary signal defect in astronomy? It is the -mathematics of the Motion of Fluids; a portion in which -extremely little progress has been made, and in which all -the more general problems of the subject have hitherto -remained entirely insoluble. The attempts of the greatest -mathematicians, Newton, Maclaurin, Bernoulli, Clairaut, -Laplace, to master such questions, all involve some -gratuitous assumption, which is introduced because the -problem cannot otherwise be mathematically dealt with: these -assumptions confessedly render the result defective, and how -defective, it is hard to say. And it was probably precisely -the absence of a theory which could be reasonably expected -to agree with the observations, which made Observations of -this very curious phenomenon, the Tides, to be so much -neglected as till very recently they were. Of late years -such observations have been pursued, and their results have -been resolved into empirical laws, so that the rules of the -phenomena have been ascertained, although the dependence of -these rules upon the lunar and solar forces has not been -shown. Here then we have a portion of our knowledge relating -to facts undoubtedly dependent upon universal gravitation, -in which Observation has outstripped Theory in her progress, -and is compelled to wait till her usual companion overtakes -her. This is a position of which Mathematical Theory has -usually been very impatient, and we may expect that she will -be no less so in the present instance. - -7. It would be easy to show from the history of other -sciences, for example, Mechanics and Optics, how essential -the cultivation of pure mathematics has been to their -progress. The parabola was already familiar among -mathematicians when Galileo discovered that it was the -theoretical path of a Projectile; and the {166} extension -and generalization of the Laws of Motion could never have -been effected, unless the Differential and Integral Calculus -had been at hand, ready to trace the results of every -hypothesis which could be made. D'Alembert's mode of -expressing the Third Law of Motion in its most general -form[25\2], if it did not prove the law, at least reduced -the application of it to analytical processes which could be -performed in most of those cases in which they were needed. -In many instances the demands of mechanical science -suggested the extension of the methods of pure analysis. The -problem of Vibrating Strings gave rise to the Calculus of -Partial Differences, which was still further stimulated by -its application to the motions of fluids and other -mechanical problems. And we have in the writings of Lagrange -and Laplace other instances equally remarkable of new -analytical methods, to which mechanical problems, and -especially cosmical problems, have given occasion. - -[Note 25\2: _Hist. Ind. Sc._ b. vi. c. vi. sect. 7.] - -8. The progress of Optics as a science has, in like manner, -been throughout dependent upon the progress of pure -mathematics. The first rise of Geometry was followed by some -advances, slight ones no doubt, in the doctrine of -Reflection and in Perspective. The law of Refraction was -traced to its consequences by means of Trigonometry, which -indeed was requisite to express the law in a simple form. -The steps made in Optical science by Descartes, Newton, -Euler, and Huyghens, required the geometrical skill which -those philosophers possessed. And if Young and Fresnel had -not been, each in his peculiar way, persons of eminent -mathematical endowments, they would not have been able to -bring the Theory of Undulations and Interferences into a -condition in which it could be tested by experiments. We may -see how unexpectedly recondite parts of pure mathematics may -bear upon physical science, by calling to mind a -circumstance already noticed in the History of -Science[26\2];--that Fresnel obtained one of the {167} most -curious confirmations of the theory (the laws of Circular -Polarization by reflection) through an interpretation of an -algebraical expression, which, according to the original -conventional meaning of the symbols, involved an impossible -quantity. We have already remarked, that in virtue of the -principle of the generality of symbolical language, such an -interpretation may often point out some real and important -analogy. - -[Note 26\2: _Hist. Ind. Sc._ b. ix. c. xiii. sect. 2.] - -9. From this rapid sketch it may be seen how important an -office in promoting the progress of the physical sciences -belongs to mathematics. Indeed in the progress of many -sciences, every step has been so intimately connected with -some advance in mathematics, that we can hardly be surprised -if some persons have considered mathematical reasoning to be -the most essential part of such sciences; and have -overlooked the other elements which enter into their -formation. How erroneous this view is we shall best see by -turning our attention to the other Ideas besides those of -space, number, and motion, which enter into some of the most -conspicuous and admired portions of what is termed exact -science; 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 geometry. - - - - -{{169}} -BOOK III. - - -THE -PHILOSOPHY -OF THE -MECHANICAL SCIENCES. - - - - -IT is only because we subject trains of phenomena, that is, -all change whatever, to the law of causality--to the -relation of cause and effect--that experience or empirical -knowledge becomes possible. - -KANT, _Kr. d. R. V._ 11 Th. 1 Abth. 11 Buch. 2 Haupt. - -Quicquid premit vel trahit alterum, tantundem ab eo premitur -vel trahitur ... Si corpus aliquod in corpus aliud impingens -motum ejus vi suâ quomodocunque mutaverit, idem quoque -vicissim in motu proprio eandem mutationem in partem -contrariam vi alterius (ob æqualitatem pressionis, mutuæ) -subibit ... Obtinet etiam hæc Lex in attractionibus. - -NEWTON, _Princip._ ad init. - - - -{{171}} -BOOK III. - - -THE PHILOSOPHY OF THE MECHANICAL SCIENCES. - - -CHAPTER I. - -OF THE MECHANICAL SCIENCES. - - -IN the History of the Sciences, that class of which we here -speak occupies a conspicuous and important place; coming -into notice immediately after those parts of Astronomy which -require for their cultivation merely the ideas of space, -time, motion, and number. It appears from our History, that -certain truths concerning the _equilibrium_ of bodies were -established by Archimedes;--that, after a long interval of -inactivity, his principles were extended and pursued further -in modern times:--and that to these doctrines concerning -equilibrium and the forces which produce it, (which -constitute the science _Statics_,) were added many other -doctrines concerning the _motions_ of bodies, considered -also as produced by forces, and thus the science of -_Dynamics_ was produced. The assemblage of these sciences -composes the province of _Mechanics_. Moreover, philosophers -have laboured to make out the laws of the equilibrium of -_fluid_ as well as solid bodies; and hence has arisen the -science of _Hydrostatics_. And the doctrines of Mechanics -have been found to have a most remarkable bearing upon the -motions of the heavenly bodies; with reference to which, -indeed, they were at first principally studied. The -explanation of those cosmical facts by means of mechanical -{172} principles and their consequences, forms the science -of _Physical Astronomy_. These are the principal examples of -mechanical science; although some other portions of Physics, -as Magnetism and Electrodynamics, introduce mechanical -doctrines very largely into their speculations. - -Now in all these sciences we have to consider _Forces_. In -all mechanical reasonings forces enter, either as producing -motion, or as prevented from doing so by other forces. Thus -force, in its most general sense, is the _cause_ of motion, -or of tendency to motion; and in order to discover the -principles on which the mechanical sciences truly rest, we -must examine the nature and origin of our knowledge of Causes. - -In these sciences, however, we have not to deal with Cause -in its more general acceptation, in which it applies to all -kinds of agency, material or immaterial;--to the influence -of thought and will, as well as of bodily pressure and -attractive force. Our business at present is only with such -causes as immediately operate upon matter. We shall -nevertheless, in the first place, consider the nature of -Cause in its most general form; and afterwards narrow our -speculations so as to direct them specially to the -mechanical sciences. - - - -{{173}} -CHAPTER II. - -OF THE IDEA OF CAUSE. - - -1. WE see in the world around us a constant succession of -causes and effects connected with each other. The laws of -this connexion we learn in a great measure from experience, -by observation of the occurrences which present themselves -to our notice, succeeding one another. But in doing this, -and in attending to this succession of appearances, of which -we are aware by means of our senses, we supply from our own -minds the Idea of Cause. This Idea, as we have already shown -with respect to other Ideas, is not derived from experience, -but has its origin in the mind itself;--is introduced into -our experience by the active, and not by the passive part of -our nature. - -By Cause we mean some quality, power, or efficacy, by which -a state of things produces a succeeding state. Thus the -motion of bodies from rest is produced by a cause which we -call _Force_: and in the particular case in which bodies -fall to the earth, this force is termed _Gravity_. In these -cases, the Conceptions of Force and Gravity receive their -meaning from the Idea of Cause which they involve: for Force -is conceived as the Cause of Motion. That this Idea of Cause -is not derived from experience, we prove (as in former -cases) by this consideration: that we can make assertions, -involving this idea, which are rigorously necessary and -universal; whereas knowledge derived from experience can -only be true as far as experience goes, and can never -contain in itself any evidence whatever of its necessity. We -assert that 'Every event must have a cause:' and this -proposition we know to be true, not only probably, and -generally, and as far as we can see: {174} but we cannot -suppose it to be false in any single instance. We are as -certain of it as of the truths of arithmetic or geometry. We -cannot doubt that it must apply to all events past and -future, in every part of the universe, just as truly as to -those occurrences which we have ourselves observed. _What_ -causes produce what effects;--what is the cause of any -particular event;--what will be the effect of any peculiar -process;--these are points on which experience may enlighten -us. Observation and experience may be requisite, to enable -us to judge respecting such matters. But that every event -has _some_ cause, Experience cannot prove any more than she -can disprove. She can add nothing to the evidence of the -truth, however often she may exemplify it. This doctrine, -then, cannot have been acquired by her teaching; and the -Idea of Cause, which the doctrine involves, and on which it -depends, cannot have come into our minds from the region of -observation. - -2. That we do, in fact, apply the Idea of Cause in a more -extensive manner than could be justified, if it were derived -from experience only, is easily shown. For from the -principle that everything must have a cause, we not only -reason concerning the succession of the events which occur -in the progress of the world, and which form the course of -experience; but we infer that the world itself must have a -cause;--that the chain of events connected by common -causation, must have a First Cause of a nature different -from the events themselves. This we are entitled to do, if -our Idea of Cause be independent of, and superior to, -experience: but if we have no Idea of Cause except such as -we gather from experience, this reasoning is altogether -baseless and unmeaning. - -3. Again; by the use of our powers of observation, we are -aware of a succession of appearances and events. But none of -our senses or powers of external observation can detect in -these appearances the power or quality which we call Cause. -Cause is that which connects one event with another; but no -sense or perception discloses to us, or can disclose, any -connexion {175} among the events which we observe. We see -that one occurrence follows another, but we can never see -anything which shows that one occurrence _must_ follow -another. We have already noticed[1\3], that this truth has -been urged by metaphysicians in modern times, and generally -assented to by those who examine carefully the connexion of -their own thoughts. The arguments are, indeed, obvious -enough. One ball strikes another and causes it to move -forwards. But by what compulsion? Where is the necessity? If -the mind can see any circumstance in this case which makes -the result inevitable, let this circumstance be pointed out. -But, in fact, there is no such discoverable necessity; for -we can conceive this event not to take place at all. The -struck ball may stand still, for aught we can see. 'But the -laws of motion will not allow it to do so.' Doubtless they -will not. But the laws of motion are learnt from experience, -and therefore can prove no necessity. Why should not the -laws of motion be other than they are? Are they necessarily -true? That they are necessarily such as do actually regulate -the impact of bodies, is at least no obvious truth; and -therefore this necessity cannot be, in common minds, the -ground of connecting the impact of one ball with the motion -of another. And assuredly, if this fail, no other ground of -such necessary connexion can be shown. In this case, then, -the events are not seen to be necessarily connected. But if -this case, where one ball moves another by impulse, be not -an instance of events exhibiting a necessary connexion, we -shall look in vain for any example of such a connexion. -There is, then, no case in which events can be observed to -be necessarily connected: our idea of causation, which -implies that the event is necessarily connected with the -cause, cannot be derived from observation. - -[Note 1\3: Book 3. chap. ii.] - -4. But it may be said, we have not any such Idea of Cause, -implying necessary connexion with effect, and a quality by -which this connexion is produced. {176} We see nothing but -the succession of events; and by _cause_ we mean nothing but -a certain succession of events;--namely, a constant, -unvarying succession. Cause and effect are only two events -of which the second invariably follows the first. We delude -ourselves when we imagine that our idea of causation -involves anything more. - -To this I reply by asking, what then is the meaning of the -maxim above quoted, and allowed by all to be universally and -necessarily true, that every event must have a cause? Let us -put this maxim into the language of the explanation just -noticed; and it becomes this:--'Every event must have a -certain other event invariably preceding it.' But why must -it? Where is the necessity? Why must like events always be -preceded by like, except so far as other events interfere? -That there is such a necessity, no one can doubt. All will -allow that if a stone ascend because it is thrown upwards in -one case, a stone which ascends in another case has also -been thrown upwards, or has undergone some equivalent -operation. All will allow that in this sense, every kind of -event must have some other specific kind of event preceding -it. But this turn of men's thoughts shows that they see in -events a connexion which is not mere succession. They see in -cause and effect, not merely what does, often or always, -precede and follow, but what _must_ precede and follow. The -events are not only conjoined, they are connected. The cause -is more than the prelude, the effect is more than the -sequel, of the fact. The cause is conceived not as a mere -occasion; it is a power, an efficacy, which has a real -operation. - -5. Thus we have drawn from the maxim, that Every Effect must -have a Cause, arguments to show that we have an Idea of -Cause which is not borrowed from experience, and which -involves more than mere succession. Similar arguments might -be derived from any other maxims of universal and necessary -validity, which we can obtain concerning Cause: as, for -example, the maxims that Causes are measured by their -Effects, and that Reaction is equal and opposite to {177} -Action. These maxims we shall soon have to examine; but we -may observe here, that the necessary truth which belongs to -them, shows that they, and the Ideas which they involve, are -not the mere fruits of observation; while their meaning, -including, as it does, something quite different from the -mere conception of succession of events, proves that such a -conception is far from containing the whole import and -signification of our Idea of Cause. - -The progress of the opinions of philosophers on the points -discussed in this chapter, has been one of the most -remarkable parts of the history of Metaphysics in modern -times: and I shall therefore briefly notice some of its -features. - - - -{{178}} -CHAPTER III. - -MODERN OPINIONS RESPECTING THE IDEA OF CAUSE. - - -1. 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 world, a strong -tendency to ascribe the whole of our Knowledge to the -teaching of Experience. This tendency, with its -consequences, including among them the reaction which was -produced when the tenet had been pushed to a length -manifestly absurd, has exercised a very powerful influence -upon the progress of metaphysical doctrines up to the -present time. I proceed to notice some of the most prominent -of the opinions which have thus obtained prevalence among -philosophers, so far as the Idea of Cause is concerned. - -Locke was one of the metaphysicians who produced the -greatest effect in diffusing this opinion, of the exclusive -dependence of our knowledge upon experience. Agreeably to -this general system, he taught[2\3] that our ideas of Cause -and Effect are got from observation of the things about us. -Yet notwithstanding this tenet of his, he endeavoured still -to employ these ideas in reasoning on subjects which are far -beyond all limits of experience: for he professed to prove, -from our idea of Causation, the existence of the Deity[3\3]. - -[Note 2\3: _Essay on the Human Understanding_, b. ii. c. xxvi.] - -[Note 3\3: B. iv. c. x.] - -Hume noticed this obvious inconsistency; but declared -himself unable to discover any remedy for a defect so fatal -to the most important parts of our knowledge. He could see, -in our belief of the succession of cause and effect, nothing -but the habit of associating in our minds what had often -been {179} associated in our experience. He therefore -maintained that we could not, with logical propriety, extend -our belief of such a succession to cases entirely distinct -from all those of which our experience consisted. We see, he -said, an actual _conjunction_ of two events; but we can in -no way detect a necessary _connexion_; and therefore we have -no means of inferring cause from effect, or effect from -cause[4\3]. The only way in which we recognize Cause and -Effect in the field of our experience, is as an unfailing -Sequence: we look in vain for anything which can assure us -of an infallible Consequence. And since experience is the -only source of our knowledge, we cannot with any justice -assert that the world in which we live must necessarily have -had a cause. - -[Note 4\3: Hume's _Phil. of the Human Mind_, vol. i. p. -94.] - -2. This doctrine, taken in conjunction with the known -skepticism of its author on religious points, produced a -considerable fermentation in the speculative world. The -solution of the difficulty thus thrown before philosophers, -was by no means obvious. It was vain to endeavour to find in -experience any other property of a Cause, than a constant -sequence of the effect. Yet it was equally vain to try to -persuade men that they had no idea of Cause; 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 happens. Accordingly these hostile and apparently -irreconcilable doctrines,--the indispensable necessity of a -cause of every event, and the impossibility of our knowing -such a necessity,--were at last allowed to encamp side by -side. Reid, Beattie, and others, formed one party, who -showed how widely and constantly the idea of a cause -pervades all the processes of the human mind: while another -sect, including Brown, and apparently Stewart, maintained -that this idea is always capable of being resolved into a -constant sequence; and these latter reasoners tried to -obviate the dangerous and shocking inferences which some -persons might try to draw from their opinion, by declaring -the {180} maxim that "Every event must have a cause," to be -an instinctive law of belief, or a fundamental principle of -the human mind[5\3]. - -[Note 5\3: Stewart's _Active Powers_, vol. i. p. 347. -Browne's _Lectures_, vol. i. p. 115.] - -3. While this series of discussions was going on in Britain, -a great metaphysical genius in Germany was unravelling the -perplexity in another way. Kant's speculations originated, -as he informs us, in the trains of thought to which Hume's -writings gave rise; and the _Kritik der Reinen Vernunft_, or -_Examination of the Pure Reason_, was published in 1787, -with the view of showing the true nature of our knowledge. - -Kant's solution of the difficulties just mentioned differs -materially from that above stated. According to Brown[6\3], -succession observed and cause inferred,--the memory of past -conjunctions of events and the belief of similar future -conjunctions,--are facts, independent, so far as we can -discover, but inseparably combined by a law of our mental -nature. According to Kant, causality is an inseparable -condition of our experience: a connexion in events is -requisite to our apprehending them _as_ events. Future -occurrences must be connected by causation as the past have -been, because we cannot think of past, present, and future, -without such connexion. We cannot fix the mind upon -occurrences, without including these occurrences in a series -of causes and effects. The relation of Causation is a -condition under which we think of events, as the relations -of space are a condition under which we see objects. - -[Note 6\3: _Lectures_, vol. i. p. 114.] - -4. On a subject so abstruse, it is not easy to make our -distinctions very clear. Some of Brown's illustrations -appear to approach very near to the doctrine of Kant. Thus -he says[7\3], 'The _form_ of bodies is the relation of their -elements to each other in space,--the _power_ of bodies is -their relation to each other in time.' Yet notwithstanding -such approximations in expression, the Kantian doctrine -appears to be different from {181} the views of Stewart and -Brown, as commonly understood. According to the Scotch -philosophers, the cause and the effect are two things, -connected in our minds by a law of our nature. But this view -requires us to suppose that we can conceive the law to be -absent, and the course of events to be unconnected. If we -can understand what is the special force of this law, we -must be able to imagine what the case would be if the law -were non-existing. We must be able to conceive a mind which -does not connect effects with causes. The Kantian doctrine, -on the other hand, teaches that we cannot imagine events -liberated from the connexion of cause and effect: this -connexion is a condition of our conceiving any real -occurrences: we cannot think of a real sequence of things, -except as involving the operation of causes. In the Scotch -system, the past and the future are in their nature -independent, but bound together by a rule; in the German -system, they share in a common nature and mutual relation, -by the act of thought which makes them past and future. In -the former doctrine cause is a tie which binds; in the -latter it is a character which pervades and shapes events. -The Scotch metaphysicians only assert the _universality_ of -the relation; the German attempts further to explain its -_necessity_. - -[Note 7\3: _Lectures_, vol. i. p. 127.] - -This being the state of the case, such illustrations as that -of Dr. Brown quoted above, in which he represents _cause_ as -a relation of the same kind with _form_, do not appear -exactly to fit his opinions. Can the relations of figure be -properly said to be connected with each other by a law of -our nature, or a tendency of our mental constitution? Can we -ascribe it to a law of our thoughts, that we believe the -three angles of a triangle to be equal to two right angles? -If so, we must give the same reason for our belief that two -straight lines cannot inclose a space; or that three and two -are five. But will any one refer us to an ultimate law of -our constitution for the belief that three and two are five? -Do we not see that they are so, as plainly as we see that -they are three and two? Can we imagine laws of our -constitution abolished, so that three and two shall {182} -make something different from five;--so that an inclosed -space shall lie between two straight lines;--so that the -three angles of a plane triangle shall be greater than two -right angles? We cannot conceive this. If the numbers _are_ -three and two; if the lines _are_ straight; if the triangle -_is_ a rectilinear triangle, the consequences are -inevitable. We cannot even imagine the contrary. We do not -want a law to direct that things should be what they are. -The relation, then, of cause and effect, being of the same -kind as the necessary relations of figure and number, is not -properly spoken of as established in our minds by a special -law of our constitution: for we reject that loose and -inappropriate phraseology which speaks of the relations of -figure and number as 'determined by laws of belief.' - -5. In the present work, we accept and adopt, as the basis of -our inquiry concerning our knowledge, the existence of -necessary truths concerning causes, as there exist necessary -truths concerning figure and number. We find such truths -universally established and assented to among the -cultivators of science, and among speculative men in -general. All mechanicians agree that reaction is equal and -opposite to action, both when one body presses another, and -when one body communicates motion to another. All reasoners -join in the assertion, not only that every observed change -of motion has had a cause, but that every change of motion -must have a cause. Here we have certain portions of -substantial and undoubted knowledge. Now the essential point -in the view which we must take of the idea of cause is -this,--that our view must be such as to form a solid basis -for our knowledge. We have, in the Mechanical Sciences, -certain universal and necessary truths on the subject of -causes. Now any view which refers our belief in causation to -mere experience or habit, cannot explain the possibility of -such necessary truths, since experience and habit can never -lead to a perception of necessary connexion. But a view -which teaches us to acknowledge axioms concerning cause, as -we acknowledge axioms {183} concerning space, will lead us -to look upon the science of mechanics as equally certain and -universal with the science of geometry; and will thus -materially affect our judgment concerning the nature and -claims of our scientific knowledge. - -Axioms concerning Cause, or concerning Force, which as we -shall see, is a modification of Cause, will flow from an -Idea of Cause, just as axioms concerning space and number -flow from the ideas of space and number or time. And thus -the propositions which constitute the science of Mechanics -prove that we possess an idea of cause, in the same sense in -which the propositions of geometry and arithmetic prove our -possession of the ideas of space and of time or number. - -6. The idea of cause, like the ideas of space and time, is a -part of the _active_ powers of the mind. The relation of -cause and effect is a relation or condition under which -events are apprehended, which relation is not given by -observation, but supplied by the mind itself. According to -the views which explain our apprehension of cause by -reference to habit, or to a supposed law of our mental -nature, causal connexion is a consequence of agencies which -the mind passively obeys; but according to the view to which -we are led, this connexion is a result of faculties which -the mind actively exercises. And thus the relation of cause -and effect is a condition of our apprehending successive -events, a part of the mind's constant and universal -activity, a source of necessary truths; or, to sum all this -in one phrase, a Fundamental Idea. - - - -{{184}} -CHAPTER IV. - -OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE. - - -1. _Causes are abstract Conceptions._--WE have now to -express, as well as we can, the fundamental character of -that Idea of Cause of which we have just proved the -existence. This may be done, at least for purposes of -reasoning, in this as in former instances, by means of -axioms. I shall state the principal axioms which belong to -this subject, referring the reader to his own thoughts for -the axiomatic evidence which belongs to them. - -But I must first observe, that in order to express general -and abstract truths concerning cause and effect, these -terms, _cause_ and _effect_, must be understood in a general -and abstract manner. When one event gives rise to another, -the first _event_ is, in common language, often called the -cause, and the second the effect. 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 moving. For -our present purposes, however, we must not apply the term -cause to such occurrences as this meeting and turning, but -to a certain conception, _force_, abstracted from all such -special events, and considered as a quality or property by -which one body affects the motion of the other. And in like -manner in other cases, cause is to be conceived as some -abstract quality, power, or efficacy, by which change is -produced; a quality not identical with the events, but -disclosed by means of them. Not only is this abstract mode -of conceiving force and cause useful in expressing the -fundamental principles of science; but it supplies us with -the only mode by which such principles can be {185} stated -in a general manner, and made to lead to substantial truth -and real knowledge. - -Understanding _cause_, therefore, in this sense, we proceed -to our Axioms. - -2. First Axiom. _Nothing can take place without a Cause._ - -Every event, of whatever kind, must have a cause in the -sense of the term which we have just indicated; and that it -must, is a universal and necessary proposition to which we -irresistibly assent as soon as it is understood. We believe -each appearance to come into existence,--we conceive every -change to take place,--not only with something preceding it, -but something by which it is made to be what it is. An -effect without a cause;--an event without a preceding -condition involving the efficacy by which the event is -produced;--are suppositions which we cannot for a moment -admit. That the connexion of effect with cause is universal -and necessary, is a universal and constant conviction of -mankind. It persists in the minds of all men, undisturbed by -all the assaults of sophistry and skepticism; and, as we -have seen in the last chapter, remains unshaken, even when -its foundations seem to be ruined. This axiom expresses, to -a certain extent, our Idea of Cause; and when that idea is -clearly apprehended, the axiom requires no proof, and indeed -admits of none which makes it more evident. That -notwithstanding its simplicity, it is of use in our -speculations, we shall hereafter see; but in the first -place, we must consider the other axioms belonging to this -subject. - -3. Second Axiom. _Effects are proportional to their Causes, -and Causes are measured by their Effects._ - -We have already said that _cause_ is that quality or power, -in the circumstances of each case, by which the effect is -produced; and this power, an abstract property of the -condition of things to which it belongs, can in no way fall -directly under the cognizance of the senses. Cause, of -whatever kind, is not apprehended as including objects and -events which share its nature by being co-extensive with -certain portions of it, as space and time are. It cannot -therefore, like them, be {186} measured by repetition of its -own parts, as space is measured by repetition of inches, and -time by repetition of minutes. Causes may be greater or -less; as, for instance, the force of a man is greater than -the force of a child. But how much is the one greater than -the other? How are we to compare the abstract conception, -force, in such cases as these? - -To this, the obvious and only answer is, that we must -compare causes by means of their effects;--that we must -compare force by something which force can do. The child can -lift one fagot; the man can lift ten such fagots: we have -here a means of comparison. And whether or not the rule is -to be applied in this manner, that is, by the number of -things operated on, (a question which we shall have to -consider hereafter,) it is clear that this form of rule, -namely, a reference to some effect or other as our measure, -is the right, because the only possible form. The cause -determines the effect. The cause being the same, the effect -must be the same. The connexion of the two is governed by a -fixed and inviolable rule. It admits of no ambiguity. Every -degree of intensity in the cause has some peculiar -modification of the effect corresponding to it. Hence the -effect is an unfailing index of the amount of the cause; and -if it be a measurable effect, gives a measure of the cause. -We can have no other measure; but we need no other, for this -is exact, sufficient and complete. - -It may be said, that various effects are produced by the -same cause. The sun's heat melts wax and expands -quicksilver. The force of gravity causes bodies to move -downwards if they are free, and to press down upon their -supports if they are supported. Which of the effects is to -be taken as the measure of heat, or of gravity, in these -cases? To this we reply, that if we had merely different -states of the same cause to compare, any of the effects -might be taken. The sun's heat on different days might be -measured by the expansion of quicksilver, or by the quantity -of wax melted. The force of gravity, if it were different at -different places, might be measured by the spaces through -which a given weight would bend an elastic {187} support, or -by the spaces through which a body would fall in a given -time. All these measures are consistent with the general -character of our idea of cause. - -4. _Limitation of the Second Axiom._--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 cause. For example, if causes are conceived -to be of such a nature as to be capable of addition, the -effects taken as their measure must conform to this -condition. This is the case with mechanical causes. The -weights of two bodies are the causes of the pressure which -they exert downwards; and these weights are capable of -addition. The weight of the two is the sum of the weight of -each. We are therefore not at liberty to say that weights -shall be measured by the spaces through which they bend a -certain elastic support, 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 weights. -Without this precaution, we might obtain inconsistent -results. Two weights, each of the magnitude 3 as measured by -their effects, might, if we took the inflections of a spring -for the effects, be together equal to 5 or to 7 by the same -kind of measurement. For the inflection produced by two -weights of 3 might, for aught we can see beforehand, be more -or less than twice as great as the inflection produced by -one weight of 3. That forces are capable of addition, is a -condition which limits, and, as we shall see, in some cases -rigorously fixes, the kind of effects which are to be taken -as their measures. - -Causes which are thus capable of addition are to be measured -by the repeated addition of equal quantities. Two such -causes are _equal_ to each other when they produce exactly -the same effect. So far our axiom is applied directly. But -these two causes can be _added_ together; and being thus -added, they are _double_ of one of them; and the cause -composed by addition of _three_ such, is _three_ times as -great as the first; and so on for any measure whatever. By -this means, and by this {188} means only, 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 multiplied. - -Causes are, in the present chapter, to be understood in the -widest sense of the term; and the axiom now under our -consideration applies to them, whenever they are of such a -nature as to admit of any measure at all. But the cases -which we have more particularly in view are _mechanical_ -causes, the causes of the motion and of the equilibrium of -bodies. In these cases, forces are conceived as capable of -addition; and what has been said of the measure of causes in -such cases, applies peculiarly to mechanical forces. Two -weights, placed together, may be considered as a single -weight, equal to the _sum_ of the two. Two pressures, -pushing a body in the same direction at the same point, are -identical in all respects with some single pressure, their -_sum_, pushing in like manner; and this is true whether or -not they put the body in motion. In the cases of mechanical -forces, therefore, we take some certain effect, velocity -generated or weight supported, which may fix the _unit_ of -force; and we then measure all other forces by the -successive repetition of this unit, as we measure all spaces -by the successive repetition of our unit of lineal measure. - -But these steps in the formation of the science of Mechanics -will be further explained, when we come to follow our axioms -concerning cause into their application in that science. At -present we have, perhaps, sufficiently explained the axiom -that causes are measured by their effects, and we now -proceed to a third axiom, also of great importance. - -5. Third Axiom. _Reaction is equal and opposite to Action._ - -In the case of mechanical forces, the action of a cause -often takes place by an operation of one body upon another; -and in this case, the action is always and inevitably -accompanied by an _opposite_ action. If I press a stone with -my hand, the stone presses my hand in return. If one ball -strike another and put it in motion, the second ball -diminishes the motion of {189} the first. In these cases the -operation is mutual; the Action is accompanied by a -Reaction. And in all such cases the Reaction is a force of -exactly the same nature as the Action, exerted in an -opposite direction. A pressure exerted upon a body at rest -is resisted and balanced by another pressure; when the -pressure of one body puts another in motion, the body, -though it yields to the force, nevertheless exerts upon the -pressing body a force like that which it suffers. - -Now the axiom asserts further, that this Reaction is -_equal_, as well as opposite, to the Action. For the -Reaction is an effect of the Action, and is determined by -it. And since the two, Action and Reaction, are forces of -the same nature, each may be considered as cause and as -effect; and they must, therefore, determine each other by a -common rule. But this consideration leads necessarily to -their equality: for since the rule is mutual, if we could -for an instant suppose the Reaction to be less than the -Action, we must, by the same rule, suppose the Action to be -less than the Reaction. And thus Action and Reaction, in -every such case, are rigorously equal to each other. - -It is easily seen that this axiom is not a proposition which -is, or can be, proved by experience; but that its truth is -anterior to special observation, and depends on our -conception of Action and Reaction. Like our other axioms, -this has its source in an Idea; namely, the Idea of Cause, -under that particular condition in which cause and effect -are mutual. The necessary and universal truth which we -cannot help ascribing to the axiom, shows that it is not -derived from the stores of experience, which can never -contain truths of this character. Accordingly, it was -asserted with equal confidence and generality by those who -did not refer to experience for their principles, and by -those who did. Leonicus Tomæus, a commentator of Aristotle, -whose work was published in 1552, and therefore at a period -when no right opinions concerning mechanical reaction were -current, at least in his school, says, in his remarks on the -Author's Questions concerning the communication of motion, -that 'Reaction is equal and {190} contrary to Action.' The -same principle was taken for granted by all parties, in all -the controversies concerning the proper measure of force, of -which we shall have to speak: and would be rigorously true, -as a law of motion, whichever of the rival interpretations -of the measure of the term 'Action' we were to take. - -6. _Extent of the Third Axiom._--It may naturally be asked -whether this third Axiom respecting causation extends to any -other cases than those of mechanical action, since the -notion of Cause in general has certainly a much wider -extent. For instance, when a hot body heats a cold one, is -there necessarily an equal reaction of the second body upon -the first? Does the snowball cool the boy's hand exactly as -much as the hand heats the snow? To this we reply, that, in -every case in which one body acts upon another by its -physical qualities, there must be some reaction. No body can -affect another without being itself also affected. But in -any physical change the _action_ exerted is an abstract term -which may be variously understood. The hot hand may _melt_ a -cool body, or may _warm_ it: which kind of effect is to be -taken as action? This remains to be determined by other -considerations. - -In all cases of physical change produced by one body in -another, it is generally possible to assume such a meaning -of action, that the reaction shall be of the same nature as -the action; and when this is done, the third axiom of -causation, that reaction is equal to action, is universally -true. Thus if a hot body heat a cold one, the change may be -conceived as the transfer of a certain substance, _heat_ or -_caloric_, from the first body to the second. On this -supposition, the first body _loses_ just as much heat as the -other _gains_; action and reaction are equal. But if the -reaction be of a different kind to the action we can no -longer apply the axiom. If a hot body _melt_ a cold one, the -latter _cools_ the former: here, then, is reaction; but so -long as the action and reaction are stated in this form, we -cannot assert any equality between them. - -In treating of the secondary mechanical sciences, we {191} -shall see further in what way we may conceive the physical -action of one body upon another, so that the same axioms -which are the basis of the science of Mechanics shall apply -to changes not at first sight manifestly mechanical. - -The three axioms of causation which we have now stated are -the fundamental maxims of all reasoning concerning causes as -to their quantities; and it will be shown in the sequel that -these axioms form the basis of the science of Mechanics, -determining its form, extent, and certainty. We must, -however, in the first place, consider how we acquire those -conceptions upon which the axioms now established are to be -employed. - -[2d Ed.] [The Axiom that _Reaction is equal and opposite to -Action_, may appear to be at variance with a maxim -concerning Cause which is commonly current; namely, that the -'Cause precedes Effect, and Effect follows Cause.' For it -may be said, if _A_, the Action, and _R_, the Reaction, can -be considered as mutually the cause of each other, _A_ must -precede _R_, and yet must follow it, which is impossible. -But to this I reply, that in those cases of direct Causation -to which the maxim applies, the Cause and Effect are not -successive, but simultaneous. If I press against some -obstacle, the obstacle resists and returns the pressure at -the instant it is exerted, not after any interval of time, -however small. The common maxim, that the effect follows the -cause, has arisen from the practice of considering, as -examples of cause and effect, not instantaneous forces or -causes, and the instantaneous changes which they produce; -but taking, instead of this latter, the _cumulative_ effects -produced in the course of time, and compared with like -results occurring without the action of the cause. Thus, if -we alter the length of a clock-pendulum, this change -produces, as its effect, a subsequent change of rate in the -clock: because the rate is measured by the accumulated -effects of the pendulum's gravity, before and after the -change. But the pendulum produces its mechanical effect upon -the escapement, at the moment of its contact, and each wheel -upon the next, at the moment of _its_ contact. As has {192} -been said in a Review of this work, 'The time lost in cases -of indirect physical causation is consumed in the movements -which take place among the parts of the mechanism in action, -by which the active forces so transformed into momentum are -transported over intervals of space to new points of action, -the motion of matter in such cases being regarded as a mere -carrier of force.' (_Quarterly Rev._ No. cxxxv. p. 212.) - -This subject I have further treated in the _Memoirs of the -Cambridge Philosophical Society_, vol. vii. part iii.] [In -this Third Edition I add this discussion.] - -_Discussion of the Question:--Are Cause and Effect -successive or simultaneous?_ - -I HAVE at various times laid before this Society -dissertations on the metaphysical grounds and elements of -our knowledge, and especially on the foundations of the -science of mechanics. As these speculations have not failed -to excite some attention, both here and elsewhere, I am -tempted to bring forward in the same manner some additional -disquisitions of the same kind. Indeed, 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 reader; for I am led to the views and -reasonings which I am now about to lay before the Society, -by some remarks in one of our most popular Reviews, (_The -Quarterly Review_, Article on the _History_ and _Philosophy -of the Inductive Sciences_, June 1841). 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 Sciences_, which remarks appear -to me in the highest degree instructive and philosophical. I -am not, however, going here to discuss fully the doctrines -contained in this critique. With respect to its general -tendency, I will only observe, that the author does not -accept, in the form in which I had given it, the account of -the origin and ground of necessary and universal truths. I -had stated that our knowledge is derived from Sensations and -Ideas; and that Ideas, which are the conditions of -perception, such as _space_, _time_, _likeness_, _cause_, -make universal and necessary knowledge possible; whereas, if -knowledge were derived from Sensation alone, it could not -have those characters. I have moreover {193} enumerated a -long series of Fundamental Ideas as the bases of a -corresponding series of sciences, of which sciences I have -shown also, by an historical survey, that they claim to -possess universal truths, and have their claims allowed. I -have gone further: for I have stated the Axioms which flow -from these Fundamental Ideas, and which are the logical -grounds of necessity and universality in the truths of each -science, when the science is presented in the form of a -demonstrated system. The Reviewer does not assent to this -doctrine, nor to the argument by which it is supported; -namely, that Experience cannot lead to universal truths, -except by means of a universal Idea supplied by the mind, -and infused into the particular facts which observation -ministers. He considers that the existence of universal -truths in our knowledge may be explained otherwise. 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 infinitum_.' I shall not here dwell -upon very strong reasons which may be assigned, as I -conceive, for not accepting this as a full and satisfactory -explanation of the difficulty. Instead of doing so, I shall -here content myself with remarking, that even if we adopt -the Reviewer's expressions, we must still contend that there -are _different forms_ of the _impulse of the mind to -generalize_, corresponding to each of the Fundamental Ideas -of our system. These Fundamental Ideas, if they be nothing -else, must at least be accepted as a classification of the -modes of action of the Inductive Propensity,--as so many -different paths and tendencies of the Generalizing Impulse: -and the Axioms which I have stated as the express results of -the Fundamental Ideas, and as the steps by which those Ideas -make universal truths possible, are still no less worthy of -notice, if they are stated as the results of our -Generalizing Impulse; and as the steps by which that -Impulse, in its many various forms, makes universal truths -possible. The Generalizing Impulse in that operation by -which it leads us to the Axioms of Geometry, and to those of -Mechanics, takes very different courses; and these courses -may well deserve to be separately studied. And perhaps, even -if we accept this view of the philosophy of our knowledge, -no simpler or clearer way can be found of describing and -distinguishing these fundamentally different operations of -the Inductive Propensity, than by saying, {194} that in the -one case it proceeds according to the Idea of Space, in -another according to the Idea of Mechanical Cause; and the -like phraseology may be employed for all the other cases. - -This then being understood, my present object is to consider -some very remarkable, and, as appears to me, novel views of -the Idea of Cause which the Reviewer propounds. And these -may be best brought under our discussion by considering them -as an attempt to solve the question, Whether, according to -our fundamental apprehensions of the relation of Cause and -Effect, effect follows cause in the order of time, or is -simultaneous with it. - -At first sight, this question may seem to be completely -decided by our fundamental convictions respecting cause and -effect, and by the axioms which have been propounded by -almost all writers, and have obtained universal currency -among reasoners on this subject. That the cause must precede -the effect,--that the effect must follow the cause,--are, it -might seem, self-evident truths, assumed and assented to by -all persons in all reasonings in which those notions occur. -Such a doctrine is commonly asserted in general terms, and -seems to be verified in all the applications of the idea of -cause. A heavy body produces motion by its weight; the -motion produced is subsequent in time to the pressure which -the weight exerts. In a machine, bodies push or strike each -other, and so produce a series of motions; each motion, in -this case, is the result of the motions and configurations -which have preceded it. The whole series of such motions -employs time; and this time is filled up and measured by the -series of causes and effects, the effects being, in their -turn, causes of other effects. This is the common mode of -apprehending the universal course of events, in which the -chain of causation, and the progress of time, are -contemplated as each the necessary condition and -accompaniment of the other. - -But this, the Critic remarks, is not true in _direct_ -causation. 'If the antecedence and consequence in question -be understood as the interposition of an interval of time, -however small, between the action of the cause and the -production of the effect, we regard it as inadmissible. In -the production of motion by force, for instance, though the -effect be cumulative with continued exertion of the cause, -yet each elementary or individual action is, to our -apprehension, _instanter_ accompanied with its corresponding -increment of momentum in the body moved. In all dynamical -{195} reasonings no one has ever thought of interposing an -instant of time between the action and its resulting -momentum; nor does it appear necessary.' This is so evident, -that it appears strange it should have the air of novelty; -yet, so far as I am aware, the matter has never before been -put in the same point of view. But this being the case, the -question occurs, how it is that time _seems_ to be employed -in the progress from cause to effect? How is it that the -opinion of the effect being subsequent to the cause has -generally obtained? And to this the Critic's answer is -obvious:--it is so in cases of indirect or of _cumulative_ -effect. If a ball _A_ strikes another, _B_, and puts it in -motion, and _B_ strikes _C_, and puts it in motion, _A_'s -impact may be considered as the cause, though not the direct -cause, of _C_'s motion. Now time, namely the time of _B_'s -motion after it is struck by _A_, and before it strikes _C_, -intervenes between _A_'s impact and the beginning of _C_'s -motion: that is, between the cause and its effect. In this -sense, the effect is subsequent to the cause. Again, if a -body be put in motion by a series of impulses acting at -finite intervals of time, all in the same direction, the -motion at the end of all these intervals is the effect of -all the impulses, and exists after they have all acted. It -is the accumulated effect, and subsequent to each separate -action of the cause. But in this case, each impulse produces -its effect instantaneously, and the time is employed, not in -the transition from any cause to its effect, but in the -intervals between the action of the several causes, during -which intervals the body goes on with the velocity already -communicated to it. In each impulse, force produces motion: -and the motion goes on till a new change takes place, by the -same kind of action. The force may be said, in the language -employed by the Critic, to be transformed into momentum; and -in the successive impulses, successive portions of force are -thus transformed; while in the intervening intervals, the -force thus transformed into momentum is carried by the body -from one place to another, where a new change awaits it. -'The cause is absorbed and transformed into effect, and -therein treasured up.' Hence, as the Writer says, '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 action, by which the active forces -so transformed into mechanism are transported over intervals -of space to new points of action, the motion of matter in -such cases being {196} regarded as a mere carrier of -force':--and when force is directly counteracted by force, -their mutual destruction must be conceived, as the Reviewer -says, to be instantaneous. We can therefore hardly resist -his conclusion, that men have been misled in assuming -sequence as a feature in the relation of cause and effect; -and we may readily assent to his suggestion, that sequence, -when observed, is to be held as a sure indication of -indirect action, accompanied with a movement of parts. - -But yet if we turn for a moment to other kinds of causation, -we seem to be compelled at every step to recognize the truth -of the usual maxim upon this subject, that effects are -subsequent to causes. Is not poison, taken at a certain -moment, the cause of disorder and death which follow at a -_subsequent_ period? Is not a man's early prudence often the -cause of his prosperity in _later_ life, and his folly, -though for a moment it may produce gratification, _finally_ -the cause of his ruin? And even in the case of mechanism, -if, in a clock which goes rightly, we alter the length of -the pendulum, is not this alteration the cause of an -alteration which _afterwards_ takes place in the rate of the -clock's going? Are not all these, and innumerable other -cases, instances in which the usual notion of the effect -following the cause is verified? and are they not -irreconcileable with the new doctrine of cause and effect -being simultaneous? - -In order to disentangle this apparent confusion, let us -first consider the case last mentioned, of a clock, in which -some alteration is made which affects the rate of going. - -So long as the parts of the clock remain unaltered, its rate -will remain unaltered; and any part which is considered as -capable of alteration, may be considered as, if we please, -the cause of the unaltered rate, by being itself unaltered. -But we do not usually introduce the positive idea of cause, -to correspond with this negation of change. If we speak of -the rate as unaltered, we may also say that it is so because -there is _no cause_ of alteration. The steady rate is the -indication of the absence of any cause of alteration; and -the rate of going measures the progress of time, in a state -of things in which causes of change are thus excluded. If an -alteration takes place in any part of the clock, once for -all, the rate is altered; but the new rate is steady as the -old rate was, and, like it, measures the uniform progress of -time. But the difference between the new rate and the old is -occasioned by {197} the difference of the parts of the -clock; and the new rate may very properly be said to be -caused by the change of the parts, and to be subsequent to -it: for it does prevail after the change, and does not -prevail before. - -But how is this view to be reconciled with the one just -quoted from the Reviewer, and, as it appeared, -satisfactorily proved by him; according to which all -mechanical effects are simultaneous with their causes, and -not subsequent to them? We have here the two views in close -contact, and in seeming opposition. - -In the going of a clock, the parts are in motion; and these -motions are determined by forces arising from the form and -connexion of the parts of the mechanism. Each of the forces -thus exerted at any instant produces its effect at the same -instant; and thus, so far as the term _cause_ refers to such -instantaneous forces, the cause and the effect are -simultaneous. But if such instantaneous forces act at -successive intervals of time, the motion during each -interval is unaltered, and by its uniform progress measures -the progress of time. And thus the motion of the machine -consists of a series of intervals, during each of which the -motion is uniform, and measures the time; separated from -each other by a series of changes, at each of which the -change measures the instantaneous force, and is simultaneous -with it. And if, in this case, we suppose, at any point of -time, the instantaneous forces to cease, the succession of -them being terminated, from that point of time the motion -would be uniform. 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 motion, the rate of -the motion in each interval of time is determined by all the -preceding instantaneous forces. Hence, when the series of -instantaneous forces stops, the rate at which the motion -goes on permanently, from that point of time, is determined -by the antecedent series of such forces, which series may be -considered as an aggregate cause; and hence it appears, that -the _permanent_ effect is determined by the _aggregate_ -cause; and in this sense the effect is subsequent to the -cause. - -Thus we obtain, in this case, a solution of the difficulty -which is placed before us. The instantaneous effect or -change is simultaneous with the instantaneous force or cause -by which it is {198} produced. But if we consider a series -of such instantaneous forces as a single aggregate cause, -and the final condition as a permanent effect of this cause, -the effect is subsequent to the cause. In this case, the -cause is immediately succeeded by the effect. The cause acts -in time: the effect goes on in time. The times occupied by -the cause and by the effect succeed each other, the one -ending at the point of time at which the other begins. But -the time which the cause occupies is really composed of a -series of instants of uniform motion interposed between -instantaneous forces; and during the time that this series -of causes is going on, to make up the aggregate cause, a -series of effects is going on to make up the final effect. -There is a progressive cause and a progressive effect which -go on together, and occupy the same finite time; and this -simultaneous progression is composed of all the simultaneous -instantaneous steps of cause and effect. The aggregate cause -is the sum of the progression of causes; the final effect is -the last term of the progression of effects. At each step, -as the Reviewer says, cause is transformed into effect; and -it is treasured up in the results during the intermediate -intervals; and the time occupied is not the time which -intervenes between cause and effect at each step, but the -time which intervenes between these transformations. - -I have supposed forces to act at distinct instants, and to -cease to act in the intervals between; and then, the -aggregate of such intervals to make up a finite time, during -which an aggregate force acts. But if the action of the -force be rigorously continuous, it will easily be seen that -all the consequences as to cause and effect will be the -same; the discontinuous action being merely the usual -artifice by which, in mathematical reasonings, we obtain -results respecting continuous changes. It will still be -true, that the uniform motion which takes place after a -continuous force has acted, is the effect subsequent to the -cause; while the change which takes place at any instant by -the action of the force, is the instantaneous effect -simultaneous with the cause. - -It may be objected, that this solution does not appear -immediately to apply: for the motion of a clock is not -uniform during any portion of the time. The parts move by -intervals of varied motion and of rest; or by oscillations -backwards and forwards; and the succession of forces which -acts during any {199} oscillation, or any cycle of motion, -is repeated during the succeeding oscillation or cycle, and -so on indefinitely; and if an alteration be made in the -parts, it is not a change once for all, but recurs in its -operation in every cycle of the motion. - -But it will be found that this circumstance does not prevent -the same explanation from being still applicable with a -slight modification. Instead of uniform motion in the -intervals of causation, we shall have to speak of _steady -going_: and instead of considering all the forces which -affect the motion as causes of change of uniform motion, we -shall have to speak of changes in the parts of the mechanism -as causes of _change of rate of going_. With this -modification, it will still be true, that any instantaneous -cause produces its instantaneous effect simultaneously, -while the permanent effect is subsequent to the change which -is its cause. The steady going of the clock is assumed as a -normal condition, in which it measures the progress of time; -and in this assumption, the notion of cause and effect is -not brought into view. But a steady rate thus denoting the -mean passage of time, a change in the rate indicates a cause -of change. The _change of rate_, as an instantaneous -_transition_ from one rate to another, is _simultaneous_ -with the change in the parts. But then the _changed rate_ as -a continued _condition_ in which, no new change supervening, -the rate again measures the progress of time, is -_subsequent_ to the change of parts, for it begins when that -ends, and continues when the progress of that has ceased. - -If, however, this be a satisfactory solution of the -difficulty in the case of mechanism, how shall we apply the -same views to the other cases? Growth, the effect of food, -is subsequent to the act of taking food; disorder, the -effect of poison, is subsequent to the introduction of -poison into the system. Can we say that the animal would -continue unchanged if it were not to take food; and that -food is the cause of a change, namely, of growth? This is -manifestly false; for if the animal were not to take food, -it would soon perish. But the analogy of the former case, of -the clock, will enable us to avoid this perplexity. As we -assumed a steady rate of going in the clock to be the -measure of time when we considered the effect of mechanism, -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 {200} development and health -of animals. Digestion, and of course nutrition, are a part -of this normal condition; they are involved in the steady -going of the animal mechanism, and we must suppose these -functions to go regularly on, in order that the animal may -preserve its character of animal. Food and digestion may be -considered as causes of the continued existence of the -animal, in the same way in which the form of the parts of a -clock is the cause of the steady going of a clock. And when -we come to consider causes of change, this kind of -causation, which produces a normal condition of things, -merely measuring the flow of time, is left out of our -account. We can conceive an uniform condition of animal -existence, the animal neither growing nor wasting. This -being taken as the normal condition, any deviation from this -condition indicates a cause, and is taken as the evidence -and measure of the cause of change. And thus, in a growing -animal, the food partly keeps the animal in continued animal -existence, and partly, and in addition to this, causes its -growth. Food, in the former view, is always circulating in -the system, and is supposed to be uniformly administered; -the cycles of nutrition being merged in the notion of -uniform existence, as the oscillations of the pendulum in a -clock are merged in the notion of uniform going; and the -elementary steps of nutrition which are, in this view, -supposed to take place at each instant, produce their -instantaneous effect, for they are requisite in the cycle of -animal processes which goes on from instant to instant. But -on the other hand, in considering growth, we compare the -state of an animal with a preceding state, and consider the -nutriment taken in the intervening time as the cause of the -change: hence this nutriment, as an aggregate, is considered -as the cause of growth of the animal; and in this view the -effect is subsequent to the cause. But yet here, as in the -case of mechanism, the progressive effect is simultaneous, -step by step, with the progressive cause. There is a series -of operations; as for instance, intussusception, digestion, -assimilation, growth: each of these is a progressive -operation; and in the progress of each operation, the steps -of the effect and the instantaneous forces are simultaneous. -But the end of one operation is the beginning of the next, -or at least in part, and hence we have time occupied by the -succession. The end of intussusception is the beginning of -digestion, the end of digestion the beginning of -assimilation, {201} and so on. These aggregate effects -succeed each other; and hence growth is subsequent to the -taking of food; though each instantaneous force of animal -life, no less than of mechanism, produces an effect -simultaneous with its action. Each of these separate -operations is an aggregate operation, and occupies time; and -each aggregate effect is a condition of the action of the -cause in the next operation. - -Again; if an animal in a permanent condition, neither waxing -nor wasting, may be taken as the normal state in which the -functions of life measure time, in order that we may -consider growth as an effect, to be referred to food as -cause; we may, for other purposes, consider, as the normal -condition, an animal waxing and then wasting, according to -the usual law of animal life: and we must take this, the -healthy progress of an animal, as our normal condition, if -we have to consider causes which produce disease. If we have -to refer the morbid condition of an animal to the influence -of poison, for example, we must consider how far the -condition deviates from what it would have been if the -poison had not been taken into the frame. The usual progress -of the animal functions including its growth, is the measure -of time; the deviation from this usual progress is the -indication of cause; and the effect of the poison is -subsequent to the cause, because the poison acts through the -cycle of the animal functions just mentioned, which occupies -time; and because the taking the poison into the system, not -any subsequent action of the animal forces in the system, is -considered as the event which we must contemplate as a -cause. To resume the analogy of the clock: the rate of the -clock is altered by altering the parts; but this alteration -itself may occupy time; as if we alter the rate of a clock -by applying a drop of acid, which gradually eats off a part -of the pendulum, the corrosion, as an aggregate effect, -occupies time; and the rates before and after the change are -separated by this time. But the application of the drop is -the cause; and thus, in this case the final effect is -subsequent to the cause, though here, as in the case of -mechanism, the instantaneous forces always produce a -simultaneous effect. - -Thus we have in every case a _uniform_ state, or a state -which is considered as uniform, or at least _normal_; and -which is taken as the indication and measure of _time_; and -we have also _change_, {202} which is contemplated as a -deviation from uniformity, and is taken as the indication -and measure of _cause_. The uniform state may be one which -never exists, being purely imaginary; as the case in which -no forces act; and the case in which animal functions go on -permanently, the animal neither growing nor wasting. The -normal state may also be a state in which change is -constantly taking place, as, in fact, even a state of motion -is a state of change; such states also are, in a further -sense, that of a clock going by starts, and that of an -animal constantly growing: in these cases the changes are -all merged in a wider view of uniformity, so that these are -taken as the normal states. And in all these cases, -successive changes which take place are separated by -intervals of time, measured by the normal progress; and each -change is produced by some _simultaneous_ instantaneous -cause. But taking the cause in a larger sense, we group -these instantaneous causes, and perhaps omit in our -contemplation some of the intervening intervals; and thus -assign the cause to a _preceding_, and the effect to a -_succeeding_ time. - -I may observe further, as a corollary from what has been -said, that the measure of time is different, when we -consider different kinds of causation; and in each case, is -_homogeneous_ with the changes which causation effects. In -the consideration of mechanical causes, we measure time by -mechanical changes;--by uniform motion, or uniform -succession of cycles of motion; by the rotation of a wheel, -or the oscillation of a pendulum. But if we have to consider -physiological changes, the progress of time is -physiologically measured;--by the normal progress of vital -operations; by the circulation, digestion or development of -the organized body; by the pulse, or by the growth. These -different measures of time give to time, so far as it is -exhibited by facts and events, a different character in the -different cases. Phenomenal time has a different nature and -essence according to the kind of the changes which we -consider, and which gives us our sole phenomenal indication -of cause. - -I fear that I am travelling into matters too abstruse and -metaphysical for the occasion: but before I conclude, I will -present one other aspect of the subject. - -In stating the difficulty, I referred to cases of moral as -well as physical causation; as when prudence produces -prosperity, or {203} when folly produces ruin. It may be -asked, whether we are here to apply the same -explanation;--whether we are to assume a normal condition of -human existence, in which neither prudence nor folly are -displayed, neither prosperity nor adversity -produced;--whether we are to conceive the progress of such a -state to measure the progress of time, and deviations from -it to denote causes of the kind mentioned. It may be asked -further, whether, if we do make this supposition, we can -resolve the influence of such causes as prudence or -imprudence into instantaneous acts, which produce their -effects immediately: and which occupy time only by being -separated by intervals of the inactive normal moral -condition. To this I must here reply, that the discussion of -such questions would carry me too far, and would involve -speculations not included within the acknowledged domain of -this Society, from which I therefore abstain. But I may say, -before quitting the subject, that I do not think the -suppositions above suggested are untenable; and that in -order to include moral causation under the maxims of -causation in general, we must necessarily make some such -hypothesis. The peculiarity of that kind of causation which -the will and the character exert, and which is exerted upon -the will and the character, would make this case far more -complex and difficult than those already considered; but, at -the same time, would offer us the means of explaining what -may seem harsh, in the above analogy. For instance, we -should have to assume such a maxim as this: that in moral -causation, time is not to be measured by the flow of -mechanical or physiological events;--not by the clock, or by -the pulse. Moral causation has its own clock, its own pulse, -in the progress of man's moral being; and by this measure of -time is the relation of moral cause and effect to be -defined. - -That in estimating moral causation, the progress of time is -necessarily estimated by moral changes, and not by -machinery,--by the progress of events, and not by the going -of the clock,--is a truth familiar as a practical maxim to -all who give their thoughts to dramatic or narrative -fictions. Who feels any thing incongruous or extravagantly -hurried in the progress of events in that great exhibition -of moral causation, the tragedy of Othello? If we were asked -what time those vast and terrible {204} and complex changes -of the being and feelings of the characters occupy, we -should say, that, measured on its own scale, the event is of -great extent;--that the transaction is of considerable -magnitude in all ways. But if, with previous critics, we -look into the progress of time by the day and the hour--what -is the measure of this history? Forty-eight hours. - - - -{{205}} -CHAPTER V. - -OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER. - - -1. _Force._--WHEN the faculties of observation and thought -are developed in man, the idea of causation is applied to -those changes which we see and feel in the state of rest and -motion of bodies around us. And when our abstract -conceptions are thus formed and named, we adopt the term -_Force_, and use it to denote that property which is the -cause of motion produced, changed, or prevented. This -conception is, it would seem, mainly and primarily suggested -by our consciousness of the exertions by which we put bodies -in motion. The Latin and Greek words for _Force_, Vis, Ϝὶς, -were probably, like all abstract terms, derived at first -from some sensible object. The original meaning of the Greek -word was a _muscle_ or _tendon_. Its first application as an -abstract term is accordingly to muscular force: - - Δεύτερος αὖτ' Αἴας πολὺ μείζονα λᾶαν ἀείρας - ἦκ' ἐπιδινήσας, ἐπέρεισε δὲ ϜÎ͂Ν' ἀπέλεθρον. - - Then Ajax a far heavier stone upheaved, - He whirled it, and impressing Force intense - Upon the mass, dismist it. - -The property by which bodies affect each other's motions, -was naturally likened to that energy which we exert upon -them with similar effect: and thus the labouring horse, the -rushing torrent, the descending weight, the elastic bow, -were said to exert force. {206} Homer[8\3] speaks of the -_force_ of the river, Ϝὶς ποταμοῖο; and Hesiod[9\3] of the -_force_ of the north wind, Ϝὶς ἀνέμου βορέαο. - -[Note 8\3: _Il._ xxi.] - -[Note 9\3: _Op. et D._] - -Thus man's general notion of force was probably first -suggested by his muscular exertions, that is, by an act -depending upon that muscular sense, to which, as we have -already seen, the perception of space is mainly due. And -this being the case, it will be easily understood that the -_Direction_ of the force thus exerted is perceived by the -muscular sense, at the same time that the force itself is -perceived; and that the direction of any other force is -understood by comparison with force which man must exert to -produce the same effect, in the same manner as force itself -is so understood. - -This abstract notion of Force long remained in a very vague -and obscure condition, as may be seen by referring to the -History for the failures of attempts at a science of force -and motion, made by the ancients and their commentators in -the middle ages. By degrees, in modern times, we see the -scientific faculty revive. The conception of Force becomes -so far distinct and precise that it can be reasoned upon in -a consistent manner, with demonstrated consequences; and a -genuine science of Mechanics comes into existence. The -foundations of this science are to be found in the Axioms -concerning causation which we have already stated; these -axioms being interpreted and fixed in their application by a -constant reference to observed facts, as we shall show. But -we must, in the first place, consider further those primary -processes of observation by which we acquire the first -materials of thought on such subjects. - -2. _Matter._--The conception of Force, as we have said, -arises with our consciousness of our own muscular exertions. -But we cannot imagine such exertions without also imagining -some bodily substance against which they are exercised. If -we press, we press something: if we thrust or throw, there -must be something {207} to resist the thrust or to receive -the impulse. Without body, muscular force cannot be exerted, -and force in general is not conceivable. - -Thus Force cannot exist without _Body_ on which it acts. The -two conceptions, Force and Matter, are co-existent and -correlative. Force implies resistance; and the force is -effective only when the resistance is called into play. If -we grasp a stone, we have no hold of it till the closing of -the hand is resisted by the solid texture of the stone. If -we push open a gate, we must surmount the opposition which -it exerts while turning on its hinges. However slight the -resistance be, there must be some resistance, or there would -be no force. If we imagine a state of things in which -objects do not resist our touch, they must also cease to be -influenced by our strength. Such a state of things we -sometimes imagine in our dreams; and such are the poetical -pictures of the regions inhabited by disembodied spirits. In -these, the figures which appear are conspicuous to the eye, -but impalpable like shadow or smoke; and as they do not -resist the corporeal impressions, so neither do they obey -them. The spectator tries in vain to strike or to grasp -them. - - Et ni docta comes tenues sine corpore vitas - Admoneat volitare cavâ sub imagine formæ, - Irruat ac frustra ferro diverberet umbras. - - The Sibyl warns him that there round him fly - Bodiless things, but substance to the eye; - Else had he pierced those shapes with life-like face, - And smitten, fierce, the unresisting space. - - Neque illum - Prensantem nequicquam umbras et multa volentem - Dicere, preterea vidit. - - He grasps her form, and clutches but the shade. - -Such may be the circumstances of the unreal world of dreams, -or of poetical fancies approaching to dreams: for in these -worlds our imaginary perceptions are bound by no rigid -conditions of force and reaction. In {208} such cases, the -mind casts off the empire of the idea of cause, as it casts -off even the still more familiar sway of the ideas of space -and time. But the character of the material world in which -we live when awake is, that we have at every instant and at -every place, force operating on matter and matter resisting -force. - -3. _Solidity._--From our consciousness of muscular exertion, -we derive, as we have seen, the conception of force, and -with that also the conception of matter. We have already -shown, in a former chapter, that the same part of our frame, -the muscular system, is the organ by which we perceive -extension and the relations of space. Thus the same organ -gives us the perception of body as resisting force, and as -occupying space; and by combining these conditions we have -the conception of _solid_ extended bodies. In reality, this -resistance is inevitably presented to our notice in the very -facts from which we collect the notion of extension. For the -action of the hand and arm by which we follow the forms of -objects, implies that we apply our fingers to their surface; -and we are stopped there by the resistance which the body -offers. This resistance is precisely that which is requisite -in order to make us conscious of cur muscular effort[10\3]. -Neither touch, nor any other mere passive sensation, could -produce the perception of extent, as we have already urged: -nor could the muscular sense lead to such a perception, -except the extension of the muscles were felt to be -resisted. And thus the perception of resistance enters the -mind along with the perception of extended bodies. All the -objects with which we have to do are not only extended but -solid. - -[Note 10\3: Brown's _Lectures_, i. 466.] - -This sense of the term _solidity_, (the general property of -all matter,) is different to that in which we oppose -_solidity_ to _fluidity_. We may avoid ambiguity by opposing -_rigid_ to _fluid_ bodies. By solid bodies, as we now speak -of them, we mean only such as resist the pressure which we -exert, so long as their parts continue in their places. By -fluid bodies, we mean those {209} whose parts are, by a -slight pressure, removed out of their places. A drop of -water ceases to prevent the contact of our two hands, not by -ceasing to have solidity in this sense, but by being thrust -out of the way. If it could remain in its place, it could -not cease to exercise its resistance to our pressure, except -by ceasing to be matter altogether. - -The perception of solidity, like the perception of -extension, implies an act of the mind, as well as an -impression of the senses: as the perception of extension -implies the idea of space, so the perception of solidity -implies the idea of action and reaction. That an Idea is -involved in our knowledge on this subject, appears, as in -other instances, from this consideration, that the -convictions of persons, even of those who allow of no ground -of knowledge but experience, do in fact go far beyond the -possible limits of experience. Thus Locke says[11\3], that -'the bodies which we daily handle hinder by an -_insurmountable_ force the approach of the parts of our -hands that press them.' Now it is manifest that our -observation can never go to this length. By our senses we -can only perceive that bodies resist the greatest actual -forces that we exert upon them. But our conception of force -carries us further: and since, so long as the body is there -to receive the action of the force, it must suffer the whole -of that action, and must react as much as it suffers: it is -therefore true, that so long as the body remains there, the -force which is exerted upon it can never surmount the -resistance which the body exercises. And thus this doctrine, -that bodies resist the intrusion of other bodies by an -insurmountable force, is, in fact, a consequence of the -axiom that the reaction is always equal to the action. - -[Note 11\3: _Essay_, b. ii. c. 4.] - -4. _Inertia._--But this principle of the equality of action -and reaction appears also in another way. Not only when we -exert force upon bodies at rest, but when, by our exertions, -we put them in motion, they react. If we set a large stone -in motion, the stone {210} resists; for the operation -requires an effort. By increasing the effort, we can -increase the effect, that is, the motion produced; but the -resistance still remains. And the greater the stone moved, -the greater is the effort requisite to move it. There is, in -every case, a resistance to motion, which shows itself, not -in preventing the motion, but in a reciprocal force, exerted -backwards upon the agent by which the motion is produced. -And this resistance resides in each portion of matter, for -it is increased as we add one portion of matter to another. -We can push a light boat rapidly through the water; but we -may go on increasing its freight, till we are barely able to -stir it. This property of matter, then, by which it resists -the reception of motion, or rather by which it reacts and -requires an adequate force in order that any motion may -result, is called its inertness, or _inertia_. That matter -has such a property, is a conviction flowing from that idea -of a reaction equal and opposite to the action, which the -conception of all force involves. By what laws this inertia -depends on the magnitude, form, and material of the body, -must be the subject of our consideration hereafter. But that -matter has this inertia, in virtue of which, as the matter -is greater, the velocity which the same effort can -communicate to it is less, is a principle inseparable from -the notion of matter itself. - -Hermann says that Kepler first introduced this 'most -significant' _inertia_. Whether it is to be found in earlier -writers I know not; 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 mechanics. He assumes the -slowness of the motions of the planets to increase, (other -causes remaining the same,) as the inertia increases; and -though, even in this assumption, there is an errour -involved, (if we adopt that interpretation of the term -_inertia_ to which subsequent researches led,) 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 -reaction. {211} - -5. We have thus seen, I trust in a satisfactory manner, the -origin of our conceptions of Force, Matter, Solidity, and -Inertness. It has appeared that the organ by which we obtain -such conceptions is that very muscular frame, which is the -main instrument of our perceptions of space; but that, -besides bodily sensations, these ideal conceptions, like all -the others which we have hitherto considered, involve also -an habitual activity of the mind, giving to our sensations a -meaning which they could not otherwise possess. And among -the ideas thus brought into play, is an idea of action with -an equal and opposite reaction, which forms a foundation for -universal truths to be hereafter established respecting the -conceptions thus obtained. - -We must now endeavour to trace in what manner these -fundamental principles and conceptions are unfolded by means -of observation and reasoning, till they become an extensive -yet indisputable science. - - - -{{212}} -CHAPTER VI. - -OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS. - - -1. _Object of the Chapter._--IN the present and the -succeeding chapters we have to show how the general axioms -of Causation enable us to construct the science of -Mechanics. We have to consider these axioms as moulding -themselves, in the first place, into certain fundamental -mechanical principles, which are of evident and necessary -truth in virtue of their dependence upon the general axioms -of Causation; and thus as forming a foundation for the whole -structure of the science;--a system of truths no less -necessary than the fundamental principles, because derived -from these by rigorous demonstration. - -This account of the construction of the science of -Mechanics, however generally treated, cannot be otherwise -than technical in its details, and will probably be -imperfectly understood by any one not acquainted with -Mechanics as a mathematical science. - -I cannot omit this portion of my survey without rendering my -work incomplete; but I may remark that the main purpose of -it is to prove, in a more particular manner, what I have -already declared in general, that there are, in Mechanics no -less than in Geometry, fundamental principles of axiomatic -evidence and necessity;--that these principles derive their -axiomatic character from the Idea which they involve, -namely, the Idea of Cause;--and that through the combination -of principles of this kind, the whole science of Mechanics, -including its most complex and remote results, exists as a -body of solid and universal truths. {213} - -2. _Statics and Dynamics._--We must first turn our attention -to a technical distinction of Mechanics into two portions, -according as the forces about which we reason produce rest, -or motion; the former portion is termed _Statics_, the -latter _Dynamics_. If a stone fall, or a weight put a -machine in motion, the problem belongs to Dynamics; but if -the stone rest upon the ground, or a weight be merely -supported by a machine, without being raised higher, the -question is one of Statics. - -3. _Equilibrium._--In Statics, forces _balance_ each other, -or keep each other _in equilibrium_. And forces which -directly balance each other, or keep each other in -equilibrium, are necessarily and manifestly equal. If we see -two boys pull at two ends of a rope so that neither of them -in the smallest degree prevails over the other, we have a -case in which two forces are in equilibrium. The two forces -are evidently equal, and are a statical exemplification of -action and reaction, such as are spoken of in the third -axiom concerning causes. Now the same exemplification occurs -in every case of equilibrium. No point or body can be kept -at rest except in virtue of opposing forces acting upon it; -and these forces must always be equal in their opposite -effect. When a stone lies on the floor, the weight of the -stone downwards is opposed and balanced by an equal pressure -of the floor upwards. If the stone rests on a slope, its -tendency to slide is counteracted by some equal and opposite -force, arising, it may be, from the resistance which the -sloping ground opposes to any motion along its surface. -Every case of rest is a case of equilibrium: every case of -equilibrium is a case of equal and opposite forces. - -The most complex frame-work on which weights are supported, -as the roof of a building, or the cordage of a machine, are -still examples of equilibrium. In such cases we may have -many forces all combining to balance each other; and the -equilibrium will depend on various conditions of direction -and magnitude among the forces. And in order to understand -what are these conditions, we must ask, in the first place, -what {214} we understand by the magnitude of such -forces;--what is the measure of statical forces. - -4. _Measure of Statical Forces._--At first we might expect, -perhaps, that since statical forces come under the general -notion of Cause, the mode of measuring them would be derived -from the second axiom of Causation, that causes are measured -by their effects. But we find that the application of this -axiom is controlled by the limitation which we noticed, -after stating that axiom; namely, the condition that the -causes shall be capable of addition. Further, as we have -seen, a statical force produces no other effect than this, -that it balances some other statical force; and hence the -measure of statical forces is necessarily dependent upon -their balancing, that is, upon the equality of action and -reaction. - -That _statical forces are capable of addition_ is involved -in our conception of such forces. When two men pull at a -rope in the same direction, the forces which they exert are -added together. When two heavy bodies are put into a basket -suspended by a string, their weights are added, and the sum -is supported by the string. - -Combining these considerations, it will appear that the -measure of statical forces is necessarily given at once by -the fundamental principle of the equality of action and -reaction. Since two opposite forces which balance each other -are equal, each force is measured by that which it balances; -and since forces are capable of addition, a force of any -magnitude is measured by adding together a proper number of -such equal forces. Thus a heavy body which, appended to some -certain elastic branch of a tree, would bend it down through -one inch, may be taken as a unit of weight. Then if we -remove this first body, and find a second heavy body which -will also bend the branch through the same space, this is -also a unit of weight; and in like manner we might go on to -a third and a fourth equal body; and adding together the -two, or the three, or the four heavy bodies, we have a force -twice, or three times, or four times the unit of weight. And -with {215} such a collection of heavy bodies, or _weights_, -we can readily measure all other forces; for the same -principle of the equality of action and reaction leads at -once to this maxim, that any statical force is measured by -the weight which it would support. - -As has been said, it might at first have been supposed that -we should have to apply, in this case, the axiom that causes -are measured by their effects in another manner; that thus, -if that body were a unit of weight which bent the bough of a -tree through one inch, _that_ body would be _two_ units -which bent it through _two_ inches, and so on. But, as we -have already stated, the measures of weight must be subject -to this condition, that they are susceptible of being added: -and therefore we cannot take the deflexion of the bough for -our measure, till we have ascertained, that which experience -alone can teach us, that under the burden of two equal -weights, the deflexion will be twice as great as it is with -one weight, which is not true, or at least is neither -obviously nor necessarily true. In this, as in all other -cases, although causes must be measured by their effects, we -learn from experience only how the effects are to be -interpreted, so as to give a true and consistent measure. - -With regard, however, to the measure of statical force, and -of weight, no difficulty really occurred to philosophers -from the time when they first began to speculate on such -subjects; for it was easily seen that if we take any uniform -material, as wood, or stone, or iron, portions of this which -are geometrically equal, must also be equal in statical -effect; since this was implied in the very hypothesis of a -uniform material And a body ten times as large as another of -the same substance, will be of ten times the weight. But -before men could establish by reasoning the conditions under -which weights would be in equilibrium, some other principles -were needed in addition to the mere measure of forces. The -principles introduced for this purpose still resulted from -the conception of equal action and reaction; but it required -no small clearness of thought to select them rightly, and to -employ them {216} successfully. This, however, was done, to -a certain extent, by the Greeks; and the treatise of -Archimedes _On the Center of Gravity_, is founded on -principles which may still be considered as the genuine -basis of statical reasoning. I shall make a few remarks on -the most important principle among those which Archimedes -thus employs. - -5. _The Center of Gravity._--The most important of the -principles which enter into the demonstration of Archimedes -is this: that "Every body has a center of gravity;" meaning -by the center of gravity, a point at which the whole matter -of the body may be supposed to be collected, to all intents -and purposes of statical reasoning. This principle has been -put in various forms by succeeding writers: for instance, it -has been thought sufficient to assume a case much simpler -than the general one; and to assert that two _equal_ bodies -have their center of gravity in the point midway between -them. It is to be observed, that this assertion not only -implies that the two bodies will _balance_ upon a support -placed at that midway point, but also, that they will -exercise, upon such a support, a _pressure equal to their -sum_; for this point being the center of gravity, the whole -matter of the two bodies may be conceived to be collected -there, and therefore the whole weight will press there. And -thus the principle in question amounts to this, that _when -two equal heavy bodies are supported on the middle point -between them, the pressure upon the support is equal to the -sum of the weights of the bodies_. - -A clear understanding of the nature and grounds of this -principle is of great consequence: for in it we have the -foundation of a large portion of the science of Mechanics. -And if this principle can be shown to be necessarily true, -in virtue of our Fundamental Ideas, we can hardly doubt that -there exist many other truths of the same kind, and that no -sound view of the evidence and extent of human knowledge can -be obtained, so long as we mistake the nature of these, its -first principles. {217} - -The above principle, that the pressure on the support is -equal to the sum of the bodies supported, is often stated as -an axiom in the outset of books on Mechanics. And this -appears to be the true place and character of this -principle, in accordance with the reasonings which we have -already urged. The axiom depends upon our conception of -action and reaction. That the two weights are supported, -implies that the supporting force must be equal to the force -or weight supported. - -In order further to show the foundation of this principle, -we may ask the question:--If it be not an axiom, deriving -its truth from the fundamental conception of equal action -and reaction, which equilibrium always implies, what is the -origin of its certainty? The principle is never for an -instant denied or questioned: it is taken for granted, even -before it is stated. No one will doubt that it is not only -true, but true with the same rigour and universality as the -axioms of Geometry. Will it be said, that it is borrowed -from experience? Experience could never prove a principle to -be universally and rigorously true. Moreover, when from -experience we prove a proposition to possess great exactness -and generality, we approach by degrees to this proof: the -conviction becomes stronger, the truth more secure, as we -accumulate trials. But nothing of this kind is the case in -the instance before us. There is no gradation from less to -greater certainty;--no hesitation which precedes confidence. -From the first, we know that the axiom is exactly and -certainly true. In order to be convinced of it, we do not -require many trials, but merely a clear understanding of the -assertion itself. - -But in fact, not only are trials not necessary to the proof, -but they do not strengthen it. 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 weights. Certainly no -person with clear mechanical conceptions ever wanted such a -trial to convince him of the truth; or thought the truth -clearer after the trial had been made. If to such a person, -an {218} experiment were shown which seemed to contradict -the principle, his conclusion would be, not that the -principle was doubtful, but that the apparatus was out of -order. Nothing can be less like collecting truth from -experience than this. - -We maintain, then, that this equality of mechanical action -and reaction, is one of the principles which do not flow -from, but regulate our experience. To this principle, the -facts which we observe must conform; and we cannot help -interpreting them in such a manner that they shall be -exemplifications of the principle. A mechanical pressure not -accompanied by an equal and opposite pressure, can no more -be given by experience, than two unequal right angles. With -the supposition of such inequalities, space ceases to be -space, force ceases to be force, matter ceases to be matter. -And this equality of action and reaction, considered in the -case in which two bodies are connected so as to act on a -single support, leads to the axiom which we have stated -above, and which is one of the main foundations of the -science of Mechanics. - -[2d ed.] [To the doctrine that mechanical principles, such -as the one here under consideration (that the pressure on -the point of support is equal to the sum of the weights), -are derived from our Ideas, and do not flow from but -regulate our experience, objections are naturally made by -those who assert all our knowledge to be derived from -experience. How, they ask, can we know the properties of -pressures, levers and the like, except from experience? 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 center? This cannot be, except we suppose in -the lever tenacity, rigidity and the like, which are -qualities known only by experience. And it is obvious that -this line of argument might be carried on through the whole -subject. - -My answer to this objection is a remark of the same kind as -one which I have made respecting the Ideas of Space, Time, -and Number, in the last Book. The mind, in apprehending -events as causes {219} and effects, is governed by Laws of -its own Activity; and these Laws govern the results of the -mind's action; and make these results conform to the Axioms -of Causation. But this activity of the mind is awakened and -developed by being exercised; and in dealing with the -examples of cause and effect here spoken of, (namely, -pressure and resistance, force and motion,) the mind's -activity is necessarily governed also by the bodily powers -of perception and action. We are human beings only in so far -as we have existed in space and time; and of our human -faculties, developed by our existence in space and time, -space and time are necessary conditions. In like manner, we -are human beings only in so far as we have bodies, and -bodily organs; and our bodies necessarily imply material -objects external to us. And hence our human faculties, -developed by our bodily existence in a material world, have -the conditions of matter for their necessary Laws. I have -already said (chap. v.) that our conception of Force arises -with our consciousness of our own muscular exertions;--that -Force cannot be conceived without Resistance to exercise -itself upon;--and that this resistance is supplied by -Matter. And thus the conception of Matter, and of the most -general modes in which Matter receives, resists, and -transmits force, are parts of our constitution which, though -awakened and unfolded by our being in a material world, are -not distinguishable from the original structure of the mind. -I do not ascribe to the mind _innate_ Ideas--Ideas which it -would have, even if it had no intercourse with the world of -space, time, and matter; because we cannot imagine a mind in -such a state. But I attempt to point out and classify those -Conditions of all Experience, to which the intercourse of -all minds with the material world has necessarily given rise -in all. Truths _thus_ necessarily acquired in the course of -all experience, cannot be said to be learnt _from -experience_, in the same sense in which particular facts, at -definite times, are learnt from experience--learnt by some -persons and not by others--learnt with more or less of -certainty. These latter _special truths of_ {220} -_experience_ will be very important subjects of our -consideration; but our whole chance of discussing them with -any profit depends upon our keeping them distinct from the -_necessary and universal conditions of experience_. Here, as -everywhere, we must keep in view the fundamental antithesis -of Ideas and Facts.] - -6. _Oblique Forces._--By the aid of the above axiom and a -few others, the Greeks made some progress in the science of -Statics. But after a short advance, they arrived at another -difficulty, that of Oblique Forces, which they never -overcame; and which no mathematician mastered till modern -times. The unpublished manuscripts of Leonardo da Vinci, -written in the fifteenth century, and the works of Stevinus -and Galileo, in the sixteenth, are the places in which we -find the first solid grounds of reasoning on the subject of -forces acting obliquely to each other. And from that period, -mathematicians, having thus become possessed of all the -mechanical principles which are requisite in problems -respecting equilibrium, soon framed a complete science of -Statics. Succeeding writers presented this science in forms -variously modified; for it was found, in Mechanics as in -Geometry, that various propositions might be taken as the -starting points; and that the collection of truths which it -was the mechanician's business to include in his course, -might thus be traversed by various routes, each path -offering a series of satisfactory demonstrations. The -fundamental conceptions of force and resistance, like those -of space and number, could be contemplated under different -aspects, each of which might be made the basis of axioms, or -of principles employed as axioms. Hence the grounds of the -truth of Statics may be stated in various ways; and it would -be a task of some length to examine all these completely, -and to trace them to their Fundamental Ideas. This I shall -not undertake here to do; 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 science. -{221} - -7. _A Force may be supposed to act at any Point of its -Direction._--It has been stated in the history of -Mechanics[12\3], that Leonardo da Vinci and Galileo obtained -the true measure of the effect of oblique forces, by -reasonings which were, in substance, the same. The principle -of these reasonings is that expressed at the head of this -paragraph; and when we have a little accustomed ourselves to -contemplate our conceptions of force, and its action on -matter, in an abstract manner, we shall have no difficulty -in assenting to the principle in this general form. But it -may, perhaps, be more obvious at first in a special case. - -[Note 12\3: _Hist. Ind. Sc._ b. vi. c. i. sect. 2.] - -If we suppose a wheel, moveable about its axis, and carrying -with it in its motion a weight, (as, for example, one of the -wheels by means of which the large bells of a church are -rung,) this weight may be supported by means of a rope (not -passing along the circumference of the wheel, as is usual in -the case of bells,) but fastened to one of the spokes of the -wheel. Now the principle which is enunciated above asserts, -that if the rope pass in a straight line across several of -the spokes of the wheel, it makes no difference in the -mechanical effect of the force applied, for the purpose of -putting the bell in motion, to _which_ of these spokes the -rope is _fastened_. In each case, the fastening of the rope -to the wheel merely serves to enable the force to produce -motion about the center; and so long as the force acts in -the same line, the effect is the same, at whatever point of -the rope the line of action finishes. - -This axiom very readily aids us in estimating the effect of -oblique forces. For when a force acts on one of the arms of -a lever at any oblique angle, we suppose another arm -projecting from the center of motion, like another spoke of -the same wheel, so situated that it is perpendicular to the -force. This arm we may, with Leonardo, call the _virtual -lever_; for, by the axiom, we may suppose the force to act -where the line of its direction meets this arm; and thus we -reduce the case {222} to that in which the force acts -perpendicularly on the arm. - -The ground of this axiom is, that matter, in Statics, is -necessarily conceived as _transmitting_ force. That force -can be transmitted from one place to another, by means of -matter;--that we can push with a rod, pull with a rope,--are -suppositions implied in our conceptions of force and matter. -Matter is, as we have said, that which receives the -impression of force, and the modes just mentioned, are the -simplest ways in which that impression operates. And since, -in any of these cases, the force might be resisted by a -reaction equal to the force itself, the reaction in each -case would be equal, and, therefore, the action in each case -is necessarily equal; and thus the forces must be -transmitted, from one point to another, without increase or -diminution. - -This property of matter, of transmitting the action of -force, is of various kinds. We have the coherence of a rope -which enables us to pull, and the rigidity of a staff, which -enables us to push with it in the direction of its length; -and again, the same staff has a rigidity of another kind, in -virtue of which we can use it as a lever; that is, a -rigidity to resist flexure, and to transmit the force which -turns a body round a fulcrum. There is, further, the -rigidity by which a solid body resists _twisting_. Of these -kinds of rigidity, the first is that to which our axiom -refers; but in order to complete the list of the elementary -principles of Statics, we ought also to lay down axioms -respecting the other kinds of rigidity[13\3]. These, -however, I shall not here state, as they do not involve any -new principle. Like the one just considered, they form part -of our fundamental conception of matter; they are not the -results of any experience, but are the hypotheses to which -we are irresistibly led, when we would liberate our -reasonings concerning force and matter from a dependence on -the special results of experience. We cannot even {223} -conceive (that is, if we have any clear mechanical -conceptions at all) the force exerted by the point of a -staff and resisting the force which we steadily impress on -the head of it, to be different from the impressed force. - -[Note 13\3: Such axioms are given in a little work (_The -Mechanical Euclid_) which I published on the Elements of -Mechanics.] - -8. _Forces may have equivalent Forces substituted for them. -The Parallelogram of Forces._--It has already been observed, -that in order to prove the doctrines of Statics, we may take -various principles as our starting points, and may still -find a course of demonstration by which the leading -propositions belonging to the subject may be established. -Thus, instead of beginning our reasonings, as in the last -section we supposed them to commence, with the case in which -forces act upon different points of the same body in the -same line of force, and counteract each other in virtue of -the intervening matter by which the effect of force is -transferred from one point to another; we may suppose -different forces to act at the same point, and may thus -commence our reasonings with a case in which we have to -contemplate force, without having to take into our account -the resistance or rigidity of matter. Two statical forces, -thus acting at a mathematical point, are equivalent, in all -respects, to some single force acting at the same point; and -would be kept in equilibrium by a force equal and opposite -to that single force. And the rule by which the single force -is derived from the two, is commonly termed _the -parallelogram of forces_; the proposition being this,--That -if the two forces be represented in magnitude and direction -by the two sides of a parallelogram, the resulting force -will be represented in the same manner by the diagonal of -the parallelogram. This proposition has very frequently been -made, by modern writers, the commencement of the science of -Mechanics: a position for which, by its simplicity, it is -well suited; although, in order to deduce from it the other -elementary propositions of the science, as, for instance, -those respecting the lever, we require the axiom stated in -the last section. - -9. _The Parallelogram of Forces is a necessary Truth._--In -the series of discussions in which we are {224} here -engaged, our main business is to ascertain the nature and -grounds of the certainty of scientific truths. We have, -therefore, to ask whether this proposition, the -parallelogram of forces, be a necessary truth; and if so, on -what grounds its necessity ultimately rests. We shall find -that this, like the other fundamental doctrines of Statics, -justly claim a demonstrative certainty. Daniel Bernoulli, in -1726, gave the first proof of this important proposition on -pure statical principles; and thus, as he says[14\3], -'proved that statical theorems are not less necessarily true -than geometrical are.' If we examine this proof of -Bernoulli, in order to discover what are the principles on -which it rests, we shall find that the reasoning employs in -its progress such axioms as this;--That if from forces which -are in equilibrium at a point be taken away other forces -which are in equilibrium at the same point, the remainder -will be in equilibrium; and generally;--That if forces can -be resolved into other equivalent forces, these may be -separated, grouped, and recombined, in any new manner, and -the result will still be identical with what it was at -first. Thus in Bernoulli's proof, the two forces to be -compounded are represented by P and Q; P is resolved into -two other forces, X and U; and Q into two others, Y and V, -under certain conditions. It is then assumed that these -forces may be grouped into the pairs X, Y, and U, V: and -when it has been shown that X and Y are in equilibrium, they -may, by what has been said, be removed, and the forces, P, -Q, are equivalent to U, V; which, being in the same -direction by the course of the construction, have a result -equal to their sum. - -[Note 14\3: _Comm. Petrop._ vol. i.] - -It is clear that the principles here assumed are genuine -axioms, depending upon our conception of the nature of -equivalence of forces, and upon their being capable of -addition and composition. If the forces, P, Q, be -_equivalent_ to forces X, U, Y, V, they are equivalent to -these forces added and compounded in any order; just as a -geometrical figure is, by our conception of {225} space, -equivalent to its parts added together in any order. The -apprehension of forces as having magnitude, as made up of -parts, as capable of composition, leads to such axioms in -Statics, in the same manner as the like apprehension of -space leads to the axioms of Geometry. And thus the truths -of Statics, resting upon such foundations, are independent -of experience in the same manner in which geometrical truths -are so. - -The proof of the parallelogram of forces thus given by -Daniel Bernoulli, as it was the first, is also one of the -most simple proofs of that proposition which have been -devised up to the present day. Many other demonstrations, -however, have been given of the same proposition. Jacobi, a -German mathematician, has collected and examined eighteen of -these[15\3]. They all depend either upon such principles as -have just been stated; That forces may in every way be -replaced by those which are equivalent to them;--or else -upon those previously stated, the doctrine of the lever, and -the transfer of a force from one point to another of its -direction. In either case, they are necessary results of our -statical conceptions, independent of any observed laws of -motion, and indeed, of the conception of actual motion -altogether. - -[Note 15\3: These are by the following mathematicians; D. -Bernoulli (1726); Lambert (1771); Scarella (1756); Venini -(1764); Araldi (1806); Wachter (1815); Kaestner; Marini; -Eytelwein; Salimbeni; Duchayla; two different proofs by -Foncenex (1760); three by D'Alembert; and those of Laplace -and M. Poisson.] - -There is another class of alleged proofs of the -parallelogram of forces, which involve the consideration of -the motion produced by the forces. But such reasonings are, -in fact, altogether irrelevant to the subject of Statics. In -that science, forces are not measured by the motion which -they produce, but by the forces which they will balance, as -we have already seen. The combination of two forces employed -in producing motion in the same body, either simultaneously -or successively, {226} belongs to that part of Mechanics -which has motion for its subject, and is to be considered in -treating of the laws of motion. The composition of motion, -(as when a man moves in a ship while the ship moves through -the water,) has constantly been confounded with the -composition of force. But though it has been done by very -eminent mathematicians, it is quite necessary for us to keep -the two subjects distinct, in order to see the real nature -of the evidence of truth in either case. The conditions of -equilibrium of two forces on a lever, or of three forces at -a point, can be established without any reference whatever -to any motions which the forces might, under _other_ -circumstances, produce. And because this can be done, to do -so is the only scientific procedure. To prove such -propositions by any other course, would be to support truth -by extraneous and inconclusive reasons; which would be -foreign to our purpose, since we seek not only knowledge, -but the grounds of our knowledge. - -10. _The Center of gravity seeks the lowest place._--The -principles which we have already mentioned afford a -sufficient basis for the science of Statics in its most -extensive and varied applications; 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 geometry. But in some of the more -complex cases, the results of long trains of reasoning may -be foreseen, in virtue of certain maxims which appear to us -self-evident, although it may not be easy to trace the exact -dependence of these maxims upon our fundamental conceptions -of force and matter. Of this nature is the maxim now -stated;--That in any combination of matter any how -supported, the Center of Gravity will descend into the -lowest position which the connexion of the parts allows it -to assume by descending. It is easily seen that this maxim -carries to a much greater extent the principle which the -Greek mathematicians assumed, that every body has a Center -of Gravity, that is, a point in which, if the whole matter -of the body be collected, the effect will remain unchanged. -For the Greeks asserted this of a {227} single rigid mass -only; whereas, in the maxim now under our notice, it is -asserted of any masses, connected by strings, rods, joints, -or in any manner. We have already seen that more modern -writers on mechanics, desirous of assuming as fundamental no -wider principles than are absolutely necessary, have not -adopted the Greek axiom in all its generality, but have only -asserted that two _equal_ weights have a center of gravity -midway between them. Yet the principle that every body, -however irregular, has a center of gravity, and will be -supported if that center is supported, and not otherwise, is -so far evident, that it might be employed as a fundamental -truth, if we could not resolve it into any simpler truths: -and, historically speaking, it was assumed as evident by the -Greeks. In like manner the still wider principle, that a -collection of bodies, as, for instance, a flexible chain -hanging upon one or more supports, has a center of gravity; -and that this point will descend to the lowest possible -situation, as a single body would do, has been adopted at -various periods in the history of mechanics; and especially -at conjunctures when mathematical philosophers have had new -and difficult problems to contend with. 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 axioms. - -11. _Stevinus's Proof for Oblique Forces._--We have an -example of this mode of dealing with problems, in Stevinus's -mode of reasoning concerning the Inclined Plane; which, as -we have stated in the History of Mechanics, was the first -correct published solution of that problem. Stevinus -supposes a loop of chain, or a loop of string loaded with a -series of equal balls at equal distances, to hang over the -Inclined Plane; and his reasoning proceeds upon this -assumption,--That such a loop so hanging will find a certain -position in which it will rest: for otherwise, says -he[16\3], its motion must go on for ever, which is absurd. -It may be asked how {228} this absurdity of a perpetual -motion appears; and it will perhaps be added, that although -the impossibility of a machine with such a condition may be -proved as a remote result of mechanical principles, this -impossibility can hardly be itself recognized as a -self-evident truth. But to this we may reply, that the -impossibility is really evident in the case contemplated by -Stevinus; for we cannot conceive a loop of chain to go on -through all eternity, sliding round and round upon its -support, by the effect of its own weight. And the ground of -our conviction that this cannot be, seems to be this -consideration; that when the chain moves by the effect of -its weight, we consider its motion as the result of an -effort to reach some certain position, in which it can rest; -just as a single ball in a bowl moves till it comes to rest -at the lowest point of the bowl. Such an effect of weight in -the chain, we may represent to ourselves by conceiving all -the matter of the chain to be collected in one single point, -and this single heavy point to hang from the support in some -way or other, so as fitly to represent the mode of support -of the chain. In whatever manner this heavy point (the -center of gravity of the chain) be supported and controlled -in its movements, there will still be some position of rest -which it will seek and find. And thus there will be some -corresponding position of rest for the chain; and the -interminable shifting from one position to another, with no -disposition to rest in any position, cannot exist. - -[Note 16\3: Stevin. _Statique_, livre i. prop. 19.] - -Thus the demonstration of the property of the Inclined Plane -by Stevinus, depends upon a principle which, though far from -being the simplest of those to which the case can be -reduced, is still both true and evident: and the evidence of -this principle, depending upon the assumption of a center of -gravity, is of the same nature as the evidence of the Greek -statical demonstrations, the earliest real advances in the science. - -12. _Principle of Virtual Velocities._--We have referred -above to an assertion often made, that we may, from the -simple principles of Mechanics, demonstrate the -impossibility of a perpetual motion. In reality, {229} -however, the simplest proof of that impossibility, in a -machine acted upon by weight only, arises from the very -maxim above stated, that the center of gravity seeks and -finds the lowest place; or from some similar proposition. -For if, as is done by many writers, we profess to prove the -impossibility of a perpetual motion by means of that -proposition which includes the conditions of equilibrium, -and is called the _Principle of Virtual Velocities_[17\3], -we are under the necessity of first proving in a general -manner that principle. And if this be done by a mere -enumeration of cases, (as by taking those five cases which -are called the _Mechanical Powers_,) there may remain some -doubts whether the enumeration of possible mechanical -combinations be complete. Accordingly, some writers have -attempted independent and general proofs of the Principle of -Virtual Velocities; and these proofs rest upon assumptions -of the same nature as that now under notice. This is, for -example, the case with Lagrange's proof, which depends upon -what he calls the _Principle of Pulleys_. For this principle -is,--That a weight any how supported, as by a string passing -round any number of pulleys any how placed, will be at rest -then only, when it cannot get lower by any small motion of -the pulleys. And thus the maxim that a weight will descend -if it can, is assumed as the basis of this proof. - -[Note 17\3: See _Hist. Ind Sc._ b. vi. c. ii. sect. 4.] - -There is, as we have said, no need to assume such principles -as these for the foundation of our mechanical science. But -it is, on various accounts, useful to direct our attention -to those cases in which truths, apprehended at first in a -complex and derivative form, have afterwards been reduced to -their simpler elements;--in which, also, sagacious and -inventive men have fixed upon those truths as self-evident, -which now appear to us only certain in virtue of -demonstration. In these cases we can hardly doubt that such -men were led to assert the doctrines which they discovered, -not by any capricious conjecture of arbitrary selection, but -by having a keener and deeper insight than other persons -{230} into the relations which were the object of their -contemplation; and in the science now spoken of, they were -led to their assumptions by possessing clearly and -distinctly the conceptions of mechanical cause and -effect,--action and reaction,--force, and the nature of its -operation. - -13. _Fluids press Equally in all Directions._--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 bodies; and the Greeks, who, as we have -seen, obtained a clear view of some of the principles of -Statics, also made a beginning in the kindred subject of -Hydrostatics. We still possess a treatise of Archimedes _On -Floating Bodies_, which contains correct solutions of -several problems belonging to this subject, and of some -which are by no means easy. In this treatise, the -fundamental assumption is of this kind: 'Let it be assumed -that the nature of a fluid is such, that the parts which are -less pressed yield to those which are more pressed.' In this -assumption or axiom it is implied that a pressure exerted -upon a fluid in one direction produces a pressure in another -direction; thus, the weight of the fluid which arises from a -downward force produces a lateral pressure against the sides -of the containing vessel. Not only does the pressure thus -diverge from its original direction into all other -directions, but the pressure is in all directions exactly -equal, an equal extent of the fluid being taken. This -principle, which was involved in the reasoning of -Archimedes, is still to the present day the basis of all -hydrostatical treatises, and is expressed, as above, by -saying that _fluids press equally in all directions_. - -Concerning this, as concerning previously-noticed -principles, we have to ask whether it can rightly be said to -be derived from experience. And to this the answer must -still be, as in the former cases, that the proposition is -not one borrowed from experience in any usual or exact sense -of the phrase. I will endeavour to illustrate this. There -are many elementary propositions in physics, our knowledge -of which {231} indisputably depends upon experience; and in -these cases there is no difficulty in seeing the evidence of -this dependence. In such cases, the _experiments_ which -prove the law are prominently stated in treatises upon the -subject: they are given with exact measures, and with an -account of the means by which errours were avoided: the -experiments of more recent times have either rendered more -certain the law originally asserted, or have pointed out -some correction of it as requisite: and the names, both of -the discoverers of the law and of its subsequent reformers, -are well known. For instance, the proposition that 'The -elastic force of air varies as the density,' was first -proved by Boyle, by means of operations of which the detail -is given in his _Defence_ of his _Pneumatical -Experiments_[18\3]; and by **Mariotte in his _Traité de -l'Équilibre des Liquides_, from whom it has generally been -termed Mariotte's law. After being confirmed by many other -experimenters, this law was suspected to be slightly -inaccurate, and a commission of the French Academy of -Sciences was appointed, consisting of several distinguished -philosophers[19\3], to ascertain the truth or falsehood of -this suspicion. The result of their investigations appeared -to be, that the law is exact, as nearly as the inevitable -inaccuracies of machinery and measures will allow us to -judge. Here we have an example of a law which is of the -simplest kind and form; and which yet is not allowed to rest -upon its simplicity or apparent probability, but is -rigorously tested by experience. In this case, the -assertion, that the law depends upon experience, contains a -reference to plain and notorious passages in the history of -science. - -[Note 18\3: Shaw's _Boyle_, Vol. ii. p. 671.] - -[Note 19\3: The members were Prony, Arago, Ampère, Girard, -and Dulong. The experiments were extended to a pressure of -twenty-seven atmospheres; and in no instance did the -difference between the observed and calculated elasticity -amount to one-hundredth of the whole; nor did the difference -appear to increase with the increase of pressure.--Fechner, -_Repertorium_, i. 110.] - -Now with regard to the principle that fluids press equally -in all directions, the case is altogether different. {232} -It is, indeed, often asserted in works on hydrostatics, that -the principle is collected from experience, and sometimes a -few experiments are described as exhibiting its effect; but -these are such as to illustrate and explain, rather than to -prove, the truth of the principle: they are never related to -have been made with that exactness of precaution and -measurement, or that frequency of repetition, which are -necessary to establish a purely experimental truth. Nor did -such experiments occur as important steps in the history of -science. It does not appear that Archimedes thought -experiment necessary to confirm the truth of the law as he -employed it: on the contrary, he states it in exactly the -same shape as the axioms which he employs in statics, and -even in geometry; namely, as an assumption. 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 him. Experiment was not -requisite for its discovery; experiment is not necessary for -its proof at present; and we may add, that experiment, -though it may make the proposition the more readily -intelligible, can add nothing to our conviction of its truth -when it is once understood. - -14. _Foundation of the above Axiom._--But it will naturally -be asked, What then is the ground of our conviction of this -doctrine of the equal pressure of a fluid in all directions? -And to this I reply, that the reasons of this conviction are -involved in our idea of a fluid, which is considered as -matter, and therefore as capable of receiving, resisting, -and transmitting force according to the general conception -of matter; and which is also considered as matter which has -its parts perfectly moveable among one another. For it -follows from these suppositions, that if the fluid be -confined, a pressure which thrusts in one side of the -containing vessel, may cause any other side to bulge -outwards, if there be a part of the surface which has not -strength to resist this pressure from within. And that this -pressure, when thus transferred into a direction different -from the original one, is not altered in intensity, {233} -depends upon this consideration; that any difference in the -two pressures would be considered as a defect of _perfect_ -fluidity, since the fluidity would be still more complete, -if this entire and undiminished transmission of pressure in -all directions were supposed. If, for instance, the lateral -pressure were less than the vertical, this could be -conceived no other way than as indicating some rigidity or -adhesion of the parts of the fluid. When the fluidity is -perfect, the two pressures which act in the two different -parts of the fluid exactly balance each other: they are the -action and the reaction; and must hence be equal by the same -necessity as two directly opposite forces in statics. - -But it may be urged, that even if we grant that this -conception of a perfect fluid, as a body which has its parts -perfectly moveable among each other, leads us necessarily to -the principle of the equality of hydrostatic pressure in all -directions, still this conception itself is obtained from -experience, or suggested by observation. And to this we may -reply, that the conception of a fluid, as contemplated in -mechanical theory, cannot be said to be derived from -experience, except in the same manner as the conception of a -solid and rigid body may be said to be acquired by -experience. For if we imagine a vessel full of small, smooth -spherical balls, such a collection of balls would approach -to the nature of a fluid, in having its parts moveable among -each other; and would approach to perfect fluidity, as the -balls became smoother and smaller. And such a collection of -balls would also possess the statical properties of a fluid; -for it would transmit pressure out of a vertical into a -lateral (or any other) direction, in the same manner as a -fluid would do. And thus a collection of solid bodies has -the same property which a fluid has; and the science of -Hydrostatics borrows from experience no principles beyond -those which are involved in the science of Statics -respecting solids. And since in this latter portion of -science, as we have already seen, none of the principles -depend for their evidence upon any special experience, the -doctrines of Hydrostatics also are not {234} proved by -experience, but have a necessary truth borrowed from the -relations of our ideas. - -It is hardly to be expected that the above reasoning will, -at first sight, produce conviction in the mind of the -reader, except he have, to a certain extent, acquainted -himself with the elementary doctrines of the science of -Hydrostatics as usually delivered; and have followed, with -clear and steady apprehension, some of the trains of -reasoning by which the pressures of fluids are determined; -as, for instance, the explanation of what is called _the -Hydrostatic Paradox_. The necessity of such a discipline in -order that the reader may enter fully into this part of our -speculations, naturally renders them less popular; but this -disadvantage is inevitable in our plan. We cannot expect to -throw light upon philosophy by means of the advances which -have been made in the mathematical and physical sciences, -except we really understand the doctrines which have been -firmly established in those sciences. This preparation for -philosophizing may be somewhat laborious; 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 reach. - -We may add, that the consequences to which we are directed -by the preceding opinions, are of very great importance in -their bearing upon our general views respecting human -knowledge. I trust to be able to show, that some important -distinctions are illustrated, some perplexing paradoxes -solved, and some large anticipations of the future extension -of our knowledge suggested, by means of the conclusions to -which the preceding discussions have conducted us. But -before I proceed to these general topics, I must consider -the foundations of some of the remaining portions of the -science of Mechanics. - - - -{{235}} -CHAPTER VII. - -OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS. - - -1. IN the History of Mechanics, I have traced the steps by -which the three Laws of Motion and the other principles of -mechanics were discovered, established, and extended to the -widest generality of form and application. We have, in these -laws, examples of principles which were, historically -speaking, obtained by reference to experience. Bearing in -mind the object and the result of the preceding discussions, -we cannot but turn with much interest to examine these -portions of science; to inquire whether there be any real -difference in the grounds and nature between the knowledge -thus obtained, and those truths which we have already -contemplated; and which, as we have seen, contain their own -evidence, and do not require proof from experiment. - -2. _The First Law of Motion._--The first law of motion is, -that _When a body moves not acted upon by any force, it will -go on perpetually in a straight line, and with a uniform -velocity._ Now what is the real ground of our assent to this -proposition? That it is not at first sight a self-evident -truth, appears to be clear; since from the time of Aristotle -to that of Galileo the opposite assertion was held to be -true; and it was believed that all bodies in motion had, by -their own nature, a constant tendency to move more and more -slowly, so as to stop at last. This belief, indeed, is -probably even now entertained by most persons, till their -attention is fixed upon the arguments by which the first law -of motion is established. It is, however, not difficult to -lead any person of a speculative habit {236} of thought to -see that the retardation which constantly takes place in the -motion of all bodies when left to themselves, is, in -reality, the effect of extraneous forces which destroy the -velocity. A top ceases to spin because the friction against -the ground and the resistance of the air gradually diminish -its motion, and not because its motion has any internal -principle of decay or fatigue. This may be shown, and was, -in fact, shown by Hooke before the Royal Society, at the -time when the laws of motion were still under discussion, by -means of experiments in which the weight of the top is -increased, and the resistance to motion offered by its -support, is diminished; for by such contrivances its motion -is made to continue much longer than it would otherwise do. -And by experiments of this nature, although we can never -remove the whole of the external impediments to continued -motion, and although, consequently, there will always be -some retardation; and an end of the motion of a body left to -itself, however long it may be delayed, must at last come; -yet we can establish a conviction that if all resistance -could be removed, there would be no diminution of velocity, -and thus the motion would go on for ever. - -If we call to mind the axioms which we formerly stated, as -containing the most important conditions involved in the -idea of Cause, it will be seen that our conviction in this -case depends upon the first axiom of Causation, that nothing -can happen without a cause. Every change in the velocity of -the moving body must have a cause; and if the change can, in -any manner, be referred to the presence of other bodies, -these are said to exert _force_ upon the moving body: and -the conception of force is thus evolved from the general -idea of cause. _Force is any cause which has motion, or -change of motion, for its effect_; and thus, all the change -of velocity of a body which can be referred to extraneous -bodies,--as the air which surrounds it, or the support on -which it rests,--is considered as the effect of forces; and -this consideration is looked upon as explaining the -difference between the motion which really takes places in -the experiment, and that motion {237} which, as the law -asserts, would take place if the body were not acted on by -any forces. - -Thus the truth of the first law of motion depends upon the -axiom that no change can take place without a cause; and -follows from the definition of force, if we suppose that -there can be none but an _external_ cause of change. But in -order to establish the law, it was necessary further to be -assured that there is no _internal_ cause of change of -velocity belonging to all matter whatever, and operating in -such a manner that the mere progress of time is sufficient -to produce a diminution of velocity in all moving bodies. It -appears from the history of mechanical science, that this -latter step required a reference to observation and -experiment; and that the first law of motion is so far, -historically at least, dependent upon our experience. - -But notwithstanding this historical evidence of the need -which we have of a reference to observed facts, in order to -place this first law of motion out of doubt, it has been -maintained by very eminent mathematicians and philosophers, -that the law is, in truth, evident of itself, and does not -really rest upon experimental proof. Such, for example, is -the opinion of d'Alembert[20\3], who offers what is called -an _à priori_ proof of this law; that is, a demonstration -derived from our ideas alone. When a body is put in motion, -either, he says, the cause which puts it in motion at first, -suffices to make it move one foot, or the continued action -of the cause during this foot is requisite for the motion. -In the first case, the same reason which made the body -proceed to the end of the first foot will hold for its going -on through a second, a third, a fourth foot, and so on for -any number. In the second case, the same reason which made -the force continue to act during the first foot, will hold -for its acting, and therefore for the body moving during -each succeeding foot. And thus the body, once beginning to -move, must go on moving for ever. - -[Note 20\3: _Dynamique._] - -{238} It is obvious that we might reply to this argument, -that the reasons for the body proceeding during each -succeeding foot may not necessarily be all the same; for -among these reasons may be the time which has elapsed; and -thus the velocity may undergo a change as the time proceeds: -and we require observation to inform us that it does not do so. - -Professor Playfair has presented nearly the same argument, -although in a different and more mathematical form[21\3]. If -the velocity change, says he, it must change according to -some expression of calculation depending upon the time, or, -in mathematical language, must be a _function_ of the time. -If the velocity diminish as the time increases, this may be -expressed by stating the velocity in each case as a certain -number, from which another quantity, or _term_, increasing -as the time increases, is subtracted. But, Playfair adds, -there is no condition involved in the nature of the case, by -which the _coefficients_, or numbers which are to be -employed, along with the number representing the time, in -calculating this second term, can be determined to be of one -magnitude rather than of any other. Therefore he infers -there can be no such coefficients, and that the velocity is -in each case equal to some constant number, independent of -the time; and is therefore the same for all times. - -[Note 21\3: _Outlines of Natural Philosophy_, p. 26.] - -In reply to this we may observe, that the circumstance of -_our not seeing_ in the nature of the case anything which -determines for us the coefficients above spoken of, cannot -prove that they have not some certain value _in nature_. We -do not see in the nature of the case anything which should -determine a body to fall sixteen feet in a second of time, -rather than one foot or one hundred feet: yet in fact the -space thus run through by falling bodies is determined to a -certain magnitude. It would be easy to assign a mathematical -expression for the velocity of a body, implying that -one-hundredth of the velocity, or any other {239} fraction, -is lost in each second[22\3]: and where is the absurdity of -supposing such an expression really to represent the -velocity? - -[Note 22\3: This would be the case, if, _t_ being the -number of seconds elapsed, and _C_ some constant quantity, -the velocity were expressed by this mathematical formula, -_C_(99/100)^_t_.] - -Most modern writers on mechanics have embraced the opposite -opinion, and have ascribed our knowledge of this first law -of motion to experience. Thus M. Poisson, one of the most -eminent of the mathematicians who have written on this -subject, says[23\3], "We cannot affirm _à priori_ that the -velocity communicated to a body will not become slower and -slower of itself, and end by being entirely extinguished. It -is only by experience and induction that this question can -be decided." - -[Note 23\3: Poisson, _Dynamique_, ed. 2, art. 113.] - -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 Motion, such as we find it, is more consonant to our -conceptions than any other would be. The Law, as it exists, -is the most simple that we can conceive. Instead of having -to determine by experiments what is the law of the natural -change of velocity, we find the Law to be that it does not -change at all. To a certain extent, the Law depends upon the -evident axiom, that no change can take place without a -cause. But the question further occurs, whether the mere -lapse of time may not be a cause of change of velocity. In -order to ensure this, we have recourse to experiment; and -the result is that time alone does not produce any such -change. In addition to the conditions of change which we -collect from our own Ideas, we ask of Experience what other -conditions and circumstances she has to offer; and the -answer is, that she can point out none; When we have removed -the alterations which external causes, in our very -conception of them, occasion, there are no longer any -alterations. Instead of having to guide ourselves {240} by -experience, we learn that on this subject she has nothing to -tell us. Instead of having to take into account a number of -circumstances, we find that we have only to reject all -circumstances. The velocity of a body remains unaltered by -time alone, of whatever kind the body itself be. - -But the doctrine that time alone is not a cause of change of -velocity in any body is further recommended to us by this -consideration;--that time is conceived by us not as a cause, -but only as a condition of other causes producing their -effects. Causes operate in time; but it is only when the -cause exists, that the lapse of time can give rise to -alterations. When therefore all external causes of change of -velocity are supposed to be removed, the velocity must -continue identical with itself, whatever the time which -elapses. An eternity of negation can produce no positive -result. - -Thus, though the discovery of the First Law of Motion was -made, historically speaking, by means of experiment, we have -now attained a point of view in which we see that it might -have been certainly known to be true independently of -experience. This law in its ultimate form, when completely -simplified and steadily contemplated, assumes the character -of a self-evident truth. We shall find the same process to -take place in other instances. 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 knowledge. - -3. _Gravity is a Uniform Force._--We shall find observations -of the same kind offering themselves in a manner more or -less obvious, with regard to the other principles of -Dynamics. The determination of the laws according to which -bodies fall downwards by the common action of gravity, has -already been noticed in the History of Mechanics[24\3], as -one of the earliest positive advances in the doctrine of -motion. These laws were first rightly stated by Galileo, and -{241} established by reasoning and by experiment, not -without dissent and controversy. The amount of these -doctrines is this: That gravity is a uniform accelerating -force; such a _uniform force_ having this for its character, -that it _makes the velocity increase in exact proportion to -the time of motion_. The relation which the spaces described -by the body bear to the times in which they are described, -is obtained by mathematical deduction from this definition -of the force. - -[Note 24\3: _Hist. Ind. Sc._ b. vi. c. ii. sect. 2.] - -The clear Definition of a uniform accelerating force, and -the Proposition that gravity is such a force, were -co-ordinate and contemporary steps in this discovery. In -defining accelerating force, reference, tacit or express, -was necessarily made to the second of the general axioms -respecting causation,--That causes are measured by their -effects. Force, in the cases now under our notice, is -conceived to be, as we have already stated, (p. 236,) any -cause which, acting from without, changes the motion of a -body. It must, therefore, in this acceptation, be measured -by the magnitude of the changes which are produced. But in -what manner the changes of motion are to be employed as the -measures of force, is learnt from observation of the facts -which we see taking place in the world. Experience -_interprets_ the axiom of causation, from which otherwise we -could not deduce any real knowledge. We may assume, in -virtue of our general conceptions of force, that under the -same circumstances, a greater change of motion implies a -greater force producing it; but what are we to expect when -the circumstances change? The weight of a body makes it fall -from rest at first, and causes it to move more quickly as it -descends lower. We may express this by saying, that gravity, -the universal force which makes all terrestrial bodies fall -when not supported, by its continuous action first _gives_ -velocity to the body when it has none, and afterwards _adds_ -velocity to that which the body already has. But how is the -velocity added proportioned to the velocity which already -exists? Force acting on a body at rest, and on a body in -motion, appears under very different {242} conditions;--how -are the effects related? Let the force be conceived to be in -both cases the same, since force is conceived to depend upon -the extraneous bodies, and not upon the condition of the -moving mass itself. But the force being the same, the -effects may still be different. It is at first sight -conceivable that the body, acted upon by the same gravity, -may receive a less addition of velocity when it is already -moving in the direction in which this gravity impels it; for -if we ourselves push a body forwards, we can produce little -additional effect upon it when it is already moving rapidly -away from us. May it not be true, in like manner, that -although gravity be always the same force, its effect -depends upon the velocity which the body under its influence -already possesses? - -Observation and reasoning combined, as we have said, enabled -Galileo to answer these questions. He asserted and proved -that we may consistently and properly measure a force by the -velocity which is by it generated in a body, in some certain -time, as one second; and further, that if we adopt this -measure, gravity will be a force of the same value under all -circumstances of the body which it affects; since it -appeared that, in fact, a falling body does receive equal -increments of velocity in equal times from first to last. - -If it be asked whether we could have known, anterior to, or -independent of, experiment, that gravity is a uniform force -in the sense thus imposed upon the term; it appears clear -that we must reply, that we could not have attained to such -knowledge, since other laws of the motion of bodies -downwards are easily conceivable, and nothing but -observation could inform us that one of these laws does not -prevail in fact. Indeed, we may add, that the assertion that -the force of gravity is uniform, is so far from being -self-evident, that it is not even true; for gravity varies -according to the distance from the center of the earth; and -although this variation is so small as to be, in the case of -falling bodies, imperceptible, it negatives the rigorous -uniformity of the force as completely, though {243} not to -the same extent, as if the weight of a body diminished in a -marked degree, when it was carried from the lower to the -upper room of a house. It cannot, then, be a truth -independent of experience, that gravity is uniform. - -Yet, in fact, the assertion that gravity is uniform was -assented to, not only before it was proved, but even before -it was clearly understood. It was readily granted by all, -that bodies which fall freely are _uniformly_ accelerated; -but while some held the opinion just stated, that uniformly -accelerated motion is that in which the velocity increases -in proportion to the _time_, others maintained, that _that_ -is uniformly accelerated motion, in which the velocity -increases in proportion to the _space_; so that, for -example, a body in falling vertically through twenty feet -should acquire twice as great a velocity as one which falls -through ten feet. - -These two opinions are both put forward by the interlocutors -of Galileo's Dialogue on this subject[25\3]. And the latter -supposition is rejected, the author showing, not that it is -inconsistent with experience, but that it is impossible in -itself: inasmuch as it would inevitably lead to the -conclusion, that the fall through a large and a small -vertical space would occupy exactly the same time. - -[Note 25\3: _Dialogo_, iii. p. 95.] - -Indeed, Galileo assumes his definition of uniformly -accelerated motion as one which is sufficiently recommended -by its own simplicity. 'If we attend carefully,' he says, -'we shall find that no mode of increase of velocity is more -simple than that which adds equal increments in equal times. -Which we may easily understand if we consider the close -affinity of time and motion: for as the uniformity of motion -is defined by the equality of spaces described in equal -times, so we may conceive the uniformity of acceleration to -exist when equal velocities are added in equal times.' - -Galileo's mode of supporting his opinion, that bodies -falling by the action of gravity are thus uniformly {244} -accelerated, consists, in the first place, in adducing the -maxim that nature always employs the most simple -means[26\3]. But he is far from considering this a decisive -argument. 'I,' says one of his speakers, 'as it would be -very unreasonable in me to gainsay this or any other -definition which any author may please to make, since they -are all arbitrary, may still, without offence, doubt whether -such a definition, conceived and admitted in the abstract, -fits, agrees, and is verified in that kind of accelerated -motion which bodies have when they descend naturally.' - -[Note 26\3: _Dialogo_, iii. p. 91.] - -The experimental proof that bodies, when they fall -downwards, are uniformly accelerated, is (by Galileo) -derived from the inclined plane; and therefore assumes the -proposition, that if such uniform acceleration prevail in -vertical motion, it will also hold when a body is compelled -to describe an oblique rectilinear path. This proposition -may be shown to be true, if (assuming by anticipation the -Third Law of Motion, of which we shall shortly have to -speak,) we introduce the conception of a uniform statical -force as the cause of uniform acceleration. For the force on -the inclined plane bears a constant proportion to the -vertical force, and this proportion is known from statical -considerations. But in the work of which we are speaking, -Galileo does not introduce this abstract conception of force -as the foundation of his doctrines. Instead of this, he -proposes, as a postulate sufficiently evident to be made the -basis of his reasonings, That bodies which descend down -inclined planes of different inclinations, but of the same -vertical height, all acquire the same velocity[27\3]. But -when this postulate has been propounded by one of the -persons of the dialogue, another interlocutor says, 'You -discourse very probably; but besides this likelihood, I wish -to augment the probability so far, that it shall be almost -as complete as a necessary demonstration.' He then proceeds -to describe a very ingenious and simple experiment, which -shows that when a body is made to swing upwards at the end -of {245} a string, it attains to the same height, whatever -is the path it follows, so long as it starts from the lowest -point with the same velocity. And thus Galileo's postulate -is experimentally confirmed, so far as the force of gravity -can be taken as an example of the forces which the postulate -contemplates: and conversely, gravity is proved to be a -uniform force, so far as it can be considered clear that the -postulate is true of uniform forces. - -[Note 276\3: _Dialogo_, iii. p. 36.] - -When we have introduced the conception and definition of -accelerating force, Galileo's postulate, that bodies -descending down inclined planes of the same vertical height, -acquire the same velocity, may, by a few steps of reasoning, -be demonstrated to be true of uniform forces: and thus the -proof that gravity, either in vertical or oblique motion, is -a uniform force, is confirmed by the experiment above -mentioned; as it also is, on like grounds, by many other -experiments, made upon inclined planes and pendulums. - -Thus the propriety of Galileo's conception of a uniform -force, and the doctrine that gravity is a uniform force, -were confirmed by the same reasonings and experiments. We -may make here two remarks; _First_, that the conception, -when established and rightly stated, appears so simple as -hardly to require experimental proof; a remark which we have -already made with regard to the First Law of Motion: and -_Second_, that the discovery of the real law of nature was -made by assuming propositions which, without further proof, -we should consider as very precarious, and as far less -obvious, as well as less evident, than the law of nature in -its simple form. - -4. _The Second Law of Motion._--When a body, instead of -falling downwards from rest, is thrown in any direction, it -describes a curve line, till its motion is stopped. In this, -and in all other cases in which a body describes a curved -path in free space, its motion is determined by the Second -Law of Motion. The law, in its general form, is as -follows:--When a body is thus cast forth and acted upon by a -force in a direction {246} transverse to its motion, the -result is, That _there is combined with the motion with -which the body is thrown, another motion, exactly the same -as that which the same force would have communicated to a -body at rest_. - -It will readily be understood that the basis of this law is -the axiom already stated, that effects are measured by their -causes. In virtue of this axiom, the effect of gravity -acting upon a body in a direction transverse to its motion, -must measure the accelerative or deflective force of gravity -under those circumstances. If this effect vary with the -varying velocity and direction of the body thus acted upon, -the deflective force of gravity also will vary with those -circumstances. The more simple supposition is, that the -deflective force of gravity is the same, whatever be the -velocity and direction of the body which is subjected to its -influence: and this is the supposition which we find to be -verified by facts. For example, a ball let fall from the top -of a ship's upright mast, when she is sailing steadily -forward, will fall at the foot of the mast, just as if it -were let fall while the ship were at rest; 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 first. This general and simple conception of -motions as _compounded_ with one another, represents, it is -proved, the manner in which the motion produced by gravity -modifies any other motion which the body may previously have had. - -The discussions which terminated in the general reception of -this Second Law of Motion among mechanical writers, were -much mixed up with the arguments for and against the -Copernican system, which system represented the earth as -revolving upon its axis. For the obvious argument against -this system was, that if each point of the earth's surface -were thus in motion from west to east, a stone dropt from -the top of a tower would be left behind, the tower moving -away from it: and the answer was, that by this law of -motion, the stone would have the earth's motion impressed -upon it, as well as that motion which would {247} arise from -its gravity to the earth; and that the motion of the stone -relative to the tower would thus be the same as if both -earth and tower were at rest. Galileo further urged, as a -presumption in favour of the opinion that the two -motions,--the circular motion arising from the rotation of -the earth, and the downward motion arising from the gravity -of the stone, would be compounded in the way we have -described, (neither of them disturbing or diminishing the -other,)--that the first motion was in its own nature not -liable to any change or diminution[28\3], as we learn from -the First Law of Motion. Nor was the subject lightly -dismissed. The experiment of the stone let fall from the top -of the mast was made in various forms by Gassendi; and in -his Epistle, _De Motu impresso a Motore translato_, the rule -now in question is supported by reference to these -experiments. In this manner, the general truth, the Second -Law of Motion, was established completely and beyond -dispute. - -[Note 28\3: _Dialogo_, ii. p. 114.] - -But when this law had been proved to be true in a general -sense, with such accuracy as rude experiments, like those of -Galileo and Gassendi, would admit, it still remained to be -ascertained (supposing our knowledge of the law to be the -result of experience alone,) whether it were true with that -precise and rigorous exactness which more refined modes of -experimenting could test. We so willingly believe in the -simplicity of laws of nature, that the rigorous accuracy of -such a law, known to be at least approximately true, was -taken for granted, till some ground for suspecting the -contrary should appear. Yet calculations have not been -wanting which might confirm the law as true to the last -degree of accuracy. Laplace relates (_Syst. du Monde_, livre -iv. chap. 16,) 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 velocity; and that in -this way an explanation might be found for the moon's -_acceleration_ (a deviation of her observed from her -calculated place, which long {248} perplexed -mathematicians). But it was after some time discovered that -this feature in the moon's motion arose from another cause; -and the second law of motion was confirmed as true in the -most rigorous sense. - -Thus we see that although there were arguments which might -be urged in favour of this law, founded upon the necessary -relations of ideas, men became convinced of its truth only -when it was verified and confirmed by actual experiment. But -yet in this case again, as in the former ones, when the law -had been established beyond doubt or question, men were very -ready to believe that it was not a mere result of -observation,--that the truth which it contained was not -derived from experience,--that it might have been assumed as -true in virtue of reasonings anterior to experience,--and -that experiments served only to make the law more plain and -intelligible, as visible diagrams in geometry serve to -illustrate geometrical truths; our knowledge not being (they -deemed) in mechanics, any more than in geometry, borrowed -from the senses. It was thought by many to be self-evident, -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 -time: or, to express it otherwise, that if the motion of the -body be compounded of a horizontal and vertical motion, the -vertical motion alone will be affected by the vertical -force. This principle, indeed, not only has appeared evident -to many persons, but even at the present day is assumed as -an axiom by many of the most eminent mathematicians. It is, -for example, so employed in the _Mécanique Céleste_ of -Laplace, which may be looked upon as the standard of -mathematical mechanics in our time; and in the _Mécanique -Analytique_ of Lagrange, the most consummate example which -has appeared of subtilty of thought on such subjects, as -well as of power of mathematical generalization[29\3]. And -{249} thus we have here another example of that circumstance -which we have already noticed in speaking of the First Law -of Motion, (Art. 2 of this chapter,) and of the Law that -Gravity is a uniform Force, (Art. 3); namely, that the law, -though historically established by experiments, appears, -when once discovered and reduced to its most simple and -general form, to be self-evident. I am the more desirous of -drawing attention to this feature in various portions of the -history of science, inasmuch as it will be found to lead to -some very extensive and important views, hereafter to be -considered. - -[Note 29\3: I may observe that the rule that we may -_compound_ motions, as the Law supposes, is involved in the -step of _resolving_ them; which is done in the passage to -which I refer. (_Méc. Analyt._ ptie. i. sect. i. art. 3. p. -225.) 'Si on conçoit que le mouvement d'un corps et les -forces qui le sollicitent soient _decomposées_ suivant trois -lignes droites perpendiculaires entre elles, on pourra -considérer séparément les mouvemens et les forces relatives -à chacun de ces trois directions. Car à cause de la -perpendicularité des directions il est visible que chacun de -ces mouvemens partiels peut être regardé comme indépendant -des deux autres, et qu'il ne peut recevoir d'altération que -de la part de la force qui agit dans la direction de ce -mouvement; l'on peut conclure que ces trois mouvemens -doivent suivre, chacun en particulier, les lois des -mouvemens rectilignes accélérés ou retardés par les forces -données.' Laplace makes the same assumption in effect, -(_Méc. Cél._ p. i. liv. i. art. 7), by resolving the forces -which act upon a point in three rectangular directions, and -reasoning separately concerning each direction. But in his -mode of treating the subject is involved a principle which -belongs to the Third Law of Motion, namely, the doctrine -that the velocity is as the force, of which we shall have to -speak elsewhere.] - -5. _The Third Law of Motion._--We have, in the definition of -Accelerating Force, a measure of Forces, so far as they are -concerned in producing motion. We had before, in speaking of -the principles of statics, defined the measure of Forces or -Pressures, so far as they are employed in producing -equilibrium. But these two aspects of Force are closely -connected; and we require a law which shall lay down the -rule of their connexion. By the same kind of muscular -exertion by which we can support a heavy stone, we can also -put it in motion. The question then occurs, how is the rate -and manner of its motion determined? The answer to this -question is contained in the Third Law {250} of Motion, and -it is to this effect: that the _Momentum_ which any pressure -produces in the mass in a given time is proportional to the -pressure. By _Momentum_ is meant the product of the numbers -which express the velocity and the mass of the body: and -hence, if the mass of the body be the same in the instances -which we compare, the rule is,--That _the velocity is as the -force which produces it_; and this is one of the simplest -ways of expressing the Third Law of Motion. - -In agreement with our general plan, we have to ask, What is -the ground of this rule? What is the simplest and most -satisfactory form to which we can reduce the proof of it? -Or, to take an instance; if a double pressure be exerted -against a given mass, so disposed as to be capable of -motion, why must it produce twice the velocity in the same time? - -To answer this question, suppose the double pressure to be -resolved into two single pressures: one of these will -produce a certain velocity; and the question is, why an -equal pressure, acting upon the same mass, will produce an -equal velocity _in addition_ to the former? Or, stating the -matter otherwise, the question is, why each of the two -forces will produce its separate effect, unaltered by the -simultaneous action of the other force? - -This statement of the case makes it seem to approach very -near to such cases as are included in the Second Law of -Motion, and therefore it might appear that this Third Law -has no grounds distinct from the Second. But it must be -recollected that the word _force_ has a different meaning in -this case and in that; in this place it signifies -_pressure_; in the statement of the Second Law its import -was _accelerative_ or _deflective force_, measured by the -velocity or deflexion generated. And thus the Third Law of -Motion, so far as our reasonings yet go, appears to rest on -a foundation different from the Second. - -Accordingly, that part of the Third Law of Motion which we -are now considering, that the velocity generated is as the -force, was obtained, in fact, by a separate train of -research. The first exemplification of this {251} law which -was studied by mathematicians, was the motion of bodies upon -inclined planes: for the force which urges a body down an -inclined plane is known by statics, and hence the velocity -of its descent was to be determined. Galileo -originally[30\3] in his attempts to solve this problem of -the descent of a body down an inclined plane, did not -proceed from the principle which we have stated, (the -determination of the force which acts down the inclined -plane from statical considerations,) obvious as it may seem; -but assumed, as we have already seen, a proposition -apparently far more precarious;--namely, that a body sliding -down a smooth inclined plane acquires always the same -velocity, so long as the _vertical_ height fallen through is -the same. And this conjecture (for at first it was nothing -more than a conjecture) he confirmed by an ingenious -experiment; in which bodies acquired or lost the same -velocity by descending or ascending through the same height, -although their paths were different in other respects. - -[Note 30\3: _Dial. della Sc. Nuov._ iii. p. 96. See _Hist. -Ind. Sci._ b. vi. c. ii. sect. 5.] - -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 Motion. But his -disciple Viviani was dissatisfied with the assumption thus -introduced; and in succeeding editions of the _Dialogues_, -the apparent chasm in the reasoning was much narrowed, by -making the proof depend upon a principle nearly identical -with the third law of motion as we have just stated it. In -the proof thus added, 'We are agreed,' says the -interlocutor[31\3], 'that in a moving body the impetus, -energy, momentum, or propension to motion, is as great as is -the force or least resistance which suffices to sustain it;' -and the impetus or momentum, in the course of the proof, -being taken to be as the velocity produced in a given time, -it is manifest that the principle so stated amounts to this; -that the velocity produced is as the statical force. And -thus this law of motion appears, {252} in the school of -Galileo, to have been suggested and established at first by -experiment, but afterwards confirmed and demonstrated by _à -priori_ considerations. - -[Note 31\3: _Dialogo_, p. 104.] - -We see, in the above reasoning, a number of abstract terms -introduced which are not, at first at least, very distinctly -defined, as _impetus_, _momentum_, &c. Of these, _momentum_ -has been selected, to express that quantity which, in a -moving body, measures the statical force impressed upon the -body. This quantity is, as we have just seen, proportional -to the velocity in a given body. It is also, in different -bodies, proportional to the mass of the body. This part of -the third law of motion follows from our conception of -matter in general as consisting of parts capable of -addition. A double pressure must be required to produce the -same velocity in a double mass; for if the mass be halved, -each half will require an equal pressure; and the addition, -both of the pressures and of the masses, will take place -without disturbing the effects. - -The measure of the quantity of matter of a body considered -as affecting the velocity which pressure produces in the -body, is termed its _inertia_, as we have already stated (c. -v.). Inertia is the property by which a large mass of matter -requires a greater force than a small mass, to give it an -equal velocity. It belongs to each portion of matter; and -portions of inertia are added whenever portions of matter -are added. Hence _inertia is as the quantity of matter_; -which is only another way of expressing this third law of -motion, so far as quantity of matter is concerned. - -But how do we know the quantity of matter of a body? We may -reply, that we take the weight as the measure of the -quantity of matter: but we may then be again asked, how it -appears that the weight is proportional to the inertia; -which it must be, in order that the quantity of matter may -be proportional to both one and the other. We answer, that -this appears to be true experimentally, because all bodies -fall with equal velocities by gravity, when the known causes -of difference are removed. The observations of falling {253} -bodies, indeed, are not susceptible of much exactness: but -experiments leading to the same result, and capable of great -precision, were made upon pendulums by Newton; as he relates -in his _Principia_, Book III. prop. 6. They all agreed, he -says, with perfect accuracy: and thus the weight and the -inertia are proportional in all cases, and therefore each -proportional to the quantity of matter as measured by the other. - -The conception of inertia, as we have already seen in -chapter V., involves the notion of action and reaction; and -thus the laws which involve inertia depend upon the idea of -mutual causation. The rule, that the velocity is as the -force, depends upon the principle of causation, that the -effect is proportional to the cause; the effect being here -so estimated as to be consistent both with the other laws of -motion and with experiment. - -But here, as in other cases, the question occurs again; Is -experiment really requisite for the proof of this law? If we -look to authorities, we shall be not a little embarrassed to -decide. D'Alembert is against the necessity of experimental -proof. 'Why,' says he[32\3], 'should we have recourse to -this principle employed, at the present day, by everybody, -that the force is proportional to the velocity? ... a -principle resting solely upon this vague and obscure axiom, -that the effect is proportional to the cause. We shall not -examine here,' he adds, 'if this principle is necessarily -true; we shall only avow that the proofs which have hitherto -been adduced do not appear to us unexceptionable: nor shall -we, with some geometers, adopt it as a purely contingent -truth; which would be to ruin the certainty of mechanics, -and to reduce it to be nothing more than an experimental -science. We shall content ourselves with observing,' he -proceeds, 'that certain or doubtful, clear or obscure, it is -useless in mechanics, and consequently ought to be banished -from the science.' Though D'Alembert rejects the third law -of motion in this form, he accepts one of {254} equivalent -import, which appears to him to possess axiomatic certainty; -and this procedure is in consistence with the course which -he takes, of claiming for the science of mechanics more than -mere experimental truth. On the contrary, Laplace considers -this third law as established by experiment. 'Is the force,' -he says'[33\3], 'proportioned to the velocity? This,' he -replies, 'we cannot know _à priori_, seeing that we are in -ignorance of the nature of moving force: we must therefore, -for this purpose, recur to experience; for all which is not -a necessary consequence of the few data we have respecting -the nature of things, is, for us, only a result of -observation.' And again he says[34\3], 'Here, then, we have -two laws of motion,--the law of inertia [the first law of -motion], and the law of the force proportional to the -velocity,--which are given by observation. They are the most -natural and the most simple laws which we can imagine, and -without doubt they flow from the very nature of matter; but -this nature being unknown, they are, for us, only observed -facts: the only ones, however, which Mechanics borrows from -experience.' - -[Note 32\3: _Dynamique_, Pref. p. x.] - -[Note 33\3: _Méc. Cél._ p. 15.] - -[Note 34\3: p. 18.] - -It will appear, I think, from the views given in this and -several other parts of the present work, that we cannot with -justice say that we have very 'few data respecting the -nature of things,' in speculating concerning the laws of the -universe; since all the consequences which flow from the -relations of our fundamental ideas, necessarily regulate our -knowledge of things, so far as we have any such knowledge. -Nor can we say that the nature of matter is unknown to us, -in any sense in which we can conceive knowledge as possible. -The nature of matter is no more unknown than the nature of -space or of number. In our conception of matter, as of space -and of number, are involved certain relations, which are the -necessary groundwork of our knowledge; and anything which is -independent of these relations, is not unknown, but -inconceivable. {255} - -It must be already clear to the reader, from the phraseology -employed by these two eminent mathematicians, 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 experience, nature and matter. But -it will probably be generally allowed, that, taking into -account the explanations already offered of the necessary -conditions of experience and of the conception of inertia, -this law of motion, that the inertia is as the quantity of -matter, is almost or altogether self-evident. - -6. _Action and Reaction are Equal in Moving Bodies._--When -we have to consider bodies as acting upon one another, and -influencing each other's motions, the third law of motion is -still applied; but along with this, we also employ the -general principle that action and reaction are equal and -opposite. Action and reaction are here to be understood as -momentum produced and destroyed, according to the measure of -action established by the Third Law of Motion: 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 used, -that some writers (Newton at the head of them) have -stated the equality of action and reaction as the third law -of motion. - -The third law of motion being once established, the equality -of action and reaction, in the sense of momentum gained and -lost, necessarily follows. Thus, if a weight hanging by a -string over the edge of a smooth level table draw another -weight along the table, the hanging weight moves more slowly -than it would do if not so connected, and thus loses -velocity by the connexion; while the other weight gains by -the connexion all the velocity which it has, for if left to -itself it would rest. And the pressures which restrain the -descent of the first body and accelerate the motion of the -second, are equal at all instants of time, for each of these -pressures is the tension of the string: and hence, by the -third law of motion, the momentum gained by the one body, -and the momentum lost by the other in virtue of the action -of this string, are equal. And similar {256} reasoning may -be employed in any other case where bodies are connected. - -The case where one body does not push or draw, but _strikes_ -another, appeared at first to mechanical reasoners to be of -a different nature from the others; but a little -consideration was sufficient to show that a blow is, in -fact, only a short and violent pressure; and that, -therefore, the general rule of the equality of momentum lost -and gained applies to this as well as to the other cases. - -Thus, in order to determine the case of the direct action of -bodies upon one another, we require no new law of motion. -The equality of action and reaction, which enters -necessarily into every conception of mechanical operation, -combined with the measure of action as given by the third -law of motion, enables us to trace the consequences of every -case, whether of pressure or of impact. - -7. _D'Alembert's Principle._--But what will be the result -when bodies do not act directly upon each other, but are -_indirectly_ connected in any way by levers, strings, -pulleys, or in any other manner, so that one part of the -system has a mechanical advantage over another? The result -must still be determined by the principle that action and -reaction balance each other. The action and reaction, being -pressures in one sense, must balance each other by the laws -of statics, for these laws determine the equilibrium of -pressure. Now action and reaction, according to their -measures in the Third Law of Motion, are momentum gained and -lost, when the action is direct; and except the indirect -action introduce some modification of the law, they must -have the same measure still. But, in fact, we cannot well -conceive any modification of the law to take place in this -case; for direct action is only one (the ultimate) case of -indirect action. Thus if two heavy bodies act at different -points of a lever, the action of each on the other is -indirect; but if the two points come together, the action -becomes direct. Hence the rule must be that which we have -already stated; for if the rule were false for indirect -action, it would {257} also be false for direct action, for -which case we have shown it to be true. And thus we obtain -the general principle, that in any system of bodies which -act on each other, action and reaction, estimated by -momentum gained and lost, balance each other according to -the laws of equilibrium. This principle, which is so general -as to supply a key to the solution of all possible -mechanical problems, is commonly called _D'Alembert's -Principle_. The experimental proofs which convinced men of -the truth of the Third Law of Motion were, many or most of -them, proofs of the law in this extended sense. And thus the -proof of D'Alembert's Principle, both from the idea of -mechanical action and from experience, is included in the -proof of the law already stated. - -8. _Connexion of Dynamical and Statical Principles._--The -principle of equilibrium of D'Alembert just stated, is the -law which he would substitute for the Third Law of Motion; -and he would thus remove the necessity for an independent -proof of that law. In like manner, the Second Law of Motion -is by some writers derived from the principle of the -composition of statical forces; and they would thus -supersede the necessity of a reference to experiment in that -case. Laplace takes this course, and thus, as we have seen, -rests only the First and Third Law of Motion upon -experience. Newton, on the other hand, recognizes the same -connexion of propositions, but for a different purpose; for -he derives the composition of statical forces from the -Second Law of Motion. - -The close connexion of these three principles, the -composition of (statical) forces, the composition of -(accelerating) forces with velocities, and the measure of -(moving) forces by velocities, cannot be denied; yet it -appears to be by no means easy to supersede the necessity of -independent proofs of the last two of these principles. Both -may be proved or illustrated by experiment: and the -experiments which prove the one are different from those -which establish the other. For example, it appears by easy -calculations, that when we apply our principles to the -oscillations of a pendulum, {258} the Second Law is proved -by the fact, that the oscillations take place at the same -rate in an east and west, and in a north and south -direction: under the same circumstances, 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 -pendulum; and similar differences might be pointed out in -other experiments, as to their bearing upon the one law or -the other. - -9. _Mechanical Principles become gradually more simple and -more evident._--I will again point out in general two -circumstances which I have already noticed in particular -cases of the laws of motion.--Truths are often at first -assumed in a form which is far from being the most obvious -or simple;--and truths once discovered are gradually -simplified, so as to assume the appearance of self-evident -truths. - -The former circumstance is exemplified in several of the -instances which we have had to consider. The assumption, -that a perpetual motion is impossible, preceded the -knowledge of the first law of motion. The assumed equality -of the velocities acquired down two inclined planes of the -same height, was afterwards reduced to the third law of -motion by Galileo himself. In the History[35\3], we have -noted Huyghens's assumption of the equality of the actual -descent and potential ascent of the center of gravity: this -was afterwards reduced by Herman and the Bernoullis, to the -statical equivalence of the solicitations of gravity and the -vicarious solicitations of the effective forces which act on -each point; and finally to the principle of D'Alembert, -which asserts that the motions gained and lost balance each -other. - -[Note 35\3: B. vi. c. v. sect. 2.] - -This early assertion of principles which now appear neither -obvious nor self-evident, is not to be considered as a -groundless assumption on the part of the discoverers by whom -it was made. On the contrary, it is evidence of the deep -sagacity and clear thought which were {259} requisite in -order to make such discoveries. For these results are really -rigorous consequences of the laws of motion in their -simplest form: and the evidence of them was probably -present, though undeveloped, in the minds of the -discoverers. We are told of geometrical students, who, by a -peculiar aptitude of mind, perceived the evidence of some of -the more advanced propositions of geometry without going -through the introductory steps. We must suppose a similar -aptitude for mechanical reasonings, which, existing in the -minds of Stevinus, Galileo, Newton, and Huyghens, led them -to make those assumptions which finally resolved themselves -into the laws of motion. - -We may observe further, that the simplicity and evidence -which the laws of mechanics have at length assumed, are much -favoured by the usage of words among the best writers on -such subjects. Terms which originally, and before the laws -of motion were fully known, were used in a very vague and -fluctuating sense, were afterwards limited and rendered -precise, so that assertions which at first appear identical -propositions become distinct and important principles. Thus -_force_, _motion_, _momentum_, are terms which were -employed, though in a loose manner, from the very outset of -mechanical speculation. And so long as these words retained -the vagueness of common language, it would have been a -useless and barren truism to say that 'the momentum is -proportional to the force,' or that 'a body loses as much -motion as it communicates to another.' But when 'momentum' -and 'quantity of motion' are defined to mean the product of -mass and velocity, these two propositions immediately become -distinct statements of the third law of motion and its -consequences. In like manner, the assertion that 'gravity is -a uniform force' was assented to, before it was settled what -a uniform force was; but this assertion only became -significant and useful when that point had been properly -determined. The statement that 'when different motions are -communicated to the same body their effects are {260} -compounded,' becomes the second law of motion, when we -define what composition of motions is. And the same process -may be observed in other cases. - -And thus we see how well the form which science ultimately -assumes is adapted to simplify knowledge. The definitions -which are adopted, and the terms which become current in -precise senses, produce a complete harmony between the -matter and the form of our knowledge; so that truths which -were at first unexpected and recondite, became familiar -phrases, and after a few generations sound, even to common -ears, like identical propositions. - -10. _Controversy of the Measure of Force._--In the History -of Mechanics[36\3], we have given an account of the -controversy which, for some time, occupied the -mathematicians of Europe, whether the forces of bodies in -motion should be reckoned proportional to the velocity, or -to the square of the velocity. We need not here recall the -events of this dispute; but we may remark, that its history, -as a metaphysical controversy, is remarkable in this -respect, that it has been finally and completely settled; -for it is now agreed among mathematicians that both sides -were right, and that the results of mechanical action may be -expressed with equal correctness by means of _momentum_ and -of _vis viva_. It is, in one sense, as D'Alembert has -said[37\3], a dispute about words; but we are not to infer -that, on that account, it was frivolous or useless; for such -disputes are one principal means of reducing the principles -of our {261} knowledge to their utmost simplicity and -clearness. The terms which are employed in the science of -mechanics are now liberated for ever, in the minds of -mathematicians, from that ambiguity which was the -battleground in the war of the _vis viva_. - -[Note 36\3: B. vi. c. v. sect. 2.] - -[Note 37\3: D'Alembert has also remarked (_Dynamique_, Pref. -xxi.) that this controversy 'shows how little justice and -precision there is in the pretended axiom that causes are -proportional to their effects.' But this reflection is by no -means well founded. For since both measures are true, it -appears that causes may be _justly_ measured by their -effects, even when very different kinds of effects are -taken. That the axiom does not point out one _precise_ -measure, till illustrated by experience or by other -considerations, we grant: but the same thing occurs in the -application of other axioms also.] - -But we may observe that the real reason of this controversy -was exactly that tendency which we have been noticing;--the -disposition of man to assume in his speculations certain -general propositions as true, and to fix the sense of terms -so that they shall fall in with this truth. It was agreed, -on all hands, that in the mutual action of bodies the same -quantity of force is always preserved; and the question was, -by which of the two measures this rule could best be -verified. We see, therefore, that the dispute was not -concerning a definition merely, but concerning a definition -combined with a general proposition. Such a question may be -readily conceived to have been by no means unimportant; and -we may remark, in passing, that such controversies, although -they are commonly afterwards stigmatized as quarrels about -words and definitions, are, in reality, events of -considerable consequence in the history of science; since -they dissipate all ambiguity and vagueness in the use of -terms, and bring into view the conditions under which the -fundamental principles of our knowledge can be most clearly -and simply presented. - -It is worth our while to pause for a moment on the prospect -that we have thus obtained, of the advance of knowledge, as -exemplified in the history of Mechanics. The general -transformation of our views from vague to definite, from -complex to simple, from unexpected discoveries to -self-evident truths, from seeming contradictions to -identical propositions, is very remarkable, but it is by no -means peculiar to our subject. The same circumstances, more -or less prominent, more or less developed, appear in the -history of other sciences, according to the point of advance -which each has reached. They bear upon very important -doctrines respecting the prospects, the {262} limits, and -the very nature of our knowledge. And though these doctrines -require to be considered with reference to the whole body of -science, yet the peculiar manner in which they are -illustrated by the survey of the history of Mechanics, on -which we have just been engaged, appears to make this a -convenient place for introducing them to the reader. - - - -{{263}} -CHAPTER VIII. - -OF THE PARADOX OF UNIVERSAL PROPOSITIONS OBTAINED FROM -EXPERIENCE. - - -1. IT was formerly stated[38\3] that experience cannot -establish any universal or necessary truths. The number of -trials which we can make of any proposition is necessarily -limited, and observation alone cannot give us any ground of -extending the inference to untried cases. Observed facts -have no visible bond of necessary connexion, and no exercise -of our senses can enable us to discover such connexion. We -can never acquire from a mere observation of facts, the -right to assert that a proposition is true in all cases, and -that it could not be otherwise than we find it to be. - -[Note 38\3: B. i. c. iv. Of Experience] - -Yet, as we have just seen in the history of the laws of -motion, we may go on collecting our knowledge from -observation, and enlarging and simplifying it, till it -approaches or attains to complete universality and seeming -necessity. Whether the laws of motion, as we now know them, -can be rigorously traced to an absolute necessity in the -nature of things, we have not ventured absolutely to -pronounce. But we have seen that some of the most acute and -profound mathematicians have believed that, for these laws -of motion, or some of them, there was such a demonstrable -necessity compelling them to be such as they are, and no -other. 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 truth; and will confess that it would be -difficult to imagine any other consistent {264} scheme of -fundamental principles. And almost all mathematicians will -allow to these laws an absolute universality; so that we may -apply them without scruple or misgiving, in cases the most -remote from those to which our experience has extended. What -astronomer would fear to refer to the known laws of motion, -in reasoning concerning the double stars; although these -objects are at an immeasurably remote distance from that -solar system which has been the only field of our -observation of mechanical facts? What philosopher, in -speculating respecting a magnetic fluid, or a luminiferous -ether, would hesitate to apply to it the mechanical -principles which are applicable to fluids of known -mechanical properties? When we assert that the quantity of -motion in the world cannot be increased or diminished by the -mutual actions of bodies, 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 tried? - -Yet no one can doubt that, in historical fact, these laws -were collected from experience. That such is the case, is no -matter of conjecture. We know the time, the persons, the -circumstances, belonging to each step of each discovery. I -have, in the History, given an account of these discoveries; -and in the previous chapters of the present work, I have -further examined the nature and the import of the principles -which were thus brought to light. - -Here, then, is an apparent contradiction. Experience, it -would seem, has done that which we had proved that she -cannot do. She has led men to propositions, universal at -least, and to principles which appear to some persons -necessary. What is the explanation of this contradiction, -the solution of this paradox? Is it true that Experience can -reveal to us universal and necessary truths? Does she -possess some secret virtue, some unsuspected power, by which -she can detect connexions and consequences which we have -declared to be out of her sphere? Can she see more than mere -appearances, and observe more than mere facts? Can {265} she -penetrate, in some way, to the nature of things?--descend -below the surface of phenomena to their causes and origins, -so as to be able to say what can and what can not be;--what -occurrences are partial, and what universal? If this be so, -we have indeed mistaken her character and powers; and the -whole course of our reasoning becomes precarious and -obscure. But, then, when we return upon our path we cannot -find the point at which we deviated, we cannot detect the -false step in our deduction. It still seems that by -experience, strictly so called, we cannot discover necessary -and universal truths. Our senses can give us no evidence of -a necessary connexion in phenomena. Our observation must be -limited, and cannot testify concerning anything which is -beyond its limits. 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 done. - -2. But in order to try to solve this Paradox, let us again -refer to the History of Mechanics. In the cases belonging to -that science, in which propositions of the most -unquestionable universality, and most approaching to the -character of necessary truths, (as, for instance, the laws -of motion,) have been arrived at, what is the source of the -axiomatic character which the propositions thus assume? The -answer to this question will, we may hope, throw some light -on the perplexity in which we appear to be involved. - -Now the answer to this inquiry is, that the laws of motion -borrow their axiomatic character from their being merely -_interpretations_ of the Axioms of Causation. Those axioms, -being exhibitions of the Idea of Cause under various -aspects, are of the most rigorous universality and -necessity. And so far as the laws of motion are -exemplifications of those axioms, these laws must be no less -universal and necessary. How these axioms are to be -understood;--in what sense _cause_ and _effect_, _action_ -and _reaction_, are to be taken, experience and observation -did, in fact, teach inquirers on this subject; and without -this teaching, the laws of motion could never have been -distinctly known. If two forces {266} act together, each -must produce its effect, by the axiom of causation; and, -therefore, the effects of the separate forces must be -_compounded_. But a long course of discussion and experiment -must instruct men of what kind this _composition_ of forces -is. Again; action and reaction must be equal; but much -thought and some trial were needed to show what _action_ and -_reaction_ are. Those metaphysicians who enunciated Laws of -motion without reference to experience, propounded only such -laws as were vague and inapplicable. But yet these persons -manifested the indestructible conviction, belonging to man's -speculative nature, that there exist Laws of motion, that -is, universal formulæ, connecting the causes and effects -when motion takes place. Those mechanicians, again, who, -observed facts involving equilibrium and motion, and stated -some narrow rules, without attempting to ascend to any -universal and simple principle, obtained laws no less barren -and useless than the metaphysicians; for they could not tell -in what new cases, or whether in any, their laws would be -verified;--they needed a more general rule, to show them the -limits of the rule they had discovered. They went wrong in -each attempt to solve a new problem, because their -interpretation of the terms of the axioms, though true, -perhaps, in certain cases, was not right in general. - -Thus Pappus erred in attempting to interpret as a case of -the lever, the problem of supporting a weight upon an -inclined plane; thus Aristotle erred in interpreting the -doctrine that the weight of bodies is the cause of their -fall; thus Kepler erred in interpreting the rule that the -velocity of bodies depends upon the force; thus -Bernoulli[39\3] erred in interpreting the equality of action -and reaction upon a lever in motion. In each of these -instances, true doctrines, already established, (whether by -experiment or otherwise,) were erroneously applied. And the -error was corrected by further reflection, which pointed out -that another mode of interpretation was requisite, in order -that the axiom {267} which, was appealed to in each case -might retain its force in the most general sense. And in the -reasonings which avoided or corrected such errors, and which -led to substantial general truths, the object of the -speculator always was to give to the acknowledged maxims -which the Idea of Cause suggested, such a signification as -should be consistent with their universal validity. The rule -was not accepted as particular at the outset, and afterwards -generalized more and more widely; but from the very first, -the universality of the rule was assumed, and the question -was, how it should be understood so as to be universally -true. At every stage of speculation, the law was regarded as -a general law. This was not an aspect which it gradually -acquired, by the accumulating contributions of experience, -but a feature of its original and native character. _What_ -should happen universally, experience might be needed to -show: but that what happened should happen _universally_, -was implied in the nature of knowledge. The universality of -the laws of motion was not gathered from experience, however -much the laws themselves might be so. - -[Note 39\3: _Hist. Ind. Sc._ b. vi. c. v. sect. 2.] - -3. Thus we obtain the solution of our Paradox, so far as the -case before us is concerned. The laws of motion borrow their -_form_ from the Idea of Causation, though their _matter_ may -be given by experience: and hence they possess a -universality which experience cannot give. They are -certainly and universally valid; and the only question for -observation to decide is, how they are to be understood. -They are like general mathematical formulæ, which are known -to be true, even while we are ignorant what are the unknown -quantities which they involve. It must be allowed, on the -other hand, that so long as these formulæ are not -interpreted by a real study of nature, they are not only -useless but prejudicial; filling men's minds with vague -general terms, empty maxims, and unintelligible -abstractions, which they mistake for knowledge. Of such -perversion of the speculative propensities of man's nature, -the world has seen too much in all ages. Yet we must not, on -that account, despise these forms of {268} truth, since -without them, no general knowledge is possible. Without -general terms, and maxims, and abstractions, we can have no -science, no speculation; hardly, indeed, consistent thought -or the exercise of reason. The course of real knowledge is, -to obtain from thought and experience the right -interpretation of our general terms, the real import of our -maxims, the true generalizations which our abstractions -involve. - -4. If it be asked, How Experience is able to teach us to -interpret aright the general terms which the Axioms of -Causation involve;--whence she derives the light which she -is to throw on these general notions; the answer is -obvious;--namely, that the relations of causation are the -_conditions_ of Experience;--that the general notions are -_exemplified_ in the particular cases of which she takes -cognizance. The events which take place about us, and which -are the objects of our observation, we cannot conceive -otherwise than as subject to the laws of cause and effect. -Every event must have a cause;--Every effect must be -determined by its cause;--these maxims are true of the -phenomena which form the materials of our experience. It is -precisely to them, that these truths apply. It is in the -world which we have before our eyes, that these propositions -are universally verified; and it is therefore by the -observation of what we see, that we must learn how these -propositions are to be understood. Every fact, every -experiment, is an example of these statements; and it is -therefore by attention to and familiarity with facts and -experiments, that we learn the signification of the -expressions in which the statements are made; just as in any -other case we learn the import of language by observing the -manner in which it is applied in known cases. Experience is -the interpreter of nature; it being understood that she is -to make her interpretation in that comprehensive phraseology -which is the genuine language of science. - -5. We may return for an instant to the objection, that -experience cannot give us general truths, since, after any -number of trials confirming a rule, we may for aught we can -foresee, have one which violates the {269} rule. When we -have seen a thousand stones fall to the ground, we may see -one which does not fall under the same apparent -circumstances. How then, it is asked, can experience teach -us that _all_ stones, rigorously speaking, will fall if -unsupported? And to this we reply, that it is not true that -we can conceive one stone to be suspended in the air, while -a thousand others fall, without believing some peculiar -cause to support it; and that, therefore, such a supposition -forms no exception to the law, that gravity is a force by -which _all_ bodies are urged downwards. Undoubtedly we can -conceive a body, when dropt or thrown, to move in a line -quite different from other bodies: thus a certain -missile[40\3] used by the natives of Australia, and lately -brought to this country, when thrown from the hand in a -proper manner, describes a curve, and returns to the place -from whence it was thrown. But did any one, therefore, even -for an instant suppose that the laws of motion are different -for this and for other bodies? On the contrary, was not -every person of a speculative turn immediately led to -inquire how it was that the known causes which modify -motion, the resistance of the air and the other causes, -produced in this instance so peculiar an effect? And if the -motion had been still more unaccountable, it would not have -occasioned any uncertainty whether it were consistent with -the agency of gravity and the laws of motion. If a body -suddenly alter its direction, or move in any other -unexpected manner, we never doubt that there is a cause of -the change. We may continue quite ignorant of the nature of -this cause, but this ignorance never occasions a moment's -doubt that the cause exists and is exactly suited to the -effect. And thus experience can prove or discover to us -general rules, but she can never prove that general rules do -not exist. Anomalies, exceptions, unexplained phenomena, may -remind us that we have much still to learn, but they can -never make us suppose that truths are not universal. We may -observe facts that show us we have not fully {270} -understood the meaning of our general laws, but we can never -find facts which show our laws to have no meaning. Our -experience is bound in by the limits of cause and effect, -and can give us no information concerning any region where -that relation does not prevail. The whole series of external -occurrences and objects, through all time and space, exists -only, and is conceived only, as subject to this relation; -and therefore we endeavour in vain to imagine to ourselves -when and where and how exceptions to this relation may -occur. The assumption of the connexion of cause and effect -is essential to our experience, as the recognition of the -maxims which express this connexion is essential to our -knowledge. - -[Note 40\3: Called the Bo-me-rang.] - -6. I have thus endeavoured to explain in some measure how, -at least in the field of our mechanical knowledge, -experience can discover universal truths, though she cannot -give them their universality; and how such truths, though -borrowing their form from our ideas, cannot be understood -except by the actual study of external nature. And thus with -regard to the laws of motion, and other fundamental -principles of Mechanics, the analysis of our ideas and the -history of the progress of the science well illustrate each -other. - -If the paradox of the discovery of universal truths by -experience be thus solved in one instance, a much wider -question offers itself to us;--How far the difficulty, and -how far the solution, are applicable to other subjects. It -is easy to see that this question involves most grave and -extensive doctrines with regard to the whole compass of -human knowledge: and the views to which we have been led in -the present Book of this work are, we trust, fitted to throw -much light upon the general aspect of the subject. But after -discussions so abstract, and perhaps obscure, as those in -which we have been engaged for some chapters, I willingly -postpone to a future occasion an investigation which may -perhaps appear to most readers more recondite and difficult -still. And we have, in fact, many other special fields of -knowledge to survey, before we are led by the order of our -subject, to {271} those general questions and doctrines, -those antitheses brought into view and again resolved, which -a view of the whole territory of human knowledge suggests, -and by which the nature and conditions of knowledge are -exhibited. - -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 science, namely, the doctrine -of universal gravitation. - - - -{{272}} -CHAPTER IX. - -OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL GRAVITATION. - - -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 doctrine. - -1. To a certain extent the doctrine of the attraction of -bodies according to the law of the inverse square of the -distance, exhibits in its progress among men the same -general features which we have noticed in the history of the -laws of motion. This doctrine was maintained _à priori_ on -the ground of its simplicity, and was asserted positively, -even before it was clearly understood:--notwithstanding this -anticipation, its establishment on the ground of facts was a -task of vast labour and sagacity:--when it had been so -established in a general way, there occurred at later -periods, an occasional suspicion that it might be -approximately true only:--these suspicions led to further -researches, which showed the rule to be rigorously -exact:--and at present there are mathematicians who -maintain, not only that it is true, but that it is a -necessary property of matter. A very few words on each of -these points will suffice. - -2. I have shown in the _History of Science_[41\3], that the -attraction of the sun according to the inverse square of the -distance, had been divined by Bullialdus, Hooke, Halley, and -others, before it was proved by Newton. Probably the reason -which suggested this conjecture was, that gravity might be -considered {273} as a sort of emanation; and that thus, like -light or any other effect diffused from a center, it must -follow the law just stated, the efficacy of the force being -weakened in receding from the center, exactly in proportion -to the space through which it is diffused. It cannot be -denied that such a view appears to be strongly recommended -by analogy. - -[Note 41\3: B. vii. c. i.] - -When it had been proved by Newton that the planets were -really retained in their elliptical orbits by a central -force, his calculations also showed that the above-stated -_law_ of the force must be at least very approximately -correct, since otherwise the aphelia of the orbits could not -be so nearly at rest as they were. Yet when it seemed as if -the motion of the moon's apogee could not be accounted for -without some new supposition, the _à 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 law: but when, in order to test the -accuracy of this hypothesis, the calculation of the motion -of the moon's apogee was pushed to a greater degree of -exactness than had been obtained before, it was found that -the new term vanished of itself; and that the inverse square -now accounted for the whole of the motion. And thus, as in -the case of the second law of motion, the most scrupulous -examination terminated in showing the simplest rule to be -rigorously true. - -3. Similar events occurred in the history of another part of -the law of gravitation: namely, that the attraction is -proportional to the quantity of matter attracted. This part -of the law may also be thus stated, That the weight of -bodies arising from gravity is proportional to their -inertia; and thus, that the _accelerating force_ on all -bodies under the same circumstances is the same. Newton made -experiments which proved this with regard to terrestrial -bodies; for he found that, at the end of equal strings, -balls of all substances, gold, silver, lead, glass, wood, -&c., oscillated in equal times[42\3]. But a few years ago, -doubts {274} arose among the German astronomers whether this -law was rigorously true with regard to the planetary bodies. -Some calculations appeared to prove, that the attraction of -Jupiter as shown by the perturbations which he produces in -the small planets Juno, Vesta, and Pallas, was different -from the attraction which he exerts on his own satellites. -Nor did there appear to these philosophers anything -inconceivable in the supposition that the attraction of a -planet might be thus _elective_. But when Mr. Airy obtained -a more exact determination of the mass of Jupiter, as -indicated by his effect on his satellites, it was found that -this suspicion was unfounded; and that there was, in this -case, no exception to the universality of the rule, that -this cosmical attraction is in the proportion of the -attracted mass. - -[Note 42\3: _Prin._ lib. iii. prop. 6.] - -4. Again: when it had thus been shown that a mutual -attraction of parts, according to the law above mentioned, -prevailed throughout the extent of the solar system, it -might still be doubted whether the same law extended to -other regions of the universe. It might have been perhaps -imagined that each fixed star had its peculiar law of force. -But the examination of the motions of double stars about -each other, by the two Herschels and others, appears to show -that these bodies describe ellipses as the planets do; and -thus extends the law of the inverse squares to parts of the -universe immeasurably distant from the whole solar system. - -5. Since every doubt which has been raised with regard to -the universality and accuracy of the law of gravitation, has -thus ended in confirming the rule, 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 truth, capable of being established by reason -alone. When it had been proved by Newton that gravity is -really a _universal_ attribute of matter as far as we can -learn, his pupils were not content without maintaining it to -be an _essential_ quality. This is the doctrine held by -Cotes in the preface to the second edition of the -_Principia_ (1712): {275} 'Gravity,' he says, 'is a primary -quality of bodies, as extension, mobility, and -impenetrability are.' But Newton himself by no means went so -far. In his second Letter to Bentley (1693), he says, 'You -sometimes speak of gravity as essential and inherent to -matter; pray do not ascribe that notion to me. The cause of -gravity,' he adds, 'I do not pretend to know, and would take -more time to consider of it.' - -Cotes maintains his opinion by urging, that we learn by -_experience_ that all bodies possess gravity, and that we do -not learn in any other way that they are extended, moveable, -or solid. But we have already seen, that the ideas of space, -time, and reaction, on which depend extension, mobility, and -solidity, are not results, but conditions, of experience. We -cannot conceive a body except as extended; we cannot -conceive it to exert mechanical action except with some kind -of solidity. But so far as our conceptions of body have -hitherto been developed, we find no difficulty in conceiving -two bodies which do not attract each other. - -6. Newton lays down, in the second edition of the -_Principia_, this 'Rule of Philosophizing' (book iii.); that -'The qualities of bodies which cannot be made more or less -intense, and which belong to all bodies on which we are able -to make experiments, are to be held to be qualities of all -bodies in general.' And this Rule is cited in the sixth -Proposition of the Third Book of the _Principia_, (Cor. 2,) -in order to prove that gravity, proportional to the quantity -of matter, may be asserted to be a quality of all bodies -universally. But we may remark that a Rule of -Philosophizing, itself of precarious authority, cannot -authorize us in ascribing universality to an empirical -result. Geometrical and statical properties are seen to be -necessary, and _therefore_ universal: but Newton appears -disposed to assert a like universality of gravity, quite -unconnected with any necessity. It would be a very -inadequate statement, indeed a false representation, of -statical truth, if we were to say, that because every body -which has hitherto been tried _has been found_ to have a -center of gravity, we venture to assert that all bodies -whatever {276} have a center of gravity. And if we are ever -able to assert the absolute universality of the law of -gravitation, we shall have to rest this truth upon the -clearer development of our ideas of matter and force; not -upon a Rule of Philosophizing, which, till otherwise proved, -must be a mere rule of prudence, and which the opponent may -refuse to admit. - -7. Other persons, instead of asserting gravity to be in its -own nature essential to matter, have made hypotheses -concerning some mechanism or other, by which this mutual -attraction of bodies is produced[43\3]. Thus the Cartesians -ascribed to a vortex the tendency of bodies to a center; -Newton himself seems to have been disposed to refer this -tendency to the elasticity of an ether; Le Sage propounded a -curious hypothesis, in which this attraction is accounted -for by the impulse of infinite streams of particles flowing -constantly through the universe in all directions. In these -speculations, the force of gravity is resolved into the -pressure or impulse of solids or fluids. On the other hand, -hypotheses have been propounded, in which the solidity, and -other physical qualities of bodies, have been explained by -representing the bodies as a collection of points, from -which points, repulsive, as well as attractive, forces -emanate. This view of the constitution of bodies was -maintained and developed by Boscovich, and is hence termed -'Boscovich's Theory:' and the discussion of it will more -properly come under our review at a future period, when we -speak of the question whether bodies are made up of atoms. -But we may observe, that Newton himself appears to have -inclined, as his followers certainly did, to this mode of -contemplating the physical properties of bodies. In his -Preface to the _Principia_, after speaking of the central -forces which are exhibited in cosmical phenomena, he says: -'Would that we could derive the other phenomena of Nature -from mechanical principles by the same mode of reasoning. -For many things move me {277} so that I suspect all these -phenomena may depend upon certain forces, by which the -particles of bodies, through causes not yet known, are -either impelled to each other and cohere according to -regular figures, or are repelled and recede from each other: -which forces being unknown, philosophers have hitherto made -their attempts upon nature in vain.' - -[Note 43\3: See Vince, _Observations on the Hypothesis -respecting Gravitation_, and the Critique of that work, -_Edinb. Rev._ vol. xiii.] - -8. But both these hypotheses;--that by which cohesion and -solidity are reduced to attractive and repulsive forces, and -that by which attraction is reduced to the impulse and -pressure of media;--are hitherto merely modes of -representing mechanical laws of nature; and cannot, either -of them, be asserted as possessing any evident truth or -peremptory authority to the exclusion of the other. 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 other; for it is often urged -that this attraction of bodies at a distance is an absurd -supposition. - -The doctrine is often thus stigmatized, both by popular and -by learned writers. It was long received as a maxim in -philosophy (as Monboddo informs us[44\3]), that a body -cannot act _where_ it is not, any more than _when_ it is -not. But to this we reply, that time is a necessary -condition of our conception of causation, in a different -manner from space. The action of force can only be conceived -as taking place in a succession of moments, in each of which -cause and effect immediately succeed each other: 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 causation. But in space, there is no -such visible necessity of continuity; the action and -reaction may take place at a distance from each other; all -that is necessary being that they be equal and opposite. - -[Note 44\3: _Ancient Metaphysics_, vol. ii. p. 175.] - -Undoubtedly the existence of attraction is rendered more -acceptable to common apprehension by supposing {278} some -intermediate machinery,--a cord, or rod, or fluid,--by which -the forces may be conveyed from one point to another. But -such images are rather fitted to satisfy those prejudices -which arise from the earlier application of our ideas of -force, than to exhibit the real nature of those ideas. If we -suppose two bodies to pull each other by means of a rod or -cord, we only suppose, in addition to those equal and -opposite forces acting upon the two bodies, (which forces -are alone essential to mutual attraction) a certain power of -resisting transverse pressure at every point of the -intermediate line: which additional supposition is entirely -useless, and quite unconnected with the essential conditions -of the case. When the Newtonians were accused of introducing -into philosophy an unknown cause which they termed -_attraction_, they justly replied that they knew as much -respecting attraction as their opponents did about impulse. -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 subjects. - -Having thus examined the degree of certainty and generality -to which our knowledge of the law of universal gravitation -has been carried, by the progress of mechanical discovery -and speculation up to the present time, we might proceed to -the other branches of science, and examine in like manner -their grounds and conditions. But before we do this, 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 persons, who share only in an indirect and derivative -manner in the influence of science. - - - -{{279}} -CHAPTER X. - -OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS. - - -1. WE have seen how the progress of knowledge upon the -subject of motion and force has produced, in the course of -the world's history, a great change in the minds of acute -and speculative men; so that such persons can now reason -with perfect steadiness and precision upon subjects on -which, at first, their thoughts were vague and confused; and -can apprehend, as truths of complete certainty and evidence, -laws which it required great labour and time to discover. -This _complete_ development and clear manifestation of -mechanical ideas has taken place only among mathematicians -and philosophers. But yet a progress of thought upon such -subjects,--an advance from the obscure to the clear, and -from errour to truth,--may be traced in the world at large, -and among those who have not directly cultivated the exact -sciences. This diffused and collateral influence of science -manifests itself, although in a wavering and fluctuating -manner, by various indications, at various periods of -literary history. The opinions and reasonings which are put -forth upon mechanical subjects, and above all, the adoption, -into common language, of terms and phrases belonging to the -prevalent mechanical systems, exhibit to us the most -profound discoveries and speculations of philosophers in -their effect upon more common and familiar trains of -thought. This effect is by no means unimportant, and we -shall point out some examples of such indications as we have -mentioned. - -2. The discoveries of the ancients in speculative mechanics -were, as we have seen, very scanty; and {280} hardly -extended their influence to the unmathematical world. Yet -the familiar use of the term 'center of gravity' preserved -and suggested the most important part of what the Greeks had -to teach. The other phrases which they employed, as -_momentum_, _energy_, _virtue_, _force_, and the like, never -had any exact meaning, even among mathematicians; and -therefore never, in the ancient world, became the means of -suggesting just habits of thought. I have pointed out, in -the History of Science, several circumstances which appear -to denote the general confusion of ideas which prevailed -upon mechanical subjects during the times of the Roman -empire. I have there taken as one of the examples of this -confusion, the fable narrated by Pliny and others concerning -the echineïs, a small fish, which was said to stop a ship -merely by sticking to it[45\3]. This story was adduced as -betraying the absence of any steady apprehension of the -equality of action and reaction; since the fish, except it -had some immoveable obstacle to hold by, must be pulled -forward by the ship, as much as it pulled the ship backward. -If the writers who speak of this wonder had shown any -perception of the necessity of a reaction, either produced -by the rapid motion of the fish's fins in the water, or in -any other way, they would not be chargeable with this -confusion of thought; but from their expressions it is, I -think, evident that they saw no such necessity[46\3]. Their -idea of mechanical action was not sufficiently distinct to -enable them to see the absurdity of {281} supposing an -intense pressure with no obstacle for it to exert itself -against. - -[Note 45\3: _Hist. Ind. Sc._ b. iv. c. i. sect. 2.] - -[Note 46\3: See Prof. Powell, _On the Nature and Evidence of -the Laws of Motion_. _Reports of the Ashmolean Society_. -Oxford. 1837. Professor Powell has made an objection to my -use of this instance of confusion of thought; the remark in -the text seems to me to justify what I said in the History. -As an evidence that the fish was not supposed to produce its -effect by its muscular power acting on the water, we may -take what Pliny says, _Nat. Hist._ xxxii. 1, 'Domat mundi -rabiem, nullo suo labore; non retinendo, aut alio modo quam -adhærendo:' and also what he states in another place (ix. -41), that when it is preserved in pickle, it may be used in -recovering gold which has fallen into a deep well. All this -implies adhesion alone, with no conception of reaction.] - -3. We may trace, in more modern times also, indications of a -general ignorance of mechanical truths. Thus the phrase of -shooting at an object 'point-blank,' implies the belief that -a cannon-ball describes a path of which the first portion is -a straight line. This errour was corrected by the true -mechanical principles which Galileo and his followers -brought to light; but these principles made their way to -popular notice, principally in consequence of their -application to the motions of the solar system, and to the -controversies which took place respecting those motions. -Thus by far the most powerful argument against the reception -of the Copernican system of the universe, was that of those -who asked, Why a stone dropt from a tower was not left -behind by the motion of the earth? The answer to this -question, now universally familiar, involves a reference to -the true doctrine of the composition of motions. Again; -Kepler's persevering and strenuous attempts[47\3] to frame a -physical theory of the universe were frustrated by his -ignorance of the first law of motion, which informs us that -a body will retain its velocity without any maintaining -force. He proceeded upon the supposition that the sun's -force was requisite to _keep up_ the motion of the planets, -as well as to deflect and modify it; and he was thus led to -a system which represented the sun as carrying round the -planets in their orbits by means of a _vortex_, produced by -his revolution. The same neglect of the laws of motion -presided in the formation of Descartes' system of vortices. -Although Descartes had enunciated in words the laws of -motion, he and his followers showed that they had not the -practical habit of referring to these mechanical principles; -and dared not trust the planets to move in free space -without some surrounding machinery to support them[48\3]. - -[Note 47\3: _Hist. Ind. Sc._ b. v. c. iv. and b. vii. c. i.] - -[Note 48\3: I have, in the History, applied to Descartes the -character which Bacon gives to Aristotle, 'Audax simul et -pavidus:' though he was bold enough to enunciate the laws of -motion without knowing them aright, he had not the courage -to leave the planets to describe their orbits by the agency -of those laws, without the machinery of contact.] - -{282} 4. When at last mathematicians, following Newton, 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 hand; and when the solution -of this problem and its immense consequences had become -matters of general notoriety and interest; the new views -introduced, as is usual, new terms, which soon became -extensively current. We meet with such phrases as 'flying -off in the tangent,' and 'deflexion from the tangent;' with -antitheses between 'centripetal' and 'centrifugal force,' or -between 'projectile' and 'central force.' 'Centers of -force,' 'disturbing forces,' 'perturbations,' and -'perturbations of higher orders,' are not unfrequently -spoken of: and the expression 'to gravitate,' and the term -'universal gravitation,' acquired a permanent place in the -language. - -Yet for a long time, and even up to the present day, we find -many indications that false and confused apprehensions on -such subjects are by no means extirpated. Arguments are -urged against the mechanical system of the universe, -implying in the opponents an absence of all clear mechanical -notions. Many of this class of writers retrograde to -Kepler's point of view. This is, for example, the case with -Lord Monboddo, who, arguing on the assumption that force is -requisite to maintain, as well as to deflect motion, -produced a series of attacks upon the Newtonian philosophy; -which he inserted in his _Ancient Metaphysics_, published in -1779 and the succeeding years. This writer (like Kepler), -measures force by the velocity which the body _has_[49\3], -not by that which it _gains_. Such a use of language would -prevent our obtaining any laws of motion at all. -Accordingly, the author, in the very next page to that which -I have just quoted, abandons this measure of force, and, in -curvilinear motion, measures {283} force by 'the fall from -the extremity of the arc.' Again; in his objections to the -received theory, he denies that curvilinear motion is -compounded, although his own mode of considering such motion -assumes this composition in the only way in which it was -ever intended by mathematicians. 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 system. - -[Note 49\3: _Anc. Met._ vol. ii. b. v. c. vi. p. 413.] - -The following extract from the _Ancient Metaphysics_, may be -sufficient to show the value of the author's criticism on -the subjects of which we are now speaking. His object is to -prove that there do not exist a centripetal and a -centrifugal force in the case of elliptical motion. 'Let any -man move in a circular or elliptical line described to him; -and he will find no tendency in himself either to the center -or from it, much less both. If indeed he attempt to make the -motion with great velocity, or if he do it carelessly and -inattentively, he may go out of the line, either towards the -center or from it: but this is to be ascribed, not to the -nature of the motion, but to our infirmity; or perhaps to -the animal form, which is more fitted for progressive motion -in a right line than for any kind of curvilinear motion. But -this is not the case with a sphere or spheroid, which is -equally adapted to motion in all directions[50\3].' We need -hardly remind the reader that the manner in which a man -running round a small circle, finds it necessary to lean -inwards, in order that there may be a centripetal -inclination to counteract the centrifugal force, is a -standard example of our mechanical doctrines; and this fact -(quite familiar in practice as well as theory) is in direct -contradiction of Lord Monboddo's assertion. - -[Note 50\3: _Anc. Met._ vol. i. b. ii. c. 19, p. 264.] - -5. A similar absence of distinct mechanical thought appears -in some of the most celebrated metaphysicians of Germany. I -have elsewhere noted[51\3] the opinion expressed by Hegel, -that the glory which belongs to {284} Kepler has been -unjustly transferred to Newton; and I have suggested, as the -explanation of this mode of thinking, that Hegel himself, in -the knowledge of mechanical truth, had not advanced beyond -Kepler's point of view. Persons who possess conceptions of -space and number, but who have not learnt to deal with ideas -of force and causation, may see more value in the -discoveries of Kepler than in those of Newton. Another -exemplification of this state of mind may be found in -Professor Schelling's speculations; for instance, in his -_Lectures on the Method of Academical Study_. In the twelfth -Lecture, on the study of Physics and Chemistry, he says, (p. -266,) '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 (Kepler's) godlike genius, -is, as is well known, this: it has attempted a construction -of those laws which, according to its foundations, is -altogether empirical. We may assume it as a general rule, -that in any proposed construction, that which is not a pure -general form cannot have any scientific import or truth. The -foundation from which the centrifugal motion of the bodies -of the world is derived, is no necessary form, it is an -empirical fact. The Newtonian attractive force, even if it -be a necessary assumption for a merely reflective view of -the subject, is still of no significance for the Reason, -which recognizes only absolute relations. The grounds of the -Keplerian laws can be derived, without any empirical -appendage, purely from the doctrine of Ideas, and of the two -Unities, which are in themselves one Unity, and in virtue of -which each being, while it is absolute in itself, is at the -same time in the absolute, and reciprocally.' - -[Note 51\3: _Hist. Ind. Sc._ b. vii. c. ii. sect. 5.] - -It will be observed, that in this passage our mechanical -laws are objected to because they are not necessary results -of our ideas; which, however, as we have seen, according to -the opinion of some eminent mechanical philosophers, they -are. But to assume this evident necessity as a condition of -every advance in science, is to mistake the last, perhaps -unattainable step, for the first, which lies before our -feet. And, {285} without inquiring further about 'the -Doctrine of the two Unities,' or the manner in which from -that doctrine we may deduce the Keplerian laws, 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 -acquired. - -6. But without going to schools of philosophy opposed to the -Inductive School, we may find many loose and vague habits of -thinking on mechanical subjects among the common classes of -readers and reasoners. And there are some familiar modes of -employing the phraseology of mechanical science, which are, -in a certain degree, chargeable with inaccuracy, and may -produce or perpetuate confusion. Among such cases we may -mention the way in which the centripetal and centrifugal -forces, and also the projectile and central forces of the -planets, are often compared or opposed. Such antitheses -sometimes proceed upon the false notion that the two members -of these pairs of forces are of the same kind: whereas on -the contrary the _projectile_ force is a hypothetical -impulsive force which may, at some former period, have -caused the motion to begin; while the _central_ force is an -actual force, which must act continuously and during the -whole time of the motion, in order that the motion may go on -in the curve. In the same manner the _centrifugal_ force is -not a distinct force in a strict sense, but only a certain -result of the first law of motion, measured by the portion -of _centripetal_ force which counteracts it. Comparisons of -quantities so heterogeneous imply confusion of thought, and -often suggest baseless speculations and imagined reforms of -the received opinions. - -7. I might point out other terms and maxims, in addition to -those already mentioned, which, though formerly employed in -a loose and vague manner, are now accurately understood and -employed by all just thinkers; and thus secure and diffuse a -right understanding of mechanical truths. Such are -_momentum_, _inertia_, _quantity of matter_, _quantity of -motion_; that _force is proportional to its effects_; that -_action and_ {286} _reaction are equal_; that _what is -gained in force by machinery is lost in time_; that _the -quantity of motion in the world cannot be either increased -or diminished_. When the expression of the truth thus -becomes easy and simple, clear and convincing, the meanings -given to words and phrases by discoverers glide into the -habitual texture of men's reasonings, and the effect of the -establishment of true mechanical principles is felt far from -the school of the mechanician. If these terms and maxims are -understood with tolerable clearness, they carry the -influence of truth to those who have no direct access to its -sources. Many an extravagant project in practical machinery, -and many a wild hypothesis in speculative physics, has been -repressed by the general currency of such maxims as we have -just quoted. - -8. Indeed so familiar and evident are the elementary truths -of mechanics when expressed in this simple form, that they -are received as truisms; and men are disposed to look back -with surprise and scorn at the speculations which were -carried on in neglect of them. 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 motions: and gives himself -credit for intellectual superiority, because he sees, as -self-evident, what such a man could not discover at all. It -is well for such a person to recollect, that the real cause -of his superior insight is not the pre-eminence of his -faculties, but the successful labours of those who have -preceded him. The language which he has learnt to use -unconsciously, has been adapted to, and moulded on, -ascertained truths. When he talks familiarly of -"accelerating forces" and "deflexions from the tangent," he -is assuming that which Kepler did not know, and which it -cost Galileo and his disciples so much labour and thought to -establish. Language is often called an instrument of -thought; but it is also the nutriment of thought; or rather, -it is the atmosphere in which thought lives: a medium -essential to the activity of our speculative power, although -invisible {287} and imperceptible in its operation; and an -element modifying, by its qualities and changes, the growth -and complexion of the faculties which it feeds. In this way -the influence of preceding discoveries upon subsequent ones, -of the past upon the present, is most penetrating and -universal, though most subtle and difficult to trace. The -most familiar words and phrases are connected by -imperceptible ties with the reasonings and discoveries of -former men and distant times. Their knowledge is an -inseparable part of ours; the present generation inherits -and uses the scientific wealth of all the past. And this is -the fortune, not only of the great and rich in the -intellectual world: of those who have the key to the ancient -storehouses, and who have accumulated treasures of their -own;--but the humblest inquirer, while he puts his -reasonings into words, benefits by the labours of the -greatest discoverers. When he counts his little wealth, he -finds that he has in his hands coins which bear the image -and superscription of ancient and modern intellectual -dynasties; and that in virtue of this possession, -acquisitions are in his power, solid knowledge within his -reach, which none could ever have attained to, if it were -not that the gold of truth, once dug out of the mine, -circulates more and more widely among mankind. - -9. Having so fully examined, in the preceding instances, the -nature of the progress of thought which science implies, -both among the peculiar cultivators of science, and in that -wider world of general culture which receives only an -indirect influence from scientific discoveries, we shall not -find it necessary to go into the same extent of detail with -regard to the other provinces of human knowledge. In the -case of the Mechanical Sciences, we have endeavoured to -show, not only that Ideas are requisite in order to form -into a science the Facts which nature offers to us, but that -we can advance, almost or quite, to a complete -identification of the Facts with the Ideas. In the sciences -to which we now proceed, we shall not seek to fill up the -chasm by which Facts and Ideas are separated; but we shall -endeavour to detect the Ideas which our {288} knowledge -involves, to show how essential these are; and in some -respects to trace the mode in which they have been gradually -developed among men. - -10. The motions of the heavenly bodies, their laws, their -causes, are among the subjects of the first division of the -Mechanical Sciences; and of these sciences we formerly -sketched the history, and have now endeavoured to exhibit -the philosophy. If we were to take any other class of -motions, _their_ laws and causes might give rise to sciences -which would be mechanical sciences in exactly the same sense -in which Physical Astronomy is so. The phenomena of magnets, -of electrical bodies, of galvanical apparatus, seem to form -obvious materials for such sciences; and if they were so -treated, the philosophy of such branches of knowledge would -naturally come under our consideration at this point of our -progress. - -But on looking more attentively at the sciences of -Electricity, Magnetism, and Galvanism, we discover cogent -reasons for transferring them to another part of our -arrangement; we find it advisable to associate them with -Chemistry, and to discuss their principles when we can -connect them with the principles of chemical science. For -though the first steps and narrower generalizations of these -sciences depend upon mechanical ideas, the highest laws and -widest generalizations which we can reach respecting them, -involve chemical relations. The progress of these portions -of knowledge is in some respects opposite to the progress of -Physical Astronomy. In this, we begin with phenomena which -appear to indicate peculiar and various qualities in the -bodies which we consider, (namely, the heavenly bodies,) and -we find in the end that all these qualities resolve -themselves into one common mechanical property, which exists -alike in all bodies and parts of bodies. On the contrary, in -studying magnetical and electrical laws, we appear at first -to have a single extensive phenomenon, attraction and -repulsion: but in our attempts to generalize this -phenomenon, we find that it is governed by conditions -depending upon something quite separate from the bodies -themselves, upon {289} the presence and distribution of -peculiar and transitory agencies; and, so far as we can -discover, the general laws of these agencies are of a -_chemical_ nature, and are brought into action by peculiar -properties of special substances. In cosmical phenomena, -everything, in proportion as it is referred to mechanical -principles, tends to simplicity,--to permanent uniform -forces,--to one common, positive, property. In magnetical -and electrical appearances, on the contrary, the application -of mechanical principles leads only to a new complexity, -which requires a new explanation; and this explanation -involves changeable and various forces,--gradations and -oppositions of qualities. The doctrine of the universal -gravitation of matter is a simple and ultimate truth, in -which the mind can acquiesce and repose. We rank gravity -among the mechanical attributes of matter, and we see no -necessity to derive it from any ulterior properties. Gravity -belongs to matter, independent of any conditions. But the -_conditions_ of magnetic or electrical activity require -investigation as much as the _laws_ of their action. Of -these conditions no mere mechanical explanation can be -given; we are compelled to take along with us chemical -properties and relations also: and thus magnetism, -electricity, galvanism, are _mechanico-chemical sciences_. - -11. Before considering these, therefore, I shall treat of -what I shall call _Secondary Mechanical Sciences_; by which -expression I mean the sciences depending upon certain -qualities which our senses discover to us in -bodies;--_Optics_, which has visible phenomena for its -subject; _Acoustics_, the science of hearing; the doctrine -of _Heat_, a quality which our touch recognizes: to this -last science I shall take the liberty of sometimes giving -the name _Thermotics_, analogous to the names of the other -two. If our knowledge of the phenomena of Smell and Taste -had been successfully cultivated and systematized, the -present part of our work would be the place for the -philosophical discussion of those sensations as the subjects -of science. - -The branches of knowledge thus grouped in one class involve -common Fundamental Ideas, from which {290} their principles -are derived in a mode analogous, at least in a certain -degree, to the mode in which the principles of the -mechanical sciences are derived from the fundamental ideas -of causation and reaction. We proceed now to consider these -Fundamental Ideas, their nature, development, and -consequences. - - - - -{{291}} -BOOK IV. - - -THE -PHILOSOPHY -OF THE -SECONDARY -MECHANICAL SCIENCES. - - - - -Πάσχοντος γάρ τι τοῦ αἰσθητικοῦ γίνεται τὸ ὁρᾶν· ὑπ' αὐτοῦ -μὲν οὖν τοῦ ὁρωμένου χρώματος ἀδύνατον· λείπεται δὴ ὑπὸ _τοῦ -μεταξύ_, ὥστ' ἀναγκαῖόν τι εἶναι _μεταξύ_· κενοῦ δὲ -γενομένου οὐχ ὅτι ἀκριβῶς, ἀλλ' ὅλως οὐθὲν ὀφθήσεται. δι' ἣν -μὲν οὖν αἰτίαν τὸ χρῶμα ἀναγκαῖον ἐν φωτὶ ὁρᾶσθαι, εἴρηται. -πῦρ δὲ ἐν ἀμφοῖν ὁρᾶται, καὶ ἐν σκότει καὶ ἐν φωτί, καὶ -τοῦτο _ἐξ ἀνάγκης_· τὸ γὰρ διαφανὲς ὑπὸ τούτου γίνεται -διαφανές. ὁ δ' αὐτὸς λόγος καὶ περὶ ψόφου καὶ ὀσμῆς ἐστιν· -οὐθὲν γὰρ αὐτῶν ἁπτόμενον τοῦ αἰσθητηρίου ποιεῖ τὴν -αἴσθησιν, ἀλλ' ὑπὸ μὲν ὀσμῆς καὶ ψόφου _τὸ μεταξὺ_ κινεῖται, -ὑπὸ δὲ τούτου τῶν αἰσθητηρίων ἑκάτερον· ὅταν δ' ἐπ' αὐτό τις -ἐπιθῇ τὸ αἰσθητήριον τὸ ψοφοῦν ἢ τὸ ὄζον, οὐδεμίαν αἴσθησιν -ποιήσει. - -ARISTOT. _De Anima_, II. 7. - - - -{{293}} BOOK IV. - - -THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES. - - -CHAPTER I. - -OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED. - - -1. _Of Primary and Secondary Qualities._--IN the same way in -which the mechanical sciences depend upon the Idea of Cause, -and have their principles regulated by the development of -that Idea, it will be found that the sciences which have for -their subject Sound, Light, and Heat, depend for _their_ -principles upon the Fundamental Idea of Media by means of -which we perceive those qualities. Like the idea of cause, -this idea of a medium is unavoidably employed, more or less -distinctly, in the common, unscientific operations of the -understanding; and is recognized as an express principle in -the earliest speculative essays of man. But here also, as in -the case of the mechanical sciences, the development of the -idea, and the establishment of the scientific truths which -depend upon it, was the business of a succeeding period, and -was only executed by means of long and laborious researches, -conducted with a constant reference to experiment and -observation. - -Among the most prominent manifestations of the influence of -the idea of a medium of which we have now to speak, is the -distinction of the qualities of bodies into _primary_, and -_secondary_ qualities. This distinction has {294} been -constantly spoken of in modern times: yet it has often been -a subject of discussion among metaphysicians whether there -be really such a distinction, and what the true difference -is. Locke states it thus[1\4]: Original or Primary qualities -of bodies are 'such as are utterly inseparable from the body -in what estate soever it may be,--such as sense constantly -finds in every particle of matter which has bulk enough to -be perceived, and the mind finds inseparable from every -particle of matter, though less than to make itself singly -perceived by our senses:' and he enumerates them as -solidity, extension, figure, motion or rest, and number. -Secondary qualities, on the other hand, are such 'which in -truth are nothing in the objects themselves, but powers to -produce various sensations in us by their primary qualities, -_i.e._ by the bulk, figure, texture, and motion of their -insensible parts, as colours, sounds, tastes, &c.' - -[Note 1\4: _Essay_, b. ii. ch. viii. s. 9, 10.] - -Dr. Reid[2\4], reconsidering this subject, puts the -difference in another way. There is, he says, a real -foundation for the distinction of Primary and Secondary -qualities, and it is this: 'That our senses give us a direct -and distinct notion of the primary qualities, and inform us -what they are in themselves; but of the secondary qualities, -our senses give us only a relative and obscure notion. They -inform us only that they are qualities that affect us in a -certain manner, that is, produce in us a certain sensation; -but as to what they are in themselves, our senses leave us -in the dark.' - -[Note 2\4: _Essays_, b. ii. c. xvii.] - -Dr. Brown[3\4] states the distinction somewhat otherwise. We -give the name of Matter, he observes, to that which has -extension and resistance: these, therefore, are Primary -qualities of matter, because they compose our definition of -it. All other qualities are Secondary, since they are -ascribed to bodies only because we find them associated with -the primary qualities which form our notion of those bodies. - -[Note 3\4: _Lectures_, ii. 12.] - -{295} It is not necessary to criticize very strictly these -various distinctions. If it were, it would be easy to find -objections to them. Thus Locke, it may be observed, does not -point out any _reason_ for believing that his secondary -qualities are produced by the primary. How are we to learn -that the colour of a rose arises from the bulk, figure, -texture, and motion of its particles? Certainly our senses -do not teach us this; and in what other way, on Locke's -principles, can we learn it? Reid's statement is not more -free from the same objection. How does it appear that our -notion of Warmth is relative to our own sensations more than -our notion of Solidity? And if we take Brown's account, we -may still ask whether our selection of certain qualities to -form our idea and definition of Matter be arbitrary and -without reason? If it be, how can it make a real -distinction? if it be not, what is the reason? - -I do not press these objections, because I believe that any -of the above accounts of the distinction of Primary and -Secondary qualities is right in the main, however imperfect -it may be. The difference between such qualities as -Extension and Solidity on the one hand, and Colour or -Fragrance on the other, is assented to by all, with a -conviction so firm and indestructible, that there must be -some fundamental principle at the bottom of the belief, -however difficult it may be to clothe the principle in -words. 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 quoted, even if none of them are -satisfactory, shows how strong and how deeply-seated is the -perception of truth which impels us to such attempts. - -The most obvious mode of stating the difference of Primary -and Secondary qualities, as it naturally offers itself to -speculative minds, appears to be that employed by Locke, -slightly modified. Certain of the qualities of bodies, as -their bulk, figure, and motion, are perceived immediately in -the bodies themselves. Certain other qualities as sound, -colour, heat, are {296} perceived by means of some medium. -Our conviction that this is the case is spontaneous and -irresistible; and this difference of qualities immediately -and mediately perceived is the distinction of Primary and -Secondary qualities. We proceed further to examine this -conviction. - -2. _The Idea of Externality._--In reasoning concerning the -Secondary Qualities of bodies, we are led to assume the -bodies to be external to us, and to be perceived by means of -some Medium intermediate between us and them. These -assumptions are fundamental conditions of perception, -inseparable from perception even in thought. - -That objects are _external_ to us, that they are _without_ -us, that they have _outness_, is as clear as it is that -these words have any meaning at all. This conviction is, -indeed, involved in the exercise of that faculty by which we -perceive all things as existing in space; for by this -faculty we place ourselves and other objects in one common -space, and thus they are exterior to us. It may be remarked -that this apprehension of objects as external to us, -although it assumes the idea of space, is far from being -implied in the idea of space. The objects which we -contemplate are considered as existing in space, and by that -means become invested with certain mutual relations of -position; but when we consider them as existing without -_us_, we make the additional step of supposing _ourselves_ -and the objects to exist in one common space. The question -respecting the Ideal Theory of Berkeley has been mixed up -with the recognition of this condition of the externality of -objects. That philosopher maintained, as is well known, that -the perceptible qualities of bodies have no existence except -in a perceiving mind. This system has often been understood -as if he had imagined the world to be a kind of optical -illusion, like the images which we see when we shut our -eyes, appearing to be without us, though they are only in -our organs; and thus this Ideal System has been opposed to a -belief in an external world. In truth, however, no such -opposition exists. The Ideal System is an attempt to explain -the {297} mental process of perception, and to get over the -difficulty of mind being affected by matter. But the author -of that system did not deny that objects were perceived -under the conditions of space and mechanical -causation;--that they were _external_ and _material_ so far -as those words describe perceptible qualities. Berkeley's -system, however visionary or erroneous, did not prevent his -entertaining views as just, concerning optics or acoustics, -as if he had held any other doctrine of the nature of -perception. - -But when Berkeley's theory was understood as a denial of the -existence of objects without us, how was it answered? If we -examine the answers which are given by Reid and other -philosophers to this hypothesis, it will be found that they -amount to this: that objects _are_ without us, since we -_perceive_ that they are so; that we perceive them to be -external, by the same act by which we perceive them to be -objects. And thus, in this stage of philosophical inquiry, -the externality of objects is recognized as one of the -inevitable conditions of our perception of them; and hence -the Idea of Externality is adopted as one of the necessary -foundations of all reasoning concerning all objects -whatever. - -3. _Sensation by a Medium._--Objects, as we have just seen, -are necessarily apprehended as _without_ us; and in general, -as removed from us by a great or small distance. Yet they -affect our bodily senses; and this leads us irresistibly to -the conviction that they are perceived by means of something -intermediate. Vision, or hearing, or smell, or the warmth of -a fire, must be communicated to us by some Medium of -Sensation. This unavoidable belief appears in all attempts, -the earliest and the latest alike, to speculate upon such -subjects. Thus, for instance, Aristotle says[4\4], 'Seeing -takes place in virtue of some action which the sentient -organ suffers: now it cannot suffer action from the colour -of the object directly: the only remaining possible case -then is, that it is acted upon by an {298} intervening -Medium; there must then be an intervening Medium.' 'And the -same may be said,' he adds, 'concerning sounding and odorous -bodies; for these do not produce sensation by touching the -sentient organ, but the intervening Medium is acted on by -the sound or the smell, and the proper organ, by the Medium -... In sound the Medium is air; in smell we have no name for -it.' In the sense of taste, the necessity of a Medium is not -at first so obviously seen, because the object tasted is -brought into contact with the organ; but a little attention -convinces us that the taste of a solid body can only be -perceived when it is conveyed in some liquid vehicle. Till -the fruit is crushed, and till its juices are pressed out, -we do not distinguish its flavour. In the case of heat, it -is still more clear that we are compelled to suppose some -invisible fluid, or other means of communication, between -the distant body which warms us and ourselves. - -[Note 4\4: Περὶ Ψυχῆς. ii. 7. See the motto to this Book.] - -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 reasonings,--that every change must have a -cause, and that bodies can act upon each other only by -contact. It cannot be denied that this principle does offer -itself very naturally as the ground of our belief in media -of sensation; and it appears to be referred to for this -purpose by Aristotle in the passage quoted above. But yet we -cannot but ask, Does the principle, that matter produces its -effect by contact only, manifestly apply here? When we so -apply it, we include _sensation_ among the _effects_ which -material contact produces;--a case so different from any -merely mechanical effect, that the principle, so employed, -appears to acquire a new signification. May we not, then, -rather say that we have here a new axiom,--That sensation -implies a material cause immediately acting on the -organ,--than a new application of our former -proposition,--That all mechanical change implies contact? - -The solution of this doubt is not of any material -consequence to our reasonings; for whatever be the {299} -ground of the assumption, it is certain that we do assume -the existence of media by which the sensations of sight, -hearing, and the like, are produced; and it will be seen -shortly that principles inseparably connected with this -assumption are the basis of the sciences now before us. - -This assumption makes its appearance in the physical -doctrines of all the schools of philosophy. It is exhibited -perhaps most prominently in the tenets of the Epicureans, -who were materialists, and extended to all kinds of -causation the axiom of the existence of a corporeal -mechanism by which alone the effect is produced. Thus, -according to them, vision is produced by certain images or -material films which flow from the object, strike upon the -eyes, and so become sensible. This opinion is urged with -great detail and earnestness by Lucretius, the poetical -expositor of the Epicurean creed among the Romans. His -fundamental conviction of the necessity of a material medium -is obviously the basis of his reasoning, though he attempts -to show the existence of such a medium by facts. Thus he -argues[5\4], that by shouting loud we make the throat sore; -which shows, he says, that the voice must be material, so -that it can hurt the passage in coming out. - Haud igitur dubium est quin voces verbaque constent - Corporeis e principiis ut lædere possint. - -[Note 5\4: _De Rerum Naturâ_, Lib. iv. 529.] - -4. _The Process of Perception of Secondary Qualities._--The -likenesses or representatives of objects by which they -affect our senses were called by some writers _species_, or -_sensible species_, a term which continued in use till the -revival of science. It may be observed that the conception -of these _species_ as films cast off from the object, and -retaining its shape, was different, as we have seen, from -the view which Aristotle took, though it has sometimes been -called the Peripatetic doctrine[6\4]. We may add that the -expression was latterly applied to express the supposition -of an emanation of any kind, and implied little {300} more -than that supposition of a Medium of which we are now -speaking. Thus Bacon, after reviewing the phenomena of -sound, says[7\4], 'Videntur motus soni fieri per _species -spirituales_: ita enim loquendum donec certius quippiam -inveniatur.' - -[Note 6\4: Brown, vol. ii. p. 98.] - -[Note 7\4: _Hist. Son. et Aud._ vol. ix. p. 87.] - -Though the fundamental principles of several sciences depend -upon the assumption of a Medium of Perception, these -principles do not at all depend upon any special view of the -Process of our perceptions. The mechanism of that process is -a curious subject of consideration; but it belongs to -physiology, more properly than either to metaphysics, or to -those branches of physics of which we are now speaking. The -general nature of the process is the same for all the -senses. The object affects the appropriate intermedium; the -medium, through the proper organ, the eye, the ear, the -nose, affects the nerves of the particular sense; and, by -these, in some way, the sensation is conveyed to the mind, -But to treat the _impression_ upon the nerves as the _act_ -of sensation which we have to consider, would be to mistake -our object, which is not the constitution of the human body, -but of the human mind. It would be to mistake one link of -the chain for the power which holds the end of the chain. No -anatomical analysis of the corporeal conditions of vision, -or hearing, or feeling warm, is necessary to the sciences of -Optics, or Acoustics, or Thermotics. - -Not only is this physiological research an extraneous part -of our subject, but a partial pursuit of such a research may -mislead the inquirer. We perceive objects _by means of_ -certain media, and _by means of_ certain impressions on the -nerves: but we cannot with propriety say that we perceive -either the media or the impressions on the nerves. What -person in the act of seeing is conscious of the little -coloured spaces on the retina? or of the motions of the -bones of the auditory apparatus whilst he is hearing? -Surely, no one. This may appear obvious enough, and yet a -writer of no common acuteness, Dr. Brown, has put forth -several {301} very strange opinions, all resting upon the -doctrine that the coloured spaces on the retina are the -_objects_ which we perceive; and there are some supposed -difficulties and paradoxes on the same subject which have -become quite celebrated (as upright vision with inverted -images), arising from the same confusion of thought. - -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 bodies, I shall -here devote a few pages to that subject. - - - -{{302}} -CHAPTER II. - -ON PECULIARITIES IN THE PERCEPTIONS OF THE DIFFERENT SENSES. - - -1. WE cannot doubt that we perceive all secondary qualities -by means of immediate impressions made, through the proper -medium of sensation, upon our organs. Hence all the senses -are sometimes vaguely spoken of as modifications of the -sense of feeling. It will, however, be seen, on reflection, -that this mode of speaking identifies in words things which -in our conceptions have nothing in common. No impression on -the organs of touch can be conceived as having any -resemblance to colour or smell. No effort, no ingenuity, can -enable us to describe the impressions of one sense in terms -borrowed from another. - -The senses have, however, each its peculiar powers, and -these powers may be in some respects compared, so as to show -their leading resemblances and differences, and the -characteristic privileges and laws of each. This is what we -shall do as briefly as possible. - - -SECT. I.--_Prerogatives of Sight._ - -THE sight distinguishes colours, as the hearing -distinguishes tones; the sight estimates degrees of -brightness, the ear, degrees of loudness; but with several -resemblances, there are most remarkable differences between -these two senses. - -2. _Position._--The sight has this peculiar prerogative, -that it apprehends the _place_ of its objects directly and -primarily. We see _where_ an object is at the same instant -that we see what it is. If we see two objects, we see their -relative position. We cannot help {303} perceiving that one -is above or below, to the right or to the left of the other, -if we perceive them at all. - -There is nothing corresponding to this in sound. When we -hear a noise, we do not necessarily assign a place to it. It -may easily happen that we cannot tell from which side a -thunder-clap comes. And though we often can judge in what -direction a voice is heard, this is a matter of secondary -impression, and of inference from concomitant circumstances, -not a primary fact of sensation. 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 ears, and on the bones of the head in -general; they are not inseparable conditions of hearing. We -may hear sounds, and be uncertain whether they are 'above, -around, or underneath!' but the moment anything visible -appears, however unexpected, we can say, 'see _where_ it -comes!' - -Since we can see the relative position of things, we can see -_figure_, which is but the relative position of the -different parts of the boundary of the object. And thus the -whole visible world exhibits to us a scene of various -shapes, coloured and shaded according to their form and -position, but each having relations of position to all the -rest; and altogether, entirely filling up the whole range -which the eye can command. - -3. _Distance._--The distance of objects from us is no matter -of immediate perception, but is a judgment and inference -formed from our sensations, in something of the same way as -our judgment of position by the ear, though more precise. -That this is so, was most distinctly shown by Berkeley, in -his _New Theory of Vision_. The elements on which we form -our judgment are, the effort by which we fix both eyes on -the same object, the effort by which we adjust each eye to -distinct vision, and the known forms, colours, and parts of -objects, as compared with their appearance. The right -interpretation of the information which these circumstances -give us respecting the true distances and forms of things, -is gradually learnt by experience, the lesson being begun in -our earliest infancy, and inculcated upon us every hour -during which we {304} use our eyes. The completeness with -which the lesson is learnt is truly admirable; for we forget -that our conclusion is obtained indirectly, and mistake a -judgment on evidence for an intuitive perception. This, -however, is not more surprizing than the rapidity and -unconsciousness of effort with which we understand the -meaning of the speech that we hear, or the book that we -read. In both cases, the habit of interpretation is become -as familiar as the act of perception. And this is the case -with regard to vision. We see the breadth of the street as -clearly and readily as we see the house on the other side of -it. We see the house to be square, however obliquely it be -presented to us. Indeed the difficulty is, to recover the -consciousness of our real and original sensations;--to -discover what is the _apparent_ relation of the lines which -appear before us. As we have already said, (book ii. chap. -6) in the common process of vision we suppose ourselves to -see that which cannot be seen; and when we would make a -picture of an object, the difficulty is to represent what is -visible and no more. - -But perfect as is our habit of interpreting what we -perceive, we could not interpret if we did not perceive. If -the eye did not apprehend visible position, it could not -infer actual position, which is collected from visible -position as a consequence: if we did not see apparent -figure, we could not arrive at any opinion concerning real -form. The perception of place, which is the prerogative of -the eye, is the basis of all its other superiority. - -The precision with which the eye can judge of apparent -position is remarkable. If we had before us two stars -distant from each other by one-twentieth of the moon's -diameter, we could easily decide the apparent direction of -the one from the other, as above or below, to the right or -left. Yet eight millions of stars might be placed in the -visible hemisphere of the sky at such distances from each -other; and thus the eye would recognize the relative -position in a portion of its range not greater than one -eight-millionth of the whole. Such is the accuracy of the -sense of vision in this {305} respect; and, indeed, we might -with truth have stated it much higher. Our judgment of the -position of distant objects in a landscape depends upon -features far more minute than the magnitude we have here -described. - -As our object is to point out principally the differences of -the senses, we do not dwell upon the delicacy with which we -distinguish tints and shades, but proceed to another sense. - - -SECT. II.--_Prerogatives of Hearing._ - -THE sense of hearing has two remarkable prerogatives; it can -perceive a definite and peculiar relation between certain -tones, and it can clearly perceive two tones together; in -both these circumstances it is distinguished from vision, -and from the other senses. - -4. _Musical intervals._--We perceive that two tones have, or -have not, certain definite relations to each other, which we -call _Concords_: one sound is a _Fifth_, an _Octave_, &c., -above the other. And when this is the case, our perception -of the relation is extremely precise. It is easy to perceive -when a fifth is out of tune by one-twentieth of a tone; that -is, by one-seventieth of itself. To this there is nothing -analogous in vision. Colours have certain vague relations to -one another; they look well together, by contrast or by -resemblance; but this is an indefinite, and in most cases a -casual and variable feeling. The relation of _complementary_ -colours to one another, as of red to green, is somewhat more -definite; but still, has nothing of the exactness and -peculiarity which belongs to a musical concord. In the case -of the two sounds, there is an exact point at which the -relation obtains; when by altering one note we pass this -point, the concord does not gradually fade away, but -instantly becomes a discord; and if we go further still, we -obtain another concord of quite a different character. - -We learn from the theory of sound that concords occur when -the times of vibration of the notes have exact simple -ratios; an octave has these times as 1 to {306} 2; a fifth, -as 2 to 3. According to the undulatory theory of light, such -ratios occur in colours, yet the eye is not affected by them -in any peculiar way. The times of the undulations of certain -red and certain violet rays are as 2 to 3, but we do not -perceive any peculiar harmony or connexion between those -colours. - -5. _Chords._--Again, the ear has this prerogative, that it -can apprehend two notes together, yet distinct. If two -notes, distant by a fifth from each other, are sounded on -two wind instruments, both they and their musical relation -are clearly perceived. There is not a mixture, but a -concord, a musical interval. In colours, the case is -otherwise. If blue and yellow fall on the same spot, they -form green; the colour is simple to the eye; it can no more -be decomposed by the vision than if it were the simple green -of the prismatic spectrum: it is impossible for us, by -sight, to tell whether it is so or not. - -These are very remarkable differences of the two senses: two -colours can be compounded into an apparently simple one; two -sounds cannot: colours pass into each other by gradations -and intermediate tints; sounds pass from one concord to -another by no gradations: the most intolerable discord is -that which is near a concord. We shall hereafter see how -these differences affect the _scales_ of sound and of -colour. - -6. _Rhythm._--We might remark, that as we see objects in -_space_, we hear sounds in _time_; and that we thus -introduce an arrangement among sounds which has several -analogies with the arrangement of objects in space. But the -conception of time does not seem to be peculiarly connected -with the sense of hearing; a faculty of apprehending tone -and time, or in musical phraseology _tune_ and _rhythm_, are -certainly very distinct. I shall not, therefore, here dwell -upon such analogies. - -The other Senses have not any peculiar prerogatives, at -least none which bear on the formation of science. I may, -however, notice, in the feeling of heat, this circumstance; -that it presents us with two opposites, heat and cold, which -graduate into each other. This {307} is not quite peculiar, -for vision also exhibits to us white and black, which are -clearly opposites, and which pass into each other by the -shades of gray. - - -SECT. III.--_The Paradoxes of Vision._ - -7. _First Paradox of Vision. Upright Vision._--All our -senses appear to have this in common; That they act by means -of organs, in which a bundle of nerves receives the -impression of the appropriate medium of the sense. In the -construction of these organs there are great differences and -peculiarities, corresponding, in part at least, to the -differences in the information given. Moreover, in some -cases, as we have noted in the case of audible position and -visible distance, that which seems to be a perception is -really a judgment founded on perceptions of which we are not -directly aware. It will be seen, therefore, that with -respect to the peculiar powers of each sense, it may be -asked;--whether they can be explained by the construction of -the peculiar organ;--whether they are acquired judgments and -not direct perceptions;--or whether they are inexplicable in -either of these ways, and cannot, at present at least, be -resolved into anything but conditions of the intellectual -act of perception. - -Two of these questions with regard to vision, have been much -discussed by psychological writers: the cause of our seeing -objects upright by inverted images on the retina; and of our -seeing single with two such images. - -Physiologists have very completely explained the exquisitely -beautiful mechanism of the eye, considered as analogous to -an optical instrument; and it is indisputable that by means -of certain transparent lenses and humours, an inverted image -of the objects which are looked at is formed upon the -_retina_, or fine net-work of nerve, with which the back of -the eye is lined. We cannot doubt that the impression thus -produced on these nerves is essential to the act of vision; -and so far as we consider the nerves {308} themselves to -feel or perceive by contact, we may say that they perceive -this image, or the affections of light which it indicates. -But we cannot with any propriety say that _we_ perceive, or -that our mind perceives, this image; for we are not -conscious of it, and none but anatomists are aware of its -existence: we perceive _by means_ of it. - -A difficulty has been raised, and dwelt upon in a most -unaccountable manner, arising from the neglect of this -obvious distinction. It has been asked, how is it that we -see an object, a man for instance, upright, when the -immediate object of our sensation, the image of the man on -our retina, is inverted? To this we must answer, that we see -him upright _because_ the image is inverted; that the -inverted image is the necessary means of seeing an upright -object. This is granted, and where then is the difficulty? -Perhaps it may be put thus: How is it that we do not judge -the man to be inverted, since the sensible image is so? To -this we may reply, that we have no notion of _upright_ or -inverted, except that which is founded on experience, and -that all our experience, without exception, must have taught -us that such a sensible image belongs to a man who is in an -upright position. Indeed, the contrary judgment is not -conceivable; a man is upright whose head is upwards and his -feet downwards. But what are the sensible images of -_upwards_ and _downwards_? Whatever be our standard of up -and down, the sensible representation of _up_ will be an -image moving on the retina towards the lower side, and the -sensible representation of _down_ will be a motion towards -the upper side. The head of the man's image is towards the -image of the sky, its feet are towards the image of the -ground; how then should it appear otherwise than upright? Do -we expect that the whole world should appear inverted? Be it -so: but if the whole be inverted, how is the relation of the -parts altered? Do we expect that we should think our own -persons in particular? This cannot be, for we look at them -as we do at other objects. Do we expect that things should -appear to fall {309} upwards? Surely not. For what do we -know of upwards, except that it is the direction in which -bodies do _not_ fall? In short, the whole of this -difficulty, though it has in no small degree embarrassed -metaphysicians, appears to result from a very palpable -confusion of ideas; from an attempt at comparison of what -_we_ see, with that which the retina feels, as if they were -separately presentable. It is a sufficient explanation to -say, that we do not see the image on the retina, but see by -_means_ of it. The perplexity does not require much more -skill to disentangle, than it does to see that a word -written in _black_ ink, may signify _white_[8\4]. - -[Note 8\4: The explanation of our seeing objects erect when -the image is inverted has been put very simply, by saying, -'We _call_ that the _lower_ end of an object which is next -the ground.' The observer cannot look into his own eye; he -knows _by experience_ what kind of image corresponds to a -man in an upright position. The anatomist tells him that -this image is _inverted_: but this does not disturb the -process of judging by experience. It does not appear why any -one should be perplexed at the notion of seeing objects -erect by means of inverted images, rather than at the notion -of seeing objects large by means of small images; or cubical -and pyramidal, by means of images on a spherical surface; or -green and red, by means of images on a black surface. Indeed -some persons have contrived to perplex themselves with these -latter questions, as well as the first. - -The above explanation is not at all affected, as to its -substance, if we adopt Sir David Brewster's expression, and -say that the _line of visible direction_ is a line passing -through the center of the spherical surface of the retina, -and therefore of course perpendicular to the surface. In -speaking of 'the inverted image,' it has always been -supposed to be determined by such lines; and though the -point where they intersect may not have been ascertained -with exactness by previous physiologists, the philosophical -view of the matter was not in any degree vitiated by this -imperfection.] - -8. _Second Paradox of Vision. Single Vision._--(1.) _Small -or Distant Objects._--The other difficulty, why with two -images on the retina we see only one object, is of a much -more real and important kind. This effect is manifestly -limited by certain circumstances of a very precise nature; -for if we direct our eyes at an object which is very near -the eye, we see {310} all other objects double. The fact is -not, therefore, that we are incapable of receiving two -impressions from the two images, but that, under certain -conditions, the two impressions form one. A little attention -shows us that these conditions are, that with both eyes we -should look at the same object; and again, we find that to -look at an object with either eye, is to direct the eye so -that the image falls on or near a particular point about the -middle of the retina. Thus these middle points in the two -retinas correspond, and we see an image single when the two -images fall on the corresponding points. - -Again, as each eye judges of position, and as the two eyes -judge similarly, an object will be seen in the same place by -one eye and by the other, when the two images which it -produces are _similarly situated_ with regard to the -_corresponding points_ of the retina[9\4]. - -[Note 9\4: The explanation of single vision with two eyes -may be put in another form. Each eye judges immediately of -the relative position of all objects within the field of its -direct vision. Therefore when we look with both eyes at a -_distant_ prospect (so distant that the distance between the -eyes is small in comparison) the two prospects, being -similar collections of forms, will coincide altogether, if a -corresponding point in one and in the other coincide. If -this be the case, the two images of every object will fall -upon corresponding points of the retina, and will appear -single. - -If the two prospects seen by the two eyes do not exactly -coincide, in consequence of nearness of the objects, or -distortion of the eyes, but if they nearly coincide, the -stronger image of an object absorbs the weaker, and the -object is seen single; yet modified by the combination, as -will be seen when we speak of the single vision of near -objects. When the two images of an object are considerably -apart, we see it double. - -This explanation is not different in substance from the one -given in the text; but perhaps it is better to avoid the -assertion that the law of corresponding points is 'a -distinct and original principle of our constitution,' as I -had stated in the first edition. The simpler mode of stating -the law of our constitution appears to be to say, that each -eye determines similarly the position of objects; and that -when the positions of an object, as seen by the two eyes, -coincide (or nearly coincide) the object is seen single.] - -This is the Law of Single Vision, at least so far as regards -small objects; namely, objects so small that in -contemplating them we consider their position only, {311} -and not their solid dimensions. Single vision in such cases -is a result of the law of vision simply: and it is a mistake -to call in, as some have done, the influence of habit and of -acquired judgments, in order to determine the result in such -cases. - -To ascribe the apparent singleness of objects to the -impressions of vision corrected by the experience of -touch[10\4], would be to assert that a person who had not -been in the habit of handling what he saw, would see all -objects double; and also, to assert that a person beginning -with the double world which vision thus offers to him, -would, by the continued habit of handling objects, gradually -and at last learn to see them single. But all the facts of -the case show such suppositions to be utterly fantastical. -No one can, in this case, go back from the habitual judgment -of the singleness of objects, to the original and direct -perception of their doubleness, as the draughtsman goes back -from judgments to perception, in representing solid -distances and forms by means of perspective pictures. No one -can point out any case in which the habit is imperfectly -formed; even children of the most tender age look at an -object with both eyes, and see it as one. - -[Note 10\4: See Brown, vol. ii. p. 81.] - -In cases when the eyes are distorted (in squinting), one eye -only is used, or if both are employed, there is double -vision; and thus any derangement of the correspondence of -motion in the two eyes will produce double-sightedness. - -Brown is one of those[11\4] who assert that two images -suggest a single object because we have _always found_ two -images to belong to a single object. He urges as an -illustration, that the _two_ words 'he conquered,' by custom -excite exactly the same notion as the _one_ Latin word -'vicit;' and thus that two visual images, by the effect of -habit, produce the same belief of a single object as one -tactual impression. But in order to make this pretended -illustration of any value, it ought to be true that when a -person has thoroughly learnt the Latin language, he can no -longer distinguish {312} any separate meaning in 'he' and in -'conquered.' We can by no effort perceive the double -sensation, when we look _at_ the object with the two eyes. -Those who squint, learn by habit to see objects single: but -the habit which they acquire is that of attending to the -impressions of one eye only at once, not of combining the -two impressions. It is obvious, that if each eye spreads -before us the same visible scene, with the same objects and -the same relations of place, then, if one object in each -scene coincide, the whole of the two visible impressions -will be coincident. And here the remarkable circumstance is, -that not only each eye judges for itself of the relations of -position which come within its field of view; but that there -is a superior and more comprehensive faculty which combines -and compares the two fields of view; which asserts or denies -their coincidence; which contemplates, as in a relative -position to one another, these two visible worlds, in which -all other relative position is given. This power of -confronting two sets of visible images and figured spaces -before a purely intellectual tribunal, is one of the most -remarkable circumstances in the sense of vision. - -[Note 11\4: _Lectures_, vol. ii. p. 81.] - -9. (2.) _Near Objects._--We have hitherto spoken of the -singleness of objects whose images occupy corresponding -positions on the retina of the two eyes. But here occurs a -difficulty. If an object of moderate size, a small thick -book for example, be held at a little distance from the -eyes, it produces an image on the retina of each eye; and -these two images are perspective representations of the book -from different points of view, (the positions of the two -eyes,) and are therefore of different forms. Hence the two -images cannot occupy corresponding points of the retina -throughout their whole extent. If the central parts of the -two images occupy corresponding points, the boundaries of -the two wall not correspond. How is it then consistent with -the law above stated that in this case the object appears -single? - -It may be observed, that the two images in such a case will -differ most widely when the object is not a {313} mere -surface, but a solid. If a book, for example, be held with -one of its upright edges towards the face, the right eye -will see one side more directly than the left eye, and the -left eye will see another side more directly, and the -outline of the two images upon the two retinas will exhibit -this difference. And it may be further observed, that this -difference in the images received by the two eyes, is a -plain and demonstrative evidence of the solidity of the -object seen; since nothing but a solid object could (without -some special contrivance) produce these different forms of -the images in the two eyes. - -Hence the absence of exact coincidence in the two images on -the retina is the necessary condition of the solidity of the -object seen, and must be one of the indications by means of -which our vision apprehends an object as solid. And that -this is so, Mr. Wheatstone has proved experimentally, by -means of some most ingenious and striking contrivances. He -has devised[12\4] an instrument (the _stereoscope_) by which -two images (drawn in outline) differing exactly as much as -the two images of a solid body seen near the face would -differ, are conveyed, one to one eye, and the other to the -other. And it is found that when this is effected, the -object which the images represent is not only seen single, -but is apprehended as solid with a clearness and reality of -conviction quite distinct from any impression which a mere -perspective representation can give. - -[Note 12\4: _Phil. Trans._ 1839.] - -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 space, and seen by the two eyes. If the images differ -more or otherwise than this condition allows, the result is, -that both are seen, their lines crossing and interfering -with one another. - -It may be observed, too, that if an object be of such large -size as not to be taken in by a single glance of the eyes, -it is no longer apprehended as single by a direct act of -perception; but its parts are looked at {314} separately and -successively, and the impressions thus obtained are put -together by a succeeding act of the mind. Hence the objects -which are directly seen as solid, will be of moderate size; -in which case it is not difficult to show that the outlines -of the two images will differ from each other only slightly. - -Hence we are led to the following, as the Law of Single -Vision for _near_ objects:--When the two images in the two -eyes are situated (part for part) nearly, but not exactly, -upon corresponding points, the object is apprehended as -single, if the two images are such as are or would be given -by a single solid object seen by the two eyes separately: -and in this case the object is necessarily apprehended as solid. - -This law of vision does not contradict that stated above for -distant objects: for when an object is removed to a -considerable distance, the images in the two eyes coincide -exactly, and the object is seen as single, though without -any direct apprehension of its solidity. The first law is a -special case of the second. Under the condition of _exactly_ -corresponding points, we have the perception of singleness, -but no evidence of solidity. Under the condition of _nearly_ -corresponding points, we may have the perception of -singleness, and with it, of solidity. - -We have before noted it as an important feature in our -visual perception, that while we have two distinct -impressions upon the sense, which we can contemplate -separately and alternately, (the impressions on the two -eyes,) we have a higher perceptive faculty which can -recognize these two impressions, exactly similar to each -other, as only two images of one and the same assemblage of -objects. But we now see that the faculty by which we -perceive visible objects can do much more than this:--it can -not only unite two impressions, and recognize them as -belonging to one object in virtue of their coincidence, but -it can also unite and identify them, even when they do not -exactly coincide. It can correct and adjust their small -difference, so that they are both apprehended as -representations of the same figure. It can infer from them a -real form, not {315} agreeing with either of them; and a -solid space, which they are quite incapable of exemplifying. -The visual faculty decides whether or not the two ocular -images can be pictures of the same solid object, and if they -can, it undoubtingly and necessarily accepts them as being -so. This faculty operates as if it had the power of calling -before it all possible solid figures, and of ascertaining by -trial whether any of those will, at the same time, fit both -the outlines which are given by the sense. It assumes the -reality of solid space, and, if it be possible, reconciles -the appearances with that reality. And thus an activity of -the mind of a very remarkable and peculiar kind is exercised -in the most common act of seeing. - -10. It may be said that this doctrine, of such a visual -faculty as has been described, is very vague and obscure, -since we are not told what are its limits. It adjusts and -corrects figures which _nearly_ coincide, so as to identify -them. But _how_ nearly, it may be asked, must the figures -approach each other, in order that this adjustment may be -possible? What discrepance renders impossible the -reconcilement of which we speak? Is it not impossible to -give a definite answer to these questions, and therefore -impossible to lay down definitely such laws of vision as we -have stated? To this I reply, that the indefiniteness thus -objected to us, is no new difficulty, but one with which -philosophers are familiar, and to which they are already -reconciled. It is, in fact, no other than the indefiniteness -of the limits of distinct vision. How near to the face must -an object be brought, so that we shall cease to see it -distinctly? The distance, it will be answered, is -indefinite: it is different for different persons; and for -the same person, it varies with the degree of effort, -attention, and habit. But this indefiniteness is only the -indefiniteness, in another form, of the deviation of the two -ocular images from one another: and in reply to the question -concerning them we must still say, as before, that in -doubtful cases, the power of apprehending an object as -single, when this _can_ be done, will vary with effort, -attention, and habit. The assumption {316} that the apparent -object exists as a real figure, in real space, is to be -verified, if possible; but, in extreme cases, from the -unfitness of the point of view, or from any other cause of -visual confusion or deception, the existence of a real -object corresponding to the appearance may be doubtful; as -in any other kind of perception it may be doubtful whether -our senses, under disadvantageous circumstances, give us -true information. The vagueness of the limits, then, within -which this visual faculty can be successfully exercised, is -no valid argument against the existence of the faculty, or -the truth of the law which we have stated concerning its -action. - - -SECT. IV.--_The Perception of Visible Figure._ - -11. _Visible Figure._--There is one tenet on the subject of -vision which appears to me so extravagant and -unphilosophical, that I should not have thought it necessary -to notice it, if it had not been recently promulgated by a -writer of great acuteness in a book which has obtained, for -a metaphysical work, considerable circulation. I speak of -Brown's opinion[13\4] that we have no immediate perception -of visible figure. I confess myself unable to comprehend -fully the doctrine which he would substitute in the place of -the one commonly received. He states it thus[14\4]: 'When -the simple affection of sight is blended with the ideas of -suggestion [those arising from touch, &c.] in what are -termed the acquired perceptions of vision, as, for example, -in the perception of a sphere, it is colour only which is -blended with the large convexity, and not a small coloured -plane.' The doctrine which Brown asserts in this and similar -passages, appears to be, that we do not by vision perceive -_both_ colour and _figure_; but that the colour which we see -is blended with the figure which we learn the existence of -by other means, as by touch. But if this were possible when -we can call in other perceptions, how is it possible when we -cannot or do not touch the object? {317} Why does the moon -appear round, gibbous, or horned? What sense besides vision -suggests to us the idea of her figure? And even in objects -which we can reach, what is that circumstance in the sense -of vision which suggests to us that the colour belongs to -the sphere, except that we see the colour where we see the -sphere? If we do not see figure, we do not see position; for -figure is the relative position of the parts of a boundary. -If we do not see position, why do we ascribe the yellow -colour to the sphere on our left, rather than to the cube on -our right? We _associate_ the colour with the object, says -Dr. Brown; but if his opinion were true, we could not -associate two colours with two objects, for we could not -apprehend the colours as occupying two different places. - -[Note 13\4: _Lectures_, vol. ii. p. 82.] - -[Note 14\4: _Ib._ vol. ii. p. 90.] - -The whole of Brown's reasoning on this subject is so -irreconcilable with the first facts of vision, that it is -difficult to conceive how it could proceed from a person who -has reasoned with great acuteness concerning touch. In order -to prove his assertion, he undertakes to examine the only -reasons which, he says[15\4], he can imagine for believing -the immediate perception of visible figure: (1) That it is -absolutely impossible, in our present sensations of sight, -to separate colour from extension; and (2) That there are, -in fact, figures on the retina corresponding to the apparent -figures of objects. - -[Note 15\4: _Lectures_, vol. ii. p. 83.] - -On the subject of the first reason, he says, that the figure -which we perceive as associated with colour, is the real, -and not the apparent figure. 'Is there,' he asks, 'the -slightest consciousness of a perception of visible figure, -corresponding to the affected portion of the retina?' To -which, though he seems to think an affirmative answer -impossible, we cannot hesitate to reply, that there is -undoubtedly such a consciousness; that though obscured by -being made the ground of habitual inference as to the real -figure, this consciousness is constantly referred to by the -draughtsman, and easily recalled by any one. We may separate -colour, he says {318} again[16\4], from the figures on the -retina, as we may separate it from length, breadth, and -thickness, which we do not see. But this is altogether -false: we cannot separate colour from length, breadth, and -thickness, _in any other way_, than by transferring it to -the visible figure which we do see. He cannot, he allows, -separate the colour from the visible form of the trunk of a -large oak; but just as little, he thinks, can he separate it -from the convex mass of the trunk, which (it is allowed on -all hands) he does not immediately see. But in this he is -mistaken: for if he were to make a _picture_ of the oak, he -would separate the colour from the convex shape, which he -does not imitate, but he could not separate it from the -visible figure, which he does imitate; and he would then -perceive that the fact that he _has not_ an immediate -perception of the convex form, is necessarily connected with -the fact that he _has_ an immediate perception of the -apparent figure; so far is the rejection of immediate -perception in the former case from being a reason for -rejecting it in the latter. - -[Note 16\4: _Lectures_, vol. ii. p. 84.] - -Again, with regard to the second argument. It does not, he -says, follow, that because a certain figured portion of the -retina is affected by light, we should see such a figure; -for if a certain figured portion of the olfactory organ were -affected by odours, we should not acquire by smell any -perception of such figure[17\4]. This is merely to say, that -because we do not perceive position and figure by one sense, -we cannot do so by another sense. But this again is -altogether erroneous. It is an office of our sight to inform -us of position, and consequently of figure; for this -purpose, the organ is so constructed that the position of -the object determines the position of the point of the -retina affected. There is nothing of this kind in the organ -of smell; objects in different positions and of different -forms do not affect different parts of the olfactory nerve, -or portions of different shape. Different objects, remote -from each other, if perceived by smell, affect the same -{319} part of the olfactory organs. This is all quite -intelligible; for it is not the office of smell to inform us -of position. Of what use or meaning would be the curious and -complex structure of the eye, if it gave us only such vague -and wandering notions of the colours and forms of the -flowers in a garden, as we receive from their odours when we -walk among them blindfold? It is, as we have said, the -_prerogative_ of vision to apprehend position: the places of -objects on the retina give this information. 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 figure; but we know that in vision it does; -and it is clear that if we did not acquire our acquaintance -with visible figure in this way, we could not acquire it in -any way[18\4]. - -[Note 17\4: _Ib._ p. 87.] - -[Note 18\4: When Brown says further (p. 87), that we can -indeed show the image in the dissected eye; but that 'it is -not in the dissected eye that vision takes place;' it is -difficult to see what his drift is. Does he doubt that there -is an image formed in the living as completely as in the -dissected eye?] - -The whole of this strange mistake of Brown's appears to -arise from the fault already noticed;--that of considering -the image on the retina as the _object_ instead of the -_means_ of vision. This indeed is what he says: 'the true -object of vision is not the distant body itself, but the -light that has reached the expansive termination of the -optic nerve[19\4].' Even if this were so, we do not see why -we should not perceive the position of the impression on -this expanded nerve. But as we have already said, the -impression on the nerve is the means of vision, and enables -us to assign a place, or at least a direction, to the object -from which the light proceeds, and thus makes vision -possible. Brown, indeed, pursues his own peculiar view till -he involves the subject in utter confusion. Thus he -says[20\4], 'According to the common theory [that figure can -be perceived by the eye,] a visible sphere is at once to my -perception convex and plane; and if the sphere be a one, it -is perceived at once to be a sphere of {320} many feet in -diameter, and a plane circular surface of the diameter of a -quarter of an inch.' It is easy to deduce these and greater -absurdities, if we proceed on his strange and baseless -supposition that the object and the image on the retina are -_both_ perceived. But who is conscious of the image on the -retina in any other way than as he sees the object by means -of it? - -[Note 19\4: _Lectures_, vol. ii. p. 57.] - -[Note 20\4: _Ib._ vol. ii. p. 89.] - -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 distance. He ought to have -recollected that such an undertaking, to be successful, -required him to show _what_ elements he analyzed it _into_. -Berkeley analyzed the perception of real figure into the -interpretation of visible figure according to certain rules -which he distinctly stated. Brown analyzes the perception of -visible figure into no elements. Berkeley says, that we do -not directly perceive distance, but that we perceive -something else, from which we infer distance, namely, -visible figure and colour, and our own efforts in seeing; -Brown says, that we do not see figure, but infer it; what -then do we see, which we infer it from? To this he offers no -answer. He asserts the seeming perception of visible figure -to be a result of 'association;'--of 'suggestion.' But what -meaning can we attach to this? Suggestion requires something -which suggests; and not a hint is given what it is which -suggests position. Association implies two things -associated; what is the sensation which we associate with -form? What is that visual perception which is not figure, -and which we mistake for figure? What perception is it that -suggests a square to the eye? What impressions are those -which have been associated with a visible triangle, so that -the revival of the impressions revives the notion of the -triangle? Brown has nowhere pointed out such perceptions and -impressions; nor indeed was it possible for him to do so; -for the only visual perceptions which he allows to remain, -those of colour, most assuredly do not suggest visible -figures by their differences; red is not associated with -square rather than with round, or with round rather than -square. On the contrary, the {321} eye, 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 -colour, has it for one of its prerogatives to give us this -information; and the perception of the relative position of -each part of the visible boundary of an object constitutes -the perception of its apparent figure; which faculty we -cannot deny to the eye without rejecting the plain and -constant evidence of our senses, making the mechanism of the -eye unmeaning, confounding the object with the means of -vision, and rendering the mental process of vision utterly -unintelligible. - -Having sufficiently discussed the processes of perception, I -now return to the consideration of the Ideas which these -processes assume. - - - -{{322}} -CHAPTER III. - -SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE -IDEA OF A MEDIUM. - - -1. IN what precedes, 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 perceiving. -Perception is affected by various peculiarities, according -to the nature of the quality perceived: but in all cases a -medium is equally essential to the process. - -This principle, which, as we have seen, is accepted as -evident by the common understanding of mankind, is confirmed -by all additional reflection and discipline of the mind, and -is the foundation of all the theories which have been -proposed concerning the processes by which the perception -takes place, and concerning the modifications of the -qualities thus perceived. The medium, and the mode in which -the impression is conveyed through the medium, seem to be -different for different qualities; but the existence of the -medium leads to certain necessary conditions or -alternatives, which have successively made their appearance -in science, in the course of the attempts of men to theorize -concerning the principal secondary qualities, sound, light, -and heat. We must now point out some of the ways, at first -imperfect and erroneous, in which the consequences of the -fundamental assumption were traced. - -2. _Sound._--In all cases the medium of sensation, whatever -it is, is supposed to produce the effect of conveying -secondary qualities to our perception by means of its -primary qualities. It was conceived to operate {323} by the -size, form, and motion of its parts. This is a fundamental -principle of the class of sciences of which we have at -present to speak. - -It was assumed from the first, as we have seen in the -passage lately quoted from Aristotle[21\4], that in the -conveyance of _sound_, the medium of communication was the -air. But although the first theorists were right so far, -that circumstance did not prevent their going entirely wrong -when they had further to determine the nature of the -process. It was conceived by Aristotle that the air acted -after the manner of a rigid body;--like a staff, which, -receiving an impulse at one end, transmits it to the other. -Now this is altogether an erroneous view of the manner in -which the air conveys the impulse by which sound is -perceived. An approach was made to the true view of this -process, 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 it. These little waves -begin from the point thus disturbed, and run outwards, -expanding on every side, in concentric circles, till they -are lost. The propagation of sound through the air from the -point where it is produced, was compared by Vitruvius to -this diffusion of circular waves in water; and thus the -notion of a propagation of impulse by the _waves_ of a fluid -was introduced, in the place of the former notion of the -impulse of an unyielding body. - -[Note 21\4: _Supr._ p. 297.] - -But though, taking an enlarged view of the nature of the -progress of a wave, this is a just representation of the -motion of air in conveying sound, we cannot suppose that the -process was, at the period of which we speak, rightly -understood. For the waves of water were contemplated only as -affecting the surface of the water; and as the air has no -surface, the communication must take place by means of an -internal motion, which can bear only a remote and obscure -resemblance to the waves which we see. And even with regard -to the waves of water, the mechanism by which they are {324} -produced and transferred was not at all understood; so that -the comparison employed by Vitruvius must be considered -rather as a loose analogy than as an exact scientific -explanation. - -No correct account of such motions was given, 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 fluid, and to -discern the forces which the process calls into play, so as -to continue the motion once begun. Newton introduced into -this subject the exact and rigorous conception of an -_Undulation_, which is the true key to the explanation of -impulses conveyed through a fluid. - -Even at the present day, 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 studies. -When we see a wave run along the surface of water, we are -apt to imagine at first that a portion of the fluid is -transferred bodily from one place to another. But with a -little consideration we may easily satisfy ourselves that -this is not so: for if we look at a field of standing corn, -when a breeze blows over it, we see waves like those of -water run along its surface. Yet it is clear that in this -case the separate stalks of corn only bend backwards and -forwards, and no portion of the grain is really conveyed -from one part of the field to the other. This is obvious -even to popular apprehension. The poet speaks of - . . . . The rye, - That stoops its head when whirlwinds rave - And springs again in eddying wave - As each wild gust sweeps by. -Each particle of the mass in succession has a small motion -backwards and forwards; and by this means a large ridge made -by many such particles runs along the mass to any distance. -This is the true conception of an undulation in general. - -Thus, when an Undulation is propagated in a fluid, it is not -_matter_, but _form_, which is transmitted from {325} one -place to another. The particles along the line of each wave -assume a certain arrangement, and this arrangement passes -from one part to another, the particles changing their -places only within narrow limits, so as to lend themselves -successively to the arrangements by which the successive -waves, and the intervals between the waves, are formed. - -When such an Undulation is propagated through air, the wave -is composed, not, as in water, of particles which are higher -than the rest, but of particles which are closer to each -other than the rest. The wave is not a ridge of elevation, -but a line of condensation; and as in water we have -alternately elevated and depressed lines, we have in air -lines alternately condensed and rarefied. And the motion of -the particles is not, as in water, up and down, in a -direction transverse to that of the wave which runs -forwards; in the motion of an undulation through air the -motion of each particle is alternately forwards and -backwards, while the motion of the undulation is constantly -forwards. - -This precise and detailed account of the Undulatory Motion -of air by which sound is transmitted was first given by -Newton. He further attempted to determine the motions of the -separate particles, and to point out the force by which each -particle affects the next, so as to continue the progress of -the undulation once begun. The motions of each particle must -be oscillatory; he assumed the oscillations to be governed -by the simplest law of oscillation which had come under the -notice of mathematicians, (that of small vibrations of a -pendulum;) 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 requires. - -Newton's proof of the exact law of Oscillatory Motion of the -aërial particles was not considered satisfactory by -succeeding mathematicians; for it was found that the same -result, the development of forces adequate to continue the -motion, would follow if any other law of the motion were -assumed. Cramer proved this by a sort of _parody_ on -Newton's proof, in which, by the {326} alteration of a few -phrases in this formula of demonstration, it was made to -establish an entirely different conclusion. - -But the general conception of an Undulation as presented by -Newton was, as from its manifest mechanical truth it could -not fail to be, accepted by all mathematicians; and in -proportion as the methods of calculating the motions of -fluids were further improved, the necessary consequences of -this conception, in the communication of sound through air, -were traced by unexceptionable reasoning. This was -especially done by Euler and Lagrange, whose memoirs on such -motions of fluids are some of the most admirable examples -which exist, of refined mathematical methods applied to the -solution of difficult mechanical problems. - -But the great step in the formation of the theory of sound -was undoubtedly that which we have noticed, the introduction -of the Conception of an Undulation such as we have attempted -to describe it:--a state, condition, or arrangement of the -particles of a fluid, which is transferred from one part of -space to another by means of small motions of the particles, -altogether distinct from the movement of the Undulation -itself. This is a conception which is not obvious to common -apprehension. It appears paradoxical at first sight to speak -of a large _wave_ (as the tide-wave) running up a river at -the rate of twenty miles an hour, while the _stream_ of the -river is all the while flowing downwards. Yet this is a very -common fact. 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 medium. - -We have described the motion of sound as produced by small -motions of the particle forwards and backwards, while the -waves, or condensed and rarefied lines, move constantly -forwards. It may be asked what right we have to suppose the -motion to be of this kind, since when sound is heard, no -such motions of the particles of air can be observed, even -by refined methods of observation. Thus Bacon declares -himself against the hypothesis of such a vibration, since, -as he remarks, it {327} cannot be perceived in any visible -impression upon the flame of a candle. And to this we reply, -that the supposition of this Vibration is made in virtue of -a principle which is involved in the original assumption of -a medium; namely, That _a Medium, in conveying Secondary -qualities, operates by means of its Primary qualities_, the -bulk, figure, motion, and other mechanical properties of its -parts. This is an Axiom belonging to the Idea of a Medium. -In virtue of this axiom it is demonstrable that the motion -of the air, when any how disturbed, must be such as is -supposed in our acoustical reasonings. For the elasticity of -the parts of the air, called into play by its expansion and -contraction, lead, by a mechanical necessity, to such a -motion as we have described. We may add that, by proper -contrivances, this motion may be made perceptible in its -visible effects. Thus the theory of sound, as an impression -conveyed through air, is established upon evident general -principles, although the mathematical calculations which are -requisite to investigate its consequences are, some of them, -of a very recondite kind. - -3. _Light._--The early attempts to explain Vision -represented it as performed by means of material rays -proceeding _from_ the eye, by the help of which the eye felt -out the form and other visible qualities of an object, as a -blind man might do with his staff. But this opinion could -not keep its ground long: for it did not even explain the -fact that light is necessary to vision. Light, as a peculiar -medium, was next assumed as the machinery of vision; but the -mode in which the impression was conveyed through the medium -was left undetermined, and no advance was made towards sound -theory, on that subject, by the ancients. - -In modern times, when the prevalent philosophy began to -assume a mechanical turn (as in the theories of Descartes), -light was conceived to be a material substance which is -emitted from luminous bodies, and which is also conveyed -from all bodies to the eye, so as to render them visible. -The various changes of direction by which the rays of light -are affected, (reflection, {328} refraction, &c.,) Descartes -explained, by considering the particles of light as small -globules, which change their direction when they impinge -upon other bodies, according to the laws of Mechanics. -Newton, with a much more profound knowledge of Mechanics -than Descartes possessed, adopted, in the most mature of his -speculations, nearly the same view of the nature of light; -and endeavoured to show that reflection, refraction, and -other properties of light, might be explained as the effects -which certain forces, emanating from the particles of -bodies, produce upon the luminiferous globules. - -But though some of the properties of light could thus be -accounted for by the assumption of particles emitted from -luminous bodies, and reflected or refracted by forces, other -properties came into view which would not admit of the same -explanation. The phenomena of _diffraction_ (the fringes -which accompany shadows) could never be truly represented by -such an hypothesis, in spite of many attempts which were -made. And the _colours of thin plates_, which show the rays -of light to be affected by an alternation of two different -conditions at small intervals along their length, led Newton -himself to incline, often and strongly, to some hypothesis -of undulation. The _double refraction_ of Iceland spar, a -phenomenon in itself very complex, could, it was found by -Huyghens, be expressed with great simplicity by a certain -hypothesis of undulations. - -Two hypotheses of the nature of the luminiferous medium were -thus brought under consideration; the one representing Light -as Matter emitted from the luminous object, the other, as -Undulations propagated through a fluid. These two hypotheses -remained in presence of each other during the whole of the -last century, neither of them gaining any material advantage -over the other, though the greater part of mathematicians, -following Newton, embraced the emission theory. But at the -beginning of the present century, an additional class of -phenomena, those of the _interference_ of two rays of light, -were brought under {329} consideration by Dr. Young; and -these phenomena were strongly in favour of the undulatory -theory, while they were irreconcilable with the hypothesis -of emission. If it had not been for the original bias of -Newton and his school to the other side, there can be little -doubt that from this period light as well as sound would -have been supposed to be propagated by undulations; although -in this case it was necessary to assume as the vehicle of -such undulations a special medium or _ether_. Several points -of the phenomena of vision no doubt remained unexplained by -the undulatory theory, as absorption, and the natural -colours of bodies; but such facts, though they did not -confirm, did not evidently contradict the theory of a -Luminiferous Ether; and the facts which such a theory did -explain, it explained with singular happiness and accuracy. - -But before this Undulatory Theory could be generally -accepted, it was presented in an entirely new point of view -by being combined with the facts of _polarization_. The -general idea of polarization must be illustrated hereafter; -but we may here remark that Young and Fresnel, who had -adopted the undulatory theory, after being embarrassed for -some time by the new facts which were thus presented to -their notice, at last saw that these facts might be -explained by conceiving the vibrations to be transverse to -the ray, the motions of the particles being not backwards -and forwards in the line in which the impulse travels, but -to the right and left of that line. This conception of -_transverse vibrations_, though quite unforeseen, had -nothing in it which was at all difficult to reconcile with -the general notion of an undulation. We have described an -undulation, or wave, as a certain condition or arrangement -of the particles of the fluid successively transferred from -one part of space to another: and it is easily conceivable -that this arrangement or wave may be produced by a lateral -transfer of the particles from their quiescent positions. -This conception of transverse vibrations being accepted, it -was found that the explanation of the phenomena of -polarization and of those of interference led to the same -theory {330} with a correspondence truly wonderful; and this -coincidence in the views, collected from two quite distinct -classes of phenomena, was justly considered as an almost -demonstrative evidence of the truth of this undulatory -theory. - -It remained to be considered whether the doctrine of -transverse vibrations in a fluid could be reconciled with -the principles of Mechanics. And it was found that by making -certain suppositions, in which no inherent improbability -existed, the hypothesis of transverse vibrations would -explain the laws, both of interference and of polarization -of light, in air and in crystals of all kinds, with a -surprizing fertility and fidelity. - -Thus the Undulatory Theory of Light, like the Undulatory -Theory of Sound, is recommended by its conformity to the -fundamental principle of the Secondary Mechanical Sciences, -that the medium must be supposed to transmit its peculiar -impulses according to the laws of Mechanics. Although no one -had previously dreamt of qualities being conveyed through a -medium by such a process, yet when it is once suggested as -the only mode of explaining some of the phenomena, there is -nothing to prevent our accepting it entirely, as a -satisfactory theory for all the known laws of Light. - -4. _Heat._--With regard to Heat as with regard to Light, a -fluid medium was necessarily assumed as the vehicle of the -property. During the last century, this medium was supposed -to be an emitted fluid. And many of the ascertained Laws of -Heat, those which prevail with regard to its radiation more -especially, were well explained by this hypothesis[22\4]. -Other effects of heat, however, as for instance _latent -heat_[23\4], and the change of _consistence_ of -bodies[24\4], were not satisfactorily brought into connexion -with the hypothesis; while {331} _conduction_[25\4], which -at first did not appear to result from the fundamental -assumption, was to a certain extent explained as internal -radiation. - -[Note 22\4: See the Account of the Theory of Exchanges, -_Hist. Ind. Sc._ b. x. c. i. sect. 2.] - -[Note 23\4: _Ib._ c. ii. sect. 3.] - -[Note 24\4: _Ib._ c. ii. sect. 2.] - -[Note 25\4: _Ib._ c. i. sect. 7.] - -But it was by no means clear that an Undulatory Theory of -Heat might not be made to explain these phenomena equally -well. Several philosophers inclined to such a theory; and -finally, Ampère 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 medium, might be so -adjusted as to explain all which the theory of emission -could explain, and moreover to account for facts and laws -which were out of the reach of that theory. About the same -time it was discovered by Prof. Forbes and M. Nobili that -radiant heat is, under certain circumstances, polarized. Now -polarization had been most satisfactorily explained by means -of transverse undulations in the case of light; while all -attempts to modify the emission theory so as to include -polarization in it, had been found ineffectual. Hence this -discovery was justly considered as lending great countenance -to the opinion that Heat consists in the vibrations of its -proper medium. - -But what is this medium? Is it the same by which the -impressions of Light are conveyed? This is a difficult -question; or rather it is one which we cannot at present -hope to answer with certainty. No doubt the connexion -between Light and Heat is so intimate and constant, that we -can hardly refrain from considering them as affections of -the same medium. But instead of attempting to erect our -systems on such loose and general views of connexion, it is -rather the business of the philosophers of the present day -to determine the laws of the operation of heat, and its real -relation to light, in order that we may afterwards be able -to connect the theories of the two qualities. Perhaps in a -more advanced state of our knowledge we may be able to state -it as an Axiom, that two Secondary Qualities, which are -intimately connected in their causes and effects, must be -affections of the same Medium. {332} But at present it does -not appear safe to proceed upon such a principle, although -many writers, in their speculations both concerning Light -and Heat, and concerning other properties, have not -hesitated to do so. - -Some other consequences follow from the Idea of a Medium -which must be the subject of another chapter. - - - -{{333}} -CHAPTER IV. - -OF THE MEASURE OF SECONDARY QUALITIES. - - -SECT. I.--_Scales of Qualities in general._ - -THE ultimate object of our investigation in each of the -Secondary Mechanical Sciences, is the nature of the -processes by which the special impressions of sound, light, -and heat, are conveyed, and the modifications of which these -processes are susceptible. And of this investigation, as we -have seen, the necessary basis is the principle, that these -impressions are transmitted by means of a medium. But before -we arrive at this ultimate object, we may find it necessary -to occupy ourselves with several intermediate objects: -before we discover the _cause_, it may be necessary to -determine the _laws_ of the phenomena. Even if we cannot -immediately ascertain the mechanism of light or heat, it may -still be interesting and important to arrange and measure -the effects which we observe. - -The idea of a Medium affects our proceeding in this research -also. We cannot measure Secondary qualities in the same -manner in which we measure Primary qualities, by a mere -addition of parts. There is this leading and remarkable -difference, that while both classes of qualities are -susceptible of changes of magnitude, primary qualities -increase by addition of _extension_, secondary, by -augmentation of _intensity_. A space is doubled when another -equal space is placed by its side; one weight joined to -another makes up the sum of the two. But when one degree of -warmth is combined with another, or one shade of red colour -with another, we cannot in like manner talk of the _sum_. -The component parts do not evidently retain their {334} -separate existence; we cannot separate a strong green colour -into two weaker ones, as we can separate a large force into -two smaller. The increase is absorbed into the previous -amount, and is no longer in evidence as a part of the whole. -And this is the difference which has given birth to the two -words _extended_, and _intense_. That is extended which has -'partes extra partes,' parts outside of parts: that is -intense which becomes stronger by some indirect and -unapparent increase of agency, like the stretching of the -internal springs of a machine, as the term _intense_ -implies. Extended magnitudes can at will be resolved into -the parts of which they were originally composed, or any -other which the nature of their extension admits; their -proportion is apparent; they are directly and at once -subject to the relations of number. Intensive magnitudes -cannot be resolved into smaller magnitudes; we can see that -they differ, but we cannot tell in what proportion; we have -no direct measure of their quantity. How many times hotter -than blood is boiling water? The answer cannot be given by -the aid of our feelings of heat alone. - -The difference, as we have said, is connected with the -fundamental principle that we do not perceive Secondary -qualities directly, but through a Medium. We have no natural -apprehension of light, or sound, or heat, as they exist in -the bodies from which they proceed, but only as they affect -our organs. We can only measure them, therefore, by some -_Scale_ supplied by their effects. And thus while extended -magnitudes, as space, time, are measurable directly and of -themselves; intensive magnitudes, as brightness, loudness, -heat, are measurable only by artificial means and -conventional scales. Space, time, measure themselves: the -repetition of a smaller space, or time, while it composes a -larger one, measures it. But for light and heat we must have -Photometers and Thermometers, which measure something which -is assumed to be an indication of the quality in question. -In the one case, the mode of applying the measure, and the -meaning of the number resulting, are seen by intuition; in -the {335} other, they are consequences of assumption and -reasoning. In the one case, they are _Units_, of which the -extension is made up; in the other, they are _Degrees_ by -which the intensity ascends. - -2. When we discover any property in a sensible quality, -which at once refers us to number or space, we readily take -this property as a measure; and thus we make a transition -from quality to quantity. Thus Ptolemy in the third chapter -of the First Book of his _Harmonics_ begins thus: 'As to the -differences which exist in sounds both in _quality_ and in -_quantity_, if we consider that difference which refers to -the acuteness and graveness, we cannot at once tell to which -of the above two classes it belongs, till we have considered -the causes of such symptoms.' But at the end of the chapter, -having satisfied himself that grave sounds result from the -magnitude of the string or pipe, other things being equal, -he infers, 'Thus the difference of acute and grave appears -to be a difference of _quantity_.' - -In the same manner, in order to form Secondary Mechanical -Sciences respecting any of the other properties of bodies, -we must reduce these properties to a dependence upon -quantity, and thus make them subject to measurement. We -cannot obtain any sciential truths respecting the comparison -of sensible qualities, till we have discovered measures and -scales of the qualities which we have to consider; and -accordingly, some of the most important steps in such -sciences have been the establishment of such measures and -scales, and the invention of the requisite instruments. - -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 century. Perhaps we -may consider Lambert, a mathematician who resided in -Switzerland, and published about 1750, as the person who -first clearly felt the importance of establishing such -sciences. His Photometry, Pyrometry, and Hygrometry, are -examples of the systematic reduction of sensible qualities -(light, heat, moisture) to modes of numerical measurement. -{336} - -We now proceed to speak of such modes of measurement with -regard to the most obvious properties of bodies. - - -SECT. II.--_The Musical Scale._ - -3. THE establishment of the _Harmonic Canon_, that is, of a -Scale and Measure of the musical place of notes, in the -relation of _high_ and _low_, was the first step in the -science of Harmonics. The perception of the differences and -relations of musical sounds is the office of the sense of -hearing; but these relations are fixed, and rendered -accurately recognizable by artificial means. 'Indeed, in all -the senses,' as Ptolemy truly says in the opening of his -Harmonics, 'the sense discovers what is approximately true, -and receives accuracy from another quarter: the reason -receives the approximately-true from another quarter, and -discovers the accurate truth.' We can have no measures of -sensible qualities which do not ultimately refer to the -sense;--whether they do this immediately, as when we refer -Colours to an assumed Standard; or mediately, as when we -measure Heat by Expansion, having previously found by an -appeal to sense that the expansion increases with the heat. -Such relations of sensible qualities cannot be described in -words, and can only be apprehended by their appropriate -faculty. The faculty by which the relations of sounds are -apprehended is a _musical ear_ in the largest acceptation of -the term. In this signification the faculty is nearly -universal among men; for all persons have musical ears -sufficiently delicate to understand and to imitate the -modulations corresponding to various emotions in speaking; -which modulations depend upon the succession of acuter and -graver tones. These are the relations now spoken of, and -these are plainly perceived by persons who have very -imperfect musical ears, according to the common use of the -phrase. But the relations of tones which occur in speaking -are somewhat indefinite; and in forming that musical scale -which is the basis of our science upon the subject, we {337} -take the most definite and marked of such relations of -notes; such as occur, not in speaking but in singing. Those -musical relations of two sounds which we call the _octave_, -the _fifth_, the _fourth_, the _third_, are recognized after -a short familiarity with them. These _chords_ or _intervals_ -are perceived to have each a peculiar character, which -separates them from the relations of two sounds taken at -random, and makes it easy to know them when sung or played -on an instrument; and for most persons, not difficult to -sing the sounds in succession exactly, or nearly correct. -These musical relations, or _concords_, then, are the -groundwork of our musical series of sounds. But how are we -to name these indescribable sensible characters? how to -refer, with unerring accuracy, to a type which exists only -in our own perceptions? We must have for this purpose a -_Scale_ and a _Standard_. - -The Musical Scale is a series of eight notes, ascending by -certain steps from the first or key-note to the octave above -it, each of the notes being fixed by such distinguishable -musical relations as we have spoken of above. We may call -these notes C, D, E, F, G, A, B, _c_; and we may then say -that G is determined by its being a fifth above C; D by its -being a fourth below G; E by its being a third above C; and -similarly of the rest. It will be recollected that the terms -a _fifth_, a _fourth_, a _third_, have hitherto been -introduced as expressing certain simple and indescribable -musical relations among sounds, which might have been -indicated by any other names. Thus we might call the fifth -the _dominant_, and the fourth the _subdominant_, as is done -in one part of musical science. But the names we have used, -which are the common ones, are in fact derived from the -number of notes which these intervals include in the scale -obtained in the above manner. The notes, C, D, E, F, G, -being five, the interval from C to G is a fifth, and so of -the rest. The fixation of this scale gave the means of -describing exactly any note which occurs in the scale, and -the method is easily applicable to notes above and below -this range; for in a series of sounds higher or lower by an -octave than {338} this standard series, the ear discovers a -recurrence of the same relations so exact, that a person may -sometimes imagine he is producing the same notes as another -when he is singing the same air an octave higher. Hence the -next eight notes may be conveniently denoted by a repetition -of the same letters, as the first; thus, C, D, E, F, G, A, -B, _c_, _d_, _e_, _f_, _g_, _a_, _b_; and it is easy to -devise a continuation of such cycles. And other admissible -notes are designated by a further modification of the -standard ones, as by making each note _flat_ or _sharp_; -which modification it is not necessary here to consider, -since our object is only to show how a standard is -attainable, and how it serves the ends of science. - -We may observe, however, that the above is not an exact -account of the first, or early Greek scale; for that scale -was founded on a primary division of the interval of two -octaves (the extreme range which it admitted) into five -_tetrachords_, each tetrachord including the interval of a -fourth. All the notes of this series had different names -borrowed from this division[26\4]; thus _mese_ was the -middle or key-note; the note below it was _lichanos mesôn_, -the next below was _parypate mesôn_, the next lower, _hypate -mesôn_. The fifth above _mese_ was _nete diazeugmenôn_, the -octave was _nete hyperbolæôn_. - -[Note 26\4: Burney's _History of Music_, vol. i. p. 28.] - -4. But supposing a complete system of such denominations -established, how could it be with certainty and rigour -applied? The human ear is fallible, the organs of voice -imperfectly obedient; if this were not so, there would be no -such thing as a _good_ ear or a _good_ voice. What means can -be devised of finding at will a _perfect_ concord, a fifth -or a fourth? Or supposing such concords fixed by an -acknowledged authority, how can they be referred to, and the -authority adduced? How can we enact a Standard of sounds? - -A Standard was discovered in the _Monochord_. A musical -string properly stretched, may be made to produce different -notes, in proportion as we intercept a longer or shorter -portion, and make this portion {339} vibrate. The relation -of the length of the strings which thus sound the two notes -G and C is fixed and constant, and the same is true of all -other notes. Hence the musical interval of any notes of -which we know the places in the musical scale, may be -reproduced by measuring the lengths of string which are -known to give them. If C be of the length 180, D is 160, E -is 144, F is 135, G is 120; and thus the musical relations -are reduced to numerical relations, and the monochord is a -complete and perfect _Tonometer_. - -We have here taken the length of the string as the measure -of the tone: 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 cause; and when we consider -the matter further, we find this cause in the frequency of -these vibrations of the string. The truth that the same note -must result from the same frequency of vibration is readily -assented to on a slight suggestion of experience. Thus -Mersenne[27\4], when he undertakes to determine the -frequency of vibrations of a given sound, says 'Supponendum -est quoscunque nervos et quaslibet chordas unisonum -facientes eundem efficere numerum recursuum eodem vel equali -tempore, quod perpetuâ constat experientiâ.' And he proceeds -to apply it to cases where experience could not verify this -assertion, or at least had not verified it, as to that of pipes. - -[Note 27\4: _Harmonia_, lib. ii. prop. 19.] - -The pursuit of these numerical relations of tones forms the -science of Harmonics; of which here we do not pretend to -give an account, but only to show, how the invention of a -Scale and Nomenclature, a Standard and Measure of the tone -of sounds, is its necessary basis. We will therefore now -proceed to speak of another subject; _colour_. - - -SECT. III.--_Scales of Colour._ - -5. _The Prismatic Scale of Colour._--A SCALE of Colour must -depend originally upon differences {340} discernible by the -eye, as a scale of notes depends on differences perceived by -the ear. In one respect the difficulty is greater in the -case of the visible qualities, for there are no relations of -colour which the eye peculiarly singles out and -distinguishes, as the ear selects and distinguishes an -octave or a fifth. Hence we are compelled to take an -arbitrary scale; and we have to find one which is fixed, and -which includes a proper collection of colours. The -_prismatic spectrum_, or coloured image produced when a -small beam of light passes obliquely through any transparent -surface (as the surface of a prism of glass,) offers an -obvious Standard as far as it is applicable. Accordingly -colours have, for various purposes, been designated by their -place in the spectrum, ever since the time of Newton; and we -have thus a means of referring to such colours as are -included in the series _red_, _orange_, _yellow_, _green_, -_blue_, _violet_, _indigo_, and the intermediate tints. - -But this scale is not capable of numerical precision. If the -spectrum could be exactly defined as to its extremities, and -if these colours occupied always the same proportional part -of it, we might describe any colour in the above series by -the measure of its position. But the fact is otherwise. The -spectrum is too indefinite in its boundaries to afford any -distinct point from which we may commence our measures; and -moreover the spectra produced by different transparent -bodies differ from each other. Newton had supposed that the -spectrum and its parts were the same, so long as the -refraction was the same; but his successors discovered that, -with the same amount of refraction in different kinds of -glass, there are different magnitudes of the spectrum; and -what is still worse with reference to our present purpose, -that the spectra from different glasses have the colours -distributed in different proportions. In order, therefore, -to make the spectrum the scale of colour, we must assume -some fixed substance; for instance, we may take water, and -thus a series approaching to the colours of the _rainbow_ -will be our standard. But we should still have an extreme -difficulty in applying such a rule. The distinctions of -{341} colour which the terms of common language express, are -not used with perfect unanimity or with rigorous precision. -What one person calls _bluish green_ another calls _greenish -blue_. Nobody can say what is the precise boundary between -red and orange. Thus the prismatic scale of colour was -incapable of mathematical exactness, and this inconvenience -was felt up to our own times. - -But this difficulty was removed by a curious discovery of -Wollaston and Fraunhofer; who found that there are, in the -solar spectrum, certain fine black Lines which occupy a -definite place in the series of colours, and can be observed -with perfect precision. We have now no uncertainty as to -what coloured light we are speaking of, when we describe it -as that part of the spectrum in which Fraunhofer's Line C or -D occurs. And thus, by this discovery, the prismatic -spectrum of sunlight became, for certain purposes, an exact -_Chromatometer_. - -6. _Newton's Scale of Colours._--Still, such a standard, -though definite, is arbitrary and seemingly anomalous. The -lines A, B, C, D, &c., of Fraunhofer's spectrum are -distributed without any apparent order or law; and we do -not, in this way, obtain numerical measures, which is what, -in all cases, we desire to have. Another discovery of -Newton, however, gives us a spectrum containing the same -colours as the prismatic spectrum, but produced in another -way, so that the colours have a numerical relation. I speak -of the laws of the _Colours of Thin Plates_. The little -rainbows which we sometimes see in the cracks of broken -glass are governed by fixed and simple laws. The kind of -colour produced at any point depends on the thickness of the -thin plate of air included in the fissure. If the thickness -be eight-millionths of an inch, the colour is orange, if -fifteen-millionths of an inch, we have green, and so on; and -thus these numbers, which succeed each other in a regular -order from red to indigo, give a numerical measure of each -colour; which measure, when we pursue the subject, we find -is one of the bases of all optical theory. The series of -colours obtained from plates of air of gradually increasing -thickness is called {342} _Newton's Scale of Colours_; but -we may observe that this is not precisely what we are here -speaking of, a scale of _simple_ colours; it is a series -produced by certain combinations, resulting from the -repetition of the first spectrum, and is mainly useful as a -standard for similar phenomena, and not for colour in -general. The real scale of colour is to be found, as we have -said, in the numbers which express the thickness of the -producing film;--in the length of a _fit_ in Newton's -phraseology, or the length of an _undulation_ in the modern -theory. - -7. _Scales of Impure Colours._--The standards just spoken of -include (mainly at least) only pure and simple colours; and -however complete these standards may be for certain objects -of the science of optics, they are insufficient for other -purposes. They do not enable us to put in their place mixed -and impure colours. And there is, in the case of colour, a -difficulty already noticed, which does not occur in the case -of sound; two notes, when sounded together, are not -necessarily heard as one; they are recognized as still two, -and as forming a concord or a discord. But two colours form -a single colour; and the eye cannot, in any way, distinguish -between a green compound of blue and yellow, and the simple, -undecomposable green of the spectrum. By composition of -three or more colours, innumerable new colours may be -generated which form no part of the prismatic series; and by -such compositions is woven the infinitely varied web of -colour which forms the clothing of nature. How are we to -classify and arrange all the possible colours of objects, so -that each shall have a place and name? How shall we find a -_chromatometer_ for impure as well as for pure colour? - -Though no optical investigations have depended on a scale of -impure colours, such a scale has been wanted and invented -for other purposes; for instance, in order to identify and -describe objects of natural history. Not to speak of earlier -essays, we may notice Werner's Nomenclature of Colours, -devised for the purpose of describing minerals. This scale -of colour was far superior to any which had previously been -promulgated. {343} It was, indeed, arbitrary in the -selection of its degrees, and in a great measure in their -arrangement; and the colours were described by the usual -terms, though generally with some added distinction; as -_blackish green_, _bluish green_, _apple-green_, -_emerald-green_. But the great merit of the scale was its -giving a _fixed_ conventional meaning to these terms, so -that they lost much of their usual vagueness. Thus -_apple-green_ did not mean the colour of any green apple -casually taken; but a certain definite colour which the -student was to bear in mind, whether or not he had ever seen -an apple of that exact hue. The words were not a -description, but a _record_ of the colour: the memory was to -retain a _sensation_, not a name. - -The imperfection of the system (arising from its arbitrary -form) was its incompleteness: however well it served for the -reference of the colours which it did contain, it was -applicable to no others; and thus though Werner's -enumeration extended to more than a hundred colours, there -occur in nature a still greater number which cannot be -exactly described by means of it. - -In such cases the unclassed colour is, by the Wernerians, -defined by stating it as intermediate between two others: -thus we have an object described as _between emerald-green -and grass-green_. The eye is capable of perceiving a -gradation from one colour to another; such as may be -produced by a gradual mixture in various ways. And if we -image to ourselves such a mixture, we can compare with it a -given colour. 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 colour. 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 -supply. For it is not always between contiguous members of -the series that the undescribed colour is found. If we place -emerald-green between apple-green and grass-green, we may -yet have a colour intermediate between emerald-green and -leek-green; and, in fact, the Wernerian series of colours is -destitute {344} of a principle of self-arrangement and -gradation; and is thus necessarily and incurably imperfect. - -8. We should have a complete Scale of Colours, if we could -form a series including all colours, and arranged so that -each colour was intermediate in its tint between the -adjacent terms of the series; for then, whether we took many -or few of the steps of the series for our standard terms, -the rest could be supplied by the law of continuity; and any -given colour would either correspond to one of the steps of -our scale or fall between two intermediate ones. The -invention of a Chromatometer for Impure Colours, therefore, -requires that we should be able to form all possible colours -by such intermediation in a systematic manner; that is, by -the mixture or combination of certain elementary colours -according to a simple rule: and we are led to ask whether -such a process has been shown to be possible. - -The colours of the prismatic spectrum obviously do form a -continuous series; green is intermediate between its -neighbours yellow and blue, orange between red and yellow; -and if we suppose the two ends of the spectrum bent round to -meet each other, so that the arrangement of the colours may -be circular, the violet and indigo will find their -appropriate place between the blue and red. And all the -interjacent tints of the spectrum, as well as the ones just -named, will result from such an arrangement. Thus all the -_pure_ colours are produced by combinations two and two of -three primary colours, Red, Yellow, and Blue: and the -question suggests itself whether these three are not really -the only Primary Colours, and whether all the impure colours -do not arise from mixtures of the three in various -proportions. There are various modes in which this -suggestion may be applied to the construction of a scale of -colours; but the simplest, and the one which appears really -to verify the conjecture that all possible colours may be so -exhibited, is the following. A certain combination of red, -yellow, and blue, will produce black, or pure grey, and when -diluted, will give all the shades of grey which intervene -between {345} black and white. By adding various shades of -grey, then, to pure colours, we may obtain all the possible -ternary combinations of red, yellow, and blue; and in this -way it is found that we exhaust the range of colours. Thus -the circle of pure colours of which we have spoken may be -accompanied by several other circles, in which these colours -are tinged with a less or greater shade of grey; and in this -manner it is found that we have a perfect chromatometer; -every possible colour being exhibited either exactly or by -means of approximate and contiguous limits. The arrangement -of colours has been brought into this final and complete -form by M. Merimée, whose Chromatic Scale is published by M. -Mirbel in his _Elements of Botany_. 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 it; or, expressing the same result otherwise, -by means of the pure colour which is involved, and the -proportion of grey by which it is rendered impure. In such a -scale the fundamental elements would be the precise tints of -red, yellow, and blue which are found or assumed to be -primary; the numerical exponents of each colour would depend -upon the arbitrary number of degrees which we interpose -between each two primary colours; and between each pure -colour and absolute blackness. No such numerical scale has, -however, as yet, obtained general acceptation[28\4]. - -[Note 28\4: The reference to _Fraunhofer's Lines_, as a -means of determining the place of a colour in the prismatic -series, has been objected to, because, as is asserted, the -colours which are in the neighbourhood of each line vary -with the position of the sun, state of the atmosphere and -the like. It is very evident that coloured light refracted -by the prism will not give the same spectrum as white light. -The spectrum given by white light is of course the one here -meant. It is an usual practice of optical experimenters to -refer to the colours of such a spectrum, defining them by -Fraunhofer's Lines. - -I do not know whether it needs explanation that the 'first -spectrum' in Newton's rings is a ring of the prismatic -colours. - -I have not had an opportunity of consulting Lambert's -_Photometria, sive de mensura et gradibus luminis, colorum, -et umbræ_, published in 1760, nor Mayer's _Commentatio de -Affinitate Colorum_, (1758), in which, I believe, he -describes a chromatometer. The present work is not intended -to be complete as a history; and I hope I have given -sufficient historical detail to answer its philosophical -purpose.] - - -{346} SECT. IV.--_Scales of Light._ - -9. _Photometer._--ANOTHER instrument much needed in optical -researches is a _Photometer_, a measure of the intensity of -light. In this case, also, the organ of sense, the eye, is -the ultimate judge; nor has any effect of light, as light, -yet been discovered which we can substitute for such a -judgment. All instruments, such as that of Leslie, which -employ the heating effect of light, or at least all that -have hitherto been proposed, are inadmissible as -photometers. But though the eye can judge of two surfaces -illuminated by light of the same colour, and can determine -when they are equally bright, or which is the brighter, the -eye can by no means decide at sight the proportion of -illumination. How much in such judgments we are affected by -contrast, is easily seen when we consider how different is -the apparent brightness of the moon at mid-day and at -midnight, though the light which we receive from her is, in -fact, the same at both periods. In order to apply a scale in -this case, we must take advantage of the known numerical -relations of light. We are certain that if all other -illumination be excluded, two equal luminaries, under the -same circumstances, will produce an illumination twice as -great as one does; and we can easily prove, from -mathematical considerations, that if light be not enfeebled -by the medium through which it passes, the illumination on a -given surface will diminish as the square of the distance of -the luminary increases. If, therefore, we can by taking a -fraction thus known of the illuminating effect of one -luminary, make it equal to the total effect of another, of -which equality the eye is a competent judge, we compare the -effects of the two luminaries. In order to make this -comparison we may, with Rumford, look at the shadows of the -same object made by the two lights, {347} or with Ritchie, -we may view the brightness produced on two contiguous -surfaces, framing an apparatus so that the equality may be -brought about by proper adjustment; and thus a measure will -become practicable. Or we may employ other methods as was -done by Wollaston[29\4], who reduced the light of the sun by -observing it as reflected from a bright globule, and thus -found the light of the sun to be 10,000,000,000 times that -of Sirius, the brightest fixed star. All these methods are -inaccurate, even as methods of comparison; and do not offer -any fixed or convenient numerical standard; but none better -have yet been devised[30\4]. - -[Note 29\4: _Phil. Trans._ 1820, p. 19.] - -[Note 30\4: Improved Photometers have been devised by -Professor Wheatstone, Professor Potter, and Professor -Steinheil; but they depend upon principles similar to those -mentioned in the text.] - -10. _Cyanometer._--As we thus measure the brightness of a -colourless light, we may measure the intensity of any -particular colour in the same way; that is, 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 object. Such an instrument we have in the -_Cyanometer_, which was invented by Saussure for the purpose -of measuring the intensity of the blue colour of the sky. We -may introduce into such an instrument a numerical scale, but -the numbers in such a scale will be altogether arbitrary. - - -SECT. V.--_Scales of Heat._ - -11. _Thermometers._--WHEN we proceed to the sensation of -heat, and seek a measure of that quality, we find, at first -sight, new difficulties. Our sensations of this kind are -more fluctuating than those of vision; for we know that the -same object may feel warm to one hand and cold to another at -the same instant, if the hands have been previously cooled -and warmed respectively. Nor can we obtain here, as in the -case of light, self-evident numerical relations of the heat -communicated in given circumstances; for we know that the -{348} effect so produced will depend on the warmth of the -body to be heated, as well as on that of the source of heat; -the summer sun, which warms our bodies, will not augment the -heat of a red-hot iron. The cause of the difference of these -cases is, that bodies do not receive the whole of their -heat, as they receive the whole of their light, from the -immediate influence of obvious external agents. There is no -readily-discovered absolute cold, corresponding to the -absolute darkness which we can easily produce or imagine. -Hence we should be greatly at a loss to devise a -_Thermometer_, if we did not find an indirect effect of heat -sufficiently constant and measurable to answer this purpose. -We discover, however, such an effect in the _expansion_ of -bodies by the effect of heat. - -12. Many obvious phenomena show that air, under given -circumstances, expands by the effect of heat; the same is -seen to be true of liquids, as of water, and spirit of wine; -and the property is found to belong also to the metallic -fluid, quicksilver. 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 quality; and the Thermometer was invented. There -were, however, many difficulties to overcome, and many -points to settle, before this instrument was fit for the -purposes of science. - -An explanation of the way in which this was done necessarily -includes an important chapter of the history of Thermotics. -We must now, therefore, briefly notice historically the -progress of the Thermometer. The leading steps of this -progress, after the first invention of the instrument, -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 heat_. - -13. It would occupy too much space to give in detail the -history of the successive attempts by which {349} these -steps were effected. A thermometer is described by Bacon -under the title _Vitrum Calendare_; this was an air -thermometer. Newton used a thermometer of linseed oil, and -he perceived that the first step requisite to give value to -such an instrument was to fix its scale; accordingly he -proposed his _Scala Graduum Caloris_[31\4]. But when -thermometers of different liquids were compared, it -appeared, from their discrepancies, that this fixation of -the scale of heat was more difficult than had been supposed. -It was, however, effected. Newton had taken freezing water, -or rather thawing snow, as the zero of his scale, which is -really a fixed point; Halley and Amontons discovered (in -1693 and 1702) that the heat of boiling water is another -fixed point; and Daniel Gabriel Fahrenheit, of Dantzig, by -carefully applying these two standard points, produced, -about 1714, thermometers, which were constantly consistent -with each other. This result was much admired at the time, -and was, in fact, the solution of the problem just stated, -the _fixation of the scale of heat_. - -[Note 31\4: _Phil. Trans._ 1701.] - -14. But the scale thus obtained is a conventional not a -natural scale. It depends upon the fluid employed for the -thermometer. The progress of expansion from the heat of -freezing to that of boiling water is different for mercury, -oil, water, spirit of wine, air. A degree of heat which is -half-way between these two standard points according to a -mercurial thermometer, will be below the half-way point in a -spirit thermometer, and above it in an air thermometer. Each -liquid has its own _march_ in the course of its expansion. -Deluc and others compared the marches of various liquids, -and thus made what we may call a _concordance_ of -thermometers of various kinds. - -15. Here the question further occurs: Is there not some -_natural measure_ of the degrees of heat? It appears certain -that there must be such a measure, and that by means of it -all the scales of different liquids must be reconciled. Yet -this does not seem to have occurred at once to men's minds. -Deluc, in speaking {350} of the researches which we have -just mentioned, says[32\4], 'When I undertook these -experiments, it never once came into my thoughts that they -could conduct me with any probability to a table of real -degrees of heat. But hope grows with success, and desire -with hope.' Accordingly he pursued this inquiry for a long -course of years. - -[Note 32\4: _Modif. de l'Atmosph._ 1782, p. 303.] - -What are the principles by which we are to be guided to the -true measure of heat? Here, as in all the sciences of this -class, we have the general principle, that the secondary -quality, Heat, must be supposed to be perceived in some way -by a material Medium or Fluid. If we take that which is, -perhaps, the simplest form of this hypothesis, that the heat -depends upon the _quantity_ of this fluid, or _Caloric_, -which is present, we shall find that we are led to -propositions which may serve as a foundation for a natural -measure of heat. The _Method of Mixtures_ is one example of -such a result. If we mix together two pints of water, one -hot and one cold, is it not manifest that the temperature of -the mixture must be midway between the two? Each of the two -portions brings with it its own heat. The whole heat, or -caloric, of the mixture is the sum of the two; and the heat -of each half must be the half of this sum, and therefore its -temperature must be intermediate between the temperatures of -the equal portions which were mixed. Deluc made experiments -founded upon this principle, and was led by them to conclude -that 'the dilatations of mercury follow an accelerated march -for successive equal augmentations of heat.' - -But there are various circumstances which prevent this -method of mixtures from being so satisfactory as at first -sight it seems to promise to be. The different capacities -for heat of different substances, and even of the same -substance at different temperatures, introduce much -difficulty into the experiments; and this path of inquiry -has not yet led to a satisfactory result. {351} - -16. Another mode of inquiring into the natural measure of -heat is to seek it by researches on the _law of cooling_ of -hot bodies. If we assume that the process of cooling of hot -bodies consists in a certain material heat flying off, we -may, by means of certain probable hypotheses, determine -mathematically the law according to which the temperature -decreases as time goes on; 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 -form. - -It appears evident from the most obvious conceptions which -we can form of the manner in which a body parts with its -superabundant heat, that the hotter a body is, the faster it -cools; though it is not clear without experiment, by what -law the rate of cooling will depend upon the heat of the -body. Newton took for granted the most simple and seemingly -natural law of this dependence: he supposed the rate of -cooling to be _proportional_ to the temperature, and from -this supposition he could deduce the temperature of a hot -iron, calculating from the original temperature and the time -during which it had been cooling. By calculation founded on -such a basis, he graduated his thermometer. - -17. But a little further consideration showed that the rate -of cooling of a hot body depended upon the temperature of -the surrounding bodies, as well as upon its own temperature. -Prevost's _Theory of Exchanges_[33\4] was propounded with a -view of explaining this dependence, and was generally -accepted. According to this theory, all bodies radiate heat -to one another, and are thus constantly giving and receiving -heat; and a body which is hotter than surrounding bodies, -cools itself, and warms the surrounding, bodies, by an -exchange of heat for heat, in which they are the gainers. -Hence if _θ_ be the temperature of the bodies, or of the -space, by which the hot body is surrounded, and _θ_ + _t_ the -temperature of the hot body, the rate of cooling will depend -{352} upon the excess of the radiation for a temperature _θ_ + -_t_, above the radiation for a temperature _θ_. - -[Note 33\4: _Recherches sur la Chaleur_, 1791. _Hist. Ind. -Sc._ b. x. c. i. sect. 2.] - -Accordingly, in the admirable researches of MM. Dulong and -Petit upon the cooling of bodies, it was assumed that the -rate of cooling of the hot body was represented by the -excess of F(_θ_ + _t_) above F(_θ_); where F represented some -mathematical _function_, that is, some expression obtained -by arithmetical operations from the temperatures _θ_ + _t_ and -_θ_; although what these operations are to be, was left -undecided, and was in fact determined by the experiments. -And the result of their investigations was, that the -function is of this kind: when the temperature increases by -equal intervals, the function increases in a continued -geometric proportion[34\4]. This was, in fact, the same law -which had been assumed by Newton and others, with this -difference, that _they_ had neglected the term which depends -upon the temperature of the surrounding space. - -[Note 34\4: The formula for the rate of cooling is _ma^(θ + -t) - ma^θ_, where the quantity _m_ depends upon the nature -of the body, the state of its surface, and other -circumstances.--_Ann. Chim._ vii. 150.] - -18. 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 caloric, that it gives great probability to -the scale of temperature on which the simplicity of the -result depends. Now the temperatures in the formulæ just -referred to were expressed by means of the _air -thermometer_. Hence MM. Dulong and Petit justly state, that -while all different substances employed as thermometers give -different laws of thermotical phenomena, their own success -in obtaining simple and general laws by means of the air -thermometer, is a strong recommendation of that as the -_natural scale of heat_. They add[35\4], 'The well-known -uniformity of the principal physical properties of all -gases, and especially the perfect identity of their laws of -dilatation by heat, [a very important discovery of {353} -Dalton and Gay Lussac[36\4],] make it very probable that in -this class of bodies the disturbing causes have not the same -influence as in solids and liquids; 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 them.' - -[Note 35\4: _Annales de Chimie_, vii. 153.] - -[Note 36\4: _Hist. Ind. Sc._ b. x. c. ii. sect. 1.] - -19. Still we cannot consider this point as settled till we -obtain a more complete theoretical insight into the nature -of heat itself. If it be true that heat consists in the -vibrations of a fluid, then, although, as Ampère has -shown[37\4], the laws of radiation will, on mathematical -grounds, be the same as they are on the hypothesis of -emission, we cannot consider the natural scale of heat as -determined, till we have discovered some means of measuring -the caloriferous vibrations as we measure luminiferous -vibrations. We shall only know what the quantity of heat is -when we know what heat itself is;--when we have obtained a -theory which satisfactorily explains the manner in which the -substance or medium of heat produces its effects. When we -see how radiation and conduction, dilatation and -liquefaction, are all produced by mechanical changes of the -same fluid, we shall then see what the nature of that change -is which dilatation really measures, and what relation it -bears to any more proper standard of heat. - -[Note 37\4: _Ib._ c. iv.] - -We may add, that while our thermotical theory is still so -imperfect as it is, all attempts to divine the true nature -of the relation between light and heat are premature, and -must be in the highest degree insecure and visionary. -Speculations in which, from the general assumption of a -caloriferous and luminiferous medium, and from a few facts -arbitrarily selected and loosely analysed, a general theory -of light and heat is asserted, are entirely foreign to the -course of inductive science, and cannot lead to any stable -and substantial truth. - -20. _Other Instruments for measuring Heat._--It does not -belong to our present purpose to speak of {354} instruments -of which the object is to measure, not sensible qualities, -but some effect or modification of the cause by which such -qualities are produced: such, for instance, are the -_Calorimeter_, employed by Lavoisier and Laplace, in order -to compare the _Specific Heat_ of different substances; and -the _Actinometer_, invented by Sir John Herschel, in order -to determine the _effect of the Sun's Rays_ by means of the -heat which they communicate in a given time; which effect -is, as may readily be supposed, very different under -different circumstances of atmosphere and position. The laws -of such effects may be valuable contributions to our -knowledge of heat, but the interpretation of them must -depend on a previous knowledge of the relations which -temperature bears to heat, according to the views just -explained. - - -SECT. VI.--_Scales of other Qualities._ - -21. BEFORE quitting the subject of the measures of sensible -qualities, we may observe that there are several other such -qualities for which it would be necessary to have scales and -means of measuring, in order to make any approach to science -on such subjects. This is true, for instance, of Tastes and -Smells. Indeed some attempts have been made towards a -classification of the Tastes of sapid substances, but these -have not yet assumed any satisfactory or systematic -character; and I am not aware that any instrument has been -suggested for _measuring_ either the Flavour or the Odour of -bodies which possess such qualities. - -22. _Quality of Sounds._--The same is true of that kind of -difference in sounds which is peculiarly termed their -_Quality_; that character by which, for instance, the sound -of a flute differs from that of a hautbois, when the note is -the same; or a woman's voice from a boy's. - -23. _Articulate Sounds._--There is also in sounds another -difference, of which the nature is still obscure, but in -reducing which to rule, and consequently to measure, some -progress has nevertheless been made. {355} I speak of the -differences of sound considered as _articulate_. -Classifications of the sounds of the usual alphabets have -been frequently proposed; for instance, that which arranges -the _Consonants_ in the following groups,: - -Sharp. Flat. Sharp Aspirate. Flat Aspirate. Nasal. - p b ph (_f_) bh (_v_) m - k g (hard) kh gh ng - t d th (sharp) th (flat) n - s z sh zh - -It is easily perceived that the relations of the sounds in -each of these horizontal lines are analogous; and -accordingly the rules of derivation and modification of -words in several languages proceed upon such analogies. In -the same manner the _Vowels_ may be arranged in an order -depending on their sound. But to make such arrangements -fixed and indisputable, we ought to know the mechanism by -which such modifications are caused. Instruments have been -invented by which some of these sounds can be imitated; and -if such instruments could be made to produce the above -series of articulate sounds, by connected and regular -processes, we should find, in the process, a _measure_ of -the sound produced. This has been in a great degree effected -for the Vowels by Professor Willis's artificial mode of -imitating them. For he finds that if a musical reed be made -to sound through a cylindrical pipe, we obtain by gradually -lengthening the cylindrical pipe, the series of vowels I, E, -A, O, U, with intermediate sounds[38\4]. In this instrument, -then, the length of the pipe would determine the vowel, and -might be used numerically to express it. Such an instrument -so employed would be a measure of vowel quality, and might -be called a _Phthongometer_. - -[Note 38\4: _Camb. Trans._ vol. iii. p. 239.] - -Our business at present, however, is not with instruments -which might be devised for measuring sensible qualities, but -with those which have been so used, and have thus been the -basis of the sciences in which {356} such qualities are -treated of; and this we have now done sufficiently for our -present purpose. - -24. There is another Idea which, though hitherto very -vaguely entertained, has had considerable influence in the -formation, both of the sciences spoken of in the present -Book, and on others which will hereafter come under our -notice: namely, the Idea of Polarity. This Idea will be the -subject of the ensuing Book. And although this Idea forms a -part of the basis of various other extensive portions of -science, as Optics and Chemistry, it occupies so peculiarly -conspicuous a place in speculations belonging to what I have -termed the Mechanico-Chemical Sciences, (Magnetism and -Electricity,) that I shall designate the discussion of the -Idea of Polarity as the Philosophy of those Sciences. - - - - -{{357}} -BOOK V. - - - -THE -PHILOSOPHY -OF THE -MECHANICO-CHEMICAL SCIENCES. - - - - -En donnant à ces côtés le nom de _poles_, j'appelerai -_polarisation_ la modification qui donne à la lumière des -propriétés relatives à ces poles. J'ai tardé jusqu'à présent -à admettre ce terme dans la description des phénomènes -physiques dont il est question; je n'ai pas osé l'introduire -dans les mémoires où j'ai publié mes dernières expériences; -mais les variétés qu'offre ce nouveau phénomène, et la -difficulté de les décrire, me forcent à admettre cette -nouvelle expression, qui signifie simplement la modification -que la lumière a subie en acquérant de nouvelles propriétés -qui ne sont pas relatives à la direction du rayon, mais -seulement à ses côtés considérés à angles droits et dans un -plan perpendiculaire à sa direction. - -Malus (1811), _Mém. de Inst._ tom. xi. p. 106. - - - -{{359}} -BOOK V. - - -THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES. - - -CHAPTER I. - -ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA OF -POLARITY. - - -1. IN some of the mechanical sciences, as Magnetism and -Optics, the phenomena are found to depend upon position (the -position of the magnet, or of the ray of light,) in a -peculiar alternate manner. This dependence, as it was first -apprehended, was represented by means of certain conceptions -of space and force, as for instance by considering the two -_Poles_ of a magnet. But in all such modes of representing -these alternations by the conceptions borrowed from other -ideas, a closer examination detected something superfluous -and something defective; and in proportion as the view which -philosophers took of this relation was gradually purified -from these incongruous elements, and was rendered more -general and abstract by the discovery of analogous -properties in new cases, it was perceived that the relation -could not be adequately apprehended without considering it -as involving a peculiar and independent Idea, which we may -designate by the term _Polarity_. - -We shall trace some of the forms in which this Idea has -manifested itself in the history of science. In doing so we -shall not begin, as in other Books of this work we have -done, by speaking of the notion as it is {360} employed in -common use: for the relation of Polarity is of so abstract -and technical a nature, that it is not employed, at least in -any distinct and obvious manner, on any ordinary or -practical occasions. The idea belongs peculiarly to the -region of speculation: in persons of common habits of -thought it is probably almost or quite undeveloped; and even -most of those whose minds have been long occupied by -science, find a difficulty in apprehending it in its full -generality and abstraction, and stript of all irrelevant -hypothesis. - -2. _Magnetism._--The name and the notion of _Poles_ were -first adopted in the case of a magnet. If we have two -magnets, their extremities attract and repel each other -alternatively. If the first end of the one attract the first -end of the other, it repels the second end, and conversely. -In order to express this rule conveniently, the two ends of -each magnet are called the _north pole_ and the _south pole_ -respectively, the denominations being borrowed from the -poles of the earth and heavens. 'These poles,' as Gilbert -says[1\5], 'regulate the motions of the celestial spheres -and of the earth. In like manner the magnet has its poles, a -northern and a southern one; certain and determined points -constituted by nature in the stone, the primary terms of its -motions and effects, the limits and governors of many -actions and virtues.' - -[Note 1\5: _De Magn._ lib. i. c. iii.] - -The nature of the opposition of properties of which we speak -may be stated thus: -The North pole of one magnet attracts the South pole of another -magnet. -The North pole of one magnet _repels_ the North pole of another -magnet. -The South pole of one magnet repels the South pole of another -magnet. -The South pole of one magnet _attracts_ the North pole of -another magnet. - -It will be observed that the contrariety of position which -is indicated by putting the South pole for the North pole in -either magnet, is accompanied by the {361} opposition of -mechanical effect which is expressed by changing attraction -into repulsion and repulsion into attraction: and thus we -have the general feature of Polarity,--A contrast of -properties corresponding to a contrast of positions. - -3. _Electricity._--When the phenomena of Electricity came to -be studied, it appeared that they involved relations in some -respects Analogous to those of magnetism. - -Two kinds of electricity were distinguished, the positive -and the negative; and it appeared that two bodies electrized -positively, or two electrized negatively, repelled each -other, like two north or two south magnetic poles; while a -positively and a negatively electrized body attracted each -other, like the north and south poles of two magnets. In -conductors of an oblong form, the electricity could easily -be made to distribute itself so that one end should be -positively and one end negatively electrized; and then such -conductors acted on each other exactly as magnets would do. - -But in conductors, however electrized, there is no peculiar -point which can permanently be considered as the _pole_. The -distribution of electricity in the conductor depends upon -external circumstances: and thus, although the phenomena -offer the general character of _polarity_--alternative -results corresponding to alternative positions,--they cannot -be referred to poles. Some other mode of representing the -forces must be adopted than that which makes them emanate -from permanent points as in a magnet. - -The phenomena of attraction and repulsion in electrized -bodies were conveniently represented by means of the -hypothesis of _two_ electric _fluids_, a positive and a -negative one, which were supposed to be distributed in the -bodies. Of these fluids, it was supposed that each repelled -its own parts and attracted those of the opposite fluid: and -it was found that this hypothesis explained all the obvious -laws of electric action. Here then we have the phenomena of -polarization explained by a new kind of machinery:--two -opposite fluids {362} distributed in bodies, and supplying -them, so to speak, with their polar forces. This hypothesis -not only explains electrical attraction, but also the -electrical spark: namely, thus: when two bodies, of which -the neighbouring surfaces are charged with the two opposite -fluids, approach near to each other, the mutual attraction -of the fluids becomes more and more intense, till at last -the excess of fluid on the one body breaks through the air -and rushes to the other body, in a form accompanied by light -and noise. When this transfer has taken place, the -attraction ceases, the positive and the negative fluid -having neutralized each other. Their effort was to unite; -and this union being effected, there is no longer any force -in action. Bodies in their natural unexcited condition may -be considered as occupied by a combination of the two -fluids: 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 kind. - -4. _Voltaic Electricity._--Such is the case in Franklinic -electricity,--that which is excited by the common electrical -machine. In studying Voltaic electricity, we are led to the -conviction that the fluid which is in a condition of -momentary _equilibrium_ in electrized conductors, exists in -the state of a _Current_ in the voltaic circuit. And here we -find polar relations of a new kind existing among the -forces. Two voltaic Currents _attract_ each other when they -are moving in the _same_, and _repel_ each other when they -are moving in _opposite_, directions. - -But we find, in addition to these, other polar relations of -a more abstruse kind, and which the supposition of two -fluids does not so readily explain. For instance, if such -fluids existed, distinct from each other, it might be -expected that it would be possible to exhibit one of them -separate from the other. Yet in all the phenomena of -electromotive currents, we attempt in vain to obtain one -kind of electricity separately. 'I have not,' says Mr. -Faraday[2\5], 'been able to find a {363} single fact which -could be adduced to prove the theory of two electricities -rather than one, in electric currents; or, admitting the -hypothesis of two electricities, have I been able to -perceive the slightest grounds that one electricity can be -more powerful than the other, or that it can be present -without the other, or that it can be varied or in the -slightest degree affected without a corresponding variation -in the other.' 'Thus,' he adds, 'the polar character of the -powers is rigorous and complete.' Thus, we too may remark, -all the superfluous and precarious parts gradually drop off -from the hypothesis which we devise in order to represent -polar phenomena; and the abstract notion of Polarity--of -equal and opposite powers called into existence by a common -condition--remains unincumbered with extraneous machinery. - -[Note 2\5: _Researches_, 516.] - -5. _Light._--Another very important example of the -application of the Idea of Polarity is that supplied by the -discovery of the polarization of light. A ray of light may, -by various processes, be modified, so that it has different -properties according to its different _sides_, although this -difference is not perceptible by any common effects. If, for -instance, a ray thus modified, pass perpendicularly through -a circular glass, and fall upon the eye, we may turn the -glass round and round in its frame, and we shall make no -difference in the brightness of the spot which we see. But -if, instead of a glass, we look through a longitudinal slice -of tourmaline, the spot is alternately dark and bright as we -turn the crystal through successive quadrants. Here we have -a contrast of Properties (dark and bright) corresponding to -a contrast of positions, (the position of a line east and -west being contrasted with the position north and south,) -which, as we have said, is the general character of -Polarity. It was with a view of expressing this character -that the term _Polarization_ was originally introduced. -Malus was forced by his discoveries into the use of this -expression. 'We find,' he says, in 1811, 'that light -acquires properties which are relative only to the sides of -the ray,--which are the same for the north and south sides -of the ray, (using {364} the points of the compass for -description's sake only,) and which are different when we go -from the north and south to the east or to the west sides of -the ray. I shall give the name of _poles_ to these sides of -the ray, and shall call _polarization_ the modification -which gives to light these properties relative to these -poles. I have _put off_ hitherto the admission of this term -into the description of the physical phenomena with which we -have to do: I did not _dare_ to introduce it into the -Memoirs in which I published my last observations: but the -variety of forms in which this new phenomenon appears, and -the difficulty of describing them, compel me to admit this -new expression; which signifies simply the modification -which light has undergone in acquiring new properties which -are not relative to the direction of the ray, but only to -its sides considered at right angles to each other, and in a -plane perpendicular to its direction.' - -The theory which represents light as an emission of -particles was in vogue at the time when Malus published his -discoveries; 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 light. On this hypothesis, light would be -polarized when the axes of all the particles were in the -same direction: and, making such a supposition, it may -easily be conceived capable of transmission through a -crystal whose axis is parallel to that of the luminous -particles, and intransmissible when the axis of the crystal -is in a position transverse to that of the particles. - -The hypothesis of particles possessing _poles_ is a rude and -arbitrary assumption, in this as in other cases; but it -serves to convey the general notion of polarity, which is -the essential feature of the phenomena. The term -'polarization of light has sometimes been complained of in -modern times as hypothetical and obscure. But the real cause -of obscurity was, that the Idea of Polarity was, till -lately, very imperfectly developed in men's minds. As we -have seen, the general notion of Polarity,--opposite -properties in opposite {365} directions,--exactly describes -the character of the optical phenomena to which the term is -applied. - -It is to be recollected that in optics we never speak of the -_poles_, but of the _plane of polarization_ of a ray. The -word _sides_, which Newton and Malus have used, neither of -them appears to have been satisfied with; Newton, in -employing it, had recourse to the strange Gallicism of -speaking of the _coast_ of usual and of unusual refraction -of a crystal. - -The modern theory of optics represents the plane of -polarization of light as depending, not on the position in -which the axes of the luminiferous particles lie, but on the -_direction_ of those _transverse vibrations_ in which light -consists. This theory is, as we have stated in the History, -recommended by an extraordinary series of successes in -accounting for the phenomena. And this hypothesis of -transverse vibrations shows us another mechanical mode, -(besides the hypothesis of particles with axes,) by which we -may represent the polarity of a ray. But we may remark that -the general notion of Polarity, as applied to light in such -cases, would subsist, even if the undulatory theory were -rejected. The idea is, as we have before said, independent -of all hypothetical machinery. - -I need not here refer to the various ways in which light may -be polarized; as, for instance, by being reflected from the -surface of water, or of glass, at certain angles, by being -transmitted, through crystals, and in other ways. In all -cases the modification produced, the polarization, is -identically the same property. Nor need I mention the -various kinds of phenomena which appear as contrasts in the -result; for these are not merely light and dark, or white -and black, but red and green, and generally, a colour and -its _complementary_ colour, exhibited in many complex and -varied configurations. These multiplied modes in which -polarized light presents itself add nothing to the original -conception of Polarization: and I shall therefore pass on to -another subject. - -6. _Crystallization._--Bodies which are perfectly -crystallized exhibit the most complete regularity and {366} -symmetry of form; and this regularity not only appears in -their outward shape, but pervades their whole texture, and -manifests itself in their cleavage, their transparency, and -in the uniform and determinate optical properties which -exist in every part, even in the smallest fragment of the -mass. If we conceive crystals as composed of particles, we -must suppose these particles to be arranged in the most -regular manner; for example, if we suppose each particle to -have an axis, we must suppose all these axes to be parallel; -for the direction of the axis of the particles is indicated -by the physical and optical properties of the crystal, and -therefore this direction must be the same for every portion -of the crystal. This parallelism of the axes of the -particles may be conceived to result from the circumstance -of each particle having poles, the opposite poles attracting -each other. In virtue of forces acting as this hypothesis -assumes, a collection of small _magnetic_ particles would -arrange themselves in parallel positions; and such a -collection of magnetic particles offers a sort of image of a -crystal. Thus we are led to conceive the particles of -crystals as polarized, and as determined in their -crystalline positions by polar forces. This mode of -apprehending the constitution of crystals has been adopted -by some of our most eminent philosophers. Thus Berzelius -says[3\5], 'It is demonstrated, that the regular forms of -bodies presuppose an effort of their atoms to touch each -other by preference in certain points; that is, they are -founded upon a Polarity;'--he adds, 'a polarity which can be -no other than an electric or magnetic polarity.' In this -latter clause we have the identity of different kinds of -polarity asserted; a principle which we shall speak of in -the next chapter. But we may remark, that even without -dwelling upon this connexion, any notion which we can form -of the structure of Crystals necessarily involves the idea -of Polarity. Whether this polarity necessarily requires us -to believe crystals to be composed of Atoms which exert an -effort to touch {367} each other in certain points by -preference, is another question. And, in agreement with what -has been said respecting other kinds of polarity, we shall -probably find, on a more profound examination of the -subject, that while the Idea of Polarity is essential, the -machinery by which it is thus expressed is precarious and -superfluous. - -[Note 3\5: _Essay on the Theory of Chemical Properties_, -1820, p. 113.] - -7. _Chemical Affinity._--We shall have, in the next Book, to -speak of Chemical Affinity at some length; but since the -ultimate views to which philosophers have been led, induce -them to consider the forces of Affinity as Polar Forces, we -must enumerate these among the examples of Polarity. In -chemical processes, opposites tend to unite, and to -neutralize each other by their union. Thus an _acid_ or an -_alkali_ combine with vehemence, and form a compound, a -neutral salt, which is neither acid nor alkaline. - -This conception of contrariety and mutual neutralization, -involves the Idea of Polarity. In the conception as -entertained by the earlier chemists, the Idea enters very -obscurely: but in the attempts which have more recently been -made to connect this relation (of acid and base), with other -relations, the chemical elements have been conceived as -composed of particles which possess poles; _like_ poles -repelling, and _unlike_ attracting each other, as they do in -magnetic and electric phenomena. This is, however, a rude -and arbitrary way of expressing Polarity, and, as may be -easily shown, involves many difficulties which do not belong -to the Idea itself. Mr. Faraday, who has been led by his -researches to a conviction of the polar nature of the forces -of chemical affinity, has expressed their character in a -more general manner, and without any of the machinery of -particles indued with poles. According to his view, chemical -synthesis and analysis must always be conceived as taking -place in virtue of equal and opposite forces, by which the -particles are united or separated. These forces, by the very -circumstance of their being polar, may be transferred from -point to point. For if we conceive a string of particles, -and if the positive force of the first particle {368} be -liberated and brought into action, its negative force also -must be set free: this negative force neutralizes the -positive force of the next particle, and therefore the -negative force of this particle (before employed in -neutralizing its positive force) is set free: this is in the -same way transferred to the next particle, and so on. And -thus we have a positive force active at one extremity of a -line of particles, corresponding to a negative force at the -other extremity, all the intermediate particles reciprocally -neutralizing each other's action. This conception of the -transfer of chemical action was indeed at an earlier period -introduced by Grotthus[4\5], and confirmed by Davy. But in -Mr. Faraday's hands we see it divested of all that is -superfluous, and spoken of, not as a line of particles, but -as 'an axis of power, having [at every point] contrary -forces, exactly equal, in opposite directions.' - -[Note 4\5: DUMAS, _Leçons sur la Philosophie Chimique_, p. 401.] - -8. _General Remarks._--Thus, as we see, the notion of -Polarity is applicable to many large classes of phenomena. -Yet the Idea in a distinct and general form is only of late -growth among philosophers. It has gradually been abstracted -and refined from many extraneous hypotheses which were at -first supposed to be essential to it. We have noticed some -of these hypotheses;--as the poles of a _body_; the poles of -the _particles_ of a fluid; _two_ opposite fluids; a single -fluid in _excess_ and _defect_; transverse _vibrations_. To -these others might be added. Thus Dr. Prout[5\5] assumes -that the polarity of molecules results from their _rotation_ -on their axes, the opposite motions of contiguous molecules -being the cause of opposite (positive and negative) -polarities. - -[Note 5\5: _Bridgewater Treatise_, p. 559.] - -But none of these hypotheses can be proved by the fact of -Polarity alone; and they have been in succession rejected -when they had been assumed on that ground. Thus Davy, in -1826, speaking of chemical forces says[6\5], 'In assuming -the idea of two ethereal, subtile, elastic {369} fluids, -attractive of the particles of each other, and repulsive as -to their own particles, capable of combining in different -proportions with bodies, and according to their proportions -giving them their specific qualities and rendering them -equivalent masses, it would be natural to refer the action -of the poles to the repulsions of the substances combined -with the excess of one fluid, and the attractions of those -united to the excess of the other fluid; and a history of -the phenomena, not unsatisfactory to the reason, might in -this way be made out. But as it is possible likewise to take -an entirely different view of the subject, on the idea of -the dependence of the results upon the primary attractive -powers of the parts of the combination on a single subtile -fluid, I shall not enter into any discussion on this obscure -part of the theory.' Which of these theories will best -represent the case, will depend upon the consideration of -other facts, in combination with the polar phenomena, as we -see in the history of optical theory. In like manner Mr. -Faraday proved by experiment[7\5] the errour of all theories -which ascribe electro-chemical decomposition to the -attraction of the poles of the voltaic battery. - -[Note 6\5: _Phil. Tr._ 1826, p. 415.] - -[Note 7\5: _Researches_, p. 495, &c.] - -In order that they may distinctly image to themselves the -Idea of Polarity, men clothe it in some of the forms of -machinery above spoken of; yet every new attempt shows them -the unnecessary difficulties in which they thus involve -themselves. But on the other hand it is difficult to -apprehend this Idea divested of all machinery; and to -entertain it in such a form that it shall apply at the same -time to magnetism and electricity, galvanism and chemistry, -crystalline structure and light. The Idea of _Polarity_ -becomes most pure and genuine, when we entirely reject the -conception of _Poles_, as Faraday has taught us to do in -considering electro-chemical decomposition; but it is only -by degrees and by effort that we can reach this point of -abstraction and generality. {370} - -9. There is one other remark which we may here make. It was -a maxim commonly received in the ancient schools of -philosophy, that 'Like attracts Like:' but as we have seen, -the universal maxim of Polar Phenomena is, that Like -_repels_ Like, and attracts Unlike. The north pole attracts -the south pole, the positive fluid attracts the negative -fluid; opposite elements rush together; opposite motions -reduce each other to rest. The permanent and stable course -of things is that which results from the balance and -neutralization of contrary tendencies. Nature is constantly -labouring after repose by the effect of such tendencies; and -so far as Polar Forces enter into her economy, she seeks -harmony by means of discord, and unity by opposition. - -Although the Idea of Polarity is as yet somewhat vague and -obscure, even in the minds of the cultivators of physical -science, it has nevertheless given birth to some general -principles which have been accepted as evident, and have had -great influence on the progress of science. These we shall -now consider. - - - -{{371}} -CHAPTER II. - -OF THE CONNEXION OF POLARITIES. - - -1. IT has appeared in the preceding chapter that in cases in -which the phenomena suggest to us the idea of Polarity, we -are also led to assume some material machinery as the mode -in which the polar forces are exerted. We assume, for -instance, globular particles which possess poles, or the -vibrations of a fluid, or two fluids attracting each other; -in every case, in short, some hypothesis by which the -existence and operation of the Polarity is embodied in -geometrical and mechanical properties of a medium; nor is it -possible for us to avoid proceeding upon the conviction that -some such hypothesis must be true; although the nature of -the connexion between the mechanism and the phenomena must -still be indefinite and arbitrary. - -But since each class of Polar Phenomena is thus referred to -an ulterior cause, of which we know no more than that it has -a polar character, it follows that _different_ Polarities -may result from the _same_ cause manifesting its polar -character under different aspects. Taking, for example, the -hypothesis of globular particles, if electricity result from -an action dependent upon the _poles_ of each globule, -magnetism may depend upon an action in the _equator_ of each -globule; or taking the supposition of transverse vibrations, -if polarized light result directly from such _vibrations_, -crystallization may have reference to the _axes_ of the -elasticity of the _medium_ by which the vibrations are -rendered transverse,--so far as the polar character only of -the phenomena is to be accounted for. I say this _may_ be -so, _in so far_ only as the polar character of the phenomena -is concerned; for whether the relation of {372} electricity -to magnetism, or of crystalline forces to light, can really -be explained by such hypotheses, remains to be determined by -the facts themselves. But since the first necessary feature -of the hypothesis is, that it shall give polarity, and since -an hypothesis which does this, may, by its mathematical -relations, give polarities of different kinds and in -different directions, any two co-existent kinds of polarity -may result from the same cause, manifesting itself in -various manners. - -The conclusion to which we are led by these general -considerations is, that two co-existing classes of polar -phenomena _may_ be effects of the same cause. But those who -have studied such phenomena more deeply and attentively -have, in most or in all cases, arrived at the conviction -that the various kinds of Polarity in such cases _must_ be -connected and fundamentally identical. As this conviction -has exercised a great influence, both upon the discoveries -of new facts and upon the theoretical speculations of modern -philosophers, and has been put forward by some writers as a -universal principle of science, I will consider some of the -cases in which it has been thus applied. - -2. _Connexion of Magnetic and Electric Polarity._--The polar -phenomena of electricity and magnetism are clearly analogous -in their laws: and obvious facts showed at an early period -that there was some connexion between the two agencies. -Attempts were made to establish an evident and definite -relation between the two kinds of force, which attempts -proceeded upon the principle now under -consideration;--namely, that in such cases, the two kinds of -Polarity must be connected. Professor Œrsted, of Copenhagen, -was one of those who made many trials founded upon this -conviction: yet all these were long unsuccessful. At length, -in 1820, he discovered that a galvanic current, passing at -right angles near to a magnetic needle, exercises upon it a -powerful deflecting force. The connexion once detected -between magnetism and galvanism was soon recognized as -constant and universal. It was represented in different -hypothetical modes by different persons; some considering -the galvanic {373} current as the primitive axis, and the -magnet as constituted of galvanic currents passing round it -at right angles to the magnetic axis; while others conceived -the magnetic axis as the primitive one, and the electric -current as implying a magnetic current round the wire. So -far as many of the general relations of these two kinds of -force were concerned, either mode of representation served -to express them; and thus the assumption that the two -Polarities, the magnetic and the electric, were -fundamentally identical, was verified, so far as the -phenomena of magnetic attraction, and the like, were -concerned. - -I need not here mention how this was further confirmed by -the experiments in which, by means of the forces thus -brought into view, a galvanic wire was made to revolve round -a magnet, and a magnet round a galvanic wire;--in which -artificial magnets were constructed of coils of galvanic -wire;--and finally, in which the galvanic spark was obtained -from the magnet. The identity which sagacious speculators -had divined even before it was discovered, and which they -had seen to be universal as soon as it was brought to light, -was completely manifested in every imaginable form. - -The relation of the electric and magnetic Polarities was -found to be, that they were _transverse_ to each other, and -this relation exhibited under various conditions of form and -position of the apparatus, gave rise to very curious and -unexpected perplexities. The degree of complication which -this relation may occasion, may be judged of from the number -of constructions and modes of conception offered by Œrsted, -Wollaston, Faraday, and others, for the purpose of framing a -technical memory of the results. The magnetic polarity gives -us the north and south poles of the needle; the electric -polarity makes the current positive and negative; and these -pairs of opposites are connected by relations of situation, -as above and below, right and left; and give rise to the -resulting motion of the needle one way or the other. {374} - -3. Ampère, by framing his hypotheses of the action of -voltaic currents and the constitution of magnets, reduced -all these technical rules to rigorous deductions from one -general principle. And thus the vague and obscure persuasion -that there _must_ be _some_ connexion between Electricity -and Magnetism, so long an idle and barren conjecture, was -unfolded into a complete theory, according to which magnetic -and electromotive actions are only two different -manifestations of the same forces; and all the -above-mentioned complex relations of polarities are reduced -to one single polarity, that of the electro-dynamic current. - -4. As the Idea of Polarity was thus firmly established and -clearly developed, it became an instrument of reasoning. -Thus it led Ampère to maintain that the original or -elementary forces in electro-dynamic action could not be as -M. Biot thought they were, a statical _couple_, but must be -directly opposite to each other. The same idea enabled Mr. -Faraday to carry on with confidence such reasonings as the -following[8\5]: 'No other known power has like direction -with that exerted between an electric current and a magnetic -pole; it is tangential, while all other forces acting at a -distance are direct. 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 caused; a -similar pole on the other side of the plate should -immediately set it free from this force; for the currents -which have to be formed by the two poles are in contrary -directions.' And in Article 1114 of his _Researches_, the -same eminent philosopher infers that if electricity and -magnetism are considered as the results of a peculiar agent -or condition, exerted in determinate directions -perpendicular to each other, one must be by some means -convertible into the other; and this he was afterwards able -to prove to be the case in fact. - -[Note 8\5: _Researches_, 244.] - -{375} Thus the principle that the Co-existent Polarities of -magnetism and electricity are connected and fundamentally -identical, is not only true, but is far from being either -vague or barren. It has been a fertile source both of -theories which have, at present, a very great probability, -and of the discovery of new and striking facts. We proceed -to consider other similar cases. - -5. _Connexion of Electrical and Chemical Polarities._--The -doctrine that the chemical forces by which the elements of -bodies are held together or separated, are identical with -the polar forces of electricity, is a great discovery of -modern times; so great and so recent, indeed, that probably -men of science in general have hardly yet obtained a clear -view and firm hold of this truth. This doctrine is now, -however, entirely established in the minds of the most -profound and philosophical chemists of our time. The -complete development and confirmation of this as of other -great truths, was preceded by more vague and confused -opinions gradually tending to this point; and the progress -of thought and of research was impelled and guided, in this -as in similar cases, by the persuasion that these -co-existent polarities could not fail to be closely -connected with each other. While the ultimate and exact -theory to which previous incomplete and transitory theories -tended is still so new and so unfamiliar, 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 point. I shall, therefore, in doing this, guide myself -mainly by the historical sketches of the progress of this -great theory, which, fortunately for us, have been given us -by the two philosophers who have played by far the most -important parts in the discovery, Davy and Faraday. - -It will be observed that we are concerned here with the -progress of theory, and not of experiment, except so far as -it is confirmatory of theory. In Davy's Memoir[9\5] of 1826, -on the Relations of Electrical and {376} Chemical Changes, -he gives the historical details to which I have alluded. -Already in 1802 he had conjectured that all chemical -decompositions might be polar. In 1806 he attempted to -confirm this conjecture, and succeeded, to his own -satisfaction, in establishing[10\5] that the combinations -and decompositions by electricity were referable to the law -of electrical attractions and repulsions; and advanced the -hypothesis (as he calls it), that chemical and electrical -attractions were produced by the same cause, acting in one -case on particles, in the other on masses. 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 applied. -'Believing,' he adds, 'that our philosophical systems are -exceedingly imperfect, I never attached much importance to -this hypothesis; but having formed it after a copious -induction of facts, and having gained by the application of -it a number of practical results, and considering myself as -much the author of it as I was of the decomposition of the -alkalies, and having developed it in an elementary work as -far as the present state of chemistry seemed to allow, I -have never,' he says, 'criticised or examined the manner in -which different authors have adopted or explained it, -contented, if in the hands of others, it assisted the -arrangements of chemistry or mineralogy, or became an -instrument of discovery.' When the doctrine had found an -extensive acceptance among chemists, attempts were made to -show that it had been asserted by earlier writers: and -though Davy justly denies all value to these pretended -anticipations, they serve to show, however dimly, the -working of that conviction of the Connexion of Co-existent -Properties which all along presided in men's minds during -this course of investigation. 'Ritter and Winterl have been -quoted,' Davy says[11\5], 'among other persons, as having -imagined or anticipated the relation between electrical -powers and chemical affinities before the discovery of the -pile {377} of Volta. But whoever will read with attention -Ritter's "Evidence that Galvanic action exists in organised -nature," and **Winterl's _Prolusiones ad Chemiam sæculi decimi -noni_, will find nothing to justify this opinion.' He then -refers to the Queries of Newton at the end of his Optics. -'These,' he says, 'contain more grand and speculative views -that might be brought to bear upon this question than any -found in the works of modern electricians; but it is very -unjust to the experimentalists who by the laborious -application of new instruments, have discovered novel facts -and analogies, to refer them to any such suppositions as -that all attractions, chemical, electrical, magnetical, and -gravitative, may depend upon the same cause.' It is -perfectly true, that such vague opinions, though arising -from that tendency to generalize which is the essence of -science, are of no value except so far as they are both -rendered intelligible, and confirmed by experimental -research. - -[Note 9\5: _Phil. Trans._ 1826, p. 383.] - -[Note 10\5: _Phil. Trans._ 1826, p. 389.] - -[Note 11\5: _Ibid._ p. 384.] - -The phenomena of chemical decomposition by means of the -voltaic pile, however, led other persons to views very -similar to those of Davy. Thus Grotthus in 1805[12\5] -published an hypothesis of the same kind. 'The pile of -Volta,' he says, 'is an electrical magnet, of which each -element, that is, each pair of plates, has a positive and a -negative pole. 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 agent; and I avow that this thought was -for me a flash of light.' - -[Note 12\5: _Ann. Chim._ lxviii. 54.] - -6. The thought, however, though thus brought into being, was -very far from being as yet freed from vagueness, -superfluities, and errours. I have elsewhere noticed[13\5] -Faraday's remark on Davy's celebrated Memoir of 1806; that -'the mode of action by which the effects take place is -stated very generally, so generally, indeed, that probably a -dozen precise schemes of electro-chemical action might be -drawn up, differing {378} essentially from each other, yet -all agreeing with the statement there given.' When Davy and -others proceeded to give a little more definiteness and -precision to the statement of their views, they soon -introduced into the theory features which it was afterwards -found necessary to abandon. Thus[14\5] both Davy, Grotthus, -Riffault, and Chompré, ascribed electrical decomposition to -the action of the _poles_, and some of them even pretended -to assign the proportion in which the force of the pole -diminishes as the distance from it increases. Faraday, as I -have already stated, showed that the polarity must be -considered as residing not only in what had till then been -called the _poles_, but at every point of the circuit. He -ascribed[15\5] electro-chemical decomposition to internal -forces, residing in the _particles_ of the matter under -decomposition, not to external forces, exerted by the poles. -Hence he shortly afterwards[16\5] proposed to reject the -word _poles_ altogether, and to employ instead, the term -_electrode_, meaning the doors or passages (of whatever -surface formed) by which the decomposed elements pass out. -What have been called the _positive_ and _negative_ poles he -further termed the _Anode_ and _Cathode_; and he introduced -some other changes in nomenclature connected with these. He -then, as I have related in the History[17\5], invented the -Volta-electrometer, which enabled him to measure the -quantity of voltaic action, and this he found to be -identical with the quantity of chemical affinity; and he was -thus led to the clearest view of the truth towards which he -and his predecessors had so long been travelling, that -electrical and chemical forces are identical[18\5]. - -[Note 13\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 1.] - -[Note 14\5: See Faraday's Historical Sketch, _Researches_, -481-492.] - -[Note 15\5: Art. 524.] - -[Note 16\5: In 1834. Eleventh Series of Researches. Art. 662.] - -[Note 17\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 2.] - -[Note 18\5: Arts. 915, 916, 917.] - -7. It will, perhaps, be said that this beautiful train of -discovery was entirely due to experiment, and not to any _à -priori_ conviction that co-existent polarities {379} must be -connected. I trust I have sufficiently stated that such an -_à priori_ principle could not be proved, nor even -understood, without a most laborious and enlightened use of -experiment; but yet I think that the doctrine, when once -fully unfolded, exhibited clearly, and established as true, -takes possession of the mind with a more entire conviction -of its certainty and universality, in virtue of the -principle we are now considering. When the theory has -assumed so simple a form, it appears to derive immense -probability (to say the least) from its simplicity. Like the -laws of motion, when stated in its most general form, it -appears to carry with it its own evidence. And thus this -great theory borrows something of its character from the -Ideas which it involves, as well as from the Experiments by -which it was established. - -8. We may find in many of Mr. Faraday's subsequent -reasonings, clear evidence that this idea of the Connexion -of Polarities, as now developed, is not limited in its -application to facts already known experimentally, but, like -other ideas, determines the philosopher's researches into -the unknown, and gives us the _form_ of knowledge even -before we possess the _matter_. Thus, he says, in his -Thirteenth Series[19\5], 'I have long sought, and still -seek, for an effect or condition which shall be to statical -electricity what magnetic force is to current electricity; -for as the lines of discharge are associated with a certain -transverse effect, so it appeared to me impossible but that -the lines of tension or of inductive action, which of -necessity precede the discharge, should also have their -correspondent transverse condition or effect.' Other similar -passages might be found. - -[Note 19\5: Art. 1658.] - -I will now consider another case to which we may apply the -Principle of Connected Polarities. - -9. _Connexion of Chemical and Crystalline Polarities._--The -close connexion between the Chemical Affinity and the -Crystalline Attraction of elements cannot be overlooked. -Bodies never crystallize but when their elements combine -chemically; and solid bodies which {380} combine, when they -do it most completely and exactly, also crystallize. The -forces which _hold together_ the elements of a crystal of -alum are the same forces which make it a _crystal_. There is -no distinguishing between the two sets of forces. - -Both _chemical_ and _crystalline_ forces are _polar_, as we -stated in the last chapter; but the polarity in the two -cases is of a different kind. The polarity of chemical -forces is then put in the most distinct form, when it is -identified with electrical polarity; the polarity of the -particles of crystals has reference to their geometrical -form. And it is clear that these two kinds of polarity must -be connected. Accordingly, Berzelius expressly asserts[20\5] -the necessary identity of these two polarities. 'The regular -forms of bodies suppose a polarity which _can be_ no other -than an electric or magnetic polarity.' This being so -seemingly inevitable, we might expect to find the electric -forces manifesting some relation to the definite directions -of crystalline forms. Mr. Faraday tried, but in vain, to -detect some such relation. He attempted to ascertain[21\5] -whether a cube of rock crystal transmitted the electrical -force of tension with different intensity along and across -the axis of the crystal. In the first specimen there seemed -to be some difference; but in other experiments, made both -with rock crystal and with calc spar, this difference -disappeared. Although therefore we may venture to assert -that there must be some very close connexion between -electrical and crystalline forces, we are, as yet, quite -ignorant what the nature of the connexion is, and in what -kind of phenomena it will manifest itself. - -[Note 20\5: _Essay on Chemical Prop._ 113.] - -[Note 21\5: _Researches_. Art. 1689.] - -10. _Connexion of Crystalline and Optical -Polarities._--Crystals present to us _optical_ phenomena -which have a manifestly polar character. The double -refraction, both of uniaxal and of biaxal crystals, is -always accompanied with opposite polarization of the two -rays; and in this and in other ways light is polarized in -directions dependent upon the axes of the crystalline form, -that is, on the directions of the polarities of the {381} -crystalline particles. The identity of these two kinds of -polarity (crystalline and optical) is too obvious to need -insisting on; and it is not necessary for us here to decide -by what hypothesis this identity may most properly be -represented. 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 crystal, and -thus as determining the refraction and polarization of the -light which the crystal transmits. But at present we merely -note this case as an additional example of the manifest -connexion and fundamental identity of two co-existent -polarities. - -11. _Connexion of Polarities in general._--Thus we find that -the Connexion of different kinds of Polarities, magnetic, -electric, chemical, crystalline, and optical, is certain as -a truth of experimental science. We have attempted to show -further that in the minds of several of the most eminent -discoverers and philosophers, such a conviction is something -more than a mere empirical result: it is a principle which -has regulated their researches while it was still but -obscurely seen and imperfectly unfolded, and has given to -their theories a character of generality and self-evidence -which experience alone cannot bestow. - -It will, perhaps, be said that these doctrines,--that -scientific researches may usefully be directed by principles -in themselves vague and obscure;--that theories may have an -evidence superior to and anterior to experience;--are -doctrines in the highest degree dangerous, and utterly at -variance with the soundest maxims of modern times respecting -the cultivation of science. - -In the justice and wisdom of this caution I entirely agree: -and although I have shown that this principle of the -_Connexion of Polarities_, rightly interpreted and -established in each case by experiment, involves profound -and comprehensive truths; I think it no less important to -remark that, at least in the present stage of our knowledge, -we can make no use of this principle without taking care, at -every step, to determine by {382} clear and decisive -experiments, its proper meaning and application. All -endeavours to proceed otherwise have led, and must lead, to -ignorance and confusion. Attempts to deduce from our bare -Idea of Polarity, and our fundamental convictions respecting -the connexion of polarities, theories concerning the forces -which really exist in nature, can hardly have any other -result than to bewilder men's minds, and to misdirect their -efforts. - -So far, indeed, as this persuasion of a connexion among -apparently different kinds of agencies, impels men, engaged -in the pursuit of knowledge, to collect observations, to -multiply, repeat, and vary experiments, and to contemplate -the result of these in all aspects and relations, it may be -an occasion of the most important discoveries. Accordingly -we find that the great laws of phenomena which govern the -motions of the planets about the sun, were first discovered -by Kepler, in consequence of his scrutinizing the recorded -observations with an intense conviction of the existence of -geometrical and arithmetical harmonies in the solar system. -Perhaps we may consider the discovery of the connexion of -magnetism and electricity by Professor Œrsted in 1820, as an -example somewhat of the same kind; for he also was a -believer in certain comprehensive but undefined relations -among the properties of bodies; and in consequence of such -views entertained great admiration for the _Prologue to the -Chemistry of the Nineteenth Century_, of Winterl, already -mentioned. M. Œrsted, in 1803, published a summary of this -work; and in so doing, praised the views of Winterl as far -more profound and comprehensive than those of Lavoisier. -Soon afterwards a Review of this publication appeared in -France[22\5], in which it was spoken of as a work only fit -for the dark ages, and as the indication of a sect which had -for some time 'ravaged Germany,' and inundated that country -with extravagant and unintelligible mysticism. It was, -therefore, a kind of triumph to M. Œrsted to be, after {383} -some years' labour, the author of one of the most remarkable -and fertile physical discoveries of his time. - -[Note 22\5: _Ann. Chim._, Tom. 1. (1804), p. 191.] - -12. It was not indeed without some reason that certain of -the German philosophers were accused of dealing in doctrines -vast and profound in their aspect, but, in reality, -indefinite, ambiguous, and inapplicable. And the most -prominent of such doctrines had reference to the principle -now under our consideration; they represented the properties -of bodies as consisting in certain polarities, and professed -to deduce, from the very nature of things, with little or no -reference to experiment, the existence and connexion of -these polarities. Thus Schelling, in his _Ideas towards a -Philosophy of Nature_, published in 1803, says[23\5], -'Magnetism is the universal act of investing Multiplicity -with Unity; but the universal form of the reduction of -Multiplicity to Unity is the Line, pure Longitudinal -Extension: hence Magnetism is determination of pure -Longitudinal Extension; and as this manifests itself by -absolute Cohesion, Magnetism is the determination of -absolute Cohesion.' And as Magnetism was, by such reasoning, -conceived to be proved as a universal property of matter, -Schelling asserted it to be a confirmation of his views when -it was discovered that other bodies besides iron are -magnetic. In like manner he used such expressions as the -following[24\5]: 'The threefold character of the Universal, -the Particular, and the Indifference of the two,--as -expressed in their Identity, is Magnetism, as expressed in -their Difference, is Electricity, and as expressed in the -Totality, is Chemical Process. Thus these forms are only one -form; and the Chemical Process is a mere transfer of the -three Points of Magnetism into the Triangle of Chemistry.' - -[Note 23\5: P. 223.] - -[Note 24\5: P. 486.] - -It was very natural that the chemists should refuse to -acknowledge, in this fanciful and vague language, -(delivered, however, it is to be recollected, in 1803,) an -anticipation of Davy's doctrine of the identity of -electrical and chemical forces, or of Œrsted's {384} -electro-magnetic agency. 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 doctrines. Accordingly we find Schelling -welcoming, with a due sense of their importance, the -discoveries of Faraday. When he heard of the experiment in -which electricity was produced from common magnetism, he -fastened with enthusiasm upon the discovery, even before he -knew any of its details, and proclaimed it at a public -meeting of a scientific body[25\5] as one of the most -important advances of modern science. We have (he thus -reasoned) three effects of polar forces;--Electro-chemical -Decomposition, Electrical Action, Magnetism. Volta and Davy -had confirmed experimentally the identity of the two former -agencies: Œrsted showed that a closed voltaic circuit -acquired magnetic properties: but in order to exhibit the -identity of electric and magnetic action it was requisite -that electric forces should be extricated from magnetic. -This great step Faraday, he remarked, had made, in producing -the electric spark by means of magnets. - -[Note 25\5: Ueber Faraday's _Neueste Entdeckung_. München. 1832.] - -13. Although conjectures and assertions of the kind thus put -forth by Schelling involve a persuasion of the pervading -influence and connexion of polarities, which persuasion has -already been confirmed in many instances, they involve this -principle in a manner so vague and ambiguous that it can -rarely, in such a form, be of any use or value. Such views -of polarity can never teach us in what cases we are and in -what we are not expected to find polar relations; and indeed -tend rather to diffuse error and confusion, than to promote -knowledge. 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 science. -This is done by the celebrated metaphysician Hegel, in his -_Encyclopædia_[26\5]. 'Since,' {385} says he, 'the plane of -incidence and of reflection in simple reflection is the same -plane, when a second reflector is introduced which further -distributes the illumination reflected from the first, the -position of the first plane with respect to the second -plane, containing the direction of the first reflection and -of the second, has its influence upon the position, -illumination or darkening of the object as it appears by the -second reflection. This influence must be the strongest when -the two planes are what we must call _negatively_ related to -each other:--that is, when they are at right angles.' 'But,' -he adds, 'when men infer (as Malus has done) from the -modification which is produced by this situation, in the -illumination of the reflection, that the molecules of light -in themselves, that is, on their different sides, possess -different physical energies; and when on this foundation, -along with the phenomena of entoptical colours therewith -connected, a wide labyrinth of the most complex theory is -erected; we have then one of the most remarkable examples of -the _inferences_ of physics from experiment.' If Hegel's -reasoning prove anything, it must prove that polarization -always accompanies reflection under such circumstances as he -describes: yet all physical philosophers know that in the -case of metals, in which the reflection is most complete, -light is not completely polarized at any angle; 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 property. His -self-complacent remark about the inferences of physics from -experiment, is intended to recommend by comparison his own -method of considering the nature of 'things in themselves;' -a mode of obtaining physical truth which had been more than -exhausted by Aristotle, and out of which no new attempts -have extracted anything of value since his time. - -[Note 26\5: Sec. 278.] - -14. Thus the general conclusion to which we are led on this -subject, is, that the persuasion of the existence and -Connexion or Identity of various Polarities in nature, -although very naturally admitted, and in many {386} cases -interpreted and confirmed by observed facts, is of itself, -so far as we at present possess it, a very insecure guide to -scientific doctrines. When it is allowed to dictate our -theories, instead of animating and extending our -experimental researches, it leads only to errour, confusion, -obscurity, and mysticism. - -This Fifth Book, on the subject of Polarities, is a short -one compared with most of the others. This arises in a great -measure from the circumstance that the Idea of Polarity has -only recently been apprehended and applied, with any great -degree of clearness, among physical philosophers; and is -even yet probably entertained in an obscure and ambiguous -manner by most experimental inquirers. I have been desirous -of not attempting to bring forward any doctrines upon the -subject, except such as have been fully illustrated and -exemplified by the acknowledged progress of the physical -sciences. If I had been willing to discuss the various -speculations which have been published respecting the -universal prevalence of Polarities in the universe, and -their results in every province of nature, I might easily -have presented this subject in a more extended form; 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 truths. -And as the influence of this Idea is clearly distinguishable -both from those which precede and those which follow, in the -character of the sciences to which it gives rise, and as it -appears likely to be hereafter of great extent and -consequence, it seemed better to treat of it in a separate -Book, although of a brevity disproportioned to the rest. - - - - -END OF VOL. I. - - - -Cambridge: Printed at the University Press. - - - - -HISTORY -OF -SCIENTIFIC IDEAS. - - - -VOLUME II. - - - - -Cambridge; -PRINTED BY C. J. CLAY, M.A. -AT THE UNIVERSITY PRESS. - - - -HISTORY -OF -SCIENTIFIC IDEAS. - -BY WILLIAM WHEWELL, D.D., -MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND -CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE. - - - -BEING THE FIRST PART OF THE PHILOSOPHY -OF THE INDUCTIVE SCIENCES. - - - -_THE THIRD EDITION._ - -IN TWO VOLUMES. - - -ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ - - -VOLUME II. - - - -LONDON: -JOHN W. PARKER AND SON, WEST STRAND. -1858. - - -CONTENTS -OF -THE SECOND VOLUME. - - -BOOK VI. - -THE PHILOSOPHY OF CHEMISTRY. - - PAGE -CHAP. I. ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION 3 - - _Art._ 1. Fundamental Ideas of Chemistry. - 2. Elements. - 3. Do Compounds resemble their Elements? - 4. The Three Principles. - 5. A Modern Errour. - 6. Are Compounds determined by the Figure of Elements? - 7. Crystalline Form depends on Figure of Elements. - 8. Are Compounds determined by Mechanical Attraction - of Elements? - 9. Newton's followers. - 10. Imperfection of their Hypotheses. - -CHAP. II. ESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF - CHEMICAL AFFINITY 15 - - _Art._ 1. Early Chemists. - 2. Chemical Affinity. - 3. Affinity or Attraction? - 4. Affinity preferable. - 5. Analysis is possible. -{vi} - 6. Affinity is Elective. - 7. Controversy on this. - 8. Affinity is Definite. - 9. Are these Principles necessarily true? - 10. Composition determines Properties. - 11. Comparison on this subject. - 12. Composition determines Crystalline Form. - -CHAP. III. OF THE IDEA OF SUBSTANCE 29 - - _Art._ 1. Indestructibility of Substance. - 2. The Idea of Substance. - 3. Locke's Denial of Substance. - 4. Is all Substance heavy? - Note on Sir W. Hamilton's objections 37 - -CHAP. IV. APPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY 39 - - _Art._ 1. A Body is Equal to its Elements. - 2. Lavoisier. - 3. Are there Imponderable Elements? - 4. Faraday's views. - 5. Composition of Water. - 6. Heat in Chemistry. - -CHAP. V. THE ATOMIC THEORY 48 - - _Art._ 1. The Theory on Chemical Grounds. - 2. Hypothesis of Atoms. - 3. Its Chemical Difficulties. - 4. Grounds of the Atomic Doctrine. - 5. Ancient Atomists. - 6. Francis Bacon. - 7. Modern Atomists. - 8. Arguments for and against. - 9. Boscovich's Theory. - 10. Molecular Hypothesis. - 11. Poisson's Inference. - 12. Wollaston's Argument. - 13. Properties are Permanent. -{vii} -BOOK VII. - -THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY. - -CHAP. I. EXPLICATION OF THE IDEA OF SYMMETRY 67 - - _Art._ 1. Symmetry, what. - 2. Kinds of Symmetry. - 3. Examples in Nature. - 4. Vegetables and Animals. - 5. Symmetry a Fundamental Idea. - 6. Result of Symmetry. - -CHAP. II. APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS 75 - - _Art._ 1. 'Fundamental Forms.' - 2. Their use. - 3. 'Systems of Crystallization.' - 4. Cleavage. - 5. Other Properties. - -CHAP. III. SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS 80 - - _Art._ 1. Integrant Molecules. - 2. Difficulties of the Theory. - 3. Merit of the Theory. - 4. Wollaston's Hypothesis. - 5. Maxim for such Hypotheses. - 6. Dalton's Hypothesis. - 7. Ampère's Hypothesis. - 8. Difficulty of such Hypotheses. - 9. Isomorphism. -{viii} -BOOK VIII. - -PHILOSOPHY OF THE CLASSIFICATORY SCIENCES. - -CHAP. I. THE IDEA OF LIKENESS AS GOVERNING THE USE OF - COMMON NAMES 95 - - _Art._ 1. Object of the Chapter. - 2. Unity of the Individual. - 3. Condition of Unity. - 4. Kinds. - 5. Not made by Definitions. - 6. Condition of the Use of Terms. - 7. Terms may have different Uses. - 8. Gradation of Kinds. - 9. Characters of Kinds. - 10. Difficulty of Definitions. - 11. 'The Five Words.' - -CHAP. II. THE METHODS OF NATURAL HISTORY, AS REGULATED - BY THE IDEA OF LIKENESS 108 - -_Sect._ I. _Natural History in General._ - _Art._ 1. Idea of Likeness in Natural History. - 2. Condition of its Use. - -_Sect._ II. _Terminology._ - _Art._ 3. Meaning of the word. - -_Sect._ III. _The Plan of the System._ - _Art._ 4. Its Meaning. - 5. Latent Reference to Natural Affinity. - 6. Natural Classes. - 7. Artificial Classes. - 8. Are Genera Natural? - 9. Natural History and Mathematics. - 10. Natural Groups given by Type, not by Definition. - 11. Physiography. - 12. Artificial and Natural Systems. -{ix} -_Sect._ IV. _Methods of framing Natural Systems._ - _Art._ 13. Method of Blind Trial. - 14. Method of General Comparison. - -_Sect._ V. _Gradation of Groups._ - _Art._ 15. Series of Subdivisions. - 16. What is a Species? - 17. The _words_ 'Species' and 'Genus.' - 18. Varieties. Races. - -_Sect._ VI. _Nomenclature._ - _Art._ 19. Binary Nomenclature. - -_Sect._ VII. _Diagnosis._ - _Art._ 20. Characteristick and Systematick. - -CHAP. III. APPLICATION OF THE NATURAL HISTORY METHOD - TO MINERALOGY 138 - - _Art._ 1. Mohs's System. - 2. His 'Characteristick.' - 3. Mineral _Species_ not yet well fixed. - 4. _Orders_ of Minerals. - 5. Nomenclature of Minerals. - 6. M. Necker's 'Règne Mineral.' - 7. Inconvenience of taking a Chemical Basis of - Mineral Systems. - 8. Relation of Natural History and Chemistry. - 9. What is a Mineralogical Individual? - 10. A well-formed Crystal is an Individual. - 11. Not the Integrant Molecules, - 12. Nor the Cleavage Forms. - 13. Compound Crystals are not Individuals. - 14. Crystalline Forms are sufficiently complete for - this. - 15. Including aggregate Masses. - 16. Do Artificial Crystals belong to Mineralogy? - 17. The Mineralogical Individual extends as far as - the same Crystalline Axes extend. - 18. Artificial Crystals do belong to Mineralogy: -{x} - 19. Cannot be excluded. - 20. Species to be determined by the Crystalline Power. - 21. Secondary Derivative Forms are Varieties: - 22. Are not Species, as M. Necker holds. - -CHAP. IV. OF THE IDEA OF NATURAL AFFINITY 159 - - _Art._ 1. The Idea of Affinity - 2. Is not to be made out by Arbitrary Rules. - 3. Functions of Living things are many, - 4. But all lead to the same arrangement. - 5. This is Cuvier's principle: - 6. And Decandolle's. - 7. Is this applicable to Inorganic Bodies? - 8. Yes; by the agreement of Physical and - Chemical Arrangement. - - -BOOK IX. - -THE PHILOSOPHY OF BIOLOGY. - -CHAP. 1. ANALOGY OF BIOLOGY WITH OTHER SCIENCES. 169 - - _Art._ 1. Biology involves the Idea of Life. - 2. This Idea to be historically traced. - 3. The Idea at first expressed by means of other - Ideas. - 4. Mystical, Mechanical, Chemical, and Vital - Fluid Hypotheses. - -CHAP. II. SUCCESSIVE BIOLOGICAL HYPOTHESES 174 - -_Sect._ I. _The Mystical School._ - -_Sect._ II. _The Iatrochemical School._ - -_Sect._ III. _The Iatromathematical School._ - -_Sect._ IV. _The Vital Fluid School._ - -_Sect._ V. _The Psychical School._ -{xi} - -CHAP. III. ATTEMPTS TO ANALYSE THE IDEA OF LIFE 195 - - _Art._ 1. Definitions of Life, - 2. By Stahl, Humboldt, Kant. - 3. Definition of Organization by Kant. - 4. Life is a System of Functions. - 5. Bichat. _Sum_ of Functions. - 6. Use of Definition. - 7. Cuvier's view. - 8. Classifications of Functions. - 9. Vital, Natural, and Animal Functions. - 10. Bichat. Organic and Animal Life. - 11. Use of this Classification. - -CHAP. IV. ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES, - AND FIRST, OF ASSIMILATION AND SECRETION 203 - -_Sect._ I. _Course of Biological Research._ - _Art._ 1. Observation and New Conceptions. - -_Sect._ II. _Attempts to form a distinct Conception - of Assimilation and Secretion._ - _Art._ 2. The Ancients. - 3. Buffon. Interior Mould. - 4. Defect of this view. - 5. Cuvier. Life a Vortex. - 6. Defect of this view. - 7. Schelling. Matter and Form. - 8. Life a constant Form of circulating Matter, &c. - -_Sect._ III. _Attempts to conceive the Forces of - Assimilation and Secretion._ - _Art._ 9. Assimilation is a Vital Force. - 10. The name 'Assimilation.' - 11. Several processes involved in Assimilation. - 12. _Absorption_. Endosmose. - 13. Absorption involves a Vital Force. - 14. _Secretion_. Glands. - 15. Motions of Vital Fluids. -{xii} -_Sect._ IV. _Attempts to conceive the Process of Generation._ - _Art._ 16. 'Reproduction' figuratively used for Generation. - 17. Nutrition different from - 18. Generation. - 19. Generations successively included. - 20. Pre-existence of Germs. - 21. Difficulty of this view. - 22. Communication of Vital Forces. - 23. Close similarity of Nutrition and Generation. - 24. The Identity of the two Processes exemplified. - -CHAP. V. ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL - FORCES, _continued_.--VOLUNTARY MOTION. 222 - - _Art._ 1. Voluntary Motion one of the animal Functions. - 2. Progressive knowledge of it. - 3. Nervous Fluid not electric. - 4. Irritability. Glisson. - 5. Haller. - 6. Contractility. - 7. Organic Sensibility and Contractility not separable. - 8. Improperly described by Bichat. - 9. Brown. - 10. Contractility a peculiar Power. - 11. Cuvier's view. - 12. Elementary contractile Action. - 13. Strength of Muscular Fibre. - 14. Sensations become Perceptions - 15. By means of Ideas; - 16. And lead to Muscular Actions. - 17. Volition comes between Perception and Action. - 18. Transition to Psychology, - 19. A center is introduced. - 20. The central consciousness may be obscure. - 21. Reflex Muscular Action. - 22. Instinct. - 23. Difficulty of conceiving Instinct. - 24. Instinct opposed to Insight. -{xiii} - -CHAP. VI. OF THE IDEA OF FINAL CAUSES 239 - - _Art._ 1. Organization. Parts are Ends and Means. - 2. Not merely mutually dependent. - 3. Not merely mutually Cause and Effect. - 4. Notion of _End_ not derived from Facts. - 5. This notion has regulated Physiology. - 6. Notion of Design comes from within. - 7. Design not understood by Savages. - 8. Design opposed to Morphology. - 9. Impression of Design when fresh. - 10. Acknowledgement of an End by adverse Physiologists. - 11. This included in the Notion of Disease. - 12. It belongs to organized Creatures only. - 13. The term Final _Cause_. - 14. Law and Design. - 15. Final Causes and Morphology. - 16. Expressions of physiological Ends. - 17. The Conditions of Existence. - 18. The asserted presumption of Teleology. - 19. Final Causes in other subjects. - 20. Transition to Palætiology. - - -BOOK X. - -THE PHILOSOPHY OF PALÆTIOLOGY. - -CHAP. I. OF PALÆTIOLOGICAL SCIENCES IN GENERAL. 257 - - _Art._ 1. Description of Palætiology. - 2. Its Members. - 3. Other Members. - 4. Connexion of the whole subject. - 5. We shall take Material Sciences only; - 6. But these are connected with others. - -CHAP. II. OF THE THREE MEMBERS OF A PALÆTIOLOGICAL SCIENCE 263 - - _Art._ 1. Divisions of such Sciences. - 2. The Study of Causes. - 3. Ætiology. -{xiv} - 4. Phenomenology requires Classification. Phenomenal - Geology. - 5. Phenomenal Uranology. - 6. Phenomenal Geography of Plants and Animals. - 7. Phenomenal Glossology. - 8. The Study of Phenomena leads to Theory. - 9. No sound Theory without Ætiology. - 10. Causes in Palætiology. - 11. Various kinds of Cause. - 12. Hypothetical Order of Palætiological Causes. - 13. Mode of Cultivating Ætiology:--In Geology: - 14. In the Geography of Plants and Animals: - 15. In Languages. - 16. Construction of Theories. - 17. No sound Palætiological Theory yet extant. - -CHAP. III. OF THE DOCTRINE OF CATASTROPHES AND THE - DOCTRINE OF UNIFORMITY 284 - - _Art._ 1. Doctrine of Catastrophes. - 2. Doctrine of Uniformity. - 3. Is Uniformity probable _a priori_? - 4. Cycle of Uniformity indefinite. - 5. Uniformitarian Arguments are Negative only. - 6. Uniformity in the Organic World. - 7. Origin of the present Organic World. - 8. Nebular Origin of the Solar System. - 9. Origin of Languages. - 10. No Natural Origin discoverable. - -CHAP. IV. OF THE RELATION OF TRADITION TO PALÆTIOLOGY 297 - - _Art._ 1. Importance of Tradition. - 2. Connexion of Tradition and Science. - 3. Natural and Providential History of the World. - 4. The Sacred Narrative. - 5. Difficulties in interpreting the Sacred Narrative. - 6. Such Difficulties inevitable. - 7. Science tells us nothing concerning Creation. -{xv} - 8. Scientific views, when familiar, do not disturb - the authority of Scripture. - 9. When should Old Interpretations be given up? - 10. In what Spirit should the Change be accepted? - 11. In what Spirit should the Change be urged? - 12. Duty of Mutual forbearance. - 13. Case of Galileo. - -CHAP. V. OF THE CONCEPTION OF A FIRST CAUSE 316 - - _Art._ 1. The Origin of things is not naturally discoverable; - 2. Yet has always been sought after. - 3. There must be a First Cause. - 4. This is an Axiom. - 5. Involved in the proof of a Deity. - 6. The mind is not satisfied without it. - 7. The Whole Course of Nature must have a Cause. - 8. Necessary Existence of God. - 9. Forms of the Proof. - 10. Idea of a First Cause is Necessary. - 11. Conception of a First Cause. - 12. The First Cause in all Sciences is the same. - 13. We are thus led to Moral Subjects. - - Conclusion of this History. - - - - -{{1}} -BOOK VI. - - -THE -PHILOSOPHY -OF -CHEMISTRY. - - - - -A PHILOSOPHER was asked:--How much does smoke weigh? He -answered: Subtract from the weight of the fuel the weight of -the ashes, and thou hast the weight of the smoke. Thus he -assumed as incontrovertible that, even in the fire, the -Substance does not perish, only its Form undergoes a change. -In like manner the proposition, _Nothing can come of -Nothing_ was only another consequence of the Principle of -Permanence, or rather of the Principle of the Enduring -Existence of the same subject with different appearances. - -Kant, _Kritik d. r. Vern._ - - - -{{3}} -BOOK VI. - - -THE PHILOSOPHY OF CHEMISTRY. - - -CHAPTER I. - -ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION. - - -1. WE have now to bring into view, if possible, the Ideas -and General Principles which are involved in Chemistry,--the -science of the composition of bodies. For in this as in -other parts of human knowledge, we shall find that there are -certain Ideas, deeply seated in the mind, though shaped and -unfolded by external observation, which are necessary -conditions of the existence of such a science. These Ideas -it is, which impel man to such a knowledge of the -Composition of bodies, which give _meaning_ to _facts_ -exhibiting this composition, and _universality_ to _special_ -truths discovered by experience. These are the Ideas of -_Element_ and of _Substance_. - -Unlike the Idea of Polarity, of which we treated in the last -Book, these Ideas have been current in men's minds from very -early times, and formed the subject of some of the first -speculations of philosophers. It happened however, as might -have been expected, that in the first attempts they were not -clearly distinguished from other notions, and were -apprehended and applied in an obscure and confused manner. -We cannot better exhibit the peculiar character and meaning -of these Ideas than by tracing the form which they have -assumed {4} and the efficacy which they have exerted in -these successive essays. This, therefore, I shall endeavour -to do, beginning with the Idea of Element. - -2. That bodies are composed or made up of certain parts, -elements, or principles, is a conception which has existed -in men's minds from the beginning of the first attempts at -speculative knowledge. The doctrine of the Four Elements, -Earth, Air, Fire and Water, of which all things in the -universe were supposed to be constituted, is one of the -earliest forms in which this conception was systematized; -and this doctrine is stated by various authors to have -existed as early as the times of the ancient Egyptians[1\6]. -The words usually employed by Greek writers to express these -elements are ἀρχὴ a _principle_ or _beginning_, and -στοιχεῖον, which probably meant a _letter_ (of a word) -before it meant an _element_ of a compound. 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 history; and might very naturally -supply a metaphor to denote the analysis of substances into -their intimate parts, when men began to contemplate such an -analysis as a subject of speculation. The Latin word -_elementum_ itself, though by its form it appears to be a -derivative abstract term, comes from some root now obsolete; -probably[2\6] from a word signifying _to grow_ or _spring up_. - -[Note 1\6: Gilbert's _Phys._ 1. i. c. iii.] - -[Note 2\6: Vossius _in voce_. "Conjecto esse ab antiqua voco -_eleo_ pro _oleo_, id est _cresco_: a qua signiflcatione -proles, _suboles_, _adolescens_: ut ab _juratum_, -_juramentum_; ab _adjutum_, _adjumentum_: sic ab _eletum_, -_elementum_: quia inde omnia crescunt ac nascuntur."] - -The mode in which elements form the compound bodies and -determine their properties was at first, as might be -expected, vaguely and variously conceived. It will, I trust, -hereafter be made clear to the reader that the relation of -the elements to the compound involves a peculiar and -appropriate Fundamental Idea, not susceptible of being -correctly represented by any comparison or combination of -other ideas, and guiding us to clear and definite results -only when it is illustrated {5} and nourished by an abundant -supply of experimental facts. But at first the peculiar and -special notion which is required in a just conception of the -constitution of bodies was neither discerned nor suspected; -and up to a very late period in the history of chemistry, -men went on attempting to apprehend the constitution of -bodies more clearly by substituting for this obscure and -recondite idea of Elementary Composition, some other idea -more obvious, more luminous, and more familiar, such as the -ideas of Resemblance, Position, and mechanical Force. We -shall briefly speak of some of these attempts, and of the -errours which were thus introduced into speculations on the -relations of elements and compounds. - -3. _Compounds assumed to resemble their Elements._--The -first notion was that compounds derive their qualities from -their elements by _resemblance_:--they are hot in virtue of -a hot element, heavy in virtue of a heavy element, and so -on. In this way the doctrine of the _four elements_ was -framed; for every body is either hot or cold, moist or dry; -and by combining these qualities in all possible ways, men -devised four elementary substances, as has been stated in -the History[3\6]. - -[Note 3\6: _Hist. Ind. Sc._ b. i. c. ii. sec. 2.] - -This assumption of the derivation of the qualities of bodies -from similar qualities in the elements was, as we shall see, -altogether baseless and unphilosophical, yet it prevailed -long and universally. It was the foundation of medicine for -a long period, both in Europe and Asia; disorders being -divided into hot, cold, and the like; and remedies being -arranged according to similar distinctions. Many readers -will recollect, perhaps, the story[4\6] of the indignation -which the Persian physicians felt towards the European, when -he undertook to cure the ill effects of cucumber upon the -patient, by means of mercurial medicine: for cucumber, which -is cold, could not be counteracted, they maintained, by -mercury, which in their classification is cold also. Similar -views of the operation of medicines might {6} easily be -traced in our own country. 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 frame, it is utterly impossible to form the most -remote conjecture what the result will be, from any such -vague notions of their qualities as the common use of our -senses can give. And in like manner the common operations of -chemistry give rise, in almost every instance, to products -which bear no resemblance to the materials employed. The -results of the furnace, the alembic, the mixture, frequently -have no visible likeness to the ingredients operated upon. -Iron becomes steel by the addition of a little charcoal; but -what visible trace of the charcoal is presented by the metal -thus modified? The most beautiful colours are given to glass -and earthenware by minute portions of the ores of black or -dingy metals, as iron and manganese. The worker in metal, -the painter, the dyer, the vintner, the brewer, all the -artisans in short who deal with practical chemistry, are -able to teach the speculative chemist that it is an utter -mistake to expect that the qualities of the elements shall -be still discoverable, in an unaltered form, in the -compound. This first rude notion of an element, that it -determines the properties of bodies _by resemblance_, must -be utterly rejected and abandoned before we can make any -advance towards a true apprehension of the constitution of -bodies. - -[Note 4\6: See _Hadji Baba_.] - -4. This step accordingly was made, when the hypothesis of -the four elements was given up, and the doctrine of the -_three Principles_, Salt, Sulphur, and Mercury, was -substituted in its place. For in making this change, as I -have remarked in the History[5\6], the real advance was the -acknowledgment of the changes, produced by the chemist's -operations, as results to be accounted for by the union and -separation of substantial elements, however great the -changes, and however unlike the product might be to the -materials. And this step once made, chemists went on -constantly {7} advancing towards a truer view of the nature -of an element, and consequently, towards a more satisfactory -theory of chemical operations. - -[Note 5\6: _Hist. Ind. Sc._ b. iv. c. 1.] - -5. Yet we may, I think, note one instance, even in the works -of eminent modern chemists, in which this maxim, that we -have no right to expect any resemblance between the elements -and the compound, is lost sight of. I speak of certain -classifications of mineral substances. Berzelius, in his -System of Mineral Arrangement, places _sulphur_ next to the -_sulphurets_. But surely this is an errour, involving the -ancient assumption of the resemblance of elements and -compounds; as if we were to expect the sulphurets to bear a -resemblance to sulphur. All classifications are intended to -bring together things resembling each other: the sulphurets -of metals have certain general resemblances to each other -which make them a tolerably distinct, well determined, class -of bodies. But sulphur has no resemblances with these, and -no analogies with them, either in physical or even in -chemical properties. It is a simple body; and both its -resemblances and its analogies direct us to place it along -with other simple bodies, (selenium, and phosphorus,) which, -united with metals, produce compounds not very different -from the sulphurets. Sulphur cannot be, nor approach to -being, a sulphuret; we must not confound what it _is_ with -what it _makes_. Sulphur has its proper influence in -determining the properties of the compound into which it -enters; but it does not do this according to resemblance of -qualities, or according to any principle which properly -leads to propinquity in classification. - -6. _Compounds assumed to be determined by the Figure of -Elements._--I pass over the fanciful modes of representing -chemical changes which were employed by the Alchemists; for -these strange inventions did little in leading men towards a -juster view of the relations of elements to compounds. I -proceed for an instant to the attempt to substitute another -obvious conception for the still obscure notion of -elementary composition. It was imagined that all the -properties of bodies and their mutual operations might be -{8} accounted for by supposing them constituted of -_particles_ of various _forms_, round or angular, pointed or -hooked, straight or spiral. This is a very ancient -hypothesis, and a favourite one with many casual speculators -in all ages. Thus Lucretius undertakes to explain why wine -passes rapidly through a sieve and oil slowly, by telling us -that the latter substance has its particles either larger -than those of the other, or more hooked and interwoven -together. And he accounts for the difference of sweet and -bitter by supposing the particles in the former case to be -round and smooth, in the latter sharp and jagged[6\6]. -Similar assumptions prevailed in modern times on the revival -of the mechanical philosophy, and constitute a large part of -the physical schemes of Descartes and Gassendi. They were -also adopted to a considerable extent by the chemists. Acids -were without hesitation assumed to consist of sharp pointed -particles; which, 'I hope,' Lemery says[7\6], 'no one will -dispute, seeing every one's experience does demonstrate it: -he needs but taste an acid to be satisfied of it, for it -pricks the tongue like anything keen and finely cut.' Such -an assumption is not only altogether gratuitous and useless, -but appears to be founded in some degree upon a confusion in -the metaphorical and literal use of such words as _keen_ and -_sharp_. The assumption once made, it was easy to -accommodate it, in a manner equally arbitrary, to other -facts. 'A demonstrative and convincing proof that an acid -does consist of pointed parts is, that not only all acid -salts do crystallize into edges, but all dissolutions of -different things, caused by acid liquors, do assume this -figure in their crystallization. These crystals consist of -points differing both in length and bigness one from -another, and this diversity must be attributed to the keener -or blunter edges of the different sorts of acids: and so -likewise this difference of the points in subtilty is the -cause that one acid can penetrate and dissolve with one sort -of _mixt_, that another can't rarify at all: Thus _vinegar_ -dissolves _lead_, {9} which _aqua fortis_ can't: _aqua -fortis_ dissolves _quicksilver_, which _vinegar_ will not -touch; _aqua regalis_ dissolves _gold_, whenas _aqua fortis_ -cannot meddle with it; on the contrary, _aqua fortis_ -dissolves _silver_, but can do nothing with gold, and so of -the rest.' - -[Note 6\6: _De Rerum Natura_, ii. 390 sqq.] - -[Note 7\6: _Chemistry_, p. 25.] - -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 substances. 'This -effect,' Lemery adds, '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 -motion.' And in a like spirit are the speculations in Dr. -Mead's _Mechanical Account of Poisons_ (1745). Thus he -explains the poisonous effect of _corrosive sublimate_ of -mercury by saying[8\6] that the particles of the salt are a -kind of lamellæ or blades to which the mercury gives an -additional weight. If resublimed with three-fourths the -quantity of mercury, it loses its corrosiveness, (becoming -_calomel_,) which arises from this, that in sublimation 'the -crystalline blades are divided every time more and more by -the force of the fire:' and 'the broken pieces of the -crystals uniting into little masses of differing figures -from their former make, those cutting points are now so much -smaller that they cannot make wounds deep enough to be -equally mischievous and deadly: and therefore do only -vellicate and twitch the sensible membranes of the stomach.' - -[Note 8\6: P. 199.] - -7. Among all this very fanciful and gratuitous assumption we -may notice one true principle clearly introduced, namely, -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 -crystallization, as well as of mere chemical change. This -principle we shall hereafter have occasion to insist upon -further. - -I now proceed to consider a more refined form of assumption -respecting the constitution of bodies, yet {10} still one in -which a vain attempt is made to substitute for the peculiar -idea of chemical composition a more familiar mechanical -conception. - -8. _Compounds assumed to be determined by the Mechanical -Attraction of the Elements._--When, in consequence of the -investigations and discoveries of Newton and his -predecessors, the conception of mechanical force had become -clear and familiar, so far as the action of external forces -upon a body was concerned, 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 together. Newton himself had pointed the way to this -attempt. In the Preface to the _Principia_, after speaking -of what he has done in calculating the effects of forces -upon the planets, satellites, &e., he adds, 'Would it were -permitted us to deduce the other phenomena of nature from -mechanical principles by the same kind of reasoning. For -many things move me to suspect that all these phenomena -depend upon certain forces, by which the particles of -bodies, through causes not yet known, are either urged -towards each other, and cohere according to regular figures, -or are repelled and recede from each other; which forces -being unknown, philosophers have hitherto made their -attempts upon nature in vain.' The same thought is at a -later period followed out further in one of the Queries at -the end of the Opticks[9\6]. 'Have not the small particles -of bodies certain Powers, Virtues, or Forces, by which they -act at a distance, not only upon the rays of light for -reflecting, refracting and inflecting them, but also upon -one another for producing a great part of the phenomena of -nature?' And a little further on he proceeds to apply this -expressly to chemical changes. 'When Salt of Tartar runs -_per deliquium_ [or as we now express it, 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 {11} the form of vapours? And why does -not common salt, or saltpetre, or vitriol, run _per -deliquium_, but for want of such an attraction? or why does -not Salt of Tartar draw more water out of the air than in a -certain proportion to its quantity, but for want of an -attractive force after it is saturated with water?' He goes -on to put a great number of similar cases, all tending to -the same point, that chemical combinations cannot be -conceived in any other way than as an attraction of -particles. - -[Note 9\6: Query 31.] - -9. Succeeding speculators in his school attempted to follow -out this view. Dr. Frend, of Christ Church, in 1710, -published his _Prælectiones Chymicæ, in quibus omne fere -Operationes Chymicæ ad vera Principia ex ipsius Naturæ -Legibus rediguntur. Oxonii habitæ_. This book is dedicated -to Newton, and in the dedication, the promise of advantage -to chemistry from the influence of the Newtonian discoveries -is spoken of somewhat largely,--much more largely, indeed, -than has yet been justified by the sequel. After declaring -in strong terms that the only prospect of improving science -consists in following the footsteps of Newton, the author -adds, 'That force of attraction, of which you first so -successfully traced the influence in the heavenly bodies, -operates in the most minute corpuscles, as you long ago -hinted in your _Principia_, and have lately plainly shown in -your _Opticks_; and this force we are only just beginning to -perceive and to study. Under these circumstances I have been -desirous of trying what is the result of this view in -chemistry.' The work opens formally enough, with a statement -of general mechanical principles, of which the most peculiar -are these:--'That there exists an attractive force by which -particles when at very small distances from each other, are -drawn together;--that this force is different, according to -the different figure and density of the particles;--that the -force may be greater on one side of a particle than on the -other;--that the force by which particles cohere together -arises from attraction, and is variously modified according -to the quantity of contacts.' But these principles are not -{12} applied in any definite manner to the explanation of -specific phenomena. He attempts, indeed, the question of -special solvents[10\6]. Why does _aqua fortis_ dissolve -silver and not gold, while _aqua regia_ dissolves gold and -not silver? which, he says, is the most difficult question -in chemistry, and which is certainly a fundamental question -in the formation of chemical theory. He solves it by certain -assumptions respecting the forces of attraction of the -particles, and also the diameter of the particles of the -acids and the pores of the metals, all which suppositions -are gratuitous. - -[Note 10\6: P. 54.] - -10. We may observe further, that by speaking, as I have -stated that he does, of the figure of particles, he mixes -together the assumption of the last section with the one -which we are considering in this. This combination is very -unphilosophical, or, to say the least, very insufficient, -since it makes a new hypothesis necessary. If a body be -composed of cubical particles, held together by their mutual -attraction, by what force are the parts of each cube held -together? In order to understand their structure, we are -obliged again to assume a cohesive force of the second -order, binding together the particles of each particle. And -therefore Newton himself says[11\6], very justly, 'The parts -of all homogeneal hard bodies which fully touch each other, -stick together very strongly: and for explaining how this -is, some have invented hooked atoms, _which is begging the -question_.' For (he means to imply,) how do the parts of the -hook stick together? - -[Note 11\6: _Opticks_, p. 364.] - -The same remark is applicable to all hypotheses in which -particles of a complex structure are assumed as the -constituents of bodies: for while we suppose bodies and -their known properties to result from the mutual actions of -these particles, we are compelled to suppose the parts of -each particle to be held together by forces still more -difficult to conceive, since they are disclosed only by the -properties of these particles, which as yet are unknown. Yet -Newton himself has not abstained from such hypotheses: thus -he says[12\6], 'A particle of {13} a salt may be compared to -a chaos, being dense, hard, dry, and earthy in the center, -and moist and watery in the circumference.' - -[Note 12\6: _Opticks_, p. 362.] - -Since Newton's time the use of the term _attraction_, as -expressing the cause of the union of the chemical elements -of bodies, has been familiarly continued; and has, no doubt, -been accompanied in the minds of many persons with an -obscure notion that chemical attraction is, in some way, a -kind of mechanical attraction of the particles of bodies. -Yet the doctrine that _chemical_ 'attraction' and -_mechanical_ attraction are forces of the same kind has -never, so far as I am aware, been worked out into a system -of chemical theory; nor even applied with any distinctness -as an explanation of any particular chemical phenomena. Any -such attempt, indeed, could only tend to bring more clearly -into view the entire inadequacy of such a mode of -explanation. For the leading phenomena of chemistry are all -of such a nature that no mechanical combination can serve to -express them, without an immense accumulation of additional -hypotheses. If we take as our problem the changes of colour, -transparency, texture, taste, odour, produced by small -changes in the ingredients, how can we expect to give a -mechanical account of these, till we can give a mechanical -account of colour, transparency, texture, taste, odour, -themselves? And if our mechanical hypothesis of the -elementary constitution of bodies does not explain _such_ -phenomena as those changes, what can it explain, or what can -be the value of it? I do not here insist upon a remark which -will afterwards come before us, that even crystalline form, -a phenomenon of a far more obviously mechanical nature than -those just alluded to, has never yet been in any degree -explained by such assumptions as this, that bodies consist -of elementary particles exerting forces of the same nature -as the central forces which we contemplate in Mechanics. - -When therefore Newton asks, 'When some stones, as spar of -lead, dissolved in proper menstruums, become salts, do not -these things show that salts are dry earth and watery acid -united by _attraction_?' we may {14} answer, that this mode -of expression appears to be intended to identify chemical -combination with mechanical attraction;--that there would be -no objection to any such identification, if we could, in -that way, explain, or even classify well, a collection of -chemical facts; but that this has never yet been done by the -help of such expressions. Till some advance of this kind can -be pointed out, we must necessarily consider the power which -produces chemical combination as a peculiar principle, a -special relation of the elements, not rightly expressed in -mechanical terms. And we now proceed to consider this -relation under the name by which it is most familiarly -known. - - - -{{15}} -CHAPTER II. - -ESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF CHEMICAL -AFFINITY. - - -1. THE earlier chemists did not commonly involve themselves -in the confusion into which the mechanical philosophers ran, -of comparing chemical to mechanical forces. Their attention -was engaged, and their ideas were moulded, by their own -pursuits. They saw that the connexion of elements and -compounds with which they had to deal, was a peculiar -relation which must be studied directly; and which must be -understood, if understood at all, in itself, and not by -comparison with a different class of relations. At different -periods of the progress of chemistry, the conception of this -relation, still vague and obscure, was expressed in various -manners; and at last this conception was clothed in -tolerably consistent phraseology, and the principles which -it involved were, by the united force of thought and -experiment, brought into view. - -2. The power by which the elements of bodies combine -chemically, being, as we have seen, a peculiar agency, -different from mere mechanical connexion or attraction, it -is desirable to have it designated by a distinct and -peculiar name; and the term _Affinity_ has been employed for -that purpose by most modern chemists. The word 'affinity' in -common language means, sometimes resemblance, and sometimes -relationship and ties of family. It is from the latter sense -that the metaphor is borrowed when we speak of 'chemical -affinity.' By the employment of this term we do not indicate -a resemblance, but a disposition to unite. Using the word in -a common unscientific manner, we might say that chlorine, -bromine, and iodine, have a great {16} _natural affinity_ -with each other, for there are considerable resemblances and -analogies among them; but these bodies have very little -_chemical_ Affinity for each other. The use of the word in -the _former_ sense, of resemblance, can be traced in earlier -chemists; but the word does not appear to have acquired its -peculiar chemical meaning till after Boerhaave's time. -Boerhaave, however, is the writer in whom we first find a -due apprehension of the peculiarity and importance of the -Idea which it now expresses. When we make a chemical -solution[13\6], he says, not only are the particles of the -dissolved body separated from each other, but they are -closely united to the particles of the solvent. When _aqua -regia_ dissolves gold, do you not see, he says to his -hearers, that there must be between each particle of the -solvent and of the metal, a mutual virtue by which each -loves, unites with, and holds the other (_amat_, _unit_, -_retinet_)? The opinion previously prevalent had been that -the solvent merely separates the parts of the body -dissolved: and most philosophers had conceived this -separation as performed by mechanical operations of the -particles, resembling, for instance, the operation of wedges -breaking up a block of timber. But Boerhaave forcibly and -earnestly points out the insufficiency of the conception. -This, he says, does not account for what we see. We have not -only a separation, but a new combination. There is a force -by which the particles of the solvent associate to -themselves the parts dissolved, not a force by which they -repel and dissever them. We are here to imagine not -mechanical action, not violent impulse, not antipathy, but -love, at least if love be the desire of uniting. (Non igitur -hic etiam actiones mechanicæ, non propulsiones violentæ, non -inimicitiæ cogitandæ, sed amicitiæ, si amor dicendus copulæ -cupido.) The novelty of this view is evidenced by the mode -in which he apologizes for introducing it. 'Fateor, paradoxa -hæc assertio.' To Boerhaave, therefore, (especially -considering his great influence as a teacher of chemistry,) -we may {17} assign the merit of first diffusing a proper -view of Chemical Affinity as a peculiar force, the origin of -almost all chemical changes and operations. - -[Note 13\6: _Elementa Chemiæ_, Lugd. Bat. 1732, p. 677.] - -3. To Boerhaave is usually assigned also the credit of -introducing the _word_ 'Affinity' among chemists; but I do -not find that the word is often used by him in this sense; -perhaps not at all[14\6]. But however this may be, the term -is, on many accounts, well worthy to be preserved, as I -shall endeavour to show. Other terms were used in the same -sense during the early part of the eighteenth century. Thus -when Geoffroy, in 1718, laid before the Academy of Paris his -Tables of Affinities, which perhaps did more than any other -event to fix the Idea of Affinity, he termed them 'Tables of -the Relations of Bodies;' '_Tables des Rapports_:' speaking -however, also, of their 'disposition to unite,' and using -other phrases of the same import. - -[Note 14\6: See Dumas, _Leçons de Phil. Chim._ p. 364. Rees' -_Cyclopædia_, Art. Chemistry. In the passage of Boerhaave to -which I refer above, _affinitas_ is rather opposed to, than -identified with, chemical combination. When, he says, the -parts of the body to be dissolved are dissevered by the -solvent, why do they remain united to the particles of the -solvent, and why do not rather both the particles of the -solvent and of the dissolved body collect into homogeneous -bodies by their _affinity_? 'denuo se affinitate suæ naturæ -colligant in corpora homogenea?' And the answer is, because -they possess another force which counteracts this affinity -of homogeneous particles, and makes compounds of different -elements. Affinity, in chemistry, now means the tendency of -_different_ kinds of matter to unite: but it appears, as I -have said, to have acquired this sense since Boerhaave's time.] - -The term _attraction_, having been recommended by Newton as -a fit word to designate the force which produces chemical -combination, continued in great favour in England, where the -Newtonian philosophy was looked upon as applicable to every -branch of science. In France, on the contrary, where -Descartes still reigned triumphant, 'attraction,' the -watch-word of the enemy, was a sound never uttered but with -dislike and suspicion. In 1718 (in the notice of Geoffroy's -Table,) the Secretary of the Academy, after pointing out -some of the peculiar circumstances of chemical {18} -combinations, says, 'Sympathies and attractions would suit -well here, if there were such things,' 'Les sympathies, les -attractions conviendroient bien ici, si elles étaient -quelque chose.' And at a later period, in 1731, having to -write the _éloge_ of Geoffroy after his death, he says, 'He -gave, in 1718, a singular system, and a Table of -_Affinities_, or Relations of the different substances in -chemistry. These affinities gave an easiness to some -persons, who feared that they were _attractions in -disguise_, and all the more dangerous in consequence of the -seductive forms which clever people have contrived to give -them. It was found in the sequel that this scruple might be -got over.' - -This is the earliest published instance, so far as I am -aware, in which the word 'Affinity' is distinctly used for -the cause of chemical composition; and taking into account -the circumstances, the word appears to have been adopted in -France in order to avoid the word _attraction_, which had -the taint of Newtonianism. Accordingly we find the word -_affinité_ employed in the works of French chemists from -this time. Thus, in the _Transactions of the French Academy_ -for 1746, in a paper of Macquer's upon Arsenic, he -says[15\6], 'On peut facilement rendre raison de ces -phenomènes par le moyen des affinités que les différens -substances qui entrent dans ces combinaisons, ont les uns -avec les autres:' and he proceeds to explain the facts by -reference to Geoffroy's Table. And in Macquer's _Elements of -Chemistry_, which appeared a few years later, the 'Affinity -of Composition' is treated of as a leading part of the -subject, much in the same way as has been practised in such -books up to the present time. From this period, the word -appears to have become familiar to all European chemists in -the sense of which we are now speaking. Thus, in the year -1758, the Academy of Sciences at Rouen offered a prize for -the best dissertation on Affinity. The prize was shared -between M. Limbourg of Theux, near Liege, and M. Le Sage -{19} of Geneva[16\6]. About the same time other persons -(Manherr[17\6], Nicolai[18\6], and others) wrote on the same -subject, employing the same name. - -[Note 15\6: _A. P._ 1746, p. 201.] - -[Note 16\6: Thomson's _Chemistry_, iii. 10. Limbourg's -Dissertation was published at Liege, in 1761; and Le Sage's -at Geneva.] - -[Note 17\6: _Dissertatio de Affinitate Corporum_. Vindob. 1762.] - -[Note 18\6: _Progr._ I. II. _de Affinitate Corporum Chimica_. -Jen. 1775, 1776.] - -Nevertheless, in 1775, the Swedish chemist Bergman, pursuing -still further this subject of Chemical Affinities, and the -expression of them by means of Tables, returned again to the -old Newtonian term; and designated the disposition of a body -to combine with one rather than another of two others as -_Elective Attraction_. And as his work on _Elective -Attractions_ had great circulation and great influence, this -phrase has obtained a footing by the side of _Affinity_, and -both one and the other are now in common use among chemists. - -4. I have said above that the term _Affinity_ is worthy of -being retained as a technical term. If we use the word -_attraction_ in this case, we identify or compare chemical -with mechanical attraction; from which identification and -comparison, as I have already remarked, no one has yet been -able to extract the means of expressing any single -scientific truth. If such an identification or comparison be -not intended, the use of the same word in two different -senses can only lead to confusion; and the proper course, -recommended by all the best analogies of scientific history, -is to adopt a peculiar term for that peculiar relation on -which chemical composition depends. The word _Affinity_, -even if it were not rigorously proper according to its -common meaning, still, being simple, familiar, and well -established in this very usage, is much to be preferred -before any other. - -But further, there are some analogies drawn from the common -meaning of this word, which appear to recommend it as -suitable for the office which it has to discharge. For -common mechanical attractions and {20} repulsions, the -forces by which one body considered as a _whole_ acts upon -another external to it, are, as we have said, to be -distinguished from those more intimate ties by which the -_parts_ of each body are held together. Now this difference -is implied, if we compare the former relations, the -attractions and repulsions, to alliances and wars between -States, and the latter, the internal union of particles, to -those bonds of affinity which connect the citizens of the -same state with one another, and especially to the ties of -Family. We have seen that Boerhaave compares the union of -two elements of a compound to their marriage; 'we must -allow,' says an eminent chemist of our own time[19\6], 'that -there is some truth in this poetical comparison.' It -contains this truth,--that the two become one to most -intents and purposes, and that the Unit thus formed (the -Family) is not a mere juxtaposition of the component parts. -And thus the Idea of Affinity as the peculiar principle of -chemical composition, is established among chemists, and -designated by a familiar and appropriate name. - -[Note 19\6: Dumas, _Leçons de Phil. Chim._ p. 363.] - -5. _Analysis is possible._--We must, however, endeavour to -obtain a further insight into this Idea, thus fixed and -named. We must endeavour to extricate, if not from the Idea -itself, from the processes by which it has obtained -acceptation and currency among chemists, some principles -which may define its application, some additional -specialities in the relations which it implies. This we -shall proceed to do. - -The Idea of Affinity, as already explained, implies a -disposition to combine. But this combination is to be -understood as admitting also of a possibility of separation. -Synthesis implies Analysis as conceivable: or to recur to -the image which we have already used, Divorce is possible -when the Marriage has taken place. - -That there is this possibility, is a conviction implied in -all the researches of chemists, ever since the true notion -of composition began to predominate in their investigations. -One of the first persons who clearly {21} expressed this -conviction was Mayow, an English physician, who published -his _Medico-Physical Tracts_ in 1674. The first of them _De -Sale-Nitro et Spiritu Nitro-Aerio_, contains a clear -enunciation of this principle. After showing how, in the -combinations of opposite elements, as acid and alkali, their -properties entirely disappear, and a new substance is formed -not at all resembling either of the ingredients, he -adds[20\6], 'Although these salts thus mixed appear to be -destroyed it is still possible for them to be separated from -each other, with their powers still entire.' He proceeds to -exemplify this, and illustrates it by the same image which I -have already alluded to: 'Salia acida a salibus -volatilibus discedunt, ut cum sale fixo tartari, tanquam -_sponso_ magis idoneo, _conjugium_ strictius ineunt.' This -idea of a synthesis which left a complete analysis still -possible, was opposed to a notion previously current, that -when two heterogeneous bodies united together and formed a -third body, the two constituents were entirely destroyed, -and the result formed out of their ruins[21\6]. And this -conception of Synthesis and Analysis, as processes which are -possible successively and alternately, and each of which -supposes the possibility of the other, has been the -fundamental and regulative principle of the operations and -speculations of analytical chemistry from the time of Mayow -to the present day. - -[Note 20\6: Cap. xiv. p. 233.] - -[Note 21\6: Thomson's _Chemistry_, iii. 8.] - -6. _Affinity is Elective._--When the idea of chemical -affinity, or disposition to unite, was brought into view by -the experiments and reasonings of chemists, they found it -necessary to consider this disposition as _elective_;--each -element _chose_ one rather than another of the elements -which were presented to it, and quitted its union with one -to unite with another which it preferred. This has already -appeared in the passage just quoted from Mayow. He adds in -the same strain, 'I have no doubt that fixed salts choose -one acid rather than another, in order that they may -coalesce with it {22} in a more intimate union.'--'Nullus -dubito salia fixa acidum unum præ aliis _eligere_, ut cum -eodem arctiore unione coalescant.' The same thought is -expressed and exemplified by other chemists: they notice -innumerable cases in which, when an ingredient is combined -with a liquid, if a new substance be immersed which has a -greater affinity for the liquid, the liquid combines with -the new substance by election, and the former **ingredient -is _precipitated_. Thus Stahl says[22\6], 'In spirit of -nitre dissolve silver; put in copper and the silver is -thrown down; put in iron and the copper goes down; put in -zinc, the iron precipitates; put in volatile alkali, the -zinc is separated; put in fixed alkali, the volatile quits -its hold.'--As may be seen in this example, we have in such -cases, not only a preference, but a long gradation of -preferences. The spirit of nitre will combine with silver, -but it prefers copper; prefers iron more; zinc still more; -volatile alkali yet more; fixed alkali the most. - -[Note 22\6: _Zymotechnia_, 1697, p. 117.] - -The same thing was proved to obtain with regard to each -element; and when this was ascertained, it became the object -of chemists to express these degrees of preference, by lists -in which substances were arranged according to their -disposition to unite with another substance. In this manner -was formed Geoffroy's Table of Affinities (1718), which we -have already mentioned. This Table was further improved by -other writers, as Gellert (1751) and Limbourg (1761). -Finally Bergman improved these Tables still further, taking -into account not only the order of affinities of each -element for others, but the _sum_ of the tendencies to unite -of each two elements, which sum, he held, determined the -resulting combination when several elements were in contact -with each other. - -7. As we have stated in the History[23\6], when the doctrine -of elective affinities had assumed this very definite and -systematic form, it was assailed by Berthollet, who -maintained, in his _Essai de Statique_ {23} _Chimique_, -(1803,) that chemical affinities are _not_ elective:--that, -when various elements are brought together, their -combinations do not depend upon the kind of elements alone, -but upon the quantity of each which is present, that which -is most abundant always entering most largely into the -resulting compounds. It may seem strange that it should be -possible, at so late a period of the science, to throw doubt -upon a doctrine which had presided over and directed its -progress so long. Proust answered Berthollet, and again -maintained that chemical affinity is elective. I have, in -the History, given the judgment of Berzelius upon this -controversy. 'Berthollet,' he says, 'defended himself with -an acuteness which makes the reader hesitate in his -judgment; but the great mass of facts finally decided the -point in favour of Proust.' I may here add the opinion -pronounced upon this subject by Dr. Turner[24\6]: '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 circumstances]: but -Berthollet ran into the opposite extreme in declaring that -the effects formerly ascribed to that power are never -produced by it. That chemical attraction is exerted between -different bodies with different degrees of energy, is, I -apprehend, indisputable.' And he then proceeds to give many -instances of differences in affinity which cannot be -accounted for by the operation of any modifying causes. -Still more recently, M. Dumas has taken a review of this -controversy; and, speaking with enthusiasm of the work of -Berthollet, as one which had been of inestimable service to -himself in his early study of chemistry, he appears at first -disposed to award to him the victory in this dispute. But -his final verdict leaves undamaged the general principle now -under our consideration, that chemical affinity is elective. -'For my own part,' he says[25\6], 'I willingly admit the -notions of Berthollet when we have to do with acids or {24} -with bases, of which the energy is nearly equal: but when -bodies endued with very energetic affinities are in presence -of other bodies of which the affinities are very feeble, I -propose to adopt the following rule: In a solution, -everything remaining dissolved, the strong affinities -satisfy themselves, leaving the weak affinities to arrange -matters with one another. The strong acids take the strong -bases, and the weak acids can only unite with the weak -bases. The known facts are perfectly in accordance with this -practical rule.' It is obvious that this recognition of a -distinction between strong and weak affinities, which -operates to such an extent as to determine entirely the -result, is a complete acknowledgement of the Elective nature -of Affinity, as far as any person acquainted with chemical -operations could contend for it. For it must be allowed by -all, that solubility, and other collateral circumstances, -influence the course of chemical combinations, since they -determine whether or not there shall take place that contact -of elements without which affinity cannot possibly operate. - -[Note 23\6: _Hist. Ind. Sc._ b. xiv. c. iii.] - -[Note 24\6: _Chemistry_, p. 199. 6th edition.] - -[Note 25\6: _Leçons de Philosophie Chimique_, p. 386.] - -8. _Affinity is Definite as to quantity._--In proportion as -chemists obtained a clearer view of the products of the -laboratory as results of the composition of elements, they -saw more and more clearly that these results were definite; -that one element not only preferred to combine with another -of a certain kind, but also would combine with it to a -certain extent and no further, thus giving to the result not -an accidental and variable, but a fixed and constant -character. Thus salts being considered as the result of the -combination of two opposite principles, acid and alkali, and -being termed _neutral_ when these principles exactly -balanced each other, Rouelle (who was Royal Professor at -Paris in 1742) admits of neutral salts with excess of acid, -neutral salts with excess of base, and perfect neutral -salts. Beaume maintained[26\6] against him that there were -no salts except those perfectly neutral, the other classes -being the results of mixture and imperfect {25} combination. -But this question was not adequately treated till chemists -made every experiment with the balance in their hands. When -this was done, they soon discovered that, in each neutral -salt, the proportional weights of the ingredients which -composed it were always the same. This was ascertained by -Wenzel, whose _Doctrine of the Affinities of Bodies_ -appeared in 1777. He not only ascertained that the -proportions of elements in neutral chemical compounds are -definite, but also that they are reciprocal; that is, (to -express his results in a manner now employed by chemists), -that if A, a certain weight of a certain acid, neutralize -_m_, a certain weight of a certain base, and B, a certain -weight of a certain other acid, neutralize _n_, a certain -weight of a certain other base; the compound of A and _n_ -will also be neutral; as also that of B and _m_. The same -views were again presented by Richter in 1792, in his -_Principles of the Measure of Chemical Elements_. And along -with these facts, that of the combination of elements in -multiple proportions being also taken into account, the -foundations of the Atomic Theory were laid; and that Theory -was propounded in 1803 by Mr. Dalton. That theory, however, -rests upon the Idea of Substance, as well as upon that Idea -of Chemical Affinity which we are here considering; and the -discussion of its evidence and truth must be for the present -deferred. - -[Note 26\6: Dumas, _Phil. Chim._ p. 198.] - -9. The two principles just explained,--that Affinity is -Definite as to the Kind, and as to the Quantity of the -elements which it unites,--have here been stated as results -of experimental investigation. That they could never have -been clearly understood, and therefore never firmly -established, without laborious and exact experiments, is -certain; but yet we may venture to say that being once fully -known, they may seem to thoughtful men to possess an -evidence beyond that of mere experiment. For how, in fact, -can we conceive combinations, otherwise than as definite in -kind and quantity? If we were to suppose each element -ready to combine with any other indifferently, and -indifferently in any quantity, we should have a world in -{26} which all would be confusion and indefiniteness. There -would be no fixed kinds of bodies. Salts, and stones, and -ores, would approach to and graduate into each other by -insensible degrees. Instead of this, we know that the world -consists of bodies distinguishable from each other by -definite differences, capable of being classified and named, -and of having general propositions asserted concerning them. -And as we cannot conceive a world in which this should not -be the case, 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 asserted. - -This will, perhaps, appear more clearly by stating our -fundamental convictions respecting chemical composition in -another form, which I shall, therefore, proceed to do. - -10. _Chemical Composition determines Physical -Properties._--However obscure and incomplete may be our -conception of the internal powers by which the ultimate -particles of bodies are held together, it involves, at -least, this conviction:--that these powers are what -determine bodies to be bodies, and therefore contain the -reason of all the properties which, as bodies, they possess. -The forces by which the particles of a body are held -together, also cause it to be hard or soft, heavy or light, -opake or transparent, black or red; for if these forces are -not the cause of these peculiarities, what can be the cause? -By the very supposition which we make respecting these -forces, they include all the relations by which the parts -are combined into a whole, and therefore they, and they -only, must determine all the attributes of the whole. The -foundation of all our speculations respecting the intimate -constitution of bodies must be this principle, that their -composition determines their properties. - -Accordingly we find our chemists reasoning from this -principle with great confidence, even in doubtful cases. -Thus Davy, in his researches concerning the diamond, says: -'That some chemical difference must exist between the -hardest and most beautiful of the {27} gems and charcoal, -between a non-conductor and a conductor of electricity, it -is scarcely possible to doubt: and it seems reasonable to -expect that a very refined or perfect chemistry will confirm -_the analogies of nature_; and show that bodies cannot be -the same in their composition or chemical nature, and yet -totally different in their chemical properties.' It is -obvious that the principle here assumed is so far from being -a mere result of experience, that it is here appealed to to -prove that all previous results of experience on this -subject must be incomplete and inaccurate; and that there -must be some chemical difference between charcoal and -diamond, though none had hitherto been detected. - -11. In what manner, according to what rule, the chemical -composition shall determine the kind of the substance, we -cannot reasonably expect to determine by mere conjecture or -assumption, without a studious examination of natural bodies -and artificial compounds. Yet even in the most recent times, -and among men of science, we find that an assumption of the -most arbitrary character has in one case been mixed up with -this indisputable principle, that the elementary composition -determines the kind of the substance. In the classification -of minerals, 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 -system. But they have appended to this principle, -arbitrarily and unjustifiably, the maxim that the element -which is _largest in quantity_ shall fix the class of the -substance. To make such an assumption is to renounce, at -once, all hope of framing a system which shall be governed -by the resemblances of the things classified; for how can we -possibly know beforehand that fifty-five per cent, of iron -shall give a substance its predominant properties, and that -forty-five per cent, shall not? Accordingly, the systems of -mineralogical arrangement which have been attempted in this -way, (those of Haüy, Phillips, and others,) have been found -inconsistent with themselves, ambiguous, and incapable of -leading to any general truths. {28} - -12. _Chemical Composition and Crystalline Form -correspond._--Thus the physical properties of bodies depend -upon their chemical composition, but in a manner which a -general examination of bodies with reference to their -properties and their composition can alone determine. We -may, however, venture to assert further, that the more -definite the properties are, the more distinct may we expect -to find this dependence. Now the most definite of the -properties of bodies are those constant properties which -involve relations of space; that is, their figure. We speak -not, however, of that external figure, derived from external -circumstances, which, so far from being constant and -definite, is altogether casual and arbitrary; but of that -figure which arises from their internal texture, and which -shows itself not only in the regular forms which they -spontaneously assume, but in the disposition of the parts to -separate in definite directions, and no others. In short, -the most definite of the properties of perfect chemical -compounds is their _crystalline structure_; and therefore it -is evident that the crystalline structure of each body, and -the forms which it affects, must be in a most intimate -dependence upon its chemical composition. - -Here again we are led to the brink of another theory;--that -of crystalline structure, which has excited great interest -among philosophers ever since the time of Haüy. But this -theory involves, besides that idea of chemical composition -with which we are here concerned, other conceptions, which -enter into the relations of figure. These conceptions, -governed principally by the Idea of Symmetry, must be -unfolded and examined before we can venture to discuss any -theory of crystallization: and we shall proceed to do this -as soon as we have first duly considered the Idea of -Substance and its consequences. - - - -{{29}} -CHAPTER III. - -OF THE IDEA OF SUBSTANCE. - - -1. _Axiom of the Indestructibility of Substance._--WE now -come to an Idea of which the history is very different from -those of which we have lately been speaking. Instead of -being gradually and recently brought into a clear light, as -has been the case with the Ideas of Polarity and Affinity, -the Idea of Substance has been entertained in a distinct -form from the first periods of European speculation. That -this is so, is proved by our finding a principle depending -upon this Idea current as an axiom among the early -philosophers of Greece:--namely, that _nothing can be -produced out of nothing_. Such an axiom, more fully stated, -amounts to this: that the substance of which a body consists -is incapable of being diminished (and consequently incapable -of being augmented) in quantity, whatever apparent changes -it may undergo. Its forms, its distribution, its qualities, -may vary, but the substance itself is identically the same -under all these variations. - -The axiom just spoken of was the great principle of the -physical philosophy of the Epicurean school, as it must be -of every merely material philosophy. The reader of Lucretius -will recollect the emphasis with which it is repeatedly -asserted in his poem: - E nilo nil gigni, in nilum nil posse reverti; - Nought comes of nought, nor ought returns to nought. - -Those who engaged in these early attempts at physical -speculation were naturally much pleased with the clearness -which was given to their notions of change, composition, and -decomposition, by keeping steadily hold of the Idea of -Substance, as marked by this {30} fundamental axiom. Nor has -its authority ever ceased to be acknowledged. A philosopher -was asked[27\6], What is the weight of smoke? He answered, -'Subtract the weight of the ashes from the weight of the -wood which is burnt, and you have the weight of the smoke.' -This reply would be assented to by all; and it assumes as -incontestable that even under the action of fire, the -material, the substance, does not perish, but only changes -its form. - -[Note 27\6: Kant, _Kritik der R. V._ p. 167.] - -This principle of the indestructibility of substance might -easily be traced in many reasonings and researches, ancient -and modern. For instance, when the chemist works with the -_retort_, he places the body on which he operates in one -part of an inclosed cavity, which, by its bendings and -communications, separates at the same time that it confines, -the products which result from the action of fire: and he -assumes that this process is an analysis of the body into -its ingredients, not a creation of anything which did not -exist before, or a destruction of anything which previously -existed. And he assumes further, that the total quantity of -the substance thus analysed is the sum of the quantities of -its ingredients. This principle is the very basis of -chemical speculation, as we shall hereafter explain more fully. - -2. _The Idea of Substance._--The axiom above spoken of -depends upon the Idea of Substance, which is involved in all -our views of external objects. We unavoidably assume that -the qualities and properties which we observe are properties -of _things_;--that the adjective implies a -substantive;--that there is, besides the external characters -of things, something _of which_ they are the characters. An -apple which is red, and round, and hard, is not merely -redness, and roundness, and hardness: these circumstances -may all alter while the apple remains the same apple. Behind -or under the appearances which we see, we conceive something -of which we think; or, to use the metaphor which obtained -currency among the ancient philosophers, the {31} attributes -and qualities which we observe are supported by and inherent -in something: and this something is hence called a -_substratum_ or _substance_,--that which stands _beneath_ -the apparent qualities and supports them. - -That we have such an _Idea_, using the term 'Idea' in the -sense in which I have employed it throughout these -disquisitions, is evident from what has been already said. -The Axiom of the Indestructibility of Substance proves the -existence of the Idea of Substance, just as the Axioms of -Geometry and Arithmetic prove the existence of the Ideas of -Space and Number. In the case of Substance, as of space or -number, the ideas cannot be said to be borrowed from -experience, for the axioms have an authority of a far more -comprehensive and demonstrative character than any which -experience can bestow. The axiom that nothing can be -produced from nothing and nothing destroyed, is so far from -being a result of experience, that it is apparently -contradicted by the most obvious observation. It has, at -first, the air of a paradox; and by those who refer to it, -it is familiarly employed to show how fallacious common -observation is. The assertion is usually made in this -form;--that nothing is created and nothing annihilated, -_notwithstanding_ that the common course of our experience -appears to show the contrary. The principle is not an -empirical, but a necessary and universal truth;--is -collected, not from the evidence of our senses, but from the -operation of our ideas. And thus the universal and -undisputed authority of the axiom proves the existence of -the Idea of Substance. - -3. _Locke's Denial of the Idea of Substance._--I shall not -attempt to review the various opinions which have been -promulgated respecting this Idea: 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_ occasioned. Locke's object was to disprove -the existence of all ideas not derived from Sensation or -Reflection: and since the idea of substance as distinct from -external qualities, is {32} manifestly not derived directly -from sensation, nor by any very obvious or distinct process -from reflection, Locke was disposed to exclude the idea as -much as possible. Accordingly, in his argumentation against -Innate Ideas[28\6], he says plainly, 'the idea of substance, -which we neither have nor can have by sensation or -reflection.' And the inference which he draws is, 'that we -have no such clear idea at all.' What then, it may be asked, -do we mean by the word _substance_? This also he answers, -though somewhat strangely, 'We signify nothing by the word -_substance_, but only an uncertain supposition of we know -not what, _i. e._ of something whereof we have no particular -distinct positive idea, which we take to be the substratum, -or support, of those ideas we know.' That while he indulged -in this tautological assertion of our ignorance and -uncertainty, he should still have been compelled to -acknowledge that the word substance had some meaning, and -should have been driven to explain it by the identical -metaphors of 'substratum' and 'support,' is a curious proof -how impossible it is entirely to reject this idea. - -[Note 28\6: _Essay_, b. i. c. iv. s. 18.] - -But as we have already seen, the supposition of the -existence of substance is so far from being uncertain, that -it carries with it irresistible conviction, and substance is -necessarily conceived as something which cannot be produced -or destroyed. It may be easily supposed, therefore, that -when the controversy between Locke and his assailants came -to this point, he would be in some difficulty. And, indeed, -though with his accustomed skill in controversy, he managed -to retain a triumphant tone, he was driven from his main -points. Thus he repels the charge that he took the being of -substance to be doubtful[29\6]. He says, 'Having everywhere -affirmed and built upon it that man is a substance, I cannot -be supposed to question or doubt of the being of substance, -till I can question or doubt of my own being.' He attempts -to make a stand by saying that _being_ of things does not -depend upon our {33} _ideas_; but if he had been asked how, -without having an _idea_ of substance, he _knew_ substance -to _be_, it is difficult to conceive what answer he could -have made. Again, he had said that our idea of substance -arises from our 'accustoming ourselves to suppose' a -substratum of qualities. Upon this his adversary, Bishop -Stillingfleet, very properly asks, Is this custom grounded -upon true reason or no? To which Locke replies, that it is -grounded upon this: That we cannot conceive how simple ideas -of sensible qualities should subsist alone; and therefore we -suppose them to exist in, and to be supported by some common -subject, which support we denote by the name substance. Thus -he allows, not only that we necessarily assume the reality -of substance, but that we cannot conceive qualities without -substance; which are concessions so ample as almost to -include all that any advocate for the Idea of Substance need -desire. - -[Note 29\6: _Essay_, b. ii. c. ii. and _First Letter to the -Bishop of Worcester_.] - -Perhaps Locke, and the adherents of Locke, in denying that -we have an idea of substance in general, were latently -influenced by finding that they could not, by any effort of -mind, call up any _image_ which could be considered as an -image of substance in general. That in this sense we have no -idea of substance, is plain enough; but in the same sense we -have no idea of space in general, or of time, or number, or -cause, or resemblance. Yet we certainly have such a power of -representing to our minds space, time, number, cause, -resemblance, as to arrive at numerous truths by means of -such representations. These general representations I have -all along called Ideas, nor can I discover any more -appropriate word; and in this sense, we have also, as has -now been shown, an Idea of Substance. - -4. _Is all Material Substance heavy?_--The principle that -the quantity of the substance of any body remains unchanged -by our operations upon it, is, as we have said, of universal -validity. But then the question occurs, how are we to -ascertain the quantity of substance, and thus, to apply the -principle in particular cases. In the case above mentioned, -where {34} smoke was to be weighed, it was manifestly -assumed that the quantity of the substance might be known by -its weight; and that the total quantity being unchanged, the -total weight also would remain the same. Now on what grounds -do we make this assumption? Is all material substance heavy? -and if we can assert this to be so, on what grounds does the -truth of the assertion rest? These are not idle questions of -barren curiosity; for in the history of that science -(Chemistry) to which the Idea of Substance is principally -applicable, nothing less than the fate of a comprehensive -and long established theory (the Phlogiston theory) depended -upon the decision of this question. When it was urged that -the reduction of a metal from a calcined to a metallic form -could not consist in the _addition_ of phlogiston, because -the metal was lighter than the calx had been; it was replied -by some, that this was not conclusive, for that phlogiston -was a principle of levity, diminishing the weight of the -body to which it was added. This reply was, however, -rejected by all the sounder philosophers, and the force of -the argument finally acknowledged. But why was this -suggestion of a substance having no weight, or having -absolute levity, repudiated by the most reflective -reasoners? It is assumed, it appears, that all matter must -be heavy; what is the ground of this assumption? - -The ground of such an assumption appears to be the -following. Our idea of substance includes in it this:--that -substance is a quantity capable of addition; and thus -capable of making up, by composition, a sum equal to all its -parts. But substance, and the quantity of substance, can be -known to us only by its attributes and qualities. And the -qualities which are capable constantly and indefinitely of -increase and diminution by increase and diminution of the -parts, must be conceived inseparable from the substance. For -the qualities, if removable from the substance at all, must -be removable by some operation performed upon the substance; -and by the idea of substance, all such operations are only -equivalent to separation, junction, and union of parts. -Hence those characters {35} which thus universally increase -and diminish by addition and subtraction of the things -themselves, belong to the substance of the things. They are -measures of its quantity, and are not merely its separable -qualities. - -The weight of bodies is such a character. However we -compound or divide bodies, we compound and divide their -weight in the same manner. We may dismember a body into the -minutest parts; but the sum of the weights of the parts is -always equal to the whole weight of the body. The weight of -a body can be in no way increased or diminished, except by -adding something to it or taking something from it. If we -bake a brick, we do not conceive that the change of colour -or of hardness, implies that anything has been created or -destroyed. It may easily be that the parts have only assumed -a new arrangement; but if the brick have lost weight, we -suppose that something (moisture for instance) has been -removed elsewhere. - -Thus weight is apprehended as essential to matter. In -considering the dismemberment or analysis of bodies, we -assume that there must be some criterion of the quantity of -substance; and this criterion can possess no other -properties than their weight possesses. If we assume an -element which has no weight, or the weight of which is -negative, as some of the defenders of phlogiston attempted -to do, we put an end to all speculation on such subjects. -For if weight is not the criterion of the quantity of one -element, phlogiston for instance, why is weight the -criterion of the quantity of any other element? We may, by -the same right, assume any other real or imaginary element -to have levity instead of gravity; or to have a peculiar -intensity of gravity which makes its weight no index of its -quantity. In short, if we do this, we deprive of all -possibility of application our notions of element, analysis, -and composition; and violate the postulates on which the -questions are propounded which we thus attempt to decide. - -We must, then, take a constant and quantitative property of -matter, such as weight is, to be an index {36} of the -quantity of matter or of substance to which it belongs. I do -not here speak of the question which has sometimes been -proposed, whether the _weight_ or the _inertia_ of bodies be -the more proper measure of the quantity of matter. For the -measure of inertia is regulated by the same assumption as -that of substance:--that the quantity of the whole must be -equal to the quantity of all the parts: and inertia is -measured by weight, for the same reason that substance is so. - -Having thus established the certainty, and ascertained the -interpretation of the fundamental principle which the Idea -of Substance involves, we are prepared to consider its -application in the science upon which it has a peculiar -bearing. - - - -{{37}} -NOTE TO CHAPTER III. - - -[3rd Ed.]--[THE doctrine here propounded, that All Matter is -Heavy, has been opposed by Sir William Hamilton of -Edinburgh. (_Works of Reid_, note, p. 853.) This writer is a -man of unquestionable acuteness and of very extensive -reading; but his acuteness shows itself in barren -ontological distinctions, 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 ages. That he should -have no conception of progressive or inductive science is -not wonderful, when we recollect that he holds, as an -important part of his philosophy, that the study of -mathematics perverts and obscures the mind. But it may be of -some interest to consider his objections to the doctrine -here maintained. - -He says, 1st, that our reasoning assumes that we must -necessarily have it in our power to ascertain the Quantity -of Matter; whereas this may be a problem out of the reach of -human determination. - -To this I reply, that my reasoning _does_ assume that there -is a science, or sciences, which make assertions concerning -the Quantity of Matter: Mechanics and Chemistry are such -sciences. My assertion is, that to make such sciences -possible, Quantity of Matter must be proportional to Weight. -If my opponent deny that Mechanics and Chemistry can exist -as sciences, he may invalidate my proof; but not otherwise. - -2. He says that there are two conceivable ways of estimating -the Quantity of Matter: by the Space occupied, and by the -Weight or Inertia; and that I assume the second measure -gratuitously. - -To which I reply, that the most elementary steps in -Mechanics and in Chemistry contradict the notion that {38} -the Quantity of Matter is proportionate to the Space. They -proceed necessarily on a distinction between Space and -Matter:--between mere Extension and material Substance. - -3. He allows that we cannot make the Extension of a body the -measure of the Quantity of Matter, because, he says, we do -not know if 'the compressing force' is such as to produce -'the closest compression.' That is, he assumes a compressing -force, assumes a closest compression, assumes a peculiar -(and very improbable) atomic hypothesis; and all this to -supply a reason why we are not to believe the first simple -principle of Mechanics and Chemistry. - -4. He speaks of 'a series of apparent fluids (as Light or -its vehicle, the Calorific, the Electro-galvanic, and -Magnetic agents) which we can neither denude of their -character of substance, nor clothe with the attribute of -weight.' - -To which my reply is, that precisely because I cannot -'clothe' these agents with the attribute of Weight, I _do_ -'denude them of the character of Substance.' They are not -substances, but agencies. These Imponderable Agents are not -properly called 'Imponderable Fluids.' This I conceive that -I have proved; and the proof is not shaken by denying the -conclusion without showing any defect in the reasoning. - -5. Finally, my critic speaks about 'a logical canon,' and -about 'a criterion of truth, subjectively necessary and -objectively certain;' which matters I shall not waste the -reader's time by discussing.] - - - -{{39}} -CHAPTER IV. - -APPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY. - - -1. _A Body is Equal to the Sum of its Elements._--FROM the -earliest periods of chemistry the balance has been -familiarly used to determine the proportions of the -ingredients and of the compound; and soon after the middle -of the last century, this practice was so studiously -followed, that Wenzel and Richter were thereby led to the -doctrine of Definite Proportions. But yet the full value and -significance of the balance, as an indispensable instrument -in chemical researches, was not understood till the gaseous, -as well as solid and fluid ingredients were taken into the -account. When this was done, it was found that the -principle, that the whole is equal to the sum of its parts, -of which, as we have seen, the necessary truth, in such -cases, flows from the idea of substance, could be applied in -the most rigorous manner. And conversely, it was found that -by the use of the balance, the chemist could decide, in -doubtful cases, which was a whole, and which were parts. - -For chemistry considers all the changes which belong to her -province as compositions and decompositions of elements; but -still the question may occur, whether an observed change be -the one or the other. How can we distinguish whether the -process which we contemplate be composition or -decomposition?--whether the new body be formed by addition -of a new, or subtraction of an old element? Again; in the -case of decomposition, we may inquire, What are the ultimate -limits of our analysis? If we decompound bodies into others -more and more simple, how far can we carry this succession -{40} of processes? How far can we proceed in the road of -analysis? And in our actual course, what evidence have we -that our progress, as far as it has gone, has carried us -from the more complex to the more simple? - -To this we reply, that the criterion which enables us to -distinguish, decidedly and finally, whether our process have -been a mere analysis of the proposed body into its -ingredients, or a synthesis of some of them with some new -element, is the principle stated above, that the weight of -the whole is equal to the weight of all the parts. And no -process of chemical analysis or synthesis can be considered -complete till it has been verified by this fact;--by finding -that the weight of the compound is the weight of its -supposed ingredients; or, that if there be an element which -we think we have detached from the whole, its loss is -betrayed by a corresponding diminution of weight. - -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 theory. The calcination of a -metal was decided to be the union of oxygen with the metal, -and not the separation of phlogiston from it, because it was -found that in the process of calcination, the weight of the -metal increased, and increased exactly as much as the weight -of ambient air diminished. When oxygen and hydrogen were -exploded together, and a small quantity of water was -produced, it was held that this was really a synthesis of -water, because, when very great care was taken with the -process, the weight of the water which resulted was equal to -the weight of the gases which disappeared. - -2. _Lavoisier._--It was when gases came to be considered as -entering largely into the composition of liquid and solid -bodies, that extreme accuracy in weighing was seen to be so -necessary to the true understanding of chemical processes. -It was in this manner discovered by Lavoisier and his -contemporaries that oxygen constitutes a large ingredient of -calcined metals, of acids, and of water. A countryman of -Lavoisier[30\6] {41} 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 balance, but -has also claimed for him the merit of having introduced the -maxim, that in chemical operations nothing is created and -nothing lost. But I think it is impossible to deny that this -maxim is assumed in all the attempts at analysis made by his -contemporaries, as well as by him. This maxim is indeed -included in any clear notion of analysis: it could not be -the result of the researches of any one chemist, but was the -governing principle of the reasonings of all. Lavoisier, -however, employed this principle with peculiar assiduity and -skill. In applying it, he does not confine himself to mere -additions and subtractions of the quantities of ingredients; -but often obtains his results by more complex processes. In -one of his investigations he says, 'I may consider the -ingredients which are brought together, and the result which -is obtained as an algebraical equation; and if I -successively suppose each of the quantities of this equation -to be unknown, I can obtain its value from the rest: and -thus I can rectify the experiment by the calculation, and -the calculation by the experiment. I have often taken -advantage of this method, in order to correct the first -results of my experiments, and to direct me in repeating -them with proper precautions.' - -[Note 30\6: M. Dumas, _Leçons de la Philosophie Chimique_. -1837. p. 157.] - -The maxim, that the whole is equal to the sum of all its -parts, is thus capable of most important and varied -employment in chemistry. But it may be applied in another -form to the exclusion of a class of speculations which are -often put forwards. - -3. _Maxim respecting Imponderable Elements._--Several of the -phenomena which belong to bodies, as heat, light, -electricity, magnetism, have been explained hypothetically -by assuming the existence of certain fluids; but these -fluids have never been shown to have weight. Hence such -hypothetical fluids have been termed _imponderable -elements_. It is however plain, that so long as these fluids -appear to be without weight, they are not _elements_ of -bodies in the same {42} sense as those elements of which we -have hitherto been speaking. Indeed we may with good reason -doubt whether those phenomena depend upon transferable -fluids at all. We have seen strong reason to believe that -light is not matter, but only motion; and the same thing -appears to be probable with regard to heat. Nor is it at all -inconceivable that a similar hypothesis respecting -electricity and magnetism should hereafter be found tenable. -Now if heat, light, and those other agents, be not matter, -they are not _elements_ in such a sense as to be included in -the principle referred to above, That the body is equal to -the sum of its elements. Consequently the maxim just stated, -that in chemical operations nothing is created, nothing -annihilated, does not apply to Light and Heat. They are not -_things_. And whether heat can be produced where there was -no heat before, and light struck out from darkness, the -ideas of which we are at present treating do not enable us -to say. In reasoning respecting chemical synthesis and -analysis therefore, we shall only make confusion by -attempting to include in our conception the Light and Heat -which are produced and destroyed. Such phenomena may be very -proper subjects of study, as indeed they undoubtedly are; -but they cannot be studied to advantage by considering them -as sharing the nature of composition and decomposition. - -Again: in all attempts to explain the processes of nature, -the proper course is, first to measure the facts with -precision, and then to endeavour to understand their cause. -Now the facts of chemical composition and decomposition, the -weights of the ingredients and of the compounds, are facts -measurable with the utmost precision and certainty. But it -is far otherwise with the light and heat which accompany -chemical processes. When combustion, deflagration, -explosion, takes place, how can we measure the light or the -heat? Even in cases of more tranquil action, though we can -apply the thermometer, what does the thermometer tell us -respecting the _quantity_ of the heat? Since then we have no -measure which is of any value as {43} regards such -circumstances in chemical changes, if we attempt to account -for these phenomena _on chemical principles_, we introduce, -into investigations in themselves perfectly precise and -mathematically rigorous, another class of reasonings, vague -and insecure, of which the only possible effect is to -vitiate the whole reasoning, and to make our conclusions -inevitably erroneous. - -We are led then to this maxim: that _imponderable fluids -are_ not _to be admitted as chemical elements of bodies_[31\6]. - -[Note 31\6: See the answer to Sir William Hamilton's -objections, at the end of the last chapter. - -Since we are thus warned by a sound view of the nature of -science, from considering chemical affinity as having any -hold upon imponderable elements, we are manifestly still -more decisively prohibited from supposing mechanical impulse -or pressure to have any effect upon such elements. To make -this supposition, is to connect the most subtle and -incorporeal objects which we know in nature by the most -gross material ties. This remark seems to be applicable to -M. Poisson's hypothesis that the electric fluid is retained -at the surface of bodies by the pressure of the -atmosphere.] - -4. It appears, I think, that our best and most philosophical -chemists have proceeded upon this principle in their -investigations. In reasoning concerning the constitution of -bodies and the interpretation of chemical changes, the -attempts to include in these interpretations the heat or -cold produced, by the addition or subtraction of a certain -hypothetical 'caloric,' have become more and more rare among -men of science. Such statements, and the explanations often -put forwards of the light and heat which appear under -various circumstances in the form of fire, must be -considered as unessential parts of any sound theory. -Accordingly we find Mr. Faraday gradually relinquishing such -views. In January, 1834, he speaks generally of an -hypothesis of this kind[32\6]: 'I cannot refrain from -recalling here the beautiful idea put forth, I believe by -Berzelius, in his development of his views of the -electro-chemical theory of affinity, that the heat and light -evolved during cases of powerful combination {44} are the -consequence of the electric discharge which is at that -moment taking place.' But in April of the same year[33\6], -he observes, that in the combination of oxygen and hydrogen -to produce water, electric powers to a most enormous amount -are for the time active, but that the flame which is -produced gives but feeble traces of such powers. 'Such -phenomena,' therefore, he adds, 'may not, cannot, be taken -as evidences of the nature of the action; but are merely -incidental results, incomparably small in relation to the -forces concerned, and supplying no information of the way in -which the particles are active on each other, or in which -their forces are finally arranged.' - -[Note 32\6: _Researches_, 870.] - -[Note 33\6: _Researches_, 960.] - -In pursuance of this maxim, we must consider as an -unessential part of the oxygen theory that portion of it, -much insisted upon by its author at the time, in which when -sulphur, for instance, combined with oxygen to produce -sulphuric acid, the combustion was accounted for by means of -the _caloric_ which was supposed to be _liberated_ from its -combination with oxygen. - -5. _Controversy of the Composition of Water._--There is -another controversy of our times to which we may with great -propriety apply the maxim now before us. 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 -Lavoisier, a claim was made in favour of James Watt as the -real author of this discovery by his son, (Mr J. Watt,) and -his eulogist, (M. Arago[34\6]). It is not to our purpose -here to discuss the various questions which have arisen on -this subject respecting priority of publication, and -respecting the translation of opinions published at one time -into the language of another period. But if we look at -Watt's own statement of his views, given soon after those of -Cavendish had been published, we shall perceive that it is -marked by a violation of this maxim: we shall find that he -does admit imponderable fluids {45} as chemical elements; -and thus shows a vagueness and confusion in his idea of -chemical composition. With such imperfection in his views, -it is not surprising that Watt, not only did not anticipate, -but did not apprehend quite precisely the discovery of -Cavendish and Lavoisier. Watt's statement of his views is as -follows[35\6]:--'Are we not authorized to conclude that -water is composed of dephlogisticated air and phlogiston -deprived of part of their latent or elementary heat; that -dephlogisticated or pure air is composed of water deprived -of its phlogiston and united to elementary heat and light; -and that the latter are contained in it in a latent state, -so as not to be sensible to the thermometer or to the eye; -and if light be only a modification of heat, or a -circumstance attending it, or a component part of the -inflammable air, then pure or dephlogisticated air is -composed of water deprived of its phlogiston and united to -elementary heat?' - -[Note 34\6: Éloge de James Watt, _Annuaire du Bur. des -Long._ 1839.] - -[Note 35\6: _Phil. Trans._ 1784, p. 332.] - -When we compare this doubtful and hypothetical statement, -involving so much that is extraneous and heterogeneous, with -the conclusion of Cavendish, in which there is nothing -hypothetical or superfluous, we may confidently assent to -the decision which has been pronounced by one[36\6] of our -own time in favour of Cavendish. And we may with pleasure -recognize, in this enlightened umpire, a due appreciation of -the value of the maxim on which we are now insisting. -'Cavendish,' says Mr. Vernon Harcourt, 'pared off {46} from -the hypotheses their theories of combustion, and _affinities -of imponderable for ponderable matter_, as complicating -chemical with physical considerations.' - -[Note 36\6: The Rev. W. Vernon Harcourt, Address to the -British Association, 1839.--Since the first edition of this -work was published, and also since the second edition of the -_History of the Inductive Sciences_, Mr. Watt's -correspondence bearing upon the question of the Composition -of Water has been published by Mr. Muirhead. I do not find, -in this publication, any reason for withdrawing what I have -stated in the text above: but with reference to the -statement in the _History_, it appears that Mr. Cavendish's -claim to the discovery was not uncontested in his own time. -Mr. Watt had looked at the composition of water, as a -problem to be solved, perhaps more distinctly than Mr. -Cavendish had done; and he conceived himself wronged by Mr. -Cavendish's putting forwards his experiment as the first -solution of this problem.] - -6. _Relation of Heat to Chemistry._--But while we thus -condemn the attempts to explain the thermotical phenomena of -chemical processes by means of chemical considerations, it -may be asked if we are altogether to renounce the hope of -understanding such phenomena? It is plain, it may be said, -that heat generated in chemical changes is always a very -important circumstance, and can sometimes be measured, and -perhaps reduced to laws; are we prohibited from speculating -concerning the causes of such circumstances and such laws? -And to this we reply, that we may properly attempt to -connect chemical with thermotical processes, _so far as_ we -have obtained a clear and probable view of the nature of the -thermotical processes. When our theory of Thermotics is -tolerably complete and certain, we may with propriety -undertake to connect it with our theory of Chemistry. But at -present we are not far enough advanced in our knowledge of -heat to make this attempt with any hope of success. We can -hardly expect to understand the part which heat plays in the -union of two bodies, when we cannot as yet comprehend in -what manner it produces the liquefaction or vaporization of -one body. We cannot look to account for Gay Lussac and -Dalton's Law, that all gases expand equally by heat, till we -learn how heat causes a gas to expand. We cannot hope to see -the grounds of Dulong and Petit's Law, that the specific -heat of all atoms is the same, till we know much more, not -only about atoms, but about specific heat. We have as yet no -thermotical theory which even professes to account for all -the prominent facts of the subject[37\6]: and the theories -which have been proposed are of the most diverse kind. -Laplace assumes particles of bodies surrounded by -atmospheres of caloric[38\6]; Cauchy makes heat consist in -longitudinal vibrations of the ether of which transverse -vibrations {47} produce light: in Ampère's theory[39\6], -heat consists in the vibrations of the particles of bodies. -And so long as we have nothing more certain in our -conceptions of heat than the alternative of these and other -precarious hypotheses, how can we expect to arrive at any -real knowledge, by connecting the results of such hypotheses -with the speculations of Chemistry, of which science the -theory is at least equally obscure? - -[Note 37\6: _Hist. Ind. Sci._ b. x. c. 4.] - -[Note 38\6: _Ib._] - -[Note 39\6: _Hist. Ind. Sci._ b. x. c. 4.] - -The largest attempts at chemical theory have been made in -the form of the Atomic Theory, to which I have just had -occasion to allude. I must, therefore, before quitting the -subject, say a few words respecting this theory. - - - -{{48}} -CHAPTER V. - -THE ATOMIC THEORY. - - -1. _The Atomic Theory considered on Chemical Grounds._--WE -have already seen that the combinations which result from -chemical affinity are definite, a certain quantity of one -ingredient uniting, not with an uncertain, but with a -certain quantity of another ingredient. But it was found, in -addition to this principle, that one ingredient would often -unite with another in different proportions, and that, in -such cases, these proportions are multiples one of another. -In the three salts formed by potassa with oxalic acid, the -quantities of acid which combine with the same quantity of -alkali are exactly in the proportion of the numbers 1, 2, 4. -And the same rule of the existence of multiple proportions -is found to obtain in other cases. - -It is obvious that such results will be accounted for, if we -suppose that the base and the acid consist each of numerous -definite equal particles, and that the formation of the -salts above mentioned consists in the combination of one -particle of the base with one particle of acid, with two -particles of acid, and with four particles of acid, -respectively. But further; as we have already stated, -chemical affinity is not only definite, but reciprocal. The -proportions of potassa and soda which form neutral salts -being 590 and 391 in one case, they are so in all cases. -These numbers represent _proportions_ of weight in which the -two bases, potassa and soda, enter into analogous -combinations; 590 of potassa is _equivalent_ to 391 of soda. -These facts with regard to combination are still expressed -by the above supposition of equal particles, assuming that -the weights of a {49} particle of potassa and of soda are in -the proportion of 590 to 391. - -But we pursue our analysis further. We find that potassa is -a compound of a metallic base, potassium, and of oxygen, in -the proportion of 490 to 100; we suppose, then, that the -particle of potassa consists of a particle of potassium and -a particle of oxygen; and these latter particles, since we -see no present need to suppose them divided, potassium and -oxygen being simple bodies, we may call _atoms_, and assume to -be indivisible. And by supposing all simple bodies to -consist of such atoms, and compounds to be formed by the -union of two, or three, or more of such atoms, we explain -the occurrence of definite and multiple proportions, and we -construct the Atomic Theory. - -2. _Hypothesis of Atoms._--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 to, it is a -clear and useful generalization. But if the Atomic Theory be -put forwards (and its author, Dr. Dalton, appears to have -put it forwards with such an intention,) as asserting that -chemical elements are really composed of _atoms_, that is, -of such particles not further divisible, we cannot avoid -remarking, that for such a conclusion, chemical research has -not afforded, nor can afford, any satisfactory evidence -whatever. The smallest observable quantities of ingredients, -as well as the largest, combine according to the laws of -proportions and equivalence which have been cited above. How -are we to deduce from such facts any inference with regard -to the existence of certain smallest possible particles? The -Theory, when dogmatically taught as a physical truth, -asserts that all observable quantities of elements _are_ -composed of proportional numbers of particles which can no -further be subdivided; but all which observation teaches us -is, that if there be such particles, they are smaller than -the smallest observable quantities. In chemical experiment, -at least, there is not the slightest positive evidence for -the existence of such atoms. The assumption of _indivisible_ -particles, smaller than the smallest {50} observable, which -combine, particle with particle, will explain the phenomena; -but the assumption of particles bearing this proportion, but -_not_ possessing the property of indivisibility, will explain -the phenomena at least equally well. The decision of the -question, therefore, whether the Atomic Hypothesis be the -proper way of conceiving the chemical combinations of -substances, must depend, not upon chemical facts, but upon -our conception of Substance. In this sense the question is -an ancient and curious controversy, and we shall hereafter -have to make some remarks upon it. - -3. _Chemical Difficulties of the Hypothesis._--But before -doing this, we may observe that there is no small difficulty -in reconciling this hypothesis with the facts of chemistry. -According to the theory, all salts, compounded of an acid -and a base, are analogous in their atomic constitution; and -the number of atoms in one such compound being known or -assumed, the number of atoms in other salts may be -determined. But when we proceed in this course of reasoning -to other bodies, as metals, we find ourselves involved in -difficulties. The protoxide of iron is a base which, -according to all analogy, must consist of one atom of iron -and one of oxygen: but the peroxide of iron is also a base, -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 oxygen. Here, then, our indivisible atoms must be -divisible, even upon chemical grounds. And if we attempt to -evade this difficulty by making the peroxide of iron consist -of two atoms of iron and three of oxygen, we have to make a -corresponding alteration in the theoretical constitution of -all bodies analogous to the protoxide; and thus we overturn -the very foundation of the theory. Chemical facts, -therefore, not only do not prove the Atomic Theory as a -physical truth, but they are not, according to any -modification yet devised of the theory, reconcileable with -its scheme. - -Nearly the same conclusions result from the attempts to -employ the Atomic Hypothesis in expressing another important -chemical law;--the law of the {51} combinations of gases -according to definite proportions of their volumes, -experimentally established by Gay Lussac[40\6]. In order to -account for this law, it has been very plausibly suggested -that all gases, under the same pressure, contain an equal -number of atoms in the same space; and that when they -combine, they unite atom to atom. Thus one volume of -chlorine unites with one volume of hydrogen, and forms -hydrochloric acid[41\6]. But then this hydrochloric acid -occupies the space of the two volumes; and therefore the -proper number of particles cannot be supplied, and the -uniform distribution of atoms in all gases maintained, -without dividing into two each of the compound particles, -constituted of an atom of chlorine and an atom of hydrogen. -And thus in this case, also, the Atomic Theory becomes -untenable if it be understood to imply the indivisibility of -the atoms. - -[Note 40\6: _Hist. Ind. Sc._ b. xiv. c. 8.] - -[Note 41\6: Dumas, _Phil. Chim._ 263.] - -In all these attempts to obtain distinct physical conception -of chemical union by the aid of the Atomic Hypothesis, the -atoms are conceived to be associated by certain forces of -the nature of mechanical attractions. But we have already -seen[42\6] that no such mode of conception can at all -explain or express the facts of chemical combination; 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 aspect, the facts on which -it grounds itself should be found not to authorize its -positive doctrines; and that when these doctrines are tried -upon the general range of chemical observation, they should -prove incapable of even expressing, without -self-contradiction, the laws of phenomena. - -[Note 42\6: See Chapter I. of this book.] - -4. _Grounds of the Atomic Doctrine._--Yet the doctrine of -atoms, or of substance as composed of indivisible particles, -has in all ages had great hold upon the minds of physical -speculators; nor would this doctrine ever have suggested -itself so readily, or have been maintained so tenaciously, -as the true mode of {52} conceiving chemical combinations, -if it had not been already familiar to the minds of those -who endeavour to obtain a general view of the constitution -of nature. The grounds of the assumption of the atomic -structure of substance are to be found rather in the idea of -substance itself, than in the experimental laws of chemical -affinity. And the question of the existence of atoms, thus -depending upon an idea which has been the subject of -contemplation from the very infancy of philosophy, has been -discussed in all ages with interest and ingenuity. On this -very account it is unlikely that the question, so far as it -bears upon chemistry, should admit of any clear and final -solution. Still it will be instructive to look back at some -of the opinions which have been delivered respecting this -doctrine. - -5. _Ancient Prevalence of the Atomic Doctrine._--The -doctrine that matter consists of minute, simple, -indivisible, indestructible particles as its ultimate -elements, has been current in all ages and countries, -whenever the tendency of man to wide and subtle speculations -has been active. I need not attempt to trace the history of -this opinion in the schools of Greece and Italy. It was the -leading feature in the physical tenets of the Epicureans, -and was adopted by their Roman disciples, as the poem of -Lucretius copiously shows us. The same tenet had been held -at still earlier periods, in forms more or less definite, by -other philosophers. It is ascribed to Democritus, and is -said to have been by him derived from Leucippus. But this -doctrine is found also, we are told[43\6], among the -speculations of another intellectual and acute race, the -Hindoos. According to some of their philosophical writers, -the ultimate elements of matter are atoms, of which it is -proved by certain reasonings, that they are each one-sixth -of one of the motes that float in the sunbeam. - -[Note 43\6: By Mr. Colebrook. _Asiatic Res._ 1824.] - -This early prevalence of controversies of the widest and -deepest kind, which even in our day remain undecided, has in -it nothing which need surprize us; or, at least, it has in -it nothing which is not in conformity {53} with the general -course of the history of philosophy. As soon as any ideas -are clearly possessed by the human mind, its activity and -acuteness in reasoning upon them are such, that the -fundamental antitheses and ultimate difficulties which -belong to them are soon brought into view. The Greek and -Indian philosophers had mastered completely the Idea of -Space, and possessed the Idea of Substance in tolerable -distinctness. They were, therefore, quite ready, with their -lively and subtle minds, to discuss the question of the -finite and infinite divisibility of matter, so far as it -involved only the ideas of space and of substance, and this -accordingly they did with great ingenuity and perseverance. - -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 matter. We must add to these ideas, that -of mechanical Force with its antagonist Resistance, and that -of the Affinity of one kind of matter for another. Now the -former of these ideas the ancients possessed in a very -obscure and confused manner; and of the latter they had no -apprehension whatever. They made vague assumptions -respecting the impact and pressure of atoms on each other; -but of their mutual attraction and repulsion they never had -any conception, except of the most dim and wavering kind; -and of an affinity different from mere local union they did -not even dream. Their speculations concerning atoms, -therefore, can have no value for us, except as a part of the -history of science. If their doctrines appear to us to -approach near to the conclusions of our modern philosophy, -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 matter. - -6. _Bacon._--Still, when modern philosophers look upon the -Atomic Theory of the ancients in a general point of view -merely, without considering the special conditions which -such a theory must fulfil, in order to represent the -discoveries of modern times, they are {54} disposed to -regard it with admiration. Accordingly we find Francis Bacon -strongly expressing such a feeling. 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 world. Among his works is a remarkable -dissertation _On the Philosophy of Democritus, Parmenides, -and Telesius_: the last mentioned of whom was one of the -revivers of physical science in modern times. In this work -he speaks of the atomic doctrine of Democritus as a -favourable example of the exertions of the undisciplined -intellect. 'Hæc ipsa placita, quamvis paulo emendatiora, -talia sunt qualia esse possunt illa quæ ab intellectu sibi -permisso, nec continenter et gradatim sublevato, profecta -videntur.'--'These doctrines, thus [in an ancient fable] -presented in a better form, are such glimpses of truth as -can be obtained by the intellect left to its own natural -impulses, and not ascending by successive and connected -steps,' [as the Baconian philosophy directs]. 'Accordingly,' -he adds, 'the doctrine of Atoms, from its going a step -beyond the period in which it was advanced, was ridiculed by -the vulgar, and severely handled in the disputations of the -learned, notwithstanding the profound acquaintance with -physical science by which its author was allowed to be -distinguished, and from which he acquired the character of a -magician.' - -'However,' he continues, 'neither the hostility of -Aristotle, with all his skill and vigour in disputation, -(though, like the Ottoman sultans, he laboured to destroy -all his brother philosophers that he might rest undisputed -master of the throne of science,) nor the majestic and lofty -authority of Plato, could effect the subversion of the -doctrine of Democritus. And while the opinions of Plato and -Aristotle were rehearsed with loud declamation and -professorial pomp in the schools, this of Democritus was -always held in high honour by those of a deeper wisdom, who -followed in silence a severer path of contemplation. In the -days of Roman speculation it kept its ground and its favour; -Cicero everywhere speaks of its author with the {55} -greatest praise; and Juvenal, who, like poets in general, -probably expressed the prevailing judgment of his time, -proclaims his merit as a noble exception to the general -stupidity of his countrymen. - . . . . Cujus prudentia monstrat - Magnos posse viros et magna exempla daturos - Vervecum in patriâ crassoque sub aere nasci. - -'The destruction of this philosophy was not effected by -Aristotle and Plato, but by Genseric and Attila, and their -barbarians. For then, when human knowledge had suffered -shipwreck, those fragments of the Aristotelian and Platonic -philosophy floated on the surface like things of some -lighter and emptier sort, and so were preserved; while more -solid matters went to the bottom, and were almost lost in -oblivion.' - -7. _Modern Prevalence of the Atomic Doctrine._--It is our -business here to consider the doctrine of Atoms only in its -bearing upon existing physical sciences, and I must -therefore abstain from tracing the various manifestations of -it in the schemes of hypothetical cosmologists;--its place -among the _vortices_ of Descartes, its exhibition in the -_monads_ of Leibnitz. I will, however, quote a passage from -Newton to show the hold it had upon his mind. - -At the close of his _Opticks_ he says, 'All these things -being considered, it seems probable to me that God, in the -beginning, formed matter in solid, massy, hard, -impenetrable, moveable particles, of such sizes and figures, -and with such other properties, and in such proportions to -space, as most conduced to the end for which He formed them; -and that the primitive particles, being solids, are -incomparably harder than any porous bodies compounded of -them, even so very hard as never to wear or break in pieces; -no ordinary power being able to divide what God had made one -in the first creation. While the particles continue entire, -they may compose bodies of one and the same nature and -texture in all ages: but should they wear away or break in -pieces, the nature of things depending on them would be -changed. Water and earth composed {56} 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 beginning. And therefore that nature may be -lasting, the changes of corporeal things are to be placed -only in the various separations and new associations and -motions of these permanent particles; compounded bodies -being apt to break, not in the midst of solid particles, but -where those particles are laid together and only touch in a -few points.' - -We shall hereafter see how extensively the atomic doctrine -has prevailed among still more recent philosophers. Not only -have the chemists assumed it as the fittest form for -exhibiting the principles of multiple proportions; but the -physical mathematicians, as Laplace and Poisson, have made -it the basis of their theories of heat, electricity, -capillary action; and the crystallographers have been -supposed to have established both the existence and the -arrangement of such ultimate molecules. - -In the way in which it has been employed by such writers, -the hypothesis of ultimate particles has been of great use, -and is undoubtedly permissible. But when we would assert -this theory, not as a convenient hypothesis for the -expression or calculation of the laws of nature, but as a -philosophical truth respecting the constitution of the -universe, we find ourselves checked by difficulties of -reasoning which we cannot overcome, as well as by -conflicting phenomena which we cannot reconcile. I will -attempt to state briefly the opposing arguments on this -question. - -8. _Arguments for and against Atoms._--The leading arguments -on the two sides of the question, in their most general -form, may be stated as follows: - -_For_ the Atomic Doctrine.--The appearances which nature -presents are compounded of many parts, but if we go on -resolving the larger parts into smaller, and so on -successively, we must at last come to something simple. For -that which is compound can be so no otherwise than by -composition of what is simple; and if we suppose all -composition to be removed, which {57} hypothetically we may -do, there can remain nothing but a number of simple -substances, capable of composition, but themselves not -compounded. That is, matter being dissolved, resolves itself -into atoms. - -_Against_ the Atomic Doctrine.--Space is divisible without -limit, as may be proved by Geometry; and matter occupies -space, therefore matter is divisible without limit, and no -portion of matter is indivisible, or an _atom_. - -And to the argument on the other side just stated, it is -replied that we cannot even hypothetically divest a body of -composition, if by composition we mean the relation of point -to point in space. However small be a particle, it is -compounded of parts having relation in space. - -The Atomists urge again, that if matter be infinitely -divisible, a finite body consists of an infinite number of -parts, which is a contradiction. To this it is replied, that -the finite body consists of an infinite number of parts in -the same sense in which the parts are infinitely small, -which is no contradiction. - -But the opponents of the Atomists not only rebut, but retort -this argument drawn from the notion of infinity. Your atoms, -they say, are indivisible by any finite force; therefore -they are infinitely hard; and thus your finite particles -possess infinite properties. To this the Atomists are wont -to reply, that they do not mean the hardness of their -particles to be infinite, but only so great as to resist all -usual natural forces. But here it is plain that their -position becomes untenable; for, in the first place, their -assumption of this precise degree of hardness in the -particles is altogether gratuitous; and in the next place, -if it were granted, such particles are not atoms, since in -the next moment the forces of nature may be augmented so as -to divide the particle, though hitherto undivided. - -Such are the arguments for and against the Atomic Theory in -its original form. But when these atoms are conceived, as -they have been by Newton, and commonly by his followers, to -be solid, hard particles exerting attractive and repulsive -forces, a new set of {58} arguments come into play. Of -these, the principal one may be thus stated: According to -the Atomic Theory thus modified, the properties of bodies -depend upon the attractions and repulsions of the particles. -Therefore, among other properties of bodies, their hardness -depends upon such forces. But if the hardness _of the -bodies_ depends upon the forces, the repulsion, for -instance, of the particles, upon what does the hardness _of -the particles_ depend? what progress do we make in -explaining the properties of bodies, when we assume the same -properties in our explanation? and to what purpose do we -assume that the particles are hard? - -9. _Transition to Boscovich's Theory._--To this difficulty -it does not appear easy to offer any reply. 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 Theory, we are led to the theory of Boscovich, -according to which matter consists not of solid particles, -but of mere mathematical centers of force. According to this -theory, each body is composed of a number of geometrical -points from which emanate forces, following certain -mathematical laws in virtue of which the forces become, at -certain small distances attractive, at certain other -distances repulsive, and at greater distances attractive -again. From these forces of the points arise the cohesion of -the parts of the same body, the resistance which it exerts -against the pressure of another body, and finally the -attraction of gravitation which it exerts upon bodies at a -distance. - -This theory is at least a homogeneous and consistent theory, -and it is probable that it may be used as an instrument for -investigating and expressing true laws of nature; although, -as we have already said, the attempt to identify the forces -by which the particles of bodies are bound together with -mechanical attraction, appears to be a confusion of two -separate ideas[44\6]. - -[Note 44\6: 'Boscovich's Theory,' that all bodies may be -considered as consisting of a mere collection of centers of -forces, may be so conceived as possibly to involve an -explanation of all the powers which their parts exert, (such -powers, namely, as those which produce optical, thermotical -and chemical phenomena;) but this theory cannot supply an -explanation of the mechanical properties of a body as a -whole, especially of its _inertia_. A collection of mere -centers of force can have no inertia. If two bodies are -considered as two collections of centers of force, the one -attracting the other, there is in this view nothing to limit -or determine the velocity with which the one body will -approach the other. A world composed of such bodies is not a -_material_ world: for matter (as we have already seen in -book iii. chapter v.) implies not only force, but something -which resists the action of force.] - -{59} 10. _Use of the Molecular Hypothesis._--In this form, -representing matter as a collection of molecules or centers -of force, the Atomic Theory has been abundantly employed in -modern times as an hypothesis on which calculations -respecting the elementary forces of bodies might be -conducted. 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 -mass. This view of the way in which the properties of bodies -are to be treated by the mechanical philosopher was -introduced by Newton, and was a natural sequel to the -success which he had obtained by reasoning concerning -central forces on a large scale. I have already quoted his -Preface to the _Principia_, in which he says, 'Many things -induce me to believe that the rest of the phenomena of -nature, as well as those of astronomy, may depend upon -certain forces by which the particles of bodies, in virtue -of causes not yet known, are urged towards each other and -cohere in regular figures, or are mutually repelled and -recede; and philosophers, knowing nothing of these forces, -have hitherto failed in their examination of nature.' Since -the time of Newton, this line of speculation has been -followed with great assiduity, and by some mathematicians -with great success. In particular Laplace has shown that the -hypothesis may, in many instances, be made a much closer -representation of nature, if we suppose the forces exerted -by the particles to decrease so rapidly with the increasing -distance from them, that {60} the force is finite only at -distances imperceptible to our senses, and vanishes at all -remoter points. He has taught the method of expressing and -calculating such forces, and he and other mathematicians of -his school have applied this method to many of the most -important questions of physics; as capillary action, the -elasticity of solids, the conduction and radiation of heat. -The explanation of many apparently unconnected and curious -observed facts by these mathematical theories gives a strong -assurance that its essential principles are true. 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 coincidences. The assumption, in the -reasoning, of certain centers of force acting at a distance, -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_ -point. It is a mathematical artifice of the same kind as the -hypothetical division of a body into infinitesimal parts, in -order to find its center of gravity; and no more implies a -physical reality than that hypothesis does. - -11. _Poisson's Inference._--When, therefore, M. Poisson, in -his views of Capillary Action, treats this hypothetical -distribution of centers of force as if it were a physical -fact, and blames Laplace for not taking account of their -different distribution at the surface of the fluid and below -it[45\6], he appears to push the claims of the molecular -hypothesis too far. The only ground for the assumption of -separate centers, is that we can thus explain the action of -the whole mass. The intervals between the centers nowhere -enter into this explanation: and therefore we can have no -reason for assuming these intervals different in one part of -the fluid and in the other. M. Poisson asserts that the -density of the fluid diminishes when we approach very near -the surface; but he allows that this diminution is not -detected by experiment, and that the formulæ on {61} his -supposition, so far as the results go, are identical with -those of Laplace. It is clear, then, 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 -experiment. It is true, that so long as we have before us -the hypothesis of separate centers, the particles very near -the surface are not in a condition symmetrical with that of -the others: but it is also true that this hypothesis is only -a step of calculation. There results, at one period of the -process of deduction, a stratum of smaller density at the -surface of the fluid; but at a succeeding point of the -reasoning the thickness of this stratum vanishes; it has no -physical existence. - -[Note 45\6: Poisson, _Théorie de l'Action Capillaire_.] - -Thus the _molecular_ hypothesis, as used in such cases, does -not differ from the doctrine of forces acting at _every -point_ of the mass; and this principle, which is common to -both the opposite views, is the true part of each. - -12. _Wollaston's Argument._--An attempt has been made in -another case, but depending on nearly the same arguments, to -bring the doctrine of ultimate atoms to the test of -observation. In the case of the air, we know that there _is_ -a diminution of density in approaching the upper surface of -the atmosphere, if it have a surface: but it is held by some -that except we allow the doctrine of ultimate molecules, it -will not be bounded by any surface, but will extend to an -infinite distance. This is the reasoning of Wollaston[46\6]. -'If air consists of any ultimate particles no longer -divisible, 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 medium.' But if there be no such -ultimate particles, every stratum will require a stratum -beyond it to prevent by its weight a further expansion, and -thus the atmosphere {62} must extend to an infinite -distance. And Wollaston conceived that he could learn from -observation whether the atmosphere was thus diffused through -all space; for if so, it must, he argued, be accumulated -about the larger bodies of the system, as Jupiter and the -Sun, by the law of universal gravitation; and the existence -of an atmosphere about these bodies, might, he remarked, be -detected by its effects in producing refraction. His result -is, that 'all the phenomena accord entirely with the -supposition that the earth's atmosphere is of finite extent, -limited by the weight of ultimate atoms of definite -magnitude, no longer divisible by repulsion of their parts.' - -[Note 46\6: _Phil. Trans._ 1822, p. 89.] - -A very little reflection will show us that such a line of -reasoning cannot lead to any result. For we know nothing of -the law which connects the density with the compressing -force, in air so extremely rare as we must suppose it to be -near the boundary of the atmosphere. 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 atoms. This may be proved by -mathematical reasoning. If we suppose the density of air to -be as the square root of the compressing force, it will -follow that at the very limits of the atmosphere, the strata -of equal thickness may observe in their densities such a law -of proportion as is expressed by the numbers 7, 5, 3, -1[47\6]. - -[Note 47\6: For the compressing force on each being as the -whole weight beyond it, it will be for the four highest -strata, 16, 9, 4 and 1, of which the square roots are as 4, -3, 2, 1, or, as 8, 6, 4, 2; and though these numbers are not -exactly as the densities 7, 5, 3, 1, those who are a little -acquainted with mathematical reasoning, will see that the -difference arises from taking so small a number of strata. -If we were to make the strata indefinitely thin, as to avoid -error we ought to do, the coincidence would be exact; and -thus, according to this law, the series of strata terminates -as we ascend, without any consideration of atoms.] - -If it be asked how, on this hypothesis, the density of the -highest stratum can be as 1, since there is {63} nothing to -compress it, we answer that the upper part of the highest -stratum compresses the lower, and that the density -diminishes continually to the surface, so that the need of -compression and the compressing weight vanish together. - -The fallacy of concluding that because the height of the -atmosphere is finite, the weight of the highest stratum must -be finite, is just the same as the fallacy of those who -conclude that when we project a body vertically upwards, -because it occupies only a finite time in ascending to the -highest point, the velocity at the last instant of the -ascent must be finite. For it might be said, if the last -velocity of ascent be not finite, how can the body describe -the last particle of space in a finite time? and the answer -is, that there is no last finite particle of space, and -therefore no last finite velocity. - -13. _Permanence of Properties of Bodies._--We have already -seen that, in explaining the properties of matter as we find -them in nature, the assumption of solid, hard, -indestructible particles is of no use or value. But we may -remark, before quitting the subject, that Newton appears to -have had another reason for assuming such particles, and one -well worthy of notice. He wished to express, by means of -this hypothesis, the doctrine that the laws of nature do not -alter with the course of time. This we have already seen in -the quotation from Newton. 'The ultimate particles of matter -are indestructible, unalterable, impenetrable; for if they -could break or wear, the structure of material bodies now -would be different from that which it was when the particles -were new.' No philosopher will deny the truth which is thus -conveyed by the assertion of atoms; but it is obviously -equally easy for a person who rejects the atomic view, to -state this truth by saying that the forces which matter -exerts do not vary with time, but however modified by the -new modifications of its form, are always unimpaired in -quantity, and capable of being restored to their former mode -of action. {64} - -We now proceed to speculations in which the fundamental -conceptions may, perhaps, be expressed, at least in some -cases, by means of the arrangement of atoms; but in which -the philosophy of the subject appears to require a reference -to a new Fundamental Idea. - - - - -{{65}} -BOOK VII. - - -THE -PHILOSOPHY -OF -MORPHOLOGY, -INCLUDING -CRYSTALLOGRAPHY. - - - - -CRYSTALLIZATION exhibits to us the effects of the natural -arrangement of the ultimate particles of various compound -bodies; but we are scarcely yet sufficiently acquainted with -chemical synthesis and analysis to understand the rationale -of this process. The rhomboidal form may arise from the -proper position of 4, 6, 8 or 9 globular particles, the -cubic form from 8 particles, the triangular form from 3, 6 -or 10 particles, the hexahedral prism from 7 particles, &c. -Perhaps, in due time we may be enabled to ascertain the -number and order of elementary particles, constituting any -given compound element, and from that determine the figure -which it will prefer on crystallization, and _vice versâ_. - -JOHN DALTON, _Chemical Philosophy_ (1808), p. 210. - - - -{{67}} -BOOK VII. - - -THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY. - - -CHAPTER I. - -EXPLICATION OF THE IDEA OF SYMMETRY. - - -1. WE have seen in the History of the Sciences, that the -principle which I have there termed[1\7] the Principle of -Developed and Metamorphosed Symmetry, has been extensively -applied in botany and physiology, and has given rise to a -province of science termed Morphology. In order to -understand clearly this principle, it is necessary to obtain -a clear idea of the Symmetry of which we thus speak. But -this Idea of Symmetry is applicable in the inorganic, as -well as in the organic kingdoms of nature; it is presented -to our eyes in the forms of minerals, as well as of flowers -and animals; we must, therefore, take it under our -consideration here, in order that we may complete our view -of Mineralogy, which, as I have repeatedly said, is an -essential part of Chemical science. I shall accordingly -endeavour to unfold the Idea of Symmetry with which we here -have to do. - -[Note 1\7: _Hist. Ind. Sc._ b. xvii. c. vi.] - -It will of course be understood that by the term _Symmetry_ -I here intend, not that more indefinite attribute of form -which belongs to the domain of the fine arts, as when we -speak of the 'symmetry' of an edifice {68} or of a -sculptured figure, but a certain definite relation or -property, no less rigorous and precise than other relations -of number and position, which is thus one of the sure guides -of the scientific faculty, and one of the bases of our exact -science. - -2. In order to explain what Symmetry is in this sense, let -the reader recollect that the bodies of animals consist of -_two_ equal and similar sets of members, the right and the -left side;--that some flowers consist of three or of five -equal sets of organs, similarly and regularly disposed, as -the iris has _three_ straight petals, and three reflexed -ones, alternately disposed, the rose has _five_ equal and -similar sepals of the calyx, and alternate with these, as -many petals of the corolla. This orderly and exactly similar -distribution of two, or three, or five, or any other number -of parts, is Symmetry; and according to its various -modifications, the forms thus determined are said to be -_symmetrical_ with various numbers of members. The -classification of these different kinds of symmetry has been -most attended to in Crystallography, in which science it is -the highest and most general principle by which the classes -of forms are governed. Without entering far into the -technicalities of the subject, we may point out some of the -features of such classes. - -[Illustration] The first of the figures (1) in the margin -may represent the summit of a crystal as it appears to an -eye looking directly down upon it; the center of the figure -represents the summit of a pyramid, and the spaces of -various forms which diverge from this point represent -sloping sides of the pyramid. Now it will be observed that -the figure consists of three portions exactly similar to one -another, and that each part or member is repeated in each of -these portions. The faces, or pairs of faces, are repeated -in _threes_, with exactly similar forms and angles. This -figure is said to be _three-membered_, or to have -_triangular_ symmetry. The same kind of {69} symmetry may -exist in a flower, as presented in the accompanying figure, -and does, in fact, occur in a large class of flowers, as for -example, all the lily tribe. The next pair of figures (2) -have four equal and similar portions, and have their members -or pairs of members four times repeated. Such figures are -termed _four-membered_, and are said to have _square_ or -_tetragonal_ symmetry. The _pentagonal_ symmetry, formed by -_five_ similar _members_, is represented in the next figures -(3). It occurs abundantly in the vegetable world, but never -among crystals; for the pentagonal figures which crystals -sometimes assume, are never exactly regular. But there is -still another kind of symmetry (4) in which the opposite -ends are exactly similar to each other and also the opposite -sides; this is _oblong_, or _two-and-two-membered_ symmetry. -And finally, we have the case of _simple_ symmetry (5) in -which the two sides of the object are exactly alike (in -opposite positions) without any further repetition. -[Illustration] - -3. These different kinds of symmetry occur in various ways -in the animal, vegetable, and mineral kingdom. Vertebrate -animals have a right and a {70} left side exactly alike, and -thus possess _simple_ symmetry. The same kind of symmetry -(simple symmetry) occurs very largely in the forms of -vegetables, as in most leaves, in _papilionaceous_, -_personate_, and _labiate_ flowers. Among minerals, crystals -which possess this symmetry are called _oblique-prismatic_, -and are of very frequent occurrence. The _oblong_, or -_two-and-two-membered_ symmetry belongs to _right-prismatic_ -crystals; and may be seen in _cruciferous_ flowers, for -though these are cross-shaped, the cross has two longer and -two shorter arms, or pairs of arms. The _square_ or -_tetragonal_ symmetry occurs in crystals abundantly; to the -vegetable world it appears to be less congenial; for though -there are flowers with four exactly similar and -regularly-disposed petals, as the herb Paris (_Paris -quadrifolia_), these flowers appear, from various -circumstances, to be deviations from the usual type of -vegetable forms. The _trigonal_, or _three-membered_ -symmetry is found abundantly both in plants and in crystals, -while the _pentagonal_ symmetry, on the other hand, though -by far the most common among flowers, nowhere occurs in -minerals, and does not appear to be a possible form of -crystals. This pentagonal form further occurs in the animal -kingdom, which the oblong, triangular, and square forms do -not. Many of Cuvier's _radiate_ animals appear in this -pentagonal form, as _echini_ and _pentacrinites_, which -latter have hence their name. - -4. The regular, or as they may be called, the _normal_ types -of the vegetable world appear to be the forms which possess -triangular and pentagonal symmetry; from these the others -may be conceived to be derived, by transformations resulting -from the expansion of one or more parts. Thus it is manifest -that if in a three-membered or five-membered flower, one of -the petals be expanded more than the other, it is -immediately reduced from pentagonal or trigonal, to simple -symmetry. And the oblong or two-and-two-membered symmetry of -the flowers of cruciferous plants, (in which the stamens are -four large and two small ones, arranged in regular -opposition,) is held by botanists to result {71} from a -normal form with ten stamens; Meinecke explaining this by -adhesion, and Sprengel by the metamorphosis of the stamens -into petals[2\7]. - -[Note 2\7: Sprengel, _Gesch. d. Bot._ ii. 304.] - -It is easy to see that these various kinds of symmetry -include relations both of form and of number, but more -especially of the latter kind; and as this symmetry is often -an important character in various classes of natural -objects, such classes have often curious numerical -properties. One of the most remarkable and extensive of -these is the distinction which prevails between -monocotyledonous and dicotyledonous plants; the number -_three_ being the ground of the symmetry of the former, and -the number _five_, of the latter. Thus liliaceous and -bulbous plants, and the like, have flowers of three or six -petals, and the other organs follow the same numbers: while -the vast majority of plants are pentandrous, and with their -five stamens have also their other parts in fives. This -great numerical distinction corresponding to a leading -difference of physiological structure cannot but be -considered as a highly curious fact in phytology. Such -properties of numbers, thus connected in an incomprehensible -manner with fundamental and extensive laws of nature, give -to numbers an appearance of mysterious importance and -efficacy. We learn from history how strongly the study of -such properties, as they are exhibited by the phenomena of -the heavens, took possession of the mind of Kepler; perhaps -it was this which, at an earlier period, contributed in no -small degree to the numerical mysticism of the Pythagoreans -in antiquity, and of the Arabians and others in the middle -ages. In crystallography, numbers are the primary characters -in which the properties of substances are expressed;--they -appear, first, in that classification of forms which depends -on the degree of symmetry, that is, upon the number of -correspondencies; and next, in the laws of derivation, -which, for the most part, appear to be common in their -occurrence in proportion to the numerical simplicity of -their expression. But the manifestation {72} of a governing -numerical relation in the organic world strikes us as more -unexpected; and the selection of the number _five_ as the -index of the symmetry of dicotyledonous plants and radiated -animals, (a number which is nowhere symmetrically produced -in inorganic bodies,) makes this a new and remarkable -illustration of the constancy of numerical relations. We may -observe, however, that the moment one of these radiate -animals has one of its five members expanded, or in any way -peculiarly modified, (as happens among the echini), it is -reduced to the common type of animals simply symmetrical, -with a right and left side. - -5. It is not necessary to attempt to enumerate all the kinds -of Symmetry, since our object is only to explain what -Symmetry is, and for this purpose enough has probably been -said already. It will be seen, as soon as the notion of -Symmetry in general is well apprehended, that it is or -includes a peculiar Fundamental Idea, not capable of being -resolved into any of the ideas hitherto examined. It may be -said, perhaps, that the Idea of Symmetry is a modification -or derivative of our ideas of space and number;--that a -symmetrical shape is one which consists of parts exactly -similar, repeated a certain number of times, and placed so -as to correspond with each other. But on further reflection -it will be seen that this repetition and correspondence of -parts in symmetrical figures are something peculiar; for it -is not _any_ repetition or any correspondence of parts to -which we should give the name of symmetry, in the manner in -which we are now using the term. Symmetrical arrangements -may, no doubt, be concerned with space and position, time -and number; but there appears to be implied in them a -Fundamental Idea of regularity, of completeness, of complex -simplicity, which is not a mere modification of other ideas. - -6. It is, however, not necessary, in this and in similar -cases, to determine whether the idea which we have before us -be a peculiar and independent Fundamental Idea or a -modification of other ideas, provided we clearly perceive -the evidence of those Axioms by {73} means of which the Idea -is applied in scientific reasonings. Now in the application -of the Idea of Symmetry to crystallography, phytology and -zoology, we must have this idea embodied in some principle -which asserts more than a mere geometrical or numerical -accordance of members. We must have it involved in some -vital or productive action, in order that it may connect and -explain the facts of the organic world. Nor is it difficult -to enunciate such a principle. We may state it in this -manner. _All the symmetrical members of a natural product -are, under like circumstances, alike affected by the natural -formative power._ The parts which we have termed -_symmetrical_, resemble each other, not only in their form -and position, but also in the manner in which they are -produced and modified by natural causes. And this principle -we assume to be necessarily true, however unknown and -inconceivable may be the causes which determine the -phenomena. Thus it has not yet been found possible to -discover or represent to ourselves, in any intelligible -manner, the forces by which the various faces of a crystal -are consequent upon its primary form: for the hypothesis of -their being built up of integrant molecules, as Haüy held, -cannot be made satisfactory. But though the mechanism of -crystals is still obscure, there is no doubt as to the -principle which regulates their modifications. The whole of -crystallography rests upon this principle, that if one of -the primary planes or axes be modified in any manner, all -the symmetrical planes and axes must be modified in the same -manner. And though accidental mechanical or other causes may -interfere with the actual exhibition of such faces, we do -not the less assume their crystallographical reality, as -inevitably implied in the law of symmetry of the -crystal[3\7]. And we apply similar considerations to -organized beings. We assume that in a regular flower, each -of the similar {74} members has the same organization and -similar powers of developement; and hence if among these -similar parts some are much less developed than others, we -consider them as _abortive_; and if we wish to remove doubts -as to what are symmetrical members in such a case, we make -the inquiry by tracing the anatomy of these members, or by -following them in their earlier states of developement, or -in cases where their capabilities are magnified by -monstrosity or otherwise. The power of developement may be -modified by external causes, and thus we may pass from one -kind of symmetry to another; as we have already remarked. -Thus a regular flower with pentagonal symmetry, growing on a -lateral branch, has one petal nearest to the axis of the -plant: if this petal be more or less expanded than the -others, the pentagonal symmetry is interfered with, and the -flower may change to a symmetry of another kind. But it is -easy to see that all such conceptions of expansion, -abortion, and any other kind of metamorphosis, go upon the -supposition of identical faculties and tendencies in each -similar member, in so far as such tendencies have any -relation to the symmetry. And thus the principle we have -stated above is the basis of that which, in the History, we -termed the Principle of Developed and Metamorphosed -Symmetry. - -[Note 3\7: Some crystalline forms, instead of being -_holohedral_ (provided with their whole number of faces), -are _hemihedral_ (provided with only half their number of -faces). But in these hemihedral forms the half of the faces -are still _symmetrically_ suppressed.] - -We shall not at present pursue the other applications of -this Idea of Symmetry, but we shall consider some of the -results of its introduction into Crystallography. - - - -{{75}} -CHAPTER II. - -APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS. - - -1. MINERALS and other bodies of definite chemical -composition often exhibit that marked regularity of form and -structure which we designate by terming them _Crystals_; and -in such crystals, when we duly study them, we perceive the -various kinds of symmetry of which we have spoken in the -previous chapter. And the different kinds of symmetry which -we have there described are now usually distinguished from -each other, by writers on crystallography. 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 capable. But this classification -was by no means invented as soon as mineralogists applied -themselves to the study of crystals. These first attempts to -arrange crystalline forms were very imperfect; those, for -example, of Linnæus, Werner, Romé de Lisle, and Haüy. The -essays of these writers implied a classification at once -defective and superfluous. They reduced all crystals to one -or other of certain _fundamental forms_; and this procedure -might have been a perfectly good method of dividing -crystalline forms into classes, if the fundamental forms had -been selected so as to exemplify the different kinds of -symmetry. But this was not the case. Haüy's fundamental or -'primitive' forms, were, for instance, the following: the -_parallelepiped_, the _octahedron_, the _tetrahedron_, the -_regular hexagonal prism_, the _rhombic dodecahedron_, and -the _double hexagonal pyramid_. Of these, the _octahedron_, -the _tetrahedron_, the _rhombic dodecahedron_, all belong to -the {76} same kind of symmetry (the TESSULAR systems); also -the _hexagonal prism_ and the _hexagonal pyramid_ both -belong to the RHOMBIC system; while the _parallelepiped_ is -so employed as to include all kinds of symmetry. - -It is, however, to be recollected that Haüy, in his -selection of primitive forms, not only had an eye to the -external form of the crystal and to its degree and kind of -regularity, but also made his classification with an -especial reference to the _cleavage_ of the mineral, which -he considered as a primary element in crystalline analysis. -There can be no doubt that the cleavage of a crystal is one -of its most important characters: it is a relation of form -belonging to the interior, which is to be attended to no -less than the form of the exterior. But still, the cleavage -is to be regarded only as determining the degree of -geometrical symmetry of the body, and not as defining a -special geometrical figure to which the body _must_ be -referred. To have looked upon it in the latter light, was a -mistake of the earlier crystallographic speculators, on -which we shall shortly have to remark. - -2. 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 them. This follows as a consequence -from the application of the Principle stated in the last -chapter, that _all symmetrical members are alike affected_. -Thus we may take an upright triangular prism as the -representative of the rhombic system, and if we then suppose -one of the upper edges to be cut off, or truncated, we must, -by the Principle of Symmetry, suppose the other two upper -edges to be truncated in precisely the same manner. By this -truncation we may obtain the upper part of a rhombohedron; -and by truncations of the same kind, symmetrically affecting -all the analogous parts of the figure, we may obtain any -other form possessing three-membered symmetry. And the same -is true of any of the other kinds of symmetry, provided we -make a proper selection of a fundamental form. And this was -really the method employed by Demeste, Werner, and Romé de -Lisle. They {77} assumed a Primitive Form, and then -conceived other forms, such as they found in nature, to be -derived from the Primitive Form by truncation of the edges, -acumination of the corners, and the like processes. This -mode of conception was a perfectly just and legitimate -expression of the general Idea of Symmetry. - -3. The true view of the degrees of symmetry was, as I have -already said, impeded by the attempts which Haüy and others -made to arrive at primitive forms by the light which -cleavage was supposed to throw upon the structure of -minerals. At last, however, in Germany, as I have narrated -in the History of Mineralogy[4\7], Weiss and Mohs introduced -a classification of forms implying a more philosophical -principle, dividing the forms into Systems; which, employing -the terms of the latter writer, we shall call the -_tessular_, the _pyramidal_ or _square pyramidal_, the -_prismatic_ or _oblong_, and the _rhombohedral_ systems. - -[Note 4\7: _Hist. Ind. Sc._ b. xv. c. iv.] - -Of these forms, the three latter may be at once referred to -those kinds of symmetry of which we have spoken in the last -chapter. The _rhombohedral_ system has _triangular_ -symmetry, or is three-membered: the _pyramidal_ has _square_ -symmetry, or is four-membered: the _prismatic_ has _oblong_ -symmetry, and is two-and-two-membered. But the kinds of -symmetry which were spoken of in the former chapter, do not -exhaust the idea when applied to minerals. For the symmetry -which was there explained was such only as can be exhibited -on a surface, whereas the forms of crystals are solid. Not -only have the right and left parts of the upper surface of a -crystal relations to each other; but the upper surface and -the lateral faces of the crystal have also their relations; -they may be different, or they may be alike. If we take a -cube, and hold it so that four of its faces are vertical, -not only are all these four sides exactly similar, so as to -give square symmetry; but also we may turn the cube, so that -any one of these four sides shall become the top, and still -the four sides which are thus made vertical, though {78} not -the same which were vertical before, are still perfectly -symmetrical. Thus this cubical figure possesses more than -square symmetry. It possesses square symmetry in a vertical -as well as in a horizontal sense. It possesses a symmetry -which has the same relation to a _cube_ which four-membered -symmetry has to a _square_. And this kind of symmetry is -termed the _cubical_ or _tessular_ symmetry. All the other -kinds of symmetry have reference to an axis, about which the -corresponding parts are disposed; but in tessular symmetry -the horizontal and vertical axes are also symmetrical, or -interchangeable; and thus the figure may be said to have no -axis at all. - -4. It has already been repeatedly stated that, by the very -idea of symmetry, all the incidents of form must affect -alike all the corresponding parts. Now in crystals we have, -among these incidents, not only external figure, but -_cleavage_, which may be considered as internal figure. -Cleavage, then, must conform to the degree of symmetry of -the figure. Accordingly cleavage, no less than form, is to -be attended to in determining to what system a mineral -belongs. If a crystal were to occur as a square prism or -pyramid, it would not on that account necessarily belong to -the square pyramidal system. If it were found that it was -cleavable parallel to one side of the prism, but not in the -transverse direction, it has only oblong symmetry; and the -equality of the sides which makes it square is only -accidental. - -Thus no cleavage is admissible in any system of -crystallization which does not agree with the degree of -symmetry of the system. On the other hand, _any_ cleavage -which _is_ consistent with the symmetry of the system, is -(hypothetically at least) allowable. Thus in the oblong -prismatic system we may have a cleavage parallel to one side -only of the prism; or parallel to both, but of different -distinctness; or parallel to the two diagonals of the prism -but of the same distinctness; or we may have both these -cleavages together. In the rhombohedral system, the cleavage -may be parallel to the sides of the rhombohedron, as in Calc -{79} Spar: or, in the same system, the cleavage, instead of -being thus oblique to the axis, may be along the axis in -those directions which make equal angles with each other: -this cleavage easily gives either a triangular or a -hexagonal prism. Again, in the tessular system, the cleavage -may be parallel to the surface of the cube, which is thus -readily separable into other cubes, as in Galena; or the -cleavage may be such as to cut off the solid angle of the -cube, and since there are eight of these, such cleavage -gives us an octahedron, which, however, may be reduced to a -tetrahedron, by rejecting all parallel faces, as being mere -repetitions of the same cleavage; this is the case with -Fluor Spar: or the cube of the tessular system may be -cleavable in planes which truncate all the edges of the -cube; and as these are twelve, we thus obtain the -dodecahedron with rhombic faces: this occurs in Zinc Blende. -And thus we see the origin of Haüy's various primitive -forms, the tetrahedron, octahedron, and rhombic -dodecahedron, all belonging to the tessular system:--they -are, in fact, different cleavage forms of that system. - -5. I do not dwell upon other incidents of crystals which -have reference to form, nor upon the lustre, smoothness, and -striation of the surfaces. To all such incidents the general -principle applies, that similar parts are similarly -affected; and hence, if any parts are found to be constantly -and definitely different from other parts of the same sort, -they are not similar parts; and the symmetry is to be -interpreted with reference to this difference. - -We have now to consider the inferences which have been drawn -from these incidents of crystallization, with regard to the -intimate structure of bodies. - - - -{{80}} -CHAPTER III. - -SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS. - - -1. WHEN a crystal, as, for instance, a crystal of Galena, -(sulphuret of lead,) is readily divisible into smaller -cubes, and these into smaller ones, and so on without limit, -it is very natural to represent to ourselves the original -cube as really consisting of small cubical elements; 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 molecules. And when the Galena crystal has -externally the form of a cube, there is no difficulty in -such a conception; for the surface of the crystal is also -conceived as made up of the surfaces of its cubical -molecules. We conceive the crystal so constituted, as we -conceive a wall built of bricks. - -But if, as often happens, the Galena crystal be an -octahedron, a further consideration is requisite in order to -understand its structure, pursuing still the same -hypothesis. The mineral is still, as in the other case, -readily cleavable into small cubes, having their corners -turned to the faces of the octahedron. Therefore these faces -can no longer be conceived as made up of the faces of -cubical elements of which the whole is constituted. If we -suppose a pile of such small cubes to be closely built -together, but with decreasing width above, so as to form a -pyramid, the face of such a pyramid will no longer be plane; -it will consist of a great number of the corners or edges of -the small elementary cubes. It would appear at first sight, -therefore, that such a face cannot represent the smooth -polished surface of a crystal. {81} - -But when we come to look more closely, this difficulty -disappears. For how large are these elementary cubes? We -cannot tell, even supposing they really have any size. But -we know that they must be, at any rate, very small; so small -as to be inappreciable by our senses, for our senses find no -limit to the divisibility of minerals by cleavage. Hence the -surface of the pyramid above described would not consist of -visible corners or edges, but would be roughened by specks -of imperceptible size; or rather, by supposing these specks -to become still smaller, the roughness becomes smoothness. -And thus we may have a crystal with a smooth surface, made -up of small cubes in such a manner that their surfaces are -all oblique to the surface of the crystal. - -Haüy, struck by some instances in which the supposition of -such a structure of crystals appeared to account happily for -several of their relations and properties, adopted and -propounded it as a general theory. The small elements, of -which he supposed crystals to be thus built up, he termed -_integrant molecules_. The form of these molecules might or -might not be the same as the _primitive form_ with which his -construction was supposed to begin; but there was, at any -rate, a close connexion between these forms, since both of -them were founded on the cleavage of the mineral. The tenet -that crystals are constituted in the manner which I have -been describing, I shall call the _Theory of Integrant -Molecules_, and I have now to make some remarks on the -grounds of this theory. - -2. In the case of which I have spoken, the mineral used as -the example, Galena, readily splits into cubes, and cubes -are easily placed together so as to fit each other, and fill -the space which they occupy. The same is the case in the -mineral which suggested to Haüy his theory, namely, Calc -Spar. The crystals of this substance are readily divisible -into rhombohedrons, a form like a brick with oblique angles; -and such bricks can be built together so as to produce -crystals of all the immense varieties of form which Calc -Spar presents. This kind of masonry is equally possible in -many other {82} minerals; but as we go through the mineral -kingdom in our survey, we soon find cases which offer -difficulties. Some minerals cleave only in two directions, -some in one only; in such cases we cannot by cleavage obtain -an integrant molecule of definite form; one of its -dimensions, at least, must remain indeterminate and -arbitrary. Again, in some instances, we have more than three -different planes of cleavage, as in Fluor Spar, where we -have four. The solid, bounded by four planes, is a -tetrahedron; or if we take four _pairs_ of parallel faces, -an octahedron. But if we attempt to take either of these -forms for our integrant molecule, we are met by this -difficulty: that a collection of such forms will not fill -space. Perhaps this difficulty will be more readily -conceived by the general reader if it be contemplated with -reference to plane figures. It will readily be seen that a -number of equal squares may be put together so as to fill -the space which they occupy; but if we take a number of -equal regular octagons, we may easily convince ourselves -that no possible arrangement can make them cover a flat -space without leaving blank spots between. In like manner -octahedrons or tetrahedrons cannot be arranged in solid -space so as to fill it. They necessarily leave vacancies. -Hence the structure of Fluor Spar, and similar crystals, was -a serious obstacle in the way of the theory of integrant -molecules. That theory had been adopted in the first -instance because portions of the crystal, obtained by -cleavage, could be built up into a solid mass; but this -ground of the theory failed altogether in such instances as -I have described, and hence the theory, even upon the -representations of its adherents, had no longer any claim to -assent. - -The doctrine of Integral Molecules, however, was by no means -given up at once, even in such instances. In this and in -other subjects, we may observe that a theory, once -constructed and carried into detail, has such a hold upon -the minds of those who have been in the habit of applying -it, that they will attempt to uphold it by introducing -suppositions inconsistent with {83} the original foundations -of the theory. Thus those who assert the Atomic Theory, -reconcile it with facts by taking the _halves of atoms_; and -thus the Theory of Integrant Molecules was maintained for -Fluor Spar, by representing the elementary octahedrons of -which crystals are built up, as touching each other only by -the _edges_. The contact of surface with surface amongst -integrant molecules had been the first basis of the theory; -but this supposition being here inapplicable, was replaced -by one which made the theory no longer a representation of -the facts (the cleavages), but a mere geometrical -construction. Although, however, the inapplicability of the -theory to such cases was thus, in some degree, disguised to -the disciples of Haüy, it was plain that, in the face of -such difficulties, the Theory of Integrant Molecules could -not hold its place as a philosophical truth. But it still -answered the purpose (a very valuable one, and one to which -crystallography is much indebted,) of an instrument for -calculating the geometrical relations of the parts of -crystals to each other: for the integrant molecules were -supposed to be placed layer above layer, each layer as we -ascend, _decreasing_ by a certain number of molecules and -rows of molecules; and the calculation of these _laws of -decrement_ was, in fact, the best mode then known of -determining the positions of the faces. The Theory of -Decrements served to express and to determine, in a great -number of the most obvious cases, _the laws of phenomena_ in -crystalline forms, though the Theory of Integrant Molecules -could not be maintained as a just view of the structure of -crystals. - -3. The Theory of Integrant Molecules, however, involved this -just and important principle: that a true view of the -intimate structure of crystals must include and explain the -facts of crystallization, that is, crystalline form and -cleavage; and that it must take these into account, -according to their degree of _Symmetry_. So far all theories -concerning the elements of crystals must agree. And it was -soon seen that this was, in reality, all that had been -established by the investigations of Haüy and his school. I -have already, in the {84} _History_, quoted Weiss's -reflections on making this step. 'When in 1809,' he -says[5\7], 'I published my Dissertation, I shared the common -opinion as to the necessity of the assumption, and the -reality of the existence of a primitive form, at least in a -sense not very different from the usual sense of the -expression.' He then proceeds to relate that he sought a -ground for such an opinion, independent of the doctrine of -_Atoms_, which he, in common with a great number of -philosophers of that time in his own country, was disposed -to reject, inclining to believe that the properties of -bodies were determined by _Forces_ which acted in them, and -not by _Molecules_ of which they were composed. He adds, -that in pursuing this train of thought, he found, 'that out -of his Primitive Forms there was gradually unfolded to his -hands that which really governs them, and is not affected by -their casual fluctuations; namely, the Fundamental Relations -of their Dimensions,' or as we now may call them, _Axes of -Symmetry_. With reference to these Axes, he found, as he -goes on to say, that 'a multiplicity of internal -Oppositions, necessarily and mutually interdependent, are -developed in the crystalline mass, each Relation having its -own Polarity; so that the Crystalline Character is -co-extensive with these Polarities.' The character of these -polarities, whether manifested in crystalline faces, -cleavage, or any other incidents of crystallization, is -necessarily displayed in the degree and kind of Symmetry -which the crystal possesses: and thus this Symmetry, in all -our speculations concerning the structure of crystals, -necessarily takes the place of that enumeration of Primitive -Forms which were rejected as inconsistent with observed -facts, and destitute of sound scientific principle. - -[Note 5\7: _Acad. Berlin._ 1816, p. 307.] - -I may just notice here what I have stated in the History of -Mineralogy[6\7], that the distinction of systems of -crystallization, as introduced by Weiss and Mohs, was -strikingly confirmed by Sir David Brewster's discoveries -respecting the optical properties of minerals. {85} The -splendid phenomena which were produced by passing polarized -light through crystals, were found to vary according as the -crystals were of the Rhombohedral, Square Pyramidal, Oblong -Prismatic, or Tessular System. The Optical Symmetry exactly -corresponded with the Geometrical Symmetry. In the two -former Systems were crystals _uniaxal_ in respect of their -optical properties; the oblong prismatic, was _biaxal_; -while in the tessular, the want of a predominant axis -prevented the phenomena here spoken of from occurring at -all. The optical experiments must have led, and would have -led, to a classification of crystals into the above systems -or something nearly equivalent, even had they not been -already so arranged by attention to their forms. - -[Note 6\7: _Hist. Ind. Sc._ b. xv. c. v.] - -4. While in Germany Weiss and Mohs with their disciples, -were gradually rejecting what was superfluous in the -previous crystallographical hypotheses, 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 -Haüyian school. These attempts, however, were not crowned -with much success. One mode of representing the structure of -crystals which suggested itself, was to reject the -polyhedral forms which Haüy gave to his integrant molecules, -and to conceive the elements of crystals as _spheres_, the -properties of the crystal being determined not by the -_surfaces_, but by the _position_ of the elements. This was -done by Wollaston, in the _Philosophical Transactions_ for -1813. He applied this view to the tessular system, in which, -indeed, the application is not difficult; and he showed that -octahedral and tetrahedral figures may be deduced from -symmetrical arrangements of equal spherules. But though in -doing this, he manifested a perception of the conditions of -the problem, he appeared to lose his hold on the real -question when he tried to pass on to other systems of -crystallization. For he accounted for the rhombohedral -system by supposing the spheres changed into _spheroids_. -Such a procedure involved him in a gratuitous and useless -hypothesis: for to what purpose do we introduce the {86} -arrangement of atoms (instead of their figure,) as a mode of -explaining the symmetry of the crystallization, when at the -next step we ascribe to the atom, by an arbitrary fiction, a -symmetry of figure of the same kind as that which we have to -explain? It is just as easy, and as allowable, to assume an -elementary rhombohedron, as to assume elementary spheroids, -of which the rhombohedrons are constructed. - -5. Many hypotheses of the same kind might be adduced, -devised both by mineralogists and chemists. 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 proceed. The principle is -this:--that _All hypotheses concerning the arrangement of -the elementary atoms of bodies in space must be constructed -with reference to the general facts of crystallization_. The -truth and importance of this principle can admit of no -doubt. For if we make any hypothesis concerning the mode of -connexion of the elementary particles of bodies, this must -be done with the view of representing to ourselves the -forces which connect them, and the results of these forces -as manifested in the properties of the bodies. Now the -forces which connect the particles of bodies so as to make -them crystalline, are manifestly chemical forces. It is only -definite chemical compounds which crystallize; 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 combined. The elements are understood to be combined, -precisely because the result is a definite, apparently -homogeneous substance. The properties of the compound bodies -depend upon the elements and their mode of combination; for, -in fact, these include everything on which they can depend. -There are no other circumstances than these which can affect -the properties of a body. Therefore all those properties -which have reference to space, namely, the crystalline -properties, cannot depend upon anything else than the -arrangement of the elementary molecules in space. These {87} -properties are the facts which any hypothesis of the -arrangement of molecules must explain, or at least render -conceivable; and all such hypotheses, all constructions of -bodies by supposed arrangements of molecules, can have no -other philosophical object than to account for facts of this -kind. If they do not do this, they are mere arbitrary -geometrical fictions, which cannot be in any degree -confirmed or authorised by an examination of nature, and are -therefore not deserving of any regard. - -6. Those philosophers who have endeavoured to represent the -mode in which bodies are constructed by the combination of -their chemical atoms, have often undertaken to show, not -only that the atoms are combined, but also in what positions -and configurations they are combined. And it is truly -remarkable, as I have already said, that they have done -this, almost in every instance, without any consideration of -the crystalline character of the resulting combinations; -from which alone we receive any light as to the relation of -their elements in space. Thus Dr. Dalton, in his _Elements -of Chemistry_, in which he gave to the world the Atomic -Theory as a representation of the doctrine of definite and -multiple proportions, also published a large collection of -Diagrams, exhibiting what he conceived to be the -configuration of the atoms in a great number of the most -common combinations of chemical elements. Now these -hypothetical diagrams do not in any way correspond, as to -the nature of their symmetry, with the compounds, as we find -them displaying their symmetry when they occur crystallized. -Carbonate of lime has in reality a triangular symmetry, -since it belongs to the rhombohedral system; Dr. Dalton's -carbonate of lime would be an oblique rhombic prism or -pyramid. Sulphate of baryta is really two-and-two membered; -Dr. Dalton's diagram makes it two-and-one membered. Alum is -really octahedral or tessular; but according to the diagram -it could not be so, since the two ends of the atom are not -symmetrical. And the same want of correspondence between the -facts and the hypothesis runs through the whole {88} system. -It need not surprise us that the theoretical arrangement of -atoms does not explain the facts of _crystallization_; for -to produce such an explanation would be a second step in -science quite as great as the first, the discovery of the -atomic theory in its _chemical_ sense. But we may allow -ourselves to be surprised that an utter discrepance between -all the facts of crystallization and the figures assumed in -the theory, did not suggest any doubt as to the soundness of -the mode of philosophizing by which this part of the theory -was constructed. - -7. Some little accordance between the hypothetical -arrangements of chemical atoms and the facts of -crystallization, does appear to have been arrived at by some -of the theorists to whom we here refer, although by no means -enough to show a due conviction of the importance of the -principle stated above. Thus Wollaston, in the Essay above -noticed, after showing that a symmetrical arrangement of -equal spherules would give rise to octahedral and other -tessular figures, remarks, very properly, that the metals, -which are simple bodies, crystallize in such forms. M. -Ampère[7\7] also, in 1814, published a brief account of an -hypothesis of a somewhat similar nature, and stated himself -to have developed this speculation in a Memoir which has not -yet, so far as I am aware, been published. In this notice he -conceives bodies to be compounded of _molecules_, which, -arranged in a polyhedral form, constitute _particles_. These -_representative forms_ of the particles depend on chemical -laws. Thus the particles of oxygen, of hydrogen, and of -azote, are composed each of four molecules. Hence it is -collected that the particles of nitrous gas are composed of -two molecules of oxygen and two of azote; and similar -conclusions are drawn respecting other substances. These -conclusions, though expressed by means of the polyhedrons -thus introduced, are supported by chemical, rather than by -crystallographical comparisons. The author does, indeed, -appeal to the crystallization of sal {89} ammoniac as an -argument[8\7]; but as _all_ the forms which he introduces -appear to belong to the _tessular_ system of -crystallization, there is, in his reasonings, nothing -distinctive; and therefore nothing, crystallographically -speaking, of any weight on the side of this theory. - -[Note 7\7: _Ann. de Chimie_, tom. xc. p. 43.] - -[Note 8\7: _Ann. de Chimie_, tom. xc. p. 83.] - -8. Any hypothesis which should introduce any principle of -chemical order among the actual forms of minerals, would -well deserve attention. At first sight, nothing can appear -more anomalous than the forms which occur. We have, indeed, -one broad fact, which has an encouraging aspect, the -tessular forms in which the pure metals crystallize. The -highest degree of chemical and of geometrical simplicity -coincide: irregularity disappears precisely where it is -excluded by the consideration above stated, that the -symmetry of chemical composition must determine the symmetry -of crystalline form[9\7]. - -[Note 9\7: Inasmuch as this law, that the simple metals -crystallize in tessular forms, is the most signal example of -that connexion between the chemical nature of a body and its -crystalline form, I in the former Edition stated it with as -much generality as I could find any ground for, and I should -have been glad if I could have added confirmation of the -law, derived from later observations. But the most recent -investigations of crystallographers appear to have afforded -exceptions rather than examples of the rule. Arsenic and -Tellurium are said to be _rhombohedral_. Antimony, stated by -Haüy to be octahedral (and therefore tessular), has been -found by more modern observers to be _rhombohedral_. Tin has -been obtained by Professor Miller in beautiful crystals -belonging to the _pyramidal_ system. Professor Nöggerath has -observed in Zinc, after cooling from fusion, hexagonal -cleavage, rendering it probable that the mineral -crystallized in _rhombohedrons_ having their axes vertical, -like ice. G. Rose conceives it highly probable that Osmium -and Iridium are _rhombohedral_. (Poggendorf. Bd. liv.) - -But all the more perfect metals are tessular; namely, Gold, -Silver, Mercury, Platinum, Iron, Copper; also Bismuth [?] -Perhaps the observation in which the crystallization of Zinc -is affected by its position is, on that very account, no -sufficient evidence of its free crystallization. We can -hardly conceive a collection of perfectly simple, similar -particles to crystallize so as to have one pre-eminent axis, -without some extraneous action affecting them.] - -But if we go on to any other class of crystalline forms, we -soon find ourselves lost in our attempts to {90} follow any -thread of order. We have indeed many large groups connected -by obvious analogies; as the rhombohedral carbonates of -lime, magnesia, iron, manganese;--the prismatic carbonates -and sulphates of lime, baryta, strontia, lead. But even in -these, we cannot form any plausible hypothesis of the -arrangement of the elements; and in other cases to which we -naturally turn, we can find nothing but confusion. For -instance, if we examine the oxides of metals:--those of iron -are rhombohedral and tessular; those of copper, tessular; -those of tin, of titanium, of manganese, square pyramidal; -those of antimony, prismatic; and we have other forms for -other substances. - -It may be added, that if we take account of the optical -properties which, as we have already stated, have constant -relations to the crystalline forms, the confusion is still -further increased; for the optical dimensions vary in -amount, though not in symmetry, where chemistry can trace no -difference of composition. - -9. We will not quit the subject, however, without noticing -the much more promising aspect which it has assumed by the -detection of such groups as are referred to in the last -article; or in other words, by Mitscherlich's discovery of -_Isomorphism_. According to that discovery, there are -various elements which may take the place of each other in -crystalline bodies, either without any alteration of the -crystalline form, or at most with only a slight alteration -of its dimensions. Such a group of elements we have in the -earths lime and magnesia, the protoxides of iron and -manganese: for the carbonates of all these bases occur -crystallized in forms of the rhombohedral system, the -characteristic angle being nearly the same in all. Now lime -and magnesia, by the discoveries of modern chemistry, are -really oxides of metals; and therefore all these carbonates -have a similar chemical constitution, while they have also a -similar crystalline form. Whether or no we can devise any -arrangement of molecules by which this connexion of the -chemical and the geometrical property can be represented, we -cannot help {91} considering the connexion as an extremely -important fact in the constitution of bodies; and such facts -are more likely than any other to give us some intelligible -view of the relations of the ultimate parts of bodies. The -same may be said of all the other isomorphous or -plesiomorphous groups[10\7]. For instance, we have a number -of minerals which belong to the same system of -crystallization, but in which the chemical composition -appears at first sight to be very various: namely, spinelle, -pleonaste, gahnite, franklinite, chromic iron oxide, -magnetic iron oxide: but Abich has shown that all these may -be reduced to a common chemical formula;--they are bioxides -of one set of bases, combined with trioxides of another set. -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 system. -Hypothetical arrangements of atoms, thus expressing both the -chemical and the crystalline symmetry which we know to -belong to the substance, would be valuable steps in -analytical science; and when they had been duly verified, -the hypotheses might easily be divested of their atomic -character. - -[Note 10\7: See _Hist. Ind. Sc._ b. xv. c. vi.] - -Thus, as we have already said, mineralogy, understood in its -wider sense, as the counterpart of chemistry, has for one of -its main objects to discover those Relations of the Elements -of bodies which have reference to Space. In this research, -the foundation of all sound speculation is the kind and -degree of Symmetry of form which we find in definite -chemical compounds: and the problem at present before the -inquirer is, to devise such arrangements of molecules as -shall answer the conditions alike of Chemistry and of -Crystallography. - -We now proceed to the Classificatory Sciences, of which -Mineralogy is one, though hitherto by far the least -successful. - - - -{{93}} -BOOK VIII. - - -THE -PHILOSOPHY -OF THE -CLASSIFICATORY SCIENCES. - - - - -WHERE a certain apparent difference between things (although -perhaps in itself of little moment) answers to we know not -what number of other differences, pervading not only their -known properties but properties yet undiscovered, it is not -optional but imperative to recognise this difference as the -foundation of a specific distinction. - -JOHN S. MILL, _System of Logic_, b. 1, ch. vii. § 4. - - - -{{95}} -BOOK VIII. - - -THE PHILOSOPHY OF THE CLASSIFICATORY SCIENCES. - - -CHAPTER I. - -THE IDEA OF LIKENESS AS GOVERNING THE USE OF COMMON NAMES. - - -1. _Object of the Chapter._--NOT only the Classificatory -Sciences, but the application of names to things in the -rudest and most unscientific manner, depends upon our -apprehending them as _like_ each other. We must therefore -endeavour to trace the influence and operation of the Idea -of Likeness in the common use of language, before we speak -of the conditions under which it acquires its utmost -exactness and efficacy. - -It will be my object to show in this, as in previous cases, -that the impressions of sense are apprehended by acts of the -mind; and that these mental acts necessarily imply certain -relations which may be made the subjects of speculative -reasoning. We shall have, if we can, to seize and bring into -clear view the principles which the relation of _like_ and -_unlike_ involves, and the mode in which these principles -have been developed. - -2. _Unity of the Individual._--But before we can attend to -several things as like or unlike, we must be able to -apprehend each of these by itself as _one thing_. {96} It -may at first sight perhaps appear that this apprehension -results immediately from the impressions on our senses, -without any act of our thoughts. A very little attention, -however, enables us to see that thus to single out special -objects requires a mental operation as well as a sensation. -How, for example, without an exertion of mental activity, -can we see one tree, in a forest where there are many? We -have, spread before us, a collection of colours and forms, -green and brown, dark and light, irregular and straight: -this is all that sensation gives or can give. But we -associate one brown trunk with one portion of the green -mass, excluding the rest, although the neighbouring leaves -are both nearer in contiguity and more similar in appearance -than is the stem. We thus have before us one tree; but this -unity is given by the mind itself. We see the green and the -brown, but we must _make_ the tree before we can see _it_. - -That this composition of our sensations so as to form _one -thing_ implies an act of our own, will perhaps be more -readily allowed, if we once more turn our attention to the -manner in which we sometimes attempt to imitate and record -the objects of sight, by drawing. When we do this, as we -have already observed, we mark this unity of each object, by -drawing a line to separate the parts which we include from -those which we exclude;--an _Outline_. This line corresponds -to nothing which we see; the beginner in drawing has great -difficulty in discerning it; he has in fact to make it. It -is, as has been said by a painter of our own time[1\8], a -fiction: but it is a fiction employed to mark a real act of -the mind; to designate the singleness of the object in our -conception. As we have said elsewhere, we see lines, but -especially outlines, by mentally drawing them ourselves. - -[Note 1\8: Phillips _On Painting_,--Design.] - -The same act of conception which the outline thus represents -and commemorates in visible objects,--the same combination -of sensible impressions into a unit,--is exercised also with -regard to the objects of all {97} our senses: and the -singleness thus given to each object, is a necessary -preliminary to its being named or represented in any other -way. - -But it may be said, Is it then by an arbitrary act of our -own that we put together the branches of the same tree, or -the limbs of the same animal? Have we equally the power and -the right to make the branch of the fir a part of the -neighbouring oak? Can we include in the outline of a man any -object with which he happens to be in contact? - -Such suppositions are manifestly absurd. And the answer is, -that though we give unity to objects by an act of thought, -it is not by an _arbitrary_ act; but by a process subject to -certain conditions;--to conditions which exclude such -incongruous combinations as have just been spoken of. - -What are these conditions which regulate our apprehension of -an object as one?--which determine what portion of our -impressions does, and what portion does not belong to the -same thing? - -3. _Condition of Unity._--I reply, that the primary and -fundamental condition is, that we must be able to make -intelligible assertions respecting the object, and to -entertain that belief of which assertions are the -exposition. A tree _grows_, _sheds_ its leaves in autumn, -and _buds_ again in the spring, _waves_ in the wind, or -_falls_ before the storm. And to the tree belong all those -parts which must be included in order that such -declarations, and the thought which they convey, shall have -a coherent and permanent meaning. Those are _its_ branches -which wave and fall with _its_ trunk; those are _its_ leaves -which grow on _its_ branches. The permanent connexions which -we observe,--permanent, among unconnected changes which -affect the surrounding appearances,--are what we bind -together as belonging to one object. This permanence is the -condition of our conceiving the object _as_ one. The -connected changes may always be described by means of -assertions; and the connexion is seen in the identity of the -subject of successive predications; in the possibility of -applying many verbs to one substantive. We may {98} -therefore express the condition of the unity of an object to -be this: that _assertions concerning the object shall be -possible_: or rather we should say, that the acts of belief -which such assertions enunciate shall be possible. - -It may seem to be superfluous to put in a form so abstract -and remote, the grounds of a process apparently so simple as -our conceiving an object to be one. But the same condition -to which we have thus been led, as the essential principle -of the unity of objects, namely, that propositions shall be -possible, will repeatedly occur in the present chapter; and -it may serve to illustrate our views, to show that this -condition pervades even the simplest cases. - -4. _Kinds._--The mental synthesis of which we have thus -spoken, gives us our knowledge of _individual_ things; it -enables me to apprehend that particular tree or man which I -now see, or, by the help of memory, the tree or the man I -saw yesterday. But the knowledge with which we have mainly -here to do is not a knowledge of individuals but of kinds; -of such classes as are indicated by common names. We have to -make assertions concerning a tree or a man in general, -without regarding what is peculiar to this man or that tree. - -Now it is clear that certain individual objects are all -called _man_, or all called _tree_, in virtue of some -resemblance which they have. If we had not the power of -perceiving in the appearances around us, likeness and -unlikeness, we could not consider objects as distributed -into kinds at all. The impressions of sense would throng -upon us, but being uncompared with each other, they would -flow away like the waves of the sea, and each vanish from -our contemplation when the sensation faded. That we do -apprehend surrounding objects as belonging to permanent -kinds, as being men and horses, oaks and roses, arises from -our having the idea of likeness, and from our applying it -habitually, and so far as such a classification requires. - -Not only can we employ the idea of likeness in this manner, -but we apply it incessantly and universally to {99} the -whole mass and train of our sensations. For we have no -external sensations to which we cannot apply some language -or other; and all language necessarily implies recognition -of resemblances. We cannot call an object _green_ or _round_ -without comparing in our thoughts its colour or its shape, -with a shape and a colour seen in other objects. All our -sensations, therefore, without any exception of kind or -time, are subject to this constant process of -classification; and the idea of likeness is perpetually -operating to distribute them into kinds, at least so far as -the use of language requires. - -We come then again to the question, Upon what principle, -under what conditions, is the Idea of Likeness thus -operative? What are the limits of the classes thus formed? -Where does that similarity end, which induces and entitles -us to call a thing a _tree_? What universal rule is there -for the application of common names, so that we may not -apply them wrongly? - -5. _Not made by Definitions._--Perhaps some one might expect -in answer to these inquiries a definition or a series of -definitions;--might imagine that some description of a tree -might be given which might show when the term was applicable -and when it was not; and that we might construct a body of -rules to which such descriptions must conform. But on -consideration it will be clear that the real solution of our -difficulty cannot be obtained in such a manner. For _first_; -such descriptions must be given in words, and must therefore -suppose that we have already satisfied ourselves how words -are to be used. If we define a tree to be 'a living thing -without the power of voluntary motion,' we shall be called -upon to define 'a living thing;' and it is manifest that -this renewal of the demand for definition might be repeated -indefinitely; and, therefore, we cannot in this way come to -a final principle. And in the _next_ place, most of those -who use language, even with great precision and consistency, -would find it difficult or impossible to give good -definitions even of a few of the general names which they -use; and therefore their practice cannot be regulated by any -{100} tacit reference to such definitions. That definitions -of terms are of great use and importance in their right -place, we shall soon see; but their place is not to regulate -the use of common language. - -What then, once more, is this regulative principle? What -rules do men follow in the use of words, so as commonly to -avoid confusion and ambiguity? How do they come to -understand each other so well as they ordinarily do, -respecting the limits of classes never defined, and which -they cannot define? What is the common Convention, or -Condition to which they conform? - -6. _Condition of the Use of Terms._--To this we reply, that -the Condition which regulates the use of language, is, that -it shall be capable of being used;--that is, that general -assertions shall be possible. The term _tree_ is applicable -as far as it is useful in expressing our knowledge -concerning trees:--thus we know that trees are fixed in the -ground, have a solid stem, branches, leaves, and many other -properties. With regard to all the objects which surround -us, we have an immense store of knowledge of such -properties, and we employ the names of the objects in such a -manner as enables us to express these properties. - -But the connexion of such properties is variable and -indefinite. Some properties are constantly combined, others -occasionally only. The leaves of different oaks resemble -each other, the branches resemble far less, and may differ -very widely. The term _oak_ does not enable us to say that all -oaks have straight branches or all crooked. Terms can only -express properties as far as they are constant. Not only, -therefore, the accumulation of a vast mass of knowledge of -the properties and attributes of objects, but also an -observation of the habitual _connexion_ of such properties -is needed, to direct us to the consistent application of -terms:--to enable us to apply them so as to express truths. -But here again we are largely provided with the requisite -knowledge and observation by the common course of our -existence. The unintermitting stream of experience supplies -us with an incalculable {101} amount of such observed -connexions. All men have observed that the associations of -the same form of leaves are more constant than of the same -form of branches;--that though persons walk in different -attitudes, none go on all fours; 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 unlike; and though we -should refuse to apply the term _man_ to a class of -creatures which habitually and without compulsion used four -legs, we make no scruple of affixing it to persons of very -different figures. The whole of human experience being -composed of such observed connexions, we have thus materials -even for the immense multiplicity of names which human -language contains; all which names are, as we have said, -regulated in their application by the condition of their -expressing such experience. - -Thus amid the countless combinations of properties and -divisions of classes which the structure of language -implies, scarcely any are arbitrary or capricious. A word -which expressed a mere wanton collection of unconnected -attributes could hardly be called a _word_; for of such a -collection of properties no truth could be asserted, and the -word would disappear, for want of some occasion on which it -could be used. Though much of the fabric of language -appears, not unnaturally, fantastical and purely -conventional, it is in fact otherwise. 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 thought; and though much in language may be -called conventional, the conventions exist for the sake of -expressing some truth or opinion, and not for their own -sake. The principle, that _the condition of the use of terms -is the possibility of general, intelligible, consistent -assertions_, is true in the most complete and extensive sense. - -7. _Terms may have different Uses._--The Terms with which we -are here most concerned are Names of Classes of natural -objects; and when we say that the principle and the limit of -such Names are their use in expressing propositions -concerning the classes, it is {102} clear that much will -depend on the kind of propositions which we mainly have to -express: and that the same name may have different limits, -according to the purpose we have in view. For example, is -the _whale_ properly included in the general term _fish_? -When men are concerned in catching marine animals, the main -features of the process are the same however the animals may -differ; hence whales are classed with fishes, and we speak -of the _whale-fishery_. But if we look at the analogies of -organization, we find that, according to these, the whale is -clearly not a fish, but a _beast_, (confining this term, for -the sake of distinctness, to suckling beasts or _mammals_). -In Natural History, therefore, the whale is not included -among fish. The indefinite and miscellaneous propositions -which language is employed to enunciate in the course of -common practical life, are replaced by a more coherent and -systematic collection of properties, when we come to aim at -scientific knowledge. But we shall hereafter consider the -principle of the classifications of Natural History; our -present subject is the application of the Idea of Likeness -in common practice and common language. - -8. _Gradation of Kinds._--Common names, then, include many -individuals associated in virtue of resemblances, and of -permanently connected properties; and such names are -applicable as far as they serve to express such properties. -These collections of individuals are termed _Kinds_, -_Sorts_, _Classes_. - -But this association of particulars is capable of degrees. -As individuals by their resemblances form Kinds, so kinds of -things, though different, may resemble each other so as to -be again associated in a higher Class; and there may be -several successive steps of such classification. _Man_, -_horse_, _tree_, _stone_, are each a name of a Kind; but -_animal_ includes the two first and excludes the others; -_living thing_ is a term which includes _animal_ and _tree_ -but not _stone_; _body_ includes all the four. And such a -subordination of kinds may be traced very widely in the -arrangements of language. {103} - -The condition of the use of the wider is the same as that of -the narrower Names of Classes;--they are good as far as they -serve to express true propositions. In common language, -though such an order of generality may in a variety of -instances be easily discerned, it is not systematically and -extensively referred to; but this subordination and -graduated comprehensiveness is the essence of the methods -and nomenclatures of Natural History, as we shall soon have -to show. - -But such subordination is not without its use, even in -common cases, and when it is expressed in the terms of -common language. Thus _organized body_ is a term which -includes plants and animals; _animal_ includes beasts, -birds, fishes; _beast_ includes horses and dogs; _dogs_, -again, are greyhounds, spaniels, terriers. - -9. _Characters of Kinds._--Now when we have such a Series of -Names and Classes, we find that we take for granted -irresistibly that each class has some _Character_ which -distinguishes it from other classes included in the superior -division. We ask what kind of beast a dog is; what kind of -animal a beast is; and we assume that such questions admit -of answer;--that each kind has some mark or marks by which -it may be described. And such descriptions may be given: an -animal is an organized body _having sensation and volition_; -man is a _reasonable_ animal. Whether or no we assent to the -exactness of these definitions, we allow the propriety of -their form. If we maintain these definitions to be wrong, we -must believe some others to be right, however difficult it -may be to hit upon them. We entertain a conviction that -there must be, among things so classed and named, a -possibility of defining each. - -Now what is the foundation of this postulate? What is the -ground of this assumption, that there must exist a -definition which we have never seen, and which perhaps no -one has seen in a satisfactory form? The knowledge of this -definition is by no means necessary to our using the word -with propriety; for any one can make true assertions about -dogs, but who can define a {104} dog? And yet if the -definition be not necessary to enable us to use the word, -why is it necessary at all? I allow that we possess an -indestructible conviction that there must be such a -character of each kind as will supply a definition; but I -ask, on what this conviction rests. - -I reply, that our persuasion that there must needs be -characteristic marks by which things can be defined in -words, is founded on the assumption of _the necessary -possibility of reasoning_. - -The reference of any object or conception to its class -without definition, may give us a persuasion that it shares -the properties of its class, but such classing does not -enable us to reason upon those properties. When we consider -man as an animal, we ascribe to him in thought the -appetites, desires, affections, which we habitually include -in our notion of animal: but except we have expressed these -in some definition or acknowledged description of the term -_animal_, we can make no use of the persuasion in -ratiocination. But if we have described animals as 'being -impelled to action by appetites and passions,' we can not -only think, but say, 'man is an animal, and therefore he is -impelled to act by appetites and passions.' And if we add a -further definition, that 'man is a reasonable animal,' and -if it appear that 'reason implies conformity to a rule of -action,' we can then further infer that man's nature is to -conform the results of animal appetite and passion to a rule -of action. - -The possibility of pursuing any such train of reasoning as -this, depends on the definitions, of _animal_ and of _man_, -which we have introduced; and the possibility of reasoning -concerning the objects around us being inevitably assumed by -us from the constitution of our nature, we assume -consequently the possibility of such definitions as may thus -form part of our deduction, and the existence of such -defining characters. - -10. _Difficulty of Definitions._--But though men are, on -such grounds, led to make constant and importunate _demands_ -for definitions of the terms which they employ in their -speculations, they are, in fact, far {105} from being able -to carry into complete effect the postulate on which they -proceed, that they must be able to find definitions which by -logical consequence shall lead to the truths they seek. The -postulate overlooks the process by which our classes of -things are formed and our names applied. This process -consisting, as we have already said, in observing permanent -connexions of properties, and in fixing them by the -attribution of names, is of the nature of the process of -Induction, of which we shall afterwards have to speak. And -the postulate is so far true, that this process of induction -being once performed, its result may usually be expressed by -means of a few definitions, and may thus lead by a deduction -to a train of real truths. - -But in the subjects where we principally find such a -subordination of classes as we have spoken of, this process -of deduction is rarely of much prominence: for example, in -the branches of natural history. Yet it is in these subjects -that the existence and importance of these characteristic -marks, which we have spoken of, principally comes into view. -In treating of these marks, however, we enter upon methods -which are technical and scientific, not popular and common. -And before we make this transition, we have a remark to make -on the manner in which writers, without reference to physics -or natural history, have spoken of kinds, their -subordination, and their marks. - -11. '_The Five Words._'--These things,--the Nature and -Relations of Classes,--were, in fact, the subjects of minute -and technical treatment by the logicians of the school of -Aristotle. Porphyry wrote an Introduction to the -_Categories_ of that philosopher, which is entitled _On the -Five Words_. The 'Five Words' are _Genus_, _Species_, -_Difference_, _Property_, _Accident_. Genus and Species are -superior and inferior classes, and are stated[2\8] to be -capable of repeated subordination. The 'most {106} general -Genus' is the widest class; the 'most special Species' the -narrowest. Between these are intermediate classes, which are -Genera with regard to those below, and Species with regard -to those above them. Thus Being is the most general Genus; -under this is Body; under Body is Living Body; under this -again Animal; under Animal is Rational Animal, or Man; under -Man are Socrates and Plato, and other individual men. - -[Note 2\8: Porphyr. _Isagog._ c. 23.] - -The _Difference_ is that which is added to the genus to make -the species; thus Rational is the Difference by which the -genus Animal is made the species Man; the Difference in this -Technical sense is the 'Specific,' or species-making -Difference[3\8]. It forms the Definition for the purposes of -logic, and corresponds to the 'Character' (specific or -generic) of the Natural Historians. Indeed several of them, -as, for instance, Linnæus, in his _Philosophia Botanica_, -always call these Characters the _Difference_, by a -traditional application of the Peripatetic terms of art. - -[Note 3\8: εἰδοποιός.] - -Of the other two words, the Property is that which though -not employed in defining the class, belongs to every part of -it[4\8]: it is, 'What happens to all the class, to it alone, -and at all times; as _to be capable of laughing_ is a -Property of man.' - -[Note 4\8: _Isagog._ c. 4] - -The Accident is that which may be present and absent without -the destruction of the subject, as to sleep is an Accident -(a thing which happens) to man. - -I need not dwell further on this system of technicalities. -The most remarkable points in it are those which I have -already noticed; the doctrine of the successive -Subordination of genera, and the fixing attention upon the -Specific Difference. These doctrines, though invented in -order to make reasoning more systematic, and at a period -anterior to the existence of any Classificatory Science, -have, by a curious contrast with the intentions of their -founders, been of scarcely {107} any use in sciences of -_Reasoning_, but have been amply applied and developed in -the _Natural History_ which arose in later times. - -We must now treat of the principles on which this science -(Natural History) proceeds, and explain what peculiar and -technical processes it employs in addition to those of -common thought and common language. - - - -{{108}} -CHAPTER II. - -THE METHODS OF NATURAL HISTORY, AS REGULATED BY THE IDEA OF -LIKENESS. - - -SECT. I.--_Natural History in general._ - -1. _Idea of Likeness in Natural History._--THE various -branches of Natural History, in so far as they are -classificatory sciences merely, and do not depend upon -physiological views, rest upon the same Idea of Likeness -which is the ground of the application of the names, more or -less general, of common language. But the nature of science -requires that, for her purposes, this Idea should be applied -in a more exact and rigourous manner than in its common and -popular employment; just as occurs with regard to the other -Ideas on which science is founded;--for instance, as the -idea of space gives rise, in popular use, to the relations -implied in the prepositions and adjectives which refer to -position and form, and in its scientific development gives -rise to the more precise relations of geometry. - -The way in which the Idea of Likeness has been applied, so -as to lead to the construction of a science, is best seen in -Botany: for, in the Classification of Animals, we are -inevitably guided by a consideration of the _function_ of -parts; that is, by an idea of _purpose_, and not of likeness -merely: and in Mineralogy, the attempts at classification on -the principles of Natural History have been hitherto very -imperfectly successful. But in Botany we have an example of -a branch of knowledge in which systematic classification has -been effected with great beauty and advantage; and in which -the peculiarities and principles on which such {109} -classification must depend have been carefully studied. Many -of the principal botanists, as Linnæus, Adanson, Decandolle, -have not only practically applied, but have theoretically -enunciated, what they held to be the sound maxims of -classificatory science: and have thus enabled us to place -before the reader with confidence the philosophy of this -kind of science. - -2. _Condition of its Use._--We may begin by remarking that -the Idea of Likeness, in its systematic employment, is -governed by the same principle which we have already spoken -of as regulating the distribution of things into kinds, and -the assignment of names in unsystematic thought and speech; -namely, the condition that _general propositions shall be -possible_. But as in this case the propositions are to be of -a scientific form and exactness, the likeness must be -treated with a corresponding precision; and its consequences -traced by steady and distinct processes. Naturalists must, -for their purposes, employ the resemblances of objects in a -technical manner. This technical process may be considered -as consisting of three steps;--The fixation of the -resemblances; The use of them in making a classification; -The means of applying the classification. These three steps -may be spoken of as the _Terminology_, the _Plan of the -System_, and the _Scheme of the Characters_. - - -SECT. II.--_Terminology._[5\8] - -[Note 5\8: Decandolle and others use the term _Glossology_ -instead of Terminology, to avoid the blemish of a word -compounded of two parts taken from different languages. The -convenience of treating the termination _ology_ (and a few -other parts of compounds) as not restricted to Greek -combinations, is so great, that I shall venture, in these -cases, to disregard this philological scruple.] - -3. _Terminology_ signifies the collection of _terms_, or -technical words, which belong to the science. But in fixing -the meaning of the terms, at least of the descriptive terms, -we necessarily fix, at the same time, the perceptions and -notions which the terms are to {110} convey; and thus the -Terminology of a classificatory science exhibits the -elements of its substance as well as of its language. A -large but indispensable part of the study of botany (and of -mineralogy and zoology also,) consists in the acquisition of -the peculiar vocabulary of the science. - -The meaning of technical terms can be fixed in the first -instance only by convention, and can be made intelligible -only by presenting to the senses that which the terms are to -signify. The knowledge of a colour by its name can only be -taught through the eye. No description can convey to a -hearer what we mean by _apple-green_ or _French grey_. It -might, perhaps, be supposed that, in the first example, the -term _apple_, referring to so familiar an object, -sufficiently suggests the colour intended. But it may easily -be seen that this is not true; for apples are of many -different hues of green, and it is only by a conventional -selection that we can appropriate the term to one special -shade. When this appropriation is once made, the term refers -to the sensation, and not to the parts of this term; for -these enter into the compound merely as a help to the -memory, whether the suggestion be a natural connexion as in -'apple-green,' or a casual one as in 'French grey.' In order -to derive due advantage from technical terms of this kind, -they must be associated _immediately_ with the perception to -which they belong; and not connected with it through the -vague usages of common language. The memory must retain the -sensation; and the technical word must be understood as -directly as the most familiar word, and more distinctly. -When we find such terms as _tin-white_ or _pinchbeck-brown_, -the metallic colour so denoted ought to start up in our -memory without delay or search. - -This, which it is most important to recollect with respect -to the simpler properties of bodies, as colour and form, is -no less true with respect to more compound notions. In all -cases the term is fixed to a peculiar meaning by convention; -and the student, in order to use the word, must be -completely familiar with the convention, so that he has no -need to frame {111} conjectures from the word itself. Such -conjectures would always be insecure, and often erroneous. -Thus the term _papilionaceous_, applied to a flower, is -employed to indicate, not only a resemblance to a butterfly, -but a resemblance arising from five petals of a certain -peculiar shape and arrangement; and even if the resemblance -to a butterfly were much stronger than it is in such cases, -yet if it were produced in a different way, as, for example, -by one petal, or two only, instead of a 'standard,' two -'wings,' and a 'keel' consisting of two parts more or less -united into one, we should no longer be justified in -speaking of it as a 'papilionaceous' flower. - -The formation of an exact and extensive descriptive language -for botany has been executed with a degree of skill and -felicity, which, before it was attained, could hardly have -been dreamt of as attainable. Every part of a plant has been -named; and the form of every part, even the most minute, has -had a large assemblage of descriptive terms appropriated to -it, by means of which the botanist can convey and receive -knowledge of form and structure, as exactly as if each -minute part were presented to him vastly magnified. This -acquisition was part of the Linnæan Reform, of which we have -spoken in the _History_. 'Tournefort,' says Decandolle[6\8], -'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 sense, and always to -express the same idea by the same word; but it was Linnæus -who really created and fixed this botanical language, and -this is his fairest claim to glory, for by this fixation of -language he has shed clearness and precision over all parts -of the science.' - -[Note 6\8: _Theor. Elem._ p. 327.] - -It is not necessary here to give any detailed account of the -terms of botany. The fundamental ones have been gradually -introduced, as the parts of plants were more carefully and -minutely examined. Thus the flower was successively -distinguished into the _calyx_, {112} the _corolla_, the -_stamens_, and the _pistils_: the sections of the corolla -were termed _petals_ by Columna; those of the calyx were -called _sepals_ by Necker[7\8]. Sometimes terms of greater -generality were devised; as _perianth_ to include the calyx -and corolla, whether one or both of these were present[8\8]; -_pericarp_ for the part inclosing the grain, of whatever -kind it be, fruit, nut, pod, &c. And it may easily be -imagined that descriptive terms may, by definition and -combination, become very numerous and distinct. Thus leaves -may be called _pinnatifid_[9\8], _pinnatipartite_, -_pinnatisect_, _pinnatilobate_, _palmatifid_, -_palmatipartite_, &c., and each of these words designates -different combinations of the modes and extent of the -divisions of the leaf with the divisions of its outline. In -some cases arbitrary numerical relations are introduced into -the definition: thus a leaf is called _bilobate_[10\8] when -it is divided into two parts by a notch; but if the notch go -to the middle of its length, it is _bifid_; if it go near -the base of the leaf, it is _bipartite_; if to the base, it -is _bisect_. Thus, too, a pod of a cruciferous plant is a -_silica_[11\8] if it be four times as long as it is broad, -but if it be shorter than this it is a _silicula_. Such -terms being established, the form of the very complex leaf -or frond of a fern is exactly conveyed by the following -phrase: 'fronds rigid pinnate, pinnæ recurved subunilateral -pinnatifid, the segments linear undivided or bifid -spinuloso-serrate[12\8].' - -[Note 7\8: Decandolle, 329] - -[Note 8\8: For this Erhart and Decandolle use _Perigone_.] - -[Note 9\8: Dec. 318.] - -[Note 10\8: _Ib._ 493.] - -[Note 11\8: _Ib._ 422.] - -[Note 12\8: Hooker, _Brit. Flo._ p. 457. _Hymenophyllum -Wilsoni_, Scottish filmy-fern, abundant in the highlands of -Scotland and about Killarney.] - -Other characters, as well as form, are conveyed with the -like precision: Colour by means of a classified scale of -colours, as we have seen in speaking of the Measures of -Secondary Qualities; to which, however, we must add, that -the naturalist employs arbitrary names, (such as we have -already quoted,) and not mere numerical exponents, to -indicate a certain number of {113} selected colours. This -was done with most precision by Werner, and his scale of -colours is still the most usual standard of naturalists. -Werner also introduced a more exact terminology with regard -to other characters which are important in mineralogy, as -lustre, hardness. But Mohs improved upon this step by giving -a numerical scale of hardness, in which _talc_ is 1, -_gypsum_ 2, _calc spar_ 3, and so on, as we have already -explained in the History of Mineralogy. Some properties, as -specific gravity, by their definition give at once a -numerical measure; and others, as crystalline form, require -a very considerable array of mathematical calculation and -reasoning, to point out their relations and gradations. In -all cases the features of likeness in the objects must be -rightly apprehended, in order to their being expressed by a -distinct terminology. Thus no terms could describe crystals -for any purpose of natural history, till it was discovered -that in a class of minerals the proportion of the faces -might vary, while the angle remained the same. Nor could -crystals be described so as to distinguish species, till it -was found that the derived and primitive forms are connected -by very simple relations of space and number. The discovery -of the mode in which characters must be apprehended so that -they may be considered as _fixed_ for a class, is an -important step in the progress of each branch of Natural -History; and hence we have had, in the History of Mineralogy -and Botany, to distinguish as important and eminent persons -those who made such discoveries, Romé de Lisle and Haüy, -Cesalpinus and Gesner. - -By the continued progress of that knowledge of minerals, -plants, and other natural objects, in which such persons -made the most distinct and marked steps, but which has been -constantly advancing in a more gradual and imperceptible -manner, the most important and essential features of -similarity and dissimilarity in such objects have been -selected, arranged, and fitted with names; and we have thus -in such departments, systems of Terminology which fix our -attention upon the resemblances which it is proper to -consider, and {114} enable us to convey them in words. We -have now to speak of the mode in which such resemblances -have been employed in the construction of a Systematic -Classification. - - -SECT. III. _The Plan of the System._ - -4. The collection of sound views and maxims by which the -resemblances of natural objects are applied so as to form a -scientific classification, is a department of the philosophy -of natural history which has been termed by some writers (as -Decandolle), _Taxonomy_, as containing the _Laws_ of the -_Taxis_ (_arrangement_). By some Germans this has been -denominated _Systematik_; if we could now form a new -substantive after the analogy of the words _Logick_, -_Rhetorick_, and the like, we might call it _Systematick_. -But though our English writers commonly use the expression -_Systematical Botany_ for the Botany of Classification, they -appear to prefer the term _Diataxis_ for the method of -constructing the classification. The rules of such a branch -of science are curious and instructive. - -In framing a Classification of objects we must attend to -their resemblances and differences. But here the question -occurs, to _what_ resemblances and differences? for a -different selection of the points of resemblance would give -different results: a plant frequently agrees in leaves with -one group of plants, in flowers with another. Which set of -characters are we to take as our guide? - -The view already given of the regulative principle of all -classification, namely, that it must enable us to assert -true and general propositions, will obviously occur as -applicable here. The object of a scientific Classification -is to enable us to enunciate scientific truths: we must -therefore classify according to those resemblances of -objects (plants or any others) which bring to light such -truths. - -But this reply to the inquiry, 'On what characters of -resemblance we are to found our system,' is still too -general and vague to be satisfactory. It carries us, {115} -however, as far as this;--that since the truths we are to -attend to are scientific truths, governed by precise and -homogeneous relations, we must not found our scientific -Classification on casual, indefinite, and unconnected -considerations. We must not, for instance, be satisfied with -dividing plants, as Dioscorides does, into _aromatic_, -_esculent_, _medicinal_ and _vinous_; or even with the long -prevalent distribution into _trees_, _shrubs_, and _herbs_; -since in these subdivisions there is no consistent -principle. - -5. _Latent Reference to Natural Affinity._--But there may be -several kinds of truths, all exact and coherent, which may -be discovered concerning plants or any other natural -objects; and if this should be the case, our rule leaves us -still at a loss in what manner our classification is to be -constructed. And, historically speaking, a much more serious -inconvenience has been this;--that the task of -classification of plants was necessarily performed when the -general laws of their form and nature were very little -known; or rather, when the existence of such laws was only -just beginning to be discerned. Even up to the present day, -the general propositions which botanists are able to assert -concerning the structure and properties of plants, are -extremely imperfect and obscure. - -We are thus led to this conclusion:--that the Idea of -Likeness could not be applied so as to give rise to a -scientific Classification of plants, till considerable -progress was made in studying the general relations of -vegetable form and life; and that the selection of the -resemblances which should be taken into account, must depend -upon the nature of the relations which were then brought -into view. - -But this amounts to saying that, in the consideration of the -Classification of vegetables, other Ideas must be called -into action as well as the Idea of Likeness. The additional -general views to which the more intimate study of plants -leads, must depend, like all general truths, upon some -regulating Idea which gives unity to scattered facts. No -progress could be made in botanical knowledge without the -{116} operation of such principles: and such additional -Ideas must be employed, besides those of mere likeness and -unlikeness, in order to point out that Classification which -has a real scientific value. - -Accordingly, in the classificatory sciences, Ideas other -than Likeness do make their appearance. Such Ideas in botany -have influenced the progress of the science, even before -they have been clearly brought into view. We have especially -the Idea of Affinity, which is the basis of all Natural -Systems of Classification, and which we shall consider in a -succeeding chapter. The assumption that there _is_ a Natural -System, an assumption made by all philosophical botanists, -implies a belief in the existence of Natural Affinity, and -is carried into effect by means of principles which are -involved in that Idea. But as the formation of all systems -of classification must involve, in a great degree, the Idea -of Resemblance and Difference, I shall first consider the -effect of that Idea, before I treat specially of Natural -Affinity. - -6. _Natural Classes._--Many attempts were made to classify -vegetables before the rules which govern a natural system -were clearly apprehended. Botanists agree in esteeming some -characters as of more value than others, before they had -agreed upon any general rules or principles for estimating -the relative importance of the characters. They were -convinced of the necessity of adding other considerations to -that of Resemblance, without seeing clearly what these -others ought to be. They aimed at a Natural Classification, -without knowing distinctly in what manner it was to be -Natural. - -The attempts to form _Natural Classes_, therefore, in the -first part of their history, belong to the Idea of Likeness, -though obscurely modified, even from an early period, by the -Ideas of Affinity, and even of Function and of Development. -Hence Natural Classes may, to a certain extent, be treated -of in this place. - -Natural Classes are opposed to Artificial Classes which are -understood to be regulated by an _assumed_ {117} character. -Yet no classes can be so absolutely Artificial in this -sense, as to be framed upon characters _arbitrarily_ -assumed; for instance, no one would speak of a class of -shrubs defined by the circumstance of each having a hundred -leaves: for of such a class no assertion could be made, and -therefore the class could never come under our notice. In -what sense then are Artificial Classes to be understood, as -opposed to Natural? - -7. _Artificial Classes._--To this question, the following is -the answer. When Natural Classes of a certain small extent -have been formed, a system may be devised which shall be -regulated by a few selected characters, and which shall not -dissever these small Natural Classes, but conform to them as -far as they go. If these selected characters be then made -absolute and imperative, and if we abandon all attempt to -obtain Natural Classes of any higher order and wider extent, -we form an Artificial System. - -Thus in the Linnæan System of Botanical Classification, it -is assumed that certain natural groups, namely, Species and -Genera, are established; it is conceived, moreover, that the -division of Classes according to the number of stamens and -of pistils does not violate the natural connexions of -Species and Genera. This arrangement, according to the -number of stamens and pistils, (further modified in certain -cases by other considerations,) is then made the ground of -all the higher divisions of plants, and thus we have an -Artificial System. - -It has been objected to this view, that the Linnæan -Artificial System does not in all cases respect the -boundaries of genera, but would, if rigorously applied, -distribute the species of the same genus into different -artificial classes; it would divide, for instance, the -genera _Valeriana_, _Geranium_[13\8], &c. To this we must -reply, that so far as the Linnæan System does this, it is an -imperfect Artificial System. Its great merit is in its -making such a disjunction in comparatively so {118} few -cases; and in the artificial characters being, for the most -part, obvious and easily applied. - -[Note 13\8: Decand. _Theor. Elem._ p. 45.] - -8. _Are Genera Natural_?--It has been objected also that -Genera are not Natural groups. Linnæus asserts in the most -positive manner that they are[14\8]. On which Adanson -observes[15\8], 'I know not how any Botanist can maintain -such a thesis: that which is certain is, that up to the -present time no one has been able to prove it, nor to give -an exact definition of a natural genus, but only of an -artificial.' He then brings several arguments to confirm -this view. - -[Note 14\8: _Phil. Bot._ Art. 165.] - -[Note 15\8: _Famille de Ph._ Pref. cv.] - -But we are to observe, in answer to this, that Adanson -improperly confounds the recognition of the existence of a -natural group with the invention of a technical mark or -definition of it. Genera are groups of species associated in -virtue of natural affinity, of general resemblance, of real -propinquity: of such groups, certain selected characters, -one or few, may usually be discovered, by which the species -may be referred to their groups. These Artificial characters -do not constitute, but indicate the genus: they are the -_Diagnosis_, not the basis of the _Diataxis_: and they are -always subject to be rejected, and to have others -substituted for them, when they violate the natural -connexion of species which a minute and enlarged study -discovers. - -It is, therefore, no proof that Genera are not Natural, to -say that their artificial characters are different in -different systems. Such characters are only different -attempts to confine the variety of nature within the limits -of definition. Nor is it sufficient to say that these groups -themselves are different in different writers; that some -botanists make genera what others make only species; as -_Pedicularis_, _Rhinanthus_, _Euphrasia_, -_Antirrhinum_[16\8]. This discrepancy shows only that the -natural arrangement is not yet completely known, even in the -smaller groups; a conclusion to which we need not refuse our -assent. But in {119} opposition to these negatives, the -manner in which Genera have been established proves that -they are regulated by the principle of being natural, and by -that alone. For they are not formed according to any _à -priori_ rule. The Botanist does not take any selected or -arbitrary part or parts of the plants, and marshal his -genera according to the differences of this part. On the -contrary, the divisions of genera are sometimes made by -means of the flower; sometimes by means of the fruit: the -anthers, the stamens, the seeds, the pericarp, and the most -varied features of these parts, are used in the most -miscellaneous and unsystematic manner. Linnæus has indeed -laid down a maxim that the characteristic differences of -genera must reside in the fructification[17\8]: but Adanson -has justly remarked[18\8], that an arbitrary restriction -like this makes the groups artificial: and that in some -families other characters are more essential than those of -the fructification; as the leaves in the families of -_Aparineæ_ and _Leguminosæ_, and the disposition of the -flowers in _Labiatæ_. And Naturalists are so far from -thinking it sufficient to distribute species into genera by -_arbitrary_ marks, that we find them in many cases lamenting -the absence of good _natural_ marks: as in the families of -_Umbelliferæ_, where Linnæus declared that any one who could -find good characters of genera would deserve great -admiration, and where it is only of late that good -characters have been discovered and the arrangement -settled[19\8] by means principally of the ribs of the -fruit[20\8]. - -[Note 16\8: Adanson, p. cvi.] - -[Note 17\8: _Phil. Bot._ Art. 162.] - -[Note 18\8: Adanson, Pref. p. cxx.] - -[Note 19\8: Lindley, _Nat. Syst._ p. 5.] - -[Note 20\8: In like manner we find Cuvier saying of Rondelet -that he has 'un _sentiment_ très vrai des genres.' _Hist. -Ichth._ p. 39.] - -It is thus clear that Genera are not established on any -assumed or preconceived basis. What, then, is the principle -which regulates botanists when they try to fix genera? What -is the arrangement which they thus wish for, without being -able to hit upon it? What is the tendency which thus drives -them from the corolla to the anthers, from the flower to the -fruit, {120} from the fructification to the leaves? It is -plain that they seek something, not of their own devising -and creating;--not anything merely conventional and -systematic; but something which they conceive to exist in -the relations of the plants themselves;--something which is -without the mind, not within;--in nature, not in art;--in -short, a Natural Order. - -Thus the regulative principle of a Genus, or of any other -natural group is, that it is, or is supposed to be, natural. -And by reference to this principle as our guide, we shall be -able to understand the meaning of that indefiniteness and -indecision which we frequently find in the descriptions of -such groups, 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 botanist. Thus in the family of -the Rose-tree, we are told that the _ovules_ are _very -rarely_ erect[21\8], the _stigmata_ are _usually_ simple. Of -what use, it might be asked, can such loose accounts be? To -which the answer is, that they are not inserted in order to -distinguish the species, but in order to describe the -family, and the total relations of the ovules and of the -stigmata of the family are better known by this general -statement. A similar observation may be made with regard to -the Anomalies of each group, which occur so commonly, that -Mr. Lindley, in his _Introduction to the Natural System of -Botany_, makes the 'Anomalies' an article in each Family. -Thus, part of the character of the Rosaceæ is that they have -alternate _stipulate_ leaves, and that the _albumen_ is -_obliterated_: but yet in _Lowea_, one of the genera of this -family, the stipulæ are _absent_; and the albumen is -_present_ in another, _Neillia_. This implies, as we have -already seen, that the artificial character (or _diagnosis_ -as Mr. Lindley calls it) is imperfect. It is, though very -nearly, yet not exactly, commensurate with the natural -group: and hence, in certain cases, this character is made -to yield to the general weight of natural affinities. - -[Note 21\8: Lindley, _Nat. Syst._ p. 81.] - -{121} 9. _Difference of Natural History and -Mathematics._--These views,--of classes determined by -characters which cannot be expressed in words,--of -propositions which state, not what happens in all cases, but -only usually,--of particulars which are included in a class -though they transgress the definition of it, may very -probably surprise the reader. They are so contrary to many -of the received opinions respecting the use of definitions -and the nature of scientific propositions, that they will -probably appear to many persons highly illogical and -unphilosophical. But a disposition to such a judgment arises -in a great measure from this;--that the mathematical and -mathematico-physical sciences have, in a great degree, -determined men's views of the general nature and form of -scientific truth; while Natural History has not yet had time -or opportunity to exert its due influence upon the current -habits of philosophizing. The apparent indefiniteness and -inconsistency of the classifications and definitions of -Natural History belongs, in a far higher degree, to all -other except mathematical speculations: and the modes in -which approximations to exact distinctions and general -truths have been made in Natural History, may be worthy our -attention, even for the light they throw upon the best modes -of pursuing truth of all kinds. - -10. _Natural Groups given by Type not by Definition._--The -further development of this suggestion must be considered -hereafter. But we may here observe, that though in a Natural -Group of objects a definition can no longer be of any use as -a regulative principle, classes are not, therefore, left -quite loose, without any certain standard or guide. The -class is steadily fixed, though not precisely limited; it is -given, though not circumscribed; it is determined, not by a -boundary line without, but by a central point within; not by -what it strictly excludes, but by what it eminently -includes; by an example, not by a precept; in short, instead -of Definition we have a _Type_ for our director. - -A Type is an example of any class, for instance, a species -of a genus, which is considered as eminently {122} -possessing the characters of the class. All the species -which have a greater affinity with this Type-species than -with any others, form the genus, and are ranged about it, -deviating from it in various directions and different -degrees. Thus a genus may consist of several species, which -approach very near the type, and of which the claim to a -place with it is obvious; while there may be other species -which straggle further from this central knot, and which yet -are clearly more connected with it than with any other. And -even if there should be some species of which the place is -dubious, and which appear to be equally bound by two generic -types, it is easily seen that this would not destroy the -reality of the generic groups, any more than the scattered -trees of the intervening plain prevent our speaking -intelligibly of the distinct forests of two separate hills. - -The Type-species of every genus, the Type-genus of every -family, is, then, one which possesses all the characters and -properties of the genus in a marked and prominent manner. -The Type of the Rose family has alternate stipulate leaves, -wants the albumen, has the ovules not erect, has the -stigmata simple, and besides these features, which -distinguish it from the exceptions or varieties of its -class, it has the features which make it prominent in its -class. It is one of those which possess clearly several -leading attributes; and thus, though we cannot say of any -one genus that it _must_ be the Type of the family, or of -any one species that it _must_ be the Type of the genus, we -are still not wholly to seek: the Type must be connected by -many affinities with most of the others of its group; it -must be near the center of the crowd, and not one of the -stragglers. - -11. It has already been repeatedly stated, as the great rule -of all classification, that the classification must serve to -assert general propositions. It may be asked _what_ -propositions we are able to enunciate by means of such -classifications as we are now treating of. And the answer -is, that the collected knowledge of the characters, habits, -properties, organization, and {123} functions of these -groups and families, as it is found in the best botanical -works, and as it exists in the minds of the best botanists, -exhibits to us the propositions which constitute the -science, and to the expression of which the classification -is to serve. All that is not strictly definition, that is, -all that is not artificial character, in the descriptions of -such classes, is a statement of truths, more or less -general, more or less precise, but making up, together, the -positive knowledge which constitutes the science. As we have -said, the consideration of the properties of plants in order -to form a system of classification, has been termed -Taxonomy, or the Systematick of Botany; all the parts of the -descriptions, which, taking the system for granted, convey -additional information, are termed the _Physiography_ of the -science; and the same terms may be applied in the other -branches of Natural History. - -12. _Artificial and Natural Systems._--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 marks, we shall now be able to -compare the nature and objects of the Artificial and Natural -Systems; points on which much has been written in recent times. - -The Artificial System is one which is, or professes to be, -entirely founded upon marks selected according to the -condition which has been stated, of not violating certain -narrow natural groups; namely in the Linnæan system, the -natural genera of plants. The marks which form the basis of -the system, being thus selected, are applied rigorously and -universally without any further regard to any other -characters or indications of affinity. Thus in the Linnæan -system, which depends mainly on the number of male organs or -stamens, and on the number of female organs or styles, the -largest divisions, or the Classes, are arranged according to -the number of the stamens, and are _monandria_, _diandria_, -_triandria_, _tetrandria_, _pentandria_, _hexandria_, and so -on: the names being formed of the Greek numerical words, and -of the word which implies _male_. And the Orders of each of -these Classes are {124} distinguished by the number of -styles, and are called _monogynia_, _digynia_, _trigynia_, -and so on, the termination of these words meaning _female_. -And so far as this numerical division and subdivision go on, -the system is a rigorous system, and strictly artificial. - -But the condition that the artificial system shall leave -certain natural affinities untouched, makes it impossible to -go through the vegetable kingdom by a method of mere -numeration of stamens and styles. The distinction of flowers -with twenty and with thirty stamens is not a fixed -distinction: flowers of one and the same kind, as roses, -have, some fewer than the former, some more than the latter -number. The Artificial System, therefore, must be modified. -And there are various relations of connexion and proportion -among the stamina which are more permanent and important -than their mere number. Thus flowers with two longer and two -shorter stamens are not placed in the class _tetrandria_, -but are made a separate class _didynamia_; those with four -longer and two shorter are in like manner _tetradynamia_, -not _hexandria_; those in **which the filaments are bound -into two bundles are _diadelphia_. All these and other -classes are deviations from the plan of the earlier Classes, -and are so far defects of the artificial system; but they -are deviations requisite in order that the system may leave -a basis of natural groups, without which it would not be a -System of _Vegetables_. And as the division is still founded -on some properties of the stamens, it combines not ill with -that part of the system which depends on the number of them. -The Classes framed in virtue of these various considerations -make up an Artificial System which is tolerably coherent. - -'But since the Artificial System thus regards natural -groups, in what does it differ from a Natural System?' It -differs in this:--That though it allows certain subordinate -natural groups, it merely allows _these_, and does not -endeavour to ascend to any wider natural groups. It takes -all the _higher_ divisions of its scheme from its artificial -characters, its stamens and pistils, without looking to any -natural affinities. It {125} accepts natural _Genera_, but -it does not seek natural _Families_, or Orders, or Classes. -It _assumes_ natural groups, but does not _investigate_ any; -it forms wider and higher groups, but professes to frame -them arbitrarily. - -But then, on the other hand, the question occurs, 'This -being the case, what can be the use of the Artificial -System?' If its characters, in the higher stages of -classification, be arbitrary, how can it lead us to the -natural relations of plants? And the answer is, that it does -so in virtue of the original condition, that there shall be -certain natural relations which the artificial system shall -not transgress; and that its use arises from the facility -with which we can follow the artificial arrangement as far -as it goes. We can count the stamens and pistils, and thus -we know the Class and Order of our plant; and we have then -to discover its Genus and Species by means less symmetrical -but more natural. The Artificial System, though arbitrary in -a certain degree, brings us to a Class in which the whole of -each Genus is contained, and there we can find the proper -Genus by a suitable method of seeking. No Artificial System -can conduct us into the extreme of detail, but it can place -us in a situation where the detail is within our reach. We -cannot find the house of a foreign friend by its latitude -and longitude; but we may be enabled, by a knowledge of the -latitude and longitude, to find the city in which he dwells, -or at least the island; and we then can reach his abode by -following the road or exploring the locality. The Artificial -System is such a method of travelling by latitude and -longitude; the Natural System is that which is guided by a -knowledge of the country. - -The Natural System, then, is that which endeavours to -arrange by the natural affinities of objects; and more -especially, which attempts to ascend from the lower natural -groups to the higher; as for example from genera to natural -families, orders, and classes. But as we have already -hinted, these expressions of natural affinities, natural -groups, and the like, when {126} considered in reference to -the idea of resemblance alone, without studying analogy or -function, are very vague and obscure. We must notice some of -the attempts which were made under the operation of this -imperfect view of the subject. - - -SECT. IV.--_Modes of framing Natural Systems._ - -13. Decandolle[22\8] distinguishes the attempts at Natural -Classifications into three sorts: those of _blind trial_ -(_tâtonnement_), those of _general comparison_, and those of -_subordination of characters_. The two former do not depend -distinctly upon any principle, except resemblance; the third -refers us to other views, and must be considered in a future -chapter. - -[Note 22\8: _Theor. Elem._ art 41.] - -_Method of Blind Trial._--The notion of the existence of -natural classes dependent on the general resemblance of -plants,--of an affinity showing itself in different parts -and various ways,--though necessarily somewhat vague and -obscure, was acted upon at an early period, as we have seen -in the formation of genera; and was enunciated in general -terms soon after. Thus Magnolius[23\8] says that he discerns -in plants an affinity, by means of which they may be -arranged in families: 'Yet it is impossible to obtain from -the fructification alone the Characters of these families; -and I have therefore chosen those parts of plants in which -the principal characteristic marks are found, as the root, -the stem, the flower, the seed. In some plants there is even -a certain resemblance; an affinity which does not consist in -the parts considered separately, but in their totality; an -affinity which may be felt but not expressed; as we see in -the families of agrimonies and cinquefoils, which every -botanist will judge to be related, though they differ by -their roots, their leaves, their flowers, and their seeds.' - -[Note 23\8: Dec. _Theor. Elem._ art. 42. Petri Magnoli, -_Prodromus Hist. Gen. Plant._ 1689.] - -{127} This obscure feeling of a resemblance on the whole, an -affinity of an indefinite kind, appears fifty years later in -Linnæus's attempts. 'In the Natural Classification,' he -says[24\8], 'no _à priori_ rule can be admitted, no part of -the fructification can be taken exclusively into -consideration; but only the simple symmetry of all its -parts.' Hence though he proposed Natural Families, and even -stated the formation of such Families to be the first and -last object of all Methods, he never gave the Characters of -those groups, or connected them by any method. He even -declared it to be impossible to lay down such a system of -characters. 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 use; he would not attempt to unravel the -Ideas of Symmetry and of Function on which the clear -establishment of natural relations must depend. He even -despised the study of the inner organization of plants; and -reckoned[25\8] the _Anatomici_, who studied the anatomy and -physiology of plants and the laws of vegetation, among the -_Botanophili_, the mere amateurs of his science. - -[Note 24\8: Dec. _Theor. Elem._ art 42.] - -[Note 25\8: _Phil. Bot._ s. 44.] - -The same notion of general resemblance and affinity, -accompanied with the same vagueness, is to be found in the -writer who least participated in the general admiration of -Linnæus, Buffon. Though it was in a great measure his love -of higher views which made him dislike what he considered -the pedantry of the Swedish school, he does not seem to have -obtained a clearer sight of the principle of the natural -method than his rival, except that he did not restrict his -Characters to the fructification. Things must be arranged by -their resemblances and differences, (he says in 1750[26\8],) -'but the resemblances and differences must be taken not from -one part but from the whole; and we must attend to the form, -the size, the habit, the number and position of the parts, -even the substance {128} of the part; and we must make use -of these elements in greater or smaller number, as we have need.' - -[Note 26\8: Adanson, p. clvi. Buffon, _Hist. Nat._ t. i. p. 21.] - -14. _Method of General Comparison._--A countryman of Buffon, -who shared with him his depreciating estimate of the Linnæan -system, and his wish to found a natural system upon a -broader basis, was Adanson; and he invented an ingenious -method of apparently avoiding the vagueness of the practice -of following the general feeling of resemblance. This method -consisted in making many Artificial Systems, in each of -which plants were arranged by some one part; and then -collecting those plants which came near each other in the -greatest number of those Artificial Systems, as plants -naturally the most related. Adanson gives an account[27\8] -of the manner in which this system arose in his mind. He had -gone to Senegal, animated by an intense zeal for natural -history; and there, amid the luxuriant vegetation of the -torrid zone, he found that the methods of Linnæus and -Tournefort failed him altogether as means of arranging his -new botanical treasures. He was driven to seek a new system. -'For this purpose,' he says, 'I examined plants in all their -parts, without omitting any, from the roots to the embryo, -the folding of the leaves in the bud, their mode of -sheathing[28\8], the situation and folding of the embryo and -of its radicle in the seed, relatively to the fruit; in -short, a number of particulars which few botanists notice. I -made in the first place a complete description of each -plant, putting each of its parts in separate articles, in -all its details; when new species occurred I put down the -points in which they differed, omitting those in which they -agreed. By means of the aggregate of these comparative -descriptions, I perceived that plants arranged themselves -into classes or families which could not be artificial or -arbitrary, not being founded upon one or two parts, which -might change at certain limits, but on all the parts; so -that the disproportion of one of these parts was corrected -and balanced by the introduction of another.' Thus the -principle of Resemblance {129} was to suffice for the -general arrangement, not by means of a new principle, as -Symmetry or Organization, which should regulate its -application, but by a numeration of the peculiarities in -which the resemblance consisted. - -[Note 27\8: Pref. p. clvii.] - -[Note 28\8: 'Leur manière de s'engainer.'] - -The labour which Adanson underwent in the execution of this -thought was immense. By taking each Organ, and considering -its situation, figure, number, &c., he framed sixty-five -Artificial Systems; and collected his Natural Families by a -numerical combination of these. For example, his -_sixty-fifth_ Artificial System[29\8] is that which depends -upon the situation of the Ovary with regard to the Flower; -according to this system he frames _ten_ Artificial Classes, -including _ninety-three_ Sections: and of these Sections the -resulting Natural Arrangement retains _thirty-five_, above -one-third: the same estimate is applied in other cases. - -[Note 29\8: Adanson, Pref. p. cccxii.] - -But this attempt to make Number supply the defects which the -vague notion of Resemblance introduces, however ingenious, -must end in failure. For, as Decandolle observes[30\8], it -supposes that we know, not only all the Organs of plants, -but all the points of view in which it is possible to -consider them; and even if this assumption were true, which -it is not, and must long be very far from being, the -principle is altogether vicious; for it supposes that all -these points of view, and all the resulting artificial -systems are of equal importance:--a supposition manifestly -erroneous. We are thus led back to the consideration of the -_Relative Importance_ of Organs and their qualities, as a -basis for the classification of plants, which no Artificial -Method can supersede; and thus we find the necessity of -attending to something besides mere external and detached -Resemblance. The method of General Comparison cannot, any -more than the method of Blind Trial, lead us, with any -certainty or clearness, to the Natural Method. Adanson's -Families are held by the best botanists to be, for the -greater part, Natural; but his hypotheses are unfounded; and -his success is {130} probably more due to the dim feeling of -Affinity, by which he was unconsciously guided, than to the -help he derived from his numerical processes. - -[Note 30\8: Dec. _Theor. Elem._ p. 67.] - -In a succeeding chapter I shall treat of that Natural -Affinity on which a Natural System must really be founded. -But before proceeding to this higher subject, we must say a -few words on some of the other parts of the philosophy of -Natural History,--the Gradation of Groups, the Nomenclature, -the Diagnosis, and the application of the methods to other -subjects. - - -SECT. V.--_Gradation of Groups._ - -15. It has been already noticed (last chapter,) that even -that vague application of the idea of resemblance which -gives rise to the terms of common language, introduces a -subordination of classes, as _man_, _animal_, _body_, -_substance_. Such a subordination appears in a more precise -form when we employ this idea in a scientific manner as we -do in Natural History. We have then a series of divisions, -each inclusive of the lower ones, which are expressed by -various metaphors in different writers. Thus some have gone -as far as eight terms of the series[31\8], and have taken, -for the most part, military names for them; as _Hosts_, -_Legions_, _Phalanxes_, _Centuries_, _Cohorts_, _Sections_, -_Genera_, _Species_. But the most received series is -_Classes_, _Orders_, _Genera_, and _Species_; in which, -however, we often have other terms interpolated, as -_Sub-genera_, or Sections of genera. The expressions -_Family_ and _Tribe_, are commonly appropriated to natural -groups; and we speak of the Vegetable, Animal, Mineral -_Kingdom_; but the other metaphors of Provinces, Districts, -&c., which this suggests, have not been commonly used[32\8]. - -[Note 31\8: Adanson, p. cvi.] - -[Note 32\8: _Sub-Kingdom_ has recently been employed by -some naturalists.] - -It will of course be understood that each ascending step of -classification is deduced by the same process from the one -below. A Genus is a collection of Species which resemble -each other more than they {131} resemble other species; an -Order is a collection of Genera having, in like manner, the -first degree of resemblance, and so on. How close or how -wide the Degrees of Resemblance are, must depend upon the -nature of the objects compared, and cannot possibly be -prescribed beforehand. Hence the same term, _Class_ and -_Order_ for instance, may imply, in different provinces of -nature, very different degrees of resemblance. The Classes -of Animals are Insects, Birds, Fish, Beasts, &c. The Orders -of Beasts are _Ruminants_, _Tardigrades_, _Plantigrades_, -&c. The two Classes of Plants (according to the Natural -Order[33\8]) are _Vascular_ and _Cellular_, the latter -having neither sexes, flowers, nor spiral vessels. The -Vascular Plants are divided into Orders, as _Umbelliferæ_, -_Ranunculaceæ_, &c.; but between this Class and its Orders -are interposed two other steps:--two Sub-classes, -_Dicotyledonous_ and _Monocotyledonous_, and two Tribes of -each: _Angiospermiæ_, _Gymnospermiæ_ of the first; and -_Petaloideæ_, _Glumaciæ_ of the second. Such interpolations -are modifications of the general formula of subordination, -for the purpose of accommodating it to the most prominent -natural affinities. - -[Note 33\8: Lindley.] - -16. _Species._--As we have already seen in tracing the -principles of the Natural Method, 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 depend, we are led to the study of Organization -and Analogy. But we make a reference to physiological -conditions even from the first, with regard to the lowest -step of our arrangement, the _Species_; for we consider it a -proof of the impropriety of separating two Species, if it be -shown that they can by any course of propagation, culture, -and treatment, the one pass into the other. It is in this -way, for example, that it has been supposed to be -established that the common Primrose, Oxlip, Polyanthus, and -Cowslip, are all the same species. Plants which thus, in -virtue of external circumstances, as soil, {132} exposure, -climate, exhibit differences which may disappear by changing -the circumstances, are called _Varieties_ of the species. -And thus we cannot say that a Species is a collection of -individuals which possess the First Degree of Resemblance; -for it is clear that a primrose resembles another primrose -more than it does a cowslip; but this resemblance only -constitutes a Variety. And we find that we must necessarily -include in our conception of Species, the notion of -propagation from the same stock. And thus a Species has been -well defined[34\8]: 'The collection of the individuals -descended from one another, or from common parents, and of -those which resemble these as much as these resemble each -other.' And thus the sexual doctrine of plants, or rather -the consideration of them as things which propagate their -kind, (whether by seed, shoot, or in any other way,) is at -the basis of our classifications. - -[Note 34\8: Cuv. _Règne Animal_, p. 19.] - -17. The First permanent Degree of Resemblance among -organized beings is thus that which depends on this relation -of generation, and we might expect that the groups which are -connected by this relation would derive their names from the -notion of generation. It is curious that both in Greek and -Latin languages and in our own, the words which have this -origin (γένος, _genus_, _kind_,) do not, in the phraseology -of science at least, denote the nearest degree of -relationship, but have other terms subordinate to them, -which appear etymologically to indicate a mere resemblance -of appearance (εἶδος, _species_, _sort_); and these latter -terms are appropriated to the groups resulting from -propagation. Probably the reason of this is, that the former -terms (_genus_, &c.) had been applied so widely and loosely -before the scientific fixation of terms, that to confine -them to what we call _species_ would have been to restrict -them in a manner too unusual to be convenient. - -18. _Varieties. Races._--The Species, as we have said, is -the collection of individuals which resemble each other as -much as do the offspring of a common {133} stock. But within -the limits of this boundary, there are often observable -differences permanent enough to attract our notice, though -capable of being obliterated by mixture in the course of -generation. Such different groups are called _Varieties_. -Thus the Primrose and Cowslip, as has been stated above, are -found to be varieties of the same plant; the Poodle and the -Greyhound are well marked varieties of the species _dog_. -Such differences are hereditary, and it may be long doubtful -whether such hereditary differences are varieties only, or -different species. In such cases the term _Race_ has been -applied. - - -SECT. VI.--_Nomenclature._ - -19. The Nomenclature of any branch of Natural History is the -collection of names of all its species; which, when they -become extremely numerous, requires some artifice to make it -possible to recollect or apply them. The known species of -plants, for example, were 10,000 at the time of Linnæus, and -are now probably 60,000. It would be useless to endeavour to -frame and employ separate names for each of these species. - -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 names. The artifice -employed to avoid this inconvenience is to name a Species by -means of two (or it might be more) steps of the successive -division. Thus in Botany, each of the genera has its name, -and the species are marked by the addition of some epithet -to the name of the genus. In this manner about 1,700 generic -names, with a moderate number of specific names, were found -by Linnæus sufficient to designate with precision all the -species of vegetables known at his time. 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 beings. - -Many other modes of Nomenclature have been tried, but no -other has at all taken root. Linnæus himself {134} appears -at first to have intended marking each species by the -Generic Name accompanied by a characteristic Descriptive -Phrase; and to have proposed the employment of a _trivial_ -Specific Name, as he termed it, only as a method of -occasional convenience. The use of these _trivial names_, -has, however, become universal, as we have said, and is by -many persons considered the greatest improvement introduced -at the Linnæan reform. - -Both Linnæus and other writers (as Adanson) have given many -maxims with a view of regulating the selection of generic -and specific names. The maxims of Linnæus were intended as -much as possible to exclude barbarism and confusion, and -have, upon the whole, been generally adopted; though many of -them were objected to by his contemporaries (Adanson and -others[35\8]), as capricious or unnecessary innovations. -Many of the names, introduced by Linnæus, certainly appear -fanciful enough: thus he gives the name of _Bauhinia_ to a -plant with leaves in pairs, because the Bauhins were a pair -of brothers; _Banisteria_ is the name of a climbing plant, -in honour of Banister, who travelled among mountains. But -such names, once established by adequate authority, lose all -their inconvenience, and easily become permanent; and hence -the reasonableness of the Linnæan rule[36\8], that as such a -perpetuation of the names of persons by the names of plants -is the only honour botanists have to bestow, it ought to be -used with care and caution. - -[Note 35\8: Pp. cxxix. clxxii.] - -[Note 36\8: _Phil Bot._ s. 239.] - -The generic name must, as Linnæus says, be fixed[37\8] -before we attempt to form a specific name; 'the latter -without the former is like the clapper without the bell.' -The name of the genus being established, the species may be -marked by adding to it 'a single word taken at will from any -quarter;' that is, not involving a description or any -essential property of the plant, but a casual or arbitrary -appellation[38\8]. Thus the {135} various species of -_Hieracium_[39\8] are _Hieracium Alpinum_, _H. Halleri_, _H. -Pilosella_, _H. dubium_, _H. murorum_, &c. where we see how -different may be the kind of origin of the words. - -[Note 37\8: _Ib._ s. 222.] - -[Note 38\8: _Ib._ s. 260.] - -[Note 39\8: Hooker, _Fl. Scot._ 228.] - -Attempts have been made at various times to form the name of -species from those of genera in some more symmetrical -manner. Thus some have numbered the species of genus, 1, 2, -3, &c.; but this method is liable to the inconveniences, -first, that it offers nothing for the memory to take hold -of; and second, that if a new species intermediate between 1 -and 2, 2 and 3, &c., be discovered, it cannot be put in its -place. It has also been proposed to mark the species by -altering the termination of the genus. Thus Adanson[40\8], -denoting a genus by the name _Fonna_ (_Lychnidea_), -conceived he might mark five of its species by altering the -last vowel, _Fonna_, _Fonna-e_, _Fonna-i_, _Fonna-o_, -_Fonna-u_; then others by _Fonna-ha_, _Fonna-ka_, and so on. -This course would be liable to the same evils which have -been noticed as belonging to the numerical method. - -[Note 40\8: Pref. clxxvi.] - -The names of plants (and the same is true of animals) have -in common practice been binary only, consisting of a generic -and a specific name. The Class and Order have not been -admitted to form part of the appellation of the species. -Indeed it is easy to see that a name which must be identical -in so many instances as that of an Order would be, would be -felt as superfluous and burdensome. Accordingly, Linnæus -makes it a precept[41\8], that the name of the Class and the -Order must not be expressed but understood: and hence, he -says, Royen, who took _Lilium_ for the name of a Class, -rightly rejected it as a generic name, and substituted -_Lirium_, with the Greek termination. - -[Note 41\8: _Phil. Bot._ s. 215.] - -Yet we must not too peremptorily assume such maxims as these -to be universal for all classificatory sciences. It is very -possible that it may be found advisable to use _three_ -terms, that of order, genus and {136} species, in -designating minerals, as is done in Mohs's nomenclature; for -example, _Rhombohedral Calc Haloide_, _Paratomous Hal -Baryte_. - -It is possible also that it may be found useful in the same -science to mark some of the steps of classification by the -termination. Thus it has been proposed to confine the -termination _ite_ to the Order _Silicides_ of Naumann, as -Apophyll_ite_, Stilb_ite_, Leuc_ite_, &c., and to use names -of different form in other orders, as Talc _Spar_ for -Brennerite, Pyramidal Titanium _Oxide_ for Octahedrite. Some -such method appears to be the most likely to give us a -tolerable mineralogical nomenclature. - - -SECT. VII.--_Diagnosis._ - -20. German Naturalists speak of a part of the general method -which they call the _Characteristik_ of Natural History, and -which is distinguished from the _Systematik_ of the science. -The _Systematick_ arranges the objects by means of all their -resemblances, the _Characteristick_ enables us to detect -their place in the arrangement by means of a few of their -characters. What these characters are to be, must be -discovered by observation of the groups and divisions of the -system when they are formed. To construct a collection of -such characters as shall be clear and fixed, is a useful, -and generally a difficult task; for there is usually no -apparent connexion between the marks which are used in -discriminating the groups, and the nature of the groups -themselves. They are assumed only because the naturalist, -extensively and exactly acquainted with the groups and the -properties of the objects which compose them, sees, by a -survey of the field, that these marks divide it properly. - -The Characteristick has been termed by some English -Botanists the _Diagnosis_ of plants; a word which we may -conveniently adopt. The Diagnosis of any genus or species is -different according to the system we follow. Thus in the -Linnæan System the Diagnosis of the Rose is in the first -place given by its Class and Order: it is {137} Icosandrous, -and Polygynous; and then the Generic Distinction is that the -calyx is five-cleft, the tube urceolate, including many -hairy achenia, the receptacle villous[42\8]. In the Natural -System the Rose-Tribe are distinguished as being[43\8] -'Polypetalous dicotyledons, with lateral styles, superior -simple ovaria, regular perigynous stamens, exalbuminous -definite seeds, and alternate stipulate leaves.' And the -true Roses are further distinguished by having 'Nuts, -numerous, hairy, terminated by the persistent lateral style -and inclosed within the fleshy tube of the calyx,' &c. - -[Note 42\8: Lindley, _Nat. Syst._ p. 149.] - -[Note 43\8: _Ib._ pp. 81, 3.] - -It will be observed that in a rigorous Artificial System the -_Systematick_ coincides with the _Characteristick_; the -_Diataxis_ with the _Diagnosis_; the reason why a plant is -put in a division is identical with the mode by which it is -known to be in the division. The Rose is in the class -_icosandria_, because it has many stamens inserted in the -calyx; and when we see such a set of stamens we immediately -know the class. But this is not the case with the Diagnosis -of Natural Families. Thus the genera _Lamium_ and -_Galeopsis_ (Dead Nettle and Hemp Nettle) are each formed -into a separate group in virtue of their general -resemblances and differences, and not because the former has -one tooth on each side of the lower lip, and the latter a -notch in its upper lip, though they are distinguished by -these marks. - -Thus so far as our Systems are natural, (which, as we have -shown, all systems to a certain extent must be), the -Characteristick is distinct both from a Natural and an -Artificial System; and is, in fact, an Artificial Key to a -Natural System. As being Artificial, it takes as few -characters as possible; as being Natural, its characters are -not selected by any general or prescribed rule, but follow -the natural affinities. The Botanists who have made any -steps in the formation of a natural method of plants since -Linnæus, have all attempted to give a Diagnosis -corresponding to the Diataxis of their method. - - - -{{138}} -CHAPTER III. - -APPLICATION OF THE NATURAL HISTORY METHOD TO MINERALOGY. - - -1. THE philosophy of the Sciences of Classification has had -great light thrown upon it by discussions concerning the -methods which are used in Botany: 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 Classification; and this application has been made -in general without giving rise to any very startling -paradoxes, or disclosing any insurmountable difficulties. -But the discussions concerning methods of Mineralogical -Classification have been instructive for quite a different -reason: they have brought into view the boundaries and the -difficulties of the process of Classification; and have -presented examples in which every possible mode of -classifying appeared to involve inextricable contradictions. -I will notice some of the points of this kind which demand -our attention, referring to the works published recently by -several mineralogists. - -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 plants. 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 attempt. We -have already said that the _Terminology_ of Mineralogy was -materially reformed by Werner; and including in this branch -of the subject (as we must do) the Crystallography of later -writers, it may be considered as to a great extent complete. -Of the attempts at a Natural arrangement, that of Mohs -appears to proceed by the {139} method of _blind trial_, the -undefinable perception of relationship, by which the -earliest attempts at a Natural Arrangement of plants were -made. Breithaupt however, has made (though I do not know -that he has published) an essay in a mode which corresponds -very nearly to Adanson's process of _multiplied -comparisons_. Having ascertained the specific gravity and -hardness of all the species of minerals, he arranged them in -a table, representing by two lines at right angles to each -other these two numerical quantities. Thus all minerals were -distributed according to two co-ordinates representing -specific gravity and hardness. He conceived that the groups -which were thus brought together were natural groups. On -both these methods, and on all similar ones, we might -observe, that in minerals as in plants, the mere general -notion of Likeness cannot lead us to a real arrangement: -this notion requires to have precision and aim given it by -some other relation;--by the relation of Chemical -Composition in minerals, as by the relation of Organic -Function in vegetables. The physical and crystallographical -properties of minerals must be studied with reference to -their constitution; and they must be arranged into Groups -which have some common Chemical Character, before we can -consider any advance as made towards a Natural Arrangement. - -In reality, it happens in Mineralogy as it happened in -Botany, that those speculators are regulated by an obscure -perception of this ulterior relation, who do not profess to -be regulated by it. Several of the Orders of Mohs have -really great unity of chemical character, and thus have good -evidence of their being really Natural Orders. - -2. Supposing the Diataxis of minerals thus obtained, Mohs -attempted the Diagnosis; and his _Characteristick of the -Mineral Kingdom_, published in Dresden, in 1820, was the -first public indication of his having constructed a system. -From the nature of a Characteristick, it is necessarily -brief, and without any ostensible principle; but its -importance was duly appreciated by the author's countrymen. -Since that {140} time, many attempts have been made at -improved arrangements of minerals, but none, I think, -(except perhaps that of Breithaupt,) professing to proceed -rigorously on the principles of Natural History;--to arrange -by means of external characters, neglecting altogether, or -rather postponing, the consideration of chemical properties. -By relaxing from this rigour, however, and by combining -physical and chemical considerations, arrangements have been -obtained (for example, that of Naumann,) which appear more -likely than the one of Mohs to be approximations to an -ultimate really natural system. Naumann's Classes are -_Hydrolytes_, _Haloides_, _Silicides_, _Metal Oxides_, -_Metals_, _Sulphurides_, _Anthracides_, with subdivisions of -Orders, as _Anhydrous unmetallic Silicides_. It may be -remarked that the designations of these are mostly chemical. -As we have observed already, Chemistry, and Mineralogy in -its largest sense, are each the necessary supplement of the -other. If Chemistry furnish the Nomenclature, Mineralogy -must supply the Physiography: if the Arrangement be founded -on External Characters and the Names be independent of -Chemistry, the chemical composition of each species is an -important scientific Truth respecting it. - -3. The inquiry may actually occur, whether any subordination -of groups in the mineral kingdom has really been made out. -The ancient chemical arrangements, for instance, that of -Haüy, though professing to distribute minerals according to -Classes, Orders, Genera, and Species, were not only -arbitrary, but inapplicable; for the first postulate of any -method, that the species should have constant characters of -unity and difference, was not satisfied. It was not -ascertained that carbonate of lime was really -distinguishable in all cases from carbonate of magnesia, or -of iron; yet these species were placed in remote parts of -the system: and the above carbonates made just so many -species; although, if they were distinct from one another at -all, they were further distinguishable into additional -species. Even now, we may, perhaps, say that the limits of -mineralogical species, and their laws of fixity, are {141} -not yet clearly seen. For the discoveries of the isomorphous -relations and of the optical properties of minerals have -rather shown us in what direction the object lies, than led -us to the goal. It is clear that, in the mineral kingdom, -the Definition of Species, borrowed from the laws of the -continuation of the kind, which holds throughout the organic -world, fails us altogether, and must be replaced by some -other condition: nor is it difficult to see that the -definite atomic relations of the chemical constituents, and -the definite crystalline angle, must supply the principles -of the _Specific_ Identity for minerals. Yet the exact -limits of definiteness in both these cases (when we admit -the effect of mechanical mixtures, &c.) have not yet been -completely disentangled. Moreover, any _arbitrary_ -assumption (as the allowance of a certain per-centage of -mixture, or a certain small deviation in the angle,) is -altogether contrary to the philosophy of the Natural System, -and can lead to no stable views. It is only by laborious, -extensive, and minute research, that we can hope to attain -to any solid basis of arrangement. - -4. Still, though there are many doubts respecting -mineralogical species, 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 -truth. Of these higher divisions, those which have been -termed _Orders_ appear to tend to something like a fixed -chemical character. Thus the _Haloids_ of Naumann, and -mostly those of Mohs, are combinations of an oxide with an -acid, and thus resemble Salts, whence their name. The -Silicides contain most of Mohs's _Spaths_: and the Orders -_Pyrites_, _Glance_, and _Blende_, are common to Naumann and -Mohs; being established by the latter on a difference of -external character, which difference is, indeed, very -manifest; and being included by the former in one chemical -_Class_, _Sulphurides_. The distinctions of _Hydrous_ and -_Anhydrous_, _Metallic_ and _Unmetallic_, are, of course, -chemical distinctions, but occur as the differences of -Orders in Naumann's mixed system. {142} - -We may observe that some French writers, following Haüy's -last edition, use, instead of _metallic_ and _unmetallic_, -_autopside metallic_ and _heteropside metallic_; meaning by -this phraseology to acknowledge the discovery that earths, -etc., _are_ metallic, though they do not _appear_ to be so, -while metals both are and appear metallic. But this seems to -be a refinement not only useless but absurd. For what is -gained by adding the word _metallic_, which is common to -all, and therefore makes no distinction? If certain metals -are distinguished by their _appearing_ to be metals, this -appearance is a reason for giving them the peculiar name, -_metals_. Nothing is gained by first bringing earths and -metals together, and then immediately separating them again -by new and inconvenient names. No proposition can be -expressed better by calling _earths_, _heteropside metallic -substances_, and therefore such nomenclature is to be -rejected. - -Granting, then, that the Orders of the best recent -mineralogical systems approximate to natural groups, we are -led to ask whether the same can be said of the Genera of the -Natural History systems, such as those of Mohs and -Breithaupt. And here I must confess that I see no principle -in these Genera; I have failed to apprehend the conceptions -by the application of which they have been constructed: I -shall therefore not pass any further judgment upon them. The -subordination of Mineralogical Species to Orders is a -manifest gain to science: in the interposition of Genera I -see nothing but a source of confusion. - -5. In Mineralogy, as in other branches of natural history, a -reformed arrangement ought to give rise to a reformed -Nomenclature; and for this, there is more occasion at -present in Mineralogy than there was in Botany at the worst -period, at least as far as the extent of the subject allows. -The characters of minerals are much more dimly and -unfrequently developed than those of plants; hence arbitrary -chemical arrangements, which could not lead to any natural -groups, and therefore not to any good names, prevailed till -recently; and this state of things produced an anarchy {143} -in which every man did what seemed right in his own -eyes,--proposed species without any ascertained distinction, -and without a thought of subordination, and gave them -arbitrary names; and thus with only about two or three -hundred known species, we have thousands upon thousands of -names, of anomalous form and uncertain application. - -Mohs has attempted to reform the Nomenclature of the subject -in a mode consistent with his attempt to reform the System. -In doing this, he has fatally transgressed a rule always -insisted upon by the legislators of Botany, of altering -usual names as little as possible; and his names are both so -novel and so cumbrous, that they appear to have little -chance of permanent currency. They are, perhaps, more -unwieldy than they need to be, by referring, as we have -said, to three of the steps of his classification, the -Species, Genus, and Order. We may, however, assert -confidently, from the whole analogy of natural history, that -no good names can be found which do not refer to at least -_two_ terms of the arrangement. This rule has been -practically adopted to a great extent by Naumann, who gives -to most of his Haloids the name _Spar_, as Calc spar, Iron -spar, &c.; to all his Oxides the terminal word _Erz_ -(_Ore_); and to the species of the orders _Kies_ -(_Pyrites_), _Glance_, and _Blende_, these names. It has -also been theoretically assented to by Beudant, who proposes -that we should say _silicate stilbite_, _silicate chabasie_; -_carbonate calcaire_, _carbonate witherite_; _sulphate -couperose_, &c. One great difficulty in this case would -arise from the great number of _silicides_; it is not likely -that any names would obtain a footing which tacked the term -_silicide_ to another word for each of these species. The -artifice which I have proposed, in order to obviate this -difficulty, is that we should make the names of the -silicides, and those alone, end in _ite_ or _lite_, which a -large proportion of them do already. - -By this and a few similar contrivances, we might, I -conceive, without any inconvenient change, introduce into -Mineralogy a systematic nomenclature. {144} - -6. I shall now proceed to make a few remarks on a work on -Mineralogy more recent than those which I have above -noticed, and written with express reference to such -difficulties as I have been discussing. I allude to the -treatise of M. Necker, _Le Règne Mineral ramené aux Methods -d'Histoire Naturelle_[44\8], which also contains various -dissertations on the Philosophy of Classification in -general, and its application to Mineralogy in particular. - -[Note 44\8: Paris, 1835.] - -M. Necker remarks very justly, that Mineralogy, as it has -hitherto been treated, differs from all other branches of -Natural History in this:--that while it is invested with all -the forms of the sciences of classification,--Classes, -Divisions, Genera, and the like,--the properties of those -bodies to which the mineralogical student's attention is -directed have no bearing whatever on the classification. A -person, he remarks[45\8], might be perfectly well acquainted -with all the characters of minerals which Werner or Haüy -examined so carefully, and might yet be quite unable to -assign to any mineral its place in the divisions of their -methods. There is[46\8] a complete separation between the -study of mineralogical characters and the recognition of the -name and systematic place of a mineral. Those who know -_mineralogy_ well, may know _minerals_ ill, or hardly at -all; the systematist may be in such knowledge vastly -inferior to the mineral-dealer or the miner. In this respect -there is a complete contrast between this science and other -classificatory sciences. - -[Note 45\8: _Règne Mineral_, p. 3.] - -[Note 46\8: _Ib._ p. 8.] - -Again, in the best-known systems of Mineralogy, (as those of -Werner and Haüy,). the bodies which are grouped together as -belonging to the same division, have not, as they have in -other classificatory sciences, any resemblance. The -different members of the larger classes are united by the -common possession of some abstract property,--as, that they -all contain iron. This is a property to which no common -circumstance in the bodies themselves corresponds. What is -there common to the minerals named oxidulous iron, sulphuret -{145} of iron, carbonate of iron, sulphate of iron, except -that they all contain iron? And when we have classed these -bodies together, what general assertion can we make -concerning them, except that which is the ground of our -classification, that they contain iron? They have nothing in -common with iron or with each other in any other way. - -Again, as these classes have no general properties, all the -properties are particular to the species; and the -descriptions of these necessarily become both tediously -long, and inconveniently insulated. - -7. These inconveniences arise from making Chemical -Composition the basis of Mineralogical Classification -without giving Chemical Analysis the first place among -Mineral Properties. Shall we, then, correct this omission, -so far as it has affected mineralogical systems? Shall we -teach the student the chemical analysis of minerals, and -then direct him to classify them according to the results of -his analysis[47\8]? - -[Note 47\8: _Règne Mineral_, p. 18.] - -But why should we do this? To what purpose, or on what -ground, do we arrange the results of chemical analysis -according to the forms and subordination of natural history? -Is not Chemistry a science distinct from Natural History? -Are not the sciences opposed? Is not natural history -confined to organic bodies? Can mere chemical elements and -their combinations be, with any propriety or consistency, -arranged into Species, Genera, and Families? What is the -principle on which genera and species depend? Do not Species -imply Individuals? What is an Individual in the case of a -chemical substance? - -8. 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 minerals. The answers to these questions -are given by M. Necker; and I shall state some of his -opinions; taking the liberty of adding such remarks as are -suggested by referring the subject {146} to those principles -which have already been established in this work. - -M. Necker asserts[48\8] that the distinctions of different -Sciences depend, not on the objects they consider, but on -the different and independent points of view on which they -proceed. Each science has its logic, that is, its mode of -applying the general rules of human reason to its own -special case. It has been said by some[49\8], that in -minerals, natural history and chemistry contemplate common -objects, and thus form a single science. But do chemistry -and natural history consider minerals in the same point of view? - -[Note 48\8: _Règne Mineral_, p. 23.] - -[Note 49\8: _Ib._ p. 27.] - -The answer is, that they do not. Physics and Chemistry -consider the properties of bodies in an abstract manner; as, -their composition, their elements, their mutual actions, -with the laws of these; their forces, as attraction, -affinity; all which objects are abstract ideas. In these -cases we have nothing to do with bodies themselves, but as -the vehicles of the powers and properties which we -contemplate. - -Natural History, on the other hand, has to do with natural -bodies: their properties are not considered abstractedly, -but only as characters. If the properties are abstracted, it -is but for a moment. Natural history has to describe and -class bodies as they are. All which cannot be perceived by -the senses, belongs not to its domain, as molecules, atoms, -elements. - -Natural history[50\8] may have recourse to physics or -chemistry in order to recognize those properties of bodies -which serve as characters; but natural history is not, on -that account, physics or chemistry. Classification is the -essential business of the natural historian[51\8], to which -task chemistry and physics are only instrumental, and the -further account of properties only complementary. - -[Note 50\8: _Ib._ p. 37.] - -[Note 51\8: _Ib._ p. 41.] - -It has been said, in support of the doctrine that chemistry -and mineralogy are identical, that chemistry does not -neglect external characters. 'The chemist in {147} -describing sulphur, mentions its colour, taste, odour, -hardness, transparence, crystalline form, specific gravity; -how does he then differ from the mineralogist?' But to this -it is replied, that these notices of the external characters -of this or any substance are introduced in chemistry merely -as convenient marks of recognition; whereas they are -essential in mineralogy. If we had taken the account given -of several substances instead of one, we should have seen -that the chemist and the naturalist consider them in ways -altogether different. The chemist will make it his business -to discover the mutual action of the substances; he will -combine them, form new products, determine the proportions -of the elements. The mineralogist will divide the substances -into groups according to their properties, and then -subdivide these groups, till he refers each substance to its -species. Exterior and physical characters are merely -accessory and subordinate for the chemist; chemistry is -merely instrumental for the mineralogist. - -This view agrees with that to which we have been led by our -previous reasonings; and may, according to our principles, -be expressed briefly by saying, that the Idea which -Chemistry has to apply is the Idea of Elementary -Composition, while Natural History applies the Idea of -Graduated Resemblances, and thus performs the task of -classification. - -9. The question occurs[52\8], whether Natural History can be -applied to Inorganic Substances? And the answer to this -question is, that it can be applied, if there are such -things as inorganic individuals, since the resemblances and -differences with which natural history has to do are the -resemblances and differences of individuals. - -[Note 52\8: _Règne Mineral_, p. 46.] - -What is an Individual? It certainly is not that which is so -simple that it cannot be divided. Individual animals are -composed of many parts. But if we examine, we shall find -that our Idea of an Individual is, that it is a whole -composed of parts, which {148} are not similar to the whole, -and have not an independent existence, while the whole has -an independent existence and a definite form[53\8]. - -[Note 53\8: _Règne Mineral_, p. 52.] - -What then is the Mineralogical Individual? At first, while -minerals were studied for their use, the most precious of -the substances which they contained was looked upon as the -characteristic of the mineral. The smallest trace of silver -made a mineral an _ore of silver_. Thus forms and properties -were disregarded, and _substance_ was considered as -identical with _mineral_. And hence[54\8] Daubenton refused -to recognize _species_ in the mineral kingdom, because he -recognized no individuals. He proposed to call _sorts_ what -we call species. In this way of considering minerals, there -are no individuals. - -[Note 54\8: _Ib._ p. 54.] - -10. But still this is not satisfactory: for if we take a -well-formed and distinct crystal, this clearly _is_ an -individual[55\8]. - -[Note 55\8: _Ib._ p. 56.] - -It may be objected, that the crystal is divisible (according -to the theory of crystallography) into smaller solids; that -these small solids are really the simple objects; and that -actual crystals are formed by combinations of these -molecules according to certain laws. - -But, as we have already said, an individual is such, not -because it cannot be divided, but because it cannot be -divided into parts similar to the whole. As to the division -of the form into its component _laws_, this is an abstract -proceeding, foreign to natural history[56\8]. Therefore -there is so far nothing to prevent a crystal from being an -individual. - -[Note 56\8: _Ib._ p. 58.] - -11. We cannot (M. Necker goes on to remark) consider the -_Integrant Molecules_ as individuals. These are useful -abstractions, but abstractions only, which we must not deal -with as real objects. Haüy himself warns us[57\8] that his -doctrine of increments is a purely abstract conception, and -that nature, in fact, follows a different process. -Accordingly, Weiss and Mohs express laws identical with -those of Haüy, without even {149} speaking of molecules; and -Wollaston and Davy have deemed it probable that the -molecules are not polyhedrons, but spheres or spheroids. -Such mere creations of the mind can never be treated as -individuals. If the maxim of natural history,--that the -Species is a collection of Individuals--be applied so as to -make those individuals mere abstractions; or if, instead of -Individuals, we take such an abstraction as Substance or -Matter, the course of natural history is altogether -violated. And yet this errour has hitherto generally -prevailed; and mineralogists have classified, not things, -but abstract ideas[58\8]. - -[Note 57\8: _Ib._ p. 61.] - -[Note 58\8: _Règne Mineral_, p. 67.] - -12. But it may be said[59\8], will not the small solids -obtained by Cleavage better answer the idea of individuals? -To this it is replied, that these small solids have no -independent existence. They are only the result of a mode of -division. They are never found separate and independent. The -secondary forms which they compose are determined by various -circumstances (the nature of the solution, &c.); and the -cleavage which produces these small solids is only one -result among many, from the crystalline forces[60\8]. - -[Note 59\8: _Ib._ p. 69.] - -[Note 60\8: _Ib._ p. 71.] - -Thus neither Integrant Molecules, nor Solids obtained by -Cleavage, can be such mineralogical Individuals as the -spirit of natural history requires. Hence it appears that we -must take the real Crystals for Individuals[61\8]. - -[Note 61\8: _Ib._ p. 73.] - -13. We must, however, reject crystals (generally large ones) -which are obviously formed of several smaller ones of a -similar form (as occurs so often in quartz and calc spar). -We must also distinguish cases in which a large regular form -is composed of smaller but different regular forms (as -octahedrons of fluor spar made up of cubes). Here the small -component forms are the individuals. Also we must notice the -cases[62\8] in which we have a natural crystal, similar to -the primary form. Here the face will show whether {150} the -body is a result obtained by cleavage or a natural individual. - -[Note 62\8: _Ib._ p. 75.] - -14. It will be objected[63\8], that the crystalline form -ought not to be made the dominant character in mineralogy, -since it rarely occurs perfect. To this it is replied, that -even if the application of the principle be difficult, still -it has been shown to be the only true principle, and -therefore we have no alternative. But further[64\8], it is -not true that amorphous substances are more numerous than -crystals. In Leonhard's _Manual of Oryctognosy_, there are -377 mineral substances. Of these, 281 have a crystalline -structure, and 96 only have not been found in a regular form. - -[Note 63\8: _Règne Mineral_, p. 79.] - -[Note 64\8: _Ib._ p. 82.] - -Again, the 281 crystalline forms have each its varieties, -some of which are crystalline, and some are not so. Now the -crystalline varieties amount to 1453, and the uncrystalline -to 186 only. Thus mineralogy, according to the view of it -here presented, has a sufficiently wide field[65\8]. - -[Note 65\8: _Ib._ p. 84.] - -15. It will be objected[66\8], that according to this mode -of proceeding, we must reject from our system all -non-crystalline minerals. But we reply, that if the mass be -composed of crystals, the size of the crystals makes no -difference. Now lamellar and other compact masses are very -generally groups of crystals in various positions. -Individuals mutilated and mixed together are not the less -individuals; and therefore such masses may be treated as -objects of natural history. - -[Note 66\8: _Ib._ p. 86.] - -If we cannot refer all rocks to crystalline species, those -which elude our method may appear as an appendix, -corresponding to those plants which botanists call _genera -incertæ sedis_[67\8]. - -[Note 67\8: _Ib._ p. 91.] - -But these genera and species will often be afterwards -removed into the crystalline part of the system, by being -identified with crystalline species. Thus _pyrope_, &c., -have been referred to _garnet_, and _basalt_, {151} _wacke_, -&c., to compound rocks. Thus veins of _Dolerite_, visibly -composed of two or three elements, pass to an apparently -simple state by becoming fine-grained[68\8]. - -[Note 68\8: _Règne Mineral_, p. 93.] - -16. Finally[69\8], we have to ask, are artificial crystals -to enter into our classification? M. Necker answers, No; -because they are the result of art, like mules, mestizos, -hybrids, and the like. - -[Note 69\8: _Ib._ p. 95.] - -17. Upon these opinions, we may observe, that they appear to -be, in the main, consistent with the soundest philosophy. -That each natural crystal is an individual, is a doctrine -which is the only basis of Mineralogy as a Natural -Historical Science; yet the imperfections and confused -unions of crystals make this principle difficult to apply. -Perhaps it may be expressed in a more precise manner by -referring to the crystalline forces, and to the axes by -which their operation is determined, rather than to the -external form. _That_ portion of a mineral substance is a -mineralogical _individual_ which is determined by -crystalline forces acting to the _same axes_. In this way we -avoid the difficulty arising from the absence of faces, and -enable ourselves to use either cleavage, or optical -properties, or any others, as indications of the identity of -the individual. The individual extends so far as the polar -forces extend by which crystalline form is determined, -whether or not those forces produce their full effect, -namely, a perfectly circumscribed polyhedron. - -18. There is only one material point on which our principles -lead us to differ from M. Necker;--the propriety of -including _artificial crystals_ in our mineralogical -classification. To exclude them, as he does, is a conclusion -so entirely at variance with the whole course of his own -reasonings, that it is difficult to conceive that he would -persist in his conclusion, if his attention were drawn to -the question more steadily. For, as he justly says[70\8], -each science has its appropriate domain, determined by its -peculiar point of view. Now artificial and natural crystals -are considered in the same point of view, (namely, with -reference to {152} crystalline, physical, and optical -properties, as subservient to classification,) and ought, -therefore, to belong to the same science. Again, he -says[71\8], that Chemistry would reject as useless all -notice of the physical properties and external characters of -substances, if a _special science_ were to take charge of -the description and classification of these products. But -such a special science must be Mineralogy; for we cannot -well make one science of the classification of natural, and -another of that of artificial substances: or if we do, the -two sciences will be identical in method and principles, and -will extend over each other's boundaries, so that it will be -neither useful nor possible to distinguish them. Again, M. -Necker's own reasonings on the selection of the individual -in mineralogy are supported by well chosen examples[72\8]; -but these examples are taken from artificial salts; as, for -instance, common salt crystallizing in different mixtures. -Again, the analogy of mules and mestizos, as products of -art, with chemical compounds, is not just. Chemical -compounds correspond rather to natural species, propagated -by man under the most natural circumstances, in order that -he may study the laws of their production[73\8]. - -[Note 70\8: _Ib._ p. 23.] - -[Note 71\8: _Règne Mineral_, p. 36.] - -[Note 72\8: _Ib._ p. 71.] - -[Note 73\8: We may remark that M. Necker, in his own -arrangement of minerals, inserts among his species Iron and -Lead, which do not occur Native.] - -19. But the decisive argument against the separation of -natural and artificial crystals in our schemes of -classification is, that we _cannot_ make such a separation. -Substances which were long known only as the products of the -laboratory, are often discovered, after a time, in natural -deposits. 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 mine? -And are the crystals which are produced where man has turned -a stream of water or air out of its course, to be separated -from natural crystals, when the composition, growth, and -properties, are exactly the same in both? And again: How -many natural crystals can we already produce by {153} -synthesis! How many more may we hope to imitate hereafter! -M. Necker himself states[74\8], that Mitscherlich found, in -the scoriæ of the mines of Sweden and Germany, artificial -minerals having the same composition and the same -crystalline form with natural minerals: as silicates of -iron, lime, and magnesia, agreeing with Peridot; bisilicate -of iron, lime, and magnesia, agreeing with Pyroxene; red -oxide of copper; oxide of zinc; protoxide of iron (_fer -oxydulé_); sulphurets of iron, zinc, lead; arseniuret of -nickel; black mica. These were accidental results of fusion. -But M. Berthier, by bringing together the elements in proper -quantities, has succeeded in composing similar minerals, and -has thus obtained artificial silicates, with the same forms -and the same characters as natural silicates. Other chemists -(M. Haldat, M. Becquerel) have, in like manner, obtained, by -artificial processes, other crystals, known previously as -occurring naturally. How are these crystals, thus identical -with natural minerals, to be removed out of the domain of -mineralogy, and transferred to a science which shall -classify artificial crystals only? If this be done, 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 art. Or is the other -alternative to be taken, and are these crystals to be given -up to mineralogy because they occur naturally also? But what -can be more unphilosophical than to refer to separate -sciences the results of chemical processes closely allied, -and all but identical? The chemist constructs bisilicates, -and these are classified by the mineralogist: but if he -constructs a trisilicate, it belongs to another science. All -these intolerable incongruities are avoided by acknowledging -that artificial, as well as natural, crystals belong to the -domain of mineralogy. It is, in fact, the _name_ only of -_Mineralogy_ which appears to discover any inconsistency in -this mode of proceeding. Mineralogy is the {154} -representative of a science which has a wider office than -mineralogists first contemplated; but which must exist, in -order that the body of science may be complete. There must, -as we have already said, be a Science, the object of which -is to classify bodies by their physical characters, in order -that we may have some means of asserting chemical truths -concerning bodies; some language in which we may express the -propositions which chemical analysis discovers. And this -Science will have its object prescribed, not by any -accidental or arbitrary difference of the story belonging to -each specimen;--not by knowing whether the specimen was -found in the mine or in the laboratory; produced by -attempting to imitate nature, or to do violence to her:--but -will have its course determined by its own character. The -range and boundaries of this Science will be regulated by -the Ideas with which it deals. Like all other sciences, it -must extend to everything to which its principles apply. The -limits of the province which it includes are fixed by the -consideration that it must be a connected whole. No previous -definition, no historical accident, no casual phrase, can at -all stand in the way of philosophical consistency;--can make -this Science exclude what that includes, or oblige it to -admit what that rejects. And thus, whatever we call our -Science;--whether we term it External Chemistry, Mineralogy, -the Natural History of Inorganic Bodies;--since it can be -nothing but the Science of the Classification of Inorganic -Bodies of definite forms and properties, it must classify -all such bodies, whether or not they be minerals, and -whether or not they be natural. - -[Note 74\8: _Règne Mineral_, p. 151.] - -20. In the application of the principles of classification -to minerals, the question occurs, What are to be considered -as mineral _Species_? By Species we are to understand, -according to the usage of other parts of natural history, -the lowest step of our subordinate divisions;--the most -limited of the groups which have definite distinctions. What -definite distinctions of groups of objects of any kind -really occur in nature, is to be learnt from an examination -of nature: and the {155} result of our inquiries will be -some general principle which connects the members of each -group, and distinguishes the members of groups which, though -contiguous, are different. In the classification of -organized bodies, the rule which thus presides over the -formation of Species is the principle of _reproduction_. -Those animals and those plants are of the same Species which -are produced from a common stock, or which resemble each -other as much as the progeny of a common stock. Accordingly -in practice, if any questions arise whether two varieties of -form in organic things be of the same or different species, -it is settled by reference to the fact of reproduction; and -when it is ascertained that the two forms come within the -habitual and regular limits of a common circle of -reproduction, they are held to be of the same species. Now -in crystals, this principle of reproduction disappears -altogether, and the basis of the formation of species must -be sought elsewhere. We must have some other principle to -replace the reproduction which belongs only to organic life. -This principle will be, we may expect, one which secures the -permanence and regularity of mineral forms, as the -reproductive power does of animal and vegetable. Such a -principle is the _Power of Crystallization_. The forces of -which solidity, cohesion, and crystallization are the -result, are those which give to minerals their permanent -existence and their physical properties; and ever since the -discovery of the distinctions of Crystalline Forms and -Crystalline Systems, it is certain that this force -distinguishes groups of crystals in the most precise and -definite manner. The rhombohedral carbonates of lime and of -iron, for instance, are distinguished exactly by the angles -of their rhombohedrons. And if, in the case of any proposed -crystal, we should doubt to which kind the specimen belongs, -the measurement of the angles of cleavage would at once -decide the question. The principle of Crystallization -therefore appears, from analogy, to be exactly fitted to -take the place of the principle of organic Generation. The -forces which make the individual permanent and its -properties definite, here stand in the place of the forces -{156} which preserve the race, while individuals are -generated and die. - -21. According to this view, the different Modifications of -the _same_ crystalline form would be _Varieties_ only of the -same Species. All the various solids, for example, which are -produced by the different laws of derivation of rhombohedral -carbonate of lime, would fall within the same Species. And -this appears to be required by the general analogy of -Natural History. For these differences of form, produced by -the laws of crystalline derivation, are not _definite_. The -faces which are added to one form in order to produce -another, may be of any size, small or large, and thus the -crystal which represents one modification passes by -insensible degrees to another. The forms of calc spar, which -we call _dog-tooth spar_, _cannon spar_, _nail-head spar_, -and the like, appear at first, no doubt, distinct enough; -but so do the races of dogs. And we find, in the mineral as -in the animal, that the distinction is obliterated by taking -such intermediate steps as really occur. And if a _fragment_ -of any of these crystals is given us, we can determine that -it is rhombohedral carbonate of lime; but it is not -possible, in general, to determine to which of the kinds of -crystals it has belonged. - -22. Notwithstanding these considerations, M. Necker has -taken for his basis of mineral species[75\8] the _Secondary_ -Modifications, and not the Primary Forms. Thus _cubical -galena_, _octahedral galena_, and _triform galena_, are, -with him, three _species_ of crystals. - -[Note 75\8: _Règne Mineral_, p. 396.] - -On this I have to observe, as I have already done, that on -this principle we have no _definite_ distinction of species; -for these forms may and do pass into each other: among -cubo-octahedrons of galena occur cubes and octahedrons, as -one face or another vanishes, and the transition is -insensible. We shall, on this principle, find almost always -three or four species in the same tuft of crystals; for -almost every individual in such assemblages may exhibit a -different combination of {157} secondary faces. Again, in -cases where the secondary laws are numerous, it would be -impracticable to enumerate all their combinations, and -impossible therefore to give a list of species. Accordingly -M. Necker[76\8] gives seventy-one Species of _spath -calcaire_, and then says, 'Nous n'avons pas énumeré la -dixième partie des espèces connues de ce genre, qui se -montent à plus de huit cents.' Again, in many substances, of -which few crystals are found, every new specimen would be a -new species; if indeed it were perfect enough to be referred -to a species at all. But from a specimen without perfect -external form, however perfect in crystalline character, -although everything else might be known,--angles, optical -properties, physical properties, and chemical -constitution,--the species could not be determined. Thus M. -Necker says[77\8] of the micas, 'Quant aux espèces propre à -chaque genre, la lacune sera presque complète; car jusqu'ici -les cristaux entiers de Mica et de Talc n'ont pas été fort communs.' - -[Note 76\8: _Règne Mineral_, p. 364.] - -[Note 77\8: _Ib._ ii. 414.] - -These inconveniences arise from neglecting the leading rule -of natural history, that the _predominant principle_ of the -existence of an object must determine the Species; whether -this principle be Reproduction operating for Development, or -Crystallization operating for Permanence of form. We may add -to the above statement of inconveniences this;--that if M. -Necker's view of mineralogical species be adopted, the -distinction of Species is vague and indefinite, while that -of Genera is perfectly precise and rigorous;--an aspect of -the system entirely at variance with other parts of Natural -History; for in all these the Species is a more definite -group than the Genus. - -This result follows, as has already been said, from M. -Necker's wish to have individuals marked by external form. -If, instead of this, we are contented to take for an -individual that portion of a mass, of whatever form, which -is connected by the continuous influence of the same -crystalline forces, by whatever incidents these forces may -be manifested, (as cleavage, {158} physical and optical -properties, and the like,) our mode of proceeding avoids all -the above inconveniences, applies alike to the most perfect -and most imperfect specimens, and gives a result agreeable -to the general analogy of natural history, and the rules of -its methods[78\8]. - -[Note 78\8: I will not again enter into the subject of -Nomenclature; but I may remark that M. Necker has adopted -(i. 415) the Nomenclature of Beudant, latinizing the names, -and thus converting each into a single word. He has also -introduced, besides the names of Genera, names of Families -taken from the _typical_ Genus. Thus the Family of -_Carbonidiens_ contains the following genera: -_Calcispathum_, _Magnesispathum_, _Dolomispathum_, -_Ferrispathum_, _&c._, _Malachita_, _Azuria_, _Gaylusacia_.] - -I now quit the subject of mere Resemblance, and proceed to -treat of that natural affinity which Natural Systems of -Classification for organic bodies must involve. - - - -{{159}} -CHAPTER IV. - -OF THE IDEA OF NATURAL AFFINITY. - - -1. 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 foundation, they -necessarily take for granted in the course of their progress -a further Idea of Natural Affinity. This appeared[79\8] by a -general consideration of the nature of Science, by the -recognition of natural species and genera, even in -Artificial Systems of Classification[80\8], and by the -**attempts of botanists to form a Natural System. It further -appeared that among the processes by which endeavours have -been made to frame a Natural System, some, as the method of -_Blind Trial_ and the method of _General Comparison_, have -been altogether unsuccessful, being founded only upon a -collection of resemblances, casual in the one case and -arbitrary in the other. In neither of these processes is -there employed any general principle by which we may be -definitely directed as to what resemblances we should -employ, or by which the result at which we arrive may be -verified and confirmed. Our object in the present chapter is -to show that the Idea of Natural Affinity supplies us with a -principle which may answer such purposes. - -[Note 79\8: Art. 5.] - -[Note 80\8: Art. 7.] - -I shall first consider the Idea of Affinity as exemplified -in organized beings. In doing this, we may appear to take -for granted Ideas which have not yet come under our -discussion, as the Ideas of Organization, and Vital -Function; but it will be found that the principle to which -we are led is independent of these additional Ideas. {160} - -2. 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 Characters_. -It is easy to see that some organs are more essential than -others to the existence of an organized being; the organs of -nutrition, for example, more essential than those of -locomotion. 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 System. This will happen, if, for example, we -begin by declaring the nutritive to be superior in -importance to the reproductive functions. It is clear that -this relation of importance of organs and functions must be -collected by the study of the organized beings; and cannot -be determined _à priori_, without depriving us of all right -to expect a general accordance between our system and the -arrangement of nature. We see, therefore, that our notion of -Natural Affinity involves in it this consequence;--that it -is not to be made out by an arbitrary subordination of characters. - -3. The functions and actions of living things which we -separate from each other in our consideration, cannot be -severed in nature. Each function is essential; Life implies -a collection of movements, and ceases when any of these -movements is stopped. A change in the organization -subservient to one set of functions may lead necessarily to -a change in the organization belonging to others. We can -often see this necessary connexion; and from a comparison of -the forms of organized beings,--from the way in which their -structure changes in passing from one class to another, we -are led to the conviction that there is some general -principle which connects and graduates all such changes. -When the circulatory system changes, the nervous system -changes also: when the mode of locomotion changes, the -respiration is also modified. - -4. These corresponding changes may be considered as ways in -which the living thing is fitted to its mode of life; as -marks of _adaptation to a purpose_; or, as it has been -otherwise expressed, as results of the {161} _conditions of -existence_. But at the present moment, we put forward these -correspondencies in a different light. We adduce them as -illustrations of what we mean by Affinity, and what we -consider as the tendency of a Natural Classification. It has -sometimes been asserted that if we were to classify any of -the departments of organized nature by means of one -function, and then by means of another, the two -classifications, if each strictly consistent with itself, -would be consistent with each other. Such an assertion is -perhaps more than we are entitled to make with confidence; -but it shows very well what is meant by Affinity. The -disposition to believe such a general identity of all -partial natural classifications, shows how readily we fix -upon the notion of Affinity, as a general result of the -causes which determine the forms of living things. When -these causes or principles, of whatever nature they are -conceived to be, vary so as to modify one part of the -organization of the being, they also modify another: and -thus the groups which exhibit this variation of the -fundamental principles of form, are the same, whether the -manifestation of the change be sought in one part or in -another of the organized structure. The groups thus formed -are related by Affinity; and in proportion as we find the -evidence of more functions and more organs to the propriety -of our groups, we are more and more satisfied that they are -Natural Classes. It appears, then, that our Idea of Affinity -involves the conviction of the _Coincidence of natural -arrangements formed on different functions_; and this, -rather than the principle of the Subordination of some -characters to others, is the true ground of the natural -method of Classification. - -5. For example, Cuvier, after speaking of the Subordination -of Characters as the guide which he intends to follow in his -arrangement of animals, interprets this principle in such a -manner[81\8] as to make it agree nearly with the one just -stated: 'In pursuance of what has been said on methods in -general, we now require to {162} know what characters in -animals are the most influential, and therefore those which -must be made the grounds of the primary divisions.' 'These,' -he says, 'it is clear must be those which are taken from the -animal functions;--sensation and motion:'--But how does he -confirm this? Not by showing that the animal functions are -independent of, or predominant over, the vegetative, but by -observing that they follow the same gradations. -'Observation,' he continues, 'confirms this view, by showing -that the degrees of development and complication of the -animal functions agree with those of the vegetative. The -heart and the organs of the circulation are a sort of center -for the vegetative functions, as the brain and the trunk of -the nervous system are for the animal functions. Now we see -these two systems descend in the scale, and disappear the -one with the other. In the lowest animals, when there are no -longer any distinct nerves, there are also no longer -distinct fibres, and the organs of digestion are simply -hollowed out in the homogeneous mass of the body. The -muscular system disappears even before the nervous, in -insects; but in general the distribution of the medullary -masses corresponds to that of the muscular instruments; a -spinal cord, on which knots or ganglions represent so many -brains, corresponds to a body divided into numerous rings -and supported on pairs of members placed at different points -of the length, and so on. - -[Note 81\8: _Règne Animal_, p. 55.] - -'This _correspondence_ of the general forms which result -from the arrangement of the motive organs, from the -distribution of the nervous masses, and from the energy of -the circulatory system, must therefore form the ground of -the first great sections by which we divide the animal kingdom.' - -6. Decandolle takes the same view. There must be, he says, -_an equilibrium_ of the different functions[82\8]. And he -exemplifies this by the case of the distinction of -monocotyledonous and dicotyledonous plants, which being at -first established by means of the organs of {163} -reproduction, was afterwards found to coincide with the -distinction of endogenous and exogenous, which depends on -the process of nutrition. 'Thus,' he adds, '_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 function_; and I find here a very -useful criterion to ascertain whether a class is natural: -namely, in order to announce that it is so, it must be -arrived at by the two roads which vegetable organization -presents. Thus I affirm,' he says, 'that the division of -monocotyledons from dicotyledons, and the distinction of -Gramineæ from Cyperaceæ, are real, because in these cases, I -arrive at the same result by the reproductive and the -nutritive organs; while the distinction of monopetalous and -polypetalous, of Rhodoraceæ and Ericineæ, appears to me -artificial, because I can arrive at it only by the -reproductive organs.' - -[Note 82\8: _Theor. Elem._ p. 79.] - -Thus the Correspondence of the indications of different -functions is the criterion of Natural Classes; and this -correspondence may be considered as one of the best and most -characteristic marks of the fundamental Idea of Affinity. -And the Maxim by which all Systems professing to be natural -must be tested is this:--that the _arrangement obtained from -one set of characters coincides with the arrangement -obtained from another set_. - -This Idea of Affinity, as a natural connexion among various -species, of which connexion all particular resemblances are -indications, has principally influenced the attempts at -classifying the animal kingdom. The reason why the -classification in this branch of Natural History has been -more easy and certain than that of the vegetable world is, -as Decandolle says[83\8], that besides the functions of -nutrition and reproduction, which animals have in common -with plants, they have also in addition the function of -sensation; and thus have a new means of verification and -concordance. But we may add, as a further reason, that the -functions of {164} animals are necessarily much more obvious -and intelligible to us than those of vegetables, from their -clear resemblance to the operations which take place in our -own bodies, to which our attention has necessarily been -strongly directed. - -[Note 83\8: _Theor. Elem._ p. 80.] - -7. The question here offers itself, whether this Idea of -Natural Affinity is applicable to inorganic as well as to -organic bodies;--whether there be Natural Affinities among -Minerals. And to this we are now enabled to reply by -considering whether or not the principle just stated is -applicable in such cases. And the conclusion to which our -principle leads us is,--that there are such Natural -Affinities among Minerals, since there are different sets of -characters which may be taken, (and have by different -writers been taken,) as the basis of classification. The -hardness, specific gravity, colour, lustre, crystallization, -and other _external_ characters, as they are termed, form -one body of properties according to which minerals may be -classified; as has in fact been done by Mohs, Breithaupt, -and others. The _chemical_ constitution of the substances, -on the other hand, may be made the principle of their -arrangement, as was done by Haüy, and more recently, and on -a different scheme, by Berzelius. Which of these is the true -and natural classification? To this we answer, that _each_ -of these arrangements is true and natural, then, and then -only, when it coincides with the other. An arrangement by -external characters which gives us classes possessing a -common chemical character;--a chemical order which brings -together like and separates unlike minerals;--such -classifications have the evidence of truth in their -agreement with one another. Every classification of minerals -which does not aim at and tend to such a result, is so far -merely arbitrary; and cannot be subservient to the -expression of general chemical and mineralogical truths, -which is the proper purpose of such a classification. - -8. In the History of Mineralogy I have related the advances -which have been made among mineralogists and chemists in -modern times towards a System {165} possessing this -character of truth. I have there described the mixed systems -of Werner and Haüy;--the attempt made by Mohs to form a pure -Natural History system;--the first and second attempt of -Berzelius to form a pure chemical system; and the failure of -both these attempts. But the distinct separation of the two -elements of which science requires the coincidence threw a -very useful light upon the subject; and the succeeding mixed -systems, such as that of Naumann, approached much nearer to -the true conditions of the problem than any of the preceding -ones had done. Thus, as I have stated, several of Naumann's -groups have both a common chemical character and great -external resemblances. Such are his _Anhydrous Unmetallic -Haloids_--his _Anhydrous Metallic Haloids_--_Hydrous -Metallic Haloids_--_Oxides_ of metals--_Pyrites_--_Glances_-- -Blendes_. The existence of such groups shows that we may hope -ultimately to obtain a classification of minerals which shall -be both chemically significant, and agreeable to the methods -of Natural History: although when we consider how very imperfect -as yet our knowledge of the chemical composition of minerals is, -we can hardly flatter ourselves that we shall arrive at such a -result very soon. - -We have thus seen that in Mineralogy, as well as in the -sciences which treat of organized bodies, we may apply the -Idea of Natural Affinity; of which the fundamental maxim is, -that _arrangements obtained from different sets of -characters must coincide_. - -Since the notion of Affinity is thus applicable to inorganic -as well as to organic bodies, it is plain that it is not a -mere modification of the Idea of Organization or Function, -although it may in some of its aspects appear to approach -near to these other Ideas. But these Ideas, or others which -are the foundation of them, necessarily enter in a very -prominent and fundamental manner into all the other parts of -Natural History. To the consideration of these, therefore, -we shall now proceed. - - - - -{{167}} -BOOK IX. - - -THE -PHILOSOPHY -OF -BIOLOGY. - - - - -LA vie est donc un TOURBILLON plus ou moins rapide, plus ou -moins compliqué, dont la direction est constante, et qui -entraine toujours des molecules de mêmes sorts, mais où les -molecules individuelles entrent et d'où elles sortent -continuellement, de manière que la _Forme_ du corps vivant -lui est plus essentielle que sa _Matière_. - -Tant que ce mouvement subsiste, le corps où il s'exerce est -_vivant_; _il vit_. Lorsque le mouvement s'arrête sans -retour, le corps _meurt_. - -CUVIER, _Règne Animal_, s. 12. - - -I REMEMBER, upon asking our famous Harvey, what induced him -to think of a circulation of the blood, he said, that -observing the valves in the veins of many parts of the body, -so placed as to give a free passage to the blood towards the -heart, but to oppose the passage of the venal blood the -contrary way, he imagined that so provident a cause as -nature had not thus placed so many valves without design; -and as no design seemed more probable than that the blood -could not well, because of the interposing valves, be sent -by the veins to the limbs, it should be sent through the -arteries and return through the veins when valves did not -oppose its course that way. - -BOYLE, _On the Final Causes of Natural Things_. On the -Proposition: _'Tis often allowable for a naturalist, from the -manifest and apposite uses of the parts of animal bodies, to -collect some of the particular ends for which the Creator -designed them: and in some cases we may, from the known -nature and structure of the parts, draw particular -conjectures about the particular offices of them._ - - - -{{169}} -BOOK IX. - - -THE PHILOSOPHY OF BIOLOGY. - - -CHAPTER I. - -ANALOGY OF BIOLOGY WITH OTHER SCIENCES. - - -1. IN the History of the Sciences, after treating of the -Sciences of Classification, we proceeded to what are there -termed the Organical Sciences, including in this term -Physiology and Comparative Anatomy. A peculiar feature in -this group of sciences is that they involve the notion of -_living_ things. The notion of _Life_, however vague and -obscure it may be in men's minds, is apprehended as a -peculiar Idea, not resolvable into any other Ideas, such, -for instance, as Matter and Motion. The separation between -living creatures and inert matter, between organized and -unorganized beings, is conceived as a positive and -insurmountable barrier. The two classes of objects are -considered as of a distinct kind, produced and preserved by -different forces. Whether the Idea of Life is really thus -original and fundamental, and whether, if so, it be one Idea -only, or involve several, it must be the province of true -philosophy to determine. What we shall here offer may be -considered as an attempt to contribute something to the -determination of these questions; 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 problems. - -Since the main feature of those sciences of which we have -now to examine the philosophy is, that they {170} involve -the Idea of Life, it would be desirable to have them -designated by a name expressive of that circumstance. The -word _Physiology_, by which they have most commonly been -described, means _the Science of Nature_; and though it -would be easy to explain, by reference to history, the train -of thought by which the word was latterly restricted to -_Living Nature_, it is plain that the name is, -etymologically speaking, loose and improper. The term -_Biology_, which means exactly what we wish to express, _the -Science of Life_, has often been used, and has of late -become not uncommon among good winters. I shall therefore -venture to employ it, in most cases, rather than the word -_Physiology_. - -2. As I have already intimated, one main inquiry belonging -to the Philosophy of Biology, is concerning the Fundamental -Idea or Ideas which the science involves. If we look back at -the course and the results of our disquisitions respecting -other sciences in this work, and assume, as we may -philosophically do, that there will be some general analogy -between those sciences and this, in their development and -progress, we shall be enabled to anticipate in some measure -the nature of the view which we shall now have to take. We -have seen that in other subjects the Fundamental Ideas on -which science depended, and the Conceptions derived from -these, were at first vague, obscure, and confused;--that by -gradual steps, by a constant union of thought and -observation, these conceptions become more and more clear, -more and more definite;--and that when they approached -complete distinctness and precision, there were made great -positive discoveries into which these conceptions entered; -and thus the new precision of thought was fixed and -perpetuated in some conspicuous and lasting truths. Thus we -have seen how the first confused mechanical conceptions -(Force, and the like,) were, from time to time, growing -clearer, down to the epoch of Newton;--how true conceptions -of Genera and of wider classes, gradually unfolded -themselves among the botanists of the sixteenth and -seventeenth centuries;--how the idea of Substance became -steady enough to govern the {171} theories of chemists only -at the epoch of Lavoisier;--how the Idea of Polarity, -although often used by physicists and chemists, is even now -somewhat vague and indistinct in the minds of the greater -part of speculators. In like manner we may expect to find -that the Idea of Life, if indeed _that_ be the governing -Idea of the Science which treats of Living Things, will be -found to have been gradually approaching towards a distinct -and definite form among the physiologists of all ages up to -the present day. And if this be the case, it may not be -considered superfluous, with reference to so interesting a -subject, if we employ some space in tracing historically the -steps of this progress;--the changes by which the originally -loose notion of Life, or of Vital Powers, became more nearly -an Idea suited to the purposes of science. - -3. But we may safely carry this analogy between Biology and -other sciences somewhat further. We have seen, in other -sciences, that while men in their speculations were thus -tending towards a certain peculiar Idea, but before they as -yet saw clearly that it was peculiar and independent, they -naturally and inevitably clothed their speculations in -conceptions borrowed from some other extraneous idea. And -the unsatisfactoriness of all such attempts, and the -necessary consequence of this, a constant alteration and -succession of such inappropriate hypotheses, were -indications and aids of the progress which was going on -towards a more genuine form of the science. For instance, we -have seen that in chemistry, so long as men refused to -recognize a peculiar and distinct kind of power in the -_Affinity_ which binds together the elements of bodies, they -framed to themselves a series of hypotheses, each -constructed according to the prevalent ideas of the time, by -which they tried to represent the relation of the compound -to the ingredients:--first, supposing that the elements -bestowed upon the whole qualities _resembling_ their -own:--then giving up this supposition, and imagining that -the properties of the body depended upon the _shape_ of the -component particles;--then, as their view expanded, assuming -that it was {172} not the shape, but the mechanical _forces_ -of the particles which gave the body its attributes;--and -finally acquiescing in, or rather reluctantly admitting, the -idea of _Affinity_, conceived as a peculiar power, different -not only from material contact, but from any mechanical or -dynamical attraction. - -Now we cannot but think it very natural, if we find that the -history of Biology offers a series of occurrences of the -same nature. The notions of Life in general, or of any Vital -Functions or Vital Forces in particular, are obviously very -loose and vague as they exist in the minds of most men. The -discrepancies and controversies respecting the definitions -of all such terms, which are found in all works on -physiology, afford us abundant evidence that these notions -are not, at least not generally, apprehended with complete -clearness and steadiness. We shall therefore find approaches -and advances, intermediate steps, gradually leading up to -the greatest degree of distinctness which has yet been -attained. 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 independently, we may -expect to find them supported and embodied by means of -hypotheses borrowed from other subjects, and thus, made so -distinct and substantial as to supply at least a temporary -possibility of scientific reasoning upon the laws of life. - -4. For example, if we suppose that men begin to speculate -upon the properties of living things, not acknowledging a -peculiar Vital Power, but making use successively of the -knowledge supplied by the study of other subjects, we may -easily imagine a series of hypotheses along which they would pass. - -They would probably, first, in this as in other sciences, -have their thoughts occupied by vague and _mystical_ notions -in which material and spiritual agency, natural and -supernatural events, were mixed together without -discrimination, and without any clear notion at all. But as -they acquired a more genuine perception of the nature of -**knowledge, they would naturally try to explain vital -motions and processes by means of {173} such forces as they -had learnt the existence of from other sciences. They might -first have a _mechanical_ hypothesis, in which the -mechanical _Forces_ of the solids and fluids which compose -organized bodies should be referred to, as the most -important influences in the process of life. They might then -attend to the actions which the fluids exercise in virtue of -their _Affinity_, and might thus form a _chemical_ theory. -When they had proved the insufficience of these hypotheses, -borrowed from the powers which matter exhibits in other -cases, they might think themselves authorized to assume some -peculiar power or agency, still material, and thus they -would have the hypothesis of a _Vital Fluid_. And if they -were driven to reject this, they might think that there was -no resource but to assume an immaterial principle of life, -and thus they would arrive at the doctrine of an _Animal Soul_. - -Now, through the cycle of hypotheses which we have thus -supposed, physiology has actually passed. The conclusions to -which the most philosophical minds have been led by a survey -of this progress is, that by the failure of all these -theories, men have exhausted this path of inquiry, and shown -that scientific truth is to be sought in some other manner. -But before I proceed further to illustrate this result, it -will be proper, as I have already stated, to exhibit -historically the various hypotheses which I have described. -In doing this I shall principally follow the _History of -Medicine_ of Sprengel. It is only by taking for my guide a -physiologist of acknowledged science and judgment, that I -can hope, on such a subject, to avoid errours of detail. I -proceed now to give in succession an account of the -Mystical, the Iatrochemical, the Iatromathematical, and the -Vital-Fluid Schools; and finally of the Psychical School, -who hold the Vital Powers to be derived from the Soul -(_Psyche_). - - - -{{174}} -CHAPTER II. - -SUCCESSIVE BIOLOGICAL HYPOTHESES. - - -SECT. I.--_The Mystical School._ - -IN order to abbreviate as much as can conveniently be done -the historical view which I have now to take, I shall -altogether pass over the physiological speculations of the -ancients, and begin my survey with the general revival of -science in modern times. - -We need not dwell long on the fantastical and unsubstantial -doctrines concerning physiology which prevailed in the -sixteenth century, and which flowed in a great measure from -the fertile but ill-regulated imaginations of the -cultivators of Alchemy and Magic. One of the prominent -doctors of this school is the celebrated Paracelsus, whose -doctrines contained a combination of biblical -interpretations, visionary religious notions, fanciful -analogies, and bold experiments in practical medicine. The -opinion of a close but mystical resemblance of parts between -the universe and the human body,--the _Macrocosm_ and the -_Microcosm_,--as these two things, thus compared, were -termed, had probably come down from the Neoplatonists; it -was adopted by the Paracelsists[1\9], and connected with -various astrological dreams and cabbalistic riddles. A -succession of later Paracelsists[2\9], Rosicrucians, and -other fanatics of the same kind, continued into the -seventeenth century. Upon their notions was founded the -pretension of curing wounds by a sympathetic powder, which -Sir Kenelm Digby, among others, asserted; while animal -magnetism, and the transfer of diseases from one person to -another[3\9], were maintained by others of this {175} -school. They held, too, the doctrines of _astral bodies_ -corresponding to each terrestrial body; and of the -_signatures_ of plants, that is, certain features in their -external form by which their virtues might be known. How -little advantage or progress real physiology could derive -from speculations of this kind may be seen from this, that -their tendency was to obliterate the distinction between -living and lifeless things: according to Paracelsus, all -things are alive, eat, drink, and excrete; even minerals and -fluids[4\9]. According to him and his school, besides -material and immaterial beings, there are _elementary -Spirit_s which hold an intermediate place, _Sylvans_, -_Nymphs_, _Gnomes_, _Salamanders_, &c. by whose agency -various processes of enchantment may be achieved, and things -apparently supernatural explained. Thus this spiritualist -scheme dealt with a world of its own by means of fanciful -inventions and mystical visions, instead of making any step -in the study of nature. - -[Note 1\9: Spr. iii. 456.] - -[Note 2\9: _Ib._ iv. 270.] - -[Note 3\9: _Ib._ iv. 276.] - -[Note 4\9: Spr. iii. 458. Parac. _De Vita Rerum Naturalium_, p. 889.] - -Perhaps, however, one of the most fantastical of the -inventions of Paracelsus may be considered as indicating a -perception of a peculiar character in the vital powers. -According to him, the business of digestion is performed by -a certain demon whom he calls _Archæus_, who has his abode -in the stomach, and who, by means of his alchemical -processes, separates the nutritive from the harmful part of -our food, and makes it capable of assimilation[5\9]. This -fanciful notion was afterwards adopted and expanded by Van -Helmont[6\9]. According to him the stomach and spleen are -both under the direction of this Master-spirit, and these -two organs form a sort of _Duumvirate_ in the body. - -[Note 5\9: _Ib._ iii. 468.] - -[Note 6\9: _Ib._ iv. 302.] - -But though we may see in such writers occasional gleams of -physiological thought, the absence of definite physical -relations in the speculations thus promulgated was -necessarily intolerable to men of sound understanding and -scientific tendencies. Such men naturally took hold of that -part of the phenomena of life which could be most distinctly -conceived, and {176} which could be apparently explained by -means of the sciences then cultivated; and this was the part -which appeared to be reducible to chemical conceptions and -doctrines. It will readily be supposed that the processes of -chemistry have a considerable bearing upon physiological -processes, and might, till their range was limited by a -sound investigation, be supposed to have still more than -they really had; and thus a Physiology was formed which -depended mainly upon Chemistry, and the school which held -this doctrine has been called the _Iatrochemical_ School. - - -SECT. II.--_The Iatrochemical School._ - -That all physical properties, and therefore chemical -relations, have a material influence on physiological -results, was already recognized, though dimly, in the -Galenic doctrine of the 'four elementary qualities.' But at -the time of Paracelsus, chemical action was more distinctly -than before separated from other kinds of physical action; -and therefore a physiological doctrine, founded upon -chemistry, and freed from the extravagance and mysticism of -the Paracelsists, was a very promising path of speculation. -Andrew Libavius[7\9] of Halle, in Saxony, Physician and -Teacher in the Gymnasium at Koberg, is pointed out by -Sprengel as the person who began to cultivate chemistry, as -distinct from the theosophic fantasies of his predecessors; -and Angelus Sala of Vienna[8\9], as his successor. The -latter has the laudable distinction of having rejected the -prevalent conceits about a potable gold, a universal -medicine, and the like[9\9]. In Germany already at the -beginning of the seventeenth century a peculiar chair of -_Chymiatria_ was already created at Marpurg: and many in -various places pursued the same studies, till, in the middle -of the seventeenth century, we come to Lemery[10\9], the -principal reformer of pharmaceutical chemistry. But we are -not here so much concerned {177} with the practical as with -the theoretical parts of Iatrochemistry; and hence we pass -on to Sylvius[11\9] and his system. - -[Note 7\9: Spr. iii. 550.] - -[Note 8\9: _Ib._ iv. 281.] - -[Note 9\9: _Ib._ iv. 283.] - -[Note 10\9: _Ib._ iv. 291.] - -[Note 11\9: Spr. iv. 336.] - -The opinion that chemistry had an important bearing upon -physiology did not, however, begin with Sylvius. Paracelsus, -among his extravagant absurdities, did some service to -medicine by drawing attention to this important truth. He -used[12\9] chemical principles for the explanation of -particular diseases: most or all diseases according to him, -arise from the effervescence of salts, from the combustion -of sulphur, or from the coagulation of mercury. His -medicines were chemical preparations; and it was[13\9] an -undeniable advantage of the Paracelsian doctrine that -chemistry thus became indispensable to the physician. We -still retain a remnant of the chemical nomenclature of -Paracelsus in the term _tartar_, denoting the stony -concretion which forms on the teeth[14\9]. According to him -there is a certain substance, the basis of all diseases -which arise from a thickening of the juices and a collection -of earthy matter; and this substance he calls _Tartarus_, -because 'it burns like the fire of hell.' Helmont, the -successor of Paracelsus in many absurdities, also followed -him in the attempt to give a chemical account, however loose -and wild, of the functions of the human body; and is by -Sprengel considered, with all his extravagancies, as a -meritorious and important discoverer. The notion of the -fermentation of fluids[15\9], and of the aërial product -thence resulting, to which he gave the name of _Gas_, forms -an important part of his doctrines; and of the six -digestions which he assumes, the _first_ prepares an acid, -which is neutralized by the gall when it reaches the -duodenum, and this constitutes the _second_ digestion. - -[Note 12\9: _Ib._ iii. 472.] - -[Note 13\9: _Ib._ iii. 482.] - -[Note 14\9: _Ib._ iii. 475.] - -[Note 15\9: Vol. v. 315.] - -I have already, in the History of Chemistry[16\9], stated, -that the doctrine of the opposition of acid and alkali, the -great step which theoretical chemistry owes to Sylvius, was -first brought into view as a physiological {178} tenet, -although we had then to trace its consequences in another -science. The explanation of all the functions of the animal -system, both healthy and morbid, by means of this and other -chemical doctrines, and the prescription of methods of cure -founded upon such explanations, form the scheme of the -_iatrochemical_ school; a school which almost engrossed the -favour of European physicians during the greater part of the -seventeenth century. - -[Note 16\9: _Hist. Ind. Sc._ b. xiii. c. 2.] - -Sylvius taught medicine at Leyden, from the year 1658, with -so much success, that Boerhaave alone surpassed him[17\9]. -His notions, although he piqued himself on their -originality, were manifestly suggested in no small degree -(as all such supposed novelties are) by the speculations of -his predecessors, and the spirit of the times. Like -Helmont[18\9], he considers digestion as consisting in a -fermentation; but he states it more definitely as the -effervescence of an acid, supplied by the saliva and the -pancreatic juice, with the alkali of the gall. By various -other hypothetical processes, all of a chemical nature, the -blood becomes a collection of various juices, which are the -subjects of the speculations of the iatrochemists, to the -entire neglect of the solid parts of the body. Diseases were -accounted for by a supposed prevalence of one or the other -of the acrid principles, the acid or the alkaline: and -Sylvius[19\9] was bold enough to found upon these hypotheses -practical methods of cure, which were in the highest degree -mischievous. - -[Note 17\9: Spr. iv. 336.] - -[Note 18\9: _Ib._ 338.] - -[Note 19\9: _Ib._ iv. 345.] - -The Sylvian doctrine was often combined with some of the -notions of the Cartesian system of philosophy; but this -mixture I shall not notice, since my present object is to -trace the history of a mere chemical physiology as one of -the unsuccessful attempts at a philosophy of life. With -various modifications, this doctrine was diffused over -Europe. It gave rise to several controversies, which turned -upon the questions of the novelty of the doctrine, and the -use of chemical remedies to which it pointed, as well as -upon its {179} theoretical truth. We need not dwell long -upon these controversies, although they were carried on with -no small vehemence in their time. Thus the school of Paris -opposed all innovation, remained true to the Galenic -dogmatism, and declared itself earnestly against all -combination of chemistry with medicine; and even against the -chemical preparation of medicaments. Guy Patin, a celebrated -and learned professor of that day, declares[20\9] that the -chemists are no better than forgers, and ought to be -punished as such. The use of antimonial medicines was a main -point of dispute between the iatrochemists and their -opponents; Patin maintained that more men had been destroyed -by antimony than by the thirty years' war of Germany; and -endeavoured to substantiate this assertion by collecting all -such cases in his _Martyrologium Antimonii_. It must have -been a severe blow to Patin when[21\9] in 1666, the Doctors -of the Faculty of Paris, assembled by command of the -parliament, declared, by a majority of ninety-two voices, -that the use of antimonial medicines was allowable and -laudable, and when all attempts to set aside this decision failed. - -[Note 20\9: Spr. 349.] - -[Note 21\9: _Ib._ iv. 350.] - -Florentius Schuyl of Leyden sought to recommend the -iatrochemical doctrines, by maintaining that they were to be -found in the Hippocratic writings; nor was it difficult to -give a chemical interpretation of the humoral pathology of -the ancients. The Italian[22\9] physicians also, for the -most part, took this line, and attempted to show the -agreement of the principles of the ancient school of -medicine with the new chemical notions. This, indeed, is the -usual manner in which the diffusion of new theoretical ideas -becomes universal. - -[Note 22\9: _Ib._ 368.] - -The progress of the chemical school of medicine in -England[23\9] requires our more especial notice. Willis was -the most celebrated champion of this sect. He assumed, but -with modifications of his own, the three Paracelsian -principles, Salt, Sulphur, and Mercury; considered digestion -as the effect of an acid, and {180} explained other parts of -the animal economy by distillation, fermentation, and the -like. All diseases arise from the want of the requisite -_ferment_; and the physician, he says[24\9], may be compared -to a vintner, since both the one and the other have to take -care that the necessary fermentations go on, that no foreign -matter mixes itself with the wine of life, to interrupt or -derange those operations. In the middle of the seventeenth -century, medicine had reached a point in which the life of -the animal body was considered as merely a chemical process; -the wish to explain everything on known principles left no -recognized difference between organized and unorganized -bodies, and diseases were treated according to this delusive -notion. The condition of chemistry itself during this -period, though not one of brilliant progress, was -sufficiently stable and flourishing to give a plausibility -to any speculation which was founded on chemical principles; -and the real influence of these principles in the animal -frame could not be denied. - -[Note 23\9: _Ib._ 353.] - -[Note 24\9: Spr. 354.] - -The iatrochemists were at first resisted, as we have seen, -by the adherents of the ancient schools; they were attacked -on various grounds, and finally deposed from them ascendancy -by another sect, which we have to speak of, as the -iatromathematical, or mechanical school. This sect was no -less unsatisfactory and erroneous in its positive doctrines -than the chemists had been; for the animal frame is no more -a mere machine than a mere laboratory: but it promoted the -cause of truth, by detecting and exposing the insufficient -explanations and unproved assertions of the reigning theory. - -Boyle was one of the persons who first raised doubts against -the current chemical doctrines of his time, as we have -elsewhere noted; but his objections had no peculiar -physiological import. Herman Coming[25\9], the most learned -physician of his time, a contemporary with Sylvius, took a -view more pertinent to our present object; for he not only -rejected the alchemical {181} and hermetical medicines, but -taught expressly that chemistry, in its then existing -condition, was better fitted to be of use in the practice of -pharmacy, than in the theories of physiology and pathology. -He made the important assertion, also, that chemical -principles do not pre-exist _as such_ in the animal body; -and that there are higher powers which operate in the -organic world, and which do not depend on the form and -mixture of matter. - -[Note 25\9: _Ib._ iv. 361.] - -Attempts were made to prove the acid and alkaline nature of -the fluids of the human body by means of experiments, as by -John Viridet of Geneva[26\9], and by Raimond -Vieussens[27\9], the latter of whom maintained that he had -extracted an acid from the blood, and detected a ferment in -the stomach. In opposition to him, Hecquet, a disciple of -the iatromathematical school, endeavoured to prove that -digestion was performed, not by means of fermentation, but -by trituration. Hecquet's own opinions cannot be defended; -but his objections to the chemical doctrines, and his -assertion of the difference of chemical and organical -processes, are evidences of just thought[28\9]. - -[Note 26\9: Spr. iv. 329.] - -[Note 27\9: _Ib._ 350, (1715).] - -[Note 28\9: _Ib._ 401.] - -The most important opponents of the iatrochemical school -were Pitcairn in England, Bohn and Hoffman in Germany, and -Boerhaave in Holland. These eminent physicians, about the -end of the seventeenth century, argued on the same grounds -of observation, that digestion is not fermentation, and that -the Sylvian accounts of the origin of diseases by means of -acid and alkali are false. The arguments and authority of -these and other persons finally gained an ascendancy in the -medical world, and soon after this period we may consider -the reign of the chemical school of physiology as past. In -fact, the attempts to prove its assertions experimentally -were of the feeblest kind, and it had no solid basis on -which it could rest, so as to resist the shock of the next -hypothesis which the progress of the physical sciences might -impel against it. We may, therefore, now consider the -opinion of the mere {182} chemical nature of the vital -processes as disproved, and we proceed next to notice the -history of another unsuccessful essay to reduce vital -actions to known actions of another kind. - - -SECT. III.--_The Iatromathematical School._ - -In the first Section of this chapter, we enumerated the -biological hypotheses which at first present themselves, as -the mystical, the mechanical, the chemical. We might have -expected that they should occur to men's minds in the order -thus stated: and in fact they did so; for the physiology of -the ancient materialists, as Democritus and Lucretius, is -mechanical so far as it is at all distinct in its views, and -thus the mechanical preceded the chemical doctrine. But in -modern times, the fluid or chemical physiology was developed -before the solid or mechanical: of which the reason appears -to have been this;--that Mechanics and Chemistry began to -assume a scientific character about the same time; and that -of the two, Chemistry not only appeared at first sight more -applicable to the functions of the body, because all the -more rapid changes appear to be connected with modifications -of the fluids of the animal system, but also, by its wider -range of facts and more indefinite principles, afforded a -better temporary refuge for the mind when perplexed by the -difficulties and mysteries which spring out of the -speculations concerning life. But if Chemistry was thus at -first a more inviting field for the physiologist, Mechanics -soon became more attractive in virtue of the splendid -results obtained by the schools of Galileo and Newton. And -when the insufficiency of chemical physiology was discovered -by trial, as we have seen it was, the hope naturally arose, -that the mechanical principles which had explained so many -of the phenomena of the external universe might also be -found, applicable to the smaller world of material -life;--that the _microcosm_ as well as the _macrocosm_ might -have its mechanical principles. From this hope sprung the -{183} Iatromathematical School, or school of Mechanical -Physiologists. - -We may, however, divide this school into two parts, the -Italian, and the Cartesio-Newtonian sect. The former -employed themselves in calculating and analysing a number of -the properties of the animal frame which are undoubtedly -mechanical; the latter, somewhat intoxicated by the supposed -triumphs of the corpuscular philosophy, endeavoured to -extend these to physiology, and for this purpose introduced -into the subject many arbitrary and baseless hypotheses. I -will very briefly mention some of the writers of both these sects. - -The main points to which the Italian or genuine Mechanical -Physiologists attended, were the application of mechanical -calculations to the force of the muscles, and of hydraulical -reasonings to the motion of the fluids of the animal system. -The success with which Galileo and his disciples had pursued -these branches of mechanical philosophy, and the ascendancy -which they had obtained, first in Italy, and then in other -lands, made such speculations highly interesting. Borelli -may be considered as the first great name in his line, and -his book, _De Motu Animalium_, (_Opus Posthumum_, Romæ, -1680,) is even now a very instructive treatise on the forces -and action of the bones and muscles. This, certainly one of -the most valuable portions of mechanical physiology, has not -even yet been so fully developed as it deserves, although -John Bernoulli[29\9] and his son Daniel[30\9] applied to it -the resources of analysis, and Pemberton[31\9] in England, -pursued the same subject. Other of these mechanico-physiological -problems consisted in referring the pressure of the blood -and of the breath to hydrostatical principles. In this -manner Borelli was led to assert that the muscles of the -heart exert a force of 180,000 pounds[32\9]. But a little -later, Keill reduced this force {184} to a few ounces[33\9]. -Keill and others attempted to determine, on similar -principles, the velocity of the blood; we need not notice -the controversies which thus arose, since there is not -involved in them any peculiar physiological principle. - -[Note 29\9: _De Motu Musculorum_.] - -[Note 30\9: _Act. Acad. Petrop._] - -[Note 31\9: _Course of Physiology_, 1773.] - -[Note 32\9: Spr. iv. 110.] - -[Note 33\9: Spr. iv. 443.] - -The peculiar character of the iatromathematical school, as -an attempt at physiological theory, is more manifest in its -other section, which we have called the Cartesio-Newtonian. -The Cartesian system pretended to account for the -appearances and changes of bodies by means of the size, -figure, and motion of their minute particles. And though -this system in its progress towards the intellectual empire -of Europe was suddenly overturned by the rise of the -Newtonian philosophy, these corpuscular doctrines rather -gained than lost by the revolution; for the Newtonian -philosophy enlarged the powers of the corpuscular -hypothesis, by adding the effects of the attractive and -repulsive forces of particles to those of their form and -motion. By this means, although Newton's discoveries did not -in fact augment the probability of the corpuscular -hypothesis, they so far increased its plausibility, that -this hypothesis found favour both with Newton himself and -his contemporaries, no less than it had done with the -Cartesians. - -The attempt to apply this corpuscular hypothesis to -physiology was made by Des Cartes himself. The general -character of such speculations may easily be guessed[34\9]. -The secretions are effected by the organs operating after -the manner of sieves. Bound particles pass through -cylindrical tubes, pyramidal ones through triangular pores, -cubical particles through square apertures, and thus -different kinds of matter are separated. Similar -speculations were pursued by other mathematicians: the -various diameter of the vessels[35\9], their curvatures, -folds, and angles, were made subjects of calculation. -Bellini, Donzellini, Gulielmini, in Italy; Perrault, Dodart, -in France; Cole, Keill, Jurin, in England, were the -principal cultivators of such studies. {185} In the earlier -part of the eighteenth century, 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 fluids, the diameter and form of the -invisible vessels. Such was, for instance, the opinion of -Cheyne[36\9], who held that acute fevers arise from the -obstruction of the glands, which occasions a more vehement -motion of the blood. Mead, the physician of the King, and -the friend of Newton, in like manner explained the effects -of poisons by hypotheses concerning the form of their -particles[37\9], as we have already seen in speaking of chemistry. - -[Note 34\9: _Ib._ 329.] - -[Note 35\9: _Ib._ 432.] - -[Note 36\9: Spr. iv. 223.] - -[Note 37\9: _ Mechanical Account of Poisons_, 1702.] - -It is not necessary for us to dwell longer on this subject, -or to point out the total insufficiency of the mere -mechanical physiology. The iatrochemists had neglected the -effect of the solids of the living frame; the -iatromathematicians attended only to these[38\9]. And even -these were considered only as canals, as cords, as levers, -as lifeless machines. These reasoners never looked for any -powers of a higher order than the cohesion, the resistance, -the gravity, the attraction, which operate in inert matter. -If the chemical school assimilated the physician to a -vintner or brewer, the mechanical physiologists made him an -hydraulic engineer; and, in fact, several of the -iatromathematicians were at the same time teachers of -engineering and of medicine. - -[Note 38\9: Spr. iv. 419.] - -Several of the reasoners of this school combined chemical -with their mechanical principles; but it would throw no -additional light upon the subject to give any account of -these, and I shall therefore go on to speak of the next form -of the attempt to explain the processes of life. - - -SECT. IV.--_The Vital-Fluid School._ - -I speak here, not of that opinion which assumes some kind of -fluid or ether as the means of {186} communication along the -_nerves_ in particular, but of the hypothesis that _all_ the -peculiar functions of _life_ depend upon some subtile -ethereal substance diffused through the frame;--not of a -_Nervous_ Fluid, but of a _Vital_ Fluid. Again, I -distinguish this opinion from the doctrine of an -_immaterial_ vital power or principle, an Animal Soul, which -will be the subject of the next Section: nor is this -distinction insignificant; for a material element, however -subtile, however much spiritualized, must still act -everywhere according to the same laws; whereas we do not -conceive an immaterial spirit or soul to be subject to this -necessity. - -The iatromathematical school could explain to their own -satisfaction how motions, once begun, were transferred and -modified; but in many organs of the living frame there -seemed to be a power of beginning motion, which is beyond -all mere mechanical action. This led to the assumption of a -Principle of a higher kind, though still material. Such a -Principle was asserted by Frederick Hoffmann, who was born -at Halle, in 1660[39\9], and became Professor of Medicine at -the newly established University there in 1694. According to -him[40\9], the reason of the greater activity of organized -bodies lies in the influence of a material substance of -extreme subtilty, volatility, and energy. This is, he holds, -no other than the Ether, which, diffused through all nature, -produces in plants the bud, the secretion and motion of the -juices, and is separated from the blood and lodged in the -brain of animals[41\9]. From this, acting through the -nerves, must be derived all the actions of the organs in the -animal frame; for when the influence of the nerve upon the -muscle ceases, muscular motion ceases also. - -[Note 39\9: Spr. v. 254.] - -[Note 40\9: _Ib._ v. 257.] - -[Note 41\9: _De Differentiâ Organismi et Mechanismi_, pp. 48, 67.] - -The mode of operation of this vital fluid was, however, by -no means steadily apprehended by Hoffmann and his followers. -Its operations are so far mechanical[42\9] that all effects -are reduced to motion, yet they {187} cannot be explained -according to known mechanical laws. At one time the effects -are said to take place according to laws of a Higher -Mechanics which are still to be discovered[43\9]. At another -time, in complete contradiction of the general spirit of the -system, metaphysical conceptions are introduced: each -particle of the vital fluid is said to have a determined -_idea_ of the whole mechanism and organism[44\9], and -according to this, it forms the body and preserves it by its -motion. By means of this fluid the soul operates upon the -body, and the instincts and the passions have their source -in this material sensitive soul. 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 system, whose Monads have also ideas. - -[Note 42\9: Spr. v. 262, 3.] - -[Note 43\9: Hoffmann, _Opp._ Vol. v. p. 123.] - -[Note 44\9: _De Diff. Organ. et Mechan._ p. 81.] - -Notwithstanding its inconsistencies, Hoffmann's system was -received with very general favour both in Germany and in the -rest of Europe; the more so, inasmuch as it fell in very -well with the philosophy both of Leibnitz and of Newton. The -Newtonians were generally inclined to identify the Vital -Fluid with the Ether, of which their master was so strongly -disposed to assume the existence: and indeed he himself -suggested this identification. - -When the discoveries made respecting Electricity in the -course of the eighteenth century had familiarized men with -the notion of a pervading subtile agent, invisible, -intangible, yet producing very powerful effects in every -part of nature, physiologists also caught at the suggestion -of such an agent, and tried, by borrowing or imitating it, -to aid the imperfection of their notions of the vital -powers. The Vital Principle[45\9] was imagined to be a -substance of the same kind, by some to be the same -substance, with the Electric Fluid. By its agency all these -processes in organized bodies were accounted for which -cannot be {188} explained by mechanical or chemical laws, as -the secretion of various matters (tears, milk, bile, &c.) -from an homogeneous fluid, the blood; the production of -animal heat, digestion, and the like. According to John -Hunter, this attenuated substance pervaded the blood itself, -as well as the solid organic frame; 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 is, for a time, -till this vital fluid evaporates, truly alive. - -[Note 45\9: Prichard, _On the Doctrine of a Vital -Principle_, p. 12.] - -The notion of a Vital Fluid appears also to be favourably -looked upon by Cuvier; although with him this doctrine is -mainly put forwards in the form of a Nervous Fluid. Yet in -the following passage he extends the operation of such an -agent to all the vital functions[46\9]: 'We have only to -suppose that all the medullary and nervous parts produce the -Nervous Agent, and that they alone conduct it; that is, that -it can only be transmitted by them, and that it is changed -or consumed by their actions. Then everything appears -simple. A detached portion of muscle preserves for some time -its irritability, on account of the portion of nerve which -always adheres to it. The sensibility and the irritability -reciprocally exhaust each other by their exercise, because -they change or consume the same agent. All the interior -motions of digestion, secretion, excretion, participate in -this exhaustion, or may produce it. All local excitation of -the nerves brings thither more blood by augmenting the -irritability of the arteries, and the afflux of blood -augments the real sensibility by augmenting the production -of the nervous agent. Hence the pleasures of titillations, -the pains of inflammation. The particular sensations -increase in the same manner and by the same causes; and the -imagination exercises, (still by means of the nerves,) upon -the internal fibres of the arteries or other parts, and -through them on the sensations, an action analogous to that -of the will upon the voluntary motions. As each exterior -sense is exclusively disposed {189} to admit the substances -which it is to perceive, so each interior organ, secretory -or other, is also more excitable by some one agent than by -another: and hence arises what has been called the _proper -sensibility_ or _proper life of the organs_; and the -influence of specifics which, introduced into the general -circulation, affect only certain parts. In fine, if the -nervous agent cannot become sensible to us, the reason is -that all sensation requires that this agent should be -altered in some way or other; and it cannot alter itself. - -[Note 46\9: _Hist. Sc. Nat. depuis_ 1789, i. 214.] - -'Such is the summary idea which we may at present form of -the mutual and general working of the vital powers in -animals.' - -Against the doctrine of a Vital Fluid as one uniform -material agent pervading the organic frame, an argument has -been stated which points out extremely well the -philosophical objection to such an hypothesis[47\9]. If the -Vital Principle be the _same_ in all parts of the body, how -does it happen, it is asked, that the secretions are so -_different_? How do the particles in the blood, separated -from their old compounds and united into new ones, under the -same influence, give origin to all the different fluids -which are produced by the glands? The liver secretes bile, -the lacrymal gland, tears, and so on. Is the Vital Principle -different in all these organs? To assert this, is to -multiply nominal principles without limit, and without any -advance in the explanation of facts. Is the Vital Principle -the same, but its operation modified by the structure of the -organ? We have then two unknown causes, the Vital Principle -and the Organic Structure, to account, for the effect. By -such a multiplication of hypotheses nothing is gained. We -may as well say at once, that the structure of the organ, -acting by laws yet unknown, is the cause of the peculiar -secretion. It is as easy to imagine this structure acting to -produce the whole effect, as it is to imagine it modifying -the activity of another agent. Thus the hypothesis of the -Vital Fluid in this form explains nothing, and does not in -any {190} way help onwards the progress of real biological -knowledge. - -[Note 47\9: Prichard, _On a Vital Principle_, p. 98.] - -The hypothesis of an _immaterial_ vital principle must now be -considered. - - -SECT. V.--_The Psychical School._ - -The doctrine of an Animal Soul as the principle which makes -the operations of organic different from those of inorganic -matter, is quite distinct from, and we may say independent -of, the doctrine of the soul as the intelligent, moral, -responsible part of man's nature. It is the former doctrine -alone of which we have here to speak, and those who thus -hold the existence of an immaterial agent as the cause of -the phenomena of life, I term the _Psychical School_. - -Such a view of the constitution of living things is very -ancient. For instance, Aristotle's Treatise '_On the Soul_,' -goes entirely upon the supposition that the Soul is the -cause of motion, and he arrives at the conclusion that there -are different _parts_ in the Soul; the _nutritive_ or -_vegetative_, the _sensitive_, and the _rational_[48\9]. - -[Note 48\9: Aristotle. Περὶ Ψυχῆς, ii. 2.] - -But this doctrine is more instructive to us, when it appears -as the antagonist of other opinions concerning the nature of -life. In this form it comes before us as promulgated by -Stahl, whom we have already noticed as one of the great -discoverers in chemistry. Born in the same year as Hoffmann, -and appointed at his suggestion professor at the same time -in the same new university of Halle, he soon published a -rival physiological theory. In a letter to Lucas Schröck, -the president of the Academy of Naturalists, he describes -the manner in which he was led to form a system for -himself[49\9]. Educated in the tenets of Sylvius and Willis, -according to which all diseases are derived from the acidity -of the fluids, Stahl, when a young student, often wondered -how these fluids, so liable to be polluted and corrupted, -are so wonderfully preserved through innumerable external -influences, and seem to {191} be far less affected by these -than by age, constitution, passion. No material cause could, -he thought, produce such effects. No attention to mechanism -or chemistry alone could teach us the true nature and laws -of organization. - -[Note 49\9: Spr. v. 303.] - -So far as Stahl recognized the influence, in living bodies, -of something beyond the range of mechanics and chemistry, -there can be no doubt of the sound philosophy of his views; -but when he proceeds to found a positive system of -physiology, his tenets become more precarious. The basis of -his theory is this[50\9]: the body has, as body, no power to -move itself, and must always be put in motion by immaterial -substances. All motion is a spiritual act[51\9]. The source -of all activity in the organic body, from which its -preservation, the permanency of its composition, and all its -other functions proceed, is an immaterial being, which Stahl -calls the _Soul_; because, as he says, when the effects are -so similar, he will not multiply powers without necessity. -Of this principle, he says, as the Hippocratians said of -Nature, that 'it does without teaching what it ought to -do[52\9],' and does it 'without consideration[53\9].' These -ancient tenets Stahl interprets in such a manner that even -the involuntary motions proceed from the soul, though -without reflection or clear consciousness. It is indeed -evident, that there are many customary motions and -sensations which are perfectly rational, yet not the objects -of distinct consciousness: and thus instinctive motions, and -those of which we are quite unconscious, may still be -connected with reason. The questions which in this view -offer themselves, as, how the soul passes from the mother to -the child, he dismisses as unprofitable[54\9]. He considers -nutrition and secretion as the work of the soul. The -corpuscular theory and the doctrine of animal spirits {192} -are, he rightly observes, mere hypotheses, which are -arbitrary in their character, and only shift the difficulty. -For, if the animal spirits are not matter, how can they -explain the action of an immaterial substance on the body; -and if they are matter, how are they themselves acted on? - -[Note 50\9: Spr. v. 308] - -[Note 51\9: _Ib._ v. 314.] - -[Note 52\9: Stahl, περὶ φύσεως ἀπαίδευτου.] - -[Note 53\9: οὐκ ἐκ διανοίης.] - -[Note 54\9: This was of course an obvious problem. Harvey, -_On Generation_ Exercise 27, p. 148, teaches, 'That the egg -is not the production of the womb, but of the soul.'] - -This doctrine of the action of the soul on the body, was -accepted by many persons, especially by the -iatromathematicians, who could not but feel the -insufficiency of their system without some such supplement: -such were Cheyne and Mead. In Germany, Stahl's disciples in -physiology were for the most part inconsiderable -persons[55\9]. Several Englishmen who speculated concerning -the metaphysics as well as the physiology of Sensation and -Motion, inclined to this psychical view, as Porterfield and -Whytt. Among the French, Boissier de Sauvages was the most -zealous defender of the Stahlian system. Actions, he -says[56\9], which belong to the preservation of life are -determined by a moral not a mechanical necessity. They -proceed from the soul, but cannot be controlled by it, as -the starting from fear, or the trembling at danger. Unzer, a -physician at Altona[57\9], was also a philosophical -Stahlian[58\9]. - -[Note 55\9: Spr. v. 339, &c.] - -[Note 56\9: _Ib._ 358.] - -[Note 57\9: A.D. 1799] - -[Note 58\9: Spr. v. 360.] - -We need not dwell on the opposition which was offered to -this theory, first by Hoffmann, and afterwards by Haller. -The former of these had promulgated, as we have seen, the -rival theory of a Nervous Fluid, the latter was the -principal assertor of the doctrine of Irritability, an -important theory on which we may afterwards have to touch. -Haller's animosity against the Stahlian hypothesis is a -remarkable feature in one who is in general so tolerant in -his judgment of opinions. His arguments are taken from the -absence of the control of the will over the vital actions, -from the want of consciousness accompanying these actions, -from the uniformity of them in different conditions of the -mind, and from the small sensibility of {193} the heart -which is the source of the vital actions. These objections, -and the too decided distinction which Haller made between -voluntary and involuntary muscles, were very satisfactorily -answered by Whytt and Platner. In particular it was urged -that the instinctive actions of brutes are inexplicable by -means of mechanism, and may be compared with the necessary -vital actions of the human body. Neither kind are -accidental, neither kind are voluntary, both are performed -without reflection. - -Without tracing further the progress of the Psychical -Doctrine, I shall borrow a few reflections upon it from -Sprengel[59\9]:-- - -'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 medicine, they talk to no purpose. The states -of the soul are objects of our internal experience, and -interest the physician too nearly to allow him to neglect -them. The innumerable unconscious efforts of the soul, the -powerful and daily effects of the passions upon the body, -too often put to confusion those who would expel into the -region of metaphysics the dispositions of the mind. The -connexion of our knowledge of the soul, as gathered from -experience, with our knowledge of the human body, is far -closer than the mechanical and chemical physiologists -suspect. - -[Note 59\9: Spr. v. 383.] - -'The strongest objection against the psychical system, and -one which has never been sufficiently answered by any of its -advocates, is the universality of organic effects in the -_vegetable_ kingdom. The comparison of the physiology of -plants with the physiology of animals puts the latter in its -true light. Without absolutely trifling with the word -_soul_, we cannot possibly derive from a soul the organic -operations of vegetables. But just as little can we, as some -Stahlians have done, draw a sharp line between plants and -animals, and ascribe the processes of the former to mere -mechanism, while {194} we derive the operations of the -latter from an intellectual principle. Not to mention that -such a line is not possible, the rise of the sap and the -alteration of the fluids of plants cannot be derived -entirely from material causes as their highest origin.' - -Thus, I may add, this psychical theory, however difficult to -defend in its detail, does in its generalities express some -important truths respecting the vital powers. It not only, -like the last theory, gives unity to the living body, but it -marks, more clearly than any other theory, the wide interval -which separates mechanical and chemical from vital action, -and fixes our attention upon the new powers which the -consideration of life compels us to assume. It not only -reminds us that these powers are elevated above the known -laws of the material world, but also that they are closely -connected with the world of thought and feeling, of will and -reason; and thus it carries us, in a manner in which none of -the preceding theories have done, to a true conception of a -living, conscious, sentient, active individual. - -At the same time we cannot but allow that the life of -plants and of the lower orders of animals shows us very -clearly that, in order to arrive at any sound and consistent -knowledge respecting life, we must form some conception of -it from which all the higher attributes which the term -'soul' involves, are utterly and carefully excluded; and -therefore we cannot but come to the conclusion that the -psychical school are right mainly in this; that in ascribing -the functions of life to a _soul_, they mark strongly and -justly the impossibility of ascribing them to any known -attributes of _body_. - - - -{{195}} -CHAPTER III. - -ATTEMPTS TO ANALYSE THE IDEA OF LIFE. - - -1. _Definitions of Life._--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 failure, and -produced nothing beyond a negative result. And the -conjecture may now naturally occur, that the cause of this -failure resides in an erroneous mode of propounding to -ourselves the problem. Instead of contemplating Life as a -single Idea, it may perhaps be proper to separate it into -several component notions: instead of seeking for one cause -of all vital operations, it may be well to look at the -separate vital functions, and to seek their causes. When the -view of this possibility opens upon us, how shall we -endeavour to verify it, and to take advantage of it? - -Let us, as one obvious course, take some of the attempts -which have been made to _define_ Life, and let us see -whether they appear to offer to us any analysis of the idea -into component parts. Such definitions, when they proceed -from men of philosophical minds, are the ultimate result of -a long course of thought and observation; and by no means -deserve to be slighted as arbitrary selections of -conditions, or empty forms of words. - -2. Life has been defined by Stahl[60\9], 'The condition by -which a body resists a natural tendency to chemical changes, -such as putrefaction.' In like manner, M. von Humboldt[61\9] -defines living bodies to be 'those which, notwithstanding -the constant operation {196} of causes tending to change -their form, are hindered by a certain inward power from -undergoing such change.' The first of these definitions -amounts only to the assertion, that vital processes are not -chemical; a negative result, which we may accept as true, -but which is, as we have seen, a barren truth. The second -appears to be, in its import, identical with the first. An -_inward_ principle can only be understood as distinguished -from known external powers, such as mechanical and chemical -agencies. Or if, by an internal principle, we mean such a -principle as that of which we are _conscious_ within -ourselves, we ascribe a soul to all living things: an -hypothesis which we have seen is not more effective than the -former in promoting the progress of biological science. -Nearly the same criticism applies to such definitions as -that of Kant: that 'Life is an internal faculty producing -change, motion, and action.' - -[Note 60\9: Treviranus, _Biologie_, p. 19. Stahlii, _**Theor. -Med._ p. 254.] - -[Note 61\9: _Aphorismen aus d. Chem. Physiol. der Pflanzen_, s. 1.] - -Other definitions refer us, not to some property residing in -the whole of an organized mass, but to the connexion and -relation of its parts. Thus M. von Humboldt[62\9] has given -another definition of a living body: that 'it is a whole -whose parts, arbitrarily separated, no longer resist -chemical changes.' But this additional assertion concerning -the parts, adds nothing of any value to the definition of -the whole. And in some of the lower kinds of plants and -animals it is hardly true as a fact. - -[Note 62\9: _Versuche über die gereitzte Muskel und -Nervenfüser_, b. ii. p. 433.] - -3. Another definition[63\9] places the character of Life in -'motions serviceable to the body moved.' To this it has been -objected[64\9], that, on this definition, the earth and the -planets are living bodies. 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 body. -We might also add, that if we speak of all vital functions -as _motions_, we make an assumption quite unauthorized, and -probably false. - -[Note 63\9: Erhard, Röschlaub's _Magazin der Heilkunde_, b. -i. st. 1. p. 69.] - -[Note 64\9: Treviranus, _Biologie_, p. 41.] - -{197} Other definitions refer the idea of Life to the idea -of Organization. 'Life is the activity of matter according -to laws of organization[65\9].' We are then naturally led to -ask, What is Organization? In reply to this is given us the -Kantian definition of Organization, which I have already -quoted elsewhere[66\9], 'An organized product of nature is -that in which all the parts are mutually ends and -means[67\9].' That this definition involves exact -fundamental ideas, and is capable of being made the basis of -sound knowledge, I shall hereafter endeavour to show. But I -may observe that such a definition leads us somewhat -further. If the parts of organized bodies are known to be -means to certain ends, this must be known because they -fulfil these ends, and produce certain effects by the -operation of a certain cause or causes. The question then -recurs, what is _the cause_ which produces such effects as -take place in organized or living bodies? and this is -identical with the problem of which in the last chapter we -traced the history, and related the failure of physiologists -in all attempts at its solution. - -[Note 65\9: Schmid, _Physiologie_, b. ii. p. 274.] - -[Note 66\9: _Hist. Ind. Sc._ b. xvii. c. viii. s. 2.] - -[Note 67\9: Kant, _Urtheilskraft_, p. 296.] - -4. But what has been just said suggests to us that it may be -an improvement to put our problem in another shape:--not to -take for granted that the cause of all vital processes is -one, but to suppose that there may be several separate -causes at work in a living body. If this be so, life is no -longer one kind of activity, but several. We have a number -of operations which are somehow bound together, and life is -the totality of all these: in short, life is not one -Function, but a System of Functions. - -5. We are thus brought very near to the celebrated -definition of life given by Bichat[68\9]: 'Life is the sum -of the functions by which death is resisted.' But upon the -definition thus stated, we may venture to observe;--first, -that the introduction of the notion of {198} _death_ in -order to define the notion of _life_ appears to be -unphilosophical. We may more naturally define death with -reference to life, as the cessation of life; or at least we -may consider life and death as correlative and -interdependent notions. Again, the word 'sum,' used in the -way in which it here occurs, appears to be likely to convey -an erroneous conception, as if the functions here spoken of -were simply added to each other, and connected by -co-existence. It is plain that our idea of life involves -more than this: the functions are all clearly connected, and -mutually depend on each other; nutrition, circulation, -locomotion, reproduction,--each has its influence upon all -the others. These functions not merely co-exist, but exist -with many mutual relations and connexions; they are -continued so as to form, not merely a _sum_, but a _system_. -And thus we are led to modify Bichat's definition, and to -say that _Life is the system of vital functions_. - -[Note 68\9: _Physiological Researches on Life and Death_.] - -6. But it will be objected that by such a definition we -explain nothing: the notion of _vital functions_, it may be -said, involves the idea of _life_, and thus brings us round -again to our starting-point. Or if not, at least it is as -necessary to define Vital Functions as to define Life -itself, so that we have made little progress in our task. - -To this we reply, that if any one seeks, upon such subjects, -some ultimate and independent definition from which he can, -by mere reasoning, deduce a series of conclusions, he seeks -that which cannot be found. In the Inductive Sciences, a -Definition does not form the basis of reasoning, _but points -out the course of investigation_. The definition must -include words; and the meaning of these words must be sought -in the progress and results of observations, as I have -elsewhere said[69\9]. 'The meaning of words is to be sought -in the progress of thought; the history of science is our -dictionary; the steps of scientific induction are our -definitions.' It will appear, I think, that it is more easy -for us to form an idea of a separate Function of the {199} -animal frame, as Nutrition or Reproduction, than to -comprehend Life in general under any single idea. And when -we say that Life is a system of Vital Functions, we are of -course directed to study these functions separately, and (as -in all other subjects of scientific research) to endeavour -to form of them such clear and definite ideas as may enable -us to discover their laws. - -[Note 69\9: _Hist. Ind. Sc._ b. xiii. c. ix.] - -7. The view to which we are thus led, of the most promising -mode of conducting the researches of Biology, is one which -the greatest and most philosophical physiologists of modern -times have adopted. Thus Cuvier considers this as the true -office of physiology at present. 'It belongs to modern -times,' he says, 'to form a just classification of the vital -phenomena; the task of the present time is to analyse the -forces which belong to each organic element, and upon the -zeal and activity which are given to this task, depends, -according to my judgment, the fortune of physiology[70\9].' -This classification of the phenomena of life involves, of -course, a distinction and arrangement of the vital -functions; and the investigation of the powers by which -these functions are carried on, is a natural sequel to such -a classification. - -[Note 70\9: _Hist. Sc. Nat. dep._ 1789, i. 218.] - -8. _Classification of Functions._--Attempts to classify the -Vital Functions of man were made at an early period, and -have been repeated in great number up to modern times. The -task of classification is exposed to the same difficulties, -and governed by the same conditions, in this as in other -subjects. Here, as in the case of other things, there may be -many classifications which are moderately good and natural, -but there is only one which is the best and the true natural -system. Here, as in other cases, one classification brings -into view one set of relations; another, another; and each -may be valuable for its special purpose. Here, as in other -cases, the classes may be well constituted, though the -boundary lines which divide them be somewhat indistinct, and -the order doubtful. Here, {200} as in other cases, we may -have approached to the natural classification without having -attained it; and here, as in other cases, to _define_ our -classes is the last and hardest of our problems. - -9. The most ancient classification of the Functions of -living things[71\9], is the division of them into _Vital_, -_Natural_, and _Animal_. The Vital Functions are those which -cannot be interrupted without loss of life, as -_Circulation_, _Respiration_, and _Nervous Communication_. -The _Natural Functions_ are those which without the -intervention of the will operate on their proper occasions -to preserve the bodies of animals; they are _Digestion_, -_Absorption_, _Nutrition_; to which was added _Generation_. -The _Animal_ Functions are those which involve perception -and will, by which the animal is distinguished from the -vegetable; they are _Sensibility_, _Locomotion_, and _Voice_. - -[Note 71\9: _Dict. des Sciences Nat._ art. _Fonctions_.] - -The two great grounds of this division, the distinction of -functions which operate continually, and those which operate -occasionally; and again, the distinction of functions which -involve sensation and voluntary motion from those which do -not; are truly of fundamental importance, and gave a real -value to this classification. It was, however, liable to -obvious objections: namely, _First_, that the names of the -classes were ill chosen; for all the functions are natural, -all are vital: _Second_, that the lines of demarcation -between the classes are indefinite and ambiguous; -Respiration is a _vital_ function, as being continually -necessary to life; but it is also a _natural_ function, -since it occurs in the formation of the nutritive fluid, and -an _animal_ function, since it depends in part on the will. -But these objections were not fatal, for a classification -may be really sound and philosophical, though its boundary -lines are vague, and its nomenclature ill selected. The -division of the functions we have mentioned kept its ground -long; or was employed with a subdivision of one class, so as -to make them four; the _vital_, _natural_, _animal_ and -_sexual_ functions. {201} - -10. I pass over many intermediate attempts to classify the -functions, and proceed to that of Bichat as that which is, I -believe, the one most generally assented to in modern times. -The leading principle in the scheme of this celebrated -physiologist is the distinction between _organic_ and -_animal_ life. This separation is nearly identical with the -one just noticed between the vital and animal functions; but -Bichat, by the contrasts which he pointed out between these -classes of functions, gave a decided prominence and -permanence to the distinction. The Organic Life, which in -animals is analogous to the life of vegetables, and the -Animal Life, which implies sensation and voluntary motion, -have each its system of organs. The center of the animal -life is the brain, of the organic life, the heart. The -former is carried on by a symmetrical, the latter, by an -unsymmetrical system of organs: the former produces -intermitting, the latter continuous actions: and, in -addition to these, other differences are pointed out. This -distinction of the two lives, being thus established, each -is subdivided into two orders of Functions. The Animal -Functions are passive, as _Sensation_: or active, as -_Locomotion_ and _Voice_; again, the Organic Functions are -those of Composition, which are concerned in taking matter -into the system; _Digestion_, _Absorption_, _Respiration_, -_Circulation_, _Assimilation_; and those of Decomposition, -which reject the materials when they have discharged their -office in the system; and these are again, _Absorption_, -_Circulation_, and _Secretion_. To these are added -_Calorification_, or the production of animal heat. It -appears, from what has been said, that _Absorption_ and -_Circulation_ (and we may add _Assimilation_ and -_Secretion_, which are difficult to separate,) belong alike -to the processes of composition and decomposition; nor in -truth, can we, with any rigour, separate the centripetal and -centrifugal movements in that vortex which, as we shall see, -is an apt image of organic life. - -Several objections have been made to this classification: -and in particular, to the terms thus employed. It has been -asserted to be a perversion of language to {202} ascribe to -animals _two lives_, and to call the higher faculties in -man, perception and volition, the _animal_ functions. But, -as we have already said, when a classification is really -good, such objections, which bear only upon the mode in -which it is presented, are by no means fatal: and it is -generally acknowledged by all the most philosophical -cultivators of biology, that this arrangement of the -functions is better suited to the purposes of the science -than those which preceded it. - -11. But according to the principles which we have already -laid down, the solidity of such a classification is to be -verified by its serving as a useful guide in biological -researches. If the arrangement which we have explained be -really founded in natural relations, it will be found that -in proportion as physiologists have studied the separate -functions above enumerated, their ideas of these functions, -and of the powers by which they are carried on, have become -more and more clear;--have tended more and more to the -character of exact and rigorous science. - -To examine how far this has been the case with regard to all -the separate functions, would be to attempt to estimate the -value of all the principal physiological speculations of -modern times; a task far too vast and too arduous for any -one to undertake who has not devoted his life to such -studies. But it may properly come within the compass of our -present plan to show how, with regard to the broader lines -of the above classification, there has been such a progress -as we have above described, from more loose and inaccurate -notions of some of the vital functions to more definite and -precise ideas. This I shall attempt to point out in one or -two instances. - - - -{{203}} -CHAPTER IV. - -ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES, AND FIRST -OF ASSIMILATION AND SECRETION. - - -SECT. I.--_Course of Biological Research._ - -1. 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 body, but of the -approach made to some distinct Idea of the specially vital -part of each process. In the History of Physiology, it has -been seen[72\9] 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 -discoveries. The discovery of the circulation of the blood -led to theories of animal heat; the discovery of the motion -of the chyle led to theories of digestion; the close -examination of the process of reproduction in plants and -animals led to theories of generation. In all these cases, -the discovery brought to light some portion of the process -which was mechanical or chemical, but it also, in each -instance, served to show that the process was something more -than mechanical or chemical. The theory attempted to explain -the process by the application of known causes; but there -always remained some part of it which must unavoidably be -referred to an unknown cause. But though unknown, such a -cause was not a hopeless object of study. As the vital -functions became better and better understood, it was seen -more and more clearly at what precise points of the process -it was necessary to assume a peculiar vital energy, and what -sort of properties {204} this energy must be conceived to -possess. It was perceived where, in what manner, in what -degree, mechanical and chemical agencies were modified, -over-ruled, or counteracted, by agencies which must be -hypermechanical and hyperchemical. And thus the discoveries -made in anatomy by a laborious examination of facts, pointed -out the necessity of introducing new ideas, in order that -the facts might be intelligible. Observation taught much; -and among other things, she taught that there was something -which could not be observed, but which must, if possible, be -conceived. I shall notice a few instances of this. - -[Note 72\9: _Hist. Ind. Sc._ b. xvii.] - - -SECT. II.--_Attempts to form a distinct Conception of -Assimilation and Secretion._ - -2. _The Ancients._--That plants and animals grow by taking -into their substance matter previously extraneous, is -obvious to all: but as soon as we attempt to conceive this -process distinctly in detail, we find that it involves no -inconsiderable mystery. How does the same food become blood -and flesh, bone and hair? Perhaps the earliest attempt to -explain this mystery, is that recorded by Lucretius[73\9] as -the opinion of Anaxagoras, that food contains some bony, -some fleshy particles, some of blood, and so on. We might, -on this supposition, conceive that the mechanism of the body -appropriates each kind of particle to its suitable place. - -[Note 73\9: Lucr. i. 855. Nunc et Anaxagoræ scrutemur -ὁμοιομέρειαν.] - -But it is easy to refute this essay at philosophizing (as -Lucretius refutes it) by remarking that we do not find milk -in grass, or blood in fruit, though such food gives such -products in cattle and in men. In opposition to this -'Homoiomereia,' the opinion that is forced upon us by the -facts is, that the process of nutrition is not a selection -merely, but an _assimilation_; the organized system does not -_find_, but _make_, the additions to its structure. {205} - -3. _Buffon._--This notion of _assimilation_ may be variously -expressed and illustrated; and all that we can do here, in -order to show the progress of thought, is to adduce the -speculations of those writers who have been most successful -in seizing and marking its peculiar character. Buffon may be -taken as an example of the philosophy of his time on this -subject. 'The body of the animal,' says he[74\9], 'is a kind -of _interior mould_, in which the matter subservient to its -increase is modelled and assimilated to the whole, in such a -way that, without occasioning any change in the order and -proportion of the parts, there results an augmentation in -each part taken separately. This increase, this development, -if we would have a _clear idea_ of it, how can we obtain it, -except by considering the body of the animal, and each of -the parts which is to be developed, as so many interior -moulds which only receive the accessory matter in the order -which results from the position of all their parts? This -development cannot take place, as persons sometimes persuade -themselves, by an addition to the outside; on the contrary, -it goes on by an intimate susception which penetrates the -mass; for, in the part thus developed, the size increases in -all parts proportionally, so that the new matter must -penetrate it in all its dimensions: and it is quite -necessary that this penetration of substance must take place -in a certain order, and according to a certain measure; for -if this were not so, some parts would develope themselves -more than others. Now what can there be which shall -prescribe such a rule to the accessory matter except the -_interior mould_?' - -[Note 74\9: _Hist. Nat._ b. i. c. iii.] - -To speak of a _mould_ simply, would convey a coarse -mechanical notion, which could not be received as any useful -contribution to physiological speculation. But this -_interior_ mould is, of course, to be understood -figuratively, not as an assemblage of cavities, but as a -collection of laws, shaping, directing, and modifying the -new matter; giving it not only form, but motion {206} and -activity, such as belong to the parts of an organic being. - -4. It must be allowed, however, that even with this -explanation, the comparison is very loose and insufficient. -A _mould_ may be permitted to mean a collection of laws, but -still it can convey no conception except that of laws -regulated by relations of space; and such a conception is -very plainly quite inadequate to the purpose. What can we -conceive of the interior mould by which chyle is separated -from the aliments at the pores of the lacteals, or tears -secreted in the lacrymatory gland? - -An additional objection to this mode of expression of Buffon -is, that it suggests to us only a single marked change in -the assimilated matter, not a continuous series of changes. -Yet the animal fluids and other substances are, in fact, -undergoing a constant series of changes. Food becomes chyme, -and chyme becomes chyle; chyle is poured into the blood; -from the blood secretions take place, as the bile; the bile -is poured into the digestive canal, and a portion of the -matter previously introduced is rejected out of the system. -Here we must have a series of 'interior moulds;' and these -must impress matter at its ejection from the organic system -as well as at its reception. But, moreover, it is probable -that none of the above transformations are quite abrupt. -Change is going on between the beginning and the end of each -stage of the nutritive circulation. To express the laws of -this continuous change, the image of an interior mould is -quite unsuited. We must seek a better mode of conception. - -5. Vegetable and animal nutrition is, as we have said, a -constant circulation. The matter so assumed is not all -retained: a perpetual subtraction accompanies a perpetual -addition. There is an excretion as well as an -intussusception. The matter which is assumed by the living -creature is retained only for a while, and is then parted -with. The individual is the same, but its parts are in a -perpetual flux: they come and go. For a time the matter -which belongs to the organic body is bound to it by certain -laws: but before it is thus bound, and {207} after it is -loose, this matter may circulate about the universe in any -other form. Life consists in a permanent influence over a -perpetually changing set of particles. - -_Cuvier._--This condition also has been happily expressed, -by means of a comparison, by another great naturalist. 'If,' -says Cuvier[75\9], 'if, in order to obtain a just idea of -the essence of life, we consider it in the beings where its -effects are most simple, 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 form; constantly attracting into their -composition a part of the surrounding substances, and giving -up in return some part of their own substance. - -[Note 75\9: _Règne Animal_, i. 11.] - -'Life is thus a _vortex_, more or less rapid, more or less -complex, which has a constant direction, and which always -carries along its stream particles of the same kinds; but in -which the individual particles are constantly entering in -and departing out; so that the _form_ of the living body is -more essential to it than its matter. - -'So long as this motion subsists, the body in which it takes -place is _alive_; it _lives_. When the motion stops finally, -the body _dies_. After death, the elements which compose the -body, given up to the ordinary chemical affinities, soon -separate, and the body which was alive is dissolved.' - -This notion of a vortex[76\9] which is permanent while the -matter which composes it constantly changes,--of peculiar -forces which act in this vortex so long as it exists, and -which give place to chemical forces when {208} the -circulatory motion ceases,--appears to express some of the -leading conditions of the assimilative power of living -things in a simple and general manner, and thus tends to -give distinctness to the notion of this vital function. - -[Note 76\9: The definition of life given by M. de Blainville -appears to me not to differ essentially from that of Cuvier: -'Un corps vivant est une sorte de foyer chimique où il-y-a à -tous momens apport de nouvelles molecules et départ de -molecules anciennes; où la composition n'est jamais fixe (si -ce n'est d'un certain nombre de parties veritablement mortes -ou en depôt), mais toujours pour ainsi dire _in nisu_, d'où -mouvement plus ou moins lent et quelquefois -chaleur.'--_Principes d'Anat._ 1822, t. i. p. 16.] - -6. But we may observe that this notion of a Vortex is still -insufficient. Particles are not only taken into the system -and circulated through it for a time, but, as we have seen, -they are altered in character in a manner to us -unintelligible, both at their first admission into the -system and at every period of their progress through it. In -the vortex each particle is constantly _transformed_ while -it whirls. - -It may be said, perhaps, that this transformation of the -kinds of matter may be conceived to be merely a new -arrangement of their particles, 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 current. But to say this, is to take for granted -the atomic hypothesis in its rudest form. What right have we -to assume that blood and tears, bile and milk, consist of -like particles of matter differently arranged? What can -arrangement, a mere relation of space, do towards explaining -such differences? Is not the insufficiency, the absurdity of -such an assumption proved by the whole course of science? -Are not even chemical changes, according to the best views -hitherto obtained, something more than a mere new -arrangement of particles? And are not vital as much beyond -chemical, as chemical are beyond geometrical modifications? -It is not enough, then, to conceive life as a vortex. The -particles which are taken into the organic frame do more -than circulate there. They are, at every point of their -circulation, acted upon by laws of an unknown kind, changing -the nature of the substance which they compose. Life is a -vortex in which vital forces act at every point of the -stream: it is not only a current of whirling _matter_, but a -cycle of recurring _powers_. - -7. _Matter and Form._--This image of a vortex is closely -connected with the representation of life offered {209} us -by writers of a very different school. In Schelling's -_Lectures on Academic Study_, he takes a survey of the -various branches of human knowledge, determining according -to his own principles the shape which each science must -necessarily assume. The peculiar character of organization, -according to him[77\9], is that the matter is only an -accident of the thing itself, and the organization consists -in Form alone. But this Form, by its very opposition to -Matter, ceases to be independent of it, and is only ideally -separable. In organization, therefore, substance and -accident, matter and form, are completely identical[78\9]. -This notion, that in organization the Form is essential and -the Matter accidental, or, in other words, that the Form is -permanent and the Matter fluctuating and transitory, agrees, -if taken in the grossest sense of matter and form, with -Cuvier's image of a Vortex. In a whirlpool, or in a -waterfall, the form remains, the matter constantly passes -away and is renewed. But we have already seen[79\9] that in -metaphysical speculations in which matter and form are -opposed, the word form is used in a far more extensive sense -than that which denotes a relation of space. It may indeed -designate any change which matter can undergo; and we may -very allowably say that food and blood are the same matter -under different _forms_. Hence if we assert that _Life is a -constant Form of a circulating Matter_, we express Cuvier's -notion in a mode free from the false suggestion which -'Vortex' conveys. - -[Note 77\9: Lect. xiii. p. 288.] - -[Note 78\9: I have not translated Schelling's words, but -given their import as far as I could.] - -[Note 79\9: Book i.] - -8. We may, however, still add something to this account of -life. The circulating parts of the system not only -circulate, but they form the non-circulating parts. Or -rather, there are no non-circulating parts: all portions of -the frame circulate more or less rapidly. The food which we -take circulates rapidly in the fluids, more slowly in the -flesh, still more slowly in the bones; but in all these -parts it is taken into the system, {210} retained there for -some time, and finally replaced by other matter. But while -it remains in the body, it exercises upon the other -circulating parts the powers by which their motion is -produced. Nutriment forms and supports the organs, and the -organs carry fresh nutriment to its destination. The -peculiar forces of the living body, and its peculiar -structure, are thus connected in an indescribable manner. -The forces produce the structure; the structure, again, is -requisite for the exertion of the forces. The Idea of an -Organic or Living Being includes this peculiar -condition--that its construction and powers are such, that -it constantly appropriates to itself new portions of -substance which, so appropriated, become indistinguishable -parts of the whole, and serve to carry on subsequently the -same functions by which they were assimilated. And thus -_Organic Life is a constant Form of a circulating Matter, in -which the Matter and the Form determine each other by -peculiar laws_ (_that is, by Vital Forces_). - - -SECT. III.--_Attempts to conceive the forces of Assimilation -and Secretion._ - -9. I have already stated that in our attempts to obtain -clear and scientific Ideas of Vital Forces, we have, in the -first place, to seek to understand the course of change and -motion in each function, so as to see at what points of the -process peculiar causes come into play; and next, to -endeavour to obtain some insight into the peculiar character -and attributes of these causes. Having spoken of the first -part of this mode of investigation in regard to the general -nutrition of organic bodies, I must now say a few words on -the second part. - -The Forces here spoken of are _Vital_ Forces. From what has -been said, we may see in some measure the distinction -between forces of this kind and mechanical or chemical -forces; the latter tend constantly to produce a final -condition, after which there is no further cause of change: -mechanical forces tend to produce equilibrium; chemical -forces tend to produce {211} composition or decomposition; -and this point once reached, the matter in which these -forces reside is altogether inert. But an organic body tends -to a constant motion, and the highest activity of organic -forces shows itself in continuous change. Again, in -mechanical and chemical forces, the force of any aggregate -is the sum of the forces of all the parts: the sum of the -forces corresponds to the sum of the matter. But in organic -bodies, the amount of effect does not depend on the matter, -but on the form: the particles lose their separate energy, -in order to share in that of the system; they are not added, -they are _assimilated_. - -10. 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 -Assimilation. It has been called _Organic Attraction_ or -_Vital Attraction_, _Organic Affinity_ or _Vital Affinity_, -being thus compared with mechanical Attraction or chemical -Affinity. But, perhaps, as the process is certainly neither -mechanical nor chemical, it is desirable to appropriate to -it a peculiar name; and the name _Assimilation_, or _Organic -Assimilation_, by the usage of good biological writers, is -generally employed for this purpose, and may be taken as the -standard name of this Vital Force. To illustrate this, I -will quote a passage from the excellent _Elements of -Physiology_ of Professor Müller. 'In the process of -nutrition is exemplified the fundamental principle of -_organic assimilation_. Each elementary particle of an organ -attracts similar particles from the blood, and by the -changes it produces in them, causes them to participate in -the vital principle of the organ itself. Nerves take up -nervous substance, muscles, muscular substance: even morbid -structures have the assimilating power; warts in the skin -grow with their own peculiar structure; in an ulcer, the -base and border are nourished in a way conformable to the -mode of action and secretion determined by the disease.' - -11. 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 {212} nutriment -received into the system, and thus is maintained and -augmented with the growth of the whole. But the growth of -the solid parts is only one portion of the function of -nutrition; besides this, we must consider the motion and -changes of the fluids, and must ask what kind of forces may -be conceived to produce these. What are the powers by which -chyle is _absorbed_ from the food, by which bile is -_secreted_ from the blood, by which the circulating _motion_ -of these and all other fluids of the body are constantly -maintained? To the questions,--What are the forces by which -_absorption_, _secretion_, and the _vital motions_, of -fluids are produced?--no satisfactory answer has been -returned. Yet still some steps have been made, which it may -be instructive to point out. - -12. In _Absorption_ it would appear that a part of the -agency is inorganic; for not only dead membranes, but -inorganic substances, absorb fluids, and even absorb them -with elective forces, according to the ingredients, of the -fluid. A force which is of this kind, and which has been -termed _Endosmose_, has been found to produce very curious -effects. When a membrane separates two fluids, holding in -solution different ingredients, the fluids pass through the -membrane in an imperceptible manner, and mix or exchange -their elements. The force which produces these effects is -capable of balancing a very considerable pressure. It -appears, moreover, to depend, at least among other causes, -upon attractions operating between the elements of the -solids and the fluids, as well as between the different -fluids; and this force, though thus apparently of a -mechanical and chemical nature, probably has considerable -influence in vital phenomena. - -13. But still, though Endosmose may account in part for -absorption in some cases, it is certain that there is some -other vital force at work in this process. There must be, as -Müller says[80\9], 'an organic attraction of a kind hitherto -unknown.' 'If absorption,' he adds[81\9], is to be explained -in a manner analogous to {213} the laws of endosmose, it -must be supposed that a chemical affinity, resulting from -the vital process itself, is exerted between the chyme in -the intestines and the chyle in the lacteals, by which the -chyle is enabled to attract the chyme without being itself -attracted by it. But such affinity or attraction would be of -a vital nature, since it does not exist after death.' - -[Note 80\9: _Physiology_, p. 299.] - -[Note 81\9: _Ib._ p. 301.] - -14. If the force of absorption be thus mysterious in its -nature, the force of _Secretion_ is still more so. In this -case we have an organ filled with a fine net-work of -blood-vessels, and in the cavities of some _gland_, or open -part, we have a new fluid formed, of a kind altogether -different from the blood itself. It is easily shown that -this cannot be explained by any action of pores or capillary -tubes. But what conception can we form of the forces by -which such a change is produced? Here, again, I shall borrow -the expressions of Müller, as presenting the last result of -modern physiology. He says[82\9], 'The more probable -supposition is, that by virtue of imbibition, or the general -organic porosity, the fluid portion of the blood becomes -diffused through the tissue of the secreting organ; that the -external surface of the glandular canals exerts a chemical -attraction on the elements of the fluid, infusing into them -at the same time a tendency to unite in new combinations; -and then repels them in a manner which is certainly quite -inexplicable, towards the inner surface of the secreting -membrane, or glandular canals.' 'Although quite unsupported -by facts,' he adds, 'this theory of attraction and repulsion -is not without its analogy in physical phenomena; and it -would appear that very similar powers effect the elimination -of the fluid in secretion, and cause it to be taken up by -the lymphatics in absorption.' He elsewhere says[83\9], -'Absorption seems to depend on an attraction the nature of -which is unknown, but of which the very counterpart, as it -were, takes place in secretion; the fluids altered by the -secreting action being repelled towards the free side or -open surface only of the {214} secreting membranes, and then -pressed forwards by the successive portions of the fluids -secreted.' - -[Note 82\9: _Physiology_, p. 464.] - -[Note 83\9: _Ib._ p. 301.] - -15. With regard to the forces which produce the _Motion_ of -absorbed or secreted fluids along their destined course, it -may be seen, from the last quoted sentence, that the same -vital force which changes the nature, also produces the -movement of the substance. The fluids are pressed forwards -by the successive portions absorbed or secreted. That this -is the sole cause, or at least a very powerful cause, of the -motion of the nutritive fluids in organic bodies, is easily -shown by experience. It is found[84\9] that the organs which -effect the ascent of the sap in trees during the spring are -the terminal parts of the roots; that the whole force by -which the sap is impelled upwards is the _vis a tergo_, as -it has been called, the force pushing from behind, exerted -in the roots. 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 appropriates. And the same may most probably be -taken for the cause of the motion of the lymph and chyle; at -least, Müller says[85\9] that no other motive power has been -detected which impels those fluids in their course. - -[Note 84\9: Müller, p. 300.] - -[Note 85\9: _Ib._ p. 254.] - -Thus, though we must confess the Vital Force concerned in -Assimilation and Secretion to be unknown in its nature, we -still obtain a view of some of the attributes which it -involves. It has mechanical efficacy, producing motions, -often such as would require great mechanical force. But it -exerts at the same point both an attraction and a repulsion, -attracting matter on one side, and repelling it on the -other; and in this circumstance it differs entirely from -mechanical forces. Again, it is not only mechanical but -chemical, producing a complete change in the nature of the -substance on which it acts; to which we must add that the -changes produced by the vital forces are such as, for the -most part, our artificial chemistry {215} cannot imitate. -But, again, by the action of the vital force at any point of -an organ, not only are fluids made to pass, and changed as -they pass, but the organ itself is maintained and -strengthened, so as to continue or to increase its -operation: and thus the vital energy supports its activity -by its action, and is augmented by being exerted. - -We have thus endeavoured to obtain a view of some of the -peculiar characters which belong to the Force of Organic -Assimilation;--the Force by which life is kept up, conceived -in the most elementary form to which we can reduce it by -observation and contemplation. It appears that it is a force -which not only produces motion and chemical change, but also -_vitalizes_ the matter on which it acts, giving to it the -power of producing like changes on other matter, and so on -indefinitely. It not only circulates the particles of -matter, but puts them in a stream of which the flow is -development as well as movement. - -The force of Organic Assimilation being thus conceived, it -becomes instructive to compare it with the force concerned -in Generation, which we shall therefore endeavour to do. - - -SECT. IV.--_Attempts to conceive the Process of Generation._ - -16. At first sight the function of Nutrition appears very -different from the function of Generation. In the former -case we have merely the existing organs maintained or -enlarged, and their action continued; in the latter, we have -a new individual produced and extricated from the parent. -The term _Reproduction_ has, no doubt, been applied, by -different writers, to both these functions;--to the -processes by which an organ when mutilated, is restored by -the forces of the living body, and to the process by which a -new generation of individuals is produced which may be -considered as taking the place of the old generation, as -these are gradually removed by death. But these are -obviously different senses of the word. In the latter case, -the {216} term _Reproduction_ is figuratively used; for the -_same_ individuals are not reproduced; but the species is -kept up by the propagation of new individuals, as in -nutrition the organ is kept up by the assimilation of new -matter. To escape ambiguity, I shall avoid using the term -_Reproduction_ in the sense of _Propagation_. - -17. In Nutrition, as we have seen, the matter, which from -being at first extraneous, is appropriated by the living -system, and directed to the sustentation of the organs, -undergoes a series of changes of which the detail eludes our -observation and apprehension. The nutriment which we receive -contributes to the growth of flesh and bone, viscera and -organs of sense. But we cannot trace in its gradual changes -a visible preparation for its final office. The portion of -matter which is destined to repair the waste of the eye or -the skin, is not found assuming a likeness to the parts of -the eye or the structure of the skin, as it comes near the -place where it is moulded into its ultimate form. The new -parts are insinuated among the old ones, in an obscure and -imperceptible matter. We can trace their progress only by -their effects. The organs _are_ nourished, and that is -almost all we can learn: we cannot discover _how_ this is -done. We cannot follow nature through a series of manifest -preparations and processes to this result. - -18. In Generation the case is quite different. The young -being is formed gradually and by a series of distinguishable -processes. It is included within the parent before it is -extruded, and approaches more or less to the likeness of the -parent before it is detached. While it is still an embryo, -it shares in the nutriment which circulates through the -system of the mother; but its destination is already clear. -While the new and the old parts, in every other portion of -the mother, are undistinguishably mixed together, this new -part, the fœtus, is clearly distinct from the rest of the -system, and becomes rapidly more and more so, as the time -goes on. And thus there is formed, not a new part, but a new -whole; it is not an organ which is kept up, but an offspring -which is prepared. The progeny is {217} included in the -parent, and is gradually fitted to be separated from it. The -young is at first only the development of a part of the -organization of the mother;--of a germ, an ovule. But it is -not developed like other organs, retaining its general form. -It does not become merely a larger bud, a larger ovule; it -is entirely changed; it becomes--from a bud--a blossom, a -flower, a fruit, a seed; from an ovule it becomes an egg, a -chick, a bird; or it may be, a fœtus, a child. The original -rudiment is not merely nourished, but unfolded and -transformed through the most marked and remote changes, -gradually tending to the form of the new individual. - -19. But this is not all. The fœtus is, as we have said, a -development of a portion of the mother's organization. But -the fœtus (supposing it female) is a likeness of the mother. -The mother, even before conception, contains within herself -the germs of her progeny; the female fœtus, therefore, at a -certain stage of development, will contain also the germs of -possible progeny; and thus we may have the germs of future -generations, pre-existing and included successively within -one another. And this state of things, which thus suggests -itself to us as possible, is found to be the case in facts -which observation supplies. Anatomists have traced ovules in -the unborn fœtus, and thus we have three generations -included one within another. - -20. Supposing we were to stop here, the process of -propagation might appear to be altogether different from -that of nutrition. The latter, as we have seen, may be in -some measure illustrated by the image of a _vortex_; the -former has been represented by the image of a series of -germs, _sheathed_ one within another successively, and this -without any limit. This view of the subject has been termed -the doctrine of the _Pre-existence of germs_; and has been -designated by German writers by a term 'Einschachtelungs-theorie' -descriptive of the successive sheathing of which I have -spoken. Imitating this term, we may call it _the Theory of -successive inclusion_. It has always had many {218} -adherents; and has been, perhaps, up to the present time, -the most current opinion on the subject of generation. -Cuvier inclines to this opinion[86\9]. 'Fixed forms -perpetuating themselves by generation distinguish the -species of living things. These forms do not produce -themselves, do not change themselves. Life supposes them to -exist already; its flame can be lighted only in organization -previously prepared; and the most profound meditations and -the most delicate researches terminate alike in the mystery -of the _pre-existence of germs_.' - -[Note 86\9: _Règne Animal_, p. 20.] - -21. Yet this doctrine is full of difficulty. It is, as -Cuvier says, a mysterious view of the subject;--so -mysterious, that it can hardly be accepted by us, who seek -distinct conceptions as the basis of our philosophy. Can it -be true, not only that the germ of the offspring is -originally included in the parent, but also the germs of -_its_ progeny, and so on without limit:--so that each -fruitful individual contains in itself an infinite -collection of future possible individuals;--a reserve of -infinite succeeding generations? This is hard to admit. Have -we no alternative? What is the opposite doctrine? - -22. The opposite doctrine deserves at least some notice. It -extends, to the production of a new individual, the -conception of growth by nutrition. According to this view, -we suppose propagation to take place, not as in the view -just spoken of, by inclusion and extrusion, but by -assimilation and development;--not by the material -pre-existence of germs, but by the communication of vital -forces to new matter. This opinion appears to be entertained -by some of the most eminent physiologists of the present -time. Thus, Müller says, 'The organic force is also -creative. The organic force which resides in the whole, and -on which the existence of each part depends, has also the -property of generating, from organic matter, the parts -necessary to the whole.' Life, he adds, is not merely a -harmony of the {219} parts. On the contrary, the harmonious -action of the parts subsists only by the influence of a -force pervading all parts of the body. 'This force exists -before the harmonizing parts, which are in fact formed by it -during the development of the embryo.' And again; 'The -creative force exists in the germ, and creates in it the -essential force of the future animal. The germ is -_potentially_ the whole animal: during the development of -the germ the parts which constitute the actual whole are -produced.' - -23. In this view, we extend to the reproduction of an -individual the same conception of organic assimilation which -we have already arrived at, as the best notion we can form -of the force by which the reproduction and sustentation of -parts takes place. And is not such an extension really very -consistent? If a living thing can appropriate to itself -extraneous matter, invest it with its own functions, and -thus put it in the stream of constant development, may we -not conceive the development of a new _whole_ to take place -in this way as well as of a _part_? If the organized being -can infuse into new matter its vital forces, is there any -contradiction in supposing this infusion to take place in -the full measure which is requisite for the production of a -new individual? The force of organic assimilation is -transferred to the very matter on which it acts; it may be -transferred so that the operation of the forces produces not -only an organ, but a system of organs. - -24. This identification of the forces which operate in -Nutrition and Generation may at first seem forced and -obscure, in consequence of the very strong apparent -differences of the two processes which we have already -noticed. But this defect in the doctrine is remedied by the -consideration of what may be considered as intermediate -cases. It is not true that, in the nutrition of special -organs, the matter is always conveyed to its ultimate -destination without being on its way moulded into the form -which it is finally to bear, as the embryo is moulded into -the form of the {220} future individual. On the contrary, -there are cases in which the waste of the organs is supplied -by the growth of new ones, which are prepared and formed -before they are used, just as the offspring is prepared and -formed before it is separated from the parent. This is the -case with the teeth of many animals, and especially with the -teeth of animals of the crocodile kind. Young teeth grow -near the root of the old ones, like buds on the stem of a -plant; and as these become fully developed, they take the -place of the parent tooth when that dies and is cast away. -And these new teeth in their turn are succeeded by others -which germinate from them. Several generations of such -teeth, it is said as many as four, have been detected by -anatomists, visibly existing at the same time; just as -several generations of germs of individuals have been, as we -already stated, observed included in one another. But this -case of the teeth appears to show very strikingly how -insufficient such observations are to establish the doctrine -of successive inclusion, or of the pre-existence of germs. -Are we to suppose that every crocodile's tooth includes in -itself the germs of an infinite number of possible teeth, as -in the theory of pre-existing germs every individual -includes an infinite number of individuals? If this be true -of teeth, we must suppose that organ to follow laws entirely -different from almost every other organ; for no one would -apply to the other organs in general such a theory of -reproduction. But if such a theory be not maintained -respecting the teeth, how can we maintain the theory of the -pre-existing germs of individuals, which has no -recommendation except that of accounting for exactly the -same phenomena? - -It would seem, then, that we are, by the closest -consideration of the subject, led to conceive the forces by -which generation is produced, as forces which vitalize -certain portions of matter, and thus prepare them for -development according to organic forms; and thus the -conception of this Generative Force is identified with the -conception of the Force of Organic Assimilation, to {221} -which we were led by the consideration of the process of -nutrition. - -I shall not attempt to give further distinctness and fixity -to this conception of one of the vital forces; but I shall -proceed to exemplify the same analysis of life by some -remarks upon another Vital Process, and the Forces of which -it exhibits the operation. - - - -{{222}} -CHAPTER V. - -ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES, -_continued_.--VOLUNTARY MOTION. - - -1. WE formerly noticed the distinctions of _organic_ and -_animal_ functions, organic and animal forces, as one of the -most marked distinctions to which physiologists have been -led in their analysis of the vital powers. I have now taken -one of the former, the _organic_ class of functions, namely, -Nutrition; and have endeavoured to point out in some measure -the peculiar nature of the vital forces by which this -function is carried on. It may serve to show the extent and -the difficulty of this subject, if, before quitting it, I -offer a few remarks suggested by a function belonging to the -other class, the _animal_ functions. This I shall briefly do -with respect to _Voluntary Motion_. - -2. In the History of Physiology, I have already related the -progress of the researches by which the organs employed in -voluntary motion became known to anatomists. It was -ascertained to the satisfaction of all physiologists, that -the immediate agents in such motion are the muscles; that -the muscles are in some way contracted, when the nerves -convey to them the agency of the will; and that thus the -limbs are moved. It was ascertained, also, that the nerves -convey sensations from the organs of sense inwards, so as to -make these sensations the object of the animal's -consciousness. In man and the higher animals, these -impressions upon the nerves are all conveyed to one internal -organ, the brain; and from this organ all impressions of the -will appear to proceed; and thus the brain is {223} the -center of animal life, towards which sensations converge, -and from which volitions diverge. - -But this being the process, we are led to inquire how far we -can obtain any knowledge, or form any conception, of the -vital forces by means of which the process is carried on. -And here I have further stated in the History[87\9], that -the transfer of sensations and volitions along the nerves -was often represented as consisting in the motion of a -Nervous Fluid. I have related that the hypothesis of such a -fluid, conveying its impressions either by motions of -translation or of vibration, was countenanced by many great -names, as Newton, Haller, and even Cuvier. But I have -ventured to express my doubt whether this hypothesis can -have much value: 'for,' I have said, 'this principle cannot -be mechanical, chemical, or physical, and therefore cannot -be better understood by embodying it in a fluid. The -difficulty we have in conceiving what the force _is_, is not -got rid of by explaining the machinery by which it is -_transferred_.' - -[Note 87\9: _Hist. Ind. Sc._ b. xvii. c. v. s. 2.] - -3. I may add, that no succeeding biological researches -appear to have diminished the force of these considerations. -In modern times, attempts have repeatedly been made to -identify the nervous fluid with electricity or galvanism. -But these attempts have not been satisfactory or conclusive -of the truth of such an identity: and Professor Müller -probably speaks the judgment of the most judicious -physiologists, when he states it as his opinion, after -examining the evidence[88\9], 'That the vital actions of the -nerves are not attended with the development of any galvanic -currents which our instruments can detect; and that the laws -of action of the nervous principle are totally different -from those of electricity.' - -[Note 88\9: _Elem. Phys._ p. 640.] - -That the powers by which the nerves are the instruments of -sensation, and the muscles of motion, are vital endowments, -incapable of being expressed or explained by any comparison -with mechanical, chemical, and electrical forces, is the -result which we should {224} expect to find, judging from -the whole analogy of science; and which thus is confirmed by -the history of physiology up to the present time. We -naturally, then, turn to inquire whether such peculiar vital -powers have been brought into view with any distinctness and -clearness. - -4. The property by which muscles, under proper stimulation, -contract and produce motion, has been termed _Irritability_ -or _Contractility_; the property by which nerves are -susceptible of their appropriate impressions has been termed -_Sensibility_. A very few words on each of these subjects -must suffice. - -_Irritability._--I have, in the History of Physiology[89\9], -noticed that Glisson, a Cambridge professor, distinguished -the Irritation of muscles as a peculiar property, different -from any merely mechanical or physical action. I have -mentioned, also, that he divides Irritation into _natural_, -_vital_, and _animal_; and points out, though briefly, the -graduated differences of Irritability in different organs. -Although these opinions did not at first attract much -notice, about seventy years afterwards attention was -powerfully called to this vital force, _Irritability_, by -Haller. I shall borrow Sprengel's reflections on this subject. - -[Note 89\9: _Hist. Ind. Sc._ b. xvii. c. v.] - -'Hitherto men had been led to see more and more clearly that -the cause of the bodily functions, the fundamental power of -the animal frame, is not to be sought in the mechanism, and -still less in the mixture of the parts. In this conviction, -they had had recourse partly to the quite supersensuous -principle of the Soul, partly to the half-material principle -of the Animal Spirits, in order to explain the bodily -motions. Glisson alone saw the necessity of assuming an -Original Power in the fibres, which, independent of the -influence of the animal spirits, should produce contraction -in them. And Gorter first held that this Original Power was -not to be confined to the muscles, but to be extended to all -parts of the living body. {225} - -'But as yet the laws of this Power were not known, nor had -men come to an understanding whether it were fully distinct -from the elasticity of the parts, or by what causes it was -put in action. They had neither instituted observations nor -experiments which established its relation to other assumed -forces of the body. There was still wanting a determination -of the peculiar seat of this power, and experiments to trace -its gradual differences in different parts of the body. In -addition to other causes, the necessity of the assumption of -such a power was felt the more, in consequence of the -prevalence of Leibnitz's doctrine of the activity of matter; -but it was an occult quality, and remained so till Haller, -by numerous experiments and solid observations, placed in a -clear light the peculiarities of the powers of the animal body.' - -5. Perhaps, however, Haller did more in the way of -determining experimentally the limits and details of the -application of this idea of Irritability as a peculiar -attribute, than in developing the Idea itself. In that way -his merits were great. As early as the year 1739, he -published his opinion upon Irritability as the cause of -muscular motion, which he promulgated again in 1743. But -from the year 1747 he was more attentive to the -peculiarities of Irritability, and its difference from the -effect of the nerves. In the first edition of his -_Physiology_, which appeared in 1747, he distinguished three -kinds of Force in muscles,--the Dead Force, the Innate -Force, and the Nervous Power. The first is identical with -the elastic force of dead matter, and remains even after -death. The _innate force_ continues only a short time after -death, and discloses itself especially by alternate -oscillations; the motions which arise from this are much -more lively than those which arise from mere elasticity: -they are not excited by tension, nor by pressure, nor by any -mechanical alteration, but only by _irritation_. The -_nervous force_ of the muscle is imparted to it from without -by the nerves; it preserves the _irritability_, which cannot -long subsist without the influence of the nervous force, but -is not identical with it. {226} - -In the year 1752, Haller laid before the Society of -Göttingen the result of one hundred and ninety experiments; -from which it appears to what parts of the animal system -Irritability and Nervous Power belong. These I need not -enumerate. He also investigated with care its gradations in -those parts which do possess it. Thus the heart possesses it -in the highest degree, and other organs follow in their -order. - -6. Haller's doctrine was, that there resides in the muscles -a peculiar vital power by which they contract, and that this -power is distinct from the attributes of the nerves. And -this doctrine has been accepted by the best physiologists of -modern times. 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 _Contractility_. This accordingly was done; it is, for -example, the phraseology used by Bichat. By speaking of -_animal sensibility_ and _animal contractility_, the passive -and the active element of the processes of animal life are -clearly separated and opposed to each other. The sensations -which we feel, and the muscular action which we exert, may -be closely and inseparably connected, yet still they are -clearly distinguishable. We can easily in our apprehension -separate the titillation felt in the nose on taking snuff, -from the action of the muscles in sneezing; or the -perception of an object falling towards the eye, from the -exertion which shuts the eye-lid; although in these cases -the passive and active part of the process are almost or -quite inseparable in fact. And this clear separation of the -active from the passive power is something, it would seem, -peculiar to the Animal Vital Powers; it is a character by -which they differ, not only from mechanical, chemical, and -all other merely physical forces, but even from Organic -Vital Powers. - -7. But this difference between the Animal and the Organic -Vital Powers requires to be further insisted upon, for it -appears to have been overlooked or denied by very eminent -physiologists. For instance, Bichat classifies the Vital -Powers as Animal Sensibility, {227} Animal Contractility, -Organic Sensibility, Organic Contractility. - -Now the view which suggests itself to us, in agreement with -what has been said, is this:--that though Animal Sensibility -and Animal Contractility are clearly and certainly distinct, -Organic Sensibility and Organic Contractility are neither -separable in fact nor in our conception, but together make -up a single Vital Power. That they are not separable in fact -is, indeed, acknowledged by Bichat himself. 'The organic -contractility,' he says[90\9], 'can never be separated from -the sensibility of the same kind; the reaction of the -excreting tubes is immediately connected with the action -which the secreted fluids exercise upon them: the -contraction of the heart must necessarily succeed the influx -of the blood into it.' It is not wonderful, therefore, that -it should have happened, as he complains, that 'authors have -by no means separated these two things, either in their -consideration or in language.' We cannot avoid asking, Are -Organic Sensibility and Organic Contractility really -anything more than two different aspects of the same thing, -like action and reaction in mechanics, which are only two -ways of considering the action which takes place at a point; -or like the positive and negative electricities, which, as -we have seen, always co-exist and correspond to each other? - -[Note 90\9: _Life and Death_, p. 94.] - -8. But we may observe, moreover, that Bichat, by his use of -the term Contractility, includes in it powers to which it -cannot with any propriety be applied. Why should we suppose -that the vital powers of absorption, secretion, -assimilation, are of such a nature that the name -_contractility_ may be employed to describe them? We have -seen, in the last chapter, that the most careful study of -these powers leads us to conceive them in a manner -altogether removed from any notion of contraction. Is it not -then an abuse of language which cannot possibly lead to -anything but {228} confusion, to write thus[91\9]: 'The -insensible organic contractility is that, by virtue of which -the excreting tubes react upon their respective fluids, the -secreting organs upon the blood which flows into them, the -parts where nutrition is performed upon the nutritive -juices, and the lymphatics upon the substances which excite -their open extremities'? In the same manner he -ascribes[92\9] to the peculiar sensibility of each organ the -peculiarity of its products and operations. An increased -absorption is produced by an increased susceptibility of the -'absorbent orifices.' And thus, in this view, each organic -power may be contemplated either as sensibility or as -contractility, and may be supposed to be rendered more -intense by magnifying either of these its aspects; although, -in fact, neither can be conceived to be increased without an -exactly commensurate increase of the other. - -[Note 91\9: _Life and Death_, p. 95.] - -[Note 92\9: _Ib._ p. 90.] - -9. This opinion, unfounded as it thus appears to be, that -all the different organic vital powers are merely different -kinds of Contractility or Excitability, was connected with -the doctrines of Brown and his followers, which were so -celebrated in the last century, that all diseases arise from -increase or from diminution of the Vital Force. The -considerations which have already offered themselves would -lead us to assent to the judgment which Cuvier has -pronounced upon this system. 'The theory of excitation,' he -says, 'so celebrated in these later times by its influence -upon pathology and therapeutick, is at bottom only a -modification of that, in which, including under a common -name Sensibility and Irritability,' and we may add, applying -this name to all the Vital Powers, 'the speculator takes -refuge in an abstraction so wide, that if, by it, he -simplifies medicine, he by it annihilates all positive -physiology[93\9].' - -[Note 93\9: _Hist. des Sc. Nat. depuis_ 1789, i. 219.] - -10. The separation of the nervous influence and the muscular -irritability, although it has led to many highly instructive -speculations, is not without its {229} difficulties, when -viewed with reference to the Idea of Vital Power. If the -irritability of each muscle reside in the muscle itself, how -does it differ from a mere mechanical force, as elasticity? -But, in point of fact, 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 system. -No muscle, or other part, removed from the body, _long_ -preserves its irritability. This power cannot subsist -permanently, except in connexion with an organic whole. This -condition peculiarly constitutes irritability a _living_ -force: and this condition would be satisfied by considering -the force as derived from the nervous system; but it appears -that though the nervous system has the most important -influence upon all vital actions, the muscular irritability -must needs be considered as something distinct. And thus the -Irritability or Contractility of the muscle is a peculiar -endowment of the texture, but it is at the same time an -endowment which can only co-exist with life; it is, in -short, a peculiar Vital Power. - -11. This necessity of the union of the muscle with the whole -nervous system, in order that it may possess irritability, -was the meaning of the true part of Stahl's psychical -doctrine; and the reason why he and his adherents persisted -in asserting the power of the soul even over involuntary -motions. This doctrine was the source of much controversy in -later times. - -'But,' says Cuvier[94\9], 'this opposition of opinion may be -reconciled by the intimate union of the nervous substance -with the fibre and the other contractile organic elements, -and by their reciprocal action;--doctrines which had been -presented with so much probability by physiologists of the -Scotch school, but which were elevated above the rank of -hypotheses only by the observations of more recent times. - -[Note 94\9: _Hist. des Sc. Nat. depuis_ 1789, i. 213.] - -'The fibre does not contract by itself, but by the influence -of the nervous filaments, which are always united with it. -The change which produces the {230} contraction cannot take -place without the concurrence of both these substances; and -it is further necessary that it should be occasioned each -time by an exterior cause, by a stimulant. - -'The Will is one of these stimulants; but it only excites -the Irritability, it does not constitute it; for in the case -of persons paralytic from apoplexy, the Irritability -remains, though the power of the Will over it is gone. Thus -_irritability_ depends in part on the _nerve_, but not on -the _sensibility_: this last is another property, still more -admirable and occult than the irritability; but it is only -one among several functions of the nervous system. It would -be an abuse of words to extend this denomination to -functions unaccompanied by perception.' - -12. Supposing, then, that Contractility is established as a -peculiar Vital Power residing in the muscles, we may ask -whether we can trace with any further exactness the seat and -nature of this power. It would be unsuitable to the nature -of the present work to dwell upon the anatomical discussions -bearing upon this point. I will only remark that some -anatomists maintain[95\9] that muscles are contracted by -those fibres assuming a zigzag form, which at first were -straight. Others (Professor Owen and Dr. A. Thompson) doubt -the accuracy of this observation; and conceive that the -muscular fibre becomes shorter and thicker, but does not -deviate from a right line. We may remark that the latter -kind of action appears to be more elementary in its nature. -We can, as a matter of geometry, conceive a straight line -thrown into a zigzag shape by muscular contractions taking -place between remote parts of it; but it is difficult to -conceive by what _elementary_ mode of action a straight -fibre could bend itself at certain points, and at certain -points only; since the elementary force must act at every -point of the fibre, and not at certain selected points. - -[Note 95\9: Müller, _Elem. Phys._ p. 887.] - -13. A circumstance which remarkably marks the difference -between the vital force of Contractility, {231} inherent in -muscles, and any merely dead or mechanical force, is this; -that in assuming their contractile state, muscles exert a -tension which they could not themselves support or convey if -not strengthened by their vital irritability. They are -capable of raising weights by their exertion, which will -tear them asunder when the power of contraction is lost by -death. This has induced Cuvier and other physiologists[96\9] -to believe 'that in the moment of action, the particles that -compose a fibre, not only approach towards each other -longitudinally, but that their cohesive attraction becomes -instantaneously much greater than it was before: for without -such an increase of cohesive force, the tendency to shorten -could not, as it would appear, prevent the fibre from being -torn.' We see here the difficulty, or rather the -impossibility, of conceiving muscular contractility as a -mere mechanical force; and perhaps there is little hope of -any advantage by calling in the aid of chemical hypothesis -to solve the mechanical difficulty. Cuvier conjectures that -a sudden change in the chemical composition may thus so -quickly and powerfully augment the cohesion. But we may ask, -are not a chemical synthesis and analysis, suddenly -performed by a mere act of the will, as difficult to -conceive as a sudden increase and decrease of mechanical -power directly produced by the same cause? - -[Note 96\9: Prichard, _Vital Prin._ p. 126.] - -14. _Sensibility._ The nerves are the organs and channels of -Sensibility. By means of them we receive our sensations, -whether of mere pleasure and pain, or of qualities which we -ascribe to external objects, as a bitter taste, a sweet -odour, a shrill sound, a red colour, a hard or a hot feeling -of touch. Some of these sensations are but obscurely the -objects of our consciousness; as for example the feeling -which our feet have of the ground, or the sight which our -eyes have of neighbouring objects, when we walk in a -reverie. In these cases the sensations, though obscure, -exist; for they {232} serve to balance and guide us as we -walk. In other cases, our sensations are distinctly and -directly the objects of our attention. - -But our Sensations, as we have already said, we ascribe as -Qualities to external objects. By our senses we perceive -objects, and thus our _sensations_ become _perceptions_. We -have not only the sensation of _round_, _purple_, and -_green_, repeated and varied, but the perception of a _bunch -of grapes_ partly ripe and partly unripe. We have not only -sensations of noise and of variously-coloured specks rapidly -changing their places, but we have perceptions, by sound and -sight, of a stone rolling down the hill and crushing the -shrubs in its path. We scarcely ever dwell upon our -Sensations; our thoughts are employed upon Objects. We -regard the impressions upon our nerves, not for what they -_are_, but for what they _tell_ us. - -But in what Language do the impressions upon the nerves thus -speak to us of an external world,--of the forms and -qualities and actions of objects? How is it that by the aid -of our nervous system we become acquainted not only with -impressions but with _things_; that we learn not only the -relation of objects to us, but to one another? - -15. It has been shown at some length in the previous Books, -that the mode in which Sensations are connected in our minds -so as to convey to us the knowledge of Objects and their -Relations, is by being contemplated with reference to -_Ideas_. Our Sensations, connected by the Idea of Space, -become Figures; connected by the Idea of Time, they become -Causes and Effects; connected by the Idea of Resemblance, -they become Individuals and Kinds; connected by the Idea of -Organization, they become Living Things. It has been shown -that without these Ideas there can be no connexion among our -sensations, and therefore no perception of Figure, Action, -Kind, or in short, of bodies under any aspect whatever. -Sensations are the rude _Matter_ of our perceptions; and are -nothing, except so far as they have _Form_ given them by -Ideas. {233} But thus moulded by our Ideas, Sensation -becomes the source of an endless store of important -Knowledge of every possible kind. - -16. But one of the most obvious uses of our perceptions and -our knowledge is to direct our Actions. It is suitable to -the condition of our being that when we perceive a bunch of -grapes, we should be able to pluck and eat the ripe ones; -that when we perceive a stone rushing down the side of a -hill, we should be able to move so as to avoid it. And this -must be done by moving our limbs; in short, by the use of -our muscles. And thus Sensation leads, not directly, but -through the medium of Ideas, to muscular Contraction. I say -that sensation and Muscular action are in such cases -connected through the medium of Ideas. For when we proceed -to pluck the grape which we see, the _sensation_ does not -determine the motion of the hand by any necessary -geometrical or mechanical conditions, as an impression made -upon a machine determines its motions; but the _perception_ -leads us to stretch forth the hand to that part of space, -wherever it is, where we _know_ that the grape is; and this, -not in any determinate path, but, it may be, avoiding or -removing intervening obstacles, which we also _perceive_. -There is in every such case a connexion between the -sensation and the resulting action, not of a material but of -a mental kind. The cause and the effect are bound together, -not by physical but by intellectual ties. - -17. And thus in such cases, between the two _vital_ -operations, Sensation and Muscular Action, there intervenes, -as an intermediate step, Perception or Knowledge, which is -not merely vital but _ideal_. But this is not all; there is -still another mental part of the process which may be -readily distinguished from that which we have described. An -act of the _Will_, a Volition, is that, in the Mind, which -immediately determines the action of the Muscles of the -Body. And thus Will intervenes between Knowledge and Action; -and the cycle of operations which take place when animals -act with reference to external objects is {234} -this:--Sensation, Perception, Volition, Muscular -Contraction. - -18. To attempt further to analyse the mental part of this -cycle does not belong to the present part of our work. But -we may remark here, as we have already remarked in the -History[97\9], how irresistibly we are led by physiological -researches into the domain of thought and mind. We pass from -the body to the soul, from physics to metaphysics; from -biology to psychology; from things to persons; from nouns to -pronouns. I have there noticed the manner in which Cuvier -expresses this transition by the introduction of the -pronoun: 'The impression of external objects upon the ME, -the production of a sensation, of an image, is a mystery -impenetrable to our thoughts.' - -[Note 97\9: _Hist. Ind. Sc._ b. xvii. c. v. s. 2.] - -19. But to return to the merely biological part of our -speculations. We have arrived, it will be perceived, at this -result: that in animal actions there intervenes between the -two terms of Sensation and Muscular Contraction, an -intermediate process; which may be described as a -communication to and from a Center. The Center is the seat -of the sentient and volent faculties, and is of a -_hyperphysical_ nature. 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 biology. This indeed may be -taken as the peculiar character of animal, as distinguished -from merely _organic_ powers. Accordingly, it is so stated -by Bichat. For although he superfluously, as I have tried to -show, introduces into his list of vital powers an organic -sensibility, he still draws the distinction of which I have -spoken; 'in the animal life, Sensibility is the faculty of -receiving an Impression _plus_ that of referring it to a -common Center[98\9].' - -[Note 98\9: _Life and Death_, p. 84.] - -20. But since Sensibility and Contractility are thus -connected by reference to a common Center, we may ask, -before quitting the subject, what are the different forms -which this reference assumes? Is the connexion {235} always -attended by the distinct steps of Knowledge and Will,--by a -clear act of consciousness, as in the case which we have -taken, of plucking a grape; or may these steps become -obscure, or vanish altogether? - -We need not further illustrate the _conscious_ connexion. -Such actions as we have described are called _voluntary_ -actions. In extreme cases, the mental part of the process is -obvious enough. But we may gradually pass from these to -cases in which the mental operation is more and more obscure. - -In walking, in speaking, in eating, in breathing, our -muscular exertions are directed by our sensations and -perceptions: yet in such processes, how dimly are we -conscious of perceptive and directive power! How the mind -should be able to exercise such a power, and yet should be -scarcely or not at all conscious of its exercise, is a very -curious problem. But in all or in most of the instances just -mentioned, the solution of this problem appears to depend -upon psychological rather than biological principles, and -therefore does not belong to this place. - -21. But in cases at the other extreme (unconscious actions) -the mental part of the operation vanishes altogether. In -many animals, even after decapitation, the limbs shrink when -irritated. The motions of the iris are determined by the -influence of light on our eyes, without our being aware of -the motions. Here Sensations produce Motions, but with no -trace of intervening Perception or Will. The Sensation -appears to be _reflected_ back from the central element of -animal life, in the form of a Muscular Contraction; but in -this case the Sensation is not modified or regulated by any -_Idea_. These reflected motions have no reference to -relations of space or force among surrounding objects. They -are blind and involuntary, like the movements of convulsion, -depending for direction and amount only on the position and -circumstances of the limb itself with its muscles. Here the -Centre from which the reflection takes place is merely -_animal_, not intellectual. - -In this case some physiologists have doubted whether the -reflection of the sensation in the form of a muscular {236} -contraction does really take place from the Center; and have -conceived that sensorial impressions might affect motor -nerves without any communication with the nervous Center. -But on this subject we may, I conceive, with safety adopt -the decision of Professor Müller, deliberately given after a -careful examination of the subject: 'When impressions made -by the action of external stimuli on sensitive nerves give -rise to motions in other parts, these motions are never the -result of the _direct_ reaction of the sensitive and motor -fibres of the nerves on each other; the irritation is -conveyed by the sensitive fibres to the brain and spinal -cord, and is by these communicated to the motor fibres.' - -22. Thus we have two extreme cases of the connexion of -sensation with muscular action; in one of which the -connexion clearly _is_, and in the other it as clearly _is -not_, determined by relations of Ideas, in its transit -through the nervous Center. There is another highly curious -case standing intermediate between these two, and extremely -difficult to refer to either. I speak of the case of _Instinct_. - -Instinct leads to actions which are _such as if they were -determined by Ideas_. The lamb follows its mother by -instinct; but the motions by which it does this, the special -muscular exertions, depend entirely upon the geometrical and -mechanical relations of external bodies, as the form of the -ground, and the force of the wind. The contractions of the -muscles which are requisite in order that the creature may -obey its instinct, vary with every variation of these -external conditions;--are not determined by any rule or -necessity, but by properties of Space and Force. Thus the -action is not governed by Sensations directly, but by -sensations moulded by Ideas. And the same is the case with -other cases of instinct. The dog hunts by instinct; but he -hunts certain kinds of animals merely, thus showing that his -instinct acts according to Resemblances and Differences; he -crosses the field repeatedly to find the track of his prey -by scent; thus recognizing the relations of Space with -reference to the track; he leaps, adjusting his Force to -{237} the distance and height of the leap with mechanical -precision; and thus he practically recognizes the Ideas of -Resemblance, Space, and Force. - -But have animals such Ideas? In any proper sense in which we -can speak of possessing Ideas, it appears plain that they -have not. Animals cannot, at any time, be said properly to -possess ideas, for ideas imply the possibility of -_speculative_ knowledge. - -23. But even if we allow to animals only the _practical_ -possession of Ideas, we have still a great difficulty -remaining. In the case of man, his ideas are unfolded -gradually by his intercourse with the external world. The -child learns to distinguish forms and positions by a -repeated and incessant use of his hands and eyes; he learns -to walk, to run, to leap, by slow and laborious degrees; he -distinguishes one man from another, and one animal from -another, only after repeated mistakes. Nor can we conceive -this to be otherwise. How should the child know at once what -muscles he is to exert in order to touch with his hand a -certain visible object? How should he know what muscles to -exert that he may stand and not fall, till he has tried -often? How should he learn to direct his attention to the -differences of different faces and persons, till he is -roused by some memory, or hope which implies memory? It -seems to us as if the sensations could not, without -considerable practice, be rightly referred to Ideas of -Space, Force, Resemblance, and the like. - -Yet that which thus appears impossible, is in fact done by -animals. The lamb almost immediately after its birth follows -its mother, accommodating the actions of its muscles to the -form of the ground. The chick, just escaped from the shell, -picks up a minute insect, directing its beak with the -greatest accuracy. Even the human infant seeks the breast -and exerts its muscles in sucking, almost as soon as it is -born. Hence, then, we see that Instinct produces at once -actions regulated by Ideas, or, at least, which take place -_as if_ they were regulated by Ideas; although the Ideas -cannot have been developed by exercise, and only appear to -exist so far as such actions are concerned. {238} - -24. The term _Instinct_ may properly be opposed to -_Insight_. The former implies an inward principle of action, -implanted within a creature and practically impelling it, -but not capable of being developed into a subject of -contemplation. While the instinctive actions of animals are -directed by such a principle, the deliberate actions of man -are governed by insight: he can contemplate the ideal -relations on which the result of his action depends. He can -in his mind map the path he will follow, and estimate the -force he will exert, and class the objects he has to deal -with, and determine his actions by the relations which he -thus has present to his mind. He thus possesses Ideas not -only practically, but speculatively. And knowing that the -Ideas by which he commonly directs his actions, Space, -Cause, Resemblance, and the like, 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 infancy, and that these Ideas are capable -of being still further unfolded into long trains of -speculative truth, he is unable to conceive the manner in -which animals possess such Ideas as their instinctive -actions disclose:--Ideas which neither require to be -unfolded nor admit of unfolding; which are adequate for -practical purposes without any previous exercise, and -inadequate for speculative purposes with whatever labour -cultivated. - -I have ventured to make these few remarks on Instinct since -it may, perhaps, justly be considered as the last province -of Biology, where we reach the boundary line of Psychology. -I have now, before quitting this subject, only one other -principle to speak of. - - - -{{239}} -CHAPTER VI. - -OF THE IDEA OF FINAL CAUSES. - - -1. BY an examination of those notions which enter into all -our reasonings and judgments on living things, it appeared -that we conceive animal life as a vortex or cycle of moving -matter in which the form of the vortex determines the -motions, and these motions again support the form of the -vortex: the stationary parts circulate the fluids, and the -fluids nourish the permanent parts. Each portion ministers -to the others, each depends upon the other. The parts make -up the whole, but the existence of the whole is essential to -the preservation of the parts. But parts existing under such -conditions are _organs_, and the whole is _organized_. This -is the fundamental conception of organization. 'Organized -beings,' says the physiologist[99\9], 'are composed of a -number of essential and mutually dependent parts.' 'An -organized product of nature,' says the great -metaphysician[100\9], 'is that in which all the parts are -mutually ends and means.' - -[Note 99\9: Müller, _Elem._ p. 18.] - -[Note 100\9: Kant, _Urtheilskraft_, p. 296.] - -2. It will be observed that we do not content ourselves with -saying that in such a whole, all the parts are _mutually -dependent_. This might be true even of a mechanical -structure; it would be easy to imagine a framework in which -each part should be necessary to the support of each of the -others; for example, an arch of several stones. But in such -a structure, the parts have no properties which they derive -from the whole. They are beams or stones when separate; they -are no more when joined. But the same is not the case in an -organized whole. The limb of an animal separated {240} from -the body, loses the properties of a limb, and soon ceases to -retain even its form. - -3. Nor do we content ourselves with saying that the parts -are _mutually causes and effects_. This is the case in -machinery. In a clock, the pendulum by means of the -escapement causes the descent of the weight, the weight by -the same escapement keeps up the motion of the pendulum. But -things of this kind may happen by accident. Stones slide -from a rock down the side of a hill and cause it to be -smooth; the smoothness of the slope causes stones still to -slide. Yet no one would call such a slide an organized -system. The system is organized, when the effects which take -place among the parts are _essential to our conception of -the whole_; when the whole would not _be_ a whole, nor the -parts, parts, except these effects were produced; when the -effects not only happen in fact, but are included in the -idea of the object; when they are not only seen, but -foreseen; not only expected, but intended: in short when, -instead of being causes and effects, they are _ends_ and -_means_, as they are termed in the above definition. - -Thus we necessarily include, in our Idea of Organization, -the notion of an End, a Purpose, a Design; or, to use -another phrase which has been peculiarly appropriated in -this case, a _Final Cause_. This idea of a Final Cause is an -essential condition in order to the pursuing our researches -respecting organized bodies. - -4. This Idea of Final Cause is not _deduced_ from the -phenomena by reasoning, but is _assumed_ as the only -condition under which we can reason on such subjects at all. -We do not deduce the Idea of Space, or Time, or efficient -Cause from the phenomena about us, but necessarily look at -phenomena as subordinate to these Ideas from the beginning -of our reasoning. It is true, our ideas of relations of -Space, and Time, and Force, may become much more clear by -our familiarizing ourselves with particular phenomena: but -still, the Fundamental Ideas are not generated, but -unfolded; not extracted from the external world, but evolved -from the world within. In like manner, in the contemplation -of organic structures, we consider {241} each part as -subservient to some use, and we cannot study the structure -as organic without such a conception. This notion of -adaptation,--this Idea of an End,--may become much more -clear and impressive by seeing it exemplified in particular -cases. But still, though suggested and evoked by special -cases, it is not furnished by them. If it be not supplied by -the mind itself, it can never be logically deduced from the -phenomena. It is not a portion of the facts which we study, -but it is a principle which connects, includes, and renders -them intelligible; as our other Fundamental Ideas do the -classes of facts to which they respectively apply. - -5. This has already been confirmed by reference to fact; in -the History of Physiology, 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 purpose;--that each member and organ not merely -produces a certain effect or answers a certain use, but is -so framed as to impress us with the persuasion that it was -constructed _for_ that use:--that it was _intended_ to -produce the effect. It was there seen that this persuasion -was repeatedly expressed in the most emphatic manner by -Galen;--that it directed the researches and led to the -discoveries of Harvey;--that it has always been dwelt upon -as a favourite contemplation, and followed as a certain -guide, by the best anatomists;--and that it is inculcated by -the physiologists of the profoundest views and most -extensive knowledge of our own time. All these persons have -deemed it a most certain and important principle of -physiology, that in every organized structure, plant or -animal, each intelligible part has its allotted -office:--each organ is designed for its appropriate -function:--that nature, in these cases, produces nothing in -vain: that, in short, each portion of the whole arrangement -has its _final cause_; an End to which it is adapted, and in -this End, the reason that it is where and what it is. - -6. This Notion of Design in organized bodies must, I say, be -supplied by the student of organization out of his own mind: -a truth which will become clearer if {242} we attend to the -most conspicuous and acknowledged instances of _design_. The -structure of the Eye, in which the parts are curiously -adjusted so as to produce a distinct image on the retina, as -in an optical instrument;--the Trochlear Muscle of the eye, -in which the tendon passes round a support and turns back, -like a rope round a pulley;--the prospective contrivances -for the preservation of animals, provided long before they -are wanted, as the Milk of the mother, the Teeth of the -child, the Eyes and Lungs of the fœtus:--these arrangements, -and innumerable others, call up in us a persuasion that -Design has entered into the plan of animal form and -progress. And if we bring in our minds this conception of -Design, nothing can more fully square with and fit it, than -such instances as these. But if we did not already possess -the Idea of Design;--if we had not had our notion of -mechanical contrivance awakened by inspection of optical -instruments, or pulleys, or in some other way:--if we had -never been conscious ourselves of providing for the -future;--if this were the case, we could not recognize -contrivance and prospectiveness in such instances as we have -referred to. The facts are, indeed, admirably in accordance -with these conceptions, when the two are brought together: -but the facts and the conceptions come together from -different quarters--from without and from within. - -7. 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 savages, they have appeared incapable of apprehending -them as proofs of design. This shows that in such cases the -Idea of Design had not been developed in the minds of the -people who were thus unintelligent: but it no more proves -that such an idea does not naturally and necessarily arise, -in the progress of men's minds, than the confused manner in -which the same savages apprehend the relations of space, or -number, or cause, proves that these ideas do not naturally -belong to their intellects. All men have these ideas; and it -is because they {243} cannot help referring their sensations -to such ideas, that they apprehend the world as existing in -time and space, and as a series of causes and effects. It -would be very erroneous to say that the belief of such -truths is obtained by logical reasoning from facts. And in -like manner we cannot logically deduce design from the -contemplation of organic structures; although it is -impossible for us, when the facts are clearly before us, not -to find a reference to design operating in our minds. - -8. Again; 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 Morphology. By cherishing such views, it is probable -that many persons, physiologists and others, have gradually -brought themselves to suppose that many or most of the -arrangements which are familiarly adduced as instances of -design may be accounted for, or explained away;--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 arrangements. And yet, even in persons accustomed -to these views, the strong and natural influence of the Idea -of a Final Cause, the spontaneous recognition of the -relation of Means to an End as the assumption which makes -organic arrangements intelligible, breaks forth when we -bring before them a new case, with regard to which their -genuine convictions have not yet been modified by their -intellectual habits. I will offer, as an example which may -serve to illustrate this, the discoveries recently made with -regard to the process of Suckling in the Kangaroo. In the -case of this, as of other pouched animals, the young animal -is removed, while very small and imperfectly formed, from -the womb to the pouch, in which the teats are, and is there -placed with its lips against one of the nipples. But the -young animal taken altogether is not so large as the nipple, -and is therefore incapable of sucking after the manner of -common mammals. Here is a difficulty: {244} how is it -overcome?--By an appropriate _contrivance_: the nipple, -which in common mammals is not furnished with any muscle, is -in the kangaroo provided with a powerful extrusory muscle by -which the mother can inject the milk into the mouth of her -offspring. And again; in order to give attachment to this -muscle there is a bone which is not found in animals of -other kinds. But this mode of solving the problem of -suckling so small a creature introduces another difficulty. -If the milk is injected into the mouth of the young one, -without any action of its own muscles, what is to prevent -the fluid entering the windpipe and producing suffocation? -How is this danger avoided?--By another appropriate -_contrivance_: there is a funnel in the back of the throat -by which the air passage is completely separated from the -passage for nutriment, and the injected milk passes in a -divided stream on each side of the larynx to the -œsophagus[101\9]. And as if to show that this apparatus is -really formed with a view to the wants of the young one, the -structure alters in the course of the animal's growth; and -the funnel, no longer needed, is modified and disappears. - -[Note 101\9: Mr. Owen, in _Phil. Trans._ 1834, p. 348.] - -With regard to this and similar examples, the remark which I -would urge is this:--that no one, however prejudiced or -unphilosophical he may in general deem the reference to -Final Causes, can, at the first impression, help regarding -this curious system of arrangement as the Means to an End. -So contemplated, it becomes significant, intelligible, -admirable: without such a principle, it is an unmeaning -complexity, a collection of contradictions, producing an -almost impossible result by a portentous conflict of -chances. The parts of this apparatus cannot have produced -one another: one part is in the mother; another part in the -young one: without their harmony they could not be -effective; but nothing except design can operate to make -them harmonious. They are _intended_ to work together; and -we cannot resist the conviction of this intention when the -facts first come before us. Perhaps {245} there may -hereafter be physiologists who, tracing the gradual -development of the parts of which we have spoken, and the -analogies which connect them with the structures of other -animals, may think that this development, these analogies, -account for the conformation we have described; and may -hence think lightly of the explanation derived from the -reference to Final Causes. Yet surely it is clear, on a calm -consideration of the subject, that the latter explanation is -not disturbed by the former; and that the observer's first -impression, that this is 'an irrefragable evidence of -creative foresight[102\9],' can never be obliterated; -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 it, and therefore cannot be contradictory. - -[Note 102\9: Mr. Owen, in _Phil. Trans._ 1834, p. 349.] - -9. I have elsewhere[103\9] remarked how physiologists, who -thus look with suspicion and dislike upon the introduction -of Final Causes into physiology, have still been unable to -exclude from their speculations causes of this kind. Thus -Cabanis says[104\9], 'I regard with the great Bacon, the -philosophy of Final Causes as sterile; but I have elsewhere -acknowledged that it was very difficult for the most -cautious man never to have recourse to them in his -explanations.' Accordingly, he says, '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 races. In no case do the means -employed appear so clearly relative to the end.' And it -would be easy to find similar acknowledgments, express or -virtual, in other writers of the same kind. Thus Bichat, -after noting the difference between the organic sensibility -by which the organs are made to perform their offices, and -the animal sensibility of which the {246} nervous center is -the seat, says[105\9], 'No doubt it will be asked, -_why_'--that is, as we shall see, for what _end_--'the -organs of internal life have received from nature an -inferior degree of sensibility only, and why they do not -transmit to the brain the impressions which they receive, -while all the acts of the animal life imply this -transmission? The reason is simply this, that all the -phenomena which establish our connexions with surrounding -objects _ought to be_, and are in fact, under the influence -of the Will; while all those which serve for the purpose of -assimilation only, escape, and _ought_ indeed to escape, -such influence.' The _reason_ here assigned is the Final -Cause; which, as Bichat justly says, we cannot help asking -for. - -[Note 103\9: _Bridgewater Treatise_, p. 352.] - -[Note 104\9: _Rapports du Physique et du Moral_, i. 299.] - -[Note 105\9: _Life and Death_, (trans.) p. 32.] - -10. Again; I may quote from the writer last mentioned -another remark, which shows that in the organical sciences, -and in them alone, the Idea of forces as Means acting to an -End, is inevitably assumed and acknowledged as of supreme -authority. In Biology alone, observes Bichat[106\9], have we -to contemplate the state of _Disease_. 'Physiology is to the -movements of living bodies, what astronomy, dynamics, -hydraulics, &e., are to those of inert matter: but these -latter sciences have no branches which correspond to them as -Pathology corresponds to Physiology. For the same reason all -notion of a Medicament is repugnant to the physical -sciences. A Medicament has for its object to bring the -properties of the system back to their Natural Type; but the -physical properties never depart from this Type, and have no -need to be brought back to it: and thus there is nothing in -the physical sciences which holds the place of Therapeutick -in Physiology.' Or, as we might express it otherwise, of -inert forces we have no conception of what they _ought to -do_, except what they _do_. The forces of gravity, -elasticity, affinity, never act in a _diseased_ manner; we -never conceive them as failing in their purpose; for we do -not conceive them as having any purpose which is answered by -one mode of their action rather than {247} another. But with -_organical_ forces the case is different; they are -necessarily conceived as acting for the preservation and -development of the system in which they reside. If they do -not do this, they fail, they are deranged, diseased. They -have for their object to conform the living being to a -certain type; and if they cause or allow it to deviate from -this type, their action is distorted, morbid, contrary to -the ends of nature. And thus this conception of organized -beings as susceptible of disease, implies the recognition of -a state of health, and of the organs and the vital forces as -means for preserving this normal condition. The state of -health, and of perpetual development, is necessarily -contemplated as the Final Cause of the processes and powers -with which the different parts of plants and animals are -endowed. - -[Note 106\9: _Anatomie Générale_, i. liii.] - -11. This Idea of a Final Cause is applicable as a -fundamental and regulative idea to our speculations -concerning organized creatures only. That there is a purpose -in many other parts of the creation, we find abundant reason -to believe, from the arrangements and laws which prevail -around us. But this persuasion is not to be allowed to -regulate and direct our reasonings with regard to inorganic -matter, of which conception the relation of means and end -forms no essential part. In mere Physics, Final Causes, as -Bacon has observed, are not to be admitted as a principle of -reasoning. But in the organical sciences, the assumption of -design and purpose in every part of every whole, that is, -the pervading idea of Final Cause, is the basis of sound -reasoning and the source of true doctrine. - -12. The Idea of Final Cause, of end, purpose, design, -intention, is altogether different from the Idea of Cause, -as Efficient Cause, which we formerly had to consider; and -on this account the use of the word Cause in this phrase has -been objected to. If the idea be clearly entertained and -steadily applied, the word is a question of subordinate -importance. The term Final Cause has been long familiarly -used, and appears not likely to lead to confusion. {248} - -13. The consideration of Final Causes, both in physiology -and in other subjects, has at all times attracted much -attention, in consequence of its bearing upon the belief of -an Intelligent Author of the Universe. I do not intend, in -this place, to pursue the subject far in this view: but -there is one antithesis of opinion, already noticed in the -History of Physiology, on which I will again make a few -remarks[107\9]. - -[Note 107\9: _Hist. Ind. Sc._ b. xvii. c. viii. On the -Doctrine of Final Causes in Physiology.] - -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 law. Without here -attempting to decide whether this is true, we may discern, -after what has been said, that the conception of Design, -arrived at in this manner, is altogether different from that -Idea of Design which is suggested to us by organized bodies, -and which we describe as the doctrine of Final Causes. The -regular form of a crystal, whatever beautiful symmetry it -may exhibit, whatever general laws it may exemplify, 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 plants, and of the young of animals. The law of -universal gravitation, however wide and simple, does not -impress us with the belief of a purpose, as does that -propensity by which the two sexes of each animal are brought -together. 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 crystals, or the -motions of the planets, the discovery might be very striking -and important, but it would not at all come under our idea -of Final Cause. - -14. Accordingly, there have been, in modern times, two -different schools of physiologists, the one proceeding upon -the idea of Final Causes, the other school {249} seeking in -the realm of organized bodies wide laws and analogies from -which that idea is excluded. All the great biologists of -preceding times, and some of the greatest of modern times, -have belonged to the former school; and especially Cuvier, -who may be considered as the head of it. It was solely by -the assiduous application of this principle of Final Cause, -as he himself constantly declared, that he was enabled to -make the discoveries which have rendered his name so -illustrious, 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 science. - -The opinions which have been put in opposition to the -principle of Final Causes have, for the most part, been -stated vaguely and ambiguously. Among the most definite of -such principles, is that which, in the History of the -subject, I have termed the Principle of Metamorphosed and -Developed Symmetry, upon which has been founded the science -of Morphology. - -The reality and importance of this principle are not to be -denied by us: we have shown how they are proved by its -application in various sciences, and especially in botany. -But those advocates of this principle who have placed it in -antithesis to the doctrine of Final Causes, have, by this -means, done far more injustice to their own favourite -doctrine than damage to the one which they opposed. The -adaptation of the bones of the skeleton to the muscles, the -provision of fulcrums, projecting processes, channels, so -that the motions and forces shall be such as the needs of -life require, cannot possibly become less striking and -convincing, from any discovery of general analogies of one -animal frame with another, or of laws connecting the -development of different parts. Whenever such laws are -discovered, we can only consider them as the means of -producing that adaptation which we so much admire. Our -conviction that the Artist works intelligently, is not -destroyed, though it may be modified and transferred, when -we obtain a sight of his tools. Our discovery of laws cannot -contradict our persuasion of ends; our Morphology cannot -prejudice our Teleology. {250} - -15. 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 expression, more or less precise, more or less -figurative; as, that 'animals are framed with a view to the -part which they have to play;'--that 'nature does nothing in -vain;' that 'she employs the best means for her ends;' and -the like. However metaphorical or inexact any of these -phrases may be in particular, yet taken altogether, they -convey, clearly and definitely enough to preclude any -serious errour, a principle of the most profound reality and -of the highest importance in the organical sciences. But -some adherents of the morphological school of which 1 have -spoken reject, and even ridicule, all such modes of -expression. 'I know nothing,' says M. Geoffroy Saint -Hilaire, 'of animals which have to play a part in nature. I -cannot make of nature an intelligent being who does nothing -in vain; who acts by the shortest mode; who does all for the -best.' The philosophers of this school, therefore, do not, -it would seem, 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 preservation, the enjoyment, the continuation of the -creatures which people the globe;--at the survey of the -mechanical contrivances, the chemical agencies, the -prospective arrangements, the compensations, the minute -adaptations, the comprehensive interdependencies, which -zoology and physiology have brought into view, more and -more, the further their researches have been carried. Yet -the clear and deep-seated conviction of the reality of these -provisions, which the study of anatomy produces in its most -profound and accurate cultivators, cannot be shaken by any -objections to the metaphors or terms in which this -conviction is clothed. In regard to the Idea of a Purpose in -organization, as in regard to any other idea, we cannot -fully express our meaning by phrases borrowed from any -extraneous source; but that impossibility arises precisely -from the circumstance of its being a Fundamental Idea which -is inevitably assumed in our {251} representation of each -special fact. The same objection has been made to the idea -of mechanical _force_, on account of its being often -expressed in metaphorical language; for writers have spoken -of an _energy_, _effort_, or _solicitation_ to motion; and -bodies have been said to be _animated_ by a force. Such -language, it has been urged, implies volition, and the act -of animated beings. But the idea of Force as distinct from -mere motion,--as the Cause of motion, or of tendency to -motion,--is not on that account less real. We endeavour in -vain to conduct our mechanical reasonings without the aid of -this idea, and must express it as we can. Just as little can -we reason concerning organized beings without assuming that -each part has its function, each function its purpose; and -so far as our phrases imply this, they will not mislead us, -however inexact, or however figurative they be. - -16. The doctrine of a purpose in Organization has been -sometimes called the doctrine of _the Conditions of -Existence_; and has been stated as teaching that each animal -must be so framed as to contain in its structure the -Conditions which its existence requires. When expressed in -this manner, it has given rise to the objection, that it -merely offers an identical proposition; since no animal can -exist without such conditions. But in reality, such -expressions as those just quoted give an inadequate -statement of the Principle of a Final Cause. For we discover -in innumerable cases, arrangements in an animal, of which we -see, indeed, that they are subservient to its well being; -but the nature of which we never should have been able at -all to conjecture, from considering what was necessary to -its existence, and which strike us, no less by their -unexpectedness than by their adaptation: so far are they -from being presented by any perceptible necessity. Who would -venture to say that the trochlear muscle, or the power of -articulate speech, must occur in man, because they are the -necessary conditions of his existence? When, indeed, the -general scheme and mode of being of an animal are known, the -expert and profound anatomist can reason concerning the -proportions and {252} form of its various parts and organs, -and prove in some measure what their relations must be. We -can assert, with Cuvier, that certain forms of the viscera -require certain forms of the teeth, certain forms of the -limbs, certain powers of the senses. But in all this, the -functions of self-nutrition and digestion are supposed -already existing as ends: and it being taken for granted, as -the only conceivable basis of reasoning, that the organs are -means to these ends, we may discover what modifications of -these organs are necessarily related to and connected with -each other. Instead of terming this rule of speculation -merely 'the Principle of the Conditions of Existence,' we -might term it 'the Principle of the conditions of organs as -_Means_ adapted to animal existence as their _End_.' And how -far this principle is from being a mere barren truism, the -extraordinary discoveries made by the great assertor of the -principle, and universally assented to by naturalists, -abundantly prove. The vast extinct creation which is -recalled to life in Cuvier's great work, the _Ossemens -Fossiles_, cannot be the consequence of a mere identical -proposition. - -17. It has been objected, also, that the doctrine of Final -Causes supposes us to be acquainted with the intentions of -the Creator; which, it is insinuated, is a most presumptuous -and irrational basis for our reasonings. But there can be -nothing presumptuous or irrational in reasoning on that -basis, which if we reject, we cannot reason at all. If men -really can discern, and cannot help discerning, a design in -certain portions of the works of creation, this perception -is the soundest and most satisfactory ground for the -convictions to which it leads. The Ideas which we -necessarily employ in the contemplation of the world around -us, afford us the only natural means of forming any -conception of the Creator and Governor of the Universe; and -if we are by such means enabled to elevate our thoughts, -however inadequately, towards Him, where is the presumption -of doing so? or rather, where is the wisdom of refusing to -open our minds to contemplations so animating and elevating, -and yet {253} so entirely convincing? We possess the ideas -of Time and Space, under which all the objects of the -universe present themselves to us; and in virtue of these -ideas thus possessed, we believe the Creator to be eternal -and omnipotent. When we find that we, in like manner, -possess the idea of a Design in Creation, and that with -regard to ourselves, and creatures more or less resembling -ourselves, we cannot but contemplate their constitution -under this idea, 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 whole. - -18. I have here considered Design as manifest in -organization only: for in that field of speculation it is -forced upon us as contained in all the phenomena, and as the -only mode of our understanding them. The existence of Final -Causes has often been pointed out in other portions of the -creation;--for instance, in the apparent adaptations of the -various parts of the earth and of the solar system to each -other and to organized beings. In these provinces of -speculation, however, the principle of Final Causes is no -longer the basis and guide, but the sequel and result of our -physical reasonings. If in looking at the universe, we -follow the widest analogies of which we obtain a view, we -see, however dimly, reason to believe that all its laws are -adapted to each other, and intended to work together for the -benefit of its organic population, and for the general -welfare of its rational tenants. On this subject, however, -not immediately included in the principle of Final Causes as -here stated, I shall not dwell. I will only make this -remark; that the assertion appears to be quite unfounded, -that as science advances from point to point, Final Causes -recede before it, and disappear one after the other. The -principle of design changes its mode of application indeed, -but it loses none of its force. We no longer consider -particular facts as produced by special interpositions, but -we consider design as exhibited in the establishment and -adjustment of the laws by which particular facts are -produced. We do not look upon each particular {254} cloud as -brought near us that it may drop fatness on our fields; but -the general adaptation of the laws of heat, and air, and -moisture, to the promotion of vegetation, does not become -doubtful. We do not consider the sun as less intended to -warm and vivify the tribes of plants and animals, because we -find that, instead of revolving round the earth as an -attendant, the earth along with other planets revolves round -him. We are rather, by the discovery of the general laws of -nature, led into a scene of wider design, of deeper -contrivance, of more comprehensive adjustments. Final -causes, if they appear driven further from us by such an -extension of our views, embrace us only with a vaster and -more majestic circuit: instead of a few threads' connecting -some detached objects, they become a stupendous net-work, -which is wound round and round the universal frame of things. - -19. I now quit the subject of Biology, and with it the -circle of sciences depending upon separate original Ideas -and permanent relations. If from the general relations which -permanently prevail and constantly recur among the objects -around us, we turn to the inquiry of what has actually -happened,--if from Science we turn to History,--we find -ourselves in a new field. In this region of speculation we -can rarely obtain a complete and scientific view of the -connexion between objects and events. The past History of -Man, of the Arts, of Languages, of the Earth, of the Solar -System, offers a vast series of problems, of which perhaps -not one has been rigorously solved. Still, man, as his -speculative powers unfold themselves, cannot but feel -prompted and invited to employ his thoughts even on these -problems. He cannot but wish and endeavour to understand the -connexion between the successive links of such chains of -events. He attempts to form a Science which shall be -applicable to each of these Histories; and thus he begins to -construct the class of sciences to which I now, in the last -place, proceed. - - - - -{{255}} -BOOK X. - - -THE -PHILOSOPHY -OF -PALÆTIOLOGY. - - - - -τὴν μὲν οὖν τοιαύτην _Αἰτιολογίαν_ ἧττον ἄν τις ἀποδέξαιτο· -μᾶλλον _δ᾽ ἀπὸ τῶν φανερωτέρων_ καὶ τῶν καθ᾽ ἡμέραν τρόπον -τινὰ ὁρωμένων ἀναπτέον τὸν λόγον. Καὶ γὰρ κατακλυσμοὶ, καὶ -σεισμοὶ, καὶ ἀναφυσήματα, καὶ ἀνοιδήσεις τῆς ὑφάλου γῆς, -μετεωρίζουσι καὶ τὴν θάλατταν· αἱ δὲ συνιζήσεις ταπεινοῦσιν -αὐτήν. - -STRABO, _Geogr._ 1. p. 54. - - -IT is therefore, not so much what these forms of the earth -actually are, as what they are continually becoming, that we -have to observe; nor is it possible thus to observe them -without an instinctive reference to the first state out of -which they have been brought.... Yet to such questions -continually suggesting themselves, it is never possible to -give a complete answer. For a certain distance, the past -work of existing forces can be traced; but then gradually -the mist gathers, and the footsteps of more gigantic -agencies are traceable in the darkness; and still as we -endeavour to penetrate further and further into departed -time, the thunder of the Almighty power sounds louder and -louder, and the clouds gather broader and more fearfully, -until at last the Sinai of the world is seen altogether upon -a smoke, and the fence of its foot is reached, where none -can break through. - -RUSKIN, _Modern Painters_, Vol. IV. p. 143. - - - -{{257}} -BOOK X. - - -THE PHILOSOPHY OF PALÆTIOLOGY. - - -CHAPTER I. - -OF PALÆTIOLOGICAL SCIENCES IN GENERAL. - - -1. I HAVE already stated in the _History of the -Sciences_[1\10], that the class of Sciences which I -designate as _Palætiological_ are those in which the object -is to ascend from the present state of things to a more -ancient condition, from which the present is derived by -intelligible causes. As conspicuous examples of this class -we may take Geology, Glossology or Comparative Philology, -and Comparative Archæology. These provinces of knowledge -might perhaps be intelligibly described as _Histories_; the -History of the Earth,--the History of Languages,--the -History of Arts. But these phrases would not fully describe -the sciences we have in view; for the object to which we now -suppose their investigations to be directed is, not merely -to ascertain what the series of events has been, as in the -common forms of History, but also how it has been brought -about. These sciences are to treat of causes as well as of -effects. Such researches might be termed _Philosophical -History_; or, in order to mark more distinctly that the -_causes_ of events are the leading object of attention, -_Ætiological History_. But since {258} it will be more -convenient to describe this class of sciences by a single -appellation, I have taken the liberty of proposing to call -them[2\10] the _Palætiological_ Sciences. - -[Note 1\10: B. xviii. Introd.] - -[Note 2\10: A philological writer, in a very interesting -work (Mr. Donaldson, in his _New Cratylus_, p. 12), -expresses his dislike of this word, and suggests that I must -mean _palæ-ætiological_. I think the word is more likely to -obtain currency in the more compact and euphonious form in -which I have used it. It has been adopted by Mr. Winning, in -his _Manual of Comparative Philology_, and more recently, by -other writers.] - -While Palæontology describes the beings which have lived in -former ages without investigating their causes, and -_Ætiology_ treats of causes without distinguishing -historical from mechanical causation; _Palætiology_ is a -combination of the two sciences; exploring, by means of the -second, the phenomena presented by the first. The portions -of knowledge which I include in this term are -palæontological ætiological sciences. - -2. All these sciences are connected by this bond;--that they -all endeavour to ascend to a past state, by considering what -is the present state of things, and what are the causes of -change. Geology examines the existing appearance of the -materials which form the earth, infers from them previous -conditions, and speculates concerning the forces by which -one condition has been made to succeed another. Another -science, cultivated with great zeal and success in modern -times, compares the languages of different countries and -nations, and by an examination of their materials and -structure, endeavours to determine their descent from one -another: this science has been termed _Comparative -Philology_, or _Ethnography_; and by the French, -_Linguistique_, a word which we might imitate in order to -have a single name for the science, but the Greek derivative -_Glossology_ appears to be more convenient in its form. The -progress of the Arts (Architecture and the like);--how one -stage of the culture produced another; and how far we can -trace their maturest and most complete condition to their -earliest form in various nations;--are problems of great -interest belonging to another subject, which we may for the -present term {259} _Comparative Archæology_. I have already -noticed, in the History[3\10] how the researches into the -origin of natural objects, and those relating to works of -art, pass by slight gradations into each other; how the -examination of the changes which have affected an ancient -temple or fortress, harbour or river, may concern alike the -geologist and the antiquary. Cuvier's assertion that the -geologist is an antiquary of a new order, is perfectly -correct, for both are palætiologists. - -[Note 3\10: B. xviii. Introd.] - -3. We are very far from having exhausted, by this -enumeration, the class of sciences which are thus connected. -We may easily point out many other subjects of speculation -of the same kind. As we may look back towards the first -condition of our planet, we may in like manner turn our -thoughts towards the first condition of the solar system, -and try whether we can discern any traces of an order of -things antecedent to that which is now established; and if -we find, as some great mathematicians have conceived, -indications of an earlier state in which the planets were -not yet gathered into their present forms, we have, in the -pursuit of this train of research, a palætiological portion -of Astronomy. Again, as we may inquire how languages, and -how man, have been diffused over the earth's surface from -place to place, we may make the like inquiry with regard to -the races of plants and animals, founding our inferences -upon the existing geographical distribution of the animal -and vegetable kingdoms: and thus the Geography of Plants and -of Animals also becomes a portion of Palætiology. Again, as -we can in some measure trace the progress of Arts from -nation to nation and from age to age, we can also pursue a -similar investigation with respect to the progress of -Mythology, of Poetry, of Government, of Law. Thus the -philosophical history of the human race, viewed with -reference to these subjects, if it can give rise to -knowledge so exact as to be properly called Science, will -supply Sciences belonging to the class I am now to consider. {260} - -4. It is not an arbitrary and useless proceeding to -construct such a Class of Sciences. For wide and various as -their subjects are, it will be found that they have all -certain principles, maxims, and rules of procedure in -common; and thus may reflect light upon each other by being -treated of together. Indeed it will, I trust, appear, that -we may by such a juxtaposition of different speculations, -obtain most salutary lessons. And questions, which, when -viewed as they first present themselves under the aspect of -a special science, disturb and alarm men's minds, may -perhaps be contemplated more calmly, as well as more -clearly, when they are considered as general problems of -palætiology. - -5. It will at once occur to the reader that, if we include -in the circuit of our classification such subjects as have -been mentioned,--politics and law, mythology and poetry,--we -are travelling very far beyond the material sciences within -whose limits we at the outset proposed to confine our -discussion of principles. But we shall remain faithful to -our original plan; and for that purpose shall confine -ourselves, in this work, to those palætiological sciences -which deal with material things. It is true, 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 -endowments. But although there may be a similarity in the -general form of such portions of knowledge, their materials -are so different from those with which we have been hitherto -dealing, that we cannot hope to take them into our present -account with any profit. Language, Government, Law, Poetry, -Art, embrace a number of peculiar Fundamental Ideas, -hitherto not touched upon in the disquisitions in which we -have been engaged; and most of them involved in far greater -perplexity and ambiguity, the subject of controversies far -more vehement, than the Ideas we have hitherto been -examining. We must therefore avoid resting any part of our -philosophy upon sciences, or supposed sciences, which treat -of such subjects. To attend to this caution, {261} is the -only way in which we can secure the advantage we proposed to -ourselves at the outset, of taking, as the basis of our -speculations, none but systems of undisputed truths, clearly -understood and expressed[4\10]. We have already said that we -must, knowingly and voluntarily, resign that livelier and -warmer interest which doctrines on subjects of Polity or Art -possess, and content ourselves with the cold truths of the -material sciences, in order that we may avoid having the -very foundations of our philosophy involved in controversy, -doubt, and obscurity. - -[Note 4\10: See Introd. p. 9.] - -6. We may remark, however, that the necessity of rejecting -from our survey a large portion of the researches which the -general notion of Palætiology includes, suggests one -consideration which adds to the interest of our task. 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 sciences, and the mode of discovering it, -must also tend to throw light upon the nature and prospects -of knowledge of all other kinds;--must be useful to us in -moral, political, and philological researches. We stated -this as a confident anticipation; and the evidence of the -justice of our belief already begins to appear. We have -seen, in the last Book, that biology leads us to psychology, -if we choose to follow the path; and thus the passage from -the material to the immaterial has already unfolded itself -at one point; and we now perceive that there are several -large provinces of speculation which concern subjects -belonging to man's immaterial nature, and which are governed -by the same laws as sciences altogether physical. It is not -our business here to dwell on the prospects which our -philosophy thus opens to our contemplation; but we may allow -ourselves, in this last stage of our pilgrimage among the -foundations of the physical sciences, to be cheered and -animated by the ray {262} that thus beams upon us, however -dimly, from a higher and brighter region. - -But in our reasonings and examples we shall mainly confine -ourselves to the physical sciences; and for the most part to -Geology, which in the _History_ I have put forwards as the -best representative of the Palætiological Sciences. - - - -{{263}} -CHAPTER II. - -OF THE THREE MEMBERS OF A PALÆTIOLOGICAL SCIENCE. - - -1. _Divisions of such Sciences._--IN each of the Sciences of -this class we consider some particular order of phenomena -now existing:--from our knowledge of the causes of change -among such phenomena, we endeavour to infer the causes which -have made this order of things what it is:--we ascend in -this manner to some previous stage of such phenomena;--and -from that, by a similar course of inference, to a still -earlier stage, and to its causes. Hence it will be seen that -each such science will consist of two parts,--the knowledge -of the Phenomena, and the knowledge of their Causes. And -such a division is, in fact, generally recognized in such -sciences: thus we have History, and the Philosophy of -History; we have Comparison of Languages, and the Theories -of the Origin and Progress of Language; we have Descriptive -Geology, and Theoretical or Physical Geology. In all these -cases, the relation between the two parts in these several -provinces of knowledge is nearly the same; and it may, on -some occasions at least, be useful to express the -distinction in a uniform or general manner. The -investigation of Causes has been termed _Ætiology_ by -philosophical writers, and this term we may use, in -contradistinction to the mere _Phenomenology_ of each such -department of knowledge. And thus we should have _Phenomenal -Geology_ and _Ætiological Geology_, for the two divisions of -the science which we have above termed _Descriptive_ and -_Theoretical Geology_. - -2. _The Study of Causes._--But our knowledge respecting the -causes which actually _have_ produced any {264} order of -phenomena must be arrived at by ascertaining what the causes -of change in such matters _can_ do. In order to learn, for -example, what share earthquakes, and volcanoes, and the -beating of the ocean against its shores, ought to have in -our Theory of Geology, we must make out what effects these -agents of change are able to produce. And this must be done, -not hastily, or unsystematically, but in a careful and -connected manner; in short, this study of the causes of -change in each order of phenomena must become a distinct -body of Science, which must include a large amount of -knowledge, both comprehensive and precise, before it can be -applied to the construction of a theory. We must have an -Ætiology corresponding to each order of phenomena. - -3. _Ætiology._--In the History of Geology, I have spoken of -the necessity for such an Ætiology with regard to geological -phenomena: this necessity I have compared with that which, -at the time of Kepler, required the formation of a separate -science of Dynamics (the doctrine of the Causes of Motion), -before Physical Astronomy could grow out of Phenomenal -Astronomy. In pursuance of this analogy, I have there given -the name of _Geological Dynamics_ to the science which -treats of the causes of geological change in general. But, -as I have there intimated, in a large portion of the subject -the changes are so utterly different in their nature from -any modification of motion, that the term _Dynamics_, so -applied, sounds harsh and strange. For in this science we -have to treat, not only of the subterraneous forces by which -parts of the earth's crust are shaken, elevated, or -ruptured, but also of the causes which may change the -climate of a portion of the earth's surface, making a -country hotter or colder than in former ages; again, we have -to treat of the causes which modify the forms and habits of -animals and vegetables, and of the extent to which the -effects of such causes can proceed; whether, for instance, -they can extinguish old species and produce new. These and -other similar investigations would not be naturally included -in the notion of _Dynamics_; and therefore it {265} might -perhaps be better to use the term _Ætiology_ when we wish to -group together all those researches which have it for their -object to determine the laws of such changes. In the same -manner the Comparison and History of Languages, if it is to -lead to any stable and exact knowledge, must have appended -to it an Ætiology, which aims at determining the nature and -the amount of the causes which really do produce changes in -language; as colonization, conquest, the mixture of races, -civilization, literature, and the like. And the same rule -applies to all sciences of this class. 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 -considerations. - -4. _Phenomenology requires Classification. Phenomenal -Geology._--The Phenomenal portions of each science imply -Classification, for no description of a large and varied -mass of phenomena can be useful or intelligible without -classification. A representation of phenomena, in order to -answer the purposes of science, must be systematic. -Accordingly, in giving the History of Descriptive or -Phenomenal Geology, I have called it _Systematic Geology_, -just as Classificatory Botany is termed _Systematic Botany_. -Moreover, as we have already seen, Classification can never -be an arbitrary process, but always implies some natural -connexion among the objects of the same Class; for if this -connexion did not exist, the Classes could not be made the -subjects of any true assertion. Yet though the classes of -phenomena which our system acknowledges must be such as -already exist in nature, the discovery of these classes is, -for the most part, very far from obvious or easy. To detect -the true principles of Natural Classes, and to select marks -by which these may be recognized, are steps which require -genius and good fortune, and which fall to the lot only of -the most eminent persons in each science. In the History, I -have pointed out Werner, William Smith, and Cuvier, as the -three great authors of Systematic Geology of Europe. The -mode of classifying the materials of the earth's surface -which was found, by these philosophers, fitted to {266} -enunciate such general facts as came under their notice, was -to consider the rocks and other materials as divided into -successive layers or strata, superimposed one on another, -and variously inclined and broken. The German geologist -distinguished his strata for the most part by their -mineralogical character; the other two, by the remains of -animals and plants which the rocks contained. After a -beginning had thus been made in giving a genuine scientific -form to phenomenal geology, other steps followed in rapid -succession, as has already been related in the -History[5\10]. The Classification of the Strata was fixed by -a suitable Nomenclature. Attempts were made to apply to -other countries the order of strata which had been found to -prevail in that first studied: and in this manner it was -ascertained what rocks in distant regions are the synonyms, -or _Equivalents_[6\10],--of each other. The knowledge thus -collected and systematized was exhibited in the form of -Geological Maps. - -[Note 5\10: _Hist. Ind. Sc._ b. xviii. c. iii.] - -[Note 6\10: _Ib._ sect. 4.] - -Moreover, among the phenomena of geology we have Laws of -Nature as well as Classes. The general form of -mountain-chains; the relations of the direction and -inclination of different chains to each other; the general -features of mineral veins, faults, and fissures; the -prevalent characters of slaty cleavage;--were the subjects -of laws established, or supposed to be established, by -extensive observation of facts. 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 in; and the evidence which they gave -of a regular zoological development. And thus, by the -assiduous labours of many accomplished and active -philosophers, Descriptive or Phenomenal Geology was carried -towards a state of completeness. - -5. _Phenomenal Uranography._--In like manner in other -palætiological researches, as soon as they approach to an -exact and scientific form, we find the necessity of -constructing in the first place a science of {267} -classification and exact description, by means of which the -phenomena may be correctly represented and compared; and of -obtaining by this step a solid basis for an inquiry into the -causes which have produced them. Thus the Palætiology of the -Solar System has, in recent times, drawn the attention of -speculators; and a hypothesis has been started, that our sun -and his attendant planets have been produced by the -condensation of a mass of diffused matter, such as that -which constitutes the nebulous patches which we observe in -the starry heavens. But the sagest and most enlightened -astronomers have not failed to acknowledge, that to verify -or to disprove this conjecture, must be the work of many -ages of observation and thought. 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 -reach, respecting the phenomena of these nebulæ, with which -we thus compare our own system; and, as a necessary element -of such knowledge, they have seen the importance of a -classification of these objects, and of others, such as -Double Stars, of the same kind. Sir William Herschel, who -first perceived the bearing of the phenomena of nebulæ upon -the history of the solar system, made the observation of -such objects his business, with truly admirable zeal and -skill; and in the account of the results of his labours, -gave a classification of Nebulæ; separating them into, -first, _Clusters of Stars_; second, _Resolvable Nebulæ_; -third, _Proper Nebulæ_; fourth, _Planetary Nebulæ_; fifth, -_Stellar Nebulæ_; sixth, _Nebulous Stars_[7\10]. And since, -in order to obtain from these remote appearances, any -probable knowledge respecting our own system, we must -discover whether they undergo any changes in the course of -ages, he devoted himself to the task of forming a record of -their number and appearance in his own time, that thus the -astronomers of succeeding generations might have a {268} -definite and exact standard with which to compare their -observations. Still, this task would have been executed only -for that part of the heavens which is visible in this -country, if this Hipparchus of the Nebulæ and Double Stars -had not left behind him a son who inherited all his father's -zeal and more than his father's knowledge. Sir John Herschel -in 1833 went to the Cape of Good Hope to complete what Sir -William Herschel left wanting; and in the course of five -years observed with care all the nebulæ and double stars of -the Southern hemisphere. This great _Herschelian Survey of -the Heavens_, the completion of which is the noblest -monument ever erected by a son to a father, must necessarily -be, to all ages, the basis of all speculations concerning -the history and origin of the solar system; and has -completed, so far as at present it can be completed, the -phenomenal portion of Astronomical Palætiology. - -[Note 7\10: _Phil. Trans._ 1786 and 1789, and Sir J. -Herschel's _Astronomy_, Art. 616.] - -6. _Phenomenal Geography of Plants and Animals._--Again, -there is another Palætiological Science, closely connected -with the speculations forced upon the geologist by the -organic fossils which he discovers imbedded in the strata of -the earth;--namely, the Science which has for its object the -Causes of the Diffusion and Distribution of the various -kinds of Plants and Animals. And the science also has for -its first portion and indispensable foundation a description -and classification of the existing phenomena. Such portions -of science have recently been cultivated with great zeal and -success, under the titles of the _Geography of Plants_, and -the _Geography of Animals_. 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 _Provinces_, each -province occupied by its own peculiar vegetable and animal -population. We find, too, in the course of these -investigations, various general laws of the phenomena -offered to our notice; such, for instance, as this:--that -the difference of the animals originally occupying each -province, which is clear and entire for the higher orders of -{269} animals and plants, becomes more doubtful and -indistinct when we descend to the lower kinds of -organizations; as Infusoria and Zoophytes[8\10] in the -animal kingdom, Grasses and Mosses among vegetables. Again, -other laws discovered by those who have studied the -geography of plants are these:--that countries separated -from each other by wide tracts of sea, as the opposite -shores of the Mediterranean, the islands of the Indian and -Pacific Oceans, have usually much that is common in their -vegetation:--and again, that in parallel climates, analogous -tribes replace each other. It would be easy to adduce other -laws, but those already stated may serve to show the great -extent of the portions of knowledge which have just been -mentioned, even considered as merely Sciences of Phenomena. - -[Note 8\10: Prichard, _Researches into the Physical History -of Mankind_, i. 55, 28.] - -7. _Phenomenal Glossology._--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 nature; and I shall, therefore, not dwell -upon a branch of research, singularly interesting, and -closely connected with the one just mentioned, but dealing -with relations of thought rather than of things;--I mean the -Palætiology of Language;--the theory, so far as the facts -enable us to form a theory, of the causes which have led to -the resemblances and differences of human speech in various -regions and various ages. This, indeed, would be only a -portion of the study of the history and origin of the -diffusion of animals, if we were to include man among the -animals whose dispersion we thus investigate; for language -is one of the most clear and imperishable records of the -early events in the career of the human race. But the -peculiar nature of the faculty of speech, and the ideas -which the use of it involves, make it proper to treat -_Glossology_ as a distinct science. And of this science, the -first part must necessarily be, as in the other sciences of -this order, a {270} classification and comparison of -languages governed in many respects by the same rules, and -presenting the same **difficulties, as other sciences of -classification. Such, accordingly, has been the procedure of -the most philosophical glossologists. They have been led to -throw the languages of the earth into certain large classes -or _Families_, according to various kinds of resemblance; as -the _Semitic_ Family, to which belong Hebrew, Arabic, -Chaldean, Syrian, Phoenician, Ethiopian, and the like; the -_Indo-European_, which includes Sanskrit, Persian, Greek, -Latin, and German; the _Monosyllabic_ languages, Chinese, -Tibetan, Birman, Siamese; the _Polysynthetic_ languages, a -class including most of the North-American Indian dialects; -and others. And this work of classification has been the -result of the labour and study of many very profound -linguists, and has advanced gradually from step to step. -Thus the Indo-European Family was first formed on an -observation of the coincidences between Sanskrit, Greek, and -Latin; but it was soon found to include the Teutonic -languages, and more recently Dr. Prichard[9\10] has shown -beyond doubt that the Celtic must be included in the same -Family. Other general resemblances and differences of -languages have been marked by appropriate terms: thus August -von Schlegel has denominated them _synthetical_ and -_analytical_, according as they form their conjugations and -declensions by auxiliary verbs and prepositions, or by -changes in the word itself: and the _polysynthetic_ -languages are so named by M. Duponceau, in consequence of -their still more complex mode of inflexion. Nor are there -wanting, in this science also, general laws of phenomena; -such, for instance, is the curious rule of the interchange -of consonants in the cognate words of Greek, Gothic, and -German, which has been discovered by James Grimm. All these -remarkable portions of knowledge, and the great works which -have appeared on Glossology, such, for example, as the -_Mithridates_ of Adelung and Vater, contain, for their -largest, and {271} hitherto probably their most valuable -part, the phenomenal portion of the science, the comparison -of languages as they now are. And beyond all doubt, until we -have brought this Comparative Philology to a considerable -degree of completeness, all our speculations respecting the -causes which have operated to produce the languages of the -earth must be idle and unsubstantial dreams. - -[Note 9\10: Dr Prichard, _On the Eastern Origin of the -Celtic Nations_. 1831.] - -Thus in all Palætiological Sciences, in all attempts to -trace back the history and discover the origin of the -present state of things, the portion of the science which -must first be formed is that which classifies the phenomena, -and discovers general laws prevailing among them. When this -work is performed, and not till then, we may begin to -speculate successfully concerning causes, and to make some -progress in our attempts to go back to an origin. We must -have a _Phenomenal_ science preparatory to each -_Ætiological_ one. - -8. _The Study of Phenomena leads to Theory._--As we have -just said, we cannot, in any subject, speculate successfully -concerning the causes of the present state of things, till -we have obtained a tolerably complete and systematic view of -the phenomena. 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 theories. Nor was it -natural, considering the speculative propensities of the -human mind, and how incessantly it is endeavouring to apply -the Idea of Cause, that it should thus restrain itself. I -have already noticed this in the History of Geology. 'While -we have been giving an account,' it is there said, 'of the -objects with which Descriptive Geology is occupied, it must -have been felt how difficult it is, in contemplating such -facts, to confine ourselves to description and -classification. Conjectures and reasonings respecting the -causes of the phenomena force themselves upon us at every -step; and even influence our classification and -nomenclature. Our Descriptive Geology impels us to construct -a Physical Geology.' And the same is the case with regard to -the other subjects which I have mentioned. The mere {272} -consideration of the different degrees of condensation of -different Nebulæ led Herschel and Laplace to contemplate the -hypothesis that our solar system is a condensed Nebula. -Immediately upon the division of the earth's surface into -botanical and zoological provinces, and even at an earlier -period, the opposite hypotheses of the Origin of all the -animals of each kind from a single pair, and of their -original diffusion all over the earth, were under -discussion. And the consideration of the families of -languages irresistibly led to speculations concerning the -Families of the earliest human inhabitants of the earth. In -all cases the contemplation of a very few phenomena, the -discovery of a very few steps in the history, made men wish -for and attempt to form a theory of the history from the -very beginning of things. - -9. _No sound Theory without Ætiology._--But though man is -thus impelled by the natural propensities of his intellect -to trace each order of things to its causes, he does not at -first discern the only sure way of obtaining such knowledge: -he does not suspect how much labour and how much method are -requisite for success in this undertaking: he is not aware -that for each order of phenomena he must construct, by the -accumulated results of multiplied observation and distinct -thought, a separate Æiology. Thus, as I have elsewhere -remarked[10\10], when men had for the first time become -acquainted with some of the leading phenomena of Geology, -and had proceeded to speculate concerning the past changes -and revolutions by which such results had been produced, -they forthwith supposed themselves able to judge what would -be the effects of any of the obvious agents of change, as -Water or Volcanic Fire. 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 knowledge. -They did not foresee that, before they could determine what -share these or any other causes had had in producing the -present condition of the earth, they must create {273} a -special science whose object should be to estimate the -general laws and effects of such assumed causes;--that -before they could obtain any sound Geological Theory, they -must carefully cultivate Geological Ætiology. - -[Note 10\10: _Hist. Ind. Sc._ b. xviii. c. v. sect. 1.] - -The same disposition to proceed immediately from the facts -to the theory, without constructing, as an intermediate -step, a Science of Causes, might be pointed out in the other -sciences of this order. But in all of them this errour has -been corrected by the failures to which it led. It soon -appeared, for instance, that a more careful inquiry into the -effects which climate, food, habit and circumstances can -produce in animals, was requisite in order to determine how -the diversities of animals in different countries have -originated. The Ætiology of Animal Life (if we may be -allowed to give this name to that study of such causes of -change which is at present so zealously cultivated, and -which yet has no distinctive designation, except so far as -it coincides with the _Organic Geological Dynamics_ of our -History) is now perceived to be a necessary portion of all -attempts to construct a history of the earth and its -inhabitants. - -10. _Cause, in Palætiology._--We are thus led to contemplate -a class of Sciences which are commenced with the study of -Causes. We have already considered sciences which depended -mainly upon the Idea of Cause, namely, the Mechanical -Sciences. 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 -formerly. Force is the _Cause_ of motion, because force at -all times and under all circumstances, if not counteracted, -produces motion; but the Cause of the present condition and -elevation of the Alps, whatever it was, was manifested in a -series of events of which each happened but once, and -occupied its proper place in the series of time. The former -is _mechanical_, the latter _historical_, _cause_. In our -present investigations, we consider the events which we -contemplate, of whatever order they be, as forming a chain -which is extended {274} from the beginning of things down to -the present time; and the causes of which we now speak are -those which connect the successive links of this chain. -Every occurrence which has taken place in the history of the -solar system, or the earth, or its vegetable and animal -creation, or man, has been at the same time effect and -cause;--the effect of what preceded, the cause of what -succeeded. By being effect and cause, it has occupied some -certain portion of time; and the times which have thus been -occupied by effects and causes, summed up and taken -altogether, make up the total of Past Time. The Past has -been a series of events connected by this historical -causation, and the Present is the last term of this series. -The problem in the Palætiological Sciences, with which we -are here concerned, is, to determine the manner in which -each term is derived from the preceding, and thus, if -possible, to calculate backwards to the origin of the series. - -11. _Various kinds of Cause._--Those modes by which one term -in the natural series of events is derived from -another,--the forms of historical causation,--the kinds of -connexion between the links of the infinite chain of -time,--are very various; nor need we attempt to enumerate -them. But these kinds of causation being distinguished from -each other, and separately studied, each becomes the subject -of a separate Ætiology. Thus the causes of change in the -earth's surface, residing in the elements, fire and water, -form the main subject of Geological Ætiology. The Ætiology -of the vegetable and animal kingdoms investigates the causes -by which the forms and distribution of species of plants and -animals are affected. The study of causes in Glossology -leads to an Ætiology of Language, which shall distinguish, -analyse, and estimate the causes by which certain changes -are produced in the languages of nations; in like manner we -may expect to have an Ætiology of Art, which shall -scrutinise the influences by which the various forms of art -have each given birth to its successor: by which, for -example, there have been brought into being those various -forms of architecture which we term Egyptian, {275} Doric, -Ionic, Roman, Byzantine, Romanesque, Gothic, Italian, -Elizabethan. It is easily seen by this slight survey how -manifold and diverse are the kinds of cause which the -Palætiological Sciences bring under our consideration. But -in each of those sciences we shall obtain solid and complete -systems of knowledge, only so far as we study, with steady -thought and careful observation, that peculiar kind of cause -which is appropriate to the phenomena under our -consideration. - -12. _Hypothetical Order of Palætiological Causes._--The -various kinds of historical cause are not only connected -with each other by their common bearing upon the historical -sciences, 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 inhabitants. Thus -assuming, merely as a momentary hypothesis, the origin of -the Solar System by the condensation of a Nebula, we have to -contemplate, first, the causes by which the luminous -incandescent diffused mass of which a nebula is supposed to -be constituted, is gradually condensed, cooled, collected -into definite masses, solidified, and each portion made to -revolve about its axis, and the whole to travel about -another body. We have no difficulty in ascribing the -globular form of each mass to the mutual attraction of its -particles: but when this form was once assumed, and covered -with a solid crust, are there, we may ask, in the -constitution of such a body, any causes at work by which the -crust might be again broken up and portions of it displaced, -and covered with other matter? Again, if we can thus explain -the origin of the Earth, can we with like success account -for the presence of the Atmosphere and the Waters of earth -and ocean? Supposing this done, we have then to consider by -what causes such a body could become stocked with vegetable -and animal Life; for there have not been wanting persons, -extravagant speculators, no doubt, who have conceived that -even this event in the history of the world might be the -work of natural causes. Supposing an origin given to life -{276} upon our earth, we have then, brought before us by -geological observations, a series of different forms of -vegetable and animal existence; occurring in different -strata, and, as the phenomena appear irresistibly to prove, -existing at successive periods: 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 next. We find, -too, that strata, which must have been at first horizontal -and continuous, have undergone enormous dislocations and -ruptures, and we have to consider the possible effect of -aqueous and volcanic causes to produce such changes in the -earth's crust. We are thus led to the causes which have -produced the present state of things on the earth; and these -are causes to which we may hypothetically ascribe, not only -the form and position of the inert materials of the earth, -but also the nature and distribution of its animal and -vegetable population. Man too, no less than other animals, -is affected by the operation of such causes as we have -referred to, and must, therefore, be included in such -speculations. But man's history only begins, where that of -other animals ends, with his mere existence. They are -stationary, he is progressive. Other species of animals, -once brought into being, continue the same through all ages; -man is changing, from age to age, his language, his -thoughts, his works. Yet even these changes are bound -together by laws of causation; and these causes too may -become objects of scientific study. And such causes, though -not to be dwelt upon now, since we permit ourselves to found -our philosophy upon the material sciences only, must still, -when treated scientifically, fall within the principles of -our philosophy, and must be governed by the same general -rules to which all science is subject. And thus we are led -by a close and natural connexion, through a series of -causes, extending from those which regulate the -imperceptible changes of the remotest nebulæ in the heavens, -to those which determine the diversities of language, the -mutations of art, and even the progress of civilization, -polity, and literature. {277} - -While I have been speaking of this supposed series of -events, including in its course the formation of the earth, -the introduction of animal and vegetable life, and the -revolutions by which one collection of species has succeeded -another, it must not be forgotten, that though I have thus -hypothetically spoken of these events as occurring by force -of natural causes, this has been done only that the true -efficacy of such causes might be brought under our -consideration and made the subject of scientific -examination. It may be found, that such occurrences as these -are quite inexplicable by the aid of any natural causes with -which we are acquainted; and thus, the result of our -investigations, conducted with strict regard to scientific -principles, may be, that we must either contemplate -supernatural influences as part of the past series of -events, or declare ourselves altogether unable to form this -series into a connected chain. - -13. _Mode of Cultivating Ætiology:--In Geology._--In what -manner, it may be asked, is Ætiology, with regard to each -subject such as we have enumerated, to be cultivated? In -order to answer this question, we must, according to our -method of proceeding, take the most successful and complete -examples which we possess of such portions of science. But -in truth, we can as yet refer to few examples of this kind. -In Geology, it is only very recently, and principally -through the example and influence of Sir Charles Lyell, that -the Ætiology has been detached from the descriptive portion -of the science; and cultivated with direct attention: in -other sciences the separation has hardly yet been made. But -if we examine what has already been done in Geological -Ætiology, or as in the History it is termed, _Geological -Dynamics_, we shall find a number of different kinds of -investigation which, by the aid of our general principles -respecting the formation of sciences, may suffice to supply -very useful suggestions for Ætiology in general. - -In Geological Ætiology, causes have been studied, in many -instances, by attending to their action in the phenomena of -the present state of things, and by inferring {278} from -this the nature and extent of the action which they may have -exercised in former times. This has been done, for example, -by Von Hoff, Sir Charles Lyell, and others, with regard to -the operations of rivers, seas, springs, glaciers, and other -aqueous causes of change, Again, the same course has been -followed by the same philosophers with respect to volcanoes, -earthquakes, and other violent agents. Sir Charles Lyell has -attempted to show, too, that there take place, in our own -time, not only violent agitations, but slow motions of parts -of the earth's crust, of the same kind and order with those -which have assisted in producing all anterior changes. - -But while we thus seek instruction in the phenomena of the -present state of things, we are led to the question, What -are the limits of this 'present' period? For instance, among -the currents of lava which we trace as part of the shores of -Italy and Sicily, _which_ shall we select as belonging to -the existing order of things? In going backwards in time, -where shall we draw the line? and why at such particular -point? These questions are important, for our estimate of -the efficacy of known causes will vary with the extent of -the effects which we ascribe to them. Hence the mode in -which we group together rocks is not only a step in -geological classification, but is also important to -Ætiology. Thus, when the vast masses of trap rocks in the -Western Isles of Scotland and in other countries, which had -been maintained by the Wernerians to be of aqueous origin, -were, principally by the sagacity and industry of -Macculloch, identified as to their nature with the products -of recent volcanoes, the amount of effect which might -justifiably be ascribed to volcanic agency was materially -extended. - -In other cases, instead of observing the current effects of -our geological causes, we have to estimate the results from -what we know of the causes themselves; as when, with -Herschel, we calculate the alterations in the temperature of -the earth which astronomical changes may possibly produce; -or when, with Fourier, we try to calculate the rate of -cooling of the earth's {279} surface, on the hypothesis of -an incandescent central mass. In other cases, again, we are -not able to calculate the effects of our causes rigorously, -but estimate them as well as we can; partly by physical -reasonings, and partly by comparison with such analogous -cases as we can find in the present state of things. 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 equator, by reasonings on the power -of land and water to contain and communicate heat, supported -by a reference to the different actual climates of places, -lying under the same latitude, but under different -conditions as to the distribution of land and water. - -Thus our Ætiology is constructed partly from calculation and -reasoning, partly from phenomena. But we may observe that -when we reason from phenomena to causes, we usually do so by -various steps; often ascending from phenomena to mere laws -of phenomena, before we can venture to connect the -phenomenon confidently with its cause. Thus the law of -subterranean heat, that it increases in descending below the -surface, is now well established, although the doctrine -which ascribes this effect to a central heat is not -universally assented to. - -14. _In the Geography of Plants and Animals._--We may find -in other subjects also, considerable contributions towards -Ætiology, though not as yet a complete System of Science. -The Ætiology of Vegetables and Animals, indeed, has been -studied with great zeal in modern times, as an essential -preparative to geological theory; for how can we decide -whether any assumed causes have produced the succession of -species which we find in the earth's strata, except we know -what effect of this kind given causes can produce? -Accordingly, we find in Sir Charles Lyell's _Treatise on -Geology_ the most complete discussion of such questions as -belong to these subjects:--for example, the question whether -species can be transmuted into other species by the -long-continued influence of external causes, as climate, -food, domestication, combined with internal {280} causes, as -habits, appetencies, progressive tendencies. We may observe, -too, that as we have brought before us, the inquiry what -change difference of climate can produce in any species, we -have also the inverse problem, how far a different -development of the species, or a different collection of -species, proves a difference of climate. In the same way, -the geologist of the present day considers the question, -whether, in virtue of causes now in action, species are from -time to time extinguished; and in like manner, the -geologists of an earlier period discussed the question, now -long completely decided, whether fossil species in general -are really extinct species. - -15. _In Languages._--Even with reference to the Ætiology of -Language, although this branch of science has hardly been -considered separately from the glossological investigations -in which it is employed or assumed to be employed, it might -perhaps be possible to point out causes or conditions of -change which, being general in their nature, must operate -upon all languages alike. Changes made for the sake of -euphony when words are modified and combined, occur in all -dialects. Who can doubt that such changes of consonants as -those by which the Greek roots become Gothic, and the -Gothic, German, have for their cause some general principle -in the pronunciation of each language? Again, we might -attempt to decide other questions of no small interest. Have -the terminations of verbs arisen from the accretion of -pronouns; or, on the other hand, does the modification of a -verb imply a simpler mental process than the insulation of a -pronoun, as Adam Smith has maintained? Again, when the -language of a nation is changed by the invasion and -permanent mixture of an enemy of different speech, is it -generally true that it is changed from a synthetic to an -analytical structure? I will mention only one more of these -wide and general glossological inquiries. Is it true, as Dr. -Prichard has suggested[11\10], that languages have become -more permanent as we come down {281} towards later times? -May we justifiably suppose, with him, that in the very -earliest times, nations, when they had separated from one -stock, might lose all traces of this common origin out of -their languages, though retaining strong evidences of it in -their mythology, social forms, and arts, as appears to be -the case with the ancient Egyptians and the Indians[12\10]. - -[Note 11\10: _Researches_, ii. 221.] - -[Note 12\10: _Researches_, ii. 192.] - -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 languages. But on the other -hand, the study of languages should be prosecuted not only -by a direct comparison of one with another, but also with a -view to the formation of a science of causes and general -principles, embracing such discussions as I have pointed -out. It is only when such a science has been formed, that we -can hope to obtain any solid and certain results in the -Palætiology of Language;--to determine, with any degree of -substantial proof, what is the real evidence which the -wonderful faculty of speech, under its present developments -and forms, bears to the events which have taken place in its -own history, and in the history of man since his first origin. - -16. _Construction of Theories._--When we have thus obtained, -with reference to any such subject as those we have here -spoken of, these two portions of science, a Systematic -Description of the Facts, and a rigorous Analysis of the -Causes,--the _Phenomenology_ and the _Ætiology_ of the -subject,--we are prepared for the third member which -completes the science, the _Theory_ of the actual facts. We -can then take a view of the events which really have -happened, discerning their connexion, interpreting their -evidence, supplying from the context the parts which are -unapparent. We can account for known facts by intelligible -causes; we can infer latent facts from manifest effects, so -as to obtain a distinct insight into the whole history of -events up to the present time, and to see the last result of -the whole in the present condition of things. {282} The term -_Theory_, when rigorously employed in such sciences as those -which we here consider, bears nearly the sense which I have -adopted: it implies a consistent and systematic view of the -actual facts, combined with a true apprehension of their -connexion and causes. Thus if we speak of 'a Theory of Mount -Etna,' or 'a Theory of the Paris Basin,' we mean a connected -and intelligible view of the events by which the rocks in -these localities have come into their present condition. -Undoubtedly the term _Theory_ has often been used in a -looser sense; and men have put forth '_Theories of the -Earth_,' which, instead of including the whole mass of -actual geological facts and their causes, only assigned, in -a vague manner, some causes by which some few phenomena -might, it was conceived, be accounted for. Perhaps the -portion of our Palætiological Sciences which we now wish to -designate, would be more generally understood if we were to -describe it as _Theoretical_ or _Philosophical History_; as -when we talk of 'the Theoretical History of Architecture,' -or 'the Philosophical History of Language.' And in the same -manner we might speak of the Theoretical History of the -Animal and Vegetable Kingdoms; meaning, a distinct account -of the events which have produced the present distribution -of species and families. But by whatever phrase we describe -this portion of science, it is plain that such a Theory, -such a Theoretical History, must result from the application -of causes well understood to facts well ascertained. And if -the term _Theory_ be here employed, we must recollect that -it is to be understood, not in its narrower sense as opposed -to facts, but in its wider signification, as including all -known facts and differing from them only in introducing -among them principles of intelligible connexion. The -Theories of which we now speak are true _Theories_, -precisely because they are identical with the total system -of the _Facts_. - -17. _No sound Palætiological Theory yet extant._--It is not -to disparage unjustly the present state of science, to say -that as yet no such theory exists on any subject. 'Theories -of the Earth' have been {283} repeatedly published; but when -we consider that even the facts of geology have been -observed only on a small portion of the earth's surface, and -even within those narrow bounds very imperfectly studied, 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 origin. Accordingly, -I have ventured in my History to designate the most -prominent of the Theories which have hitherto prevailed as -_premature_ geological theories[13\10]: and we shall soon -see that geological theory has not advanced beyond a few -conjectures, 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 other. And if we have no theoretical History -of the Earth which merits any confidence, still less have we -any theoretical History of Language, or of the Arts, which -we can consider as satisfactory. The Theoretical History of -the Vegetable and Animal Kingdoms is closely connected with -that of the Earth on which they subsist, and must follow the -fortunes of Geology. And thus we may venture to say that no -Palætiological Science, as yet, possesses all its three -members. Indeed most of them are very far from having -completed and systematized their Phenomenology: in all, the -cultivation of Ætiology is but just begun, or is not begun; -in all, the Theory must reward the exertions of future, -probably of distant, generations. - -[Note 13\10: _Hist. Ind. Sc._ b. xviii. c. vii. sect. 3.] - -But in the mean time we may derive some instruction from the -comparison of the two antagonist hypotheses of which I have spoken. - - - -{{284}} -CHAPTER III. - -OF THE DOCTRINE OF CATASTROPHES AND THE DOCTRINE OF -UNIFORMITY. - - -1. _Doctrine of Catastrophes._--I HAVE already shown, in the -History of Geology, that the attempts to frame a theory of -the earth have brought into view two completely opposite -opinions:--one, which represents the course of nature as -_uniform_ through all ages, the causes which produce change -having had the same intensity in former times which they -have at the present day;--the other opinion, which sees, in -the present condition of things, evidences of -_catastrophes_;--changes of a more sweeping kind, and -produced by more powerful agencies than those which occur in -recent times. Geologists who held the latter opinion, -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 action: they pointed to vast masses -of strata hundreds of miles long, thousands of feet thick, -thrown into highly-inclined positions, fractured, -dislocated, crushed: they remarked that upon the shattered -edges of such strata they found enormous accumulations of -fragments and rubbish, rounded by the action of water, so as -to denote ages of violent aqueous action: they conceived -that they saw instances in which whole mountains of rock in -a state of igneous fusion, must have burst the earth's crust -from below: they found that in the course of the revolutions -by which one stratum of rock was placed upon another, the -whole collection of animal species which tenanted the earth -and the seas had been removed, and a new set of living -things introduced in its place: finally, they found, above -all the strata, {285} vast masses of sand and gravel -containing bones of animals, and apparently the work of a -mighty deluge. With all these proofs before their eyes, 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 -violent, more powerful, than any which we see at work around -us. They conceived that the evidence of 'catastrophes' was -irresistible. - -2. _Doctrine of Uniformity._--I need not here repeat the -narrative (given in the History[14\10]) of the process by -which this formidable array of proofs was, in the minds of -some eminent geologists, weakened, and at last overcome. -This was done by showing that the sudden breaks in the -succession of strata were apparent only, the discontinuity -of the series which occurred in one country being removed by -terms interposed in another locality:--by urging that the -total effect produced by existing causes, taking into -account the accumulated result of long periods, is far -greater than a casual speculator would think possible:--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 species:--by -proving that it is not universally true that the strata -separated in time by supposed catastrophes contain distinct -species of animals:--by pointing out the limited fields of -the supposed diluvial action:--and finally, by remarking -that though the _creation_ of species is a mystery, the -_extinction_ of species is going on in our own day. -Hypotheses were suggested, too, by which it was conceived -that the change of climate might be explained, which, as the -consideration of the fossil remains seemed to show, must -have taken place between the ancient and the modern times. -In this manner the whole evidence of catastrophes was -explained away: the notion of a series of paroxysms of -violence in the causes of change was represented as a -delusion arising from our {286} contemplating short periods -only, in the action of present causes: length of time was -called in to take the place of intensity of force: and it -was declared that Geology need not despair of accounting for -the revolutions of the earth, as Astronomy accounts for the -revolutions of the heavens, by the universal action of -causes which are close at hand to us, operating through time -and space without variation or decay. - -[Note 14\10: _Hist. Ind. Sc._ b. xviii. c. viii. sect. 2.] - -An antagonism of opinions, somewhat of the same kind as -this, will be found to manifest itself in the other -Palætiological Sciences as well as in Geology; and it will -be instructive to endeavour to balance these opposite -doctrines. I will mention some of the considerations which -bear upon the subject in its general form. - -3. _Is Uniformity probable à priori?_--The doctrine of -Uniformity in the course of nature has sometimes been -represented by its adherents as possessing a great degree of -_à priori_ probability. It is highly unphilosophical, it has -been urged, to assume that the causes of the geological -events of former times were of a different kind from causes -now in action, if causes of this latter kind can in any way -be made to explain the facts. The analogy of all other -sciences compels us, it was said, to explain phenomena by -known, not by unknown, causes. And on these grounds the -geological teacher recommended[15\10] 'an earnest and -patient endeavour to reconcile the indications of former -change with the evidence of gradual mutations now in -progress.' - -[Note 15\10: Lyell, 4th ed. b. iv. c. i. p. 328.] - -But on this we may remark, that if by _known_ causes we mean -causes acting with the same intensity which they have had -during historical times, the restriction is altogether -arbitrary and groundless. Let it be granted, for instance, -that many parts of the earth's surface are now undergoing an -imperceptible rise. It is not pretended that the rate of -this elevation is rigorously uniform; what, then, are the -limits of its velocity? Why may it not increase so as to -assume that character of violence which we may term a {287} -_catastrophe_ with reference to all changes hitherto -recorded? Why may not the rate of elevation be such that we -may conceive the strata to assume _suddenly_ a position -nearly vertical? And is it, in fact, easy to conceive a -position of strata nearly vertical, a position which occurs -so frequently, to be _gradually_ assumed? In cases where the -strata are nearly vertical, as in the Isle of Wight, and -hundreds of other places, or where they are actually -inverted, as sometimes occurs, are not the causes which have -produced the effect as truly known causes, as those which -have raised the coasts where we trace the former beach in an -elevated terrace? If the latter case proves _slow_ -elevation, does not the former case prove _rapid_ elevation? -In neither case have we any measure of the time employed in -the change; but does not the very nature of the results -enable us to discern, that if one was gradual, the other was -comparatively sudden? - -The causes which are now elevating a portion of Scandinavia -can be called known _causes_, only because we know the -_effect_. Are not the causes which have elevated the Alps -and the Andes known causes in the same sense? We know -nothing in either case which confines the intensity of the -force within any limit, or prescribes to it any law of -uniformity. Why, then, should we make a merit of cramping -our speculations by such assumptions? Whether the causes of -change do act uniformly;--whether they oscillate only within -narrow limits;--whether their intensity in former times was -nearly the same as it now is;--these are precisely the -questions which we wish Science to answer to us impartially -and truly: where is then the wisdom of 'an earnest and -patient endeavour' to secure an _affirmative_ reply? - -Thus I conceive that the assertion of an _à priori_ claim to -probability and philosophical spirit in favour of the -doctrine of uniformity, is quite untenable. We must learn -from an examination of all the facts, and not from any -assumption of our own, whether the course of nature be -uniform. The limit of intensity being really unknown, -catastrophes are just as probable {288} as uniformity. If a -volcano may repose for a thousand years, and then break out -and destroy a city; why may not another volcano repose for -ten thousand years, and then destroy a continent; or if a -continent, why not the whole habitable surface of the earth? - -4. _Cycle of Uniformity indefinite._--But this argument may -be put in another form. When it is said that the course of -nature is uniform, the assertion is not intended to exclude -certain smaller variations of violence and rest, such as we -have just spoken of;--alternations of activity and repose in -volcanoes; or earthquakes, deluges, and storms, interposed -in a more tranquil state of things. With regard to such -occurrences, terrible as they appear at the time, they may -not much affect the average rate of change; there may be a -_cycle_, though an irregular one, of rapid and slow change; -and if such cycles go on succeeding each other, we may still -call the order of nature uniform, notwithstanding the -periods of violence which it involves. The maximum and -minimum intensities of the forces of mutation alternate with -one another; and we may estimate the average course of -nature as that which corresponds to something between the -two extremes. - -But if we thus attempt to maintain the uniformity of nature -by representing it as a series of _cycles_, we find that we -cannot discover, in this conception, any solid ground for -excluding catastrophes. What is the length of that cycle, -the repetition of which constitutes uniformity? What -interval from the maximum to the minimum does it admit of? -We may take for our cycle a hundred or a thousand years, but -evidently such a proceeding is altogether arbitrary. We may -mark our cycles by the greatest known paroxysms of volcanic -and terremotive agency, but this procedure is no less -indefinite and inconclusive than the other. - -But further; since the cycle in which violence and repose -alternate is thus indefinite in its length and in its range -of activity, what ground have we for assuming more than one -such cycle, extending from the origin of things to the -present time? Why may we not suppose the maximum force of -the causes of change {289} to have taken place at the -earliest period, and the tendency towards the minimum to -have gone on ever since? Or instead of only one cycle, there -may have been several, but of such length that our -historical period forms a portion only of the last;--the -feeblest portion of the latest cycle. And thus violence and -repose may alternate upon a scale of time and intensity so -large, that man's experience supplies no evidence enabling -him to estimate the amount. The course of things is -_uniform_, to an Intelligence which can embrace the -succession of several cycles, but it is _catastrophic_ to -the contemplation of man, whose survey can grasp a part only -of one cycle. And thus the hypothesis of uniformity, since -it cannot exclude degrees of change, nor limit the range of -these degrees, nor define the interval of their recurrence, -cannot possess any essential simplicity which, previous to -inquiry, gives it a claim upon our assent superior to that -of the opposite catastrophic hypothesis. - -5. _Uniformitarian Arguments are Negative only._--There is -an opposite tendency in the mode of maintaining the -catastrophist and the uniformitarian opinions, which depends -upon their fundamental principles, and shows itself in all -the controversies between them. The Catastrophist is -affirmative, the Uniformitarian is negative in his -assertions: the former is constantly attempting to construct -a theory; the latter delights in demolishing all theories. -The one is constantly bringing fresh evidence of some great -past event, or series of events, of a striking and definite -kind; his antagonist is at every step explaining away the -evidence, and showing that it proves nothing. One geologist -adduces his proofs of a vast universal deluge; but another -endeavours to show that the proofs do not establish either -the universality or the vastness of such an event. The -inclined broken edges of a certain formation, covered with -their own fragments, beneath superjacent horizontal -deposits, are at one time supposed to prove a catastrophic -breaking up of the earlier strata; but this opinion is -controverted by showing that the same formations, when -pursued into other countries, {290} exhibit a uniform -gradation from the lower to the upper, with no trace of -violence. Extensive and lofty elevations of the coast, -continents of igneous rock, at first appear to indicate -operations far more gigantic than those which now occur; 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 changes. Each new fact adduced by the catastrophist -is at first striking and apparently convincing; but as it -becomes familiar, it strikes the imagination less -powerfully; and the uniformitarian, constantly labouring to -produce some imitation of it by the machinery which he has -so well studied, at last in every case seems to himself to -succeed, so far as to destroy the effect of his opponent's -evidence. - -This is so with regard to more remote, as well as with -regard to immediate evidences of change. When it is -ascertained that in every part of the earth's crust the -temperature increases as we descend below the surface, at -first this fact seems to indicate a central heat: and a -central heat naturally suggests an earlier state of the -mass, in which it was incandescent, and from which it is now -cooling. But this original incandescence of the globe of the -earth is manifestly an entire violation of the present -course of things; it belongs to the catastrophist view, and -the advocates of uniformity have to explain it away. -Accordingly, 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 center. The heat which increases at first as -we descend, may, he conceives, afterwards decrease; and he -suggests causes which may have produced such a succession of -hotter and colder shells within the mass of the earth. I -have mentioned this suggestion in the History of Geology; -and have given my reasons for believing it altogether -untenable[16\10]. Other persons also, desirous of -reconciling this subterraneous heat with the tenet of -uniformity, have {291} offered another suggestion:--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 cooling, but results from chemical action -constantly going on among the materials of the earth's -substance. And thus new attempts are perpetually making, to -escape from the cogency of the reasonings which send us -towards an original state of things different from the -present. Those who theorize concerning an origin go on -building up the fabric of their speculations, while those -who think such theories unphilosophical, ever and anon dig -away the foundation of this structure. As we have already -said, the uniformitarian's doctrines are a collection of -negatives. - -[Note 16\10: _Hist. Ind. Sc._ b. xviii. c. v. sect. 5, and note.] - -This is so entirely the case, that the uniformitarian would -for the most part shrink from maintaining as positive tenets -the explanations which he so willingly uses as instruments -of controversy. He puts forward his suggestions as -difficulties, but he will not stand by them as doctrines. -And this is in accordance with his general tendency; for any -of his hypotheses, if insisted upon as positive theories, -would be found inconsistent with the assertion of -uniformity. For example, the nebular hypothesis appears to -give to the history of the heavens an aspect which -obliterates all special acts of creation, for, according to -that hypothesis, new planetary systems are constantly -forming; but when asserted as the origin of our own solar -system, it brings with it an original incandescence, and an -origin of the organic world. And if, instead of using the -chemical theory of subterraneous heat to neutralize the -evidence of original incandescence, we assert it as a -positive tenet, we can no longer maintain the infinite past -duration of the earth; for chemical forces, as well as -mechanical, tend to equilibrium; and that condition once -attained, their efficacy ceases. Chemical affinities tend to -form new compounds; and though, when many and various -elements are mingled together, the play of synthesis and -analysis may go on for a long time, it must at last end. If, -for instance, a large portion of the earth's mass were -originally pure potassium, we {292} can imagine violent -igneous action to go on so long as any part remained -unoxidized; but when the oxidation of the whole has once -taken place, this action must be at an end; for there is in -the hypothesis no agency which can reproduce the deoxidized -metal. Thus a perpetual motion is impossible in chemistry, -as it is in mechanics; and a theory of constant change -continued through infinite time, is untenable when asserted -upon chemical, no less than upon mechanical principles. And -thus the Skepticism of the uniformitarian is of force only -so long as it is employed against the Dogmatism of the -catastrophist. When the Doubts are erected into Dogmas, they -are no longer consistent with the tenet of Uniformity. When -the Negations become Affirmations, the Negation of an Origin -vanishes also. - -6. _Uniformity in the Organic World._--In speaking of the -violent and sudden changes which constitute catastrophes, -our thoughts naturally turn at first to great _mechanical_ -and _physical_ effects;--ruptures and displacements of -strata; extensive submersions and emersions of land; rapid -changes of temperature. But the catastrophes which we have -to consider in geology affect the _organic_ as well as the -inorganic world. The sudden extinction of one collection of -species, and the introduction of another in their place, is -a Catastrophe, even if unaccompanied by mechanical violence. -Accordingly, the antagonism of the catastrophist and -uniformitarian schools has shown itself in this department -of the subject, as well as in the other. When geologists had -first discovered that the successive strata are each -distinguished by appropriate organic fossils, they assumed -at once that each of these collections of living things -belonged to a separate creation. But this conclusion, as I -have already said, Sir C. Lyell has attempted to invalidate, -by proving that in the existing order of things, some -species become extinct; and by suggesting it as possible, -that in the same order, it may be true that new species are -from time to time produced, even in the present course of -nature. And in this, as in the other part of the subject, he -calls in {293} the aid of vast periods of time, in order -that the violence of the changes may be softened down: 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 obtained; and yet may be rapid -enough, considering the immensity of geological periods, to -produce such a succession of different collections of -species as we find in the strata of the earth's surface. - -7. _Origin of the present Organic World._--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 seats. And we may form various hypotheses with -regard to the sudden or gradual manner in which we may -suppose this distribution to have taken place. We may assume -that at the beginning of the present order of things, a -stock of each species was placed in the vegetable or animal -_province_ to which it belongs, by some cause out of the -common order of nature; or we may take a uniformitarian view -of the subject, and suppose that the provinces of the -organic world derived their population from some anterior -state of things by the operation of natural causes. - -Nothing has been pointed out in the existing order of things -which has any analogy or resemblance, of any valid kind, to -that creative energy which must be exerted in the production -of a new species. And to assume the introduction of new -species as 'a part of the order of nature,' without pointing -out any natural fact with which such an event can be -classed, would be to reject creation by an arbitrary act. -Hence, even on natural grounds, the most intelligible view -of the history of the animal and vegetable kingdoms seems to -be, that each period which is marked by a distinct -collection of species forms a cycle; and that at the -beginning of each such cycle a creative power was exerted, -of a kind to which there was nothing at all analogous in the -succeeding part of the same cycle. If it be urged that in -some cases the same species, or the same genus, runs through -two geological formations, {294} which must, on other -grounds, be referred to different cycles of creative energy, -we may reply that the creation of many new species does not -imply the extinction of all the old ones. - -Thus we are led by our reasonings to this view, that the -present order of things was commenced by an act of creative -power entirely different to any agency which has been -exerted since. 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 first. We are -necessarily driven to assume, as the beginning of the -present cycle of organic nature, an event not included in -the course of nature. And we may remark that this necessity -is the more cogent, precisely because other cycles have -preceded the present. - -8. _Nebular Origin of the Solar System._--If we attempt to -apply the same antithesis of opinion (the doctrines of -Catastrophe and Uniformity) to the other subjects of -palætiological sciences, we shall be led to similar -conclusions. Thus, if we turn our attention to Astronomical -Palætiology, we perceive that the Nebular Hypothesis has a -uniformitarian tendency. According to this hypothesis the -formation of this our system of sun, planets, and -satellites, was a process of the same kind as those which -are still going on in the heavens. One after another, nebulæ -condense into separate masses, which begin to revolve about -each other by mechanical necessity, and form systems of -which our solar system is a finished example. But we may -remark, that the uniformitarian doctrine on this subject -rests on most unstable foundations. We have as yet only very -vague and imperfect reasonings to show that by such -condensation a _material_ system such as ours could result; -and the introduction of _organized_ beings into such a -material system is utterly out of the reach of our -philosophy. Here again, therefore, 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 grasp. {295} - -9. _Origin of Languages._--We may venture to say that we -should be led to the same conclusion once more, if we were -to take into our consideration those palætiological sciences -which are beyond the domain of matter; for instance, the -History of Languages. We may explain many of the differences -and changes which we become acquainted with, by referring to -the action of causes of change which still operate. But what -glossologist will venture to declare that the efficacy of -such causes has been uniform;--that the influences which -mould a language, or make one language differ from others of -the same stock, operated formerly with no more efficacy than -they exercise now. 'Where,' as has elsewhere been asked, 'do -we now find a language in the process of formation, -unfolding itself in inflexions, terminations, changes of -vowels by grammatical relations, such as characterise the -oldest known languages?' Again, as another proof how little -the history of languages suggests to the philosophical -glossologist the persuasion of a uniform action of the -causes of change, I may refer to the conjecture of Dr. -Prichard, that the varieties of language produced by the -separation of one stock into several, have been greater and -greater as we go backwards in history:--that[17\10] the -formation of sister dialects from a common language (as the -Scandinavian, German, and Saxon dialects from the Teutonic, -or the Gaelic, Erse and Welsh from the Celtic) belongs to -the first millennium before the Christian era; while the -formation of cognate languages of the same family, as the -Sanskrit, Latin, Greek and Gothic, must be placed at least -two thousand years before that era; and at a still earlier -period took place the separation of the great families -themselves, the Indo-European, Semitic, and others, in which -it is now difficult to trace the features of a common -origin. No hypothesis except one of this kind will explain -the existence of the families, groups, and dialects of -languages, which we find in existence. Yet this is an -entirely different view from that which {296} the hypothesis -of the uniform progress of change would give. And thus, in -the earliest stages of man's career, the revolutions of -language must have been, even by the evidence of the -theoretical history of language itself, of an order -altogether different from any which have taken place within -the recent history of man. And we may add, 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 causes, we cannot place the origin -of language in any point of view in which it comes under the -jurisdiction of natural causation at all. - -[Note 17\10: _Researches_, ii. 224.] - -10. _No Natural Origin discoverable._--We are thus led by a -survey of several of the palætiological sciences to a -confirmation of the principle formerly asserted[18\10], That -in no palætiological science has man been able to arrive at -a beginning which is homogeneous with the known course of -events. We can in such sciences often go very far -back;--determine many of the remote circumstances of the -past series of events;--ascend to a point which seems to be -near the origin;--and limit the hypotheses respecting the -origin itself: but philosophers never have demonstrated, -and, so far as we can judge, probably never will be able to -demonstrate, what was that primitive state of things from -which the progressive course of the world took its first -departure. In all these paths of research, when we travel -far backwards, the aspect of the earlier portions becomes -very different from that of the advanced part on which we -now stand; but in all cases the path is lost in obscurity as -it is traced backwards towards its starting-point: it -becomes not only invisible, but unimaginable; it is not only -an interruption, but an abyss, which interposes itself -between us and any intelligible beginning of things. - -[Note 18\10: _Hist. Ind. Sc._ b. xviii. c. vi. sect 5.] - - - -{{297}} -CHAPTER IV. - -OF THE RELATION OF TRADITION TO PALÆTIOLOGY. - - -1. _Importance of Tradition._--SINCE the Palætiological -Sciences have it for their business to study the train of -past events produced by natural causes down to the present -time, the knowledge concerning such events which is supplied -by the remembrance and records of man, in whatever form, -must have an important bearing upon these sciences. All -changes in the condition and extent of land and sea, which -have taken place within man's observation, all effects of -deluges, sea-waves, rivers, springs, volcanoes, earthquakes, -and the like, which come within the reach of human history, -have a strong interest for the palætiologist. Nor is he less -concerned in all recorded instances of the modification of -the forms and habits of plants and animals, by the -operations of man, or by transfer from one land to another. -And when we come to the Palætiology of Language, of Art, of -Civilization, we find our subject still more closely -connected with history; for in truth these are historical, -no less than palætiological investigations. But, confining -ourselves at present to the material sciences, we may -observe that though the importance of the information which -tradition gives us, in the sciences now under our -consideration, as, for instance, geology, has long been -tacitly recognised; 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 -kind. The Essay of Von {298} Hoff[19\10], _On the Natural -Alterations in the Surface of the Earth which are proved by -Tradition_, was the work which first opened the eyes of -geologists to the extent and importance of this kind of -investigation. Since that time the same path of research has -been pursued with great perseverance by others, especially -by Sir C. Lyell; and is now justly considered as an -essential portion of Geology. - -[Note 19\10: Vol. i. 1822; vol. ii. 1824.] - -2. _Connexion of Tradition and Science._--Events which we -might naturally expect to have some bearing on geology, are -narrated in the historical writings which, even on mere -human grounds, have the strongest claim to our respect as -records of the early history of the world, and are confirmed -by the traditions of various nations all over the globe; -namely, the formation of the earth and of its population, -and a subsequent deluge. It has been made a matter of -controversy how the narrative of these events is to be -understood, 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 us. Such controversies, when -they are considered as merely archæological, may occur in -any of the palætiological sciences. We may have to compare -and to reconcile the evidence of existing phenomena with -that of historical tradition. But under some circumstances -this process of conciliation may assume an interest of -another kind, on which we will make a few remarks. - -3. _Natural and Providential History of the World._--We may -contemplate the existence of man upon the earth, his origin -and his progress, in the same manner as we contemplate the -existence of any other race of animals; namely, in a purely -palætiological view. We may consider how far our knowledge -of laws of causation enables us to explain his diffusion and -migration, his differences and resemblances, his actions and -works. And this is the view of man as a member of the -_Natural_ Course of Things. {299} - -But man, at the same time the contemplator and the subject -of his own contemplation, endowed with faculties and powers -which make him a being of a different nature from other -animals, cannot help regarding his own actions and -enjoyments, his recollections and his hopes, under an aspect -quite different from any that we have yet had presented to -us. We have been endeavouring to place in a clear light the -Fundamental Ideas, such as that of Cause, on which depends -our knowledge of the natural course of things. But there are -other Ideas to which man necessarily refers his actions; he -is led by his nature, not only to consider his own actions, -and those of his fellow-men, as springing out of this or -that cause, leading to this or that material result; but -also as _good_ or _bad_, as what they _ought_ or _ought not_ -to be. He has Ideas of moral relations as well as those -Ideas of material relations with which we have hitherto been -occupied. He is a moral as well as a natural agent. - -Contemplating himself and the world around him by the light -of his Moral Ideas, man is led to the conviction that his -moral faculties were bestowed upon him by design and for a -purpose; that he is the subject of a Moral Government; that -the course of the world is directed by the Power which -governs it, to the unfolding and perfecting of man's moral -nature; that this guidance may be traced in the career of -individuals and of the world; that there is a _Providential_ -as well as a Natural Course of Things. - -Yet this view is beset by no small difficulties. The full -development of man's moral faculties;--the perfection of his -nature up to the measure of his own ideas;--the adaptation -of his moral being to an ultimate destination, by its -transit through a world full of moral evil, in which evil -each person has his share;--are effects for which the -economy of the world appears to contain no adequate -provision. Man, though aware of his moral nature, and ready -to believe in an ultimate destination of purity and -blessedness, is too feeble to resist the temptation of evil, -and too helpless to restore his purity when once lost. He -cannot but look for {300} some confirmation of that -providential order which he has begun to believe; some -provision for those deficiencies in his moral condition -which he has begun to feel. - -He looks at the history of the world, and he finds that at a -certain period it offers to him the promise of what he -seeks. When the natural powers of man had been developed to -their full extent, and were beginning to exhibit symptoms of -decay;--when the intellectual progress of the world appeared -to have reached its limit, without supplying man's moral -needs;--we find the great Epoch in the Providential History -of the world. We find the announcement of a Dispensation by -which man's deficiencies shall be supplied and his -aspirations fulfilled: we find a provision for the -purification, the support, and the ultimate beatification of -those who use the provided means. And thus the providential -course of the world becomes consistent and intelligible. - -4. _The Sacred Narrative._--But with the new Dispensation, -we receive, not only an account of its own scheme and -history, but also a written narrative of the providential -course of the world from the earliest times, and even from -its first creation. This narrative is recognized and -authorized by the new dispensation, and accredited by some -of the same evidences as the dispensation itself. That the -existence of such a sacred narrative should be a part of the -providential order of things, cannot but appear natural; -but, naturally also, the study of it leads to some -difficulties. - -The Sacred Narrative in some of its earliest portions speaks -of natural objects and occurrences respecting them. In the -very beginning of the course of the world, we may readily -believe (indeed, as we have seen in the last chapter, our -scientific researches lead us to believe) that such -occurrences were very different from anything which now -takes place;--different to an extent and in a manner which -we cannot estimate. 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 things. When applied to an initial {301} -supernatural state therefore, these words and phrases cannot -help being to us obscure and mysterious, perhaps ambiguous -and seemingly contradictory. - -5. _Difficulties in interpreting the Sacred Narrative._--The -moral and providential relations of man's condition are so -much more important to him than mere natural relations, that -at first we may well suppose he will accept the Sacred -Narrative, as not only unquestionable in its true import, -but also as a guide in his views even of mere natural -things. He will try to modify the conceptions which he -entertains of objects and their properties, 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 language. - -But man is so constituted that he cannot persist in this -procedure. 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 -themselves. For instance, when he at first read of a -firmament dividing the waters above from the waters below, -he perhaps conceived a transparent floor in the skies, on -which the superior waters rested, which descend in rain; but -as his observations and his reasonings satisfied him that -such a floor could not exist, he became willing to allow (as -St. Augustine allowed) that the waters above the firmament -are in a state of vapour. And in like manner in other -subjects, men, as their views of nature became more distinct -and precise, modified, so far as it was necessary for -consistency's sake, their first rude interpretations of the -Sacred Narrative; so that, without in any degree losing its -import as a view of the providential course of the world, it -should be so conceived as not to contradict what they knew -of the natural order of things. - -But this accommodation was not always made without painful -struggles and angry controversies. When men had conceived -the occurrences of the Sacred Narrative in a particular -manner, they could not readily and willingly adopt a new -mode of conception; and all attempts to recommend to them -such novelties, they {302} resisted as attacks upon the -sacredness of the Narrative. They had clothed their belief -of the workings of Providence in certain images; and they -clung to those images with the persuasion that, without -them, their belief could not subsist. Thus they imagined to -themselves that the earth was a flat floor, solidly and -broadly laid for the convenience of man; and they felt as if -the kindness of Providence was disparaged, when it was -maintained that the earth was a globe held together only by -the mutual attraction of its parts. - -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 acceptance. On this controversy I have already made -some remarks in the _History of Science_[20\10], and have -attempted to draw from it some lessons which may be useful -to us when any similar conflict of opinions may occur. I -will here add a few reflections with a similar view. - -[Note 20\10: B. v. c. iii. sect. 4.] - -6. _Such difficulties inevitable._--In the first place, 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 Science. -Science is constantly teaching us to describe known facts in -new language; but the language of Scripture is always the -same. And not only so, but the language of Scripture is -necessarily adapted to the common state of man's -intellectual development, in which he is supposed not to be -possessed of science. Hence the phrases used by Scripture -are precisely those which science soon teaches man to -consider as inaccurate. Yet they are not, on that account, -the less fitted for their proper purpose: for if any terms -had been used, adapted to a more advanced state of -knowledge, they must have been unintelligible among those to -whom the Scripture was first addressed. If the Jews had been -told that water existed in the clouds in small drops, they -would have marvelled that it did {303} not constantly -descend; and to have explained the reason of this, would -have been to teach Atmology in the sacred writings. If they -had read in their Scripture that the earth was a sphere, -when it appeared to be a plain, they would only have been -disturbed in their thoughts or driven to some wild and -baseless imaginations, by a declaration to them so strange. -If the Divine Speaker, instead of saying that he would set -his bow in the clouds, had been made to declare that he -would give to water the property of refracting different -colours at different angles, how utterly unmeaning to the -hearers would the words have been! And in these cases, the -expressions, being unintelligible, startling, and -bewildering, would have been such as tended to unfit the -Sacred Narrative for its place in the providential -dispensation of the world. - -Accordingly, in the great controversy which took place in -Galileo's time between the defenders of the then customary -interpretations of Scripture, and the assertors of the -Copernican system of the universe, when the innovators were -upbraided with maintaining opinions contrary to Scripture, -they replied that Scripture was not intended to teach men -astronomy, and that it expressed the acts of divine power in -images which were suited to the ideas of unscientific men. -To speak of the rising and setting and travelling of the -sun, of the fixity and of the foundations of the earth, was -to use the only language which would have made the Sacred -Narrative intelligible. To extract from these and the like -expressions doctrines of science, was, they declared, in the -highest degree unjustifiable; and such a course could lead, -they held, 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 it. 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 nature. - -7. _Science tells us nothing concerning Creation._--Other -apparent difficulties arise from the accounts given in the -Scripture of the first origin of the world {304} in which we -live: for example, Light is represented as created before -the Sun. With regard to difficulties of this kind, it -appears that we may derive some instruction from the result -to which we were led in the last chapter;--namely, that in -the sciences which trace the progress of natural -occurrences, we can in no case go back to an origin, but in -every instance appear to find ourselves separated from it by -a state of things, and an order of events, of a kind -altogether different from those which come under our -experience. The thread of induction respecting the natural -course of the world snaps in our fingers, when we try to -ascertain where its beginning is. Since, then, science can -teach us nothing positive respecting the beginning of -things, she can neither contradict nor confirm what is -taught by Scripture on that subject; and thus, as it is -unworthy timidity in the lover of Scripture to fear -contradiction, so is it ungrounded presumption to look for -confirmation, in such cases. The providential history of the -world has its own beginning, and its own evidence; and we -can only render the system insecure, by making it lean on -our material sciences. If any one were to suggest that the -nebular hypothesis countenances the Scripture history of the -formation of this system, by showing how the luminous matter -of the sun might exist previous to the sun itself, we should -act wisely in rejecting such an attempt to weave together -these two heterogeneous threads;--the one a part of a -providential scheme, the other a fragment of a physical -speculation. - -We shall best learn those lessons of the true philosophy of -science which it is our object to collect, by attending to -portions of science which have gone through such crises as -we are now considering; nor is it requisite, for this -purpose, to bring forwards any subjects which are still -under discussion. It may, however, be mentioned that such -maxims as we are now endeavouring to establish, and the one -before us in particular, bear with a peculiar force upon -those Palætiological Sciences of which we have been treating -in the present Book. {305} - -8. _Scientific views, when familiar, do not disturb the -authority of Scripture._--There is another reflection which -may serve to console and encourage us in the painful -struggles which thus take place, between those who maintain -interpretations of Scripture already prevalent and those who -contend for such new ones as the new discoveries of science -require. It is this;--that though the new opinion is -resisted by one party as something destructive of the credit -of Scripture and the reverence which is its due, yet, in -fact, when the new interpretation has been generally -established and incorporated with men's current thoughts, it -ceases to disturb their views of the authority of the -Scripture or of the truth of its teaching. When the language -of Scripture, invested with its new meaning, has become -familiar to men, it is found that the ideas which it calls -up are quite as reconcileable as the former ones were, with -the most entire acceptance of the providential dispensation. -And when this has been found to be the case, 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 narrative. At the present day, we can hardly -conceive how reasonable men could ever have imagined that -religious reflections on the stability of the earth, and the -beauty and use of the luminaries which revolve round it, -would be interfered with by an acknowledgment that this rest -and motion are apparent only[21\10]. 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 occurrences; provided -the new interpretation is admitted at a proper season, and -in a proper spirit; so as to soften, as much as possible, -both the public controversies and the private scruples which -almost inevitably accompany such an alteration. - -[Note 21\10: I have here borrowed a sentence or two from my -own _History_.] - -9. _When should old Interpretations be given up?_--But the -question then occurs, What is the proper {306} season for a -religious and enlightened commentator to make such a change -in the current interpretation of sacred Scripture? At what -period ought the established exposition of a passage to be -given up, and a new mode of understanding the passage, such -as is, or seems to be, required by new discoveries -respecting the laws of nature, accepted in its place? It is -plain, that to introduce such an alteration lightly and -hastily would be a procedure fraught with inconvenience; for -if the change were made in such a manner, it might be -afterwards discovered that it had been adopted without -sufficient reason, and that it was necessary to reinstate -the old exposition. And the minds of the readers of -Scripture, always to a certain extent and for a time -disturbed by the subversion of their long-established -notions, would be distressed without any need, and might be -seriously unsettled. While, on the other hand, a too -protracted and obstinate resistance to the innovation, on -the part of the scriptural expositors, would tend to -identify, at least in the minds of many, the authority of -the Scripture with the truth of the exposition; and -therefore would bring discredit upon the revealed word, when -the established interpretation was finally proved to be -untenable. - -A rule on this subject, propounded by some of the most -enlightened dignitaries of the Roman Catholic church, on the -occasion of the great Copernican controversy begun by -Galileo, seems well worthy of our attention. The following -was the opinion given by Cardinal Bellarmine at the -time:--'When a _demonstration_ shall be found to establish the -earth's motion, 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 heavens.' This -appears to be a judicious and reasonable maxim for such -cases in general. So long as the supposed scientific -discovery is doubtful, the exposition of the meaning of -Scripture given by commentators of established credit is not -wantonly to be disturbed: but when a scientific theory, -irreconcileable with this ancient {307} interpretation, is -clearly proved, we must give up the interpretation, and seek -some new mode of understanding the passage in question, by -means of which it may be consistent with what we know; for -if it be not, our conception of the things so described is -no longer consistent with itself. - -It may be said that this rule is indefinite, for who shall -decide when a new theory is completely demonstrated, and the -old interpretation become untenable? But to this we may -reply, that if the rule be assented to, its application will -not be very difficult. For when men have admitted as a -general rule, that the current interpretations of scriptural -expressions respecting natural objects and events may -possibly require, and in some cases certainly will require, -to be abandoned, and new ones admitted, they will hardly -allow themselves to contend for such interpretations as if -they were essential parts of revelation; and will look upon -the change of exposition, whether it come sooner or later, -without alarm or anger. And when men lend themselves to the -progress of truth in this spirit, it is not of any material -importance at what period a new and satisfactory -interpretation of the scriptural difficulty is found; 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 revelation. - -10. _In what Spirit should the Change be accepted?_--Still -these revolutions in scriptural interpretation must always -have in them something which distresses and disturbs -religious communities. And such uneasy feelings will take a -different shape, according as the community acknowledges or -rejects a paramount interpretative authority in its -religious leaders. In the case in which the interpretation -of the Church is binding upon all its members, the more -placid minds rest in peace upon the ancient exposition, till -the spiritual authorities announce that the time for the -adoption of a new view has arrived; but in these -circumstances, the more stirring and inquisitive minds, -which cannot refrain from the pursuit of new truths {308} -and exact conceptions, are led to opinions which, being -contrary to those of the Church, are held to be sinful. On -the other hand, if the religious constitution of the -community allow and encourage each man to study and -interpret for himself the Sacred Writings, we are met by -evils of another kind. In this case, although, by the -unforced influence of admired commentators, there may -prevail a general agreement in the usual interpretation of -difficult passages, yet as each reader of the Scripture -looks upon the sense which he has adopted as being his own -interpretation, he maintains it, not with the tranquil -acquiescence of one who has deposited his judgment in the -hands of his Church, but with the keenness and strenuousness -of self-love. In such a state of things, though no judicial -severities can be employed against the innovators, there may -arise more angry controversies than in the other case. - -It is impossible to overlook the lesson which here offers -itself, that it is in the highest degree unwise in the -friends of religion, whether individuals or communities, -unnecessarily to embark their credit in expositions of -Scripture on matters which appertain to natural Science. By -delivering physical doctrines as the teaching of revelation, -religion may lose much, but cannot gain anything. This maxim -of practical wisdom has often been urged by Christian -writers. Thus St. Augustine says[22\10]: 'In obscure matters -and things far removed from our senses, if we read anything, -even in the divine Scripture, which may produce diverse -opinions without damaging the faith which we cherish, let us -not rush headlong by positive assertion to either the one -opinion or the other; lest, when a more thorough discussion -has shown the opinion which we had adopted to be false, our -faith may fall with it: and we should be found contending, -not for the doctrine of the sacred Scriptures, but for our -own; endeavouring to make our doctrine to be that of the -Scriptures, instead of taking the doctrine of the Scriptures -to be ours.' And in nearly the same spirit, at the {309} -time of the Copernican controversy, it was thought proper to -append to the work of Copernicus a postil, to say that the -work was written to account for the phenomena, and that -people must not run on blindly and condemn either of the -opposite opinions. Even when the Inquisition, in 1616, -thought itself compelled to pronounce a decision upon this -subject, the verdict was delivered in very moderate -language;--that 'the doctrine of the earth's motion appeared -to be contrary to Scripture:' and yet, moderate as this -expression is, it has been blamed by judicious members of -the Roman church as deciding a point such as religious -authorities ought not to pretend to decide; and has brought -upon that church no ordinary weight of general condemnation. -Kepler pointed out, in his lively manner, the imprudence of -employing the force of religious authorities on such -subjects: _Acies dolabræ in ferrum illisa, postea nec in -lignum valet amplius. Capiat hoc cujus interest_. 'If you -_will_ try to chop iron, the axe becomes unable to cut even -wood. I warn those whom it concerns.' - -[Note 22\10: Lib. i. _de Genesi_, cap. xviii.] - -11. _In what Spirit should the Change be urged?_--But while -we thus endeavour to show in what manner the interpreters of -Scripture may most safely and most properly accept the -discoveries of science, we must not forget that there may be -errours committed on the other side also; and that men of -science, in bringing forward views which may for a time -disturb the minds of lovers of Scripture, should consider -themselves as bound by strict rules of candour, moderation, -and prudence. Intentionally to make their supposed -discoveries a means of discrediting, contradicting, or -slighting the sacred Scriptures, or the authority of -religion, is in them unpardonable. As men who make the -science of Truth the business of their lives, and are -persuaded of her genuine superiority, and certain of her -ultimate triumph, they are peculiarly bound to urge her -claims in a calm and temperate spirit; not forgetting that -there are other kinds of truth besides that which they -peculiarly study. They may properly reject authority in -matters of science; but they are to leave {310} it its -proper office in matters of religion. I may here again quote -Kepler's expressions: 'In Theology we balance authorities, -in Philosophy we weigh reasons. A holy man was Lactantius -who denied that the earth was round; a holy man was -Augustine, who granted the rotundity, but denied the -antipodes; a holy thing to me is the Inquisition, which -allows the smallness of the earth, but denies its motion; -but more holy to me is Truth; and hence I prove, from -philosophy, that the earth is round, and inhabited on every -side, of small size, and in motion among the stars,--and -this I do with no disrespect to the Doctors.' I the more -willingly quote such a passage from Kepler, because the -entire ingenuousness and sincere piety of his character does -not allow us to suspect him in anything of hypocrisy or -latent irony. That similar professions of respect may be -made ironically, we have a noted example in the celebrated -Introduction to _Galileo's Dialogue on the Copernican -System_; probably the part which was most offensive to the -authorities. 'Some years ago,' he begins, 'a wholesome edict -was promulgated at Rome, which, in order to check the -perilous scandals of the present age, imposed silence upon -the Pythagorean opinion of the mobility of the earth. There -were not wanting,' he proceeds, 'persons who rashly asserted -that this decree was the result, not of a judicious inquiry, -but of passion ill-informed; and complaints were heard that -councillors, utterly unacquainted with astronomical -observation, ought not to be allowed, with their sudden -prohibitions, to clip the wings of speculative intellects. -_At the hearing of rash lamentations like these, my zeal -could not keep silence._' And he then goes on to say, that -he wishes, in his _Dialogue_, to show that the subject had -been fully examined at Rome. Here the irony is quite -transparent, and the sarcasm glaringly obvious. I think we -may venture to say that this is not the temper in which -scientific questions should be treated; although by some, -perhaps, the prohibition of public discussion may be -considered as justifying any evasion which is likely to pass -unpunished. {311} - -12. _Duty of Mutual Forbearance._--We may add, as a further -reason for mutual forbearance in such cases, that the true -interests of both parties are the same. The man of science -is concerned, no less than any other person, in the truth -and import of the divine dispensation; the religious man, no -less than the man of science, is, by the nature of his -intellect, incapable of believing two contradictory -declarations. Hence they have both alike a need for -understanding the Scripture in some way in which it shall be -consistent with their understanding of nature. It is for -their common advantage to conciliate, as Kepler says, the -finger and the tongue of God, his works and his word. And -they may find abundant reason to bear with each other, even -if they should adopt for this purpose different -interpretations, each finding one satisfactory to himself; -or if any one should decline employing his thoughts on such -subjects at all. I have elsewhere[23\10] quoted a passage -from Kepler[24\10] which appears to me written in a most -suitable spirit: 'I beseech my reader that, not unmindful of -the divine goodness bestowed upon man, he do with me praise -and celebrate the wisdom of the Creator, which I open to him -from a more inward explication of the form of the world, -from a searching of causes, from a detection of the errours -of vision; 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 -God: but also that in its motion, so recondite, so -admirable, we may acknowledge the wisdom of the Creator. But -whoever is too dull to receive this science, or too weak to -believe the Copernican system without harm to his piety, -him, I say, I advise that, leaving the school of astronomy, -and condemning, if so he please, any doctrines of the -philosophers, he follow his own path, and desist from this -wandering through the universe; and that, lifting up his -natural eyes, with which alone he can see, {312} he pour -himself out from his own heart in worship of God the -Creator, being certain that he gives no less worship to God -than the astronomer, to whom God has given to see more -clearly with his inward eyes, and who, from what he has -himself discovered, both can and will glorify God.' - -[Note 23\10: _Bridgewater Tr._ p. 314.] - -[Note 24\10: _Com. Stell. Mart._ Introd.] - -13. _Case of Galileo._--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 Sciences_. Complaint has been made[25\10] that the -character of the Roman church, as shown in its behaviour -towards Galileo, is misrepresented in the account given of -it in the History of Astronomy. It is asserted that Galileo -provoked the condemnation he incurred; first, by -pertinaciously demanding the assent of the ecclesiastical -authorities to his opinion of the consistency of the -Copernican doctrine with Scripture; and afterwards by -contumaciously, and, as we have seen, contumeliously -violating the silence which the Church had enjoined upon -him. 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 unfounded; as well as the -opinion that in consequence of this habit, new scientific -truths were promulgated less boldly in Italy than in other -countries. I shall reply very briefly on these subjects; 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 chapter, nor, I hope, to satisfy my reader that my -views have been collected from an impartial consideration of -scientific history. - -[Note 25\10: _Dublin Review_, No. ix. July, 1838, p. 72.] - -With regard to Galileo, I do not think it can be denied that -he obtruded his opinions upon the ecclesiastical authorities -in an unnecessary and imprudent manner. He was of an ardent -character, strongly convinced himself, and urged on still -more by the conviction which he produced among his -disciples, and {313} thus he became impatient for the -triumph of truth. This judgment of him has recently been -delivered by various independent authorities, and has -undoubtedly considerable foundation[26\10]. As to the -question whether authority in matters of natural science -were habitually claimed by the authorities of the Church of -Rome, I have to allow that I cannot produce instances which -establish such a habit. We, who have been accustomed to have -daily before our eyes the Monition which the Romish editors -of Newton thought it necessary to prefix--_Cæterum latis a -summo Pontifice contra telluris motum Decretis, nos obsequi -profitemur_--were not likely to conjecture that this was a -solitary instance of the interposition of the Papal -authority on such subjects. But although it would be easy to -find declarations of heresy delivered by Romish -Universities, and writers of great authority, against tenets -belonging to the natural sciences, 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 sentence. I am well -contented to acknowledge this; 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 -respect, than by having to sow enmity between the admirers -of the past and the present through any disparaging -contrast[27\10]. - -[Note 26\10: Besides the _Dublin Review_, I may quote the -_Edinburgh Review_, which I suppose will not be thought -likely to have a bias in favour of the exercise of -ecclesiastical authority in matters of science; though -certainly there is a puerility in the critic's phraseology -which does not add to the weight of his judgment. 'Galileo -contrived to surround the truth with every variety of -obstruction. The tide of knowledge, which had hitherto -advanced in peace, he crested with angry breakers, and he -involved in its surf both his friends and his foes.'--_Ed. -Rev._ No. cxxiii. p. 126.] - -[Note 27\10: I may add that the most candid of the adherents -of the Church of Rome condemn the assumption of authority in -matters of science, made, in this one instance at least, by -the ecclesiastical tribunals. The author of the _Ages of -Faith_ (book viii. p. 248), says, 'A Congregation, it is to -be lamented, declared the new system to be opposed to -Scripture, and therefore heretical.'] - -{314} With respect to the attempt made in my History to -characterize the intellectual habits of Italy as produced by -her religious condition,--certainly it would ill become any -student of the history of science to speak slightingly of -that country, always the mother of sciences, always ready to -catch the dawn and hail the rising of any new light of -knowledge. But I think our admiration of this activity and -acuteness of mind is by no means inconsistent with the -opinion, that new truths were promulgated more boldly beyond -the Alps, and that the subtilty of the Italian intellect -loved to insinuate what the rough German bluntly asserted. -Of the decent duplicity with which forbidden opinions were -handled, the reviewer himself gives us instances, when he -boasts of the liberality with which Copernican professors -were placed in important stations by the ecclesiastical -authorities, soon after the doctrine of the motion of the -earth had been declared by the same authorities to be -contrary to Scripture. 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 -pleased. I think it is easy to believe that among persons so -little careful to reconcile public profession with private -conviction, official decorum was all that was demanded. When -Galileo had made his renunciation of the earth's motion on -his knees, he rose and said, as we are told, _E pur si -muove_--'and yet it _does_ move.' This is sometimes -represented as the heroic soliloquy of a mind cherishing its -conviction of the truth, in spite of persecution; I think we -may more naturally conceive it uttered as a playful epigram -in the ear of a cardinal's secretary, with a full knowledge -that it would be immediately repeated to his master[28\10]. - -[Note 28\10: I have somewhat further discussed the case of -Galileo in the later editions of the _History_, book v. -chap. iii. sect. 4.] - -Besides the Ideas involved in the material sciences, {315} -of which we have already examined the principal ones, there -is one Idea or Conception which our Sciences do not indeed -include, but to which they not obscurely point; and the -importance of this Idea will make it proper to speak of it, -though this must be done very briefly. - - - - -{{316}} -CHAPTER V. - -OF THE CONCEPTION OF A FIRST CAUSE. - - -1. AT the end of the last chapter but one, we were led to -this result,--that we cannot, in any of the Palætiological -Sciences, ascend to a beginning which is of the same nature -as the existing cause of events, and which depends upon -causes that are still in operation. Philosophers never have -demonstrated, and probably never will be able to -demonstrate, what was the original condition of the solar -system, of the earth, of the vegetable and animal worlds, of -languages, of arts. On all these subjects the course of -investigation, followed backwards as far as our materials -allow us to pursue it, ends at last in an impenetrable -gloom. We strain our eyes in vain when we try, by our -natural faculties, to discern an origin. - -2. Yet speculative men have been constantly employed in -attempts to arrive at that which thus seems to be placed out -of their reach. The Origin of Languages, the Origin of the -present Distribution of Plants and Animals, the Origin of -the Earth, have been common subjects of diligent and -persevering inquiry. Indeed inquiries respecting such -subjects have been, at least till lately, the usual form -which Palætiological researches have assumed. _Cosmogony_, -the Origin of the World, of which, in such speculations, the -earth was considered as a principal part, has been a -favourite study both of ancient and of modern times: and -most of the attempts at Geology previous to the present -period have been _Cosmogonies_ or _Geogonies_, rather than -that more genuine science which we have endeavoured to -delineate. Again: Glossology, though now an extensive body -of solid knowledge, was {317} mainly brought into being by -inquiries concerning the Original Language spoken by men; -and the nature of the first separation and diffusion of -languages, the first peopling of the earth by man and by -animals, were long sought after with ardent curiosity, -although of course with reference to the authority of the -Scriptures, as well as the evidence of natural phenomena. -Indeed the interest of such inquiries even yet is far from -being extinguished. The disposition to explore the past in -the hope of finding, by the light of natural reasoning as -well as by the aid of revelation, the origin of the present -course of things, appears to be unconquerable. 'What was the -beginning?' is a question which the human race cannot desist -from perpetually asking. And no failure in obtaining a -satisfactory answer can prevent inquisitive spirits from -again and again repeating the inquiry, although the blank -abyss into which it is uttered does not even return an echo. - -3. What, then, is the reason of an attempt so pertinacious -yet so fruitless? By what motive are we impelled thus -constantly to seek what we can never find? Why are the -errour of our conjectures, the futility of our reasonings, -the precariousness of our interpretations, over and over -again proved to us in vain? Why is it impossible for us to -acquiesce in our ignorance and to relinquish the inquiry? -Why cannot we content ourselves with examining those links -of the chain of causes which are nearest to us,--those in -which the connexion is intelligible and clear; instead of -fixing our attention upon those remote portions where we can -no longer estimate its coherence? In short, why did not men -from the first take for the subject of their speculations -the Course of Nature rather than the Origin of Things? - -To this we reply, that in doing what they have thus done, in -seeking what they have sought, men are impelled by an -intellectual necessity. They cannot conceive a Series of -connected occurrences without a Commencement; they cannot -help supposing a cause for the Whole, as well as a cause for -each part; they cannot be satisfied with a succession of -causes without {318} assuming a First Cause. Such an -assumption is necessarily impressed upon our minds by our -contemplation of a series of causes and effects; that _there -must be a First Cause_, is accepted by all intelligent -reasoners as an Axiom: and like other Axioms, its truth is -necessarily implied in the Idea which it involves. - -4. The evidence of this axiom may be illustrated in several -ways. In the first place, the axiom is assumed in the -argument usually offered to prove the existence of the -Deity. Since, it is said, the world now exists, and since -nothing cannot produce something, something must have -existed from eternity. This Something is the First Cause: it -is God. - -Now what I have to remark here is this:--the conclusiveness -of this argument, as a proof of the existence of one -independent, immutable Deity, depends entirely upon the -assumption of the axiom above stated. The World, a **series -of causes and effects, exists: therefore there must be, not -only this series of causes and effects, but also a First -Cause. It will be easily seen, that without the axiom, that -in every series of causes and effects there must be a First -Cause, the reasoning is altogether inconclusive. - -5. Or to put the matter otherwise: The argument for the -existence of the Deity was stated thus: Something exists, -therefore something must have existed from eternity. -'Granted,' the opponent might say; 'but this something which -has existed from eternity, why may it not be this very -series of causes and effects which is now going on, and -which appears to contain in itself no indication of -beginning or end?' And thus, without the assumption of the -necessity of a First Cause, the force of the argument may be -resisted. - -6. But, it may be asked, how do those who have written to -prove the existence of the Deity reply to such an objection -as the one just stated? It is natural to suppose that, on a -subject so interesting and so long discussed, all the -obvious arguments with their replies, have been fully -brought into view. What is the result in this case? {319} - -The principal modes of replying to the above objection, that -the series of causes and effects which now exists, may have -existed from eternity, appear to be these. - -In the first place, our minds cannot be satisfied with a -series of successive, dependent, causes and effects, without -something first and independent. We pass from effect to -cause, and from that to a higher cause, in search of -something on which the mind can rest; but if we can do -nothing but repeat this process, there is no use in it. We -move our limbs, but make no advance. Our question is not -answered, but evaded. The mind cannot acquiesce in the -destiny thus presented to it, of being referred from event -to event, from object to object, along an interminable vista -of causation and time. Now this mode of stating the -reply,--to say that the mind _cannot thus be satisfied_, -appears to be equivalent to saying that the mind is -conscious of a Principle, in virtue of which such a view as -this must be rejected;--the mind takes refuge in the -assumption of a First Cause, from an employment inconsistent -with its own nature. - -7. Or again, we may avoid the objection, by putting the -argument for the existence of a Deity in this form: The -series of causes and effects which we call the _world_, or -the _course of nature_, may be considered as a _whole_, and -this whole must have a cause of its existence. The whole -collection of objects and events may be comprehended as a -single effect, and of this effect there must be a cause. -This Cause of the Universe must be superior to, and -independent of the special events, which, happening in time, -make up the universe of which He is the cause. He must exist -and exercise causation, before these events can begin: He -must be the First Cause. - -Although the argument is here somewhat modified in form, the -substance is the same as before. For the assumption that we -may consider the whole series of causes and effects as a -_single effect_, is equivalent to the assumption that -besides partial causes we must have a First Cause. And thus -the Idea of a First Cause, and {320} the axiom which asserts -its necessity, are recognized in the usual argumentation on -this subject. - -8. This Idea of a First Cause, and the principle involved in -the Idea, have been the subject of discussion in another -manner. As we have already said, we assume as an axiom that -a First Cause must exist; and we assert that God, the First -Cause, exists eternal and immutable, by the necessity which -the axiom implies. Hence God is said to exist -necessarily;--to be a necessarily existing being. And when -this _necessary existence_ of God had been spoken of, it -soon began to be contemplated as a sufficient reason, and as -an absolute demonstration of His existence; without any need -of referring to the world as an effect, in order to arrive -at God as the cause. And thus men conceived that they had -obtained a proof of the existence of the Deity, _à priori_, -from Ideas, as well as _à posteriori_, from Effects. - -9. Thus, Thomas Aquinas employs this reasoning to prove the -_eternity_ of God[29\10]: 'Oportet ponere aliquod primum -necessarium quod est per se ipsum necessarium; et hoc est -Deus, cum sit prima causa ut dictum est: igitur Deus æternus -est, cum omne necessarium per se sit æternum.' It is true -that the schoolmen never professed to be able to prove the -_existence_ of the Deity _à priori_: but they made use of -this conception of necessary existence in a manner which -approached very near to such an attempt. Thus Suarez[30\10] -discusses the question, 'Utrum aliquo modo possit _à priori_ -demonstrari Deum esse.' And resolves the question in this -manner: 'Ad hunc ergo modum dicendum est: Demonstrato _à -posteriori_ Deum esse ens necessarium et a se, ex hoc -attributo posse _à priori_ demonstrari præter illud non -posse esse aliud ens necessarium et a se, et consequenter -demonstrari Deum esse.' - -[Note 29\10: Aquin. _Cont. Gentil._ lib. i. c. xiv. p. 21.] - -[Note 30\10: _Metaphys._ tom. ii. disp. xxix. sect. 3, p. 28.] - -But in modern times attempts were made by Descartes and -Samuel Clarke, to prove the Divine {321} existence at once -_à priori_, from the conception of necessary existence; -which, it was argued, could not subsist without actual -existence. This argumentation was acutely and severely -criticised by Dr. Waterland. - -10. Without dwelling upon a subject, the discussion of which -does not enter into the design of the present work, I may -remark that the question whether an _à priori_ proof of the -existence of a First Cause be possible, is a question -concerning the nature of our Ideas, and the evidence of the -axioms which they involve, of the same kind as many -questions which we have already had to discuss. Is our -Conception or Idea of a First Cause gathered from the -effects we see around us? It is plain that we must answer, -here as in other cases, that the Idea is not extracted from -the phenomena, but assumed in order that the phenomena may -become intelligible to the mind;--that the Idea is a -necessary one, inasmuch as it does not depend upon -observation for its evidence; but that it depends upon -observation for its development, since without some -observation, we cannot conceive the mind to be cognizant of -the relation of causation at all. In this respect, however, -the Idea of a First Cause is no less necessary than the -ideas of Space, or Time, or Cause in general. And whether we -call the reasoning derived from such a necessity an argument -_à priori_ or _à posteriori_, in either case it possesses -the genuine character of demonstration, being founded upon -axioms which command universal assent. - -11. I have, however, spoken of our _Conception_ rather than -of our _Idea_ of a First Cause; for the notion of a First -Cause appears to be rather a modification of the Fundamental -Idea of Cause, which was formerly discussed, than a separate -and peculiar Idea. And the Axiom, _that there must be a -First Cause_, is recognised by most persons as an -application of the general Axiom of Causation, _that every -effect must have a Cause_; this latter Axiom being applied -to the World, considered in its totality, as a single -Effect. This distinction, however, between an Idea and a -Conception, is of no material consequence to our argument; -provided we {322} allow the maxim, that there must be a -First Cause, to be necessarily and evidently true; whether -it be thought better to speak of it as an independent Axiom, -or to consider it as derived from the general Axiom of Causation. - -12. Thus we necessarily infer a First Cause, although the -Palætiological Sciences only point _towards_ it, and do not -lead us _to_ it. But I must observe further; that in each of -the series of events which form the subject of -Palætiological research, the First Cause is the _same_. -Without here resting upon reasoning founded upon our -Conception of a First Cause, I may remark that this identity -is proved by the close connexion of all the branches of -natural science, and the way in which the causes and the -events of each are interwoven with those which belong to the -others. 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 surface; that the First Cause of -the vegetable and of the animal world are the same; that the -First Cause which produced light produced also eyes; that -the First Cause which produced air and organs of -articulation produced also language and the faculties by -which language is rendered possible: and if _those_ -faculties, then also all man's other faculties;--the powers -by which, as we have said, he discerns right and wrong, and -recognises a providential as well as a natural course of -things. Nor can we think otherwise than that the Being who -gave these faculties, bestowed them for some -purpose;--bestowed them for that purpose which alone is -compatible with their nature:--the purpose, namely, of -guiding and elevating man in his present career, and of -preparing him for another state of being to which they -irresistibly direct his hopes. And thus, although, as we -have said, no one of the Palætiological Sciences can be -traced continuously to an Origin, yet they not only each -point to an Origin, but all to the same Origin. Their lines -are broken indeed, as they run backwards into the early -periods of the world, but yet they all appear to converge to -the same invisible point. And {323} this point, thus -indicated by the natural course of things, can be no other -than that which is disclosed to us as the starting-point of -the providential course of the world; for we are persuaded -by such reasons as have just been hinted, that the Creator -of the natural world can be no other than the Author and -Governor and Judge of the moral and spiritual world. - -13. Thus we are led, by our material Sciences, and -especially by the Palætiological class of them, to the -borders of a higher region, and to a point of view from -which we have a prospect of other provinces of -knowledge;--to contemplations in which other faculties of -man are concerned besides his intellectual, other interests -involved besides those of speculation. On these it does not -belong to our present plan to dwell: but even such a brief -glance as we have taken of the connexion of material with -moral speculations may not be useless, since it may serve to -show that the principles of truth which we are now -laboriously collecting among the results of the physical -sciences, may possibly find some application in those parts -of knowledge towards which men most naturally look with -deeper interest and more serious reverence. - - -We have been employed hitherto in examining the materials of -knowledge, Facts and Ideas;--Facts in our former History, -and Ideas in the present History. We have dwelt at length on -this latter element; inasmuch as the consideration of it is, -on various accounts, and especially at the present time, by -far the most important, having hitherto been least -distinctly attended to as a special element of scientific -knowledge. - -There still remains an important task, with a view to which -we have undertaken this survey of the past course of human -thought and discovery:--namely, the task of determining the -processes by which these materials may actually be made to -constitute knowledge. {324} We have surveyed the stones -which lie before us, partly built and partly ready for -building: we have found them exactly squared, and often -curiously covered with significant imagery and important -inscriptions. We have now to discover how they may best be -fitted into their places, and cemented together, so that -rising stage above stage, they may grow at last into that -fair and lofty temple of Truth, for which we cannot doubt -that they were intended by the Great Architect. - -This task, the description of the processes by which -Scientific Truth is discovered and established, we shall, as -has already been said, entitle, in reference to previous -attempts of the same kind, _Novum Organum Renovatum_. - - -END OF VOL. II. - - - -_Cambridge: Printed at the University Press._ - - - - -Transcriber's Note - -Whewell published the first edition of the _Philosophy of the -Inductive Sciences_ in 1840, as a companion to the 1837 -_History of the Inductive Sciences_. Revised second editions -of both works appeared in 1847. The third editions saw a -major reshaping of the _Philosophy_: a two volume _History -of Scientific Ideas_ (1858 - the present text, relying upon -resources kindly provided by the Internet Archive), _Novum -Organon Renovatum_ (1858), and _ On the Philosophy of -Discovery: chapters historical and critical_ (1860 - already -in Project Gutenberg's collection: #5155). - -The present text has combined the two volumes into one continuous -text. Footnotes are numbered by Book and marked [m\n] where m = -the number of the note within the Book, and n = the number of the -Book. In the original, notes were numbered by chapter. Page numbers -appear in { }, or {{ }} where there is no printed number; where a -word was hyphenated across pages the number has been placed before -the word. - -Superscripts are marked with ^. - -There is one significant problem to report. For Book IX chapter VI, -the Table of Contents lists 20 articles, but the actual text has -only 19 numbered paragraphs. The text version leaves this -inconsistency untouched; in the htm version, a correction has been -made by numbering the paragraph beginning on p. 244 as #9, and -renumbering those that follow, thereby matching the descriptions in -the Table of Contents. - -Other corrections to the text are marked with ** and are listed -below. - -Location Text of printed edition Emendation -Vol. 1 -p. 71 conlcusion conclusion -p. 87 vi. vii. -p. 157 sciences science -note 1\3 Book 1. chap. xii. Book 3. chap. ii. -p. 231 Marriotte Mariotte -p. 377 Winter's Winterl's -Vol. 2 -p. 22 ingedient ingredient -p. 124 wich which -p. 159 attemps attempts -p. 172 knowlege knowledge -note 60\9 Their. 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