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 1880. 
 The credentials of science 
 
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THE CREDENTIALS OF SCIENCE 
 THE WARRANT OF FAITH. 
 
<0 : 
 
 THE 
 
 OCT 04 1912 
 
 ^GAL » 
 
 Credentials of Science 
 
 777£ WARRANT OF FAITH. 
 
 BY 
 
 JOSIAH PARSONS COOKE, LL.D., 
 
 ERVING PROFESSOR OF CHEMISTRY AND MINERALOGY IN 
 HARVARD UNIVERSITY. 
 
 SECOND EDITION. 
 
 NEW YORK: 
 
 D. APPLETON AND COMPANY. 
 
 1893. 
 
Copyright, 1888, 
 Bv ROBERT CARTER AND BROTHERS. 
 
 Copyright, 1893, 
 By JOSIAH P. COOKE. 
 
IN MEMORIAM 
 
 'QUI docti fuerint fulgebunt quasi splendor firmamenti; 
 
 ET QUI AD JUSTITIAM ERUDIUNT MULTOS, QUASI 
 STELLA IN PERPETUAS yETERNITATES." 
 
PREFACE TO SECOND EDITION. 
 
 THE subject of this volume was first developed 
 by the author as a course of lectures at the 
 invitation of the Union Theological Seminary of 
 New York City, and the lectures were delivered in 
 the Adams Chapel of the Seminary during the early 
 spring of 1887, the course of eight lectures closing 
 on Easter Eve. The course was given on a founda- 
 tion established by Mr. Zebulon Stiles Ely to sup- 
 port a lectureship on the Evidences of Christianity. 
 The material was subsequently considerably ampli- 
 fied, and delivered as a course of twelve lectures 
 before the Lowell Institute of Boston, closing on 
 Christmas Eve of the same year. The lectures have 
 been printed as thus extended, although in some 
 cases the limitations of a lecture hour compelled 
 a division of subjects, which are here united under 
 the same heading, thus reducing the number of 
 chapters in the book to ten. 
 
 The motive of the work is indicated by the title, 
 the chief argument being that the popular objec- 
 tions to Christian beliefs might be urged with equal 
 force against each of the predominant systems of 
 
Vlll PREFACE TO SECOND EDITION. 
 
 science of the present day, and are the necessary- 
 result of the limitations of our human knowledge ; 
 that so far from proving the inconsequence of our 
 religious beliefs, the oppositions so greatly magnified 
 plainly point to a condition in which the limitations 
 that now narrow our vision will be removed. In 
 following out this argument the author has discussed 
 the basis of scientific systems ; the modes of thought 
 distinguished as induction and deduction, by which 
 general principles have been apprehended and their 
 scope constantly widened ; the significance of the so- 
 called laws of Nature ; the validity of the prevailing 
 theories or systems of science ; and the predominant 
 principles of scientific thought. 
 
 By the terms of the appointment to the Ely Lec- 
 tureship the copyright of this book was vested in 
 the Union Theological Seminary, and the first edition 
 was published by Robert Carter and Brothers, under 
 the auspices of the Seminary ; but after that firm 
 retired from business, the directors of the Seminary, 
 by vote at a meeting held on November 10, 1891, 
 transferred the copyright to the author, who has 
 carefully revised the work for a new edition. No 
 important changes have been made in the form of 
 the argument or in the mode of presentation, but 
 the text has been revised, and misprints, as far as 
 discovered, corrected. 
 
 Cambridge, April 22, i8gj. 
 
CONTENTS. 
 
 Lecture Page 
 
 I. The Argument of Natural Theology . . i 
 
 II. Preparing the Way 29 
 
 III. The Induction of Newton 59 
 
 IV. Deduction 93 
 
 V. Examples of Scientific Investigation . . 127 
 
 VI. Laws of Nature 158 
 
 VII. Determinate and Indeterminate Laws . ■ 184 
 
 VIII. Theories or Systems of Science .... 209 
 
 IX. Predominant Principles of Scientific 
 
 Thought 260 
 
 X. The Systems Compared. — Religion and 
 
 Science 289 
 
The Credentials of Science 
 
 THE WARRANT OF FAITH. 
 
 LECTURE I. 
 
 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 NATURAL Religion is as old as man's conscious- 
 ness of dependence, and Natural Theology is 
 coeval with literature. Its fundamental arguments 
 were urged by the Greek and Roman philosophers, 
 and the illustrations of the subject by Galen have 
 scarcely been equalled in modern times. During 
 the last two centuries works on natural theology 
 have formed a conspicuous feature in English litera- 
 ture, — in consequence chiefly of several pious foun- 
 dations which have provided for the discussion of the 
 subject at stated intervals. These works have as a 
 rule been written in a popular style, and have dealt 
 with illustrations of old arguments rather than with 
 the arguments themselves. They have served an ex- 
 cellent purpose by keeping before the popular mind 
 the ever accumulating mass of evidence of skill and of 
 plan which nature offers, and by exhibiting the reli- 
 gious aspects of scientific facts and theories. Unfor- 
 
2 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 tunately they have often been open to criticism, and 
 too frequently have justified the contempt into which 
 teleology has so generally fallen. 
 
 A recent writer, in his " Critique of Design Argu- 
 ments," x has done an excellent work, not only by fix- 
 ing attention on the arguments, but also by furnishing 
 a carefully prepared synopsis of all the important 
 writings bearing on natural theology from the earliest 
 times. But while freely admitting the justice of this 
 writer's criticism in many respects, even when we our- 
 selves have fallen under the ban, we cannot concur 
 with him either in his general estimate of design argu- 
 ments, or in the essential character of the distinction 
 which he seeks to draw between the argument from 
 general plan and the so-called argument from design. 
 This last phrase has become one of the universal 
 terms of our language, and it is not to be supposed 
 that acute Scotch logicians like Dugald Stewart and 
 Reid overlooked the obvious begging of the question 
 which a precise definition of the words would involve. 
 There has been undoubtedly as frequent misuse of 
 language in essays on natural theology as in similar 
 popular expositions ; but much of this has resulted 
 from the necessities of the case. 
 
 In popular discourse language cannot be used with 
 the precision of mathematical terrn.3, and often a 
 hypercritical spirit defeats the main object of the 
 teacher. Singular as it is, the more a man knows, the 
 more difficult it becomes to present a subject in lan- 
 guage that can be easily comprehended. The teacher 
 
 1 Critique of Design Arguments, by L. E. Hicks. New York. 
 Charles Scribner's Sons, 1883. 
 
DESIGN SUPPOSES A DESIGNER. 
 
 is hampered by his knowledge of the limitations to 
 the general propositions he enunciates, and he is 
 forced to avail himself of all the latitude which the 
 most liberal interpretation of language will allow. 
 No one who has not had the experience knows how 
 difficult it often is to reconcile exact accuracy with 
 that concise statement which is one of the essential 
 conditions of effective teaching; and the intended pur- 
 port of rhetorical writing can always be misrepre- 
 sented by the quotation of isolated passages. 
 
 When an able theologian writes, " Design supposes 
 a designer," it is reasonable to infer that he does not 
 intend to involve his readers in the logical absurdity 
 of an identical proposition, but simply intends to de- 
 clare the undoubted fact, that a multitude of relations 
 in nature suggest to the mind of man an intelligent 
 author. 
 
 The confusion implied in this and in similar phrase- 
 ology arises from an attempt to gauge such reason- 
 ing by the rules of deductive logic. Man has not 
 risen to knowledge of Divine things by deduction but 
 by induction. These things always have been, and 
 always will continue to be to the logical Greeks of 
 every age foolishness, and so long as the theologian 
 cherishes the conceit that the Godhead can be dem- 
 onstrated, he cannot hope to escape from the web of 
 logical fallacies which his argument must involve. 
 
 The knowledge of God has come to man through 
 nature precisely in the same way as the generaliza- 
 tions of science, and is subject to the same limitations 
 and carries the same conviction as all general truths. 
 Man knows God by the same means and through the 
 
4 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 same sources that he knows the principles of gravita- 
 tion, heat, and electricity. In each case an assumed 
 energy acting through special channels under definite 
 laws is the best explanation he can form of a certain 
 class of phenomena. So also the assumption of an 
 Intelligent Will, with power to create and power to 
 sustain, is the commonly received explanation which 
 man has formed of the origin and continuance of this 
 universe in which he dwells. 
 
 The fundamental principles of science may be said 
 to be suggestions of nature confirmed by experience. 
 When once conceived, we can often deduce from a 
 general principle, mathematically or otherwise, a host 
 of inferences which observation substantiates. This 
 indeed is the normal way by which our knowledge of 
 nature is enlarged ; and such deductions, verified by 
 experience, furnish the strongest confirmation of the 
 truth of the principle with which we started. But the 
 principle itself was no deduction, it was a suggestion 
 of nature ; and this is all we know of its origin. We 
 may seek to study the conditions and circumstances 
 under which such suggestions have come into the 
 minds of the favored men of the race, but we get no 
 nearer to the source. 
 
 Among essential conditions we at once recognize 
 a familiar acquaintance with nature, and a powerful 
 but well regulated imagination. We also readily trace 
 the influence of analogies, and even of accidental asso- 
 ciations. We easily see anthropomorphic elements 
 in such conceptions ; but all these things are merely 
 accessories to a mental process of which the discoverer 
 himself can give no clear account, as the trivial stories 
 
THE CONCEPTION OF GOD AN INDUCTION. 5 
 
 of swinging lamps and falling apples so plainly show. 
 It is a mental faculty which, though in its highest 
 manifestation only known to a few highly gifted men, 
 is in some small measure within the experience of 
 every student of nature. To such students the 
 method seems perfectly natural, even when they may 
 not be able to discover its elements. Many philoso- 
 phers, like Bacon, have attempted to analyze the 
 method, and have named it " induction ; " but few of 
 those who are in the habit of using the method would 
 recognize the mechanism that has been described. 
 The so-called induction resembles inspiration, and 
 the loftiest inspiration seems to be only the same fac- 
 ulty of mind more highly developed. 
 
 As are the fundamental principles of science, so is 
 the conception of God a suggestion of nature con- 
 firmed by experience. It is an induction which com- 
 mands belief, not a deduction which compels consent. 
 This difference between inductive and deductive truth 
 does not depend upon the degree of certitude, but on 
 the completeness of knowledge. The highest truths 
 can be known only in part, and it is such truths that 
 are reached by induction. Thus alone can men " rise 
 on stepping-stones of their dead selves to higher 
 things." Moreover, of such truths certitude of con- 
 viction comes only with experience. Christ said " If 
 ye do my will ye shall know of the doctrine " and the 
 principle thus announced applies to all inductive 
 truths. 
 
 It is only beliefs thus attested which command the 
 enthusiasm of men. For such beliefs alone will men 
 sacrifice their lives. The deductions of Geometry are 
 
RELIGION AND CHEMISTRY. 
 
 great truths fully comprehended ; but how inconceiv- 
 able, a martyr to the theorem of Pythagoras ! And 
 there never would have been a martyr to religious be- 
 liefs, if these verities could have been reached by de- 
 duction, — in a word, could have been demonstrated. 
 
 Regard now the fundamental truth of natural re- 
 ligion as an induction, comprehended only in part, 
 but having all the certitude which the experience of 
 the ages has given, and your natural theology becomes 
 a system which is not only consistent throughout, but 
 which harmonizes with all knowledge. Attempt, how- 
 ever, to claim for this truth deductive demonstration, 
 and you at once involve your system in contradictions, 
 and miss the very certitude you are seeking to secure. 
 
 More than twenty-five years ago the writer de- 
 livered a course of lectures at Brooklyn, on the Gra- 
 ham Foundation, in which the position just defined 
 was distinctly taken. These lectures were subse- 
 quently published, and the book is well known under 
 the title of" Religion and Chemistry, or Proofs of God's 
 Plan in the Constitution of the Atmosphere." The 
 lectures were written for a popular audience, and there- 
 fore in a rhetorical form, and it would be easy to mis- 
 represent the argument by a quotation of isolated 
 passages ; but no one who actually reads the book 
 can mistake either the intentions of the writer or the 
 spirit of his work. No one could have been more 
 dissatisfied with the work than the author himself, 
 and for this reason he suffered the book to remain 
 out of print for many years; and when after repeated 
 requests from clerical friends the work was revised for 
 the recent edition, the expository and rhetorical form 
 
CONFLICT BETWEEN SCIENCE AND THEOLOGY. J 
 
 was retained simply because in the judgment of these 
 friends the usefulness of the book depended in no 
 small measure on its popular style. Thus called upon 
 to review what was written at a time when it might be 
 expected that logic should be somewhat blinded by en- 
 thusiasm, the writer could find nothing in the tenor or 
 spirit of the work that he desired to change; and the 
 general argument appears to him still, as it did at first, 
 unanswerable. 
 
 Now, however, that I am invited to address the 
 members of this influential theological seminary on 
 the same general subject, I feel that the best service 
 I can render is to present the same argument in a 
 more methodical and compact form, — a form in 
 which its strength will better appear, and its weak- 
 ness, if any, will be more conspicuously exposed. 
 With no desire to magnify my office, I cannot but 
 feel that the subject under discussion is one of great 
 importance to theological students. It is the ground 
 on which the conflict between science and theology 
 has always been fought. Whatever may have been 
 the incidental advantages, no one can question that the 
 conflict itself is a great evil. Is it, indeed, necessary 
 that the promulgation of every important doctrine of 
 science should be followed by a partial eclipse of 
 faith, like that through which so many minds have 
 recently been passing? Brought as I have been into 
 sympathy with the advocates on both sides, I believe 
 I am in a position to form an impartial judgment; 
 and while fully recognizing the narrowness and evil 
 spirit which men even of large knowledge have often 
 exhibited, I feel constrained to express the opinion that 
 the clergy are largely responsible for the bad effects 
 
8 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 of the controversy. Remember that science is para- 
 mount in its own sphere, that its methods are legiti- 
 mate, and its only object is truth ; and be assured 
 that if any one of its devotees is irregular in his 
 methods, or false to his profession, his own associates 
 will be the first to criticise and condemn his errors. 
 Moreover, the doctrines of science are held with 
 great jealousy; and, although the evils of partisan- 
 ship are as great in scientific controversies as else- 
 where, the doctrines themselves will stand or fall 
 solely on their own merit in the end. Once attested 
 they cease to be safe subjects for the uninitiated to 
 discuss, and much less, proper objects to anathema- 
 tize. I can assure you that there have been times 
 when the obligation which the church enjoins to hear 
 sermons has been a painful duty to one who holds 
 the truth in reverence, and desires also to reverence 
 the defenders of the " faith once delivered to the 
 saints." I cannot but believe that if the clergy 
 understood more fully the true relations of scientific 
 doctrines, and saw clearly that the fundamental postu- 
 late of theology rests on the same basis, they would 
 be more patient with the inevitable friction which 
 attends the progress of truth as well as the coming 
 of the kingdom. 
 
 In discussing the broad subject of natural theology 
 the limitations of my own studies must necessarily 
 constrain me to confine myself to those arguments 
 which may be drawn from the facts of external na- 
 ture; and this I shall do without in the least under- 
 valuing the purely ontological arguments based on 
 the equally definite facts of consciousness. But let it 
 
DEVELOPMENT OF THE CONCEPTION OF GOD. 9 
 
 also be clearly understood that I shall regard as a 
 part of the phenomena of nature the undoubted his- 
 torical facts of Christianity, as well as the clearly 
 established facts connected with other religions ; and 
 in my opinion the evidences of natural theology are 
 most incomplete when these all-important phenom- 
 ena are left out of view. Of course such facts will 
 be here studied in their objective, and not in their 
 subjective aspect. 
 
 By considering the development of the conception 
 of God in the mind of man, I think we can gain some 
 insight into the nature of the mental process by 
 which the conception is reached, and in the same 
 way that by the study of embryology we gain a 
 better knowledge of animal structure. There can be 
 no question that there are certain uniform stages in 
 the order of this development, both in the history of 
 the race and in the education of each individual 
 man. This very uniformity under such diverse con- 
 ditions plainly shows that the conception is not the 
 accident of circumstances, but the normal product 
 of the human mind under its environment. We do 
 not call it intuitive, because we do not care to raise 
 the question that the word intuition suggests, — a 
 question with which we have no immediate concern. 
 But whether the result of intuition or of inspiration, 
 or, more probably, of both of these ideal functions of 
 the mind, acting, as we have said before, under its 
 environments, the conception is unquestionably as 
 spontaneous as it is real. 
 
 In discussing the development of the fundamental 
 conceptions of all religions, it is not necessary for us 
 
10 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 to enter upon any abstruse questions of ethnology, 
 archaeology, or philology, although all this learning 
 might be brought to bear on the subject. The gen- 
 eral conclusions with which alone we shall have to 
 deal, are so patent that they will be accepted by 
 every one, and this circumstance alone shows how 
 fundamental are the phenomena we are considering. 
 
 When the child first becomes conscious of his free 
 will he finds that will opposed by other wills like his 
 own, and we all know what an essential condition 
 of education is the conflict which results. In our 
 short-sightedness how greatly do we regret this con- 
 flict, how earnestly seek to avoid it, and how often 
 do we shun the responsibility it involves ; and yet 
 how fully do we recognize that no strength of char- 
 acter, no force of will, no power of intellect, no assur- 
 ance of faith, can be gained except by conflict ; how 
 often only after repeated disasters are these virtues 
 secured, and how forcibly does some of the most 
 beautiful imagery of our language illustrate this 
 truth. 
 
 As to every child, so with freedom of the will 
 there must have come at some first time to primeval 
 man the conception of an opposing will ; and the 
 warfare then began through which the race has been 
 educated. Admit that this conflict is but a continu- 
 ation of the struggle for existence which began with 
 life, yet now certainly the struggle involves for the 
 first time conscious personality, and the mysterious 
 knowledge of good and evil, so inseparably associ- 
 ated with that freedom which makes us responsible 
 beings. 
 
THE ARGUMENT OF MIGHT. i i 
 
 Through the conflicts of his will man acquired 
 his first conception of power, the earliest measure 
 of his own strength. In his fellow-men he at once 
 recognized powers commensurate with his own, to 
 which he was frequently forced to yield, but which 
 he could often overcome ; and with such powers he 
 from the first associated personality. But it required 
 only a short experience with nature to force upon 
 him the knowledge that he was under the control of 
 powers vastly superior to those of men, which he 
 could not withstand, and by which his fellows were 
 frequently overwhelmed, — powers so mighty and so 
 hidden that he quailed and trembled before them. 
 As he knew power only as an attribute of personality, 
 he ascribed the powers of nature to mighty and 
 exalted personages capable of such vast effects ; and 
 hence came man's first conception of God. The God 
 thus conceived was merely the God of might, the 
 God who rules in the tempest and directs the thun- 
 derbolts, the God who rejoices in war and carnage. 
 Moreover, these powers did not seem to be wielded by 
 a single person. Man was still far from the concep- 
 tion of a Jehovah ; but as he was opposed by many 
 persons so his fancy filled the heavens with a host of 
 warring gods. 
 
 It is not our purpose to sketch the numberless 
 fanciful forms which under different associations the 
 early conception assumed. We desire only to em- 
 phasize the fact that the earliest conception of God 
 was that of a God of Might, and that this conception 
 came to the savage as an obvious suggestion of na- 
 ture. It was an induction from observed facts; and 
 
12 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 simple and obvious as the induction was, the mental 
 process by which it was reached differed in degree 
 only, not in kind, from the inductions of modern 
 science. 
 
 Such inductions do not of course bring with them 
 their credentials ; but in so far as they embody truth, 
 they become accredited through experience, and 
 chiefly in two ways : first, by their universality, that 
 is, by coming to many persons independently, thus 
 showing that they are in harmony with the constitu- 
 tion of the human mind ; and secondly, by their 
 permanency in retaining their hold on men, indicat- 
 ing that they have stood the test to which they have 
 been exposed, and by which they have been tried. 
 
 The primitive inductions of men must necessarily 
 be very partial truths, and the grain of truth is con- 
 stantly so incrusted with error that it is with difficulty 
 discovered ; but I feel persuaded that beliefs which 
 are long held in reverence owe their power to this 
 grain of truth, however small. 
 
 A most striking feature of inductions, by which 
 they are plainly distinguished from deductions, is to 
 be found in that inductions are progressive, and 
 become clarified with experience. A deduction is 
 demonstrative, and if the premises are correct, the 
 conclusion naturally follows. There is no question 
 as to degree, no room for doubt except as regards 
 the premises of the argument. An induction, how- 
 ever, may have every possible degree of certitude, 
 from an unverified conjecture to a law of nature con- 
 firmed by experience. Moreover, in the progress of 
 knowledge it has been constantly the case that the 
 
INDUCTIONS BECOME SLOWLY CLARIFIED. 1 3 
 
 conjecture has appeared as a law only after a slow 
 clarifying process. As the dregs have settled from 
 the intellectual medium, the truth has been seen in 
 ever clearer outlines ; its essential features have be- 
 come evident, while the grosser aspects of the orig- 
 inal crude conception have disappeared. Such has 
 been the uniform history of the great generalizations 
 of science, and through such a clarifying process are 
 most, if not all, of them still passing. Possibly in 
 a very few cases the truth even now appears in all 
 its simplicity; but there can be no question that in 
 the case of most of the fundamental principles of 
 modern science of which we feel so proud, and which 
 have been such valuable guides in the study of na- 
 ture, the truths they embody are still only seen as 
 in a glass darkly. It has been the privilege of a few 
 gifted minds to see the truth of the inductions they 
 have made generally recognized during their life on 
 earth, but as a rule so many minds have concurred in 
 developing these general truths that they must be re- 
 garded as the product of the age, rather than as the 
 gift of any one man to the knowledge of the world. 
 
 These features of scientific generalizations are strik- 
 ingly characteristic of the fundamental religious con- 
 ception, which is also, as we have claimed, an induc- 
 tion from observed facts. As first seen through the 
 mists of barbarism, God was a Moloch, or a Thor, or 
 at best a Jupiter; but as in proportion to his men- 
 tal growth man's spiritual vision became clearer, the 
 image became ever more definite, more beautiful, 
 and more lovely. It is not our purpose to trace 
 the connection between the thousands of fantastic 
 
14 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 shapes which the first crude shadowy form assumed, 
 in the history of different peoples, but we must mark 
 four important stages of the conception, that are asso- 
 ciated with different phases of the argument of nat- 
 ural theology. 
 
 It was a very important, although doubtless a very 
 early advance in the progress of our race, when men 
 first invented weapons and tools, in order to apply 
 their brute strength more effectively, or direct it to 
 more useful ends. By the use of tools primeval man 
 was most markedly distinguished from all the ani- 
 mals with which he was associated, including the 
 highest anthropoids, from some of whose progenitors 
 man is supposed to have descended. 
 
 No one has claimed that even the rudest tools were 
 ever made by anthropoids, however close their re- 
 semblance to man ; and the appearance of stone im- 
 plements in the strata marks the introduction of man 
 upon the earth with remarkable sharpness. There 
 seems to be here a most striking break of continuity, 
 which the doctrine of gradual evolution has not hith- 
 erto explained. The bones which we invariably find 
 with these rude tools are those of well developed 
 men, oftentimes with skulls at least as capacious as 
 our own. 
 
 However the evolutionists may explain these note- 
 worthy facts, there can be no question that tools, 
 even in their most primitive form, are proofs of a de- 
 gree of intelligence which did not appear on earth 
 until, outwardly at least, man had become essentially 
 the same creature that he is to-day. In proportion 
 as man has risen in the scale of intelligence he has 
 
INTELLIGENT USE. 1 5 
 
 displayed an ever increasing ingenuity in the inven- 
 tion of tools ; and the printing-press, the power-loom, 
 the steam-engine, the electric telegraph, are the tools 
 of our civilization, as the flint arrow-heads and stone 
 axes were those of primeval man. 
 
 Obviously, all tools or other implements are evi- 
 dences of intelligence. If now we inquire on what 
 basis this evidence rests, I think it will be found to 
 depend on the fitness of these implements for an in- 
 telligent use. We use the word " implements " here 
 in the broadest sense, for any utensils, even orna- 
 ments, wrought for a specific use ; and it is the fitness 
 of such implements for an intelligent use which consti- 
 tutes the evidence of intelligence that such objects as 
 are collected in an archaeological museum afford. It 
 may be that the archaeologist cannot determine the use 
 of certain objects, but even such objects bear marks 
 of having been wrought with tools, whose intelligent 
 use is known, and must therefore be classed with 
 them. In the last analysis intelligent use is the funda- 
 mental evidence on which our conclusion as regards 
 the intelligence of the agency which fashioned the im- 
 plements depends ; and the fitness of the implements 
 for such use, or even the traces of tools having such 
 fitness, are a secondary but still a conclusive evidence 
 of intelligence; because such fitness, or traces, dis- 
 tinctly point out the intelligent use for which the 
 implements were made. It is not the marks of the in- 
 scription which are the fundamental evidence of the 
 intelligence that an inscription always suggests, but 
 the thought which these marks have often concealed. 
 Before the Assyrian characters could be read it was 
 
I 6 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 not seriously doubted that they were the writings of 
 men, because they bore a close resemblance to such 
 writings. But evidently if the arrow-head characters 
 had proved to be simply the effect of natural causes, 
 like the crystal outlines on a slab of graphic granite, 
 such markings would be no longer any evidence of 
 intelligence. On the other hand, if they had proved 
 to be simple ornamentations they would still be evi- 
 dences of intelligence ; and, even if it had only ap- 
 peared that they had been cut or moulded with tools, 
 however rude, they would likewise be evidences of 
 intelligence through the intelligent use of the tools 
 employed. 
 
 In discussing this question we cannot be too care- 
 ful constantly to bear in mind that it is the intelligent 
 use of tools which is the evidence of intelligence ; and 
 that the fitness of the tools is also a proof of intelli- 
 gence only so far as it clearly indicates an intelligent 
 use. It is not necessary in this connection to distin- 
 guish the fabrication of a tool from its use; for the 
 fabrication implies the use, and also the use of other 
 tools, from the most complex down to the simplest 
 tools furnished by nature, — a bamboo from the 
 thicket, a stalk of flax from the field, or a sharp stone 
 from the brook. It may often be that a tool will be 
 found better adapted for some other use than for the 
 one for which it was originally made, when its use in 
 the new relation will be just as much an evidence of 
 intelligence as its first use. 
 
 Every one has heard the story of Timothy Dexter, 
 who, in his absurd, and probably not very truthful, 
 personal narrative, says he made a successful venture 
 
INTELLIGENT USE. 1 7 
 
 by sending a cargo of warming-pans to the West 
 Indies, where they were found to be admirably fitted 
 for the purpose of straining sugar. Evidently the use 
 of the pan for straining sugar was as much an evi- 
 dence of intelligence as its use as a warming-pan ; 
 but the fitness of the tool for either purpose was of 
 value as evidence only so far as it indicated an intel- 
 ligent use. The warming-pan, however admirably 
 adapted for the purpose, was not designed for strain- 
 ing sugar; and the illustration, whether authentic or 
 not, plainly shows that in human relations fitness 
 proves design, that is, intelligence, only so far as it 
 indicates intelligent use. In the relations of an infin- 
 ite being who knows all the ends from the beginning 
 it is doubtless otherwise ; but this we cannot assume 
 in our argument from design, and the failure to make 
 the distinction we have drawn has often exposed this 
 argument to undeserved contempt. 
 
 Another anecdote illustrating the same distinction 
 has the advantage of being certainly true. A West 
 India planter sent to his overseer from New York a 
 number of wheelbarrows, by whose use he expected 
 to economize labor on his plantation. They were 
 duly received, and the overseer wrote that they had 
 been found to be very useful ; but what was the plant- 
 er's surprise on returning home, to see the negroes, 
 after shovelling in the earth, lift the barrows on to 
 their heads and march off with the load in their old 
 accustomed way. One can easily see that, compared 
 with the wicker basket previously used, the wheel- 
 barrows, even thus handled, might prove a saving of 
 labor, and can recognize a low intelligence in the 
 
I 8 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 negroes who accommodated the new tool to their old 
 habits. But if they ever thought at all, those negroes 
 must have been puzzled by the wheel, and it must have 
 presented to them a problem of very much the same 
 kind that the much discussed rudimentary organs 
 offer to the modern teleologist. Certainly, the wheel- 
 barrow was not designed to be carried on the head, 
 and the neglected wheel was the constant witness of 
 this fact; but the ultimate evidence of intelligence in 
 the wheelbarrow was not in its fitness for one use or 
 for the other, but in the use itself which the fitness 
 indicated. The fitness is important solely as testify- 
 ing to the intelligent use. 
 
 Our early ancestors, however, were not troubled by 
 the analysis of any such distinctions as those to which 
 we resort, to justify their usually correct conclusions, 
 however much they may have erred in special cases. 
 They associated an intelligent personality directly 
 with fitness, wherever found. As nature offers num- 
 berless examples of fitness vastly more wonderful than 
 that displayed by any human tools, they ascribed all 
 such relations in the scheme of nature to the wise de- 
 signs of the gods whom they already recognized as 
 wielding the powers of the world. From the brain 
 of Jupiter came Minerva with her loom, and Vulcan 
 with his forge; and from such beginnings the argu- 
 ment from design has been handed down to our day. 
 And so closely have men always associated fitness with 
 personal intelligence that in all languages the words 
 expressing these relations have acquired such a color- 
 ing that when we use them in connection with teleo- 
 logical arguments we appear to beg the question in 
 
FITNESS IN NATURE. 1 9 
 
 the simple statement of the case. Such words as " de- 
 sign," "contrivance," and "adaptation," all imply a 
 personal agent; and in looking for a word which 
 would express simply the external relation from 
 which the inference of personal agency is drawn we 
 could find no other than the one which we have so 
 continually used, namely, fitness. Largely in conse- 
 quence of the misuse of terms the argument from 
 design has in recent years fallen into such disfavor 
 that the very word, " teleology," carries with it a sug- 
 gestion of opprobrium ; and yet the argument is in- 
 trenched as strongly as ever behind defences which 
 have always been assaulted in vain ; but let us be 
 sure that we fully know where the strength of our 
 position lies. 
 
 It is not true that fitness in nature in any limited 
 relations is satisfactory evidence of design, and the 
 easy " reductio ad absurdum" with which such an 
 assumption is readily met has done not a little to bring 
 teleology into contempt. As has been shown, this 
 assumption is not true even in human relations. With 
 the tools of men it is not their fitness for certain uses 
 but the intelligent use which is the real evidence of an 
 intelligent mind ; and far less in nature can we claim 
 to know the purposes of the Original ; and if we at- 
 tempt to enforce our argument by the plea that there 
 can be no use which Omniscience could not have fore- 
 seen, as before intimated we directly assume the very 
 point we are attempting to prove. Nevertheless the 
 premises of our argument are unquestioned ; and 
 these are the relations of fitness in nature, wonderful 
 beyond language to express, intricate beyond thought 
 
20 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 to unravel, sublime beyond imagination to conceive, 
 useful beyond words to admire. Now men have been 
 able to discover but one satisfactory explanation of 
 these relations, namely, that they are the outcome of 
 an intelligence like their own, only of an immeasur- 
 ably higher order, — in a word, that they were created 
 by the Jehovah of the Bible. We must not claim 
 that we have here logical proof, for we cannot have 
 any such demonstration. But we have something 
 which is far better than all logical proof, something 
 which, while it carries conviction, inflames our imagi- 
 nation, and appeals to our faith. We have what we 
 technically call an induction. But it is an induction 
 of the highest order, with material so ample and ex- 
 perience so extended as to leave no room for reason- 
 able doubt. 
 
 In claiming for an induction the validity of a de- 
 ductive demonstration, we compromise the whole 
 strength of our logical position; and hence many 
 writers on natural theology, even though they may 
 not have attempted to analyze the argument from de- 
 sign, have discussed the examples of fitness in nature 
 as illustrations of an admitted principle, and not as 
 proofs of an intelligent author. In the book before 
 referred to, we ourselves have most distinctly and 
 emphatically maintained this attitude towards the 
 subject. It must be remembered, moreover, that on 
 this view and for the argument's sake such discussions 
 are perfectly legitimate ; for the conviction which an 
 induction produces depends chiefly on the extent of 
 the field which it grasps; and when we study this 
 great induction of natural theology how wonder- 
 
THE ARGUMENT FROM SKILL. 21 
 
 fully do we find that it has borne the tests both of 
 universality and of experience. Not only is it an in- 
 duction which omits no known fact, but it is an induc- 
 tion of all people, in all ages, and under all conditions. 
 How unmoved also has it borne the test of experi- 
 ence. Every attempt has been made to set it aside 
 by showing how this universe might have issued 
 without an intelligent Creator, — from the time of 
 the " fortuitous concourse of atoms " of Lucretius 
 to the " struggle for life " of Darwin. But although 
 by stimulating thought and inciting deeper study 
 these attempts have profoundly modified and en- 
 larged man's earlier crude conceptions of the Divine 
 methods, they have always resulted at last in impress- 
 ing the great mass of thinking men with a deeper con- 
 viction of His being, with a grander conception of His 
 power, and with a more profound reverence for His 
 skill, who is the Alpha and Omega of all knowledge, 
 the Beginning and End of all life. 
 
 Beauty is simply that harmony of proportions and 
 qualities which results from the most complete fitness 
 of all the parts in a perfect whole ; and in the educa- 
 tion of mankind the worship of skill naturally grew 
 into the worship of beauty, or rather of that material 
 perfection which is manifested in beauty. Early in the 
 history of civilization the culture of beauty reached 
 its highest development in ancient Greece ; and then 
 appeared another phase of the argument of natural 
 theology, which, for the sake of distinguishing the 
 stages in the development of the subject, we may call 
 the argument from beauty, although it does not differ 
 essentially from the argument from design. As before, 
 
22 THE ARGUMENT FROM BEAUTY. 
 
 the argument is solely an induction. We have for 
 the premises the infinite beauty of nature, and for the 
 induction the inference that all this beauty must have 
 issued from a Personal Being vastly more susceptible 
 than any human nature to the harmonies of form, of 
 color, and of sound. 
 
 This argument, although not recognized as such, 
 has a singular attraction to a well marked class in 
 modern society, who, having revolted from the pre- 
 vailing creeds, seek satisfaction for their minds and 
 hearts in the contemplation of all that is most perfect 
 in art; and this argument strongly appeals to a vivid 
 imagination and a cultivated taste. These worship- 
 pers of the beautiful hold in highest honor the pro- 
 ducts of Greek art which have come down to us, and 
 often even look back with regret to that old civiliza- 
 tion as the highest stage ever reached in the intellec- 
 tual development of man. But Greek beauty was 
 simply a material beauty, and the God which the 
 Greek apprehended was simply a perfect sensuous 
 being, capable of realizing in his person and his cre- 
 ation the most perfect harmonies, but also revelling 
 in the sensuality with which, before Christianity, ma- 
 terial beauty was always associated. Lifted into a 
 more spiritual sphere, and protected by the safe- 
 guards of Christian morality, the modern devotees of 
 art may disassociate material beauty from such gross 
 accompaniments; but who that has known human 
 nature in its lower moods can for a moment question 
 that the vilest orgies would again become rife if the 
 religious convictions by which alone our Christian 
 civilization is maintained were undermined? 
 
THE ARGUMENT FROM LAW. 23 
 
 As the Greek passed under the Roman sway, so 
 did the supremacy of beauty yield to the supremacy 
 of law; and this was a natural and an intellectual pro- 
 gress. Beauty, as we have seen, is the harmony of 
 relations which perfect fitness produces ; but law is 
 the prevailing principle which underlies that har- 
 mony, and without which no harmony can be main- 
 tained. In the ancient world Greece appeared as the 
 representative of beauty, and Rome succeeded as 
 the expositor of law. In the fluctuations of nature 
 the material forms of beauty are transient, and unless 
 constantly reproduced under the operations of per- 
 manent laws can have no lasting influence. In Greece 
 the productiveness of art soon ceased, through failure 
 of the authority of law to restrain her civil dissen- 
 sions, and the power of beauty to mould men lay 
 dormant until Christianity had wrought its work, and 
 the genius of beauty became wedded to the spirit of 
 the new religion. On the other hand, the fundamental 
 principles of law are eternal, and Rome, through her 
 civil law, has never ceased to rule the world. 
 
 It was a very long step in the progress of mankind 
 from the promulgation of the civil law of Rome to 
 the recognition of the laws of nature, — from Justinian 
 to Newton ; and since the discovery of the law of 
 gravitation so slowly has this conception pervaded 
 the popular mind that not until our own day have 
 even cultivated men fully realized that their race has 
 been educated under a reign of law, which embraces 
 the universe, and which began with time, — a system 
 of laws of which the best of human codes offers only 
 a feeble type. 
 3 
 
24 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 The study of natural laws has brought fresh evi- 
 dence to the support of the conclusions of natural 
 theology, and evidence of the most impressive kind. 
 These laws are at once so grand and yet so simple, 
 so high and yet so near, so universal and yet so par- 
 ticular, so far reaching and yet so present, so invari- 
 able and yet so beneficent, that while they tax to the 
 utmost his intellectual power, they are calculated to 
 impress the mind of the student with awe, with rever- 
 ence, and with trust. Newton has described the im- 
 pression which the discovery of the law of gravitation 
 made on him, and many of the great masters of 
 science join to his their united testimony that the 
 study of the laws of nature has wrought the most 
 profound conviction of the presence of an overruling 
 Mind. The devout student of science finds it difficult 
 to conceive how it could be otherwise, and simply 
 wonders at the perversion of the intellectual vision to 
 which the heaviness of the flesh or the subtleties of 
 the brain may sometimes lead. 
 
 The phase of the argument of natural theology 
 which is based on the laws of nature, we have called 
 in another place the argument from general plan; 
 although, like the argument from beauty, it is not 
 essentially different from the argument from design. 
 The writer to whom we have before referred regards 
 the argument from general plan as the only legiti- 
 mate form of the argument from design, and urges 
 that while we cannot prove that fitness may not have 
 resulted from natural selection, or from some other 
 undefined principle of nature, order must always be a 
 product of intelligence. But, obviously, — as long ago 
 
LAW IMPLIES A LAWGIVER. 25 
 
 Spinoza so powerfully argued, — order, or law, may- 
 be merely a subjective attitude or posture of our own 
 minds towards external nature ; and the words " law," 
 "order," "plan," imply personal intelligence as plainly 
 as do the words "design," "contrivance" and "adapta- 
 tion" before discussed. To say that law implies a law- 
 giver is just as much a begging of the question as to 
 say that design implies a designer. The truth simply is 
 that this last phase of the argument of natural theol- 
 ogy, like all the other phases, is an induction, and not a 
 necessary deduction. Of this induction the premises 
 are the invariable relations of natural phenomena; 
 and the inference is that these fixed relations must 
 have been determined by a Supreme Intelligence, 
 who ordained the order and law of which the universe 
 is the expression. Christian students are most firmly 
 persuaded that this conclusion is the only reasonable 
 or intelligible explanation of the facts, and the wider 
 our knowledge becomes, the more fully is their con- 
 viction confirmed. But it is easy to cavil, — that 
 the observed constancy of relations may have been 
 caused by some undefinable potency of material 
 things (the law of philotaxis, for example, resulting 
 from a tendency in the leaves of a plant to expose 
 the most surface to the sun), and then the whole 
 matter is summed up with the scoffing remark of 
 Voltaire, " The heavens only declare the glory of the 
 astronomers," who see their own intelligence reflected 
 in the circling orbs. If we would protect our sacred 
 cause from such sneers, we must be careful to estab- 
 lish it in truth, and not claim for it a sanction which 
 it does not, and never can possess. 
 
26 THE ARGUMENT OF NATURAL THEOLOGY. 
 
 We have now passed in rapid review four phases 
 of the argument of natural theology, corresponding 
 to four stages in human development, — namely, the 
 argument from might, the argument from design, the 
 argument from beauty, and the argument from gen- 
 eral plan. Corresponding to the recognition in na- 
 ture of energy, fitness, beauty, and order, we have 
 the inferences that might, skill, perfection, and law 
 are the attributes of an Intelligence which created 
 and sustains the whole. Here the scheme of natural 
 theology ordinarily ends ; but, as it seems to us, the 
 culminating phase of the argument, corresponding to 
 the highest phase of human development, still re- 
 mains to be stated. 
 
 The doctrines of Christianity as a system of re- 
 vealed religion do not of course come under our 
 consideration ; but the facts of Christianity as histor- 
 ical verities are as much subjects of natural theology 
 as any other natural phenomena. The movements 
 of history are phenomena of nature as well as the 
 movements of the planets ; and considering the ad- 
 mitted facts of our holy religion from this point of 
 view, what a broad basis for induction do they fur- 
 nish ! Indeed, the basis is so ample that we may at 
 once waive everything that any sceptic will question. 
 We may admit that all the miraculous features of the 
 narrative are myths, and that the Bible has no more 
 authority than the plays of Shakspeare, or any other 
 book that portrays character. Still, after all conces- 
 sions, there remains the character of Jesus, the reve- 
 lation of perfect holiness, the exemplar of the noblest 
 self-sacrifice, the manifestation of the purest love. 
 
THE ARGUMENT AN INDUCTION. 2"] 
 
 Admit that the same traits have in some degree 
 appeared in the founders of other religions, and even 
 in classical literature, as they have in thousands of 
 humble Christian lives ever since. Still, there re- 
 mains the wonderful fact that this one character 
 has transformed the world, and led to incompar- 
 ably the highest and the purest civilization which 
 the race has known. From these premises there never 
 has been but one inference which has satisfied the 
 mass of mankind who have come to the full knowl- 
 edge of the facts, — the conclusion of that great apostle 
 who, himself overpowered by the force of the evi- 
 dence, declared that " God was in Christ reconciling 
 the world unto himself." 
 
 Here as in every other previous phase of our argu- 
 ment we have simply an induction ; not a demonstra- 
 tion, but an induction which has produced conviction 
 in a multitude which no man can number; which has 
 satisfied the deepest yearnings of humanity; which 
 has given superhuman courage to martyrs, and sus- 
 tained the unwavering devotion of saints. It is an 
 induction, moreover, which has always stood the test 
 of experience under every circumstance of life ; and 
 among its confessors have been all sorts and condi- 
 tions of men, from the humblest intellect to the most 
 gifted genius. It is never outgrown, but its power 
 increases as men grow in wisdom and in virtue. It 
 is an induction which opens ever fresh fields of spir- 
 itual knowlege, and directs in the way of truth. In 
 a word, as it is the noblest induction that man has 
 ever grasped, it is also the greatest power in the 
 world. 
 
28 THE ARGUMENT FROM LOVE. 
 
 We thus lay hold of the last phase of the argument 
 of natural theology; and this we may call the argu- 
 ment from love. At the same time we reach the 
 highest stage in the development of man's concep- 
 tion of God. How gradual but how majestic has 
 been the progress in the education of mankind from 
 the first! How large the result ! In nature man found 
 Energy, Fitness, Beauty, Order, and Sacrifice; and 
 through these he has been led to recognize Might, 
 Skill, Perfection, Law, and Love, in a Supreme Intelli- 
 gence. The argument, however its materials may 
 differ, is in spirit one throughout all its varied phases; 
 and the one point we would impress is that this argu- 
 ment is an induction. To show the validity of the 
 argument by comparing the inductions of natural 
 theology with the inductions of science will be the 
 object of these lectures. 
 
INDUCTION AS DEFINED BY ARISTOTLE. 29 
 
 LECTURE II. 
 
 PREPARING THE WAY. 
 
 IN the first lecture, when drawing the distinction 
 between inductive cognition and deductive dem- 
 onstration, we used the word " induction " in the fa- 
 miliar sense in which it is usually employed among 
 physicists, to include the numerous phases of the 
 experimental method of discovering general truths, 
 without overlooking the fact that the logicians have 
 generally given to the same term a more precise and 
 definite meaning. In its Greek form the word " induc- 
 tion " is as old as Aristotle, who gives a formal anal- 
 ysis of this mode of reasoning, which is not more 
 obscure than a similar philosophical analysis of so 
 complex a mental process might be at the present 
 day. 
 
 Certainly the great Stagirite had grasped the essen- 
 tial distinction between induction and deduction when 
 he wrote : " Induction makes clear only, and does 
 not prove." And although he confuses his modern 
 reader when he discusses induction as a proof which 
 may be formulated in a syllogism, he elsewhere 
 clearly recognizes this mode of reasoning as a kind 
 of inference through which we arrive at general prin- 
 
30 INDUCTION AS DEFINED BY BACON. 
 
 ciples. A more precise definition of the mental part 
 of the process could not now be given. 
 
 Bacon, who is regarded by English scholars as the 
 father of the inductive method, held a more mechan- 
 ical view of the subject. In nature general truths are 
 constantly obscured through the complexity of the 
 data furnished by experience ; and Bacon proposed 
 to sift them out, as it were, by a perfectly definite 
 method of exclusion or elimination. We seek the 
 cause of a certain class of effects ; say, for example, 
 of motion in circular orbits. Bacon would make a 
 critical comparison of all cases in which the effect is 
 produced until by exclusion of one after another of 
 the various circumstances he is able to detect some 
 phenomenon constantly present when the effect is 
 present, and varying in degree with the effect, and 
 without which the effect is never produced; when 
 this phenomenon — if one lived long enough to 
 distinguish it — must be a cause of the effect in 
 question. Obviously, an exhaustive elimination of 
 conditions is rarely possible; and this Bacon recog- 
 nizes, and gives rules for procedure in various cases 
 and recommends various aids to induction, — " ad- 
 mincula " as he calls them, — by which the process 
 may be greatly expedited. 
 
 Bacon's method was the normal outcome of his 
 metaphysics, — that is, of his a priori conception of 
 nature and of natural processes, — and as the con- 
 ception was very partial the method was necessarily, 
 even in theory, equally limited. Practically no great 
 originator in science ever followed Bacon's rules, or 
 any other rules; although under the circumscribed 
 
bacon's influence. 31 
 
 conditions of ordinary experimental work every phys- 
 ical investigator naturally resorts to a method of 
 elimination in seeking the cause of any accidental 
 disturbance, such as a leak in his apparatus, or a 
 break in his electrical connections. 
 
 It is a singular fact that Bacon, who is usually re- 
 garded among English-speaking people as the cham- 
 pion who freed the human mind from servitude to a 
 priori dogmas, should himself have been so greatly 
 influenced by his metaphysics. Bacon constantly set 
 induction in opposition to deduction, and regarded 
 syllogism as of service only for the communication of 
 knowledge. But, obviously, wherever the universal 
 can be connected with the particular the process of 
 thought can be expressed in a syllogism ; and if 
 Bacon could have succeeded in realizing his meta- 
 physical conception he would have also succeeded 
 in placing induction on the same basis as deduction, 
 and rendered the method equally demonstrative. 
 
 It is also a current opinion that Bacon was the first 
 to make the results of observation and experiment 
 essential factors in scientific reasoning. But this, 
 again, is only partially true. Aristotle constantly 
 appealed to the facts of nature in support of his con- 
 clusions, and there are at least hints in his writings of 
 experimental methods; and in classical writings of 
 a later date we have abundant evidence of accurate, 
 discriminating, and intelligent observations. As com- 
 pared with Aristotle, the greater influence of Bacon 
 on the advancement of knowledge is not to be found 
 so much in the superiority of his methods as in the 
 larger knowledge of nature and the clearer scientific 
 
32 BACON DID NOT INVENT " INDUCTION." 
 
 conceptions among the men whom he influenced ; 
 and it is safe to say that if the " Novum Organum " 
 had been given to the world a few centuries earlier 
 it would have led to no greater results than those 
 produced by the far older " Organon " which it 
 superseded. 
 
 One influence of Bacon's great genius has been to 
 spread very widely the narrow meaning which he ap- 
 propriated for the word " induction." Indeed, accord- 
 ing to a common popular misapprehension, Bacon 
 invented the word, as well as the mechanical method 
 which it is often used to indicate. But, as has been 
 intimated, this word, or its equivalent in different 
 languages, has been in constant use from the time of 
 Aristotle ; and was employed by the Stagirite with a 
 far more comprehensive and deeper meaning than 
 was ever conceived by King James's at once great 
 and contemptible chancellor. We now use the term 
 in a far broader sense than ever before ; but so far as 
 the preliminary mental act is concerned, our concep- 
 tion of the process of induction does not differ ma- 
 terially from that of Aristotle. Its essential features 
 are, first, the conception or guess ; secondly, the 
 verification of this conception by experiment and 
 observation. The verification may be direct, or 
 through some more or less remote deduction ; and if 
 the appeal to nature shows that the first conception 
 must be rejected, the experience will probably sug- 
 gest some modification which will be tested in like 
 manner in its turn, until the truth in more or less 
 completeness is reached. 
 
 This system of observation and experiment, con- 
 
BASIS OF SUCCESSFUL INDUCTION. 33 
 
 tinued during a long period of time, has given to the 
 modern world a far more intimate acquaintance with 
 natural phenomena than the ancients possessed ; and 
 it is to this, and not to superior philosophy, that our 
 great success in the advancement of knowledge is 
 to be attributed. 
 
 You pronounce with confidence on the probability 
 of a friend's action in a given case in measure as you 
 are acquainted with his principles and inclinations. 
 In a very similar way the investigator who is ac- 
 quainted with nature and her processes is likely to 
 make inferences, which will be confirmed by experi- 
 ence in just the proportion that his knowledge is 
 wider and more exact. The ancients were often as 
 ingenious and as profound in their conceptions 
 as modern philosophers, and their anticipations of 
 knowledge surprise us. But as their conceptions 
 remained unverified, they laid no sure foundations 
 on which they could build. Because wild and scat- 
 tered, all their ingenuity was misdirected and unavail- 
 ing. The value of a man's guess depended on his 
 reputation ; and questions of fact were settled on 
 authority. Thus it came to pass that Aristotle's 
 unverified conjectures, through the sheer force of his 
 intellectual pre-eminence, misled the world for two 
 thousand years. 
 
 Besides his more intimate acquaintance with na- 
 ture, the modern student is constantly acquiring im- 
 proved methods of testing his inferences ; and such 
 instruments as the telescope, the microscope, the 
 polariscope, the spectroscope, the thermometer, the 
 galvanometer, and the telephone have not only im- 
 
34 PREPARING THE WAY. 
 
 mensely widened his field of observation, but also 
 vastly increased his power of experimenting ; so that 
 his progress in knowledge has been so constantly 
 and so rapidly accelerated that more has been 
 gained during the lifetime of men still living than 
 during all human history before. 
 
 As our object in these lectures is to show that the 
 inductions of natural theology are as legitimate as the 
 inductions of physical science, it is essential that we 
 should first describe the characteristics of scientific 
 inductions, in the broad sense with which we use this 
 term ; and since, as we have endeavored to show, it 
 is impossible to define this mode of reasoning by any 
 concise formula, we shall best attain our object by 
 studying a few striking examples, — selecting for ex- 
 amination great discoveries whose history is well 
 known, and of which the important steps can readily 
 be traced. Let us begin, however, with a brief de- 
 scription of some of the speculations of the old 
 Greek philosophers, in order that by comparison we 
 may more fully appreciate the value of our modern 
 inductive methods. 
 
 It will be remembered that the Father of History, 
 when seeking to explain the cause of the annual in- 
 undations of the Nile, — after giving his reasons with 
 a truly scientific spirit (if sometimes with insufficient 
 knowledge) for rejecting the hypotheses which had 
 been proposed to him, — proceeds to argue that the 
 effect is caused by the sun, which unequally draws 
 the water from the sources of the stream at different 
 seasons of the year ; and that the overflow takes 
 place when the sun has gone north, and draws less 
 
ILLUSTRATION FROM HERODOTUS. 35 
 
 powerfully on the Libyan fountains, which then pour 
 out their full supply. 
 
 Assuming the sufficiency of the alleged cause, the 
 explanation of Herodotus is still confused; but what, 
 as it seems to me, he distinctly implies is this : The 
 Nile is unique among rivers, first, because it flows 
 from the south to the north, across the region twice 
 traversed by the sun in the course of the seasons ; 
 and secondly, because, having no tributaries, it is not 
 affected by the rains along its banks. Hence the 
 alternations of its floods must depend on its sources 
 alone ; and the sun-god must produce the greatest 
 possible difference of effect on these springs when 
 at the extreme limits of his annual journey. 
 
 Were the cause adequate this explanation certainly 
 would not be unphilosophical; but all turns on this 
 one point. Herodotus does not appear to have had 
 any doubts about the adequacy of the sun's agency, 
 or to have made any attempts to estimate the magni- 
 tude of the effect which could thus be produced. 
 His whole theory was expressed by the phrase, "he 
 (the sun) draws the water to him," — a form of 
 words which has been used to describe a certain fa-, 
 miliar appearance in the heavens from that day until 
 this. In using this expression — with which his read- 
 ers at once associated the optical phenomenon just 
 referred to, and which they connected in an obscure 
 way with the evaporation of water — Herodotus felt 
 that he was giving a triumphant explanation ; and 
 this example shows in a marked way the reason of 
 the unsoundness of the Greek philosophy when 
 applied to the study of nature. The old Greeks had 
 
36 PREPARING THE WAY. 
 
 as vivid imaginations, and were as acute reasoners as 
 ourselves ; they were also in many cases diligent 
 and careful observers. But they mistook abstract con- 
 ceptions for realities ; and having given names to 
 these forms of thought, they sought to advance 
 knowledge by analyzing the words and the thoughts 
 suggested, instead of studying the facts which the 
 words signify. 
 
 This vicious method of Greek philosophy is well 
 described by Whewell in his " History of the Induc- 
 tive Sciences : " " As soon as they had introduced 
 into their philosophy any abstract and general con- 
 ceptions, they proceeded to scrutinize these by the 
 internal light of the mind alone, without any longer 
 looking abroad into the world of sense. They took 
 for granted that philosophy must result from the re- 
 lations of those notions which are involved in the 
 common use of language, and they proceeded to 
 seek their philosophical doctrines by studying such 
 notions. They ought to have reformed and fixed 
 their usual conceptions by observation ; they only 
 analyzed and expanded them by reflection. They 
 ought to have sought by trial, among the notions 
 which passed through their minds, some one which 
 admitted of exact application to facts ; they selected 
 arbitrarily, and consequently erroneously, the notions 
 according to which facts should be assembled and 
 arranged. They ought to have collected clear fun- 
 damental ideas from the world of things by induc- 
 tive acts of thought; they only derived results by 
 deduction from one or other of their familiar 
 conceptions." 
 
SLAVERY TO LANGUAGE. 37 
 
 But although the false method, thus so clearly de- 
 scribed, was especially characteristic of the ancient 
 philosophy, it is a vice from which the modern world 
 has by no means wholly escaped. How often do the 
 controversies of the present day turn on purely ver- 
 bal distinctions. How imperiously, and yet often how 
 insensibly, are our thoughts ruled by the mysterious 
 mechanism of language. How conscious is the effort 
 to force language to express our exact and deliberate 
 thought, and to prevent our thought from being 
 moulded by language. Of course to a very large 
 extent the influence of language is legitimate. Lan- 
 guage is the medium of thought, and cannot be sep- 
 arated from it. Exact thought is not practicable 
 without language, and the very effort to clothe thought 
 in words awakens thought. Moreover, the general 
 terms in language represent stages of intellectual 
 progress. They form a scaffolding, as it were, by 
 which the mind mounts to ever higher levels from 
 which it gains a more general and wider prospect. 
 But it is one thing to use language, and another thing 
 to be a slave to it. Some men are slaves to language 
 all their lives, and from such a slavery the ancient 
 philosophy was not liberated until modern times. 
 
 Man was made in the image of his Maker; or, to 
 express the same truth in the phraseology of a re- 
 cent philosophy, has developed into harmony with 
 his environment; and, undoubtedly for this reason, 
 those acute thinkers of ancient time in their unveri- 
 fied conceptions not unfrequently anticipated the 
 results of modern science. So it was with Herodo- 
 tus ; and, although he attached no definite meaning 
 
38 PREPARING THE WAY. 
 
 to it, his explanation of the annual overflow of the 
 Nile was in the main correct. The sun is indeed the 
 cause ; and the great pump which the sun maintains 
 in ceaseless action not only supplies the Nile, but 
 also all the rivers of the globe. Moreover, such is 
 the peculiar equatorial position of the basin of drain- 
 age of this remarkable river that the evaporation 
 from this area greatly diminishes as the sun moves 
 north of the equator, when naturally an increased 
 amount of water flows down the only other outlet. 
 
 By the Greek philosophers the contrasts empha- 
 sized by language were regarded as fundamental dis- 
 tinctions in nature, or first principles, which they 
 made the basis of discussion, and from which they 
 sought to deduce general truths. Aristotle enumer- 
 ates ten such principles, as based by the Pythag- 
 oreans on the contrasts of number: limited and 
 unlimited, odd and even, one and many, right and 
 left, male and female, rest and motion, straight 
 and curved, light and darkness, good and evil, square 
 and oblong; and from oppositions of this kind Aris- 
 totle himself deduced the doctrine of the four 
 elements. 
 
 " We seek," he says, 1 " the principles of sensible 
 things, — that is, of tangible bodies. We must take, 
 therefore, not all the contrarieties of quality, but 
 those only which have reference to the touch. Thus 
 black and white, sweet and bitter, do not differ as 
 
 1 As translated from De Gen. et Corrupt. : Whewell's His- 
 tory of the Inductive Sciences, vol. i. page 49, edition of 1847 ; 
 and the translations from Aristotle which follow are quoted 
 from the same standard work. 
 
 
 
DOCTRINE OF THE FOUR ELEMENTS. 39 
 
 tangible qualities, and therefore must be rejected from 
 our consideration. Now the contrarieties of quality 
 which refer to the touch are these : hot, cold ; dry, 
 wet; heavy, light; hard, soft; unctuous, meagre; 
 rough, smooth ; dense, rare." Then, after rejecting 
 all but the first four of these, either because they 
 are not active and passive qualities, or because they 
 are combinations of the four first, and concluding for 
 these reasons that the four retained must be elements, 
 he proceeds : — 
 
 " Now in four things there are six combinations of 
 two ; but the combinations of two opposites, as hot 
 and cold, must be rejected. We have therefore four 
 elementary combinations which agree with the four 
 apparently elementary bodies ; fire is hot and dry ; 
 air is hot and wet (for steam is air) ; water is cold 
 and wet; earth is cold and dry." 
 
 In a similar way by considering light as opposite 
 to heavy Aristotle came to regard levity as a quality 
 of a body, and distinguished bodies as absolutely 
 heavy or absolutely light. " Former writers " he 
 says, "have considered heavy and light relatively 
 only, — taking cases where both things have weight, 
 but one is lighter than the other; and they imagined 
 that in this way they defined what was absolutely 
 heavy and light." Fire and air, according to Aristotle, 
 were absolutely light, with fire the lighter of the 
 two. Hence it followed " that each of the four ele- 
 ments tends to its own place, — fire being the highest, 
 air the next, water the next, and earth the lowest." 
 In another place he writes : " heavy and light are, as 
 it were, the embers or sparks of motion ; " and he 
 4 
 
40 SPECIFIC GRAVITY AND SPECIFIC LEVITY. 
 
 considered that the tendency of light bodies to rise, 
 like the tendency of heavy bodies to fall, was an in- 
 herent quality. 
 
 It is obvious that all this fallacious reasoning had a 
 purely verbal origin; and that the great error con- 
 sisted in inferring that there must be an opposition 
 of material qualities corresponding to verbal distinc- 
 tions. Since light was opposite to heavy, the con- 
 clusion was drawn that levity, like weight, must be a 
 quality of matter; and it was nearly two thousand 
 years before men found out that levity, or buoy- 
 ancy, — as we now call the upward tendency of tim- 
 ber in the sea, or of flame and other forms of heated 
 vapors in the atmosphere, — the phenomena out of 
 which the Stagirite made so much, — was simply an 
 effect of the weight of a surrounding fluid ; and we 
 retain in our language the term specific gravity — 
 originally opposed to specific levity — as a constant 
 reminder of the persistency of error. Moreover, it is 
 a striking illustration of the spirit with which the an- 
 cient philosophy was cultivated, that this error pre- 
 vailed in spite of the fact that Archimedes discovered 
 and correctly enunciated the simple principle of buoy- 
 ancy, — a discovery rendered most notable by its con- 
 nection with the testing of King Hiero's crown. 
 
 We must also briefly notice Aristotle's absurd con- 
 clusions in regard to motion ; since they were gen- 
 erally received even down to the period of the great 
 astronomical inductions which we are next to con- 
 sider, and without some knowledge of them we can- 
 not comprehend the intellectual conditions under 
 which the great astronomers of the sixteenth and 
 
MOTION AN INHERENT TENDENCY. 4 1 
 
 seventeenth centuries studied and labored. Motion, 
 according to the Stagirite, was simply the effect of 
 the inherent tendency of the body. In consequence 
 of their nature, light bodies move upwards and heavy 
 bodies downwards; and, as was fully recognized, 
 such motions acquire an ever increasing velocity. 
 Since, then, acceleration was the characteristic of 
 the motion of a body obeying its natural tendency, 
 such motions were regarded as natural. On the 
 other hand, when a ball is rolled along the ground 
 the motion rapidly diminishes, and finally ceases, 
 because the ball is forced against its inherent dis- 
 position; and hence, on the principle of oppositions, 
 such retarded motions were distinguished as violent. 
 
 This explanation, if it may be so called, of the 
 motions of bodies remained almost unquestioned to 
 the time of Galileo ; and the results of his exper- 
 iments were gravely questioned because they were 
 inconsistent with the Aristotelian dogmas. But the 
 climax of these unbridled dynamical speculations 
 remains yet to be stated, and will form the turning- 
 point in this discourse. 
 
 In his book " On the Heavens" Aristotle wrote: 
 " The simple elements must have simple motions ; 
 and thus fire and air have their natural motions 
 upward, and water and earth have their natural mo- 
 tions downward. But besides these motions there 
 is motion in a circle, which is unnatural to these ele- 
 ments, but which is a more perfect motion than the 
 other, because a circle is a perfect line, and a straight 
 line is not; and there must be something to which 
 this motion is natural. From this it is evident that 
 
42 THE QUINTA ESSENTIA. 
 
 there is some essence of body different from those 
 of the four elements, more divine than those and su- 
 perior to them. If things which move in a circle 
 move contrary to nature, it is marvellous, or rather 
 absurd, that this, the unnatural motion, should alone 
 be continuous and eternal ; for unnatural motions de- 
 cay speedily. And so from all this we must collect 
 that besides the four elements which we have here 
 and about us, there is another removed far off, and 
 the more excellent in proportion as it is more dis- 
 tant from us." This fifth element was called the 
 " quinta essentia " by Latin writers ; and the word 
 " quintessence " in our own language frequently brings 
 to mind this singular conception, which, although so 
 absurd to us, held for ages a wonderful control over 
 the human mind. 
 
 Having thus shown how vain and foolish are the 
 imaginations of men unless directed and controlled 
 by experience, we turn next with satisfaction to a far 
 more glorious record, and shall attempt to illustrate 
 by a conspicuous example how this same noble and 
 powerful imagination of man becomes like a divine 
 inspiration if only he approaches nature with meek- 
 ness, and strives to learn what she alone can teach. 
 It is the disposition of the mind and the fulness of 
 knowledge, more than method, more than skill, more 
 than ingenuity, more than intellect, which makes the 
 difference between foolish speculation and pregnant 
 conception. 
 
 The change from the ancient philosopher to the 
 modern investigator is as great as the difference 
 between the sophist and the scholar, between self- 
 
INFLUENCE OF CHRISTIANITY. 43 
 
 assertion and self-devotion, between conceit and hu- 
 mility, between pretension and worship. This change 
 of attitude of the students of nature since the revival 
 of learning is often ascribed to the influence of Bacon. 
 But great thinker as Bacon was, he did not lead the 
 change, and knew little of its true spirit. To explain 
 such a wide-spread intellectual movement we must 
 look to a more potent cause than the influence of 
 any man, however great; and, as it seems to me, this 
 great revolution can be directly traced to the in- 
 fluence of Christianity, and to the spirit of humility 
 and self-devotion which its Founder sanctified and 
 rendered glorious. 
 
 The Law of Universal Gravitation, says Dr. Whewell, 
 the historian of the inductive sciences 1 "is indisputa- 
 bly and incomparably the greatest scientific discov- 
 ery ever made, whether we look at the advance 
 which it involved, the extent of the truth disclosed, 
 or the fundamental and satisfactory nature of this 
 truth." And although it may be doubted whether 
 this discovery was as an intellectual achievement any 
 greater than many others which have been made since, 
 there can be no question that not one of these, how- 
 ever brilliant, has had so great and lasting an effect in 
 the advancement of learning. Selecting, therefore, 
 the law of gravitation as a most conspicuous example 
 of a scientific induction, let us endeavor to follow, as 
 far as is possible, the several steps by which the great 
 result was achieved, in order that we may thus gain 
 a clearer conception of the mental process, called in- 
 duction, which we are seeking to illustrate. 
 
 1 Whewell's History of the Inductive Sciences, vol. ii. p. 187. 
 
44 PRELUDE TO NEWTON. 
 
 In order to understand what Newton accomplished, 
 it is essential that by studying the state of knowledge 
 at his time we should put ourselves in some measure 
 in his position when, at the age of twenty-three, he 
 received the degree of Bachelor of Arts at the Uni- 
 versity of Cambridge. Thorough mathematical stu- 
 dent of great ability that he was, we must suppose 
 him versed in all the astronomical learning of the 
 day ; but at the same time he must have been more 
 or less hampered and prejudiced by the forms and doc- 
 trines in which he had been educated, — limitations 
 from which only men of genius are able to escape. 
 On the other hand we must remember that besides 
 the astronomical works which had been actually pub- 
 lished and were then common property, Newton also 
 had the advantage of a large amount of floating dis- 
 cussion, which did not ripen into definite results until 
 a later day, but which made Newton's grasp of the 
 great ideas involved in his discovery a more natural 
 and less transcendent effort than it would otherwise 
 appear. 
 
 Such historical relations as we would establish are, 
 however, very difficult to secure ; for even if we can 
 fully realize the conditions of actual knowledge in 
 Newton's time we cannot appreciate those influences 
 of education, surroundings, and other circumstances 
 which so greatly modify the intellectual atmosphere 
 in which men live and work, and by which facts and 
 opinions are always more or less colored. Hence, it 
 is impossible for any one at the present day, even 
 after long continued study and investigation, to stand 
 where Newton stood in his opening manhood, and 
 
THE ALMAGEST. 45 
 
 view the field of knowledge as he saw it ; and for me 
 it is only practicable to sketch the situation in rudest 
 outlines. 
 
 The knowledge of astronomical facts acquired by 
 the ancients was very extensive. From the time of 
 the Chaldean shepherds there were always numerous 
 and assiduous observers of celestial phenomena. In- 
 deed, among eastern nations the heavenly hosts were 
 so universally objects of worship, and the conjunc- 
 tions of the planets were supposed to be so intimately 
 connected with men's lives that astronomical occur- 
 rences received an attention which no other phe- 
 nomena of nature secured. As early as 150 B.C. 
 Hipparchus constructed a system of astronomy which 
 even now commands our admiration. We have a 
 very full exposition of this system by Ptolemy, who 
 lived under the Emperor Hadrian two hundred and 
 fifty years later, and whose work has been preserved 
 for us by the Arab astronomers under the title of "The 
 Almagest." Ptolemy added but little to the theory of 
 Hipparchus, but he did a great deal to extend and 
 verify it. " The Almagest" is a monument to his learn- 
 ing, accuracy, judgment, and skill; and is by far the 
 most important contribution to scientific knowledge 
 which we have received from the ancient world. 
 
 When we remember that the observations of the 
 ancients were made with no aids, or with only the 
 rudest tools, the knowledge of celestial phenomena 
 which had been acquired at the time of Hippar- 
 chus appears wonderful. The fixity of the stars had 
 been established. The brighter stars had not only 
 been grouped in constellations and mapped, but their 
 
46 ASTRONOMY OF THE ANCIENTS. 
 
 relative positions had been determined, by alignments, 
 with such accuracy that the observations arc of value 
 at the present day. The paths of the planets and of 
 the moon — and what is still more remarkable, the 
 course of the sun through the constellations — had 
 been followed, and the varying rapidity of their mo- 
 tions in different parts of their sinuous, and often in- 
 voluted, courses recorded. Numerous cycles had 
 been discovered which enabled the astronomers to 
 regulate the calendar, predict eclipses, and foretell 
 other astronomical conjunctions. Some of these 
 cycles, like the cycle of Meton, — which is still used 
 for calculating the time of Easter, and in which the 
 Golden Number is the number of the current year, — 
 are so extended that their discovery implies the 
 maintenance of observations and the preservation of 
 the records through long periods of time. In addi- 
 tion to all this the great circles of the celestial sphere 
 had been marked out, the equinoctial and solstitial 
 points had been fixed, and Hipparchus himself had 
 discovered the precession of the equinoxes. Lastly, 
 the spherical form of the earth had been recognized, 
 and some approach had been made to a knowledge 
 of its dimensions. 
 
 The circumstance that the vault of the sky forms a 
 sort of natural map on which the paths of the planets 
 and of the moon can be directly traced by the un- 
 aided eye, and that of the sun readily inferred from 
 what was called the " heliacal " rising and setting of 
 known stars, in connection with the religious impor- 
 tance attached to the subject, was undoubtedly the 
 reason that the ancients acquired an acquaintance 
 
THEIR PRACTICAL KNOWLEDGE. 47 
 
 with astronomical facts so far beyond their general 
 knowledge of natural phenomena; and it is not to 
 the credit of our modern education that the learned 
 men of those early times had a better acquaintance 
 with the changing appearances of the spangled dome 
 of heaven than any of our scholars at the present 
 day, except those who especially devote themselves 
 to astronomical studies. It is certainly a matter of 
 great regret that our methods of education should 
 not invite our children to observe what is going on 
 around and above them. With the help of diagrams 
 and orreries they learn from more or less popular 
 text-books the outlines of the modern system of 
 astronomy, and perhaps gain some conception of the 
 immensity of space ; but they remain ignorant of the 
 appearances which the skies unroll every clear night 
 before their eyes. 
 
 When looking from my summer home towards an 
 uninterrupted eastern horizon I have often heard in- 
 telligent people express surprise that the full-orbed 
 moon which rose from the waves the previous night 
 should rise behind the hills the next; and although 
 this maybe an unusual experience, I question whether 
 many of the graduates of our colleges have a clear 
 conception of the singular involutes which the plan- 
 ets would be seen to follow if each left a shining track 
 in its wake; and certainly still fewer have any idea of 
 the very tortuous course of the moon in her succes- 
 sive lunations, until after a long period she retraces 
 very nearly the same course again. But these are 
 the very phenomena out of which our system of as- 
 tronomy was constructed; and if we would under- 
 
48 COPERNICUS. 
 
 stand what the great astronomers did we must first 
 become acquainted with the appearances whose coils 
 they unwound and whose complexity they unravelled. 
 During the long night of the dark ages which suc- 
 ceeded the fall of the Roman Empire, the records of 
 ancient astronomy were preserved at Bagdad, at Cairo, 
 and at Cordova, those centres of Moslem culture. 
 With the revival of learning in the Christian world, 
 soon after the capture of Cordova by Ferdinand the 
 Third, of Castile, in 1236, astronomy became a favor- 
 ite subject of study throughout Europe, and in this 
 study the " Almagest " of Ptolemy was the great au- 
 thority ; and two centuries and a half later, just at the 
 dawn of the Reformation, when Ferdinand and Isa- 
 bella were raising the united standards of Aragon and 
 Castile on the last stronghold of the Moors in Spain, 
 where Columbus was present seeking from their Cath- 
 olic Majesties commission and supplies for his first 
 memorable voyage, there was at the University of Cra- 
 cow in Poland a young student, named Nicholas Co- 
 pernicus, who was soon to become the greatest master 
 of the astronomical knowledge of his age. After 
 finishing his course at Cracow, Copernicus studied 
 astronomy first at Bologna, then at Padua, and after- 
 wards at Rome ; but having gained the highest honors 
 at these great seats of mediaeval scholarship, and the 
 reputation of being the most learned man of his time, 
 at the age of thirty he retired to the little town of 
 Frauenburg in eastern Prussia, where he spent the re- 
 maining forty years of his life as a tender and devoted 
 pastor of a rude and ignorant flock. To Frauenburg 
 Copernicus had carried a grand conception, and in 
 
COPERNICUS. 49 
 
 his simple lodgings, still shown in the neighboring 
 hamlet of Allenstein, that conception was matured. 
 
 The astronomy of which Copernicus was so great 
 a master was the science constructed by Hipparchus 
 and illustrated by Ptolemy, and which had remained 
 essentially unaltered for more than a thousand years. 
 The chief merit of existing treatises was the wealth of 
 facts, and the records of conscientious observations 
 which they contained ; and Copernicus was as famil- 
 iar with the dubious ways of the celestial wanderers 
 as is a shepherd with the by-paths of his straying 
 lambs. His knowledge, moreover, was not mere eru- 
 dition ; but the facts were ever present with him, and 
 the paths of the heavenly bodies were engraved as 
 clearly on the crystal sphere of his imagination as if 
 on the firmament they were marked with a shining 
 thread among the stars. 
 
 But all this real knowledge came to Copernicus in 
 the guise of a system which, although based on as- 
 sumption, was consecrated by authority and tradition, 
 and held by the learned world with the same rever- 
 ence with which it still honors the models of clas- 
 sical literature. As the earth was regarded as the 
 centre of the universe, and the circle as the most 
 perfect of figures, the astronomers assumed that the 
 heavenly bodies must move around this globe in cir- 
 cular orbits. But as the involutions of the planetary 
 paths were obviously inconsistent with this simple 
 assumption, Hipparchus sought to explain the an- 
 omaly by what has ever since been known as the 
 system of epicycles. The planets were assumed to 
 move in circular paths around an immaterial point, 
 
50 COPERNICUS. 
 
 which was itself moving in a circle around the earth ; 
 just as if the planets were fastened to the rim of a 
 vast wheel, revolving in a plane passing through the 
 earth, while the wheel was rolling round the crystal 
 sphere which formed the celestial vault. Perhaps the 
 wheels of the chariot of the Sun in the Greek mythol- 
 ogy suggested the idea ; and absurd as it seems to us, 
 it was not inconsistent with the philosophy of motion 
 taught by Aristotle, and universally held even at the 
 time of Copernicus. In its more abstract f6rm the 
 conception had indeed an element of truth, and has 
 been preserved by modern astronomy in the devices 
 of mathematical analysis for computing a planet's ap- 
 parent place. That such a device would give a gen- 
 eral explanation of the stationary and retrograde 
 phases in the planetary motions is obvious. But to 
 the Ptolemaic school the conception was of far greater 
 value than this. By carefully collating and plotting 
 observations, they were enabled to determine the 
 periods of revolution both in the epicycle and in the 
 cycle, and thus they calculated tables predicting the 
 planets' positions; which, although vastly inferior 
 both in accuracy and reach to similar tables in our 
 nautical almanacs, were wonderful achievements for 
 the time, and tended to give great confidence in the 
 theory on which the calculations were based. 
 
 To rude observation the motions of the sun and 
 moon are far more regular than those of the planets ; 
 and Hipparchus was able to explain the anomalies, 
 so far as they were known to him, by a theory of 
 eccentrics which placed the earth, not at the centre 
 of the circles around which these great luminaries 
 
COPERNICUS. 5 1 
 
 moved, but at another point some distance from the 
 centre, called the equant. As before, the conception 
 was perfectly definite, and received a quantitative ex- 
 pression. The position of the earth with regard to 
 the centre of motion was determined, the points of 
 apogee and perigee in the heavens were marked out, 
 and from these data Hipparchus calculated tables of 
 the sun and moon. In the time of Ptolemy, when 
 the inequalities of the motions of all the heavenly 
 bodies were better known, it became necessary to add 
 epicycle to eccentric in order to reconcile the obser- 
 vations ; and the result was a most complex system, 
 which is graphically described by Milton : — 
 
 " . . . how gird the sphere 
 With centric and eccentric scribbled o'er — 
 Cycle in epicycle, orb in orb ! " 
 
 This was the system in which Copernicus was edu- 
 cated, and by whose traditions and methods he must 
 have been more or less bound. It would be very 
 easy to misrepresent this system, and thus to under- 
 value the work of Copernicus, by showing how ab- 
 surd and childish were the theories he overthrew. 
 In many of the materialistic aspects in which it was 
 presented by classical writers, with its mechanism of 
 crystalline spheres, it does seem as if the Ptolemaic 
 system must have appeared to thinking men even 
 then incredible and monstrous ; and one sympathizes 
 with the King of Castile, who, when the system was 
 explained to him, is said to have remarked that, "if 
 God had consulted him at the Creation, the universe 
 would have been made on a better and simpler plan." 
 
52 COPERNICUS. 
 
 But when regarded abstractly, as the resolution of 
 unequal motions of the heavenly bodies into two or 
 more equable circular motions, it was not only a legi- 
 timate scientific method, but is closely analogous to 
 the empirical methods followed at the present day to 
 connect a series of observations in any department 
 of physical science when, as is usually the case, the 
 dynamical causes are unknown; and, as before inti- 
 mated, is essentially the same method which is fol- 
 lowed by the modern astronomer when he resolves 
 unequal motions into a series of terms or expressions 
 of partial motions involving the trigonometric values 
 of circular arcs. 
 
 This point, which has been so well made by 
 Whewell, should be strongly emphasized. The dy- 
 namical law which governs the motions of the heav- 
 enly bodies was wholly unknown until discovered by 
 Newton ; and as a system of calculation the theory 
 of Hipparchus was not only good, but, as Whewell 
 adds, " no better has yet been discovered ; " and the 
 maze of epicycles is simply the complexity which 
 the calculations of apparent place in astronomy al- 
 ways present. Moreover it appears very plainly 
 from the writings of Ptolemy that his school regarded 
 the whole machinery of epicycles and eccentrics as 
 imaginary, and used them simply as devices for the 
 graphical representation of apparent motions. As 
 such they are true expressions, and the best that 
 have been yet devised. Indeed more than one half 
 of our modern physics rests on no better basis to- 
 day. We have learned, however, to dissociate our 
 partial generalizations from the material symbols in 
 
COPERNICUS. 53 
 
 which they find expression, and are content to use 
 these aids as guides so long as they lead us aright, 
 and to wait until advancing knowledge shall give to 
 them a wider and a fuller significance. The tendency 
 among the ancients was the very reverse of this. They 
 sought to materialize everything, as their mythology 
 so plainly shows. But at the same time we have 
 the best of evidence, as in the works of Ptolemy, that 
 their more gifted minds rose superior to this spirit, 
 and were able to discern the true ideal under the 
 conventional dress of the symbols they habitually 
 employed ; and it may be questioned whether the 
 " crystalline spheres " by which in the imagery of 
 their poets the complex motions of the heavens were 
 maintained are one whit more absurd than the " lumi- 
 niferous ether," without substance but with indefinite 
 elasticity, with which modern science has filled the 
 inter-planetary spaces. 
 
 If we would appreciate what Copernicus achieved 
 we must remember that he was educated in the sys- 
 tem whose striking features we have been attempting 
 to sketch, — a system which had all the authority of 
 tradition, all the charm of antiquity, all the attrac- 
 tions of learning, and beneath its conventional sym- 
 bols all the sanctions of sound philosophy and all the 
 spirit of true science. 
 
 We are familiar with the outlines of the Coper- 
 nican system, and I trust are now prepared to see 
 clearly just what this great master contributed to the 
 world's real knowledge, just how far his keen intellec- 
 tual vision was able to penetrate the darkness of the 
 then unknown. It can be stated in a few words ; for 
 
54 COFERNICUS. 
 
 the offering which any man, however great, can bring 
 to the altar of truth, though relatively it may be 
 large, is always absolutely very small. 
 
 Amidst the complexities of the apparent, Coperni- 
 cus discovered the simplicity of the real. He saw 
 law under inequalities, regularity under variation, 
 order under confusion ; and having gained a glimpse 
 of the true structure of the solar system, he showed, 
 by a careful comparison of the theory with observa- 
 tions, that the facts of nature harmonized with this 
 conception. The large knowledge, the grand con- 
 ception, the scrupulous confirmation, — these were 
 the essential and inseparable stages of this grand dis- 
 covery. 
 
 Popular writers on astronomy often lay great stress 
 on the statement that a heliocentric hypothesis was 
 a favorite tenet among the disciples of Pythagoras, 
 and therefore not original with Copernicus. But if 
 they cite this well-known fact in disparagement of 
 the work of the great father of modern astronomy, 
 they must wholly misconceive the character of a 
 scientific induction. Those speculative philosophers 
 of antiquity did not place the sun in the centre of 
 the solar system on any basis of facts, but merely as 
 an idle fancy by which they sought to pay honor to 
 the sun-god. How utterly different with the system 
 of Copernicus ! This was not only an inference from 
 the largest knowledge of facts which the best scholar 
 of his age could gain, but was also an inference veri- 
 fied by observation, and by the most exact meas- 
 urements which could then be made. Unverified 
 hypotheses are accounted of no value in exact science, 
 
COPERNICUS. 55 
 
 and in the opinion of competent judges no such an- 
 ticipations in the least detract from the merit of a 
 real discovery. 
 
 It is not the least among the noble qualities of this 
 hero of science that throughout all his work he dis- 
 played such deep humility of spirit and such profound 
 reverence for truth. His system must have been 
 matured soon after he settled at Frauenburg, if not 
 before. It was a vision of his youth over which he 
 thought and worked for forty years before he told it 
 to the world. He did not hasten like a young knight 
 to slay the dragon which had guarded so long the 
 opening of the pathway to the great treasure. He 
 did not at once enter the lists against the defenders 
 of old dogmas, because they were antiquated and 
 seemed to him erroneous. Truth was sacred ; but 
 so was just authority, so was noble learning, so were 
 old institutions. And truth could wait; and truth did 
 wait, fresh and unimpaired, long, long years. In those 
 lonely lodgings at Allenstein amidst the humblest 
 pastoral and charitable duties, he questioned night 
 after night that vision of his youth, multiplying ob- 
 servations and repeating calculations, until the truth 
 grew upon him with such conviction that he could 
 no longer be silent; and then he declared it, in spite 
 of interest, in spite of opposition, in spite of contumely, 
 in spite of persecution. 
 
 In the long record of illustrious men who have 
 devoted their lives to the advancement of knowledge 
 for truth's sake alone, I know of no incident more 
 impressive, more truly sublime, than that which is 
 narrated of the death of Copernicus. The forty 
 5 
 
56 COPERNICUS. 
 
 years of patient labor in confirmation of the early- 
 vision had passed. The book had been written, and 
 under great opposition had been printed at Nurem- 
 berg. The last revisions had been made ; but the 
 author, worn out at seventy years with labor and 
 anxiety, lay dying without any token of the travail 
 of his soul. Indeed reports have come that bigotry 
 has succeeded in stopping the publication for which 
 his life has been spent, and all hope has fled, — when 
 at the last moment a special messenger arrives, and 
 places in the hands of Copernicus the long expected 
 volume fresh from the press. The dying man is just 
 able to return a sign of recognition, and whisper the 
 final prayer, " Nunc dimittis servum tuum, Dom- 
 INE ! " 
 
 Were study always conducted in the spirit in which 
 that book was written, the harmony of all real knowl- 
 edge would become clearly manifest. In the dedi- 
 cation of the work " De Revolutionibus Orbium 
 COELESTIUM " to Pope Paulus III., Copernicus ex- 
 pressly states that he has kept his book by him 
 for four times the nine years recommended by Hor- 
 ace ; and remarks that " the study of a philosopher 
 is to seek out truth in all things so far as is permitted 
 by God to human reason." 
 
 The Copernican system was not at once generally 
 accepted. Long cherished doctrines with their pre- 
 scriptive rights are not so readily set aside ; nor is 
 it well that they should be. But the system did very 
 soon receive from astronomers that form of recog- 
 nition which would most have pleased its author. 
 In 155 1 Rcinhold published tables, or" ephemerides," 
 
COPERNICUS. 57 
 
 as they are usually called, based on the principles of 
 Copernicus, whose verified predictions tended greatly 
 to strengthen his theory ; and the demonstration was 
 complete when in 1610 Galileo's new telescope re- 
 vealed to sight, in the system of Jupiter's satellites, a 
 model on a small scale of the solar system according 
 to the views of Copernicus, and not long after showed 
 that Venus had phases like the moon, thus making 
 visibly manifest the planet's relation to the sun ; so 
 that in less than a century after the death of its au- 
 thor, in spite of prejudice and in spite of theological 
 rancor, the heliocentric theory was almost everywhere 
 received by learned men as an established doctrine 
 of astronomical science. It is a striking illustration, 
 however, of the conservatism of philosophical thought 
 that Lord Bacon, who lived until 1628, long after the 
 decisive discoveries of Galileo, never gave his assent 
 to the Copernican doctrine, and even Descartes, who 
 lived until 1650, gave to it at most only an implied 
 recognition, rejecting the form while he adopted the 
 substance. 
 
 We can readily account for the position of Des- 
 cartes, who had a theory of his own which seemed 
 to him to include all that Copernicus had discovered ; 
 but we cannot but be surprised that Bacon was so 
 blind. It is one thing, however, to think and write 
 learnedly about induction, and another thing to make 
 discoveries. Bacon was a metaphysician, not a phys- 
 icist, much less an astronomer. He had not the 
 familiarity with nature by which alone an insight into 
 her methods and processes can be gained. He could 
 not therefore comprehend the vision of Copernicus, 
 
58 COPERNICUS. 
 
 and it seemed to him a dream. To his introspective 
 mind the order and finish of the Ptolemaic system 
 had a great charm ; and he was bound hand and foot 
 by traditions while protesting against them. Should 
 we have been wiser? And may not his experience 
 lead us not only to honor more highly the great man 
 whose character I have sought to portray, but also 
 to appreciate more fully, and value more highly, that 
 wonderful power by which he accomplished such 
 great results? 
 
TYCHO BRAHE. pq 
 
 LECTURE III. 
 
 THE INDUCTION OF NEWTON. 
 
 DURING the fifty years that followed the death 
 of Copernicus, preparations were being made 
 for another great advance in the theory of astron- 
 omy. These preparations consisted chiefly in the 
 extension of observations, the calculation of tables, 
 the improvement of methods, — all resulting in the 
 collection of fuller and more accurate data in regard 
 to the motions of the heavenly bodies. A very skil- 
 ful observer appeared, the accuracy of whose meas- 
 urements exceeded anything that had yet been 
 obtained. Copernicus had declared to a pupil, who 
 was disturbed about single minutes, that " if he could 
 be sure to ten minutes of space, he should be as 
 much delighted as Pythagoras was when he dis- 
 covered the property of the right-angled triangle ; " 
 but it was claimed for Tycho Brahe that an error of 
 eight minutes in his observations was impossible. 
 
 In the last year of his life at Prague Tycho re- 
 ceived into his observatory, as an assistant, a young 
 man named Johann Kepler, who with these eight 
 minutes, to use his own boastful words, was able to 
 reconstruct the whole of astronomy. There could not 
 be a greater contrast than that between Copernicus 
 
60 KEPLER. 
 
 and Kepler, — the one, the ideal philosopher; the 
 other, a veritable astronomical Don Quixote, turn- 
 ing what he must have known to have been a dishon- 
 est penny by astrology in his youth, and in his mature 
 manhood discussing like a Lothario the qualifications 
 of eleven different damsels to become his second 
 wife. There never was a wilder imagination than 
 that of Kepler, and he gave it full rein. The wisest 
 of men have doubtless at times idle fancies ; but then 
 they have the wisdom to keep their folly to them- 
 selves, or at least to their homes. Kepler, on the 
 other hand, seems to have had no sense of decorum. 
 He not only entertains and cherishes the most ab- 
 surd speculations, but he publishes them all to the 
 world ; so that his voluminous works are a most 
 singular medley of sound thoughts and unmitigated 
 nonsense. But beneath all this there is the true sci- 
 entific spirit. He submits his ridiculous conceptions 
 to the test of experience, and rejects them at once 
 if they do not stand the trial. He displays without 
 reserve all the inner processes of his thoughts, ex- 
 aggerating his follies, and parading his conceits like an 
 actor; and this makes his works a curious study of 
 the inductive method of reasoning; for among all 
 these wild guesses he discovered three great truths, 
 which have ever since been known as Kepler's Laws, 
 and which will render his name honored so long as 
 astronomy is studied. 
 
 Copernicus had divined the great central feature 
 of the solar system, but he was trammelled to the 
 last by the Aristotelian dogmas in regard to the na- 
 ture of motion, and assumed throughout that the 
 
KEPLER. 6l 
 
 heavenly bodies must maintain an equable circular 
 motion in their orbits ; and in order to explain the 
 obvious anomalies which remained, even on his helio- 
 centric theory, he was obliged to retain the system 
 of eccentrics and epicycles of the Ptolemaic school, 
 although very greatly reduced in proportions. This 
 was a manifest blemish on the Copernican system ; 
 but these devices were evidently regarded by Coper- 
 nicus as temporary modes of representing the irreg- 
 ularities, for the purposes of computation. And it 
 must be remembered that in physical science appar- 
 ent irregularities are inseparable from observation 
 and experiment ; and that the most conspicuous feat- 
 ure of modern astronomy is the discussion of just 
 such seeming discrepancies, only of course of a much 
 lower order of magnitude. In reducing the magni- 
 tude of the anomalies Copernicus recognized that 
 he was approaching a true theory ; and in the study 
 of nature this is all any man is permitted to do. The 
 inmost shrine cannot be entered ; and Copernicus 
 did not feel the necessity of reconciling his empirical 
 methods with modern dynamics. 
 
 Kepler had no better knowledge than Copernicus of 
 the laws of motion,— although he was a younger man 
 by seven years than Galileo, and the experiments 
 of the Pisan professor on falling bodies, and his sar- 
 castic attacks on the notions of the Aristotelians, had 
 been published long before the famous laws of plan- 
 etary motion were discovered. Kepler not only held 
 to the dynamical conceptions of Aristotle, but put 
 them into the most grotesque guise, likening the 
 planets to huge animals rushing through the skies. 
 
62 KEPLER. 
 
 He was not, however, hampered by deference to dog- 
 mas of any kind. He had no more respect for a 
 circle than for any other curve ; and since an oval, 
 like a circle, returns upon itself, and would thus obvi- 
 ously satisfy one fundamental condition of a planet's 
 orbit, he inquired, with the aid of careful plottings 
 and computations, how far observations of positions 
 in the case of the planet Mars could be satisfied on 
 the assumption of an oval orbit. 
 
 In the first place he found that by considering the 
 plane of the planet's orbit with reference to the sun 
 alone, a position could be given to this plane from 
 which the planet had none of the librations which 
 both Ptolemy and Copernicus had attributed to it. 
 Copernicus, influenced evidently by his Ptolemaic 
 education, had assumed that the orbits of the planets 
 must have some connection with the plane in which 
 the earth moved ; and this simple step of Kepler's 
 at once freed the heliocentric theory from the ma- 
 chinery of epicycles with which Copernicus had left 
 it encumbered. 
 
 But the eccentrics remained, for they were facts 
 of nature ; and it was then apparent that the planet 
 did not have an equable motion in its orbit, as had 
 been until then assumed ; so that with the epicycles 
 the old dogma of equable circular motions was ban- 
 ished forever from astronomy. Thus freed from a 
 blinding prejudice, Kepler was soon able to take a 
 great step forward. In studying the conditions which 
 on the new theory regulated the changing velocity 
 of the planet's motion in different parts of its orbit, 
 he discovered what has since been known as Kepler's 
 
KEPLER'S LAWS. 63 
 
 " Second Law," that the areas described, or swept, 
 by the line drawn from the planet to the sun are 
 always equal in equal times, or are proportional 
 to the durations of the motion. The "First Law," 
 that the orbits of the planets are true ellipses, 
 of small eccentricity, with the sun at one of the foci, 
 was not reached until some time after the " Second 
 Law," and the step between the two was a very long 
 one for Kepler. He tried all sorts of hypotheses 
 of circular and oval orbits before he hit on what 
 would seem to us the most obvious conception of 
 all ; and the detailed history of his struggles with 
 this problem occupies thirty-nine chapters of his 
 work " De Stella Martis. " The " Third Law," that 
 the squares of the periodic times of the planets are 
 proportional to the cubes of the solar distances, 
 had in Kepler's mind no logical connection with the 
 first two, but was the one valuable result of the ex- 
 travagant and often preposterous speculations which 
 he narrates at great length in his book on " The 
 Harmonies of the Universe." 
 
 There is a great deal in Kepler's character which 
 might naturally impair that respect for the scientific 
 investigator which the graces of Copernicus have 
 done so much to establish. It seems inscrutable that 
 such a " krank," as Kepler appears in a large part of 
 what he wrote, should have accomplished such great 
 results; and it would be natural to judge the work 
 by the man. But this was not the first case in which 
 " God hath chosen the foolish things of the world to 
 confound the wise; " and it is possible that just such 
 a man was required to break up the superstitions 
 
64 KEPLER'S CHARACTER. 
 
 which the dogmas of Aristotle had become. And 
 however weak in some of the relations of life, Kepler 
 united all the conditions of successful induction. He 
 had a very large knowledge of astronomical facts, and 
 was familiar with all their limitations. He had an 
 exuberant imagination, and great fertility of invention. 
 He was loyal to nature, and never harbored his errors 
 when once refuted. As Whewell very justly says, 
 "Kepler certainly was remarkable for the labor which 
 he gave to such self-refutations, and for the candor 
 and copiousness with which he narrated them; his 
 works are in this way extremely curious and amus- 
 ing, and are a very instructive exhibition of the 
 mental process of discovery." 
 
 To illustrate the characteristic features of the in- 
 ductive method here referred to is the chief object of 
 these lectures ; and I trust that the story of Kepler 
 has made prominent three essential conditions of 
 success : first, a large knowledge of facts, based on 
 an intimate acquaintance with the phenomena of na- 
 ture; secondly, a fertile imagination, ready to sug- 
 gest the possible relations of these facts ; thirdly, a 
 conscientious scientific spirit, which submits every 
 hypothesis to the test of observation or experiment. 
 
 The laws of Kepler were purely formal ; that is, 
 they were expressions of facts or relations for which 
 no explanation was given, or could be given at that 
 time. It was a fact that the planets moved in ellip- 
 tical orbits ; it was a fact that the radius vector swept 
 over equal areas in equal times ; it was a fact that the 
 squares of the periodic times were proportional to 
 the cubes of the sun's mean distance; and the cir- 
 
FORMAL AND DYNAMICAL LAWS. 6$ 
 
 cumstance that these facts were learned by inference, 
 and not by direct observation, does not alter their re- 
 lation to the scheme of knowledge. They are in no 
 respect efficient causes. They are simply facts and 
 nothing more, and to Kepler they were wholly dis- 
 connected facts ; and this distinction between a for- 
 mal or phenomenal law, which merely expresses a 
 general fact of nature, and a dynamical law, which 
 gives the mode of action of an efficient cause, corres- 
 ponds to a most important step in the progress of 
 science. We can distinguish three stages in this pro- 
 gress : first, the phenomenal stage, in which only 
 isolated facts are observed and recorded ; secondly, 
 the formal stage, in which facts of general relation- 
 ship are discovered ; thirdly, the dynamical stage, in 
 which the relations are traced to some efficient cause. 
 Astronomy was raised to its second stage by Hippar- 
 chus, to its third stage by Newton. Until the end 
 of the seventeenth century it was still in the formal 
 stage, and the discoveries of Kepler did not alter its 
 position, although they prepared the way for the 
 great advance which was soon to follow. According 
 to Kepler's loftiest conceptions the planets moved in 
 the manner which he had discovered simply because 
 it was their nature so to move. But a far more gifted 
 seer was soon to come, who should show that the laws 
 of Kepler were the necessary and very partial re- 
 sults of the action of a force which controlled the 
 universe. 
 
 If after his work was done Kepler had been told 
 that in less than a century the laws he had discovered 
 would be shown to be merely phases of the action of 
 
66 KEPLER'S IDEA OF FORCE. 
 
 universal gravitation, there can be little doubt that he 
 would have regarded the prophecy as grandiloquent 
 nonsense. Kepler associated no clear conception 
 with the word " force," and did not recognize a force 
 of gravitation. By Kepler, and by all scholars before 
 him, as well as by many after him, the word " force " 
 was used to denote any manifestation of energy, which 
 might vary widely not only in its nature but also in 
 its mode of action. There were forces innumerable, 
 each with its own special virtue and mode of action. 
 It was obvious then as now that muscular force would 
 produce motion, and that a moving body would exert 
 force ; but there were no clear conceptions of the re- 
 lation of motion to force. A stone fell to the ground, 
 not because it was pulled by a force which we now 
 call gravity, but because it was the tendency of heavy 
 bodies to move downward, through a virtue residing 
 in the body itself, not in the earth. It must have been 
 known to Kepler that while he was at work on the 
 theory of Mars an Italian named Galileo, with whom 
 subsequently he maintained a friendly correspond- 
 ence, had been making some curious experiments on 
 swinging pendulums and falling bodies, which were 
 subversive of all the old mechanical notions ; but he 
 did not dream that they had any bearing on his 
 studies. Yet Galileo was doing for mechanics almost 
 precisely what Kepler was doing for astronomy, and 
 the labors of both men were the necessary prelude to 
 the induction of Newton. In order that we may the 
 better understand the bearing of this new and con- 
 verging line of investigation it may be well for me to 
 review very briefly the fundamental conceptions of 
 
FORCE AND MOTION. 67 
 
 the modern theory as to the relations of motion and 
 force. 
 
 We know nothing more about the origin of force 
 than our fathers, but we have a very clear idea about 
 the uniformity of its manifestation. Force, however 
 produced, always manifests itself either as a pull or a 
 push, and no matter what may be the circumstances, 
 this pull or push varies only in strength. The force 
 may be produced by muscular action ; it may be due 
 to electrical excitation ; it may be an effect of mag- 
 netism ; it may be caused by heat; it may be grav- 
 ity ; but in all these cases the ultimate effect is a pull 
 or a push. We do not, of course, by this analysis, 
 remove in the least degree the mystery which still 
 surrounds the origin of force; we know nothing 
 more about the nature of gravity than we knew be- 
 fore : but we do know that gravity acts as a pull of 
 definite strength ; and we have made a great advance 
 towards clear thinking when we have been able to 
 banish from our minds all the indefinite and mys- 
 terious accessories with which the term has been as- 
 sociated, and whenever the word " force" is used, to 
 think only of a pull or a push between two definite 
 bodies. So also with motion. It would be easy to 
 bewilder the imagination by attempting to combine 
 the various motions of which every object on the sur- 
 face of the earth must simultaneously partake; or 
 confuse the mind by discussing whether independent 
 motion in space is oonceivable. But in physics we 
 deal only with relative motions. We do not recog- 
 nize absolute rest or motion. An object is at rest or 
 in motion solely with reference to some other object. 
 
68 FORCE AND MOTION. 
 
 A body, therefore, may be at the same time at rest 
 in relation to one object and in motion in regard to 
 another. If two bodies are moving with relation to 
 each other it is wholly arbitrary which is regarded as 
 at rest and which in motion. It is not necessary to 
 dwell on illustrations of these points, which the mov- 
 ing trains on our railroads so frequently bring to 
 mind. Rest and motion in mechanics are, therefore, 
 simply relative states, and should only be considered 
 from this point of view. Never think of motion as 
 an attribute of a body, but only as change of place 
 with reference to some other body. If the old Greeks 
 could have realized this simple conception the prog- 
 ress of astronomy would have been hastened by at 
 least a thousand years. 
 
 It will now be seen to be an obvious phase of the 
 fundamental conception, that the same body may par- 
 take of several motions at once, and that each of these 
 motions will be entirely independent of the others, 
 and uninfluenced by them ; so that the resulting path 
 and final goal will be simply the combined effect of 
 all. This conclusion, if not at once obvious, will ap- 
 pear if it is remembered that according to the fun- 
 damental conception of motion, a body assumed to 
 be at rest in relation to several other bodies assumed 
 to be in motion is in the same condition towards 
 each one as if these assumed states were reversed ; 
 and hence, that its relations to the several bodies 
 must be as independent in one state as in the other. 
 Thus arise all the familiar principles of the composition 
 and resolution of motions, which, however complex in 
 some of their applications, are very simple in theory. 
 
DIRECTION. 69 
 
 As with motion, so also in regard to direction, we 
 have only relative knowledge. It is useless to inquire 
 whether we could form any idea of direction indepen- 
 dently of the objects around us ; and it was merely 
 their limited acquaintance with the dimensions of the 
 universe which led the Greeks to speculate about 
 absolute directions. Upward and downward have 
 reference solely to the earth ; and directions can be 
 known only in relation to the positions or features of 
 material bodies. Practically, we refer both direction 
 and motion to the earth, with its fixed axis and con- 
 stant time of rotation, and with well marked features 
 on its surface ; and we come to associate our ideas of 
 motion and direction solely with this standard. But 
 we should bear in mind that this standard, though 
 natural, is arbitrary, — that other standards might be 
 used, and are used in astronomy. When in analytical 
 geometry or crystallography we refer directions and 
 positions to a set of arbitrary lines called axes, we 
 merely do for our problems what nature has done 
 for our every-day life, by placing us on a globe with 
 definite outlines which set bounds to our habitation, 
 and fixed limits on which our thoughts may rest. 
 To the young student of mathematics all this sys- 
 tem of co-ordinates, with the arbitrary transforma- 
 tions, seems very artificial ; but they are essential 
 conditions of clear thought ; and it was the want of 
 the very conception which they embody which made 
 the method of Euclid so limited in its applications. 
 
 Few works that have come down to us so strik- 
 ingly illustrate the fertility, acuteness, and versatility 
 of the Greek mind as the " Geometry of Euclid ; " and 
 
70 DEFECT OF THE GREEK GEOMETRY. 
 
 it remains to our time one of the chief tools in educa- 
 tion. As a training in intellectual gymnastics it is an 
 admirable study, but as a means of investigating na- 
 ture it is practically useless ; and the defect of the 
 Greek geometry, like the defect of the Greek me- 
 chanics, arose from seeking the fundamental con- 
 ceptions, not in the observation of nature, but in the 
 accidents of thought, — although, from the nature of 
 the subject, the first defect was, of the two, far the 
 less serious in its consequences. This defect appears 
 conspicuously in Euclid's treatment of the straight 
 line, which is defined as the shortest distance be- 
 tween two points ; leaving out of account the funda- 
 mental characteristic, that of definite direction. The 
 Greeks were, with reason, very proud of their ge- 
 ometry; but the science could not measure the earth, 
 as its name denotes, much less the heavens, until it 
 was re-established by Descartes on the basis of accu- 
 rate conceptions of direction. Even at the present 
 day, since most of us have derived our knowledge 
 of geometry either directly or indirectly from Euclid, 
 it is not unimportant to insist that direction, like mo- 
 tion, is a fundamental condition or state, inseparable 
 from material existence, whose relations we must ac- 
 cept as facts of observation, and not merely as modes 
 of consciousness. 
 
 With the fundamental conceptions clearly estab- 
 lished, see how very simple all the relations of force 
 to motion at once become; and how intelligible, in 
 the light of our familiar experience. If a body is at 
 rest with reference to another it can be set in motion 
 only by the application of force, — that is, by what 
 
LAWS OF FALLING BODIES. J I 
 
 is the equivalent of a pull or a push between the two ; 
 if it is in motion it can only be brought to rest in the 
 same way ; and to start a body when at rest, or to 
 stop it when moving, are, mechanically, equivalent 
 operations. 
 
 When a constant force acts on a body in the direc- 
 tion of its motion, the velocity of the motion must be 
 constantly accelerated, because the effect of the pull 
 at any instant must be added to the previous condi- 
 tion. Remembering that the pull or push at each 
 instant simply adds its effect to the previous state, 
 it will be seen that the laws of accelerated or re- 
 tarded motions — including the laws of falling bodies 
 — follow at once from the fundamental principles ; 
 and that acceleration or retardation are indications of 
 the action of some force; and that the amount of 
 acceleration or retardation is the measure of that 
 force. If a body is acted on by two or more forces 
 at once, each produces its effect independently of the 
 others, and the final result is found by simply com- 
 bining the several effects. 
 
 Evidently, very complex problems may arise under 
 the conditions last named. One of the simplest is 
 when a bomb-shell is thrown from a mortar. The 
 exploding gunpowder gives to the ball a tremendous 
 push in a given direction, and were it not for the 
 pull of the earth and the resistance of the air, — which 
 last we here leave out of the account, — the ball, with 
 reference to the gun, would move on forever and 
 with a uniform velocity; but the moment it starts 
 from the gun it begins to fall to the earth, and falls 
 the same number of feet in a given time that a stone, 
 - 6 
 
72 PROBLEM OF CENTRAL FORCES. 
 
 or any other object, would fall if dropped from an 
 elevation. The actual path is a combination of the 
 two motions, and would be a parabola were it not 
 for the resistance just referred to. Another and some- 
 what similar problem assumes great importance from 
 its astronomical relations. A body is moving with 
 reference to another, and much more massive, object, 
 which for distinction we will call the central body, — 
 not directly to or from it, but on a line which leaves 
 the central body on one side at a greater or less 
 distance. On this moving mass the central body 
 exerts a constant pull. What will be the effect? 
 This will depend on the strength of the pull ; but, 
 in general, the path assumed by the moving body 
 will be that of one of the conic sections, drawn 
 round the central body as the nearer focus, and in a 
 plane containing both this centre of force and the 
 original path. If the force were comparatively feeble 
 the body would describe the arc of an hyperbola, 
 and fly off on a new course in the direction of the 
 asymptote to this curve ; but if the force were be- 
 yond certain limits the path would be a circle or an 
 ellipse returning on itself; and we should then have 
 the counterpart of the motions of the planets. 
 
 In this connection it is to no immediate purpose to 
 inquire what was the cause of the primitive motion, 
 unless as a matter of curious speculation about world- 
 building; for the motion was a primitive state, just as 
 much as the chemical elements or any other funda- 
 mental conditions. The solution of the problem of 
 central forces, as it has been called, is independent of 
 such considerations, and is complete without them. 
 
THE THREE LAWS OF MOTION. 73 
 
 With our present conceptions of force and motion it 
 seems perfectly simple, and as given in our college 
 text-books it can be followed by any scholar with a 
 moderate knowledge of mathematics ; but only two 
 hundred years ago it taxed the best minds of an age 
 remarkable for the powerful intellects it produced. 
 
 From the primary conceptions of direction, motion, 
 and force, it would be very easy to develop all the 
 fundamental principles of mechanics, — to show that 
 when a pull or a push acts between two bodies both 
 must partake equally in the effect, or in other words 
 that action and reaction must be equal and opposite, 
 — to make evident that the mass of the bodies, as 
 measured by their weight, is a most important factor 
 in the result, and that the velocity imparted by a force 
 of constant strength, other things being equal, must 
 be proportional to the amount of material on which 
 the force acts, — to point out the distinction between 
 tension, or pressure, and work, or between momen- 
 tum and vis viva, a distinction which, although now 
 so familiar, was during the eighteenth century the 
 subject of a long and warm controversy among the 
 most eminent mathematicians of Europe. But these 
 points have only an indirect bearing on my present 
 argument; and I will close this summary of essential 
 preliminaries with the statement of the three laws of 
 motion as given by Newton in his " Principia." First 
 Law : Every body continues in a state of rest, or of 
 uniform motion in a straight line, unless acted on 
 by some external force. Second Law: Change of 
 motion is proportional to the force impressed, and is 
 in the line in which the force acts. Third Law: 
 
74 GALILEO. 
 
 To every action there is always opposed an equal 
 reaction. 
 
 Although at the present day the relations of force 
 to motion might be summarized to advantage in more 
 general terms, yet these formulas show a perfectly 
 clear conception, on the part of Newton, of the true 
 relations, and indicate a wonderful advance in clear- 
 ness of thought on this subject between the publica- 
 tion of Kepler's work " De Stella Martis " in 1608, 
 and that of the " Principia " in 1686. This is not the 
 place to follow in detail the history of this progress ; 
 but we will touch on one or two points, of which the 
 summary we have just given will enable you to see 
 the bearings. 
 
 Galileo — who was born in 1564, and became a 
 teacher at the University of Pisa in 1589 — laid the 
 foundations of modern mechanics ; and chiefly by 
 the remarkable series of experiments which he made 
 at Pisa during the three years (1589-91). In gen- 
 eral terms it may be stated that Galileo discovered, 
 and verified by experiment as formal laws, most of 
 the fundamental principles of dynamics. He taught 
 that all matter has weight, and that gravity and 
 levity are only relative terms. He pointed out the 
 relations of the centre of gravity, and insisted 
 that weight was a constant force, pulling all bodies 
 towards the centre of the earth. He maintained that 
 motion was the result of force, and clearly enunciated 
 the laws of falling bodies, — illustrating the theory 
 by experiments from the "Leaning Tower of Pisa" 
 which have become memorable in the history of sci- 
 ence. He clearly distinguished between uniform and 
 
GALILEO'S DISCOVERIES. 75 
 
 accelerated motion. He showed that motion caused 
 by a single force is always in a straight line, — that is, 
 in a definite direction; but that under the influence 
 of several forces a body may move in as many direc- 
 tions at once, simultaneously and independently. He 
 established the principle of the composition of forces, 
 and gave the true theory of projectiles. He distinctly 
 recognized, at least by implication, the principles of 
 action and reaction, and even of virtual velocities. 
 His works are full of ingenious demonstrations of 
 mechanical theorems, both theoretical and experi- 
 mental ; and he was versatile as an experimenter 
 as he was sound as a reasoner. But still, his results 
 were for the most part formal, and not co-ordinated 
 under general principles. Unquestionably, the prin- 
 ciples of Newton's three laws of motion may be re- 
 garded as implied in the whole tenor of Galileo's 
 experiments and computations, but they are no- 
 where definitely formulated in his writings, — although 
 in the review of the principles of mechanics which 
 he published near the close of his life he shows much 
 more distinct conceptions of the nature and relations 
 of force and motion than he did in his earlier work. 
 This book, entitled " Dialoghi delle Nuove Scienze," 
 and printed by the Elzevirs at Leyden in 1638, 
 gained universal admiration, and drew wide attention 
 to the subject. Like a well-known book, " Heat as 
 a Mode of Motion," which has done a similar work 
 in our own day, this last and best of the publications 
 of the great Florentine familiarized men's minds 
 with the interdependence of force and motion, which 
 up to this time had been only a disputed doctrine 
 
j6 GALILEO A POPULAR LECTURER. 
 
 known to a few scholars. The works of Galileo were 
 among the most important means of education for 
 the future Newton, and through them this noble 
 father of mechanical science, as well as great dis- 
 coverer in astronomy, was in fact one of the chief 
 teachers of his far greater successor. 
 
 In estimating the ability of Galileo and the merit 
 of his labors, we must remember that, like Coper- 
 nicus, he had to contend with the prejudices among 
 all scholars in favor of the dogmas of Aristotle; 
 which at the time were not only a belief but a reli- 
 gion. Still, we cannot but regret that so much of the 
 energy of this great originator was wasted in fruitless 
 disputations with the upholders of the old doctrines, 
 whom he followed with such pertinacity and bitterness 
 that they became his violent enemies. In this, how- 
 ever, he was but taking the course to which his disposi- 
 tions and abilities inclined him ; for Galileo had a 
 most remarkable power both as an expositor and as a 
 writer. He was what we should call a most success- 
 ful popular lecturer ; and when, driven by the old 
 schoolmen from Pisa, he accepted a professorship at 
 Padua, a hall holding two thousand persons was pro- 
 vided to receive the vast audiences which thronged 
 to his lectures. 
 
 It was his controversial spirit, rendered especially 
 irritating by the great influence of his powerful utter- 
 ance, which led to the collision of Galileo with the 
 Papal authorities. At heart he was a good Catholic 
 and a faithful son of the Church. He had many 
 friends among the most influential of the clergy ; 
 and there can be no question that he would have 
 
GALILEO'S CONFLICT WITH THE CHURCH. JJ 
 
 been left to teach as he pleased, and even been 
 honored for his innovations, if only he had avoided 
 theological issues, instead of rushing into them. 
 There was no need of forcing that greatly irritated 
 lion caged at the Vatican to show its claws. Neither 
 truth nor honor required it; and though we may not 
 think that a scholar can honorably hold an equivocal 
 position in regard to facts of demonstration, yet the dis- 
 tinction between " ex hypothesi " and " ex animo " was 
 one which Galileo avowedly accepted. And when he 
 violated his pledges, and again revived the old issues, 
 we cannot wonder that his conduct provoked censure ; 
 and it may be questioned whether he was treated any 
 more harshly than is many a man at the present day, 
 for a much less departure from prescribed creeds. 
 
 In the next generation after Galileo the theory of 
 mechanics became much more clearly developed, and 
 chiefly by his pupils or by those whom he directly 
 influenced. Of this generation, although only surviv- 
 ing Galileo eight years, was Descartes, one of the most 
 powerful minds which the world has ever produced. 
 Descartes, however, was a metaphysician rather than 
 a physicist ; a better reasoner than observer ; a better 
 mathematician than experimentalist. He never fully 
 entered into the spirit of the inductive method, or 
 made any far-reaching induction, — although he spent 
 much time in experimental work, especially in phys- 
 iology, and made some notable discoveries in phys- 
 ics, particularly the cause of the rainbow. His theory 
 of vortices, received with great applause at the time 
 as a mode of explaining the motions of the heavenly 
 bodies, and in its essential features revived of late in 
 
78 THE INFLUENCE OF DESCARTES. 
 
 connection with molecular physics, plainly shows that 
 Descartes had not a clear appreciation of the funda- 
 mental conceptions of mechanics. Nevertheless his 
 enunciation — for little less can it be called — of the 
 principle of the conservation of energy is an anticipa- 
 tion of one of the very latest results of science, than 
 which none more remarkable can be found in the whole 
 history of speculative thought; and this prevision will 
 appear still more wonderful when it is remembered 
 that it involved the assumption of molecular motion, 
 with the plain suggestion that heat may be a mani- 
 festation of the internal motions of material bodies. 
 Nevertheless, apart from his metaphysical writings, the 
 great contribution that Descartes made to the world's 
 progress was his geometry, to which we have before 
 referred, and whose leading principle we have pointed 
 out. Descartes not only gave a new life to this oldest 
 of the sciences, but he endowed it with a power of 
 interpretation which has done more than all other 
 agencies combined to extend our knowledge of the 
 heavenly bodies. 
 
 Into a world thus prepared for a great revelation of 
 knowledge was born, Christmas day, 1642, at the 
 close of the very year in which Galileo died, the child 
 who was to render illustrious his father's homely 
 name of ISAAC NEWTON. 
 
 It is always highly interesting to study the career 
 of a man who has fulfilled an important mission, — to 
 attempt to discover inherited tendencies ; to trace the 
 influences by which his mind was moulded ; to notice 
 early indications of peculiar power, even if remark- 
 able only because they seem prophetic ; to mark the 
 
EARLY LIFE OF NEWTON. 79 
 
 guidings of opportunities, if not the leadings of Provi- 
 dence ; to discriminate between native genius and ac- 
 quired talent; to see force of intellect and of will 
 rising superior to circumstances ; or, what is often 
 most singular, to find in the limitations of mental en- 
 dowments a more potent influence than natural abili- 
 ties in leading the specialist apart from the beaten 
 track; to realize what were the conditions under 
 which the great leader worked, and what were the 
 materials at his command ; and finally, to learn how 
 small, after all, were the single steps by which he 
 attained success. 
 
 Unfortunately, we have only the most meagre out- 
 lines of the early life of Newton. He does not seem to 
 have been a precocious child ; and the tales of early 
 mechanical skill are only such as are told of many a 
 boy who has become only an ordinary man. Even at 
 college — to which he appears to have been sent on 
 an after-thought, like the weakly son of a New Eng- 
 land farmer — there is no evidence that he gained 
 great distinction; so that when, in 1667, at the age 
 of twenty-five, two years after he received the Bach- 
 elor's degree, he was appointed Fellow of Trinity 
 College, Cambridge (his own college), we are sur- 
 prised to find him in possession of a power of 
 mathematical analysis far in advance of the best 
 mathematicians of his day. He himself tells us that 
 while an undergraduate he studied the Geometry of 
 Descartes, which he had some difficulty in mastering; 
 and already by his method of fluxions he had vastly 
 extended the grasp of the new Cartesian instrument 
 of research. 
 
SO HIS SYSTEM OF FLUXIONS. 
 
 As is well known, " Fluxions " was the name given 
 by Newton to the Infinitesimal, or, as it is now more 
 frequently called, the Differential and Integral Cal- 
 culus ; and the advance made by the introduction of 
 this new method into geometry was incomparably 
 greater than any step which had hitherto been taken. 
 It was, moreover, peculiarly an intellectual achieve- 
 ment; and, although some advance had previously 
 been made in the mathematical treatment of the in- 
 finitesimal quantities of geometry, especially by Fer- 
 mat and also by Barrow, Newton's predecessor in the 
 Lucasian chair of mathematics at Cambridge, yet the 
 improvement made by Newton was very great. That 
 this improvement should have been made by an 
 undergraduate was wonderful ; and we find it diffi- 
 cult to explain why it did not at once win admira- 
 tion, and was not widely proclaimed and highly 
 honored, except on the assumption that though 
 far in advance of his instructors, Newton's abilities 
 and attainments were limited to special lines, which 
 did not at the time find favor among the university 
 authorities. 
 
 The method of fluxions, although from this early 
 period constantly used by Newton in his own work, 
 and doubtless taught by him as Professor of Mathe- 
 matics, — an office which he filled at Cambridge from 
 1669 to 1 701, — was not fully described in print until 
 1691, and then not by himself; although the prin- 
 ciple of the method was given in a geometrical form 
 in the " Principia" four years earlier. It fTius came to 
 pass that in publication Newton was anticipated by 
 Leibnitz, who, in the " Acta Eruditorum," Leipsic, 
 
THE CALCULUS OF LEIBNITZ. 
 
 1684, described essentially the same method, though 
 under a different name and with a different notation. 
 In England Leibnitz was accused of borrowing his 
 first conceptions from hints in letters of Newton, and 
 no little bitterness on both sides was the result. But 
 in the discussion which arose, while Newton's priority 
 was established beyond a question, the originality of 
 Leibnitz was also made equally clear ; and it is the 
 notation and forms of Leibnitz, and not those of 
 Newton, which have been retained in science. 
 
 We do not know how early Newton applied his 
 new calculus to the solution of the so-called problem 
 of central forces. Since the principles of the compo- 
 sition of forces had been established by Galileo it 
 had become evident that the path of a planet might 
 be, as we have already pointed out, the resultant of 
 a primary motion of translation, modified by some 
 power constantly pulling the body towards the centre 
 of motion ; and the question was, what would be the 
 form of the orbit under such conditions. Attention 
 had been drawn to this problem in many quarters, 
 but the resources even of the geometry of Descartes 
 were not adequate to a complete solution. One con- 
 clusion, however, quite plainly followed from the 
 third law of Kepler, — although the complete demon- 
 stration even of this point was first given by Newton, 
 — and this conclusion was that if such a central force 
 as had been assumed existed, it must diminish as the 
 square of the distance from the sun ; otherwise the 
 squares of the periodic times of the different planets 
 would not be proportional to the cubes of the dis- 
 tances, as Kepler had found them to be. 
 
82 PROBLEM OF CENTRAL FORCES. 
 
 As early as January, 1684, the problem of central 
 forces was discussed by three eminent English mathe- 
 maticians, Sir Christopher Wren, Halley, and Hooke ; 
 but the discussion leading to no definite result, 
 Halley, in August of the same year, went to Cam- 
 bridge, to consult Newton on the subject; and without 
 mentioning that a discussion had been held, " went 
 straight to the point, and asked what would be the 
 curve described by a planet round the sun, on the 
 assumption that the sun's force diminished as the 
 square of the distance." Newton replied promptly, 
 " An ellipse ; " and on being questioned by Halley as 
 to the reason for his answer, he replied, "Why, I have 
 calculated it." That the calculation had been made 
 some time previously is evident from the further cir- 
 cumstance, we learn through Halley, that Newton could 
 not at once put his hand upon his former work ; but he 
 soon afterwards reproduced it, and in November sent 
 Halley a copy of the result. Soon after, Halley again 
 visits Cambridge to confer with Newton about the 
 same problem, and these conferences led to the prep- 
 aration of the " Principia," which was published under 
 the auspices of the Royal Society, at Halley's own 
 charge, two years later. The demonstration of the 
 law of gravitation first appeared in the " Principia ; " 
 and it is a most noteworthy fact — which marks a most 
 striking difference between the scientific activity of 
 those days and the investigations of our time — that 
 so important a result, which in all its essential features 
 must have been reached at least ten years before, 
 should have been kept so long by the author to him- 
 self, and even by him so far forgotten that he could 
 
PROBLEM OF CENTRAL FORCES. 83 
 
 not at once reproduce one of the chief steps in his 
 reasoning. 
 
 The problem of central forces as solved by New- 
 ton involved, as we have seen, two distinct questions. 
 In the first place, it was necessary to determine the 
 rate according to which the central force varied with 
 the distance ; and Newton had shown that it followed 
 from the third law of Kepler that the force must 
 diminish with the square of the distance; but in this 
 he had been to some extent anticipated. In the 
 second place, assuming a force thus varying, it was 
 required to find what would be the character of the 
 orbit of a body revolving round the centre of force 
 under its control. Newton was the first to answer 
 this last question correctly, and he had shown, not 
 only that the orbit would be an ellipse as the first 
 law of Kepler required, but also that, as the second 
 law required, the radius vector must describe equal 
 areas in equal tinies. 
 
 These results, however, had been deductions drawn 
 from established principles of mechanics by the aid 
 of the new calculus. No one thus far had suspected 
 the nature of this central force ; and by most scholars 
 of the period it would have been thought degrading 
 to astronomy to associate the mechanism of the 
 heavens with the mechanics of the earth. The two 
 subjects were never thought of in the same connec- 
 tions. There were, it is true, the deductions just re- 
 ferred to, by which it appeared that the planets 
 might be sustained in their motions round the sun by 
 the action of a constant central force controlling their 
 primary motions. There were also the undoubted 
 
84 LAW OF GRAVITATION. 
 
 facts of mechanics, that weight was the effect of a 
 direct pull or force exerted by the earth on all bodies, 
 and that the strength of this pull was directly propor- 
 tional to the amount of material on which it acted. 
 As yet, however, these two classes of facts, so closely 
 associated in our own minds, belonged to wholly dis- 
 tinct categories of thought, and were no more asso- 
 ciated than we connect the fluctuations of the market 
 with the motions of the moon. Indeed that there 
 was any intimate relation between force and motion 
 was then a very modern conception. 
 
 The idea, that, after all, this sublime, inscrutable, 
 central force of astronomy was simple commonplace 
 gravity seems suddenly to have flashed into the mind 
 of Newton. We all know the anecdote of the falling 
 apple. The authority for the story is Voltaire, who 
 narrates it in a somewhat popular account of New- 
 ton's work, which he wrote for French readers soon 
 after his return from England in 1.729. He gives as 
 his authority Catharine Barton, a favorite niece of 
 Newton. She married Conduit, a Fellow of the 
 Royal Society and one of her uncle's intimate friends, 
 with whom also Voltaire was intimate during his well 
 known residence in London from 1726 to 1729; and 
 it was during this time, in 1727, that Newton died. 
 The story has been discredited by Sir David Brew- 
 ster in his "Life of Newton ;" but, as must be admitted, 
 it is as authentic as such a personal reminiscence 
 could well be ; and it is certain that tradition marked 
 the tree near his mother's house at Woolthorpe in 
 Lincolnshire as that from which the apple fell, till 
 1 820, when owing to decay it was cut down, and the 
 
THE INDUCTION OF NEWTON. 85 
 
 wood carefully preserved. Tradition also fixes the 
 date as 1666, soon after Newton's graduation from 
 Trinity, when he was passing several months at his 
 old home on account of the fear of the plague at 
 Cambridge. 
 
 Why may not the force which pulls the apple pull 
 the moon? We are left in no doubt whatever in re- 
 gard to the general tenor of Newton's thoughts, 
 either in the garden at Woolthorpe or elsewhere ; for 
 we are told the story by Pemberton in the preface to 
 his " View of Newton's Philosophy," and he had it 
 from Newton himself. If the power of gravity, New- 
 ton thought, is not sensibly diminished at the greatest 
 heights to which we can rise from the earth's surface, 
 neither at the tops of the loftiest buildings nor even 
 on the summits of the highest mountains, why may it 
 not extend much further than is usually thought? 
 Why not as high as the moon? If so, her motion 
 must be influenced by it; perhaps she is retained in 
 her orbit thereby. 
 
 This was the simple thought suggested, and it was 
 this which constituted the greatest induction ever 
 made in physical science. The moon is only distant 
 from us some sixty times the earth's radius, and why 
 should not the immense pull of the earth on all mat- 
 ter near itself be felt at that distance? Of course if 
 this is the force which holds the moon and the planets 
 to their orbits it must, as can be proved by Kepler's 
 third law, diminish with the square of the distance 
 from the centre of motion. From the well known 
 relations of the centre of gravity, the pull of the 
 earth on all bodies near its surface, as well as its pull 
 
86 METHOD OF CALCULATION. 
 
 on distant bodies, may be regarded as proceeding 
 from its centre of figure. Hence the force of the pull 
 at the moon must be as much less than the pull at 
 the earth's surface as the square of sixty-one is greater 
 than the square of unity, that is, 3721 times less. But 
 as the earth's pull is proportional to the quantity of 
 matter on which it acts, so that all bodies great or 
 small fall towards the earth with the same rapidly 
 increasing velocity, — the moon just as fast and no 
 faster than a stone under the same conditions, — we 
 ought to expect that the moon, at its distance, would 
 fall 3721 times more slowly than a stone near the sur- 
 face. Now such a stone falls 16 feet the first second, 
 and would fall if it had a chance 57,600 feet the first 
 minute ; so that the moon should fall about fifteen 
 and a half feet during the first minute of time. But 
 how much does the moon fall? This is the next 
 question which Newton asked ; and it is by no means 
 so easily answered as the one we have just solved so 
 readily. 
 
 If the moon and planets have the compound mo- 
 tion which Newton assigned to them, they are in the 
 paradoxical condition of beginning to fall at every 
 moment of time towards their primaries; always be- 
 ginning to fall but never falling. Should the earth's 
 pull at any instant suddenly cease the moon would at 
 once resume its primary motion of translation, start- 
 ing off on a tangent with the uniform velocity which 
 it had at that moment in its orbit. If now we con- 
 struct in imagination an arc of the moon's orbit de- 
 scribed around a centre representing the earth, with 
 a tangent starting off at the point where the earth's 
 
FIRST RESULT UNSATISFACTORY. 87 
 
 pull is assumed to stop ; and from this point of con- 
 tact measure off the distance on the arc over which 
 the moon actually moves in one minute ; and finally 
 through the extremity of the arc thus found draw 
 from the centre a radius, and extend the line until it 
 intersects the tangent, — then this intersection will be 
 the point which the moon would have reached in one 
 minute had it started off on the tangent as assumed ; 
 and the portion of the radius between the tangent and 
 the arc will represent the distance through which the 
 moon actually falls to the earth during this same 
 minute of time. Knowing the radius of the orbit 
 and the angle subtended by the arc at the centre, 
 and assuming — as we may — that such a small arc 
 is practically circular, it would be the simplest of 
 trigonometrical problems to calculate the distance in 
 question. In Newton's time, however, the calcula- 
 tion involved many uncertain elements, which he 
 showed great judgment in selecting and skill in com- 
 bining. But the first result was unsatisfactory, for it 
 appeared that the fall was only thirteen feet, instead 
 of fifteen and one half feet as the theory required. 
 
 Most men would have regarded this as at least a 
 sufficient approximation to induce them to continue 
 the investigation ; and no circumstance indicates 
 more plainly the balance of Newton's mind and the 
 dispassionateness of his temperament than that he re- 
 garded the result as disproof, and at once dismissed 
 the theory from his thoughts. 
 
 In a few years, however, the cause of this failure 
 to verify the theory was fully explained. The cal- 
 culation which Newton had made involved a know- 
 
 7 
 
88 THE THEORY VERIFIED. 
 
 ledge of the moon's distance in feet, while the 
 astronomical determination of this distance depended 
 on trigonometrical measurements of which the earth's 
 radius was the base ; and only gave the information 
 that the distance was about sixty-one times this ra- 
 dius. To reduce the result to feet, it was necessary 
 to know the length of the earth's radius in feet, and 
 here was the difficulty. We cannot of course meas- 
 ure the radius directly, but we can measure an arc 
 of a meridian circle on the earth's surface, and from 
 the length of an arc of known extent — say five de- 
 grees — calculate the length of the radius. This is what 
 Newton had done, assuming, according to the received 
 estimate at the time, that one degree on the meridian 
 measured sixty miles. In 167 1, however, a new 
 measurement of an arc of a meridian, between Ami- 
 ens and Malvoisine in France, was made by the 
 astronomer Picard, which showed that the received 
 length of a degree was greatly in error; and that 
 instead of being sixty it was sixty-nine English stat- 
 ute miles of 5280 feet each. When this result be- 
 came accredited in England, Newton revised the 
 calculation which had so long been laid aside ; and 
 the result was an agreement with theory so exact as 
 to leave no longer any doubt in his mind of the truth 
 of his early conception. As the story is told by 
 Robinson, " He went home, took out his old papers, 
 and resumed his calculations. As they drew to a 
 close he was so much agitated that he was obliged 
 to desire a friend to finish them." 
 
 This in outline is the history of the greatest scien- 
 tific induction which man has ever made. In draw- 
 
THE INDUCTION OF NEWTON. 89 
 
 ing the sketch, I have given prominence to those 
 features which from my point of view seemed most 
 essential, and have doubtless passed unnoticed facts 
 and relations which others might deem more impor- 
 tant. But the interaction of mind on mind, which 
 scientific progress involves, is usually very complex ; 
 and, in the absence of detailed information, there is 
 room for great differences of opinion. It is much to 
 be regretted that we have not fuller knowledge, espe- 
 cially in regard to the sequence in which the various 
 elements of the problem were presented to Newton's 
 mind ; but he, unlike his predecessor Kepler, was very 
 reticent, and did not display all the processes of his 
 thoughts. 
 
 We might, with Whewell, classify the general results 
 of Newton's work under five different propositions, 
 which undoubtedly came before him at one time 
 or another as separate problems: first, that the 
 strength of the pull of the sun on different planets 
 diminishes with the square of the distance; secondly, 
 that a force so acting would cause the planet to 
 move in elliptical orbits, in accordance with the first 
 and second laws of Kepler; thirdly, that the earth 
 so acts on the moon, and that this force is identical 
 with gravity; fourthly, that this force is universal, 
 causing an attraction between all bodies under all 
 conditions ; fifthly, that the strength of the force 
 increases in the same proportion as the combined 
 weights of the attracting bodies, and may be re- 
 garded as the sum of the actions of the various par- 
 ticles or units of mass of which they consist. 
 
 Such a classification is useful, as a summary of 
 
90 THE INDUCTION OF NEWTON. 
 
 what has been — in great measure — already stated, 
 as pointing out the separate elements of the problem, 
 and as showing how great the work really was. But 
 all these propositions except the third, were deduc- 
 tions from known principles ; and the identity of the 
 central force with gravity being granted, the rest 
 necessarily followed. Not that we would in the least 
 degree depreciate the skill with which these deduc- 
 tions were worked out. On the contrary, as with 
 every investigation, this was Newton's real work ; " hie 
 labor, hoc opus est;" and it has always won, and ever 
 will claim the admiration of the world. But it was 
 the great induction, and not these deductions which 
 we are endeavoring to illustrate. The induction was 
 to a large extent — if not wholly — a spontaneous 
 action of the mind ; but it is by just such action that 
 the level of knowledge is raised. After any great 
 induction it always requires time — it may be long 
 time — to work up to the new level. It was so after 
 Hipparchus ; it was so after Copernicus ; it was so 
 after Kepler ; and astronomy has not yet reached the 
 level which Newton set. The deductions may require 
 greater intellectual skill, as they necessarily involve 
 incomparably greater labor; but they do not raise 
 the level. As in building, it requires little work to 
 raise the scaffolding, but then comes the long and 
 arduous toil of the builders to prepare the walls on 
 which to mount still higher. 
 
 If gravity reaches to the tops of the highest moun- 
 tains, why not as high as the moon ? This was the 
 fundamental conception which led to the great result. 
 Seeing how apparently trivial and accidental was the 
 
THE INDUCTION OF NEWTON. 9 1 
 
 thought which bound together the universe in its all 
 embracing grasp, some may imagine that the individ- 
 ual merit of the conception was inconsiderable. But 
 they must remember that the thought would have been 
 barren without the knowledge to make it pregnant, 
 or without the labor to make it real. Others, like 
 Hooke and Cassini, did claim to have had the thought 
 as well as Newton ; but their thought was barren, and 
 the world has paid no regard to their claims. Again, 
 some may think that, given the knowledge and the 
 intellectual power, the thought came without observa- 
 tion, and that to God and not to man belongs all the 
 glory. If by this is meant that the thought came as 
 an inspiration to a mind prepared to receive it, I 
 should agree to the proposition; 
 
 " For merit lives from man to man, 
 And not from man, O Lord, to Thee." 
 
 And I myself believe that just as to the intellectually 
 strong and teachable there come revelations of larger 
 knowledge about material things, so to the spiritually 
 minded and open-hearted there comes in a similar 
 way a deeper insight into the spiritual life; and it is 
 because I believe these material relations to be a 
 type of the spiritual, and to have the same, though 
 no more certain sanctions, and it is because I hope, 
 through a more intimate knowledge of the facts, to 
 aid in reconciling the two orders of truth, that I have 
 dwelt so long on this instructive history. 
 
 The character of Newton was entirely in harmony 
 with his lofty career. It was marked by sedateness 
 of demeanor; soberness of conversation; sobriety of 
 
92 THE CHARACTER OF NEWTON. 
 
 conduct; persistency in effort; devotion of will; hu- 
 mility of disposition ; reverence of mind, and absorp- 
 tion in thought. He never would admit there was 
 any difference between himself and other men ; and 
 when asked how he made his discoveries, replied, " I 
 keep the subject of my inquiry constantly before me, 
 and wait till the first dawning opens gradually, by 
 little and little, into a full and clear light." It is into 
 minds in such a frame that the light shines ; and by 
 waiting on the Eternal Purpose the revelations of 
 great truths come. 
 
INDUCTION RAISES THE LEVEL OF KNOWLEDGE. 93 
 
 LECTURE IV. 
 
 DEDUCTION. 
 
 IN my last lecture I said that a new induction raises 
 the level of human knowledge; and this figura- 
 tive expression very exactly indicates the new rela- 
 tions which are thus introduced into the world of 
 thought. There is not simply an addition to knowl- 
 edge, but the old knowledge is seen in a new light. 
 Facts previously disconnected are found to be united 
 by common bonds. Phenomena which appeared 
 mysterious and fortuitous now appear regular and 
 natural. Principles which were supposed to be fun- 
 damental are found to be dependent. Partial and 
 formal laws are merged in more universal and sim- 
 pler modes of action. Order and harmony prevail 
 where before was only confusion and discord. 
 
 But to show what are the results of the new princi- 
 ple that has been introduced, to trace all its connec- 
 tions, to develop the consequences, both near and 
 remote, to test by observation or experiment, the 
 deductions in every detail, and to follow out the 
 lines of investigation thus opened, requires a great 
 amount of thought and labor, and the more in pro- 
 portion as the previous induction is broader and 
 more commanding. In this way the general standard 
 
94 DEDUCTION BROADENS KNOWLEDGE. 
 
 of knowledge is brought up to the new level, and the 
 foundations are laid on which to rise to a still more 
 commanding position. It is work of this sort which 
 almost exclusively occupies the time and taxes the 
 energies of the great body of scientific investigators ; 
 and in the economy of nature many thousand workers 
 are ready to carry out the conceptions of one great 
 master. 
 
 The great originator is highly favored among men, 
 but let it not be inferred that the part of his fellow- 
 workers is less honorable, or their labor less difficult, 
 or less necessary. Not only is it that 
 
 "All are architects of Fate, 
 
 Building on these walls of time," 
 
 but it is also true that some of the greatest intellect- 
 ual achievements have consisted wholly in following 
 out well-established principles to their necessary con- 
 sequences. Newton's great induction commands our 
 highest admiration, but so do equally the deductions 
 which Laplace and Lagrange and Gauss severally 
 drew from Newton's all-embracing law. No work 
 of science can be compared with the " Principia " in 
 the effect produced on the progress of knowledge; 
 but it may be questioned whether it shows as great 
 intellectual power as the " Mecanique Celeste." 
 
 The mathematical sciences give us the most char- 
 acteristic examples of the deductive method, and 
 mathematics is the most important tool in such pro- 
 cesses of thought. The necessity of such aid arises 
 from the limited power of the human mind in com- 
 bining details, in following sequences, in remember- 
 
ARABIC NUMBERS. 95 
 
 ing successive steps, and in general in concentrating 
 thought. The various forms of calculus help the rea- 
 soning powers very much in the same way that the 
 microscope, the telescope, or the telephone, aid the 
 eye or the ear in observing natural phenomena. 
 
 This fact we recognize in the simplest forms of 
 mathematical calculation. The Arabic numerals, 
 with the so-called decimal system of arithmetic, en- 
 able any one readily to obtain results which, without 
 their aid, would be attainable only by a mathematical 
 genius; and if we analyze the mental processes of 
 the remarkable calculators who from time to time 
 appear, we find that their wonderful ability depends 
 chiefly on a vividness of memory and imagination, 
 which enables them to keep before their minds, and 
 thus combine, a great number of partial results. 
 Each of these by itself might have been obtained 
 mentally by the average man ; but he finds it neces- 
 sary to aid his memory by noting down every step 
 of his calculation on slate or paper. 
 
 Men with such a knack at figures are also able 
 to combine results by quick methods which are out 
 of the reach of ordinary computers; while the com- 
 mon rules of decimal arithmetic are adapted to the 
 average mind, and give just the aid which will enable 
 it to reach most rapidly and accurately, the required 
 result. 
 
 It may be well here to set right a common mis- 
 apprehension, that the rules of arithmetic have some 
 special relation to the number ten. Since Nature 
 gave man ten "fingers or digits, which make a very 
 simple but efficient calculating engine, he instinc- 
 
96 DECIMAL SYSTEM. 
 
 tively, at a very early period, distinguished and gave 
 names to ten corresponding numerals, also frequently 
 called digits; but it was not until man had tried vari- 
 ous clumsy expedients of combining these digits to 
 express larger numbers, that some good genius, sup- 
 posed to have been an Arabian, devised our simple 
 method of expressing numerical values. The arith- 
 metical rules are the outcome of this method, and 
 would work just as well with any other number of 
 digits as with ten. Eight digits would have given us 
 a simpler arithmetic, and twelve digits, in many re- 
 spects, a more convenient one. Such, however, is 
 the force of habit and the conservatism of education 
 that a change now would probably be impracticable ; 
 but we cannot but regret that our early parents did 
 not omit the thumbs in the first count. Eight units 
 can be evenly divided three times, ten units but once; 
 and this power of successive subdivision is of para- 
 mount importance in commercial transactions, as the 
 experience in France with decimal weights and 
 measures plainly shows. 1 
 
 1 The truth of this statement, although really so simple, 
 seems so inconsistent with our familiar habits and ordinary 
 experience, that some further illustrations of it may be desired. 
 In our system of enumeration we use in addition to the zero 
 mark separate signs for the first nine digits, and express all 
 higher numbers by an ingenious method of combining these 
 signs, or figures, as the signs are called. The system consists 
 in writing the figures in a definite order on a horizontal line, 
 and assigning to the digits a value increasing by powers of ten 
 as we proceed from right to left. The figure in the first or 
 units' place stands for single digits ; the figure in the second or 
 tens' place stands for ten times the number indicated by the 
 
OCTUPLE SYSTEM. 97 
 
 The French system of weights and measures is 
 constantly advocated on account of its decimal sub- 
 division, but these are a positive disadvantage. The 
 one valuable feature of the French system is the 
 simple relation which it establishes between measures 
 and weights, and it would doubtless be a great gain 
 if such a system were adopted by all nations ; but it 
 would be a still greater gain if we could get rid of 
 
 sign ; the figure in the third or hundreds' place for ten times 
 ten, or one hundred times, the number indicated ; that in the 
 fourth or thousandths' place for ten times ten times ten, or one 
 thousand times, the number expressed ; and so on. The ex- 
 pression 63,597, for example, signifies six ten thousand, added 
 to three thousand, added to five hundred, added to nine tens, 
 added to seven ; and we are so familiar with this method of 
 enumeration that we are apt to forget how artificial it is, and 
 how much we are indebted to the ingenious men of Arabia, or 
 elsewhere in the East, who invented the system. 
 
 The efficiency of this system, and the validity of the rules 
 which arise under it, depend not on any peculiar virtue in the 
 number ten, but simply on the mode of combining the figures 
 to express values. As above said, there was no reason for 
 selecting the number ten more weighty than the authority of 
 the ten of fingers and the ten of toes ; and any other number 
 might have been taken as the basis of the system equally well. 
 For example, we might use eight as the basis of the system, and 
 assign to the digits, arranged as before, values increasing by 
 powers of eight. We should then discard two of our figures, 8 
 and 9, and omit the corresponding names in counting, thus : — 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 Sec. 
 
 Decimals 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 10 
 
 11 
 
 12 
 
 Sec. 
 
 Octuples. 
 
 We might use the same names and figures for all the numbers 
 up to seven ; but we should be obliged to give a wholly different 
 significance to all compound numbers, while assigning to them 
 
98 OCTUPLE SYSTEM. 
 
 two of our digits, and establish our system of arith- 
 metic on an octonary instead of a decimal basis. 
 
 the names we use for the corresponding; compounds (not the 
 corresponding numbers) on the decimal system. Thus ten 
 (10) in the octuples would have the same value as eight (8) in 
 the decimals ; twenty in the octuples the same value as sixteen 
 in the decimals; one hundred in the octuples the same value 
 as eight times eight, or sixty-four, in the decimals, &c. How 
 completely the introduction of a new system would destroy our 
 association with numbers will be evident from the following 
 multiplication table on the octonary system : — 
 
 MULTIPLICATION TABLE. 
 Octonary System. 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 10 
 
 2 
 
 4 
 
 6 
 
 10 
 
 12 
 
 14 
 
 16 
 
 20 
 
 3 
 
 6 
 
 ii 
 
 14 
 
 17 
 
 22 
 
 25 
 
 30 
 
 4 
 
 10 
 
 14 
 
 20 
 
 24 
 
 30 
 
 34 
 
 40 
 
 5 
 
 12 
 
 17 
 
 24 
 
 3i 
 
 36 
 
 43 
 
 50 
 
 6 
 
 14 
 
 22 
 
 30 
 
 36 
 
 44 
 
 5- 
 
 60 
 
 7 
 
 16 
 
 25 
 
 34 
 
 43 
 
 5 2 
 
 61 
 
 70 
 
 10 
 
 20 
 
 3° 
 
 40 
 
 50 
 
 60 
 
 70 
 
 100 
 
 Obviously, it would be impracticable for us who learned to 
 cipher by the decimal system to change our habits of thought, 
 and acquire a second nature under which twice four would sug- 
 gest involuntarily ten, or four times six thirty, with correspond- 
 ing changes in all processes of simple addition and subtraction. 
 Think of the confusion of bank clerks and other lightning cal- 
 culators if six and seven became fifteen, or three from ten five ! 
 Nevertheless, apart from the force of habit the transition would 
 be a very simple one. The fundamental operations of arithme- 
 tic would not be essentially altered thereby ; and to those edu- 
 cated in it the octuple system would appear as natural as the 
 one we so familiarly employ. A single example will make this 
 point clear. 
 
 Let us assume that we have two numbers 234 and 345 writ- 
 ten on the octuple system to multiply together. We proceed 
 
OCTUPLE SYSTEM. 99 
 
 Although this digression has no immediate bearing 
 on our subject, it shows how conventional our system 
 
 exactly as we should on the decimal system only using the new 
 multiplication table, and making the corresponding additions, 
 thus : — 
 
 234 156 
 
 345 _ 229 
 
 1414 1404 
 
 1 160 312 
 
 l-\ 312 
 
 i°5> 6x 4 35-7-4 
 
 We read the two numbers two hundred and thirty four and 
 three hundred and forty-five, and the product one hundred and 
 five thousand six hundred and fourteen just as we should on 
 the decimal system. But on the octuple system the same num- 
 bers express wholly different values. These values, however, 
 can be readily reduced to the decimal basis, if we remember 
 that on this basis the value of the successive places in the oc- 
 tuple enumeration increase by powers of eight. Hence, the 
 value of 234 in octuples would be found in decimals thus : — 
 
 Octuples. 
 
 
 
 
 D 
 
 ecimals. 
 
 200 = 
 
 2 
 
 X 8 
 
 X 8 
 
 =3 
 
 I2S 
 
 30 = 
 
 3 
 
 X 8 
 
 
 = 
 
 24 
 
 4 = 
 
 
 
 
 = 
 
 4 
 
 2 34 156 
 
 So also the value of 345 in octuples would be found : — 
 
 300 = 3 X 8 X 8 = 192 
 
 40 = 4 X 8 =32 
 
 5 = =_5 
 
 345 229 
 
 The product of 156 by 229 decimals has already been found 
 above to be 35,724, and we can now prove that the ordinary rule 
 of multiplication applies to octuples as well as to decimals, by 
 
100 MATHEMATICS AIDS DEDUCTION. 
 
 of arithmetic really is, and what an efficient aid it is 
 in our mental processes. 
 
 As we go forward in the study of mathematical 
 subjects the more necessary does the aid furnished 
 by mathematical symbols become, and we very soon 
 reach a point where even the most gifted intellect 
 cannot dispense with their arbitrary forms. They 
 enable the mind to combine conditions and see rela- 
 tions which otherwise it could not possibly grasp. 
 Hence it is that every great improvement in math- 
 ematical methods has always been followed by a 
 great extension in our knowledge of material re- 
 lations; new deductions from old principles have 
 become possible, and thus knowledge has been broad- 
 ened and the way made ready for larger inductions. 
 
 showing that this product is the exact equivalent of the octuple 
 product 105,614 also before obtained by following the regular 
 arithmetical rule, of course using the octuple multiplication 
 table and the corresponding octuple additions as before de- 
 scribed. 
 
 Octuples. Decimals. 
 
 100000 = iX8X8XSX8X8 = 32768 
 
 5000 = 5x8x8x8 = 2560 
 
 600 = 6X8X8 =384 
 
 10 = 1 X 8 =8 
 
 4 = =4 
 
 105,614= =35.724 
 
 The same point could be illustrated by other arithmetical oper- 
 ations ; but the above example is sufficient to enforce the state- 
 ment made above ; and it must now be evident that the great 
 merit of what we wrongly call "decimal" arithmetic depends on 
 the system of Arabic numerals, and not at all on the number of 
 digits it employs. 
 
SCIENCE OF QUANTITATIVE RELATIONS. IOI 
 
 It was so when the Cartesian geometry gave a knowl- 
 edge of the properties and relations of curved lines 
 and surfaces before unsuspected. It was so when 
 Newton and Leibnitz invented general methods of 
 dealing with the so-called infinitesimal quantities of 
 algebra and geometry, which led at once to the suc- 
 cessful solution of the problem of central forces. It 
 was so again, after Newton's death, when the conse- 
 quences of the law of gravitation were developed in 
 proportion as the resources of the new calculus were 
 enlarged by the great mathematicians of the eight- 
 eenth century, — such men as Euler, Laplace, and 
 Lagrange. 
 
 Mathematics, however, is a great deal more than 
 an instrument for deductive reasoning. Just as logic 
 has loftier aims than merely to dissect arguments and 
 to lay bare their syllogistic forms and becomes in its 
 larger expressions the science of thought, so math- 
 ematics is the science of quantitative relations wholly 
 independent of their material expressions; and the 
 so-called multiple algebra of our own day has been 
 developed far beyond our positive knowledge of ma- 
 terial relations, and it is at this moment waiting for 
 some higher induction or broader generalization to 
 open new worlds to conquer. Indeed, so transcen- 
 dental are the abstractions involved that few educated 
 men, not mathematical specialists, are able to follow 
 them; although in some curious works of fiction at- 
 tempts have been made to show the possibilities of 
 conceiving of extension in more than three dimen- 
 sions. In less abstract relations, on the other hand, 
 mathematical analysis has not yet satisfied the de- 
 
102 SYMBOLICAL LANGUAGE OF CHEMISTRY. 
 
 mands of existing physical problems ; and more 
 satisfactory and exhaustive methods of solving equa- 
 tions of higher degrees would enable the physicists 
 to broaden their deductions in many directions. 
 
 To a limited extent the symbolical language of 
 chemistry may be used like mathematical formulae, 
 and has a similar value in facilitating deduction. 
 But its terms have a far more restricted meaning, 
 and are therefore less general ; and moreover, the 
 chemical formulae, which we call reactions, only ex- 
 press the very simple relations of combination and 
 decomposition. 
 
 As the use of the symbolical notation of chemistry 
 is for the most part restricted to chemical students, a 
 brief description of the system may be necessary in 
 order to render the statement just made generally 
 intelligible. 
 
 We recognize at the present time about seventy 
 well-defined elementary substances, and in addition 
 to these there are several others whose authenticity 
 has not yet been satisfactorily established. From 
 these elementary substances all known materials can 
 be formed ; and into these the various substances 
 which exist on the surface of the earth can be re- 
 solved by processes with which all chemists are 
 familiar. Moreover, when these elementary sub- 
 stances unite to form compound bodies, the combi- 
 nation takes place in certain definite proportions by 
 weight. 
 
 The modern theory of chemistry, which we shall 
 have occasion to discuss more at length hereafter, 
 assumes that each elementary substance is an aggre- 
 
THE "ATOMS'" OF CHEMISTRY. 103 
 
 gate of exceedingly minute particles, called atoms, 
 which are indivisible by any chemical means now 
 known, and which are alike in every respect. Thus 
 a mass of the elementary substance sulphur is an 
 aggregate of atoms, all of which are exactly alike, 
 but wholly different from the atoms of any other 
 elementary substance. These atoms, being definite 
 masses of matter, must have definite weights ; all the 
 atoms of sulphur, for example, absolutely the same 
 weight, but a very different weight from that of the 
 atoms of iron or from that of the atoms of oxygen, 
 two other elementary substances. 
 
 If the mental concepts we call atoms are really 
 entities, they must have a degree of minuteness 
 which vastly surpasses our powers of observation. 
 Granting the existence of such minute particles, there 
 are known facts of physics and chemistry which com- 
 pel us to assign limits to their magnitude on either 
 side ; and Sir William Thomson has estimated that if 
 a drop of water were magnified to the size of the 
 world, the atoms of which it consists would certainly 
 appear larger than boys' marbles, and with equal 
 certainty smaller than cricket balls. The almost in- 
 conceivable minuteness of the assumed atoms is, 
 however, in itself no weighty argument against the 
 atomic theory ; for in a universe in which we recog- 
 nize the infinitely great, why should we not expect to 
 find also the infinitely small? If there be a macro- 
 cosmos around us, why should not there be also a 
 microcosmos? And if creation be not limited by the 
 powers of the telescope, why should it be limited by 
 the powers of the microscope? The proof of the 
 
104 ATOMS AND MOLECULES. 
 
 existence of atoms is solely a question of sufficient 
 evidence, and may be reached in time ; but as yet 
 they can only be regarded as postulates of our scien- 
 tific systems, the ultimate material units out of which 
 the mind seeks to construct masses of matter. To 
 our crude conceptions they are the bricks, as it were, 
 of the material universe. 
 
 According to the atomic theory, when elementary 
 substances combine, the union takes place between 
 the atoms; and the groups of atoms thus formed are 
 called molecules, and only like molecules aggregate 
 together to form masses of different substances. Thus 
 when oxygen gas unites with hydrogen gas to form 
 water, one atom of oxygen unites with two atoms 
 of hydrogen to form one molecule of water; and a 
 drop of water is simply an aggregate of molecules 
 of this kind, so numerous that they can only be 
 counted when all the sands of the earth have been 
 numbered ; but all these molecules are exactly alike, 
 each consisting of two atoms of hydrogen and one 
 of oxygen. 
 
 If the atoms have definite weights, such a combi- 
 nation as we have just described must take place in 
 the definite proportions of these weights. As the 
 combined weight of two atoms of hydrogen is to the 
 weight of one atom of oxygen, so and in just this 
 proportion by weight must hydrogen gas combine 
 with oxygen gas to form water ; and the same gen- 
 eral principle must hold in the combination of all 
 other atoms, and in the production of all other com- 
 pounds. Hence, according to the atomic theory, the 
 combining proportions of chemistry are simply the 
 
COMBINING PROPORTIONS OF CHEMISTRY. 105 
 
 relative weights of the atoms. Obviously, then, we 
 can infer from the combining weights of the ele- 
 mentary substances, which can be accurately ob- 
 served, the relative weights of those abstract units 
 we call atoms; and in our modern chemistry the 
 combining proportions of the elementary substances 
 are called, under certain limitations, the atomic 
 weights of the chemical elements. The smallest of 
 these weights is the weight of the atom of hydrogen, 
 which we take as the unit of the system. The atom 
 of oxygen weighs sixteen of these units; the atom of 
 sulphur thirty-two ; and the atom of iron fifty-six of 
 the same units. In general, the atomic weight of an 
 elementary substance indicates how many times the 
 atoms of which it consists weigh more than the 
 atoms of hydrogen. 
 
 And here it must not be forgotten that although 
 the atoms are wholly theoretical concepts, these rela- 
 tive weights are definite facts of observation ; and, as 
 already stated, are deduced directly from the definite 
 proportions in which the elementary substances are 
 known to combine. These values are independent 
 of the atomic theory ; but we can most easily make 
 the facts intelligible in the terms of this theory, for 
 the theory gives to the phenomena a concrete expres- 
 sion, and thus enables us to relate them to the rest of 
 our knowledge. 
 
 If we know the number of atoms of each kind 
 which enter into the composition of a molecule of 
 any substance, we can find the weight of that mole- 
 cule by simply adding the weights of the several 
 atoms. Thus a molecule of water, consisting of one 
 
106 EXAMPLES OF CHEMICAL SYMBOLS. 
 
 atom of oxygen and two atoms of hydrogen, must 
 weigh 16 + 2 = 18. 
 
 Now it will be obvious that if we arbitrarily select 
 a symbol to stand for an atom of each element, we 
 can readily represent the molecule of any substance 
 whose composition is known, by simply writing to- 
 gether these symbols like letters in a word. 
 
 In our text-books of chemistry you will find a table 
 giving, after the name of each elementary substance, 
 the symbol which has been selected to represent its 
 atom, and also the value of the atomic weight. Thus 
 the atom of hydrogen is represented by H ; and its 
 atomic weight, as we have said, is the unit of the sys- 
 tem. The atom of oxygen is represented by O, and 
 its atomic weight is 16. The atom of carbon is rep- 
 resented by C, and its atomic weight is 12. The atom 
 of nitrogen is represented by N, and its atomic weight 
 is 14. 
 
 We represent, then, a molecule of water by H 2 0, 
 thus indicating that this molecule consists of two 
 atoms of hydrogen and one atom of oxygen, as just 
 stated ; also indicating, further, that the weight of 
 this molecule is 16 -f- 2 = 18 ; and still further show- 
 ing that in water oxygen and hydrogen are united in 
 the proportions by weight of 16: 2. 
 
 In like manner we represent a molecule of carbonic 
 acid gas by C0. 2 , a symbol which indicates, first, that 
 the molecule of carbonic acid gas consists of one 
 atom of carbon and two atoms of oxygen ; secondly, 
 that the weight of the molecule is 12 -f- 2 X 16 =44; 
 thirdly, that in carbonic acid gas carbon and oxy- 
 gen are combined in the proportion of 12 : 32. 
 
CHEMICAL REACTIONS. 107 
 
 We call these groups the symbols of the different 
 substances. 
 
 Every chemical process may be regarded as the 
 breaking up of the molecules of one or more sub- 
 stances into atoms, and the regrouping of these same 
 atoms to form the molecules of new substances. In 
 chemistry we technically call such processes reac- 
 tions; the substances which concur in the process 
 we call the factors, and the substances formed by the 
 process we call the products of the reaction. As no 
 atom can be destroyed, every atom coming from the 
 factors, and none others, must be found among the 
 products; and hence the total weight of the products 
 must be exactly equal to the total weights of the 
 factors. Therefore we can represent such processes 
 by equations, writing on the left-hand side of the 
 equation mark the symbols of the several factors 
 connected by the sign of addition, and on the right- 
 hand side the symbols of the products in a similar 
 way. A few illustrations will make clear the meaning 
 of such expressions. 
 
 Grape Sugar. Alcohol. Carbonic Acid Gas. 
 
 C 6 H 12 6 = 2C 2 H 6 + 2C0 2 
 
 This reaction expresses the well-known fact that in 
 fermentation grape sugar breaks up into alcohol and 
 carbonic acid gas. The one factor is the symbol of 
 a molecule of grape sugar. This single molecule 
 yields two molecules of alcohol and two molecules of 
 carbonic acid gas, or four molecules in all. Notice 
 how we write two molecules of alcohol, using figures 
 to express several molecules, like coefficients in alge- 
 
108 CHEMICAL REACTIONS. 
 
 bra; and notice also that there are as many atoms of 
 each elementary substance in the one molecule of the 
 single factor grape sugar, as in the two molecules of 
 alcohol and the two molecules of carbonic acid result- 
 ing from the decomposition. 
 
 Nitrate of Ammonia. Nitrous Oxide. Water. 
 
 N 2 H 4 8 = N 2 + 2H,0 
 
 (2Xi4)+4+(3Xi6) = 8o (2Xi4)+i6 = 44 2(2+16) =36 
 
 The second reaction expresses that the salt nitrate 
 of ammonia yields, when heated, nitrous oxide gas 
 and water. Here, as before, the atoms of the one 
 molecule which is the factor of the reaction break 
 apart, and rearrange themselves to form one molecule 
 of nitrous oxide gas and two molecules of water. 
 Since the symbols stand for definite relative weights, 
 the reaction informs us further that from eighty parts 
 of the salt we obtain forty-four parts of nitrous oxide 
 gas and thirty-six parts of water. 
 
 Dilute Sulphuric Acid. Zinc. Zinc Sulphate. Hydrogen Gas. 
 
 (H 2 S0 4 + Aq.) + Zn = (ZnS0 4 + Aq.) + H 2 
 
 The third reaction represents the process by which 
 hydrogen gas is made from dilute sulphuric acid and 
 zinc. It gives in general, in regard to this chemical 
 change, information similar to that we have learned 
 from the two preceding examples. Moreover, it 
 shows that the change consists essentially in this : 
 that the atom of zinc replaces the two atoms of 
 hydrogen in the acid ; when these hydrogen atoms 
 pair together to form molecules of hydrogen gas. 
 It will be unnecessary for my present purpose to 
 
VALUE OF CHEMICAL SYMBOLS. IO9 
 
 dwell on other and more abstruse points of significa- 
 tion which this symbolical language conveys. It is 
 sufficient if I have made clear the more obvious 
 meaning and prepared the way for a further inference, 
 which can easily be drawn from the principles of the 
 system which have been thus far explained. 
 
 It can now easily be seen that this symbolical 
 notation gives an admirable basis for classifying 
 chemical compounds; and further that it brings out 
 analogies and enables us to draw inferences which 
 otherwise would never have been suggested. If one 
 substance undergoes certain changes it is probable 
 that an allied substance, having a similar constitution 
 and therefore represented by a like symbol, would 
 partake of similar changes ; and the analogy sug- 
 gested by the symbols often leads us to test our in- 
 ferences by experiment, and thus we are constantly 
 led to the discovery of new truths. 
 
 There is, however, a most important difference 
 between a chemical reaction and a mathematical 
 equation, which should be always kept in mind. 
 From a mathematical equation any result that can 
 be deduced by the principles of algebra must in some 
 sense be true. But in chemistry we have discovered 
 no such far-reaching principles; and our chemical 
 reactions merely express the known facts in regard 
 to each process they represent ; and we can draw no 
 certain conclusions one step removed from the facts 
 which the symbols signify. The notation is fruitful 
 in suggestions, nothing more. 
 
 When the laws which govern the grouping of 
 chemical atoms have been formulated we may hope 
 
IIO THE SYLLOGISM. 
 
 for an all-embracing calculus of chemical operations ; 
 but from want of precise and exhaustive knowledge 
 of these principles, all attempts in this direction have 
 been thus far failures. Nevertheless, the conven- 
 tional symbolism of chemistry has been of the very 
 greatest value in suggesting possible relations and 
 pointing out fruitful lines of investigation. 
 
 Of most subjects the fundamental conceptions and 
 processes do not admit of more precise designations 
 than ordinary language affords, and the arguments 
 which arise are discussed under the conditions which 
 the science of logic seeks to analyze and classify in 
 the various forms of the syllogism. We may often 
 thus arrive at as complete certainty as by mathemat- 
 ics, — although it is important not to wander far from 
 the boundaries of known truth, and to verify every 
 step of our progress by an appeal to observation or 
 experiment. But whether the conclusions be reached 
 by mathematical, chemical, or syllogistic reasoning, 
 the method is essentially deductive; and implicitly 
 the results were involved in the premises with which 
 we started. 
 
 No fountain can rise higher than its source, and 
 no process of reasoning, however conducted, can 
 mount above the general principles or fundamental 
 truths on which the reasoning rests. These are the 
 essential conditions or premises of the mental pro- 
 cess, and necessarily imply previous generalizations 
 which were acquired by induction. While, however, 
 we admit that the results of deductive reasoning, 
 however conducted, were implicitly contained in the 
 data of the calculation or the premises of the argu- 
 
DEDUCTIONS MUST BE TESTED. Ill 
 
 ment, we must not infer that knowledge cannot be 
 increased by such means. 
 
 Before an Infinite Intelligence all the relations of 
 truth must be open ; but how far this is from being 
 possible to a finite intelligence we have all sadly ex- 
 perienced ; and to man the deductions of science are 
 as much new truths as if they were direct revelations ; 
 and the greatest discoveries have been made by 
 strictly deductive processes of investigation. Indeed, 
 as I have already said, knowledge is enlarged chiefly 
 by deductive reasoning, verified by observation and 
 experiment. Nevertheless, as has also been said, de- 
 duction implies previous induction, and differs from 
 induction, not in that its results are less real or less 
 novel to men, but in that they are of a different 
 order, and sustain different relations. What this dif- 
 ference is, we shall still further endeavor to illustrate. 
 If a general principle, like the law of gravitation, 
 is absolutely true, everything that can be deduced 
 from it by legitimate processes must be equally true. 
 But in science we have constantly to deal with induc- 
 tions which are only partial truths. Under such 
 circumstances, entire reliance cannot be placed on 
 the deductions ; and hence the importance of testing 
 each step of the argument by observation or experi- 
 ment. In proportion as the predictions are verified, 
 the greater confidence do we place in the universality 
 of the principle on which the deductions were based. 
 
 Excepting, however, the axioms of mathematics, 
 the laws of motion, and a few similar principles, there 
 are no generalizations which can be regarded as ab- 
 solutely beyond question ; and it is conceivable that 
 
112 CAUSES OF UNCERTAINTY. 
 
 conditions may arise under which even the law of 
 gravitation will fail. It is, therefore, only in pure 
 mathematics and in simple physical problems, that 
 we can feel safe in our deductions without submitting 
 them to the test of experience. 
 
 Uncertainty in regard to the results of deduction 
 may arise, not only from failure in the particular case 
 of the general principle on which dependence has 
 been placed, but also from inherent difficulties in the 
 deductive process. In algebra, mathematicians have 
 not been able, except in special cases, to obtain com- 
 plete solutions of equations of higher degrees than 
 the fourth, and the ingenious methods which they 
 employ with problems which give equations of a 
 higher order, yield at best only partial solutions. So 
 also in chemistry, the methods of analysis give only 
 approximate results, and for this reason the conclu- 
 sions based upon them are more or less indefinite. 
 Hence arises the importance, in all physical science, 
 of the discussion of what is called the probable error 
 of observations, and also of the personal error of the 
 observer ; and in this connection a few words on the 
 errors which are inherent in all scientific methods, 
 and necessarily affect their results, will not be out of 
 place. 
 
 Even among scholars, who while familiar with the 
 general results of science are strangers to its methods, 
 there is a common misapprehension in regard to the 
 certainty of scientific conclusions, or in regard to the. 
 infallibility of scientific evidence. Physical science 
 is constantly spoken of as exact, and as yielding pos- 
 itive proofs, in contrast with the moral sciences, whose 
 
MEASUREMENTS NEVER ABSOLUTELY EXACT. 113 
 
 results are less definite and more questionable. As 
 regards physical science all this is to a great extent 
 true, — since a large mass of the facts which have been 
 established in relation to the phenomena of nature 
 are as certain as the axioms of geometry ; but no re- 
 sults of measurements are absolutely exact, and the 
 accredited values have every possible degree of pre- 
 cision. There are very few magnitudes of nature 
 which are known accurately within a thousandth part 
 of their value; and our knowledge of such funda- 
 mental quantities is often in error to the extent of 
 one-tenth. To scientific experts this is a familiar 
 fact, and in all their deductions they take into ac- 
 count the resulting uncertainty; but literary men are 
 apt to reason as if they thought everything accepted 
 in science was known with equal exactness, and are 
 led into error by this unconscious assumption. A 
 very small experience with the reality would dispel 
 this illusion ; and hence the importance to all scholars 
 of that limited experience with scientific methods 
 which will give an understanding, not only of the true 
 relations of scientific facts, but also of the limitations 
 of scientific results. 
 
 The unavoidable errors of scientific methods may 
 be classed under two heads; and we must distin- 
 guish the constant errors, which are inherent in the 
 process employed or in the observer himself, from 
 the accidental errors, which are determined solely by 
 chance. The last are as likely to be in one direction 
 as another; while the first, under the same conditions, 
 are always in the same direction. 
 
 Of the two classes of errors the accidental errors 
 
114 ACCIDENTAL ERRORS. 
 
 are by far the less important, and to a great extent 
 can be eliminated by multiplying observations. The 
 arithmetical mean of several observations is always 
 far more trustworthy than any single observation, 
 and the theory of probabilities gives us in such 
 cases a method of estimating, not only the probable 
 error of any one observation of the set, but also the 
 probable error of the mathematical mean. The dis- 
 cussion of probable errors is one of the most impor- 
 tant applications of mathematics, which is generally 
 known as the " Method of Least Squares;" and it is 
 certainly a most remarkable result of science that what 
 would seem to be at first sight so wholly accidental 
 and utterly lawless, should be found to be regulated 
 by definite principles and become a matter of exact 
 computation. Yet this is strictly true. If, for ex- 
 ample, we first eliminate from a series of observa- 
 tions of some definite quantity, as for example the 
 value of an angle, all evident mistakes and known 
 causes of error, there will still remain differences in 
 the results, which will appear the more pronounced 
 in proportion as we seek to secure greater accuracy 
 in our measurements. Such differences we call acci- 
 dental errors, and they are due to numberless causes 
 which we cannot estimate, depending upon the im- 
 perfection of our instruments, or of our senses, or on 
 the varying conditions under which all experiments 
 must be made. Now if we take the arithmetical 
 mean of all the numbers obtained as the most prob- 
 able value, and call the difference between the mean 
 value and each separate value the error of that 
 observation, it will always appear, — 
 
" PROBABLE ERROR." 115 
 
 First, that small errors are more frequent than 
 large ones. 
 
 Secondly, that positive and negative errors are 
 equally frequent. 
 
 Thirdly, that very large errors do not occur. 
 
 Observations. 
 
 V. 
 
 v\ 
 
 / // 
 
 
 
 Il6 43 44.45 
 
 5.19 
 
 26.94 
 
 SO-55 
 
 — 0.91 
 
 0.83 
 
 50.95 
 
 — 1.31 
 
 1.72 
 
 48.90 
 
 0.74 
 
 0.55 
 
 49-20 
 
 0.44 
 
 0.19 
 
 48.85 
 
 0.79 
 
 0.63 
 
 47.40 
 
 2.24 
 
 5.02 
 
 47-75 
 
 1.89 
 
 3-57 
 
 51.05 
 
 — 1.41 
 
 2.00 
 
 47.85 
 
 1.79 
 
 3.20 
 
 50.60 
 
 — 0.96 
 
 0.92 
 
 48.45 
 
 1. 19 
 
 1.42 
 
 51-75 
 
 — 2. 1 I 
 
 4-45 
 
 49.00 
 
 O.64 
 
 0.41 
 
 52-35 
 
 — 2.71 
 
 7-34 
 
 51.05 
 
 — 1. 41 
 
 2.00 
 
 51.70 
 
 — 2.06 
 
 4.24 
 
 49.05 
 
 O.59 
 
 o-35 
 
 50-55 
 
 — O.9I 
 
 0.83 
 
 49.25 
 
 o-39 
 
 0.15 
 
 46.75 
 
 2.89 
 
 8-35 
 
 49.25 
 
 o-39 
 
 0.15 
 
 53-4o 
 
 —3-76 
 
 14.14 
 
 5i-3o 
 
 —1.66 
 
 2.75 
 
 s= 1 1 6° 43' 49".64 
 
 71 = 24 
 
 2 v- = 92.15 
 
 v = 0.6745 l/S = 
 
 i-"35 
 
 r -3S „ 
 
 V 2 4 
 
 On these fundamental principles derived from ex- 
 perience all our reasoning on the subject is based. 
 
Il6 CONSTANT ERROR. 
 
 An examination of tables of observations, such as are 
 given in the Reports of our Coast Survey, may be 
 very instructive as they exhibit in a most remarkable 
 manner the principles we have been endeavoring to 
 illustrate. 
 
 Thus, in a series of twenty-four measurements of 
 an angle of the primary triangulation made at the 
 station Pocasset in Massachusetts, and cited on the 
 previous page, all the above principles are strikingly 
 illustrated ; and it further appears that while the 
 largest difference from the mean value amounts to 
 5". 19, the probable error of a single observation is 
 but i"-3 5, and the probable error of the mean value 
 only o".28. The term " probable error," as thus used, 
 has a conventional meaning, and simply signifies 
 that there is an even chance that the true value is 
 within the limit assigned. 
 
 But while such accidental errors as have been de- 
 scribed are constantly reminding us of the restric- 
 tions of our powers, they are limited in extent, and 
 as also we have seen, can be to a large extent elim- 
 inated. Not so with the constant errors which arise 
 from unknown causes of various kinds, or even from 
 the idiosyncrasies of the observers. These may be 
 very large, are likely to operate only in one direc- 
 tion, and may thus seriously vitiate our results. 
 They are an insidious foe against which all our 
 watchfulness and care cannot protect us, an enemy 
 in the dark, of whose direction and magnitude we 
 can form no estimate. These constant errors are 
 the chief source of difficulty in all experimental 
 investigation ; they have occasioned incalculable loss 
 
CONSTANT ERROR. 117 
 
 of labor; and besides discouraging the investigator, 
 they frequently introduce an element of uncertainty 
 into his results. Years of conscientious and careful 
 investigation have thus been rendered unavailing by 
 an unsuspected error which has vitiated the whole 
 work ; and values which had been regarded as among 
 the best-established data of science have subsequently 
 been found to be erroneous, owing to the discovery of 
 a source of error in the method by which they were 
 determined. A remarkable example from my own 
 experience will illustrate these important points. 
 
 The atomic weights are among the most important 
 constants of science, and. the accurate determination 
 of these numerical values involves analytical work of 
 great refinement and accuracy. In 1856 Schneider, 
 of Berlin, made a determination of the atomic weight 
 of antimony, and obtained the number 120.3. The 
 work was done with all the skill and precision that a 
 master of analytical chemistry could devise, and every 
 known and conceivable cause of error appeared to 
 have been foreseen and allowed for. Eight separate 
 determinations were made, no one of which differed 
 from the extreme value more than 0.23. Neverthe- 
 less, a year later Mr. W. P. Dexter, working with a 
 different method, but with equal refinement, obtained 
 as a mean of ten determinations 122.34, that is, a value 
 two whole units greater than the first, — although here 
 again the results of the several determinations agreed 
 so closely with each other that the maximum differ- 
 ence from the mean value was only 0.14. At very 
 nearly the same time the famous chemist Dumas 
 made at Paris still a third independent determination 
 
Il8 CONSTANT ERROR. 
 
 of the constant under consideration, using a wholly 
 different method from either Schneider or Dexter, 
 and obtained 122.00, — nearly the same value as Dex- 
 ter, and with a similar close agreement between the 
 results of four separate experiments. The deserved 
 reputation of Dumas for accuracy, skill, and judgment 
 gave such authority to his result that it was at once 
 adopted, and remained for twenty years the accepted 
 value of the atomic weight of antimony. 
 
 In 1877 I was myself led to repeat the determina- 
 tion of Schneider, only reversing his processes, and 
 obtained very closely his value of about 120. This 
 led me to repeat the process of Dumas, when I ob- 
 tained a still closer confirmation of the larger number, 
 122. What could be the occasion of this large differ- 
 ence? The discrepancy could not arise from the 
 ordinary errors of analytical work, which in either 
 process was far less than this ; as the close agreement 
 of the separate results obtained by the same process 
 plainly showed. There must be some unknown con- 
 stant error affecting one or both of the results. To 
 confirm this conclusion I made a third determination 
 of the atomic weight, by a process which had never 
 been employed before and which admitted of great 
 accuracy. This gave me with great exactness the 
 first value, 120; and when a fourth determination 
 by still another process also gave the same value, I 
 felt convinced that the higher number, which had 
 been so long accepted, was the one which had been 
 affected by the constant error, but I did not feel sat- 
 isfied until I detected the cause of the error and 
 showed in what it consisted. 
 
COINCIDENCES MAY BE ILLUSORY. IIO, 
 
 This experience is a fair illustration of what is con- 
 stantly met with in scientific investigation, and indi- 
 cates moreover the only general method of ferreting 
 out constant errors. When determinations of a given 
 value made by essentially different methods are ac- 
 cordant, we have a well-grounded confidence in their 
 accuracy; but mere coincidences of numbers obtained 
 in the same way are no proof of truthfulness, for con- 
 stancy of results often arises from constancy of errors. 
 I would that I could convey to you the full force of 
 the impression which is left on the mind after repeated 
 experiences such as I have described. The helpless- 
 ness which one feels while thus working in the dark 
 gives a reality to the sense of the limitations of our 
 knowledge, of which so much is said and so little 
 appreciated. If anything will lead man to hold his 
 knowledge in humility and reverence it is the con- 
 sciousness that results so laboriously obtained may 
 be invalidated by circumstances over which he has 
 no control, and of whose existence he is wholly 
 unaware. 
 
 I would that I could also give an adequate concep- 
 tion of the great amount of conscientious work which 
 is expended on the deductions of science for the sole 
 love of truth. Were it possible, I am sure that your 
 respect for the scientific investigator would be greatly 
 increased and your belief in his sincerity established, 
 however mistaken you may at times deem his opin- 
 ions or his judgment. Of course in the cultivation 
 of science, as in every other pursuit of life there is 
 abundant room for the display of unworthy motives 
 and ignoble passions ; but I venture to assert that 
 9 
 
120 COMPLEXITY OF NATURAL PHENOMENA. 
 
 there is no class of men in the world among whom is 
 found more unselfish devotion and more personal sac- 
 rifice than among the great army of scientific workers. 
 The love of abstract truth may be a much lower 
 motive than the love of man, but it equally calls 
 forth the very noblest qualities of the mind. More- 
 over, in most cases the constancy and courage of the 
 scientific investigator meet with no reward except 
 the satisfaction which unselfish duty conscientiously 
 discharged always brings; and, as Professor Tyndall 
 has said, " There is a morality brought to bear on 
 such matters which in point of severity is probably 
 without a parallel in any other domain of intellectual 
 action." 
 
 The difficulties of scientific deduction are further 
 vastly increased by the circumstance that in the 
 phenomena of nature the effects of various causes are 
 usually so correlated and intertwined that the task of 
 separating them or of determining their precise rela- 
 tions is well-nigh hopeless. Take such an apparently 
 simple phenomenon as the rise of the column of mer- 
 cury in the stem of such a thermometer as is univer- 
 sally used to measure changes of temperature. The 
 height of the mercury column depends on a number 
 of causes which combine to produce the result we 
 observe. Besides slight effects arising from mechani- 
 cal strain or irregularities of the tube, we must distin- 
 guish, first, the expansion of the mercury, of which 
 the rate slowly increases as the temperature rises, 
 and which tends to raise the column ; secondly, the 
 expansion of the glass, which is very irregular and 
 tends to depress the column ; thirdly, certain obscure 
 
ILLUSTRATED BY THE THERMOMETER. 121 
 
 changes in the texture of the glass itself which act 
 slowly, but which on the whole tend slightly to raise 
 the column. It is true that the last two effects are so 
 inconsiderable as compared with the first that they do 
 not seriously interfere with the use of the instrument 
 as a rough measure of temperature in our houses. 
 But when in scientific investigation we seek an exact 
 measure, to the hundredth of a centigrade degree, 
 they interfere most seriously ; so that while small dif- 
 ferences of temperature may be thus closely estimated 
 under restricted conditions, we have no means of meas- 
 uring large changes of temperature with any such 
 approach to exactness ; and beyond a certain limit 
 of accuracy the use of this simple instrument is one 
 of the difficult problems of science. Even in the 
 ordinary use of the thermometer for determining the 
 temperature of the external air, very considerable 
 differences may be caused by radiation, from the 
 ground, from the sky, or from surrounding objects, 
 depending on the exposure of the instrument; and 
 the discrepancies between neighbors on the state of 
 the weather — which are often so amusingly paraded 
 — are simple illustrations of what is very familiar to 
 every scientific observer. 
 
 If, now, instead of using the thermometer as a 
 measure of temperature, we seek to estimate each of 
 the separate effects whose combined action the in- 
 strument registers, we are met at once with almost 
 insuperable difficulties, and the approximate solution 
 of this problem by Regnault was one of the triumphs 
 of experimental science. By an ingenious method of 
 experimenting, first devised by Dulong and Petit, he 
 
122 ILLUSTRATED BY THE BAROMETER. 
 
 succeeded in measuring the absolute expansion of 
 mercury, and when this was known he could estimate 
 the expansion of the bulb and tube of which the 
 thermometer was made. 
 
 As with the thermometer, so again with the barom- 
 eter. The height of the mercury column in the 
 barometer depends not only on the pressure of the 
 air which the instrument is intended to measure, but 
 is also perceptibly influenced by a variety of other 
 causes, such as temperature, the force of gravity, and 
 capillary attraction. For some of these effects we 
 can make accurate corrections, but for others we can- 
 not ; so that the readings of a barometer made with 
 the greatest refinement at Paris, are not strictly com- 
 parable with those of one made with equal care at 
 New York; and the only way in which we could 
 make an exact comparison would be by transport- 
 ing the same instrument to and fro between the two 
 places, as we might a metre measure. 
 
 These are but two examples of a universal experi- 
 ence. All the phenomena which we attempt to 
 observe are obscured by other phenomena with which 
 they are associated, and all the instruments with 
 which we make our measurements are more or less 
 fallible and faulty. Hence the general principles we 
 deduce from our observations partake of the same 
 limitations. This is no hair-splitting metaphysical 
 refinement ; for, with the exception of a few of the 
 great primary principles of nature, like the law of 
 gravitation or the conservation of energy, there is 
 hardly one of the so-called laws of physics or chem- 
 istry which we should implicitly trust in circum- 
 
LIMITATIONS OF HUMAN FACULTIES. 1 23 
 
 stances widely differing from those under which they 
 are established. As a rule, mathematical deductions 
 are based not on actual qualities of bodies, but on 
 ideal relations which have no exact material repre- 
 sentatives. There are no such things as the rigid 
 bars, the simple pendulums, and perfect fluids of our 
 theoretical mechanics. These are as much abstrac- 
 tions as are points, lines, and surfaces ; and in many 
 respects the sciences of mechanics and astronomy are 
 as much products of pure thought as geometry. 
 
 In order to bring the problems suggested by nature 
 within the grasp of his analysis, the mathematician is 
 forced to simplify them by leaving out of considera- 
 tion every accessory circumstance. As the late Stan- 
 ley Jevons has so strikingly said in his " Principles 
 of Science," " The faculties of the human mind, even 
 when aided by the wonderful powers of abbreviation 
 conferred by analytical methods, are utterly unable 
 to cope with the complications of any one real prob- 
 lem." Of course the mathematician endeavors to 
 approach the natural problem as nearly as possible, 
 and in most cases the differences do not alter essen- 
 tially the character of the solution within reasonable 
 limits ; but they do narrow, and often most seriously, 
 the scope of the deductions. 
 
 Many educated men who are familiar with the 
 great definiteness of the elementary mathematics, 
 form an exaggerated conception of the power and 
 infallibility of mathematical analysis ; and from their 
 limited observation infer that mathematics has the 
 power of solving, in a perfect manner, all problems 
 which involve only quantitative relations. And when 
 
124 LIMITATIONS OF MATHEMATICAL ANALYSIS. 
 
 we consider what they have accomplished, the powers 
 of such minds as those of Lagrange and Laplace do 
 appear almost miraculous. But when we compare 
 the simple problems which they have solved with 
 the complicated relations which modern investigation 
 has revealed, even the powers of such masters are 
 seen to be inadequate ; and to follow out the deduc- 
 tions from principles already known, appears to be a 
 hopeless undertaking. 
 
 Jevons, whom we have just quoted, also says 
 that " if a mathematical problem were selected by 
 pure chance out of the whole variety which might be 
 proposed, the probability is infinitely slight that a 
 human mathematician could solve it." Let me cite 
 a familiar instance. 
 
 The undulatory theory of light presents relations 
 peculiarly favorable to mathematical analysis, and 
 from which a great wealth of deductions has been 
 drawn. But the colors of the rainbow, or more gen- 
 erally the whole range of phenomena attending the 
 dispersion of light by refracting media, still remain 
 essentially unexplained ; and the most that Cauchy — 
 perhaps the ablest mathematician of this century — 
 was able to accomplish was to show that under 
 certain assumed circumstances such a result might 
 follow from the undulatory theory, and to make evi- 
 dent that the complete solution of the problem was 
 beyond our present powers of mathematical analysis. 
 
 So also in regard to the finality of mathematical 
 deductions. It is a common remark that figures 
 cannot lie ; but, as many have found to their cost, 
 they may be made to bewilder the ignorant and 
 
LIMITATIONS OF MATHEMATICAL ANALYSIS. 1 25 
 
 cover up a great deal of error. Mathematical results 
 are conclusive only as regards the assumed relations 
 with which the analysis starts ; and these may be so 
 different from the relations of any real problem of 
 nature as to render the conclusions inapplicable in 
 any specific case. 
 
 It should be clearly understood that there is noth- 
 ing mysterious about mathematics ; that even when 
 its processes cannot be followed except by adepts, 
 its premises and conclusions can always be clearly 
 stated. The operations or processes of thought 
 which it combines by means of its admirable sym- 
 bolism, are severally perfectly intelligible ; but in the 
 multiplicity of the possible relations confusion may 
 readily arise, and it requires a keen intellect, with 
 great power of abstraction and concentration, to trace 
 out these relations to their consequences. Without 
 the symbols the task would have been beyond the 
 best human faculties, except in the simplest prob- 
 lems ; and even with all the aids which an ingenious 
 symbolism can give, the power of combination is 
 very limited and wholly inadequate to grasp the 
 complex relations which the real phenomena of 
 nature invariably present. 
 
 In thus dwelling on the limitations of scientific 
 deductions, I am not overlooking its grand results. 
 These last speak for themselves, and are fully appre- 
 ciated and honored. They have become an impor- 
 tant element of our daily life, and have profoundly 
 modified the thought of our time ; and while we are 
 thankful for the acquisitions of the past, we look for 
 still greater rewards in the near future. It is well, 
 
126 RESERVE OF SCIENCE. 
 
 however, at times, instead of looking back at what 
 has been done, to look forward to what remains to 
 be accomplished, and to compare our knowledge, not 
 with what our fathers knew, but with the universe 
 about us. Courage, enterprise, and confidence are 
 great virtues, but so are also modesty, caution, and 
 reservation of judgment. When men venture to 
 frame theories of creation and claim that the existing 
 order might have resulted from the principles of 
 action now known, I am at a loss which most to 
 admire, their unconsciousness or their boldness. My 
 only attempt at refutation would be to ask these 
 would-be world-builders to work themselves for a 
 while in unravelling a web of material conditions in 
 the darkness of the unknown. If they work faith- 
 fully I am sure that in distinguishing the ends of a 
 few threads they will be rewarded for all their pains ; 
 but I am equally confident that at the same time 
 they will gain the conviction that hidden causes, as 
 yet unsuspected, may intervene in the commonest 
 phenomena of nature. Do not think I am a pessi- 
 mist because I feel it my duty to emphasize these 
 well-known facts. In the admirable work of Jevons, 
 to which I have referred, you will find the same gen- 
 eral doctrine still more emphatically stated and more 
 fully illustrated. 
 
THE ATOMIC THEORY. \2J 
 
 LECTURE V. 
 
 EXAMPLES OF SCIENTIFIC INVESTIGATION. 
 
 IN the present lecture I shall ask your attention to 
 two examples of scientific investigation, which 
 will give a better idea than can any general dis- 
 cussion, of the difficulties and uncertainties which 
 perplex the student in almost every attempt to sub- 
 stantiate the deductions from scientific generaliza- 
 tions. I select the first example because it is within 
 my own very recent experience ; and although the 
 history of science may present far more striking 
 illustrations, I can speak of the perplexities incident 
 to this investigation from personal knowledge ; and 
 as the results of the investigation have only recently 
 been published, 1 this fresh example may have the 
 interest of novelty. 
 
 The atomic theory is as old as Greek philosophy, 
 and the best and most original exposition of the 
 theory is still to be found in the famous heroic poem 
 of Lucretius, " De Rerum Natura," which appears to 
 have been written about 58 B. c. The adaptation of 
 the theory to explain the definite combining propor- 
 tions of chemistry was made by John Dalton, of 
 
 1 Published in Proceedings of the American Academy of 
 Arts and Sciences, vol. xxiii. p. 119. 
 
128 prout's hypothesis. 
 
 Manchester, in the early part of the present century, 
 and since then these combining proportions have 
 generally been called atomic weights. 
 
 It was obvious from the first that of all the ele- 
 mentary substances hydrogen gas must have the 
 smallest atomic weight, and it was a natural inference 
 that the atoms of all the elementary substances 
 might be aggregates of this smallest indivisible unit. 
 
 Such a theory was in harmony with the philosoph- 
 ical conception that in the last analysis all materials 
 could be reduced to the same ultimate essence, and 
 that differences of qualities depended on the differ- 
 ent affections of which this primordial material was 
 susceptible. This theory was strongly advocated by 
 Dr. Prout, an eminent physician in London, during 
 the first half of this century, and the author of one 
 of the well-known Bridgewater Treatises ; and is 
 known in science as " Prout's hypothesis." Obvi- 
 ously, if this theory be true it would follow that all 
 the atomic weights must be multiples of the atomic 
 weight of hydrogen ; and if this last, as is usual, be 
 taken as the unit of the system, the values of all 
 other atomic weights must be expressed in whole 
 numbers. Here, then, was an obvious deduction, 
 which, if not substantiated by experiment must be 
 fatal to Prout's hypothesis, an induction on trial. 
 
 At the time when Prout wrote, the accepted values 
 of many of the smaller weights were in accordance 
 with his views ; and the methods of chemical anal- 
 ysis, by which the combining proportions of the 
 elementary substances were determined, were not 
 sufficiently accurate to distinguish, in the case of the 
 
DUMAS'S CONCEPTION. 129 
 
 higher atomic weights, even the difference of a whole 
 unit. As analytical methods were improved, marked 
 discrepancies with the theory appeared; but so 
 strong a hold had the conception taken on the minds 
 of chemical students that these anomalies were over- 
 looked or attributed to errors of observation; and 
 for many years it was customary in works on chem- 
 istry, to give as the values of the atomic weights the 
 nearest whole numbers, instead of the actual mean 
 of the observed values, and the practice is still con- 
 tinued in many works of accepted authority. 
 
 At an early period in the discussion, a marked 
 exception to the theory had appeared in one of 
 the smaller and best known of the atomic weights. 
 The combining proportion of chlorine, which forms 
 with metallic silver one of the best defined chemical 
 compounds, could be determined with great accu- 
 racy; and all the experiments gave a value for its 
 atomic weight closely approximating 35.5. This, 
 and a few other similar facts, led the late Professor 
 Dumas of Paris to entertain the idea that the atomic 
 weights, if not all multiples of the whole hydrogen 
 atom, might be multiples of the half or quarter atom ; 
 or, in other words, that the hydrogen atom might 
 itself be an aggregate of two or more smaller masses, 
 which were the real units of the system ; and he was 
 thus led to undertake the redetermination of a large 
 number of the atomic weights, with the view of test- 
 ing this modification of the original conception. His 
 experiments were conducted with wonderful skill; 
 and many of the new values he obtained for the 
 atomic weights are still universally accepted by 
 
130 INVESTIGATION OF STAS. 
 
 chemists. But the results had little bearing on the 
 question at issue ; for it is obvious that by taking 
 the unit small enough any result could be regarded 
 as an even multiple of this unit within the limit of 
 experimental errors. 
 
 Soon after the publication of Dumas's paper, Profes- 
 sor Stas of Brussels undertook a work of still greater 
 magnitude. Stas had never been a believer in the 
 hypothesis of Prout, and his aim was to push the 
 analytical work to such a degree of refinement as to 
 show conclusively that the results could not possibly 
 be reconciled with any modification of that theory. 
 
 Stas had been an associate of Dumas, and the lat- 
 ter always spoke of his former assistant in terms of 
 the highest admiration, declaring that he was the most 
 accomplished experimentalist he had ever known. 
 Thus Stas brought to the new investigation the 
 highest skill, and, moreover, his position as the di- 
 rector of the Belgian mint gave him command of 
 means and appliances which enabled him to work 
 on far larger quantities of material than any previous 
 experimenter. As the error of an analytical process, 
 other things being equal, is less in proportion to the 
 quantity of material used, the advantage gained from 
 the large scale of his experiments was very great. 
 But at the same time these large amounts of material 
 greatly increased the toil involved ; and the amount 
 of labor which Stas devoted to this investigation was 
 extremely great ; it can be appreciated only by 
 those who are familiar with such processes. In this 
 way however, Stas was able to reduce the merely 
 accidental errors of the processes he employed within 
 
STRIKING FEATURE. 131 
 
 wonderfully narrow limits. He obtained values for 
 several of the most fundamental atomic weights, 
 which, though approaching whole numbers, still dif- 
 fered from a multiple of the hydrogen unit by quan- 
 tities far exceeding the probable error. At first 
 these results were accepted as conclusive, and it 
 seemed as if the hypothesis of Prout had been for- 
 ever consigned to the tomb of unverified theories. 
 
 Still, however, even from Stas's work the remark- 
 able fact appeared that the atomic weights thus de- 
 termined with so great labor and skill, though not 
 exact multiples, approached very nearly to exact 
 multiples of the atomic weight of hydrogen. If the 
 several values were absolutely independent and dis- 
 tributed by chance, the probabilities that they would 
 all so nearly approach whole numbers was exceed- 
 ingly small, and there was not one chance in ten 
 thousand that such a distribution would occur as 
 Stas's results exhibited ; so that on the whole Stas's 
 work seemed to indicate that there might be some 
 truth in the theory after all, if not in the exact form 
 that had been supposed. 
 
 This feature in the distribution of the atomic 
 weights became still more marked as accurate values 
 of the atomic weights of additional elements were 
 obtained. Professor Mallet, of the University of Vir- 
 ginia, was one of the first to call attention to the point 
 just mentioned, in his admirable paper on the atomic 
 weight of Aluminum, which his very accurate and 
 accordant determinations had shown was very closely, 
 if not exactly, a whole number; and Professor F. W. 
 Clarke, of Washington, in his work entitled " A Re- 
 
132 
 
 ATOMIC WEIGHTS. 
 
 calculation of the Atomic Weights," after summing 
 up the results of a careful collation of all the trust- 
 worthy determinations of these constants of nature, 
 writes : " Enough has been said in this brief re- 
 sume to show that none of the seeming exceptions 
 to Prout's law are inexplicable. Some of them in- 
 deed, carefully investigated, support it strongly. In 
 short, admitting half-multiples as legitimate, it is 
 more probable that the few apparent exceptions are 
 due to undetected constant errors than that the great 
 number of close agreements should be merely acci- 
 dental. I began this recalculation of the atomic 
 weights with a strong prejudice against Prout's hy- 
 pothesis, but the facts as they came before me have 
 forced me to give it a very respectful consideration." 
 The following table from the writer's work on " Chem- 
 ical Philosophy," will make clear the point we are 
 discussing: — 
 
 ATOMIC WEIGHTS, MOST ACCURATELY DETERMINED. 
 
 Hydrogen 
 
 1.002 
 
 Chlorine 
 
 3546 
 
 Lithium 
 
 7.01 
 
 Potassium 
 
 39- 14 
 
 Carbon 
 
 12.00 
 
 Calcium 
 
 40.00 
 
 Nitrogen 
 
 14.04 
 
 Bromine 
 
 79-94 
 
 Oxygen 
 
 16.00 
 
 Silver 
 
 107.93 
 
 Aluminum 
 
 27.02 
 
 Antimony 
 
 120.00 
 
 Sodium 
 
 23.05 
 
 Iodine 
 
 126.85 
 
 Magnesium 
 
 24.00 
 
 Barium 
 
 137-14 
 
 Phosphorus 
 
 31-05 
 
 Thallium 
 
 204. 1 1 
 
 Sulphur 
 
 32.07 
 
 Lead 
 
 206.91 
 
 This table includes all the values of atomic weights 
 which up to 1882 could be regarded as known to 
 within 1-1000 of their value; and with one or two 
 notable exceptions, there is no instance in which the 
 
DISTRIBUTION OF VALUES. 1 33 
 
 value differs from a whole number by a quantity 
 greater than the possible error, though not always 
 the "probable error" of the processes employed in 
 their determination. 
 
 Were these numbers wholly independent of each 
 other and distributed by no law, we should expect to 
 find every possible intermediate value; and the fact 
 that they so nearly approach whole numbers cannot 
 fail to produce on the mind the impression that there 
 is some influence which tends to bring about this 
 result. It may be that the discrepancies are due to 
 such unknown constant errors as we have already 
 described, and which, as every experimentalist knows, 
 are always greatly to be feared. Or it may be that 
 there is in nature a tendency to whole multiples, 
 which in many cases is not fully reached. This last 
 view, to be sure, is not compatible with our present 
 conceptions of the atomic theory; but nature is not 
 bound by this theory, nor should be our philosophy. 
 
 The force of the evidence which such a distribution 
 of values as the above table presents was brought 
 home to the writer in his investigation on the atomic 
 weight of antimony referred to in the previous 
 lecture. After eliminating various causes of error, 
 he was enabled to determine with great accuracy 
 the atomic weights of antimony, silver, and bromine, 
 in one and the same series of experiments, and it 
 appeared that this ratio was — 
 
 120.00 : 108.00 : 80.00, 
 with a probable error of less than one in the last 
 decimal place. Here, then, is a ratio of whole num- 
 bers, within the 1-100 of a single unit; and although 
 
134 REMARKABLE RATIO. 
 
 the result may be no more impressive to others than 
 many of the facts exhibited by the table, yet to 
 the experimentalist who after long continued labor 
 reaches such a result as this, the impression is in- 
 evitable that there must be something more than 
 mere chance in such coincidences. 
 
 Since the ratio of the atomic weights of silver and 
 oxygen have been determined with great accuracy, 
 we can extend the above proportion to a fourth 
 term, the atomic weight of oxygen, which appears 
 also as a whole number, with a somewhat larger 
 probable error. Still we have not reached the unit 
 of the system, and when we attempt to extend the 
 ratio to the atomic weight of hydrogen, we find 
 that the most probable value from all experiments 
 hitherto made gives the ratio, not of 16 to I, but of 
 16 to 1.0025. 
 
 If now we wished to refer to the hydrogen unit 
 the atomic weights of antimony, silver, bromine, and 
 oxygen, whose ratios of whole numbers had been 
 determined as above, it was only necessary to divide 
 all the terms of the above proportion by 1.0025, when 
 we obtain the series of values given below the others, 
 and all semblance of conformity to the hypothesis 
 of Prout disappears, although of course the second 
 series of numbers bear the same ratios to each other 
 as the first. 
 
 Antimony. Silver. Bromine. Oxygen. Hydrogen. 
 
 120.00 10S.00 80.00 16.00 1.0025 
 
 119.70 107.73 79-So 15-96 I. 
 
 The numbers in the lower of the two proportions 
 appear as incommensurable as Stas maintained that 
 
QUESTION SUGGESTED. 1 35 
 
 they were ; and the same is true of most of the 
 atomic weights when given, as is usual in recent 
 text-books on chemistry, on the basis of the same 
 hydrogen unit. 
 
 When, as the result of my investigation in the 
 atomic weight of antimony, there were presented to 
 me the ratios of whole numbers, as shown in the 
 first of the above proportions, with the single ex- 
 ception of the atomic weight of hydrogen, the 
 question was at once suggested, Is the ratio of the 
 atomic weight of oxygen and hydrogen in fact that 
 of 16: 1.0025, as the general average of all trust- 
 worthy determinations hitherto made seemed to in- 
 dicate ; or was there a constant error lurking in 
 these results, which caused the very slight variation 
 from the ratio from 16 to 1 required by the theory? 
 I must confess that as I looked at the proportion as 
 drawn out above, the conviction pressed upon me 
 that this variation from the theory must be apparent, 
 and I determined to ferret out the hidden error if 
 possible. 
 
 The problem was easily stated, but as is usual in 
 questioning Nature, her answer was not so easily in- 
 terpreted, and it has required several years of work 
 to reach a definite conclusion. The results were at 
 first baffling, and it was not until grave experimental 
 difficulties had been overcome that definite conclu- 
 sions could be reached ; and these conclusions were 
 quite different from what had been anticipated. It 
 is because this investigation is a good example of 
 the methods of science, and an illustration drawn 
 from personal experience of the general subject we 
 
136 FORMER INVESTIGATIONS. 
 
 are discussing, that I venture to ask your attention 
 to some of its details. 
 
 On studying the methods by which the ratios of 
 the atomic weights of oxygen and hydrogen had 
 been determined, it was evident that they could be 
 divided into two classes : first, the direct methods of 
 determining the ratio, in which the proportions of 
 oxygen and hydrogen uniting to form water were 
 actually weighed ; secondly, the confirmatory methods, 
 to whose results small value could be assigned inde- 
 pendently of the first. Disregarding the last, as yield- 
 ing no conclusive evidence on the question at issue, 
 it appeared that all the trustworthy determinations 
 had been made by essentially the same chemical 
 process. This process consists in burning an unde- 
 termined amount of hydrogen by means of oxide of 
 copper, and weighing the water which results, and 
 further determining the amount of oxygen combined 
 from the loss of weight of the oxide of copper. 
 
 The chemical process is a very simple one. Oxide 
 of copper is a compound solely of copper and 
 oxygen, and when hydrogen gas is passed over the 
 heated oxide it takes up the oxygen to form water, 
 and the copper is left in the metallic state. 
 
 By weighing the glass tube containing the oxide 
 before and after the experiment, we can determine 
 the weight of oxygen which has combined with the 
 hydrogen ; and by collecting the water formed, in 
 appropriate desiccators, which are also "weighed be- 
 fore and after the experiment, we can find the weight 
 of this sole product of the process, with extreme 
 accuracy. 
 
NECESSARY CONDITIONS. 1 37 
 
 By subtracting now the weight of the oxygen 
 found, from the weight of the water found, we have 
 the weight of the hydrogen which has combined with 
 the oxygen in the process ; and the proportion be- 
 tween the weight of the oxygen and the weight of 
 the hydrogen is one half of the atomic ratio we 
 are seeking; because, according to our theories, one 
 atom of oxygen combines with two atoms of hydro- 
 gen to form one molecule of water. 
 
 The proportion by weight in which hydrogen com- 
 bines with oxygen to form water is about that of 1 
 to 8. The atomic ratio about that of 1 to 16. 
 
 Considering now the observed ratio of 1 to 8, it can 
 be seen that the highest accuracy demands that each 
 term of the proportion should be determined to an 
 equal degree of exactness. Thus, if in a given ex- 
 periment we have 8 grams of oxygen uniting with 
 1 gram of hydrogen, it is of no avail to weigh the 
 oxygen to a tenth of a milligram, unless we can 
 weigh the hydrogen to the same proportionate de- 
 gree of accuracy; for an error 9-10 of a milligram in 
 the weight of the water, or of 8-10 of a milligram in 
 the weight of the oxygen, will have no more influence 
 on the resulting ratio we are seeking than an error of 
 1-10 of a milligram in the weight of the hydrogen. 
 Remembering now that 1-10 of a milligram is about 
 the extreme limit of accuracy of our best balances, 
 when loaded with more than a few grams of material, 
 it can easily be seen that there is an obvious source 
 of error in the determination we have described. 
 
 The weights actually observed are, first, that of the 
 water formed, and secondly, that of the oxygen used. 
 
138 SOURCE OF ERROR. 
 
 The weight of »the water can be determined to within 
 a few tenths of a milligram ; that is, with all the 
 accuracy with which our problem requires that the 
 larger term of the proportion 8 to 1 should be 
 known ; and for the moment this weight may be 
 regarded as established. 
 
 It is quite different with the weight of the oxygen ; 
 this last is found by weighing the glass tube contain- 
 ing oxide of copper, before and after the experiment, 
 and between the two weighings the tube is heated to 
 a low red heat for several hours, while a stream of 
 hydrogen gas is passing through it; and there are 
 several causes which might lead to a slight variation 
 in these weights, independently of the loss of oxygen, 
 which has been used up in the process. It is un- 
 necessary to discuss here what these causes are, but 
 their effect would be unimportant if they only led 
 to a small error in the observed weight of the oxygen. 
 Unfortunately, this is not the case; for when, in order 
 to find the weight of the hydrogen, we subtract from 
 the weight of the water, accurately known, the weight 
 of the oxygen — which maybe for the causes referred 
 to, slightly erroneous — the whole error appears in 
 the weight of the hydrogen thus found, and in the 
 opposite direction. If, for example, the weight of 
 the oxygen is too large, the weight of the hydrogen 
 will be too small by exactly the same amount ; and 
 although the error may be an inconsiderable part of 
 the weight of the oxygen, it may be a very appre- 
 ciable quantity in the weight of the hydrogen. 
 
 On the other hand, if a means could be devised for 
 weighing the hydrogen, leaving the oxygen to be 
 
DUMAS'S REMARKS. 1 39 
 
 determined by subtracting this smaller weight from 
 the weight of the water, then a small error in the 
 observed weight of the hydrogen would have no 
 appreciable effect on the weight of the oxygen. 
 
 Professor Dumas, who made by far the most ex- 
 tended series of observations by the old method, 
 fully recognized the source of error to which I have 
 referred, and in his paper on the subject wrote as 
 follows : — 
 
 " Of all analyses which a chemist can undertake, 
 that of water is the one which offers the greatest un- 
 certainty. In fact, one part of hydrogen unites with 
 eight parts of oxygen to form water; and nothing 
 would be more exact than the analysis of water, if 
 we could weigh the hydrogen as well as the water 
 which results from its combustion. 
 
 " But the experiment is not possible under this 
 form. We are obliged to weigh the water formed 
 and the oxygen used to produce it, and to calculate 
 the weight of the hydrogen consumed in the process 
 from the difference of these two weights. Thus an 
 error of 1-900 in the weight of the water, or of 1-800 
 in the weight of the oxygen, affects the weight of the 
 hydrogen by a quantity equal to 1-90 or 1-80 of its 
 value. As these errors are in the same direction 
 they are added to each other, and we shall have an 
 error amounting to 1-40." 
 
 On entering upon the investigation it was evident 
 from the outset that no advantage was to be gained 
 by multiplying determinations by the old methods. 
 The work had repeatedly been done by the best 
 masters of the science, with all the accuracy of which 
 
140 WEIGHING A GAS. 
 
 the method was capable. The only hope of improve- 
 ment lay in finding some method of weighing the 
 hydrogen with sufficient accuracy; and it was essen- 
 tial to determine this weight to within 1-10,000, or 
 at least 1-5000 of its value. 
 
 A gas can only be weighed by enclosing it in a 
 glass globe or some similar receiver, and hydrogen 
 is so exceedingly light that its total weight can only 
 be a very small fraction of the containing vessel ; 
 moreover, as the buoyancy of the air is fourteen and 
 one half times as great as the weight of the hydrogen, 
 the variations in buoyancy caused by changes in at- 
 mospheric conditions have an all-important effect in 
 the apparent weight. The late Professor Regnault, 
 of Paris, devised a very ingenious method of com- 
 pensation which could readily be applied in this case. 
 It consisted in balancing the globe containing the 
 hydrogen, hung to one arm of the balance, by a sec- 
 ond globe of exactly the same volume and made of 
 the same material, hung to the opposite arm, and so 
 arranging the balance-case that both globes should 
 hang in the same enclosure and therefore be equally 
 affected by atmospheric changes. This method I 
 applied in the problem before us, and after a number 
 of trials I found it possible to make the compensation 
 so accurate that the weight of my globe holding 
 five litres of gas did not vary more than 1-10 of a 
 milligram through large changes of temperature and 
 pressure. In order now to weigh the hydrogen with 
 this degree of accuracy, it was only necessary to ex- 
 haust the air from the glass receiver, and after bal- 
 ancing it as described, to fill it with hydrogen, when 
 
METHOD OF BURNING. 141 
 
 the increased weight (only about 4-10 of a gram 
 with my apparatus) was the weight of the hydrogen 
 required. 
 
 In order to burn this hydrogen I used essentially 
 the same apparatus as previous experimenters, pas- 
 sing the gas over heated oxide of copper, collecting 
 the water formed, and determining its weight. Every 
 detail of the apparatus was the result of careful con- 
 sideration, and in many cases was only reached after 
 numerous experiments. 
 
 There were many difficulties to be overcome, but 
 the result left nothing to be desired, and thus far the 
 method was as perfect as the conditions required. 
 
 Everything now turned upon introducing into our 
 globe absolutely pure hydrogen, and here the great- 
 est difficulties were met. 
 
 Fortunately at this point I secured for my work 
 the assistance of a young chemist, Mr. T. W. Rich- 
 ards, my former pupil and present assistant, of whose 
 experimental skill I can speak as warmly as did Du- 
 mas of Stas. 
 
 A part of the difficulties of filling the globe with 
 pure hydrogen were wholly mechanical, and the only 
 ones which it is important I should mention here are 
 the difficulties we met in procuring absolutely pure 
 gas. 
 
 It will be obvious that an exceedingly small amount 
 of impurity would be fatal to the accuracy of my 
 method. If the hydrogen we introduced into our 
 globe carried with it only 1-10,000 part of its volume 
 of atmospheric air, — an impurity which it is exceed- 
 ingly difficult to avoid, on account of the rapid dif- 
 
142 EFFECT OF SLIGHT IMPURITY. 
 
 fusion of hydrogen and the pervasiveness of our 
 atmosphere, — this impurity would increase the appar- 
 ent weight of the hydrogen by i-io of a per cent, and 
 cause an error that would be fatal to the degree of 
 accuracy we were seeking. 
 
 In our earlier determinations we drew the hydrogen 
 gas from a large self-acting generator charged with 
 sulphuric acid and zinc. We used in the generator 
 pure, but not the purest materials, which it would 
 not have been practicable to procure on the scale on 
 which we then expected to work ; and we trusted to 
 a complicated system of purifiers to remove the 
 traces of sulphurous oxide or other chance impuri- 
 ties which the gas might contain. With hydrogen 
 thus prepared and purified, we made a large number 
 of determinations. We give only a few of these in 
 the table below, but those here exhibited are a fair 
 specimen of the whole. In each case the numbers 
 express the atomic weight of oxygen referred to 
 hydrogen as unity ; and it will be noticed that these 
 values are not only far below the average of the 
 previous results, 15.96, but also that they differ 
 widely from each other. 
 
 PRELIMINARY RESULTS. 
 
 15-793 !5- 8 5° I5-835 
 
 15.790 15.937 I 5-82o 
 
 It was now obvious that the varying values must 
 result from impurities in the hydrogen, and as we 
 knew that our purifiers did their work efficiently, we 
 were persuaded that the impurity must be the nitro- 
 gen of the atmosphere which entered our apparatus 
 
FIRST SERIES OF RESULTS. 143 
 
 by diffusion at its many joints. We sought to stop 
 such leaks by every means possible, and we thus suc- 
 ceeded in obtaining better and better' results, but 
 there was still far too great irregularity to make the 
 determinations of any value, and we were finally 
 forced to reduce the scale of our experiments. 
 
 We then constructed an apparatus in which hydro- 
 gen was prepared on a smaller scale from chemically 
 pure zinc and hydrochloric acid. The extent of the 
 purifiers was greatly reduced; and the number of 
 joints reduced to only two or three, and these were 
 all carefully sealed with impervious cement. With 
 this apparatus we made the first five determinations 
 given in the table on page 148. In this table we 
 give, in the first column, the weight of the hydrogen 
 burnt; in the second column, the weight of water 
 obtained ; in the third column, the atomic weight of 
 oxygen deduced from these weights after making 
 allowance for the buoyancy of the air; and in the 
 last column, the difference between each atomic 
 weight and the average of the five- 
 It will be seen that we had now reached a very 
 different result. All the values are closely concord- 
 ant, the maximum difference from the average cor- 
 responding to less than 1-10 of a milligram of the 
 hydrogen weighed; and also this mean value very 
 closely agrees with 15.96, the average deduced from 
 previous results. 
 
 Indeed, the agreement was as close as we could 
 possibly expect. If there was an error it could not 
 arise from any fluctuating cause, like the diffusion of 
 air which we had previously encountered ; it must 
 
144 SECOND AND THIRD SERIES OF RESULT& 
 
 be some constant error depending on the process. 
 Moreover, we felt equally sure that the error, if any, 
 could not arise from our method of weighing the 
 hydrogen, for our result was essentially the same as 
 that obtained by the older process, in which the oxy- 
 gen, and not the hydrogen, was weighed. Still, to 
 trace out any error, if existing, we next sought to 
 vary the process of preparing the hydrogen, and con- 
 structed an apparatus with equal care in which hydro- 
 gen was evolved by electrolysis, that is, by the action 
 of a current of electricity on a mixture of water and 
 hydrochloric acid. With the gas procured from the 
 new apparatus, we made five additional determina- 
 tions, which follow the first five in the table just re- 
 ferred to. By inspecting the column of differences, 
 it will be seen that the concordance in this second 
 set is even greater than in the first. Apparently, then, 
 we had reached a maximum which we could not 
 exceed by varying the process ; but that there might 
 be no question on this point, we set up an apparatus 
 still simpler than the last two, by which hydrogen 
 gas was prepared from the metal aluminum, and a 
 solution of caustic potash ; and with hydrogen thus 
 obtained, we made still five other determinations, 
 whose results are given below in the same table. 
 Here again, the average given is essentially identical 
 with the averages of the other two series. 
 
 The evidence now seemed to be conclusive; the 
 average of these fifteen experiments must be the true 
 value of the atomic weight of oxygen, within a very 
 small limit of probable error. The process had been 
 varied in every conceivable way, and with the same 
 
CONSTANT ERROR DISCOVERED. 145 
 
 identical result. Nevertheless, these results were 
 affected by an important constant error, which, al- 
 though so obvious when pointed out, had been over- 
 looked in spite of all our care. The publication 
 above referred to was already in print when our 
 attention was called to the point by Lord Rayleigh, 
 who had been working on a similar problem. 
 
 In adopting the method of Regnault for weighing 
 the hydrogen gas subsequently burnt, we had as- 
 sumed with this eminent physicist that the volume 
 of the globe remained invariable after the air had 
 been exhausted, when of course the pressure of the 
 air on the exterior surface was no longer balanced 
 by the tension of the gas within. As Regnault had 
 himself experimented on the compressibility of glass, 
 and as the least change in the volume of the ten 
 litre globe which he used must have most seriously 
 affected the values he obtained for the densities of 
 the aeriform substances on which he experimented, 
 — namely, air, oxygen, nitrogen, hydrogen, and car- 
 bonic acid, values which have since been regarded as 
 among the most accurate constants of science, — it 
 seemed safe to assume with him that the effect of the 
 atmospheric pressure on the globe when exhausted 
 was insensible. And it should be remembered that 
 the investigator must always build on previous work, 
 and that there could be no progress if he felt obliged 
 to verify all the data which he necessarily employs. 
 He must accept data which are regarded as well- 
 established, and in selecting these data he is neces- 
 sarily guided by authority. There could be no 
 better authority than Regnault on the point in ques- 
 
I46 AFFECTS PREVIOUS RESULTS. 
 
 tion ; his results have been hitherto accepted without 
 question, and a vast amount of experimental work 
 has been based upon them. 
 
 Nevertheless, the globe which Regnault used in 
 his determinations of gas densities, when exhausted, 
 must have been sensibly compressed by the atmos- 
 pheric pressure ; and must, therefore, have appeared 
 to weigh more than when full of gas, in consequence 
 of the diminished displacement, and hence the less- 
 ened buoyancy of the atmosphere. This increase of 
 weight must have been about 1.29 milligrams for 
 every cubic centimeter by which the volume of the 
 globe was compressed ; and the observed weights 
 of this globe-full of the different gases on which 
 Regnault experimented must, therefore, have been 
 too small by the same quantity. 
 
 Unless the globe which Regnault used has been 
 preserved it is not now possible to correct his re- 
 sults ; since the amount of compression of a glass 
 vessel under a constant pressure depends on condi- 
 tions which vary widely and must be separately 
 determined for each vessel. Fortunately, in our 
 work the same glass globe had been used from the 
 first, and there was no difficulty in determining the 
 exact amount by which our results had been influ- 
 enced by the effect under discussion. For this pur- 
 pose it was only necessary to weigh the globe under 
 water, first when exhausted, and afterwards when 
 full of air. Under these circumstances, if there was 
 any change of volume, the difference of buoyancy 
 would become very marked, and could be accurately 
 estimated. 
 
CORRECTION FOUND. 1 47 
 
 A description of the details of these additional 
 experiments would be out of place here. It is suffi- 
 cient to say that the shrinkage of the glass balloon 
 we used, when exhausted, amounted to nearly two 
 cubic centimeters, or about 0.0004 of its exterior 
 volume; that in each of our determinations the true 
 weight of the hydrogen gas burnt was nearly two 
 milligrams greater than the apparent weight; and 
 that after making correction for this altered weight 
 the atomic weight of oxygen deduced from our ex- 
 periments is 15.869, instead of 15-953 as before given. 
 
 After such a catalogue of difficulties encountered, 
 and errors avoided, it may well be asked, How can 
 we be sure that there may not be still other causes 
 of constant error invalidating our results? Obvi- 
 ously we cannot be sure. All we can do is to work 
 earnestly and conscientiously for the truth, and leave 
 the future to revise our results and correct our mis- 
 takes. In this way the truth will be finally reached, 
 although the progress may be slow and halting, and 
 our individual labor may appear to have been lost. 
 
 But although the exact value of the atomic weight 
 of oxygen may hereafter be found to differ more or 
 less from the number we have finally reached, the 
 general result of our work has been to invalidate 
 the hypothesis of Prout. This theory appears to 
 fail at the most critical juncture. Is there then no 
 significance in the analogies we have pointed out? 
 Has the close approximation of the ratios of so 
 many of the atomic weights to a proportion between 
 whole numbers no meaning? I feel persuaded that 
 there is a significance in the analogies, and a mean- 
 
I48 TABLE OF RESULTS. 
 
 ing in the coincidences; but it is not a significance 
 or meaning that we can as yet interpret, and we mu&t 
 be content to wait for more knowledge and larger 
 views. 
 
 ATOMIC WEIGHT OF OXYGEN. 
 
 First Scries. 
 
 Weight of Hydrogen. Weight of Water. Atomic Weight of Oxygen. 
 
 0.4233 3.804S 15 977 
 
 0.4136 3-7094 15-937 
 
 0.4213 3.7834 15.960 
 
 0.4163 3-7345 I5-94I 
 
 0.4131 37085 15-954 
 
 0.4112 
 0.4089 
 0.4261 
 0.4197 
 0.4144 
 
 0.42205 
 0.4284 
 0.4205 
 0.43205 
 
 0-4I53 
 0.4167 
 
 15.952 ±0.0035 
 
 Total Average 15. 953 4- 0.0017'. 
 
 After correcting for shrinkage of balloon under the atmos- 
 pheric pressure, — 
 
 Final result . . . 15.869 ± 0.0017. 
 
 
 15.954 4^ 0048 
 
 Second Series. 
 
 
 36930 
 
 15.962 
 
 3.6709 
 
 15-955 
 
 3-8253 
 
 15-955 
 
 3-7651 
 
 15.942 
 
 3-7I97 
 
 15-953 
 
 
 15.953 i 0.0022 
 
 Third Series. 
 
 
 3-7865 
 
 •5-943 
 
 38436 
 
 15.944 
 
 3-777^ 
 
 15.967 
 
 3.8748 
 
 15-937 
 
 3.7281 
 
 15-954 
 
 3-7435 
 
 15.967 
 
DEDUCTIONS FROM THE LAW OF GRAVITATION. 1 49 
 
 The history of physical astronomy since the publi- 
 cation of the " Principia " furnishes abundant illustra- 
 tions of the various features of scientific deduction on 
 which we have dwelt in this lecture. There has been 
 a continuous development of the deductions from the 
 law of gravitation, and in this work the mathematical 
 genius of two centuries has found abundant employ- 
 ment. The law of gravitation is one of the few 
 fundamental principles of nature of which we feel 
 confident that we have found the exact expression. 
 Most of the laws of physical science are only laws of 
 approximation ; that is, laws with which the phe- 
 nomena of nature closely agree, but which exhibit 
 certain discrepancies that lead us to believe that with 
 larger knowledge we may reach more accurate repre- 
 sentations of the truth. But the law of gravitation 
 appears to be exact, and we have every reason to 
 believe that in the progress of science it will remain 
 essentially unaltered. It is, moreover, a very simple 
 relation. In consequence of the mode of action 
 which we call gravity, and which is as mysterious an 
 agent now as when first recognized, a pull is exerted 
 between any two masses of matter in the universe, or 
 the parts of any two masses, which is proportional 
 directly to the products of the two masses, and in- 
 directly to the square of their distance apart, — as 
 may be expressed by the very simple algebraic 
 formula: 
 
 F MM' 
 
 r — £>2 
 
 Unlike any other physical forces with which we are 
 familiar, this attraction is not influenced by the na- 
 
150 PROBLEM OF THE THREE BODIES. 
 
 ture of the material of the masses, by the nature of 
 the medium interposed, by the proximity of other 
 masses, or by any other conditions, except solely the 
 quantity of material in the masses and the distance 
 between them. Newton himself made these points 
 the subject of an experimental investigation, and his 
 results have been confirmed by other astronomers, 
 who, like Gauss, have been ready enough to question 
 the finality of the law ; and it is only after repeated 
 doubts have been resolved in its favor that we have 
 settled into the belief that it is precisely correct. 
 Still, simple as the law is, to trace its action between 
 the heavenly bodies becomes at once a problem of 
 great difficulty. 
 
 So long as astronomers limited themselves to the 
 question of central forces and considered only the 
 action of the sun on the individual planets, the prob- 
 lem was comparatively simple, and admitted of the ele- 
 gant solution which Newton gave in the " Principia; " 
 but when the universality of gravity came to be recog- 
 nized, and it became a question of the mutual action 
 and reaction of all the bodies in the universe, not only 
 of the sun on the planets but of all the planets on each 
 other, the problem assumed a complication with which 
 no human power could grapple, and whose complete 
 solution was impossible. But setting aside for the 
 time the more general problem in which many of the 
 forces acting were so slight that they could be over- 
 looked, there was in the fore-front of astronomy the 
 case of the moon, acted on strongly by both the 
 earth and the sun ; and thus arose the famous prob- 
 lem of the three bodies, which alone has exhausted 
 
PLANETARY PERTURBATIONS. 151 
 
 the powers of the mathematicians from Newton's 
 time to our own. When only three bodies simultan- 
 eously attract each other the complication of effects 
 is so great that only approximate calculations are 
 possible, and the complete solution of this compara- 
 tively simple astronomical problem has yet to be 
 given. Newton himself grappled with this subject, 
 and so far succeeded as to give a tolerably accurate 
 representation of the moon's motions ; and the only 
 open bitterness shown during his life appears to have 
 been displayed towards his contemporary Flamstead, 
 the first Astronomer Royal, who showed unwilling- 
 ness to furnish him with the observations he needed 
 to compare with his theory. 
 
 The consideration of the mutual attractions of the 
 planets and the sun brings us to the more complex 
 problem of planetary perturbations. The complete 
 solution of this problem even in its simplest form is 
 hopeless, and the principle on which the calculation 
 of planetary perturbations proceeds is to reject every 
 effect which does not lead to a quantity appreciable 
 in observation. The quantities thus rejected are 
 indefinitely more numerous and complex than the 
 few larger terms which are retained ; and in combin- 
 ing these last, numerous assumptions have to be 
 made in order to simplify the problem. The solution 
 reached therefore is merely partial, and the results 
 approximate ; but by such tentative methods great 
 perfection has been reached in the theory of the 
 planetary orbits. 
 
 One of the greatest triumphs of astronomical de- 
 duction, and yet one of the most striking illustrations 
 11 
 
152 PERTURBATIONS OF URANUS. 
 
 of the incompleteness of its methods, was the dis- 
 covery of the planet Neptune. For many years the 
 observations of the planet Uranus, discovered by the 
 elder Herschel in 1781, had differed markedly from 
 the theory of its orbit, even after making every allow- 
 ance for the perturbations caused by its nearest 
 associates, Saturn and Jupiter ; and what was more 
 note-worthy, the error had gone on increasing rapidly 
 from year to year. That this effect might be due to 
 the disturbing influence of an unknown outer mem- 
 ber of the solar system was a reasonable supposi- 
 tion; and if so, the theory of astronomy ought to 
 be able to predict the elements of the orbit, and, 
 therefore, to point out at any moment the position of 
 the disturbing body. Here, however, as in other 
 problems involving the mutual action of several 
 bodies, a complete solution was impossible, and the 
 tentative methods of calculation were long and te- 
 dious; so that astronomers were slow to undertake 
 the work. But in 1843 the investigation was be- 
 gun by Adams at Cambridge, England, and also, at 
 about the same time, by Leverrier at Paris, and the 
 issue is well known. 
 
 Leverrier communicated his result to the astrono- 
 mer Galle, by a letter received at Berlin September 
 23, 1846; and the same evening the planet was 
 found, nearly in the place pointed out. By a for- 
 tunate coincidence, a map of that portion of the 
 heavens — one of the sheets of Bremiker's Berlin star 
 map, then recently published — facilitated the search; 
 and Galle quickly found a star of the eighth magni- 
 tude, not on the map, which the observations of the 
 
DISCOVERY OF NEPTUNE. 1 53 
 
 next two days showed must be the object sought. 
 A year previously, however, Adams had communi- 
 cated to Professor Challis of the Cambridge Observa- 
 tory, the results of his independent calculation, which 
 subsequently proved to correspond closely with those 
 of Leverrier; but although search had been made, 
 and, as afterwards appeared, the planet had been 
 seen, it had not been recognized from want of such 
 a map as the Berlin astronomer possessed. 
 
 Thus two separate mathematicians, without concert 
 with each other, reached the same solution of this 
 difficult problem, and their prediction appeared to be 
 precisely verified. Could there be a more striking 
 confirmation of theory, a greater achievement of 
 human intellect? And yet in its greatest triumph 
 mathematical analysis displayed its weakness. 
 
 On March 16, 1847, within six months of the dis- 
 covery of the new planet, Professor Benjamin Peirce 
 stated to the American Academy of Arts and Sci- 
 ences, in words which I quote from their Proceed- 
 ings, " The planet Neptune is not the planet to 
 which geometrical analysis has directed the tele- 
 scope." This declaration, first received with distrust, 
 proved to be fully justified. The planet of the theory 
 had a mean distance from the sun of from 35 to 37.9 
 times that of the earth, with a corresponding period 
 of revolution of from 207 to 233 years. The actual 
 Neptune has a mean distance of only 30, with a 
 period of about 168 years. At the time of the dis- 
 covery, the planet of the theory and the actual 
 Neptune had approximately the same apparent posi- 
 tion, or, as astronomers say, were in conjunction. 
 
154 HAPPY ACCIDENT. 
 
 But this was a " happy accident," and to this chance 
 the discovery of the actual planet must be ascribed. 
 
 As Professor Peirce clearly showed at the time, 
 this singular result depended on the approximate 
 and tentative character of the method of calculation 
 necessarily employed. Had the conditions been ex- 
 actly known, and had the mathematical analysis been 
 exhaustive, the actual planet which caused the per- 
 turbations would doubtless have been at once pointed 
 out; but several approximate solutions of the prob- 
 lem were possible. Of these the theoretical planet 
 was one, the actual planet was a second, and still 
 others might be distinguished. 
 
 The problem could not be approached without 
 making an assumption in regard to the solar dis- 
 tance, and as both mathematicians were led, by the 
 so-called law of Bode, to make the same assumption, 
 they came to the same approximate result. Unfortu- 
 nately, the law assumed to regulate the relative dis- 
 tances of the planets from the sun conspicuously 
 failed in the case of Neptune, and we have heard but 
 little of it since. According to this law, the solar 
 distance of Neptune should have been about 39.6 
 times the earth's distance. Leverrier tried successive 
 assumptions, beginning with 39.1, and finding that 
 with a diminishing value the conditions of the prob- 
 lem were at first better satisfied, while afterwards the 
 discrepancies increased, he concluded that the value 
 must be within the limits stated above. Adams 
 followed in part the same course, although his cal- 
 culations were less full. The planet found had a 
 distance of 30 only, and if the calculations had been 
 
METHOD OF CALCULATION. 155 
 
 extended to this limit, another solution of the prob- 
 lem would have appeared which proved to be the 
 true one. But the second solution was not suspected ; 
 because at an assumed distance of 35.3 there was a 
 singular point which introduced peculiar disturbances. 
 In a word, the theoretical planet was an approximate 
 solution of the problem for the field of research cov- 
 ered by the analysis ; while the real planet was out- 
 side of this field, and separated from it by a barrier 
 which the partial analysis could not overstep. 
 
 You cannot find in the whole history of science a 
 more striking illustration than this, both of the power 
 and of the limitations of deductive thought. The dis- 
 covery of a new planet appeals strongly to the imagi- 
 nation of men ; and the story of the mathematician 
 who from his study directed the astronomer where to 
 find a predicted member of the solar system, is con- 
 stantly told as an evidence of intellectual power, — less 
 frequently as a signal instance of mental limitations 
 and human fallibility; and yet the last is the more 
 impressive lesson. Here, however, as so often in 
 human affairs, weakness was made strength. Through 
 striving, the planet was discovered and the boundaries 
 of knowledge were extended. 
 
 Obviously there was a large element of chance, or 
 — as I prefer to call it — Providence, in the discovery 
 of Neptune ; and such chances have been repeatedly 
 the turning-points in the history of science. The 
 accidental breaking of a crystal of Iceland spar re- 
 vealed to Hawy the structure of crystalline bodies. 
 A chance reflection of light from the windows of the 
 Luxembourg Palace in Paris disclosed to Malus the 
 
156 RESULTS OF CHANCE. 
 
 laws of polarization. The twitching of the legs of a 
 frog first made known to Galvani the existence of low 
 tension electricity. The swing of a compass-needle 
 on his lecture-table opened to Oersted the phenomena 
 of electro-magnetism, and was the simple beginning 
 from which have come all the wonderful applications 
 of electrical currents. In the remark that Lagrange 
 is said to have made of Newton, that " such accidents 
 happen only to those who deserve them," there is a 
 deeper philosophy than was probably intended. It 
 must be remembered that to a higher intelligence 
 there can be no such thing as accident; and that 
 " the fortuitous concourse of atoms," like any other 
 event, would be seen to have its antecedents and 
 causes if our imperfect perceptions could take cog- 
 nizance of their existence. Moreover, even on our 
 plane, numbers would fail to convey a conception of 
 the utter hopelessness of the chance, on the doctrine 
 of probabilities, that the right accident would happen 
 to the right man at the right time. 
 
 On the other hand, such experience as I have 
 narrated should show us that close coincidences of 
 approximate results are in themselves no sure test of 
 truthfulness, and carry with them but little weight. 
 Men of science are familiar with this principle, and 
 almost every investigator could enforce it by numer- 
 ous examples. But on most men such coincidences 
 make an extraordinary impression ; and many of the 
 delusions of society, including the astrology of the 
 past and the pseudo-spiritualism of the present, find 
 their chief support in the apparent coincidences which 
 a wide latitude of variation permits. 
 
COINCIDENCES OFTEN ILLUSORY. 1 57 
 
 Lastly, such experience should teach us how unsafe 
 it is to rely implicitly on popular statements of scien- 
 tific deductions. An impression widely prevails that 
 however important a knowledge of the general results 
 of science may be, it is not necessary that the literary 
 man or the general scholar should acquaint himself 
 with scientific methods. But it is obvious, from what 
 has been said, that no accurate knowledge of the facts 
 of nature is possible without a knowledge of the 
 methods by which the facts have been established. 
 The phenomena of nature are so complex, and the 
 simplest effects so modified by concurring agencies, 
 that they cannot be fully comprehended unless 
 studied in their natural relations. The phenomena 
 described in text-books are often not realities of 
 nature, but ideal relations which are as much abstrac- 
 tions as the conceptions of geometry. As systems 
 of science such books have their value; but their 
 necessarily general statements are not often a sound 
 basis for theological arguments. We cannot safely 
 reason from the facts of nature until we know them 
 with all their limitations ; and if I have enabled you 
 to realize this truth, my chief object in this lecture 
 has been gained. 
 
158 INDUCTION AND DEDUCTION CONTRASTED. 
 
 LECTURE VI. 
 
 LAWS OF NATURE. 
 
 TN the previous lectures we have endeavored to 
 ■*■ make clear the distinction between induction and 
 deduction in scientific investigation. Induction is the 
 discernment, recognition, and verification of- a general 
 principle of nature previously unknown. The dis- 
 cernment may be more or less accurate, the recogni- 
 tion more or less satisfactory, the verification more 
 or less complete ; but the process is essentially an 
 intuitive act of the mind working upon previous 
 knowledge or experience, and familiar acquaintance 
 with natural phenomena. Hence, under favorable 
 conditions, it is more or less spontaneous, and cannot 
 be regulated by methods or directed by rules. It is, 
 in a word, the product of genius. 
 
 Deduction is the evolution by logical processes, 
 mathematical or otherwise, of the consequences, in- 
 ferences, or implications which a general principle 
 includes or suggests. It may be more or less direct, 
 more or less difficult, more or less exhaustive ; but in 
 any case the results were implicitly involved in the 
 premises established or assumed. It is a creature of 
 methods, a slave to rules, and deals with syllogisms, 
 equations, observations, experiments, and measure- 
 
OPINION OF JEVONS. 1 59 
 
 ments of every kind. It is the task of the many, the 
 work of the great army of scientific laborers. 
 
 Induction raises the level of human knowledge; 
 deduction expands that knowledge. Induction opens 
 new fields of investigation ; deduction explores these 
 fields. Induction discloses hidden treasures ; deduc- 
 tion appropriates and uses them. Induction soars; 
 deduction creeps. Induction aspires ; deduction con- 
 templates. Induction is imaginative; deduction is 
 realistic. Induction is theoretical; deduction is prac- 
 tical. Induction is bold and confident; deduction is 
 cautious and sceptical. 
 
 I am well aware that the position I have taken 
 is not wholly in harmony with the mechanical view 
 of induction which the authority of Bacon has so 
 strongly impressed on English thought; but I still 
 feel confident that I am in sympathy with the great 
 body of scholars who are practically familiar with 
 scientific methods. 
 
 Professor Jevons, who as a logician classified in- 
 duction as inverse deduction, thus wrote in regard to 
 the nature of the process itself: "All induction is 
 but the inverse application of deduction ; and it is by 
 the inexplicable mental action of a gifted mind that a 
 multitude of heterogeneous facts are caused to range 
 themselves in luminous order as the results of some 
 uniformly acting law." This is the best authority I 
 could quote ; and I now pass on to consider certain 
 distinctions among the results of induction, which 
 I hope will serve to make our conceptions of the 
 subject still clearer. 
 
 Of all the results of induction there are none so 
 
160 LAWS OF NATURE DEFINED. 
 
 familiar or so striking as the laws of nature ; and of 
 the aspects of the material universe there is none 
 which is more appalling to the religious mind than 
 the reign of law. Law and Providence seem incom- 
 patible and mutually exclusive. " The wind bloweth 
 where it listeth," without regard to the tempest-tossed 
 ship freighted with the hopes of nations. The laws 
 of motion do not spare precious lives when a broken 
 rail turns the rushing train from its appointed track. 
 The law of gravitation made no discrimination among 
 the victims on whom the Tower of Siloam fell ; and 
 so fire and flood, pestilence and famine, tornado and 
 earthquake, have ever involved the good and the bad 
 alike in common ruin. 
 
 Law is inexorable, cruel, pitiless ; and no wonder 
 that as thus viewed the conception of law should be 
 a hindrance to faith. But this view of nature is a 
 misconception which arises from a superficial knowl- 
 edge of the facts ; and the law of the text-books, or 
 of the popular imagination, is for the most part an 
 ideal phantom. Correct views on this subject are of 
 such supreme importance in natural theology that I 
 propose to devote two lectures to a discussion of some 
 of the distinctive features and manifold variations 
 which the so-called laws of nature present. 
 
 A law of nature is simply a declaration or state- 
 ment of a certain order, sequence, or relation, observed 
 among material phenomena. Jevons says, " The laws 
 of nature are simply general propositions concerning 
 the correlation of properties which have been found 
 to hold true of bodies hitherto observed." And 
 again: "A law of nature is not a uniformity which 
 
LAWS OF NATURE NOT EFFICIENT CAUSES. l6l 
 
 must be obeyed by all objects; but merely a uni- 
 formity which is, as a matter of fact, obeyed by those 
 objects which have come beneath our observation." 
 Thus the first law of motion declares that any mass 
 of matter continues in its state of rest or motion until 
 acted on by some force external to itself. The law 
 of Mariotte affirms that the volume of a given mass 
 of gas is inversely proportional to its tension. The 
 law of gravitation states that any two masses of matter 
 attract each other with a force directly proportional 
 to the product of the two masses, and inversely pro- 
 portional to the square of the distance between them ; 
 and so we might multiply examples. Notice, noth- 
 ing is affirmed in regard to the mode of action in 
 either case. The phenomena observed may be the effect 
 of a single cause, or the resultant of several causes ; 
 but the law takes no cognizance of any such feature. 
 It only recognizes the order, sequence, or relations 
 it describes. This is a most important point, to which 
 I would ask your special attention. 
 
 The laws of nature are simply statements of ob- 
 served relations. They are not efficient causes or 
 modes of action of any kind; and whatever features 
 with such an aspect may be superimposed upon the 
 formal propositions in the description or by the im- 
 agination, is something superadded to their only real 
 sanction as laws of nature. 
 
 There may seem to be in the statement of the law 
 of gravitation, as usually given and as enunciated 
 above, something conflicting with the positive position 
 here laid down. When it is said that one mass of 
 matter attracts another, or, as Newton himself enun- 
 
1 62 " HYPOTHESES NON FINGO." 
 
 ciatcd the law, every particle of matter in the universe 
 attracts every other particle, it might appear as if a 
 mode of action was declared in the proposition ; and 
 I have no doubt that the law is so understood by 
 nine out of ten of the students who repeat the state- 
 ment. But Newton intended to convey no such con- 
 ception ; and no such conception was received by the 
 scholars for whom he wrote. 
 
 It is true, however, that one mode of explaining 
 the law is to assume that there resides in the ulti- 
 mate particles of matter some unknown virtue which 
 determines the attraction. But this is a pure hypo- 
 thesis, one of those redundancies referred to above, 
 for which the law must not be held accountable. 
 When Newton himself was asked whether he had any 
 conception of this kind he is said to have replied : 
 " Hypotheses non fingo." 
 
 Moreover, the whole tendency of modern science is 
 entirely opposed to any theory which assumes an 
 inherent potency in the particles of matter; and, in 
 the case of gravitation, such an hypothesis, as we 
 shall see in the next lecture, is beset with insuperable 
 difficulties and objections. It would be better if we 
 could enunciate the law without using the word " at- 
 tract; " but this cannot be done without an awkward 
 circumlocution. Of course what is meant is simply 
 that two bodies, if free to move, would act as if they 
 were pulled by a force varying according to the well- 
 known law; and what is true of this proposition is 
 equally true of the statement of every recognized law 
 of nature. All such propositions are intended to 
 declare solely a relation between -phenomena ; and in 
 
DANGER OF MISAPPREHENSION. 1 63 
 
 any case if the language implies more, there is some- 
 thing accessory, which careful criticism will distin- 
 guish and eliminate. 
 
 When such propositions are briefly enunciated in 
 ordinary language there is always danger of misap- 
 prehension and confusion ; and hence one of the 
 objections to unguarded popular statements of scien- 
 tific principles to which I have referred. For instance, 
 from the ordinary statement of the law of inertia — 
 every mass of matter continues in its state of rest or 
 motion until acted on by some force — I know by 
 experience that a large majority of students derive 
 the idea that an original state of motion must have 
 been the effect of some force ; and yet this is pre- 
 cisely the reverse of the impression that the words 
 were intended to convey ; and in general I may say 
 that it is rare that students acquire from text-books 
 on physics correct conceptions of the fundamental 
 principles of mechanics. 
 
 The popular conception which so constantly asso- 
 ciates causation with a law of nature undoubtedly 
 arises from the figurative use of the word law in this 
 connection. Law in human relations implies a law- 
 giver; and therefore we associate with human laws 
 the personal attributes of the law-giver. The laws of 
 the Medes and Persians were inflexible ; the laws of 
 the Romans were equitable; the old laws of England 
 were cruel ; the modern English laws are more mer- 
 ciful, — simply because, each and all, they reflected 
 the character of the men who made and administered 
 them ; but to call the law of gravitation pitiless is 
 like calling the multiplication table inexorable, or a 
 
1 64 EVIL AND LAW. 
 
 prisoner's chains cruel. Of course it will be said such 
 language is figurative; but the difficulty is that the 
 distinction between the figurative and the real is not 
 always kept clear ; and this is not the only case in 
 which mental confusion and logical fallacy have 
 arisen from the use of familiar terms. 
 
 Still, while all must admit that the definition of a 
 law of nature as here given is conformable to the 
 best usage among scientific scholars, it may be said, 
 the awful fact remains that amidst the misfortunes of 
 man, the whole aspect of external nature is hard and 
 pitiless, and fine-drawn distinctions do not relieve 
 the suffering that the relentless march of natural 
 phenomena entails. Certainly not ! We cannot solve 
 the terrible problem which the evil of the world 
 everywhere presents. This is a fact of nature, as well 
 as law. But do not confound it with law. Its sources 
 are far deeper, among those hidden springs of being 
 whence flow also the equally mysterious relations of 
 personality and free will. Do not then by any per- 
 version of thought associate malevolence with the 
 laws of nature. To a finite being, law means reliance, 
 confidence, and repose. It is heaven-born, beneficent 
 order; but it has no potency in itself, and may be 
 used by the powers of evil as well as by the powers 
 of good. 
 
 Another popular misconception of the relations of 
 a law of nature appears in the trite argument so often 
 urged as a disproof of the Christian miracles. It is 
 impossible to conceive, it is said, that a law of nature 
 should be broken. Certainly it is, and so it is im- 
 possible to conceive that the qualities of metallic 
 
CONSTANCY OF LAW. 165 
 
 gold should be changed. Were the properties of 
 gold changed in the least degree the material would 
 be no longer gold ; and so, were the relations predi- 
 cated by the law of gravitation altered, we should at 
 once have a different law. I do not say that either 
 of these changes is possible, much less probable; but 
 I do maintain that they are both conceivable, and 
 not so inconsistent with our actual knowledge of the 
 order of nature as to render the supposition inhe- 
 rently absurd. So far from this, the transmutation of 
 the metals was the favorite problem of the elder 
 chemists ; and it is well known that Sir Isaac New- 
 ton, whose scientific sobriety cannot be questioned, 
 devoted a great deal of time to experiments in this 
 direction; and, although in a somewhat different 
 form, the question has been reopened in our own 
 day. So also, as before said, the most eminent men 
 of science have seriously considered whether the 
 law of gravitation might not be modified under new 
 conditions. 
 
 Could each law be traced to a single definite cause, 
 it is obvious that a change in the law would imply a 
 corresponding change in the cause, and, therefore an 
 alteration of purpose, or method, inconsistent with 
 our philosophy either of an intelligent first cause or 
 even of a self-evolving, self-sustained cosmogony. 
 But these are not the conditions. The laws of nature 
 are relations of phenomena which, in most cases, at 
 least, are obviously resultants of many causes whose 
 action is inextricably commingled ; and it is perfectly 
 possible to conceive of a new element introduced 
 into one of the chains of causation which would 
 
!66 CONSTANCY OF LAW. 
 
 utterly alter the final result. I do not say that this is 
 possible ; but I do say that we have no positive knowl- 
 edge which makes such a contingency impossible. 
 
 Man cannot increase by the smallest fraction either 
 the material or the energy he employs ; but he can 
 introduce conditions into the chain of causation, by 
 which he is able to control and determine events, and 
 even to alter the face of the earth. Why, then, may 
 not new issues appear in nature? Why may not 
 a new force overrule an old one? Why indeed may 
 not unrecognized agencies, which have always existed, 
 and whose effects have been slowly accumulating, at 
 any moment appear as important factors in human 
 affairs and relations? Not only do I see no reason 
 for believing that we possess an exhaustive knowl- 
 edge of nature's powers ; but on the contrary I am 
 persuaded that even in the most familiar fields, there 
 may at any time appear indications of forces hitherto 
 undiscovered, which may be capable of momentous 
 effects. Remember that it is only a century ago 
 that the first indications were noticed of a power 
 which is now one of the chief agencies of our civiliza- 
 tion. And what were these indications? Only the 
 momentary twitching of a frog's legs ! 
 
 Let it be understood that I make no claim to sub- 
 stantiate or explain miracles ; but I do maintain that 
 we cannot disprove Divine interference in the course 
 of nature ; and that the scientific probabilities against 
 such occurrences may be fairly set off against the 
 moral presumptions in their favor. To me it seems 
 to be a question of evidence, upon which our knowl- 
 edge of the laws of nature has no bearing. More- 
 
"SPIRITUAL MANIFESTATIONS." 167 
 
 over, to my mind the marvellous in these events is no 
 weighty evidence against their credibility. What could 
 be more marvellous than many of the revelations of 
 modern science? As I distinctly remember, the re- 
 volving of the vanes of Crooke's radiometer, seemed 
 to me, when I first saw the instrument, as much out 
 of the ordinary course of nature, as would the turning 
 of water into wine. Investigation showed that the 
 motion was the normal result of a force which had 
 always been acting, though unsuspected ; and so at 
 any moment a strange phenomenon may put us in 
 possession of a new force which will overrule all the 
 powers of the world, and make more than the dreams 
 of Aladdin sober realities. Nothing is too marvellous 
 to be believed, provided it is substantiated by satis- 
 factory evidence. 
 
 Why, then, it may be asked, do you not believe in 
 mind-reading, clairvoyance, faith-cure, and other so- 
 called spiritual manifestations, with which the popu- 
 lar mind is from time to time deluded? Simply 
 because they are not attested by satisfactory evidence. 
 It is upon this ground, and not on account of their 
 strangeness or improbability, that we hesitate to ac- 
 cept them. There are doubtless facts, and very in- 
 credible facts, concerning these matters, that are well 
 attested ; and there may be agencies which have 
 never been recognized. But the phenomena claimed 
 to exist are so complex, and so obscured by uncon- 
 scious self-deception, or by actual imposture, that no 
 undoubted truth, or definite relation, has as yet been 
 established. 
 
 Societies have been formed, both in this country 
 
1 68 GLOOMY ASPECT OF NATURE. 
 
 and in England, for the promotion of psychical re- 
 search; but it may be questioned if, in the presence 
 of so many problems of nature which are within our 
 grasp, it is good policy to expend energy on those 
 which, for the time at least, are hopelessly involved ; 
 and also whether it is wise to concentrate public at- 
 tention on abnormal states, or diseased conditions of 
 mind, which will certainly be excited and spread 
 thereby. Nevertheless, if a single clearly new phe- 
 nomenon were elicited by such investigations, who 
 can question that it would be studied with the same 
 zest as was Crooke's radiometer? 
 
 Of course I do not forget the paralyzing impression 
 of desolation and despair which in some moods the 
 uniformity of nature forces on the mind; but this 
 impression, though an unquestionable feature of hu- 
 man experience from the earliest times, has no per- 
 tinency to the laws of nature. This aspect of nature 
 affects most strongly minds of an imaginative temper- 
 ament, and is one which the study of science rather 
 tends to soften and elucidate. It is seen as clearly 
 by the poet as by the philosopher; and it inspires 
 fatalism more often than scepticism. It is a part of 
 the discipline of life, to which all sorts and conditions 
 of men must bow. This aspect of nature has, then, 
 no special relations to our scientific knowledge ; only 
 the facts of science are often perverted to sustain the 
 terribly gloomy philosophy it suggests. Moreover, 
 science has pointed out the one consideration which 
 may solve the mystery. 
 
 The insect's life is often only a summer's day 
 whose sunshine knows no change; and may not the 
 
babbage's calculating engine. 169 
 
 uniformity of nature during human life be like a 
 shifting scene to Him with whom we have to do? 
 Such a doctrine is wholly consistent with our knowl- 
 edge of the laws of nature ; and the point has been 
 so forcibly put by the late Charles Babbage, in the 
 " Ninth Bridgewater Treatise," the most profound of 
 those celebrated works, that I cannot do better than 
 to quote his words. After describing the calculating 
 machine, which is so inseparably associated with his 
 name, and showing that such an engine might work 
 invariably by one law of action, during any finite 
 number of steps however great, and yet at a prede- 
 termined point introduce a break in the series, — for 
 instance, after counting up the natural number to a 
 term expressed by a hundred million digits, — he 
 writes : " If every letter now before the reader's eye 
 were changed into a figure, and if all the figures con- 
 tained in a thousand such volumes were arranged 
 in order, the whole together would yet fall far 
 short of the vast induction the observer would have 
 had in favor of the truth of the law of natural num- 
 bers ; yet shall the engine, true to the prediction of 
 its director, after the lapse of myriads of ages, fulfil 
 its task and give that one, the first and only excep- 
 tion, to that time-sanctioned law." What would 
 have been the chances in favor of the perfect contin- 
 uity of the series immediately prior to this break? 
 Certainly, we may add, as great as are the chances 
 that the sun will rise to-morrow. 
 
 Now this same machine, as Mr. Babbage also 
 showed, may be so constructed and set as to change 
 its law after an appointed number of terms, and then 
 
170 babbage's calculating engine. 
 
 proceed to follow a new law as invariably as before. 
 Thus, after giving the natural numbers for a certain 
 period, it might suddenly begin to give square or 
 cube numbers ; and it is possible to conceive of a 
 machine by which such transitions might be indefi- 
 nitely repeated. 
 
 If such things are possible in human mechanism, 
 why not in the scheme of nature? That in the 
 short history of science we have not observed such 
 changes is no proof that they may not take place. 
 If they do come to pass we should expect from all 
 analogies that they would come with extreme slow- 
 ness, according to our measures of time, and without 
 observation. And certainly during the geological 
 ages changes have come to pass for which we can 
 give otherwise no clear account. 
 
 Of course such considerations as Babbage has 
 so eloquently urged are no arguments, but they do 
 help the imagination ; and this is a question in which 
 the imagination has raised all the difficulty, and is 
 therefore chiefly to be addressed. 
 
 We have tacitly assumed thus far that the laws of 
 nature are all equally definite and equally exact; but 
 this is very far from being true. In most cases, at 
 least, the phenomena correlated under a law admit 
 of a more or less wide variation ; and the proposi- 
 tion which we call a law is an ideal rather than an 
 actual relation, — an abstraction, rather than an entity. 
 This is the next point to which I wish to ask your 
 attention ; and its bearing on the previous consider- 
 ations is obvious. For if it shall appear that the laws 
 of nature vary with different relations, and are not 
 
DEFINITE LAWS. \Ji 
 
 the hard and fast rules which have been assumed; 
 that they are modes of thought, and not modes of 
 action ; then all that has been said in regard to the 
 independence of causation, and the possibility of 
 interference, will be seen to have still greater force 
 than at first appeared. 
 
 Very few of the recognized laws of nature are ab- 
 solutely definite ; and of these few, with the exception 
 possibly of the law of gravitation, the invariability 
 must be assumed ; for it cannot be proved, at least 
 absolutely. In the present state of knowledge we 
 should class as among these definite laws, the law of 
 conservation of mass, the law of conservation of 
 energy, the laws of motion, and the law of gravita- 
 tion. Now, although we may have no question that 
 all these laws are absolutely fixed, and can never be 
 expected in the least degree to alter in their mani- 
 festation, yet there is not one of them which is sus- 
 ceptible of experimental proof, except, to a limited 
 extent, the law of gravitation. 
 
 Take, for example, the first law of motion, the law 
 of inertia, as it is also called, and which we have 
 before more than once enunciated. We cannot 
 demonstrate experimentally that a body will con- 
 tinue in a state of motion until acted on by some 
 external force. On the surface of the earth, even 
 under the most favorable conditions, all motion is 
 soon arrested by friction, or by some other mode of 
 impact ; and the most we can do is to show that in 
 proportion as such resistances are removed, the 
 longer the motion continues, — a form of inference 
 which has been called " the principle of successive 
 
172 LAW OF INERTIA. 
 
 approach," but which is obviously no proof. Could 
 the law of inertia be verified experimentally, perpet- 
 ual motion would be possible; but even with all 
 our experimental skill we have not made the most 
 distant approach to such a condition. 
 
 It is a mistake of ignorance to infer that perpetual 
 motion means unlimited work; and yet it is this very 
 erroneous inference which alone gives a popular in- 
 terest to the question. Work done by a moving 
 body necessarily involves loss of motion; and the 
 effects of friction are merely examples of this general 
 principle. Perpetual motion is theoretically possible, 
 but work without the loss of motion, or the expendi- 
 ture of energy in some form, is inconceivable ; and 
 the assumption implies a confusion of mechanical 
 conceptions. It is unnecessary for our purpose to 
 dwell on this point, and we allude to it only because 
 it serves indirectly to illustrate the character of the 
 law under consideration. Nor need we do more than 
 refer to the grand displays of perpetual motion re- 
 vealed to us by astronomy, which seem at first sight 
 to be most conspicuous illustrations of the principle. 
 But the law is here so overlaid and obscured that 
 observations on the motions of the planets cannot 
 be regarded as a direct proof of its validity. Indeed, 
 originally the law was an assumption made to ex- 
 plain these very motions, and is, therefore, an induc- 
 tion based on astronomical facts, not a deduction 
 that can be demonstrated by them. 
 
 As with the law of inertia so is it with the law of 
 conservation of mass. We cannot demonstrate that 
 the amount of material in nature has never been 
 
CONSERVATION OF MASS. 173 
 
 increased by the smallest amount. All we can do 
 in any case is to show that the amount of material 
 with which we experiment is not perceptibly altered 
 in the various transformations through which it 
 passes, — assuming of course that the amount of ma- 
 terial, or to use a technical term, the mass, is accu- 
 rately measured by the weight. In a chemical 
 process, when we can weigh all the materials con- 
 cerned, we find that within the unavoidable experi- 
 mental errors, often very large, the sum of the 
 weights of the products of the process is exactly 
 equal to the sum of the weights of the factors ; and 
 after a very wide experience with similar results we 
 assume that the two sums are always exactly equal. 
 Hence we represent every chemical process as an 
 equation, writing on the left of the sign of equality 
 the several symbols which represent the weights of 
 the factors, and on the right the corresponding sym- 
 bols which represent the weights of the products. 
 Obviously, however, we can never demonstrate the 
 exactness and universality of the law which our 
 chemical equations assume. The constancy of the 
 law is of necessity a question of inference. Still, as 
 in the case of inertia, we can appeal to phenomena 
 which render the inference in the highest degree 
 conclusive. 
 
 There are, for example, a very large number of 
 chemical processes which it is possible to conduct 
 in an hermetically closed vessel, — as in a sealed pre- 
 serve jar; so that by weighing the vessel before 
 and after the experiment, it can be shown that no 
 change of weight has come from the chemical pro- 
 
174 CONSERVATION OF MASS. 
 
 cess which has taken place inside, — a result which 
 we should confidently expect, since nothing could 
 get in or out of the sealed vessel. 
 
 The burning of charcoal in oxygen gas, under 
 such conditions as just described, furnishes a very 
 striking illustration of the principle under discussion. 
 When a lump of charcoal burns, a solid material, 
 the fuel, is converted into an aeriform substance, 
 the smoke ; and the result seems at first sight glar- 
 ingly to contradict the assumed law; but when we 
 burn the coal in a closed jar it is obvious that as 
 there has been no change of weight, there can have 
 been no loss of material; and it is further evident 
 that the substance of the coal must have been ab- 
 sorbed by the oxygen gas to form the aeriform 
 product we call smoke. 
 
 We can now pass to the earth as a whole ; and re- 
 garding our dwelling-place as a globe isolated in space 
 from which no material escapes, and into which none 
 enters, — except an occasional meteorite, — we can at 
 once recognize relations similar to those of a sealed 
 jar, in which all terrestrial nature appears as a grand 
 illustration of the conservation of mass. But obvi- 
 ously such illustrations, although they may be the 
 basis of well-founded inferences, are no proofs of the 
 absolute exactness and invariability of the law; and 
 a study of either of the other laws we have classed 
 as exact would bring out the same features. But 
 this is a subsidiary point, and it is not necessary to 
 dwell upon it further. 
 
 The laws classed as exact present also another 
 character worthy of your consideration, which, al- 
 
FUNDAMENTAL CONDITIONS. 1 75 
 
 though it cannot be definitely formulated in the 
 present state of our knowledge, is probably funda- 
 mental ; and it distinguishes these special cases from 
 the great body of the laws of nature whose relations 
 we shall study later. Such principles as the laws of 
 motion, and the laws of conservation, whether of 
 mass or of energy, seem to be fundamental relations 
 of the material universe; and not the modes of ac- 
 tion of external agencies. They are like the essen- 
 tial qualities of matter, — extension, impenetrability, 
 mobility, — and not like the accidental qualities, which 
 may be regarded as superimposed upon matter by 
 the action of some mode of energy, — such as color, 
 temperature, or magnetism. Consequently they are 
 simple instead of complex relations. 
 
 Consider, for instance, inertia, which is often classed 
 as a quality of matter. This is not an active but 
 wholly a passive relation, as the common use of the 
 word " inert " indicates. Matter has no power within 
 itself to change its state or condition in any way. 
 Such changes in all cases imply an external agent, 
 and an expenditure of energy, which is to be distin- 
 guished from the passive mass on which it acts. 
 
 It has been said that the original atoms contained 
 the potency of all possible being; and if by this is 
 meant that they were the beginnings of things, — 
 
 u . . . rudis indigestaque moles, 
 Nee quicquam nisi pondus iners, congestaque eadem 
 Non bene junctarum discordia semina rerum, — " 
 
 the proposition is harmless enough, if we accept the 
 general theory that atoms are the final result of the 
 
I76 POTENTIALITY OF ATOMS. 
 
 analysis of matter; but if it is meant that the atoms 
 have actual creative potency, and all future being 
 involved in their substance, in the same sense that 
 the flower is infolded in the bud, then it is a suffi- 
 cient answer to all such speculations to say that 
 they are wholly at variance 1 with the manifest ten- 
 dency of modern science. If there be one thing 
 more marked in that tendency than another, it is to 
 distinguish energy and matter as two distinct and 
 separate entities ; and to regard matter as wholly 
 inert, utterly lifeless and dead, except in so far as it 
 is controlled and energized from without. We be- 
 lieve this to be the correct view, not only in regard 
 to such manifestations of material bodies as we refer 
 to heat, light, and electricity ; but also in regard to 
 those seemingly inherent forces which hold the parts 
 of a body together, and determine the effects of 
 cohesion, elasticity, and the like. 
 
 For example, we distinguish among the conditions 
 of magnetic phenomena what we call the " field of 
 force." Masses of iron brought into that field — that 
 is, into any space thus conditioned — become at once 
 magnetic, and attract or repel each other as the case 
 may be. Now it is a plausible conception that we 
 live in a space conditioned not only by magnetism, 
 but by various other agencies, which may determine 
 the cohesion and structure of solid bodies. Every 
 year I show to my class an experiment which I 
 never witness myself without being strongly im- 
 pressed by the wonderful relations which it illus- 
 trates, and the still more wonderful relations it 
 suggests. On the top of a board, resting on the 
 
FIELD OF FORCE. 177 
 
 poles of a powerful electro-magnet, I place a large, 
 loose pile of wrought-iron nails. When the current 
 of a dynamo-machine passes through the coil of the 
 instrument, a magnetic field is established through- 
 out all the space in the neighborhood of the poles ; 
 and with this the board in no way interferes, al- 
 though it keeps the nails from direct contact with 
 the magnet itself. As soon as the current passes, 
 and the field is established, the loose nails, by their 
 mutual attractions, — thus determined, — become a 
 tough, plastic mass, which can be moulded into the 
 form of an arch, or of any similar structure. But 
 when the current is broken the magnetic virtue of 
 the field disappears, and the structure that had been 
 reared, crumbles into nails. Analogy suggests that 
 the atoms of matter, inert in themselves, are simi- 
 larly conditioned, and that all structures would be 
 resolved, and all forms of matter disappear, if the 
 Presence which sustains them were withdrawn. 
 
 Now, just as the first law of motion appears to be 
 merely a declaration of a passive quality of matter, 
 so it seems to me all the other laws we have classed 
 as exact are fundamental attributes either of matter 
 or of energy. This may not appear as the laws are 
 usually stated ; but an analysis of the relations thus 
 enunciated will always show their true character. 
 Thus in regard to the law of conservation of mass, 
 to which we have just referred in another connection, 
 — it would be easy so to state the law as to make it 
 appear arbitrary and anomalous. That in every 
 chemical change the sum of the weights of the prod- 
 ucts formed should be exactly equal to the weights 
 
178 CONSERVATION OF MASS. 
 
 of the factors consumed ; for example, that when 
 water is resolved by an electrical current into oxygen 
 and hydrogen, the combined weights of these two 
 aeriform substances should be exactly equal to the 
 weight of the liquid water used up in the process ; 
 or, what is still more remarkable, that when coal or 
 wood burn, the weight of the smoke added to the 
 weight of the ashes will be, to the smallest fraction of 
 a grain, exactly equal to the weight of the fuel which 
 has disappeared, and for the most part flown up the 
 chimney, — all this does seem at first sight to be such 
 a precise conformity to weights and measures as 
 could never have been secured unless specially or- 
 dained ; but a few moments' consideration will show 
 that this law, so far from being an ordinance super- 
 imposed as it were upon matter, is a relation neces- 
 sarily arising from its very constitution. In any 
 mechanical process you at once recognize that there 
 can be no real loss of material. When silver and 
 gold bullion are coined or made into ware and trink- 
 ets, you confidently expect, from your knowledge of 
 material relations, to find all the metal in the manu- 
 factured articles, — of course excepting a small loss 
 from dispersion by attrition, abrasure, or otherwise, 
 for which you can readily account. Why should not 
 the same be true in a chemical process? If there be 
 no loss of precious metal when one hundred pounds 
 of silver are coined at the mint, why should there be 
 any loss when the same amount of bullion is con- 
 verted into nitrate of silver by the manufacturing 
 chemist? Certainly, not only can we find no "suffi- 
 cient reason " for expecting a change of relations 
 
LAW OF COMBINING PROPORTIONS. 1 79 
 
 under such circumstances, but also the more we 
 study material relations the more evident does it 
 appear that conservation of mass is simply the mani- 
 festation of the persistency of the mode of being we 
 call matter. In other words, the study of the rela- 
 tions of matter, and even our own familiar experience, 
 has produced the conviction that beneath the eva- 
 nescent qualities of changing substances and the de- 
 caying forms of organic structures, there is a material 
 substratum which is permanent and unchangeable; 
 and that the law of chemistry we have been studying 
 is simply the manifestation of this fundamental es- 
 sence of matter. The illusion which is produced by 
 the escape of colorless aeriform matter in the burning 
 of fuel, and in many other less familiar chemical pro- 
 cesses, is easily corrected by conducting the ex- 
 periment in an air-tight vessel, as we have before 
 described. 
 
 The same essential feature appears in the second 
 of the great laws of chemistry, which we have already 
 described as the law of combining proportions. 
 That hydrogen gas should combine with oxygen gas 
 to form water in the exact proportions of 2.000 to 
 15.869, as was shown in the last lecture, does seem 
 at first sight as accidental or arbitrary a relation as 
 could well be imposed on these elementary sub- 
 stances ; but if we look at the subject from another 
 point of view, it will be seen that some definiteness of 
 relation is implied by the other essential attributes of 
 matter, even though our present knowledge may not 
 enable us to see the reason of the precise value of 
 the proportion in a given case. It is obvious, for 
 
ISO LAW OF COMBINING PROPORTIONS. 
 
 example, that assuming the supply of oxygen unlim- 
 ited, we should expect to obtain twice as much water 
 by burning twice as much hydrogen ; and so, on the 
 other hand, were the supply of hydrogen unlimited, 
 we should expect the same result by using twice as 
 much oxygen ; otherwise all our knowledge of ma- 
 terial relations would be confounded. But this implies 
 that the relative weights of hydrogen, oxygen, and 
 water, which concur in the familiar process of burning 
 hydrogen gas, must be definite, — although we have 
 no means of predicting that the definite proportion 
 should be exactly that of 2.000 to 15.869 to 17.869. 
 
 Take, as another example, the simple chemical pro- 
 cess which results when, we bring together carbonate 
 of soda, hydrochloric acid, and water. The products 
 of this process are common salt, carbonic acid gas, 
 and a small additional amount of water. Here again 
 common-sense, as we might say, tells us that we must 
 proportion our carbonate of soda to the amount of 
 carbonic acid gas we desire to make. If we need 
 three times as much gas we must take three times as 
 much soda, and so in regard to any of the other 
 materials concerned in the process ; but this implies 
 a definite relation between the several factors and 
 products of the chemical change, or, in other words, 
 this familiar experience and common-sense imply 
 the law of definite proportions. 
 
 In the two cases last cited these so-called laws of 
 chemistry are evidently, as we have before said, 
 merely fundamental relations of matter, and not the 
 modes of action of external agents. To the same 
 category belongs the law of conservation of energy, 
 
LAW OF GRAVITATION. l8l 
 
 and so obviously that I need not press the point ; but 
 in regard to the great law of gravitation there is a 
 manifest difficulty of interpreting the phenomena 
 from this point of view. As we have already pointed 
 out, the usual statement of the law implies an 
 attractive force, and therefore an active power of 
 great potency. Nevertheless, I am inclined to the 
 opinion that here also the facts are best explained 
 on the view that gravitation is simply a manifesta- 
 tion of a fundamental relation between energy and 
 mass. 
 
 There are several circumstances which would sup- 
 port the opinion thus expressed, although I have 
 only time to allude to them here. In the first place, 
 gravity is the only attractive force which is directly 
 proportional to the mass. Magnetic and electrical 
 attractions follow wholly different and far more com- 
 plex laws. In the second place, the diminution of 
 gravity with the square of the distance is simply the 
 law of the diffusion of any radiant energy through 
 space; as may be seen in the intensity of illumination 
 on screens at different distances from a luminous 
 source. In the third place, the attraction of one 
 mass is not in the least influenced by the proximity 
 of similarly attracting masses. Thus, each of two 
 weights on a scale-pan exerts its specific effect inde- 
 pendent of its association ; but two magnets or two 
 electrified bodies when placed in juxtaposition do 
 not exert the same invariable concurrent action. In 
 the fourth place, the attraction of gravity is wholly 
 independent of the intervening medium. Two bodies 
 on the opposites sides of this globe would attract 
 
1 82 LAW OF GRAVITATION. 
 
 each other with the same force whether the earth 
 were in the way or not; while electrical or magnetic 
 attraction is very greatly influenced by the nature of 
 the dielectric or diamagnetic which intervenes. In 
 fine, activities which are superinduced, like electrical 
 or magnetic attractions, follow wholly different and 
 vastly more complex laws than the simple relations 
 to mass and space which gravity exhibits. Hence 
 the grounds of the opinion expressed above that the 
 law of gravitation is a proposition which expresses, 
 not the mode of action of a special force or agency, 
 but simply a fundamental and necessary relation 
 between energy and mass. 
 
 I freely admit that the opinion I have expressed 
 in regard to the laws classed as exact may be open 
 to philosophical objections, and I do not advance it 
 as a well-grounded, much less as an accepted doc- 
 trine. Since, however, I expect to show in my next 
 lecture that the great body of natural laws, as enun- 
 ciated in our systems of science, are merely ideal 
 relations, which the phenomena of nature approach, 
 but which are rarely if ever realized, I felt it incum- 
 bent on me to give a clear account of those funda- 
 mental principles that appear to be more exact. 
 My one. object is to make clear to you the aspect 
 of the laws of nature as seen from the standpoint 
 of a student of physical science, with all the in- 
 definiteness which the view presents, and with the 
 impenetrable clouds which limit the prospect on 
 every side. Do not, however, accept my opinions, 
 or rely on my judgment; but study the phenomena 
 for yourselves, not as drawn in sharp outlines by popu- 
 
CAUTION REQUIRED. 183 
 
 lar writers, but as exhibited by nature, with all their 
 limitations, all their variations, and all their obscurity. 
 Make sure of the actual facts; so that you shall build 
 your philosophy on a firm and enduring basis that 
 cannot be moved. 
 
 13 
 
1 84 LAW OF MARIOTTE. 
 
 LECTURE VII. 
 
 DETERMINATE AND INDETERMINATE LAWS. 
 
 OF the great body of the laws of physical science 
 which are described in the treatises on physics 
 or chemistry, I could not select a fairer illustration 
 than the law of Mariotte. This law was discovered 
 during the last half of the seventeenth century, wholly 
 independently, by the Abbe Mariotte in France and 
 by the famous English philosopher Boyle, and is 
 often called by English writers " the law of Boyle." 
 Since that time all the relations of the law have been 
 repeatedly and carefully investigated, and there are 
 few principles of science in regard to which our 
 knowledge is more precise. According to the usual 
 formula this law declares that the volume of a given 
 mass of gas is inversely as the pressure to which it 
 is exposed ; or in other words, that as the pressure 
 increases or diminishes, the volume contracts or ex- 
 pands in precisely the same proportion. For exam- 
 ple, if we have a perfectly flexible balloon, partially 
 inflated, the volume of the confined gas will contract 
 or expand in absolutely the same proportion as the 
 pressure of the air on the outside is increased or 
 diminished. We can also enunciate the law in another 
 
CONCOMITANT CONDITIONS. 1 85 
 
 form, which applies to any mass of aeriform matter, 
 whether confined or not, — saying that the density of 
 a given atmosphere is directly proportional to its 
 tension. But since the tension of a gas must neces- 
 sarily balance the pressure to which it is exposed, 
 and since the density of a gas must increase as its 
 volume diminishes, the last statement only describes 
 another phase of the same principle. 
 
 This law discovered by Mariotte is of fundamental 
 importance in many departments of chemistry and 
 physics, especially in meteorology; but in nature its 
 simple working rarely if ever appears. The volume 
 and density of a mass of aeriform matter not only 
 varies with the external pressure or internal tension, 
 but similar and as great changes are caused by varia- 
 tions of temperature. Considerable although less 
 marked effects are produced by moisture, and in pass- 
 ing from one place to another a sensible change may 
 be caused by the variations in the intensity of gravity. 
 In any case the observed phenomenon is the resultant 
 of all these partial effects, which may either concur or 
 tend to balance each other. Constantly, then, in 
 practice, the law must be disguised and its action 
 obscured. The same is true of all similar laws. The 
 phenomena of nature are usually very complex results, 
 and such laws as the one we are discussing are the 
 simpler elements into which we attempt to analyze 
 the phenomena. But this, although a perplexing, is 
 only an incidental circumstance, and we must con- 
 sider the aberrations of the law itself. 
 
 Even when abstracted from all concomitant condi- 
 tions, so far is the law of Mariotte from exact that it 
 
1 86 DEVIATIONS FROM THE LAW. 
 
 holds absolutely in no single instance, unless inferen- 
 tially as a passing phase of a continuous change. 
 When we study the subject minutely and pay regard 
 to small differences we find that each distinct aeriform 
 substance has a rate of its own, and is, as it were, a 
 law unto itself. At the common temperature most 
 gases, as nitrous oxide, carbonic acid, ammonia, 
 oxygen, nitrogen, and the mixture of the last two we 
 call air, contract under pressure to a perceptibly 
 greater extent than the law authorizes. At high 
 pressures the deviation becomes very marked, and as 
 we approach the pressures under which the gases 
 are condensed to liquids no semblance of the law is 
 left. Hydrogen, on the other hand, the lightest con- 
 dition of aeriform matter, alone contracts less than the 
 law requires. Hydrogen therefore seems to present 
 unique relations, and to stand apart by itself. But 
 the experiments of Regnault indicate that this rela- 
 tion depends to a large extent on temperature. He 
 observed that although carbonic acid deviates widely 
 from the law of Mariotte at the freezing-point of 
 water, it conforms almost precisely to it at the boiling- 
 point. So also he noticed that air deviates from the 
 law much less at an elevated temperature than at the 
 ordinary temperature of the atmosphere ; and he con- 
 cluded that a temperature could easily be attained at 
 which the deviation would become insensible to our 
 means of observation. He even thought it probable 
 that at a very high temperature the air would again 
 deviate from the law, but in the opposite direction, like 
 hydrogen at the ordinary temperature. Generalizing 
 these observations it is supposed that the same would 
 
HISTORY OF THE LAW. 1 87 
 
 be true of all gases, — namely, that with each aeriform 
 substance there is some temperature at which it con- 
 forms to Mariotte's law ; that at all temperatures below 
 this point the gas is compressed more than the law 
 authorizes, and at all temperatures above this point it 
 is compressed less than the law demands. In a word, 
 the law is an ideal relation, which is realized, if at all, 
 only under the concurrence of conditions which it is 
 impossible to command. 
 
 Mariotte's law illustrates in a very forcible manner 
 the character of the large class of the so-called laws 
 of nature we are considering, and its history furnishes 
 one of the best examples of refined scientific investi- 
 gation. I could readily multiply examples, but further 
 discussion would be tedious, and would add nothing 
 to the force of my argument; for I feel confident 
 that it will be generally allowed that I have selected 
 as fair and as typical an illustration as I could find. 
 In my work on " Chemical Physics " I have given at 
 some length the history of the law of Mariotte, and I 
 would refer you to that book for the details ; feeling 
 confident that while they fully bear out the impres- 
 sion I have endeavored to give here in a few words, 
 a careful study of the particulars will give you a much 
 larger comprehension of the subject I am seeking to 
 illustrate. In bare outline the history can be briefly 
 told. 
 
 The compressibility of gases was in the first place 
 studied with a comparatively rude apparatus, and a 
 simple law was discovered, which was accepted as 
 the absolute truth. Later, when the methods of 
 investigation had become more accurate, it was 
 
1 83 THE GRAPHICAL METHOD 
 
 found that the law was not general; but it was still 
 maintained in regard to air, until finally the refined 
 experiments of Regnault proved that it failed here 
 also. Still the law remains as an ideal truth toward 
 which nature tends, but which is never fully reached, 
 and we can even trace the action of the agents which 
 produce the perturbations. So it is with most physi- 
 cal laws. They are not realized with mathematical 
 exactness, but are ideal truths always more or less 
 false in each particular case. When we are able to 
 go behind the phenomena to their proximate causes, 
 we shall undoubtedly find that the law and its varia- 
 tions are merely different phases of the workings of 
 one complex system ; but it is doubtful whether by 
 man's limited powers the anomalies of nature will 
 ever be fully explained, or its discords resolved. 
 More probably, as we go forward in our investiga- 
 tions, and continually widen our generalizations, the 
 last generalization of all will bring us into the pres- 
 ence of that Intelligence of which all natural phe- 
 nomena are the direct manifestation. 
 
 When a physicist can discover no simple relations 
 between conditions or phenomena obviously inter- 
 dependent, his usual method of proceeding is to plot 
 his observations on paper, on some system of co- 
 ordinates, and draw a curve through the points thus 
 found. The process is a simple one, and with the 
 aid of an example can easily be made intelligible, 
 even to those who do not understand the technical 
 terms with which the so-called graphical method is 
 usually described. 
 
 The solubility of a substance in water varies with 
 
OF REPRESENTING PHYSICAL RELATIONS. 1 89 
 
 the temperature, usually increasing, but sometimes 
 diminishing, as the temperature rises, and at rates 
 which vary with different substances between wide 
 limits. There is an obvious connection between the 
 weight of a substance which will dissolve in one 
 hundred parts of water and the temperature ; but 
 no definite law connecting these quantities can be 
 discovered. Assume that we have determined ex- 
 perimentally the weight in grams of some salt, for 
 example, nitre (KNO s ), that will dissolve in one 
 hundred grams of water at various temperatures be- 
 tween its freezing and boiling points, and that we 
 have tabulated the results. Assume also that we have 
 a sheet of what is called " co-ordinate" paper, divided 
 off into little squares like a multiplication table, as 
 in the accompanying figure. On the lower horizon- 
 tal line, called the " axis of abscissas," we mark off 
 the temperature in degrees, and on the left-hand ver- 
 tical line, called the "axis of ordinates," we mark the 
 weight in grams. Taking now the data we have tab- 
 ulated, and noticing that at o° thirteen grams of nitre 
 (KNO3) dissolve in one hundred parts of water, we 
 follow up the vertical line marked o°, until we come 
 to the horizontal line marked thirteen grams, and 
 there fix the first point. Seeing next that at 15 
 one hundred grams of water dissolve twenty-five 
 grams of nitre, we follow up the vertical line marked 
 1 5 to the horizontal line marked twenty-five grams, 
 and the intersection fixes a second point. As at 
 30 one hundred grams of water dissolve forty-five 
 grams of nitre, we find a third point by following up 
 the vertical line marked 30 to the horizontal line 
 
190 
 
 THE GRAPHICAL METHOD 
 
 marked forty-five grams ; and so we proceed with 
 each of the experimental data we have found. Thus 
 we obtain as many points as there are observations, 
 and then with a free hand we draw a curve as nearly 
 as possible through all the points. On the diagram 
 we have given, a number of curves showing the vary- 
 ing solubility of several chemical compounds in water 
 have been thus drawn. Such curves represent to 
 
 the eye what has been called the " law of the vari- 
 ation," using however the word " law " in a still less 
 definite sense than we have as yet employed it. 
 They not only exhibit the general order of the phe- 
 nomena, but they enable us to fix with close approx- 
 imation values between the points at which the 
 observations were made. Thus we see from the 
 figure above that while the solubility both of potas- 
 sium chloride (K CI) and of barium chloride (Ba Cl 2 ) 
 
OF REPRESENTING PHYSICAL RELATIONS. 191 
 
 increases slowly, but at a uniform rate with the tem- 
 perature, the solubility of nitre (K N O s ) varies very 
 rapidly, and at a constantly increasing rate. Again, 
 the solubility of sodium sulphate (Na 2 S0 4 ) presents 
 what is called a singular point, increasing rapidly 
 up to 34 and then diminishing. Lastly, if we wish 
 to determine the solubility at a given temperature 
 of any of the salts here represented, we have only 
 to follow up the vertical line corresponding to the 
 temperature, until it intersects the curve of the 
 substance in question. Then on following from 
 the point of intersection the horizontal line to the 
 left, we read off on the vertical axis, the number 
 of grams of the substance which will dissolve in 
 one hundred parts of water at that temperature. 
 Other physical phenomena can be plotted and in- 
 terpreted in a similar way. 
 
 Every algebraic equation involving two variable 
 quantities corresponds to some kind of plane curve; 
 and so, on the other hand, every plane curve may be 
 represented symbolically by an algebraic equation 
 of a more or less complex character, containing the 
 unknown quantities. Thus, for example, the solu- 
 bility of nitre graphically represented by the curve 
 above described, may also be expressed by the 
 equation — 
 
 S = 13.32-}- 0.5738/ -(-o.oi7i6S/ 2 -[-o.ooooo35977/ 3 
 
 in which t stands for the temperature in degrees 
 centigrade, and S for the number of grams of salt 
 which at this temperature will dissolve in one hun- 
 dred grams of water. In this expression the value 
 
192 ALGEBRAIC EXPRESSION. 
 
 of one of the variables, the quantity sought, is given 
 in the terms of the ascending powers of the other 
 variable, in this case the temperature, — each term 
 being multiplied by a numerical coefficient, whose 
 values are deduced from experimental data. Equa- 
 tions of this general form are the simplest, although 
 not always the most concise, means by which such 
 relations can be algebraically expressed. The sci- 
 ence of mathematics, however, gives us the means of 
 treating the subject exhaustively, so that after distrib- 
 uting the errors, we can express our results in the 
 most concise manner of which the observations admit, 
 as well as in the form best adapted to computation. 
 It furnishes us with methods and guides for interpola- 
 ting, — that is, of calculating from numerical results of 
 definite experiments, what would have been the value 
 of intermediate results, — or even for assigning values 
 beyond the limits of the experimental data, exterpo- 
 lating, as Airy called it. But in its details this sub- 
 ject cannot be understood without some knowledge 
 of mathematics ; and further discussion would be out 
 of place in these lectures. It is only with the broader 
 relations of the subject that we are here concerned ; 
 and it is obvious that such algebraic expressions as 
 I have described represent what we may call an in- 
 determinate law. Such expressions are sometimes 
 called empirical laws, because they are really conven- 
 tional expressions of the results of experiments, and 
 can never be trusted far beyond the limits of the ex- 
 perimental data. From another point of view these 
 formulae may be regarded simply as methods of ap- 
 proximation to indeterminate results. 
 
THREE CLASSES OF LAWS. 1 93 
 
 Still, in discussing the nature and character of the 
 laws of nature, these important modes of representing 
 physical relations must not be overlooked, and they 
 may be regarded as a third class of laws ; so that we 
 have to distinguish the fixed laws, like the laws of 
 motion, the determinate laws, like the law of Mariotte, 
 and the indeterminate laws, such as we have just de- 
 scribed. That these last are in the fullest sense mere 
 abstractions is sufficiently evident from what has 
 already been said ; but after all, they do not differ 
 essentially from the more determinate laws, as will 
 appear from this final consideration. 
 
 In those laws which can only be geometrically or 
 algebraically expressed, we find the greatest differ- 
 ences in the complexity of the relations which the 
 curves or formulae exhibit; and sometimes the ex- 
 pression is so simple that it might well be questioned 
 under which of the two artificial categories we have 
 made, the given relation should be classed. Between 
 classes which thus blend there are not usually any 
 essential differences, and such differences as we find 
 probably depend on the greater or less complexity 
 of the phenomena under consideration. The distinc- 
 tion between the fixed and the variable laws appears 
 to be more fundamental; and the first, as we have 
 before said, seem to be expressions of the essential 
 properties or relations of matter and energy. 
 
 The conception of the distinction I have drawn as 
 it exists in my own mind, may be readily illustrated 
 by the well-known Jacquard loom, which with numer- 
 ous modifications is used for weaving almost every 
 kind of fabric having inwrought designs. In such a 
 
194 JACQUARD LOOM. 
 
 machine, a carpet-loom for example, although the 
 parts work in harmony, we may distinguish between 
 the essential machinery of a loom common to all 
 looms, and the ingenious devices of Jacquard by which 
 the pattern is determined. Without these additions, 
 the loom would weave a perfectly uniform plain 
 fabric, with fixed and unvarying relations of the woof 
 and warp ; but Jacquard's perforated cards determine 
 a selection of the threads, and through a combination 
 of these variable conditions, so complex that the ob- 
 server cannot follow their intricate workings, the pre- 
 designed pattern appears. 
 
 So is it, as it seems to me, in the loom of nature. 
 Mass and energy are the woof and warp, with their 
 commingled tints, out of which the tissue of events 
 has been woven ; and these fundamental relations are 
 fixed and invariable. But ten thousand changing 
 conditions, fore-ordained by Omniscience and di- 
 rected by Unerring Wisdom, select the threads, and 
 thus gradually the great design is unrolled. 
 
 I might push the analogy further; but such simil- 
 itudes are of value only as suggestions to thought, 
 and I leave the subject to your reflections. 
 
 From the very necessities of the case the analysis 
 of the laws of nature, which I have given in this lec- 
 ture, is far from complete ; and I cannot, therefore, 
 hope that it is conclusive. Only in proportion as 
 one sees clearly is it possible to describe clearly what 
 appears; and when peering through a mist all out- 
 lines are ill-defined. But such is the condition under 
 which the investigator must work, and he can only 
 tell you faithfully what he thinks he discerns. Some- 
 
EDUCATIONAL ASPECTS. 195 
 
 times, however, the clouds break, and he gains a 
 vision of the truth in its glory; and I trust one con- 
 clusion at least remains clear to you after this dis- 
 cussion. 
 
 From no point of view can the laws of nature be 
 regarded as efficient causes ; and this ruler which a 
 materialistic philosophy has attempted to enthrone 
 over the universe is no potentate in any sense, but 
 merely a very intangible, indistinct, and protean 
 mental image of man's abstraction. 
 
 As has already been intimated, this sophistry of 
 materialism has been very widely disseminated in 
 consequence of our imperfect methods of education. 
 The only knowledge of material relations which most 
 even of our educated people acquire is derived from 
 elementary text-books, whose formal statements con- 
 stantly convey false impressions ; and hence arises 
 much of the fallacy which prevails. It may not 
 therefore be out of place to devote the remainder of 
 the hour to a short discussion of the educational 
 aspects of our subject. 
 
 One of the most brilliant and influential writers of 
 our day, while fully conceding the very great im- 
 portance to the scholar of the general results of 
 science, as furnishing an essential part of the ma- 
 terials of modern literature, has expressed the opinion 
 that the details and methods of science are of value 
 chiefly to experts, and are unfit materials to form the 
 basis of liberal culture. 
 
 With the general spirit of Mr. Matthew Arnold's 
 address on " Literature and Science " (first delivered 
 as the Rede Lecture at the University of Cambridge 
 
196 LITERATURE AND SCIENCE. 
 
 in England, and afterwards often repeated in this 
 country) I entirely sympathize. I freely admit that 
 as a means of liberal culture that knowledge is most 
 important which, to use Mr. Arnold's striking ex- 
 pression, can be most directly related to the sense 
 for beauty and the sense for conduct; as well as I 
 should add to all the senses which make up that won- 
 derful composite we call character. Character is the 
 great end of education ; and that which arouses in 
 man elevated thoughts and conceptions, and that 
 which stirs within him great resolves that lead to 
 noble deeds, has more influence on character than 
 any special knowledge however profound, and how- 
 ever valuable in itself considered to the welfare of 
 society. 
 
 The term " science " was used by Mr. Arnold in its 
 broadest sense, to include any body of systematized 
 facts, whether of nature or of any department of 
 human learning; and I wholly agree with him that 
 the mere acquisition of knowledge, however useful, is 
 a very insufficient means of liberal culture ; and also 
 that it is equally unimportant to the great mass of 
 educated men whether the products of the combus- 
 tion of a wax taper be carbonic acid and water, or 
 whether the genitive plural o>{ pais and pas take the 
 circumflex on the termination. The practice in so 
 many of our schools of cramming immature minds 
 with heterogeneous information, which they at least 
 are unable to relate to the sense of beauty, to the 
 sense of conduct, or to the sense of fitness of any 
 kind, is to my mind a waste of golden opportunities, 
 and productive of no permanent good. 
 
CLAIMS OF SCIENCE. 1 97 
 
 But while conceding all this, I claim for the study 
 of physical science, if rightly pursued, the highest 
 value, even when judged by the very criteria which 
 Mr. Arnold has so acutely laid down. The grand re- 
 sults of physical science are most closely related to 
 the sense for beauty, and to the sense for conduct; 
 and as a matter of fact they have satisfied the needs 
 of the noblest men for beauty, for conduct, — and for 
 holiness also, — as fully as any earth-born knowledge 
 ever can. The beauty of God's creation loses none 
 of its loveliness to him who knows the fitness of all 
 the parts. Beauty, as we have before said, is simply 
 that harmony of proportions and qualities which re- 
 sults from the most complete fitness of all the parts 
 in a perfect whole, and becomes the more apparent, 
 and the more commanding, in the exact proportion 
 as that fitness becomes known and appreciated 
 through study and investigation. His mind must 
 be dull indeed whose noblest impulses are not awak- 
 ened, and aroused to action, by the revelations of in- 
 telligence and forethought which come from the 
 study of the material universe; and we can aptly 
 quote, though with a somewhat different interpreta- 
 tion, the refrain of Mr. Arnold's noble address, — 
 " no wisdom, nor understanding, nor counsel, against 
 the eternal ! " 
 
 Passing now for a moment from the subject matter 
 to the methods of science, I may venture to assert, as 
 the conclusion from an unusually long experience as 
 a teacher, that no one can acquire an adequate 
 knowledge of scientific results without such an ac- 
 quaintance with the methods by which the results 
 
198 KNOWLEDGE OF METHODS ESSENTIAL. 
 
 were obtained as will give a correct appreciation of 
 the limitations under which the conclusions must be 
 received ; and that in many cases no language, how- 
 ever skilfully used, is adequate to convey an accurate 
 conception of the truth. A student must observe 
 and experiment for himself if he would acquire clear 
 and correct ideas of natural phenomena. Every 
 teacher of experience knows that the conceptions 
 acquired from elementary text-books and popular 
 lectures are constantly erroneous, and often absurd. 
 
 Take such a simple result of chemistry as that 
 water is composed of oxygen and hydrogen. I am 
 sure from my own experience that not one in ten of 
 the young men and women who learn to repeat this 
 statement at our high schools and academies have 
 any clear idea of what it means. For many years 
 I have asked questions on the examination papers 
 for admission to Harvard College to test this very 
 point, and it has been the rarest exception to re- 
 ceive an intelligent answer. Although I have re- 
 peated the same question year after year, the result 
 has been uniformly unsatisfactory; and not until ex- 
 perimental teaching was introduced into some of the 
 preparatory schools was there any improvement. 
 To most of the men the names oxygen and hydrogen 
 conveyed no conception of definite substances ; and in 
 what sense it could be said that the familiar liquid 
 water was composed of two aeriform substances, and 
 on what evidence this remarkable scientific conclu- 
 sion is based, almost no one had clear ideas. The 
 laboratory student, however, who has actually made 
 oxygen and hydrogen gases from water, and who has 
 
NATURE THE ONLY AUTHORITY. 1 99 
 
 satisfied himself with this evidence that these aeriform 
 products came from the material of water and from 
 nothing else ; who also has mixed two volumes of 
 hydrogen gas with one volume of oxygen gas, and 
 after exploding the mixture with an electric spark 
 has seen that the result is two volumes of vapor 
 which condense on cooling into liquid water, and 
 must therefore be steam, — has a knowledge of a 
 wholly different kind. He knows that the conclusion 
 so tersely stated in his text-book is far from self-evi- 
 dent; he has experienced the difficulties which had 
 to be overcome before the truth was established ; he 
 has seen the limitations under which this truth must 
 be held ; and his knowledge is complete and final. 
 
 In literature the printed record is the final appeal ; 
 but in science books are at best only a secondary 
 authority, and can never supply the place of direct 
 observation and experiment. All descriptions of 
 natural phenomena are necessarily partial and im- 
 perfect; and in elementary works they are as a rule 
 so inadequate as to be constantly misleading. Any 
 one who relies upon them is liable to be led into 
 serious error. Hence it is that students of nature 
 often hold in such slight esteem popular expositions 
 of scientific subjects, feeling that they often convey 
 false impressions and inculcate error in spirit, if not 
 in substance. Nevertheless, such popular expositions 
 have their proper place, and are of the greatest im- 
 portance, not only by awakening interest in scientific 
 subjects but also by exhibiting large views of scien- 
 tific relations. They are avenues to knowledge which 
 men may wisely follow, and by which many have been 
 14 
 
200 EDUCATIONAL NEEDS. 
 
 led into the sanctuaries of truth ; but the scholar must 
 worship at the shrine and wait on the altars, if he 
 would interpret the oracles aright. 
 
 One of the great educational needs of our day is 
 such a training by the schools in experimental 
 methods as will enable the great body of our edu- 
 cated men to weigh scientific evidence, and thus to 
 protect the community from the frauds and sophis- 
 tries of which otherwise intelligent, instructed, and 
 even shrewd men are now so frequently the dupes. 
 Of the common-school system, so early established 
 and carefully fostered by our forefathers, we are justly 
 proud; but let us not be blind to the fact that this 
 system has grave defects, and has been excelled in 
 several countries whose governments entered on the 
 great work of popular education long after ourselves. 
 In many respects our methods of elementary educa- 
 tion are inferior to those of Germany, of Sweden, or 
 of Italy. Two very obvious reasons may be assigned 
 for this result. In the first place, the details of our 
 system are ordered by the average, and not by the 
 highest intelligence of the community; and in the 
 second place, our school boards are greatly hampered 
 in all efforts for reform by the cost of labor. 
 
 The ingenuity of our people has not failed to devise 
 expedients for economizing the labor of the teacher, 
 and thus for enabling one man to control the greatest 
 possible number of pupils. In almost every subject 
 taught in our secondary schools books are provided 
 in which each day's lesson is exactly proportioned, 
 and the questions to be asked definitely appointed. 
 The teacher's work is made as mechanical as possible, 
 
MECHANICAL TEACHING. 201 
 
 and the pupil's task becomes a mere exercise of the 
 memory. Under such conditions there is no need 
 that a teacher should have any special knowledge 
 of the subject taught ; and untrained persons are em- 
 ployed, whose whole knowledge of the subject is 
 bounded by the covers of a school-book; which too 
 often has been prescribed by a school committee, 
 under the influence of interested publishers. Thus 
 education is cheapened in our country, like so many 
 other products of labor, at the expense of refinement 
 and finish. 
 
 It is no wonder that the overworked and under- 
 paid teachers should oppose any change which neces- 
 sarily involves a large increase of labor, even when 
 they fully recognize the ruinous effects of the me- 
 chanical system under which they are compelled 
 to work. Obviously, however, this substitution* of 
 indiscriminate cramming, in place of intelligent acqui- 
 sition is fatal to the efficiency of our school system, 
 and a reform should be demanded at any cost. 
 
 Fortunately, our political system is as flexible as it 
 is crude ; and if the demand is seriously made the 
 reform is sure to follow. But let it be remembered 
 that the changes required will be necessarily costly, 
 and we must be prepared to bear the increased ex- 
 pense. Do not, however, be deceived by any make- 
 shifts which are often paraded as scientific education. 
 If teaching is to be simply a process of loading the 
 memory with more or less useful, as well as more or 
 less ephemeral, information it makes little difference 
 in the end what are the materials used in the process 
 of cramming. The material may as well be the long 
 
202 CONDITIONS OF SUCCESSFUL TEACHING. 
 
 list of exceptions to the rules of prosody, required in 
 the Latin schools of former days, as descriptions of 
 experiments in physics or chemistry so glibly recited 
 by the pupils of our modern high schools. 
 
 No teaching of science is of any value which is not 
 a direct appeal from the mind of the teacher to the 
 intelligence of the pupil. The teaching must be 
 direct and personal, and this necessarily implies a 
 large expenditure of time and patience, a special 
 training on the part of the teacher, and a great 
 increase of teaching force. 
 
 The successful teaching of natural science also 
 requires that the teacher should be independent of 
 all books. The great object of science-training is to 
 enable the scholar to interpret nature; and the book 
 of nature is the only text-book which should be pre- 
 scribed. As in the study of ancient classics the one 
 great aim is to acquire such a command of Latin or 
 Greek, such a knowledge of the circumstances and 
 relations of these elder nations, as will enable the 
 student to render not only the general sense, but also 
 the delicate shades of meaning and the coloring of 
 the language of their writers; so in the study of 
 science the great object is to interpret the meaning 
 of natural phenomena, to decipher the significance 
 of every feature, and to show forth the intelligence of 
 which nature is the expression. 
 
 Books have their value chiefly as guides, and as 
 records of what has already been accomplished ; but 
 in the study of nature they hold a secondary and 
 subordinate, and not a chief place. To train young 
 minds to interpret nature is a perfectly practical 
 
THE TRUE AIM. 203 
 
 scheme. The power can be acquired as readily as 
 the ability to translate Virgil or Homer, although of 
 course with limitations which are similar in both 
 cases ; and it is this power, and not the mere acqui- 
 sition of scientific knowledge, at which the so-called 
 " new education " aims. This all-important state- 
 ment cannot be too often repeated, or too strongly 
 emphasized. The advocates of an exclusively clas- 
 sical culture constantly describe the new education 
 as an attempt to substitute the acquisition of useful 
 knowledge for mental discipline; or, at best, to re- 
 place serious intellectual work with superficial object- 
 teaching; and, as we have before intimated, there 
 has been an attempt on the part of some schools to 
 satisfy an obvious demand with such contemptible 
 shifts. Let me then repeat that the great aim of sci- 
 entific training should be the ability to interpret 
 nature ; and that in large measure the acquisition is 
 within the reach of every educated man, although 
 in its higher manifestations the successful exercise 
 of this ability may be a privilege of only the most 
 gifted intellects. 
 
 That such training is of the highest value and is a 
 legitimate aim of education, must, I think, be univer- 
 sally admitted; but it cannot be secured without 
 trained teachers, without well-appointed laboratories, 
 and except at a cost proportionate to such require- 
 ments. Certainly we cannot afford to fall behind the 
 most favored nations of the earth on the very ground 
 which we first occupied ; and it is equally certain that 
 no investment will yield a larger return than the money 
 expended in the acquisition of real knowledge. 
 
 The distinction between real knowledge and formal 
 
204 REAL AND FORMAL KNOWLEDGE. 
 
 knowledge is one of paramount importance, which 
 should never be overlooked in our plans of educa- 
 tion. That knowledge alone is real to a student 
 which is obviously related to some need of his life, 
 or to some phase of his intelligence. All other 
 knowledge, however valuable in itself considered, is 
 to him formal. Obviously, the distinction here in- 
 sisted on is purely a relative one; for the same 
 knowledge which is formal to one man may be very 
 real indeed to his next-door neighbor. The para- 
 digms of grammar are formal knowledge to the young 
 student who memorizes them for the first time, but 
 are very real knowledge to the grammarian. Even 
 formal knowledge has its right place ; and there are 
 exigencies under which its acquisition is to be en- 
 couraged or even enforced. Man is a creature of 
 habit, and his usefulness requires that certain essen- 
 tial truths should become so woven into his nature as 
 to be always at hand on every emergency. Certainly 
 the multiplication-table and the spelling-book repre- 
 sent formal knowledge of this sort; but I do maintain 
 that it should be the great object of education to re- 
 late all knowledge, so far as possible, to the pupil's 
 understanding. 
 
 I know that on this point I differ from many old 
 experienced teachers whom I greatly respect. It was 
 formerly held almost universally, and even now it is 
 believed by many teachers, to be best for a child to 
 acquire knowledge at first in a formal way, and to 
 wait for the development of his intelligence to ex- 
 hibit its relations. On this theory, boys preparing 
 for college in my own school-days were compelled to 
 
REAL AND FORMAL KNOWLEDGE. 205 
 
 > . 
 
 learn the Latin grammar by rote before they under- 
 stood the meaning of one half of the terms employed. 
 The vivid remembrance of my own experience may 
 lend undue proportions to this abuse of the memory; 
 still, after a long experience as a teacher myself, I 
 cannot but regard such discipline as a great waste of 
 mental energy, if not absolutely cruel ; and no one 
 can deny that the acquisition of any knowledge is 
 greatly facilitated when the relations of the knowledge 
 are understood. I have granted that in certain cases 
 the acquisition of formal knowledge is necessary; nev- 
 ertheless, it should be the study of the teacher to les- 
 sen the requirement as far as possible ; and certainly in 
 science, formal knowledge is wholly without value. 
 
 Some years ago, while working in the mineralogical 
 cabinet under my charge at Cambridge, I was ad- 
 dressed by two lady visitors who had evidently found 
 great interest in the collection, and asked some very 
 intelligent questions in regard to several of the more 
 common mineral species. It gave me great pleasure 
 to answer their inquiries, and I passed a pleasant 
 hour in pointing out some of the characteristic feat- 
 ures of quartz, feldspar, mica, pyroxene, hornblende, 
 and similarly familiar minerals which are the constitu- 
 ents of our common rocks. At the close of this im- 
 provised lecture, one of the ladies said to me in an 
 apologetic tone, — evidently deeming some excuse re- 
 quired for such an unusual feminine taste, — " We are 
 
 teachers in the High School," naming a town 
 
 not one hundred miles distant from Boston, " and I 
 have been taking a class through the sections on 
 mineralogy, introductory to Dana's Geology ; and I 
 
206 REAL AND FORMAL KNOWLEDGE. 
 
 was interested to see some of the minerals described 
 in them." 
 
 I think this incident, without further comment, will 
 illustrate what I mean by a formal knowledge of ele- 
 mentary science, and will also show how utterly worth- 
 less all such acquisition must be. The incident has 
 an amusing side, but it also exhibits a very sad aspect 
 of our secondary education. This lady was evidently 
 a conscientious teacher, who had a conception of 
 something better than the mechanical routine in which 
 she was forced to work, and this had led her to seek 
 some real knowledge of the subject she had to teach. 
 I know that there has been a great improvement in 
 our schools during the last few years ; and the prac- 
 tical classes supported by the Lowell Fund, under the 
 direction of the teachers of the Boston Institute of 
 Technology, as well as similar courses under the aus- 
 pices of the adjacent Natural History Society, have 
 done not a little to hasten the reform. But our best 
 teachers are still constrained by over-crowded class 
 rooms, and the mechanical routine which this condition 
 of things necessarily implies. Of this I know. There 
 is not a more devoted or more conscientious class of 
 workers in our community than the teachers of the 
 secondary schools ; and if our people realized how 
 much mental energy was wasted in these schools by 
 just such senseless tasks as attempting to teach min- 
 eralogy from a book, the teachers would soon be 
 relieved from such profitless and thankless duties. 
 
 What I have said in regard to the teaching of 
 science, applies with almost equal force to literary 
 studies as well. Real knowledge has the same great 
 
REAL AND FORMAL KNOWLEDGE. 207 
 
 worth in every department of learning, and formal 
 teaching the same deadening influence ; and let it 
 not be inferred from anything I have said, that I 
 desire to exalt scientific culture at the expense of 
 literary or artistic culture of any kind. All mental 
 culture is alike good ; and it is not by a one-sided 
 growth, but by a symmetrical development of all its 
 powers, that a community can secure the largest 
 productiveness and acquire the widest influence. 
 
 I have elsewhere expressed myself so strongly on 
 this point that it does not seem to me necessary that 
 I should guard the language here used against any 
 misinterpretation ; but that I may make the dec- 
 laration still more emphatic, let me repeat that I 
 still believe the old forms of literary culture to be 
 for the large majority of scholars the best prepara- 
 tion for useful lives. I merely claim that there is an 
 important class of the students who now seek a col- 
 lege education, for whom, on the other hand, a sci- 
 entific culture will best secure their future usefulness ; 
 and I have already indicated sufficiently clearly what 
 I mean by scientific culture in this connection. Let 
 not scientific culture be confounded with technical 
 training, and let it not be misjudged by any counter- 
 feits which have assumed its name. Several of the 
 sciences have opened lucrative fields for professional 
 labor; and the engineer, the chemist, and the electri- 
 cian follow as learned vocations as the lawyer or the 
 physician. For each of these new professions, as 
 for those of the elder triad, special training is re- 
 quired ; and in all of them some of the subjects 
 involved are the same as those studied in view solely 
 
208 TECHNICAL TRAINING AND LIBERAL CULTURE. 
 
 of a general education. The difference between 
 technical training and liberal culture depends, not 
 chiefly on the subject-matter studied, but on the 
 purposes and spirit with which the study is pursued. 
 Thus, chemistry studied with the object of manufac- 
 turing chemical products, or of directing other chem- 
 ical industries, or of solving the numerous sanitary 
 and technical problems which constantly arise in 
 every highly civilized community, is a legitimate 
 and learned profession ; but when studied for the 
 sole object of interpreting nature and extending 
 knowledge, it is one of the liberal arts. I do not 
 say that one object is more worthy or more noble 
 than the other ; but I do maintain that any country 
 becomes more enlightened and more honored in 
 proportion as liberal culture is fostered and main- 
 tained. That it will have its proper place in our 
 community is already assured ; and the movement 
 recently inaugurated by Harvard College is already 
 producing visible effects. 
 
 To this reform in education, and to the substitu- 
 tion of real for formal knowledge which it involves, 
 I look more than to anything else for the reconcilia- 
 tion between science and theology. When all the 
 wisdom and learning of this world has been related 
 not only to man's need of beauty and to man's need 
 of conduct, but also to man's need of understanding 
 and man's need of religion, the harmony between 
 material and spiritual truths will plainly appear; and 
 thus it is that this discussion of what seemed at first 
 a purely educational problem, has an important 
 bearing on the larger subject we have in hand. 
 
THE MEANING OF LAWS. 20O. 
 
 LECTURE VIII. 
 
 THEORIES OR SYSTEMS OF SCIENCE. 
 
 IN my last lecture I defined a law of nature as a 
 declaration or statement of a certain order, se- 
 quence, or relation observed among natural phenom- 
 ena, and aimed to show that such propositions could 
 be regarded from no point of view as efficient causes. 
 It is not in the study of nature alone that the mind 
 of man does not rest satisfied with laws. In social 
 relations as well as in science, men demand to know 
 the meaning of laws, and their demands are the more 
 imperative in proportion as they become more en- 
 lightened. The scientific investigator is not con- 
 tent with a knowledge of the outward relations of 
 phenomena. He seeks to discover the proximate 
 causes of the order he has observed, and although 
 he may not be able to reach certainty, he is not 
 satisfied until he has framed some explanation by 
 which he can classify his facts, and which at the same 
 time will give the form and body to his thoughts 
 so indispensable for successful study. Hence arise 
 of necessity the hypotheses, theories, and systems of 
 science. 
 
 Using the term in its broadest sense, an hypothesis 
 is a postulate imagined or assumed to account for 
 
2IO H\TOTHESIS. 
 
 what is not understood. Its derivative meaning from 
 vTTodeo-Ls (a supposition) is closely followed in the 
 meaning here assigned to the word. These suppo- 
 sitions may be based on a larger or smaller knowl- 
 edge, they may be more or less in harmony with nat- 
 ural phenomena, they may more or less fully agree 
 with generally accepted systems of science ; but they 
 differ from the laws of nature in that they seek to go 
 behind the external relations of things, and explain 
 how this order might have been produced. The 
 word " hypothesis," unfortunately for our purpose, 
 has acquired a coloring which suggests a deprecia- 
 tory inference. A plausible supposition is sometimes 
 spoken of contemptuously as " a mere hypothesis ; " 
 and possibly for this reason the term " theory," al- 
 though often branded in a similar way, is frequently 
 used by scientific writers to distinguish such hypoth- 
 eses as they regard as more credible or more fully 
 established. But until the truth of an hypothesis 
 has been placed beyond doubt, — when of course it 
 ceases to be a supposition, and is classed among 
 fixed facts, — the degree of credibility must be to a 
 great extent a matter of opinion, and no definite line 
 of distinction can be drawn. Moreover, the word 
 " theory " has a very important use, corresponding 
 also to its derivation, which we cannot afford to have 
 compromised. We shall use, therefore, the word 
 " hypothesis " to designate any assumed explanation 
 of natural phenomena, without any implication as to 
 the plausibility of the supposition. 
 
 As is well known, it is a fundamental doctrine of 
 the positive philosophy that man can know nothing 
 
MAN'S DISCERNMENT, AND GOD'S INSPIRATION. 211 
 
 of efficient causes. Hence all hypotheses are vani- 
 ties, and the only reasonable course for helpless man 
 is to limit his attention to determinate relations of 
 phenomena ; that is, to natural laws. But this phil- 
 osophy utterly ignores the only power by which the 
 level of human knowledge can be raised ; that is, in- 
 duction : and as we have shown in previous lectures, 
 the whole history of science is simply the story of 
 verified inductions. Guesses at truth are not to be 
 despised, for they have been again and again divina- 
 tions. 
 
 We cannot expect fruitful suggestions except from 
 men who are thoroughly acquainted with the subject 
 they are studying; but to gain any insight into 
 nature's processes, something more than erudition is 
 required; call it genius, call it intuition, call it in- 
 spiration, or by whatever other name, there is an 
 element, although we may not be able to define it 
 precisely, which we all recognize in such creative 
 minds. Man's discernment and God's inspiration 
 blend together, and no one can distinguish the point 
 where they meet. 
 
 There is a certain sense in which the suggestions 
 of gifted minds maybe said to be the oracles of God ; 
 and there is another sense in which they must be 
 regarded as the conceits of very fallible and short- 
 sighted men; and it is no wonder that their value 
 will be very differently estimated according as they 
 are regarded from one or the other point of view. I 
 have the greatest respect for the love of truth and 
 accuracy which the positive philosophy so strongly 
 inculcates ; but, as it seems to me, this doctrine finds 
 
212 SYMPATHY BETWEEN MIND AND NATURE. 
 
 its chief disciples among scholars who have been so 
 engrossed in deductive methods as to overlook the 
 mental visions by which the broader relations of truth 
 have been discovered. 
 
 To my mind there is a deeper and nobler philoso- 
 phy than positivism, which explains that mysterious 
 sympathy between mind and nature so evident in the 
 great discoverers, — a philosophy proclaimed in the 
 declaration of Holy Scripture that man was created 
 in the image of God. Only in proportion as man par- 
 takes of the Divine intelligence can he understand the 
 Divine creation, and just in proportion as he is in 
 sympathy with the Divine mind will he recognize the 
 Divine thought which has been manifested in nature. 
 And even if we take no higher view than that man 
 has grown into harmony with his environments 
 through the influence of what is called natural selec- 
 tion, we must at least recognize in such antecedents 
 a close relationship with the rest of nature ; and this 
 affinity alone would help to explain the power of 
 genius to frame fruitful hypotheses. 
 
 As we have already explained, there is but one sat- 
 isfactory test of the Divine afflatus in such imagin- 
 ings ; and that is the test of experience. Hypothesis 
 is of value only in so far as it explains facts, and by 
 pointing out consequences directs investigation, — as 
 has been already fully illustrated. In this way hypo- 
 theses have been the chief means by which science 
 has been advanced. The great discoverers have been 
 the men who were the most fruitful in hypotheses, 
 and at the same time most skilful and conscientious 
 in submitting them to the test of observation and ex- 
 
THEORIES OF SCIENCE. 213 
 
 periment, — men like Copernicus, Kepler, Galileo, 
 Huygens, Newton, Oersted and Faraday. 
 
 I have already shown out of what copious and often 
 grotesque fancies the laws of Kepler were educed; 
 and Faraday, although far more sober-minded, was 
 equally distinguished by exuberance of fancy; but, 
 like Kepler, he submitted his hypotheses to the 
 severest tests. So also Newton, while emphatically 
 expressing his contempt for idle speculations in his 
 celebrated aphorism already quoted, constantly made 
 use of legitimate hypotheses in his own investiga- 
 tions, — as both his "Optics" and his " Principia " 
 give abundant evidence. 
 
 The word " theory " — from Oewpeay, to see or con- 
 template — is correctly used in speaking of a system 
 of science, as the theory of music, or the theory of the 
 moon; and to this meaning it is best limited. In 
 this sense a theory may involve many principles and 
 complex relations. It may be based on known laws 
 or definite facts, as is, for example, the theory of 
 sound ; or it may rest to a greater or less extent on 
 hypotheses, as does the undulatory theory of light on 
 the assumption of an adamantine ether. It is there- 
 fore plainly to be distinguished on the one hand from 
 a law, which is the declaration of known relations, and 
 on the other hand from an hypothesis, which is an 
 assumption of unknown conditions. Indeed, it often 
 includes both laws and hypotheses, and attempts to 
 correlate them in a consistent system. The theories 
 of science are of the very greatest value, and chiefly 
 in two ways. 
 
 In the first place, a good theory has a very great 
 
214 VALUE OF THEORIES. 
 
 educational value. It classifies facts, it unfolds phe- 
 nomena in logical sequences, and exhibits events in 
 intelligible relations. As thus presented, the mind is 
 able to grasp the subject as a whole, to view it in 
 many relations, and through their relationships to 
 gain a command of a mass of facts which otherwise 
 the most retentive memory could not hold. We are 
 all acquainted with this use of theory. We know 
 how completely our working knowledge in almost 
 any department of learning is associated with the 
 system in which it was acquired, and many of us 
 know by experience how difficult it is to work with a 
 new system when the progress of knowledge demands 
 a change. Theories are thus necessities of our men- 
 tal constitution, and essential conditions of effective 
 thought. 
 
 In the second place, theories are of the very great- 
 est use in directing investigation, and in natural science 
 their efficiency in this respect is their chief merit. 
 The highest recommendation we can give to a system 
 of science is to say that it is a good working theory; 
 and in saying this we do not necessarily pass any 
 judgment on the credibility of the system as abstract 
 truth. As I shall soon show, we have good working 
 theories whose postulates cannot for a moment be 
 regarded as realities ; but so long as the theories 
 direct us to new discoveries it would be the height of 
 folly to abandon them simply because they cannot be 
 squared with our speculative philosophy. There has 
 been a great deal of misunderstanding on this point 
 which, in the interest both of religion and of sound 
 philosophy, ought to have been avoided. Sober- 
 
RESERVATION OF JUDGMENT. 21$ 
 
 minded men have been accused again and again of 
 being false to religion because they entertained theo- 
 ries which the Church at the time regarded as incon- 
 sistent with sound doctrine ; and, in defending their 
 position, I have known men of great power driven 
 into extreme positions by an intolerance which forced 
 a mental conflict where none need to have followed. 
 If in the study of nature there is one truth more than 
 another which it is important for the student to learn, 
 it is that in a great many cases reservation of judg- 
 ment is the only honest attitude of the mind ; and 
 that man is to be honored, and not persecuted, who 
 can use his theories for what they are worth and 
 keep his faith in eternal verities pure and radiant. 
 
 As we cannot expect a theory fully to harmonize 
 with our philosophy, so we cannot expect that its 
 predictions will always be verified. Of course the 
 failure of a theory to account for well-established 
 phenomena shows that either the theory or our 
 powers of deduction must be at fault; but this is no 
 reason for rejecting the system, until we can find a 
 better theory to take its place. How foolish it would 
 have been for Columbus to throw overboard his com- 
 pass-needles when he discovered that they did not 
 point exactly to the north star. Like all human in- 
 ventions, systems of science are imperfect; and we 
 must accept them for what they are worth, and use 
 them only so long as they give us essential help in 
 our search for knowledge. It has been repeatedly 
 the case in the history of science, that theories have 
 failed so completely to do their legitimate work that 
 they have been deposed and new theories enthroned 
 15 
 
2l6 HYPOTHETICAL MAGNITUDES. 
 
 in their place; but so intimately are theories asso- 
 ciated with our processes of thought, that the change 
 has usually been attended with an intellectual revolu- 
 tion. As I have shown in these lectures, it was so 
 when the Ptolemaic theory was set aside ; and we 
 have had a similar experience in chemistry since I 
 have been a teacher of the science. 
 
 We have said that a system of science might in- 
 volve postulates wholly inconsistent with sound phil- 
 osophy, and yet remain a good working theory; we 
 have now to add, what is still more surprising, that 
 such a theory may give us accurate measurements of 
 magnitudes which are wholly hypothetical, and of 
 whose relations we have otherwise no positive knowl- 
 edge. Such, for example, are the absolute lengths 
 of the so-called waves of light, and the relative 
 weights of the chemical molecules and atoms. There 
 cannot be a question that the values obtained are 
 real magnitudes; and, although we have made our 
 measurements in the dark and have not known cer- 
 tainly what we were measuring, yet the definiteness 
 of the results gives us the strongest assurance that 
 our theories contain an element of truth, although the 
 truth may be clothed with much error. 
 
 We have already seen what a mighty influence the 
 Ptolemaic system and the " Organon " of Aristotle 
 exerted over the intellectual world for more than a 
 thousand years ; and at the present day, besides the 
 many subsidiary theories, there are four great systems 
 of science which possess a similar authority. These 
 are the Theory of Universal Gravity, the Undulatory 
 Theory of Light, the Molecular Theory of Chemistry 
 
DOMINANT THEORIES OF SCIENCE. 2iy 
 
 and Physics, and the Theory of Organic Develop- 
 ment; and I propose in this lecture to show that 
 these famous systems of science exhibit in a most 
 striking manner the characteristic features of all 
 human theories to which I have referred. 
 
 In my last lecture I not only pointed out the clear 
 distinction between the law of gravitation and the 
 theory of universal gravity, but I also discussed some 
 of the incongruities which this assumed mode of 
 action presents, showing that the idea of independent 
 attractive forces exerted by separate particles of mat- 
 ter was not only inconsistent with the fundamental 
 conception of inertia, but also entirely out of har- 
 mony with our knowledge of other attractive forces, 
 like those exerted by electricity and magnetism. 
 Remember that each particle of matter of this earth 
 is assumed to attract each particle of the planet 
 Jupiter, each one every other, as if there were no 
 other material in the universe. 
 
 Now besides the improbability and incongruity of 
 such independent action, the whole idea is at utter 
 variance with a principle which in all philosophical 
 thought has always been regarded as a prime condi- 
 tion of every mode of action, and which is expressed 
 in the aphorism " Nulla actio in distans." This prin- 
 ciple has been universally recognized in other systems 
 of science. It was recognized by Newton himself in 
 his emission theory of light, which ascribed the lumi- 
 nous power to small projectiles darting through the 
 intervening space and carrying the energy from the 
 luminous body to the point of application; and to 
 these projectiles Newton gave form and imparted ro- 
 
2l8 THEORY OF UNIVERSAL GRAVITY. 
 
 tation in order to explain what he called " fits of easy 
 transmission" or reflection. The same philosophical 
 necessity for a medium of transmission led Huygens, 
 in framing his wave theory of light, to fill all space 
 with an elastic medium, through which the waves might 
 be propagated. This medium, which to his conception 
 was an indefinitely attenuated but highly elastic con- 
 dition of aeriform matter, as its name denotes, the de- 
 mands of modern science, as we shall soon see, have 
 converted into an adamantine solid. It was again the 
 same necessity of thought which, in a most memo- 
 rable investigation, led Faraday to search for the 
 medium through which electrical attractions and re- 
 pulsions are exerted, and to distinguish, as he did 
 with so much skill, the qualities and relations of the 
 dielectric. While, however, we have met the neces- 
 sity by interposing a medium through which a par- 
 ticle of sodium at the sUn sends to our spectroscope 
 an intelligible signal, that same particle is assumed 
 by the theory of gravitation to exert an attraction on 
 every particle of that instrument at the distance of 
 ninety millions of miles, not only independent of any 
 medium, but also irrespective of any conditions or 
 relations except mass. 
 
 Although I feel strongly the philosophical objec- 
 tion to the theory of gravitation which I have en- 
 deavored to present; and although I feel under the 
 constraint of the same limitations of thought to 
 which I have referred, — yet sometimes I cannot but 
 fear that we are influenced by the old aphorism more 
 than we ought to allow ourselves to be; and that, 
 after all, we may be but repeating the experience of 
 
NULLA ACTIO IN DISTANS. 219 
 
 the Aristotleans at the time of Galileo. Who can 
 question that Nature's abhorrence of a vacuum was 
 as much a philosophical necessity to them as " Nulla 
 actio in distans " is to us. Man cannot act where he 
 is not, or where he cannot reach, — although the elec- 
 trical nerves of modern science enable him to reach 
 across oceans and continents, and almost even to 
 clasp the globe itself. Moreover, on the earth we 
 cannot transmit energy without an adequate medium. 
 The falling water acts directly on the turbine, but 
 power cannot be transmitted from this water-wheel 
 to the spindle and looms except through adequate 
 shafting, pulleys, and belts. So also the power of 
 steam, however far the steam may be carried through 
 pipes, must do its work ultimately against the piston 
 of the motor. Even the more modern dynamo- 
 machine, by which power can be transmitted to 
 greater distances than by any other means, must 
 have a line of electrical conductors through which 
 the energy passes. In all these cases power is lost 
 in the transmission in such a way as to show that the 
 transmission takes place from point to point along 
 the line. All such analogies give a strong support 
 to the doctrine that no action can take place except 
 between contiguous masses; but should we not be 
 careful not to limit in our thoughts the possibilities 
 of nature by our own experience? It seems to me 
 that such an attitude of the mind is required by 
 philosophical sobriety; and although I have given 
 a very different interpretation to the seeming non- 
 conformity, it is possible that gravitation is the first 
 exceptional phenomenon which has shown the short- 
 
220 UNDULATORY THEORY OF LIGHT. 
 
 sightedness of our philosophy. Still the main fact 
 which I have been endeavoring to illustrate remains. 
 This grand theory of universal gravitation, from 
 which has been developed the wonderful deduc- 
 tions of modern astronomy, presents anomalies which 
 our philosophy has been wholly unable to reconcile. 
 
 Of the four great theories of modern science, the 
 one which is to me the most fascinating is the un- 
 dulatory theory of light. As a student of crystallo- 
 graphy and of crystal optics, I have been charmed 
 by the completeness with which it not only explains 
 the general order of these phenomena, but also pre- 
 dicts the magnitude, intensity, and other relations of 
 each minute detail. Moreover, the remarkable pre- 
 diction of conical fraction first made known on theo- 
 retical grounds by Hamilton, and afterwards verified 
 by Lloyd, will always be cited as one of the most 
 striking examples of the prescience of physical sci- 
 ence. Nevertheless, in spite of all its elegance and 
 efficiency, the undulatory theory of light is imperfect, 
 and demands postulates which even the wildest im- 
 agination cannot reconcile with common-sense. 
 
 The earlier exposition of the undulatory theory 
 was published by Huygens nearly contemporane- 
 ously with that of the emission theory by Newton ; 
 but although from the first much more elegant in 
 mathematical form, the theory of waves did not for 
 a long time acquire nearly as great authority as the 
 theory of corpuscles ; and even down to the middle 
 of this century the two theories were described as 
 rival systems in most text-books on optics. Sir 
 David Brewster, one of the most successful students 
 
NEWTON AND HUYGENS. 221 
 
 of optics in this century, who died in 1868, defended 
 the Newtonian theory to the last. Unquestionably, 
 the paramount authority of Newton in astronomy 
 gave greater weight to his hypothesis in optics than 
 it intrinsically merited ; for there are not to be 
 found in the whole history of science more elegant 
 demonstrations than those which Huygens originally 
 gave, deducing the fundamental principles of optics 
 from the theory of the wave motion, — such principles, 
 for example, as the rectilinear path of a beam of 
 light, the laws of reflection and refraction, and above 
 all, the phenomena of double refraction, then recently 
 observed by Erasmus Bartolinus in Iceland spar. 
 
 Huygens was undoubtedly led to his wave theory 
 by the analogy which the phenomena of light and 
 sound exhibit, and conceived of waves of light as 
 transmitted like waves of sound in the atmosphere, 
 only through a vastly more attenuated, but at the 
 same time more elastic, medium which he called the 
 " luminiferous ether." But in an aeriform medium, 
 elasticity, the force by which waves are transmitted, 
 can be developed only by compression. Of course 
 compression at one point must be attended by expan- 
 sion at contiguous points, and waves of sound consist 
 in alternating states of compression and expansion 
 spreading from every centre of disturbance. Such 
 alternating conditions must produce variations of 
 pressure at the surfaces which the medium touches, 
 and the phenomena of wave motion result from the 
 concurrence or interference of such partial effects, as 
 Huygens so beautifully showed. 
 Although the general order of the appearances 
 
222 OBSERVATION OF MALUS. 
 
 observed in the double refraction of light by Iceland 
 spar was beautifully explained by the wave theory of 
 Huygens, yet there remained certain features of this 
 striking phenomenon — described both by Huygens 
 and Newton — which were inexplicable until in 1810, 
 when Malus, while looking through a double refrac- 
 ting prism at the light of the setting sun reflected 
 from the windows of the Luxembourg Palace at 
 Paris, first observed the most fundamental of that 
 remarkable series of phenomena which he afterwards 
 developed and referred to what he called the " polar- 
 ization of light." Malus, who was a disciple of the 
 emission theory, ascribed all these effects to a po- 
 larity in the light-bearing corpuscles; and hence 
 arose a name which is meaningless, and indeed con- 
 fusing, on the basis of the theory of undulations. 
 As soon, however, as the new facts came to be 
 studied in the light of the undulatory theory, it was 
 seen that the essential feature of the condition which 
 had been called "polarization" was the transmission of 
 the luminous energy in a definite plane; and that the 
 elementary motions in that plane which constituted 
 the wave motion must take place at right angles to 
 the direction of the rays of light. These considera- 
 tions led to a profound alteration of the wave theory, 
 first recognized by Thomas Young, but afterwards 
 worked out with great ability by Fresnel. The wave 
 motion could no longer be regarded as transmitted 
 through an attenuated gas by the elasticity of com- 
 pression, and it became necessary to conceive of the 
 ether with parts held in definite relative positions, as 
 in a solid, through which the waves are transmitted 
 
ETHER OF SPACE. 223 
 
 by the elasticity of tension. In a word, the theory 
 now filled space with an attenuated solid, whose 
 parts are bound together far more firmly than those 
 of steel. 
 
 Consider now the apparently contradictory quali- 
 ties which it has been found necessary to attribute to 
 the ether of space, in order to explain the known 
 phenomena of light and heat. In the first place, as 
 the ether does not give rise to any sensible perturba- 
 tions in the motions of the heavenly bodies, we must 
 assume that it has no perceptible mass ; so that a solid 
 block of ether of the size of this room cannot weigh 
 more than a fraction of a grain. But while having 
 such an excessive tenuity, we must in the next place 
 assume that this singular solid consists of parts 
 bound together with such an incredible force that, 
 as the waves in passing through this medium tend to 
 part or force together the ultimate particles, the ac- 
 tion and reaction over each inch of surface must be 
 measured by millions on millions of pounds. 
 
 Why it is necessary to ascribe such an incredible 
 elasticity to the luminiferous ether will in general ap- 
 pear from two considerations. In the first place the 
 immense velocity of light requires this great elasti- 
 city. Assuming that two media have the same den- 
 sity, their elasticities are proportional to the squares 
 of the velocities with which a wave travels through 
 them. The velocity of the sound wave in air is 1100 
 feet a second, or about one fifth of a mile, and that of 
 the light wave about 183,000 miles a second, or 
 nearly one million times faster; so that in proportion 
 to its density the ether must have an elasticity a mil- 
 
224 TRANSMISSION OF POWER. 
 
 lion million times greater than air. In the second 
 place, this great elasticity is required in order to trans- 
 mit power from the sun. The earth is but one of a 
 number of great machines which are run by the sun. 
 There is no form of energy manifested on the earth 
 which cannot be traced to the sun. The sun is the 
 great motor from which all this power comes, just as 
 directly as the power which runs the spindles and 
 looms of a manufactory is transmitted by shafts, pul- 
 leys, and belts, from a turbine wheel in the basement. 
 Now these connections must be strong in proportion 
 as the power to be transmitted is great ; and so the 
 ether which transmits the power from the sun must 
 be strong enough to do the work ; and if you reduce 
 the material in it to next to nothing you must make 
 what is left proportionally strong, — that is, ascribe to 
 it this immense elasticity. Of course the imagination 
 knows no bounds, and you may ascribe to the ether 
 any extravagant relations you please ; just as you 
 can imagine materials so strong that the power of 
 Niagara could be transmitted with shafts no larger 
 than wires, and belts no larger than horse-hairs. 
 And if you are not to take into any account the har- 
 monies of nature, one supposition is as reasonable as 
 the other. 
 
 It is not, therefore, without reason that, following 
 the authority of Jevons, I have called the luminifer- 
 ous ether an adamantine solid ; and yet in the midst 
 of this adamantine mass we live and move without 
 perceiving the least resistance. In general two ex- 
 planations have been given to show how motion in 
 such a solid medium is possible. In the first place, it 
 
A SEMI-LIQUID. 
 
 --:> 
 
 has been suggested that the molecules of a body 
 may pass between the ultimate particles of the ether ; 
 just as a flock of birds, regarded as constituting one 
 mass, would pass between the branches of a forest, — 
 the body not displacing the ether but, as it were, pene- 
 trating it. I need not say that besides the difficulties 
 of conception, there are insuperable philosophical 
 objections to this view. The second suggestion is 
 that the ether is a semi-liquid, which, like pitch or 
 ice near the melting-point, has a great elasticity as- 
 sociated with an equally great degree of liquidity. 
 
 Ice, as is well known, flows down-hill in the glacier's 
 streams; and so will pitch, although masses of either 
 substance have marked elasticity, and will break with 
 a conchoidal fracture like glass. Now conceive of 
 the ether as pouring round a body, passing through 
 it, without a parting of the ultimate particles of the 
 medium, which continue to cling together with the 
 immense force I have mentioned, — and you have 
 the most recent conception that has been advanced 
 of the relations of this inconceivable material. But 
 obviously, such devices of the imagination do not in 
 the least degree remove the difficulty of the concep- 
 tion. Fundamentally, this difficulty consists in asso- 
 ciating great extremes of qualities which from our 
 experience seem to be incompatible. In ice or pitch 
 a very small degree of liquidity is associated with 
 elasticity of tension ; but in similar semi-liquids the 
 elasticity diminishes in proportion as the liquidity in- 
 creases, while in the ether we are asked to associate 
 indefinitely great elasticity with indefinitely perfect 
 liquidity. 
 
226 ' IRRECONCILABLE RELATIONS. 
 
 Such utterly incongruous and irreconcilable rela- 
 tions may not discredit a theory as a system of sci- 
 ence, but they must shake our faith in its credibility as 
 a reality of nature. As we have already said, there is 
 nothing in science so improbable, or so inconceivable, 
 that it may not be realized. With all the unknown 
 relations of nature it is not safe to say that anything 
 is impossible, unless it absolutely conflicts with funda- 
 mental laws. We are doubtless safe in expressing 
 the opinion that no form of matter or energy can be 
 produced without a corresponding expenditure ; and 
 that those who stake ventures in processes for making 
 materials or obtaining work from nothing are de- 
 luded ; but much further than this it is not safe to 
 prophesy. It is within our own experience that 
 steam navigation, ocean telegraphy, and electrical 
 lighting, were pronounced impracticable by men of 
 large knowledge and great intelligence; and we have 
 lived to witness their confusion in the accomplished 
 results. 
 
 In all such cases, however, when the improbable 
 has been once realized, it has been found to be in 
 harmony with the rest of our knowledge; and it has 
 been seen that the seeming incongruity arose from 
 our ignorance of general principles, or other links 
 through which the relationship became evident. 
 Therefore, while repeated experience of this kind 
 should make us cautious, it cannot but increase our 
 confidence in the general trustworthiness of the anal- 
 ogies by which the student of nature is so greatly 
 guided. But the same experience should also make 
 us duly sensible of the limitations of our knowledge, 
 
A REAL CORRESPONDENCE. 227 
 
 and inculcate largeness in thought and reservation in 
 judgment. 
 
 That such an adamantine medium as the ether of 
 our theories actually exists I cannot for a moment 
 believe ; but that the ether is our crude conception 
 of some reality which bridges the celestial spaces I 
 have no question. Perhaps in time the fulness of 
 knowledge will come; perhaps it is incomprehensible 
 to our limited faculties ; but that there is something 
 corresponding to the ether of our imaginings, I feel 
 as confident as that there is a solid crust of earth 
 under my feet. In some way illimitable power 
 crosses the immense gulfs of space ; and what we 
 catch glimpses of in the darkness, and try to express 
 in our material symbols — whose inadequacy appears 
 in the extravagances of our theories — is simply an 
 order of being recognized as fully in the infancy of our 
 race as now ; and of which it may be said as in the 
 days of Job : " Where is the way where light dwell- 
 eth? . . . Knowest thou the ordinances of heaven? 
 Canst thou set the dominion thereof in the earth?" 
 
 It is undoubtedly in consequence of the large ele- 
 ment of truth which the great systems of science 
 contain, in spite of all their philosophical absurdities 
 and formal inconsistencies, that they have led us in 
 several cases to a knowledge of magnitudes which, 
 although entirely beyond our powers of direct obser- 
 vation, have been measured with the greatest accuracy. 
 In the undulatory theory this is true in regard to 
 the lengths of the waves of light; and although there 
 is such large room for doubt in regard to the nature 
 of these magnitudes, our knowledge of their values is 
 
228 WAVES OF LIGHT. 
 
 so exact that it has been seriously proposed to use 
 them as standards of linear measurement. Remember 
 that the longest of the luminous waves only measure 
 1-39,000 of an inch — counted as with a water-wave 
 from crest to crest — and you can see what such a 
 proposition implies, and also what must be the order 
 of the unknown quantity which we are able to meas- 
 ure so accurately. And not only do we know the 
 values of those magnitudes, but we have followed out 
 their relations through most intricate conditions, and 
 found our deductions most completely verified at 
 every step of our inquiry. That these values are 
 the magnitude of real things, we can have no more 
 question than that the measurements given by Piazzi 
 Smyth, in his work on the Egyptian Pyramids are 
 the dimensions of actual blocks of stone, however 
 much archaeologists may question this learned as- 
 tronomer's theory in regard to the purposes for 
 which these blocks were originally wrought. 
 
 But besides presenting in its postulates the philo- 
 sophical and formal incongruities I have pointed out, 
 the undulatory theory is by no means perfect in its 
 appropriate relations ; for there is a most important 
 and conspicuous class of optical facts which it has 
 as yet essentially failed to explain. I refer to the 
 beautiful phenomena on which spectrum analysis is 
 based. Newton's earliest experiment, in which he 
 separated the colored rays composing white light 
 by means of a glass prism, still challenges the 
 undulatory theory. I have already referred to the 
 remarkable investigation of Cauchy on this very 
 point, which has been justly regarded as a monument 
 
THE DISPERSION OF LIGHT. 229 
 
 of mathematical skill ; but this investigation wholly 
 failed in its main purpose. The most that Cauchy 
 accomplished with his profound mathematical anal- 
 ysis was to show that such effects might follow from 
 wave motion on certain assumptions in regard to 
 the molecular structure of the dispersing media; so 
 that when our knowledge of molecular structure is 
 more complete, the undulatory theory may possibly 
 be able to explain the phenomena in question. He 
 did not in any proper sense bring the phenomena of 
 dispersion under the control of the theory; and to 
 the average student they remain to the present day 
 as inexplicable as ever. If, however, Cauchy's anal- 
 ysis gives us good reason for expecting that with 
 larger knowledge we may be able to include the 
 phenomena of dispersion in our system, there are 
 also equally strong grounds for the opinion that 
 before this can be done the present undulatory 
 theory must be profoundly modified. 
 
 I fear that in thus dwelling on the inconsistencies 
 and imperfections of the undulatory theory, it may 
 seem as if I were aiming to discredit the system ; 
 when on the contrary I desire to exalt it. The last 
 word has always such undue force that, to avoid mis- 
 apprehension, it is almost necessary to reiterate the 
 opinion I expressed at first, — that the undulatory 
 theory of light is one of the noblest creations of 
 science, one of the greatest achievements of the 
 human intellect, and that its value can not be over- 
 estimated. I believe that the system is no more 
 imperfect than is necessarily implied in saying that 
 it is a product of human thought, that it involves 
 
230 THE MOLECULAR THEORY. 
 
 human conceptions, and must necessarily be subject 
 to human limitations. My aim has been to exhibit 
 the system in its true relations, and to show that we 
 must be content to use it for what it is worth, and 
 not expect to reconcile it at all points with either 
 our speculative opinions or our limited experience. 
 
 We come now to the third of the three great sys- 
 tems of science which we have called the Molecular 
 Theory, and this presents two very distinct aspects, 
 according as we study the theory from a physical 
 or from a chemical standpoint. On certain features, 
 however, both the physicists and the chemists agree. 
 By students of both classes the mass of material 
 bodies is regarded not as uniformly and continuously 
 distributed through the spaces they seem to occupy, 
 but as segregated into an innumerable number of 
 excessively minute masses called " molecules," each 
 of which is a separate unit, — as much so as a planet. 
 
 There must be as many different kinds of molecules 
 as there are distinct substances, but all the molecules of 
 the same substance — as, for example, the molecules 
 of water — are assumed to be the exact counterparts 
 of every other. Of the absolute size of the molecules 
 we can only form a very rude estimate, but the esti- 
 mates made in different ways quite closely agree, and 
 a conception of the order of magnitudes with which 
 our theory deals is best given by means of the illus- 
 tration already cited, which we owe to Sir William 
 Thompson, who said that if a drop of water were 
 magnified to the size of the earth, and the molecules 
 of water magnified in the same proportion, they 
 would certainly appear larger than " marbles," and 
 
HEAT A MODE OF MOTION. 23 1 
 
 smaller than cricket-balls. Wonderfully small as 
 these magnitudes must be, the theory does not on 
 this account present any insuperable difficulties of 
 conception ; for it only asks us to believe in a micro- 
 cosmos beneath us, in some measure comparable 
 with the macrocosmos which astronomy has shown 
 to exist above us. The difficulties appear when we 
 come to consider the attributes and relations which 
 our theory compels us to ascribe to these minute 
 masses. 
 
 In physics the molecules are regarded as the 
 points of application of forces ; as for example, when 
 a body is expanded, melted, or volatilized by heat. 
 Indeed, limiting our attention in this direction to 
 thermal phenomena, heat itself is regarded as mo- 
 lecular motion, and it is an established fact that a 
 given quantity of heat corresponds to a definite 
 amount of mechanical work. On the molecular 
 theory, quantity of heat means simply quantity of 
 molecular motion, and temperature is the average 
 moving energy of individual molecules. Molecular 
 and mechanical motion are interchangeable. When 
 a cannon-ball strikes a target and buries itself in the 
 iron plate, the increased temperature of the united 
 metallic masses is the result of the transfer of the 
 motion of the ball, as a whole, to the molecules of 
 which both ball and target consist ; and on the other 
 hand, the piston of a steam-engine receives all its 
 power from the molecules of steam which rebound 
 from its surface. 
 
 Sir William Thompson used the word " atoms," 
 meaning the units which chemists now distinguish by 
 16 
 
232 THE THEORY RESTS ON ANALOGY. 
 
 the word "molecules;" but both atoms and mole- 
 cules are of the same order of magnitude. 
 
 Motion is thus transferred between large and small 
 masses indifferently, as it would be transferred be- 
 tween two elastic billiard-balls ; and indeed the well- 
 known laws of collision between elastic bodies were 
 the basis of the analogy which led to the molecular 
 theory. But in transferring our conceptions from 
 ivory balls to molecules we are obliged to call on the 
 imagination to take one of those extreme flights 
 which all similar theories demand. Balls of ivory or 
 steel, although made of the most elastic materials 
 with which we are acquainted, would very soon come 
 to rest in knocking about among each other ; but our 
 molecules must be so perfectly elastic that though 
 each one makes millions of collisions every second, 
 yet throughout all time no moving power is lost. 
 
 If we think only of their minuteness, the moving 
 power of molecules may seem insignificant; but the 
 molecules are as numerous as they are small, and 
 their aggregate moving power is enormous. When 
 a quart of water is heated from the freezing to the 
 boiling point, as in the familiar process of boiling a 
 teakettle, an amount of moving power is imparted to 
 the molecules of water which, if transferred to a 
 pound cannon-ball, would impart to it an initial ve- 
 locity of 4,715 feet a second. 
 
 In a solid body the molecular motions are limited 
 by the various forces which determine its structure, 
 and are supposed to be restricted to a definite orbit. 
 In a liquid the motion is less constrained, but is lim- 
 ited by the boundaries of the liquid mass. In a gas, 
 
SUCCESS OF THE THEORY. 233 
 
 however, the molecular motions are supposed to be 
 entirely free, limited only by mutual collisions, or by 
 the walls of the containing vessel. In both solids 
 and liquids the relations are both so complex and 
 obscure that the molecular theory has not been able 
 to solve, except to a very limited extent, the difficult 
 problems which they present; but with aeriform 
 matter the theory has been far more successful, and 
 gives a very satisfactory explanation of most of the 
 observed phenomena. The tension or pressure ex- 
 erted by a gas is the effect of molecular bombard- 
 ment; and the well-known laws of Mariotte, of Charles, 
 and of Avogadro, which define the condition o( aeri- 
 form matter have been shown to be necessary con- 
 sequences of the molecular theory. 
 
 Like the modulatory theory, the molecular theory 
 has also led us to a knowledge of magnitudes which 
 must ever evade our senses, and which almost defy 
 our imagination. Thus we can calculate with great 
 accuracy the average velocity of the molecular mo- 
 tion in any gas under given conditions, — that in 
 hydrogen gas at the freezing-point, for example, being 
 6,099 f ee t m a second. And what is still more singu- 
 lar, we can calculate the average number of collisions 
 per second, as well as the average length of the mo- 
 lecular path between two successive collisions, of 
 course under definite conditions. In hydrogen gas, 
 under the standard conditions of temperature and 
 pressure, each molecule strikes against its fellows 
 17,750 million times a second; and the average mo- 
 lecular path is only 3 1 ten-millionths of an inch. This 
 last seems incredibly small, but it is at least 136 
 
234 DIFFICULTIES OF CONCEPTION. 
 
 times the average distance between two molecules ; 
 and in an assembly of men such an allowance would 
 be regarded as very liberal. 
 
 These few data, which might be greatly multiplied, 
 will show how definite are the conceptions which the 
 molecular theory involves ; and my brief description 
 will give some idea, although very imperfect, of the 
 scope of the theory itself. I can only add that in its 
 relations to aeriform matter the theory has been de- 
 veloped mathematically by such men as Rankine, 
 Clausius, and Maxwell ; and that it gives a satisfac- 
 tory account of the efficiency and mode of action of 
 all thermo-motors, which, like the steam-engine, are 
 such important factors in our civilized life. 
 
 But while in that special field known as the " kin- 
 etic theory of gases," the molecular theory is one of 
 the best elaborated systems of modern science, it 
 involves difficulties of conception fully as great as 
 those we met in connection with the undulatory the- 
 ory of light. Not only must we ascribe to the mole- 
 cules a perfection of attributes, like perfect elasticity, 
 which we only find in material bodies to a very 
 limited degree, but also we must associate together 
 attributes which from our experience seem to be in- 
 compatible. We must, in a word, give up all our or- 
 dinary prepossessions, and accept provisionally what 
 seem to us monstrous hypotheses because they ex- 
 plain facts and relations which would be otherwise 
 isolated phenomena, and because they are parts of a 
 system which as a whole is a good working theory. 
 
 Having discussed similar difficulties of conception 
 in the undulatory theory of light, it is unnecessary for 
 
CHEMICAL ASPECTS OF THE THEORY. 235 
 
 me to dwell on the corresponding features in the sys- 
 tem now before us. They obviously result from the 
 same incompleteness of knowledge, and teach the 
 same lessons already sufficiently enforced. Any one, 
 however, who desires to study the details, will find 
 them very clearly stated by J. B. Stallo, in his admir- 
 able book on "The Concepts and Theories of Modern 
 Physics," — a volume of the International Series to 
 which I take great pleasure in referring. 
 
 I wish next to ask your attention to the chemical 
 side of the molecular theory ; for it is in this direc- 
 tion that it has run into the greatest extravagances ; 
 and yet, singular as it may seem, it is just here that 
 it has proved of the most value as a working theory. 
 In addition to molecules, the chemist is obliged to 
 distinguish a still smaller subdivision of matter, which 
 he calls " atoms." The ultimate analysis of the physi- 
 cist goes no further than molecules; but the ultimate 
 analysis of the chemist breaks up the molecules and 
 gives us atoms. There must be as many kinds of 
 molecules as there are distinct substances ; but only 
 as many kinds of atoms as there are elementary sub- 
 stances, some seventy at most. In a physical change 
 in which the distinctions of substance remain unaltered 
 the integrity of the molecules is preserved ; but in a 
 chemical change, which necessarily involves a change 
 of substance, the molecules are broken up, and the 
 atoms regroup themselves to form the molecules of 
 the resulting products. 
 
 Thus when water is converted into steam, the mole- 
 cules of water remain unchanged, and are only driven 
 more widely apart; but when under the action of an 
 
236 THE CHEMICAL MOLECULE. 
 
 electric current water yields oxygen and hydrogen 
 gases, the molecules of water are broken up into 
 atoms of oxygen and hydrogen, which regroup them- 
 selves to form the molecules of these aeriform 
 products. 
 
 In fact the chemist regards the molecule in quite 
 a different light from the physicist. To the latter, 
 molecules are chiefly centres of force ; while to the 
 chemist they are more or less complex structures on 
 which depend the distinctions and relations of sub- 
 stance. The qualities of substances are all referred 
 to the molecules. The properties which distinguish 
 water from alcohol, or sugar from salt, depend, not 
 on the relations of any perceptible masses of these 
 substances, but ultimately on the constitution of their 
 molecules. Divide up a lump of sugar, and you may 
 still distinguish the qualities of sugar in the smallest 
 visible particles ; but the chemist declares such a sub- 
 division could not be carried on indefinitely, even if 
 our senses could follow it. We should soon come to 
 the smallest possible mass of sugar, which on push- 
 ing our subdivision further would break up into atoms 
 of carbon, hydrogen, and oxygen, three well-known 
 chemical elements. This smallest possible mass of a 
 substance is the chemist's molecule; and hence his 
 definition, — " the smallest mass of a substance which 
 can exist by itself." 
 
 The forces which bind together atoms into mole- 
 cules we distinguish as chemical forces, while such 
 as determine the aggregation of molecules to form 
 material masses are said to be physical, although we 
 have no sufficient reason for assuming that there is 
 
DISSOCIATION. 237 
 
 any essential difference between the two ; and all such 
 forces, whatever may be their nature, are overcome 
 by heat. At the intensely high temperatures which 
 rule at the sun or at the fixed stars, it is supposed 
 that the elementary atoms are isolated and intermin- 
 gled, if not still further resolved ; and as in the pro- 
 cess of evolution of our system the planetary masses 
 have cooled, it is held that the atoms have united to 
 form the molecules of various substances, and that 
 similar molecules have then aggregated to form defi- 
 nite material products. When, now, on the surface of 
 the earth we heat such materials to the highest tem- 
 peratures we can command, the process of world- 
 building is to a limited extent reversed, presenting 
 us with a remarkable class of phenomena known as 
 dissociation. But why in the process of evolution 
 unlike atoms should unite by preference to form 
 molecules, while in the further aggregation to form 
 material products only like molecules should asso- 
 ciate together, remains an unexplained enigma. 
 
 A confusion often arises from the use of the word 
 " elementary" in connection with substances as well as 
 with atoms. The atoms are the only true chemical 
 elements. An elementary substance like oxygen gas, 
 sulphur, or iron, is an aggregate of molecules like 
 any other substances, and externally presents no 
 characters by which it can be recognized as elemen- 
 tary. But on analysis we find that its molecules are 
 formed by the union of atoms of the same kind only, 
 while the molecules of compound substances consist 
 of atoms of different kinds. The molecules of oxygen 
 gas, for example, are aggregates of atoms, as well as 
 
238 PHILOSOPHY OF CHEMISTRY. 
 
 the molecules of water ; but while the first consist of 
 oxygen atoms only, the second contain atoms of 
 hydrogen united to the atoms of oxygen. 
 
 Upon the distinction between atoms and molecules 
 the philosophy of modern chemistry rests, and its 
 symbolical language is based. Each one of the 
 seventy chemical symbols stands for an atom. By 
 grouping these symbols together, like letters to form 
 a word, we represent the infinite possible varieties of 
 molecules ; and then all chemical changes are repre- 
 sented by an equation, writing the symbols of the 
 substances concurring to produce the change in the 
 first member, and the symbols of the substances 
 resulting from the change in the second member. 
 Such an equation declares that the process consists, 
 as already said, in the breaking up of the so-called 
 factors into atoms, and the regrouping of the result- 
 ing atoms to form the molecules of new substances, 
 the products. 
 
 In the vapor of mercury immediately above the 
 boiling-point, the atoms appear to be completely dis- 
 sociated, so that this aeriform substance must be re- 
 garded as a mass of isolated atoms ; but this is a very 
 exceptional condition on the surface of the earth. In 
 a few of the elementary gases or vapors, and in some 
 of the simpler compounds, we are able to recognize 
 — when the substances are aeriform — molecules con- 
 sisting of only two or three atoms. But the molecules 
 of most bodies are far more complex; and although 
 as the complexity increases, our confidence in our 
 inferences diminishes, yet with a considerable degree 
 of confidence we can say that the molecules of some 
 
MOLECULAR STRUCTURE. 239 
 
 of the most familiar materials are aggregates of more 
 than a hundred of these assumed ultimate elements 
 of matter. 
 
 It was formerly thought that the qualities and 
 chemical relations of a substance depended on the 
 nature of the elementary atoms of which its molecules 
 consisted, and resulted from a blending of the quali- 
 ties of the chemical elements in some mysterious 
 way ; but we now recognize that the chemical prop- 
 erties of substances depend in great measure, at least, 
 on the manner in which the atoms are grouped in 
 their molecules ; and the order in which the different 
 atoms are grouped in the molecules of substances is 
 not only a legitimate object of inquiry, but is a sub- 
 ject which has nearly engrossed the attention of the 
 chemists of the world for the past twenty-five years. 
 
 It would be impracticable in this course of lectures 
 to give any clear conception of the nature of the 
 evidence on which our knowledge of the atomic 
 structure of molecules is based, or of the course of 
 reasoning by which the accepted conclusions have 
 been established. The subject is abstruse, and could 
 not be made intelligible without entering largely into 
 the details of chemistry. 1 In any modern work on 
 organic chemistry, you can see our conceptions of 
 the atomic structures of the molecules of various 
 substances exhibited by placing the atomic symbols 
 in definite relations to each other and connecting 
 them by dashes supposed to represent the atomic 
 
 1 I have endeavored to present the subject in a popular form 
 in my " New Chemistry," and to that book I must refer any one 
 who desires such information. 
 
240 
 
 STRUCTURAL FORMULAE. 
 
 bonds. Such graphic representations are called struc- 
 tural formulae, and are supposed to show at least the 
 order in which the several atoms are united in the 
 molecule. A single example of a structural formula 
 will suffice as an illustration : — 
 
 II 
 
 H 
 
 
 
 
 H 
 
 H 
 
 
 
 
 C 
 
 r, \ 
 
 C 
 
 C 
 
 x c c 
 
 
 c 
 
 c 
 
 c c 
 c 
 
 \ 
 
 o c 
 c 
 
 c 
 c 
 
 H 
 
 
 
 H 
 
 O' 
 
 H 
 
 II 
 
 Alizarine. 
 
 To one who realizes what is thus represented, but 
 who is not familiar with the evidence, or imbued 
 with the spirit of the matter, it must seem incredible 
 that these apparently fanciful groupings should be 
 sober results of science; and yet a reason can be 
 given for the position of every symbol and of every 
 dash, which — if the postulates are granted — must 
 be admitted to be cogent. Moreover — what is the 
 more remarkable fact — by following out the indica- 
 tions of such structural formulae chemists have suc- 
 ceeded in preparing artificially a very large number 
 of exceedingly complex compounds whose produc- 
 tion under such circumstances could not but inspire 
 the greatest confidence in the general correctness 
 of the reasoning on which the structural formulae 
 were based. Some of these products, like alizarine, 
 
CONVENTIONAL SYMBOLS. 24I 
 
 the coloring- matter of madder-root, — now prepared 
 artificially from anthracene, one of the constitu- 
 ents of coal tar, — have such great commercial im- 
 portance that these theoretical investigations have 
 completely revolutionized large branches of human 
 industry. Indeed if certainty of prediction is to be 
 regarded as the test of validity, there is not one of 
 the great systems of science, excepting the the- 
 ory of gravitation, which has so completely vindi- 
 cated its legitimacy as has this molecular theory of 
 chemistry. 
 
 But although our structural formulae have this 
 wonderful power of prediction, and are therefore of 
 the highest value as a system of science, yet no 
 philosophical chemist thinks of regarding them as 
 more than conventional symbols of relations which 
 are at present incomprehensible. I would urge this 
 point with special emphasis; because, although the 
 same feature appears, as I have shown, in connection 
 both with the theory of gravitation and with the un- 
 dulatory theory of light, it has been said that the 
 difficulties of conception, which an inherent gravitat- 
 ing force or an adamantine ether present are of no 
 weight in view of the so general accordance of these 
 theories with observed facts. In the present case no 
 such claim can for a moment be maintained. All the 
 conceptions are 'obviously conventional ; and yet we 
 have the same wonderful gift of prophecy. Is not 
 the lesson plain? Man must work under limitations; 
 he must often be content with the shadow instead of 
 the substance of realities; but he may with confi- 
 dence follow his earth-born systems of philosophy, if 
 
242 THEORY OF ORGANIC DEVELOPMENT. 
 
 only they are grounded on experience and estab- 
 lished in loyalty to truth. 
 
 And if this course of conduct be safe and legiti- 
 mate in one realm of thought it certainly must be 
 equally so in every other. Spiritual experience can 
 be no exception to the general principle. 
 
 " Finding, following, keeping, struggling, 
 Is He sure to bless ? 
 Saints, apostles, prophets, martyrs 
 Answer, ' Yes.' " 
 
 Of the four great dominant systems in modern 
 science to which I referred at the opening of this 
 lecture I have as yet spoken of but three. The fourth 
 during the last twenty-five years has attracted more 
 attention than all the rest combined, and is insepara- 
 bly associated with the name of that chief of natural- 
 ists, Charles Darwin. All these systems have been in 
 their turn the subject of controversy; and too often 
 the introduction of irrelevant theological issues has 
 added acrimony to the debate. I say irrelevant be- 
 cause, if the position I have taken in regard to the 
 relations of scientific systems to actual knowledge be 
 correct, there can be no real issue between theology 
 and the theories of science, — any more than between 
 theology and the theory of music. In my view of 
 the subject it is as useless to seek for theological an- 
 tagonism in Darwinism as it would be to look for it 
 in the Calculus. 
 
 In regard to the other systems, whatever differ- 
 ences of opinion may remain, all feeling about the 
 matter has long since disappeared ; but in regard to 
 Darwinism, while the blaze of theological protest with 
 
POSTULATES OF DARWINISM. 243 
 
 which the theory was first received has died down, 
 the embers of the excitement still remain; and it is 
 more difficult to discuss the subject dispassionately. 
 In another place I have before strongly urged the 
 irrelevancy of theological issues on this question; 
 and I will only add here a few remarks, which may 
 be deemed pertinent because showing how the subject 
 is viewed by a student familiar with the bearings and 
 use of theories in a very different department of 
 science. Further than this I do not feel that it is 
 within my province to discuss the subject; for my 
 special studies have been limited to a very different 
 field ; and I have not that detailed knowledge which 
 alone would entitle me to express an authoritative 
 opinion on the merits of the system. 
 
 The theory of Darwin rests on three distinct postu- 
 lates. The first is that the existing species of plants 
 and animals are not independent creations, but the 
 results of a gradual evolution from earlier forms. 
 The second is that while in the provisions of nature 
 for the propagation of all living beings there is evi- 
 dently a strong striving for the conservation of types, 
 there is also a manifest tendency to variation, which 
 although barely perceptible in single steps may go 
 on increasing in successive generations to an unlim- 
 ited extent. The third is that in the struggle for 
 existence those variations are preserved which are 
 best adapted to the environment, and which therefore 
 protect the individuals possessing them in the midst 
 of the terrible mortality which the struggle for exist- 
 ence entails. 
 
 However many facts or considerations may be 
 
244 ANTIQUITY OF MAN. 
 
 urged in their support, there is not one of these 
 propositions which has been demonstrated beyond 
 reasonable doubt ; so that this theory, like the other 
 great theories of science, rests on hypotheses, and 
 must be judged as a scientific system by the com- 
 pleteness with which it explains the phenomena of 
 nature. 
 
 In regard to the first proposition it seems strange 
 that with all the attention which has been directed to 
 the point during the last twenty-five years the fact of 
 a transition between two well-marked species has not 
 yet been established conclusively. For, admitting 
 all that has been said in regard to the slowness of 
 the transition, or the imperfection of the geological 
 record, yet considering the extent of the field that 
 has been surveyed, it seems very strange that more 
 of the missing links have not been found. We can 
 point with great precision to definite geological hori- 
 zons — to use a now familiar technical term — on 
 which certain species of well-marked types appeared 
 on earth; and certainly, on the hypothesis we are 
 considering, it is strange that we can in no case point 
 unhesitatingly to other species in lower strata from 
 which they descended, on the evidence of an un- 
 broken series of the intermediate forms between 
 the two. 
 
 Take the case in which we are the most interested, 
 that of our own race. Assume all that is claimed 
 in regard to the antiquity of man. Still, there is a 
 definite horizon of the tertiary epoch below which 
 man is not, but above which his remains are found 
 in ever increasing abundance, with all the features 
 
GROWTH THE ORDER OF NATURE. 245 
 
 of man and his works as strongly marked as they 
 are to-day. Skeletons of these primeval men, and 
 their belongings, are to be seen in our ethnological 
 museums; and there are no greater differences of 
 structure between them and ourselves than between 
 the different races which inhabit the earth at the 
 present day. But if man be descended from "an 
 anthropoid animal of arboreal habits," it is passing 
 strange that so far as any direct evidence goes, he 
 should have appeared on the earth thus suddenly, 
 and that we can find no traces of his progenitors 
 either of the first, second, third, or of any other 
 generation. 
 
 Nevertheless, the hypothesis of a gradual genesis 
 of organic types seems to me not only reasonable 
 in itself, but also in harmony with what we know of 
 nature's workings. Growth, and not spasmodic ef- 
 fort, is the usual order of the divine government 
 both in the material and in the spiritual world ; and, 
 reasoning from analogy, it is the method by which 
 we should expect a new race of plants or animals 
 would be introduced into the world. Indeed, from a 
 scientific point of view any other mode is wholly un- 
 thinkable. Conceive of an elephant suddenly appear- 
 ing in a tropical jungle, like a jack in a box, without 
 any antecedents except a fiat; and see if the thought 
 does not put to confusion every dictate of your expe- 
 rience, and every principle of your intelligence. You 
 will then clearly see that if by mortifying reason the 
 doctrine of independent creations can be accepted 
 as a wonder, it cannot possibly be reconciled with 
 the rest of your knowledge. Attempt further to 
 
246 QUESTION OF INTERPRETATION. 
 
 realize in imagination the genesis of the first man. 
 Was he suddenly created in his full development 
 and strength, prepared to subdue nature? or did he 
 come into the world as an infant, as have come 
 all of his race since, — even the Saviour of the 
 world? 
 
 Do not deem such questions irreverent. They are 
 asked in that spirit of truth and soberness which 
 sanctifies any inquiry. They ought not to be further 
 pushed in this place ; but the suggestions they make, 
 if followed out in your own reflections, will bring you 
 to the point of view from which a naturalist is com- 
 pelled to look at the question of the origin of spe- 
 cies. Roman mythology provided the heaven-born 
 founders of their state with a foster-mother; and it 
 is a similar necessity of thought which has led to 
 what is usually regarded as the most objectionable 
 feature of Darwinism. And apart from the au- 
 thority of any undoubted declaration to the con- 
 trary, why should we be shocked by the hypothesis 
 here involved? 
 
 On the other hand, it may be said, You admit that 
 any prodigy must be accepted in science on ade- 
 quate evidence ; why not then receive the plain doc- 
 trine of independent creations taught by the Hebrew 
 Scriptures? To this the Christian naturalist replies 
 that all such inferences from the Scriptures must be 
 to a very great extent questions of interpretation; 
 and that in this case, as in so many instances before, 
 the interpretation will be reconciled with the facts as 
 soon as the truth plainly appears. And in the sec- 
 ond place, he will add that while in science no won- 
 
POSSIBILITY OF INTERFERENCE. 247 
 
 der is so great that it may not be realized, so also 
 no marvel is so sacred that it may not be reverently 
 investigated ; and that, whatever the event, the show- 
 ing forth of the truth can only redound to the glory 
 of God. Again, he may urge that this is a question 
 between the interpretation of Nature on one side and 
 of Scripture on the other, and that it ought not to 
 be prejudged by assuming the infallibility of our ren- 
 dering .of either of these two co-ordinate authorities. 
 
 Moreover, this is not a question of creative power 
 nor of Divine Providence. After all has been granted 
 that any one can claim in regard to the constancy of 
 the laws which we fully understand, there is, as has 
 been plainly shown, abundant room left for interfer- 
 ence; and it is more consistent with our conceptions 
 of the Divine method to suppose that God works by 
 introducing new conditions into old chains of causa- 
 tion than by spasmodic acts of creation, which must 
 inevitably confuse and confound the intelligences 
 he holds so dear. That such interference has taken 
 place, it seems to me that the transition from a geo- 
 logical to an archaeological museum as plainly shows 
 as any record can whose meaning has been left to 
 human interpretation. And when with every Yule- 
 tide the Christ Child becomes the emblem of all 
 that is lovely, pure, and holy, why should we be 
 alarmed at the supposition that as the Child of 
 Mary "grew and waxed strong in spirit" so in the 
 beauty of innocence, human intelligence at first slowly 
 awakened to the wonders of this earth ? 
 
 In regard to the second postulate on which Dar- 
 winism rests, we must admit that this also is to a great 
 17 
 
248 EVIDENCE INCONCLUSIVE. 
 
 extent in harmony with well-established facts. No 
 one can study the aspects and characters of a family 
 of children without being struck with the undoubted 
 truth that while minute details of features both of 
 body and mind are wonderfully preserved, striking 
 variations from the parent type are equally conspic- 
 uous. The same is seen to be even more markedly 
 true of the lower animals when we watch them as 
 closely ; and when we think of it, the wonder is that 
 the variations are not greater than they are. 
 
 There is nothing in our actual knowledge of na- 
 ture which makes it any less strange that an acorn 
 should always grow into an oak than that a race 
 of monkeys after unnumbered generations should 
 assimilate to men ; and we know of no reason what- 
 ever why, with an equal experience, one change 
 should not appear as natural as the other. Indeed 
 I feel confident that, with all our knowledge of em- 
 bryology, any one who reflects on the mysteries 
 which the beginnings of life both in plants and ani- 
 mals present, will conclude that it is a far more re- 
 markable fact that every creature should produce of 
 its kind, than that occasional variations should occur. 
 Nor is there any reason why we should be surprised 
 to learn that in successive generations the variations 
 should become cumulative, and lead to such a de- 
 parture from the original type as to amount to a 
 difference of species. 
 
 As before said, however, it is strange that the 
 evidence of such a transition is so limited and incon- 
 clusive ; and moreover, as was so strongly urged by 
 the late Professor Agassiz, that the variations pro- 
 
NATURAL SELECTION. 249 
 
 duced by domestication — which have been so care- 
 fully studied by the propagators of plants, and the 
 breeders of stock — all tend to revert to the original 
 wild condition. 
 
 Coming lastly to the third postulate, we find in this 
 also a general principle which appears to a student 
 of nature highly plausible. The struggle for life 
 among the lower animals is a condition, the violence 
 and destructiveness of which is wholly unappreciated 
 except by those who have made a special study of 
 the subject. The survivors of this internecine war- 
 fare who finish their allotted span of life are fre- 
 quently not one in a hundred, often not one in a 
 thousand. Tennyson quite understates the condition 
 when he speaks of — 
 
 " finding that of fifty seeds 
 She often brings but one to bear." 
 
 Even in our own race the mortality is frightful to con- 
 template, — as Malthus has so vividly depicted it in 
 his great work on population. Professor Wallace, who, 
 independently of Darwin, and almost at the same 
 time, originated the doctrine of natural selection, has 
 distinctly said that it was the work of Malthus which 
 gave him the key to the problem; and it is well 
 known that Darwin himself was also strongly influ- 
 enced by the facts so powerfully set forth in that re- 
 markable book. I only repeat what some of you must 
 have heard from Professor Wallace's own lips when 
 I say that until one realizes the prodigal destruc- 
 tiveness of nature it is impossible to appreciate the 
 strength of the doctrine of natural selection. Wallace 
 also has stated that the generalization came to him as 
 
2 50 ADAPTATION TO THE ENVIRONMENT. 
 
 a sudden thought, — when, overpowered with what 
 he was constantly witnessing in the East Indies, he 
 stopped to reflect on the necessary issues of such 
 fearful mortality. The "survival of the fittest" was to 
 him a fact of observation; and by the indiscriminate 
 slaughter of all others, a selection was seen to be 
 made of those creatures whose features best fitted 
 them to cope with their surroundings. The conclu- 
 sion was that any accidental variation in color or 
 form which better equipped the animal for the in- 
 evitable fight must be preserved ; and that thus came 
 the gradual adaptation to the environment in which 
 natural selection consists. 
 
 All this is plausible, and to most naturalists con- 
 clusive ; and that the struggle for existence must 
 tend to perpetuate varieties seems to be beyond 
 question. It still remains, however, to determine 
 how far variations thus caused can proceed ; and 
 whether they can ever lead to fundamental differ- 
 ences of type. The assumption that all forms of 
 plants and animals may have been thus produced 
 from a few germs is as yet an hypothesis, to be 
 judged, like any other hypothesis, by the extent to 
 which it explains and correlates facts. Let it not be 
 prejudged on any theory of Divine government, or 
 on the basis of any speculative views about the na- 
 ture of causation ; for, were the hypothesis estab- 
 lished without reservation, — a most improbable event, 
 judging from the past history of science, — the new 
 truth would only serve to enlarge our views of the 
 mode of the Divine government ; and there is abun- 
 dant room for causation left. 
 
VALUE OF THE THEORY. 25 I 
 
 Assume that the variations preserved by natural 
 selection are all accidental, a point on which natu- 
 ralists greatly differ, still what is the result? An 
 adaptation to the environment. According to the 
 theory, then, the conditions of the environment are 
 a determining cause ; and unless we believe that all 
 nature was the result of a fortuitous concourse of 
 atoms, we can find in these conditions abundant 
 opportunities where intelligent causation can act. 
 And the thought which the terrible facts implied in 
 our theory force on the mind, are they not wholly in 
 harmony with what we believe in regard to the Di- 
 vine plan? Everywhere in this world are not benefi- 
 cent results worked out through suffering? And to 
 the lines of the English poet which I have just 
 quoted, must I not add the anti-strophe from pre- 
 ceding stanzas? — 
 
 " O yet we trust, that somehow good 
 Will be the final goal of ill, 
 To pangs of nature, sins of will, 
 Defects of doubt and taints of blood. 
 
 " That nothing walks with aimless feet, 
 That not one life shall be destroyed, 
 Or cast as rubbishto the void, 
 When God hath made the pile complete." 
 
 Finally, looking at the Darwinian theory of devel- 
 opment for a few moments as a whole, I would re- 
 mark that it has not the completeness of the other 
 dominant theories of science; and that the modes of 
 action which it predicates have not been worked out. 
 It is a doctrine rather than a complete system of 
 science. Nevertheless, it is a doctrine which exerts 
 
252 ORGANIC TYPES. 
 
 very great power. It owes its influence over natural 
 history students solely to the wonderful effect it has 
 exerted in directing and stimulating investigation, as 
 well as to its capability of exhibiting order and har- 
 mony among many classes of facts whose relations 
 before were very obscure, if not wholly unrecogniz- 
 able. Its influence on the religious thought of the 
 student will depend very greatly on the manner in 
 which its philosophy is presented by his religious 
 teachers ; and I therefore greatly deprecate hasty 
 judgment or indiscriminating censure. Remember 
 that, though not proven, it is a useful and admirable 
 theory of science, and can be made an influence for 
 good instead of for evil, if only set forth in the right 
 light, and candidly accepted for its great worth 
 within its proper sphere and just limitations. Set 
 at naught all questions of intelligent or unintelligent 
 causation as irrelevant, on which scientific theories 
 have no bearing. The character of the First Cause 
 cannot be judged from the mode of action of any 
 secondary agencies. One mode of action is as mys- 
 terious as another, so far as any relations to a First 
 Cause are concerned. The intelligence of the First 
 Cause can only be judged from the result. Each 
 man has grown from a germ ; and we do not disown 
 creative power when, for the sake of a consistent 
 system, we assume that the species grew as well. 
 
 I myself deprecate the present domination of the 
 Darwinian theory, not on account of what it is in 
 itself, but because it has for a time thrust to one side, 
 and cast into the shade, the doctrine of " organic 
 types " so ably and so forcibly advocated by my late 
 
ORGANIC TYPES. 253 
 
 teacher and colleague, Professor Louis Agassiz, and 
 which I believe to be the more valuable system of 
 the two, at least in one important respect. 
 
 The conception that each of the four great fam- 
 ilies of the animal kingdom is a definite plan, a spe- 
 cific design, a creative thought, worked out in infinite 
 variety, and adapted, possibly through the principles 
 of natural selection, to varying conditions of soil or 
 climate, is to me a far grander and more compre- 
 hensive doctrine than the one which now so exclu- 
 sively prevails. The idea that types of structure are 
 forms of thought is moreover an hypothesis which 
 has very great intellectual reach and educational 
 value ; and for this great virtue of the older theory, 
 Darwinism offers no sufficient substitute. When now 
 we consider that the educational power of a scientific 
 system is its chief element of strength, we cannot but 
 regret that the present generation will lose much of 
 the charm which the grand conceptions of Cuvier and 
 Agassiz imparted to the study of natural history. 
 
 It is to be expected that a theory at once so origi- 
 nal and so fruitful of suggestions as Darwinism 
 should for a season control thought, and engross 
 attention. But time may be trusted to place all 
 human systems in their true relations; and I feel 
 confident that the doctrine of organic types will 
 before long exert its just influence. The new and 
 the older conceptions are not mutually exclusive. 
 Whatever is true in each will survive; whatever is 
 false will be forgotten; and out of the limited hy- 
 potheses of to-day will grow the larger views of 
 coming generations. 
 
254 THE DOGMATIST. 
 
 Having discussed the more characteristic features 
 of the dominant systems of science, I will next add a 
 few words in regard to the attitude of scientific schol- 
 ars towards these systems, as there are marked differ- 
 ences in this respect which strikingly illustrate a 
 point I desire to emphasize. 
 
 In the first place, then, we distinguish a very large 
 and efficient class of scientific scholars who are wholly 
 wedded to the system of science by which their stud- 
 ies are directed. They are men to whom the system 
 gives strength and motive, and their whole intellectual 
 life has been moulded by their guide. No wonder 
 that they value the system, for it has made them what 
 they are, and without it they would be to a great 
 extent helpless. They are not men who originate 
 systems or strike out new paths of discovery, but 
 they are men who with a well-defined aim work zeal- 
 ously and efficiently. The system has opened to 
 them new fields of investigation from which they 
 have reaped an abundant harvest. They have thus 
 extended the boundaries of knowledge, and are in 
 consequence deservedly highly honored by their fel- 
 low-men. It is impossible that a system through 
 which they have realized such great results, should 
 be at fault or even have a blemish. Imperfections, 
 which to other men appear glaring, they refer to 
 errors of observation ; inconsistencies are overlooked 
 or ingeniously explained away, and mere philosophi- 
 cal objections are laughed to scorn. By such men 
 the obvious symbolism of the system often comes to 
 be regarded as a likeness of real things ; and they 
 dwell with equal emphasis on the essentials and the 
 
THE DOGMATIST. 255 
 
 non-essentials of these arbitrary signs. Sometimes 
 they even parade the extravagances of the system in 
 order to testify more conspicuously their allegiance 
 to their leader. 
 
 Such men are apt to be dogmatic, and to demand 
 conformity to their well-grounded opinion as well as 
 deference to their long experience. They do not 
 readily brook dissent, especially from younger men ; 
 and when they have the power, they are sometimes 
 tyrannical. The tyranny of a system is often as cruel 
 as the tyranny of a despot, and may be exercised 
 with complacency and self-respect by the " mens sibi 
 conscia recti," who thinks he holds the keys of knowl- 
 edge. We must not overlook what is often noble 
 and worthy in these men. They are actuated by the 
 power of conviction which a successful system in- 
 spires, and the intolerance of conviction is often asso- 
 ciated with all that is pure, lovely, and of good report. 
 There is a still nobler charity, which never faileth ; 
 but scholars are not always saints, and ostracism is 
 a form of persecution which requires no sanguinary 
 edicts. The noblest martyrs of science are not those 
 who have braved great dangers and succumbed only 
 before the unattainable; but rather those who have 
 suffered even unto death, in consequence of deprecia- 
 tion, deprivation, and neglect. I have known of such, 
 and among them the founders of one of the now 
 dominant systems of science. Boycotting did not 
 originate in Ireland ; and among men of learning 
 supercilious sneers may cause more suffering than 
 blackballing. Scientific societies are probably no 
 worse than other associations of men ; but they have 
 
256 THE THEORIST. 
 
 often been subservient to the intolerance of doctrine, 
 and the domination of system. 
 
 A very much smaller class of scientific scholars 
 display a habit of mind the very reverse of that I 
 have just described. These men are superior to 
 systems, of which, however, they speak with respect 
 and condescension as the necessities of weak minds. 
 They boast of their freedom from prejudice, and of 
 their eclecticism in thought. They magnify incon- 
 sistencies of doctrine, or incompleteness of evidence. 
 They expose the extravagances of the assumptions, 
 or the unsoundness of the philosophy on which the 
 dominant system is based. They are apt to be severe 
 critics, and not to make due allowance for the limita- 
 tions of methods or the necessary imperfections of 
 all material results. They deal with negations rather 
 than with affirmations, and see blemishes more readily 
 than beauties. They are largely tolerant in theory, 
 but they esteem the freedom of dissent more than 
 the freedom of conviction. Such persons are usually 
 prone to speculation, and are often fruitful in in- 
 genious suggestions ; but they have seldom the incli- 
 nation or the patience for the tedious experimental 
 work required to verify their hypotheses. They are, 
 as a rule, highly imaginative, and their fancy paints 
 with glowing colors every subject which they study ; 
 but their deductions are not always trustworthy, and 
 their generalizations are often more subtile than pro- 
 found. They are sanguine students, and their enthu- 
 siasm invests their teaching with a peculiar charm ; 
 but their zeal is not always tempered by prudence, 
 and they are apt to be better expositors of what is 
 
THE POSITIVIST. 257 
 
 known than investigators of what is unknown. Men 
 of this temperament are not unfrequently truly liberal- 
 minded, capable of large views, and fitted to be 
 leaders ; and have exerted more influence on the ad- 
 vancement of knowledge than many a harder student 
 or deeper thinker. 
 
 Then there is another class of scientific students 
 quite different from either of the two types we have 
 sketched, and one which the specialism of our day is 
 tending very greatly to multiply. Among this class 
 are to be found many of the exact anatomists in 
 natural history, the accurate analysts in chemistry, 
 the untiring observers in astronomy, men who do 
 much of the hard work of science, and on whose un- 
 swerving truthfulness and scrupulous exactness entire 
 confidence can be placed. Minds which are occupied 
 with minute details, which delight in delicate distinc- 
 tions, and find pleasure in pushing observations to 
 the extreme limit of accuracy, are apt to overlook 
 the broader relations of truth, and value only definite 
 results ; and it is among such students that the posi- 
 tive philosophy finds most of its disciples. The class 
 of men to whom we refer includes not only those 
 who actually avow the doctrines of positivism, but 
 also those who cherish a similar habit of mind, — 
 men who worship facts and have little faith in ideals ; 
 men who never had any visions themselves, and there- 
 fore regard all visions as hallucinations ; men to whom 
 the material is the only reality, and the spiritual a 
 dream. Such men often condemn as idle specula- 
 tions the very hypotheses by which their own studies 
 have been guided, and despise the theories which 
 
258 THE TRUE SPIRIT. 
 
 alone give significance to the facts that have cost 
 them so dearly. These are worthy men and sincerely 
 devoted to the truth ; but their range is narrow, and 
 their prospect restricted. They have always dwelt in 
 a narrow valley amid pleasant pastures and beside 
 still waters. They have never ascended unto the hills 
 around them ; they never have been awed by the 
 mountain torrent; they never have been oppressed 
 by the mountain gloom ; they never have been glad- 
 dened by the mountain vision. 
 
 These are not ideal sketches which I have at- 
 tempted to draw. They are lineaments of real men, 
 whose biographies you may read in the history of 
 science ; whom you may meet to-day in every large 
 society of scholars ; whom you all must have known. 
 Such characters are not the products of scientific 
 study only. They are equally marked in every de- 
 partment of learning. In politics they are conserva- 
 tists, liberals, or bureaucratists. In philosophy they 
 become realists, nominalists, or positivists. In the- 
 ology they are classed as low, broad, or high church ; 
 and they are recognized as conventionalists, impres- 
 sionists, or preraphaelites in art. We must seek for 
 the origin of such distinctions far down in the varying 
 dispositions of the human mind and in the influences 
 of education. However much they may be exagger- 
 ated by passion, or misguided by evil counsel, these 
 traits of character are all good in themselves ; and 
 when blended in due proportion, they make the Solons, 
 the Washingtons, the Shakspeares, the Miltons, the 
 Newtons, the Faradays, of history. But so rarely are 
 such qualities of mind combined that we often regard 
 
THE TRUE SPIRIT. 259 
 
 them as incompatible. You do not expect to find in 
 a poet that attention to minute details which marks 
 the man of affairs ; nor in a wise counsellor the im- 
 agination of an artist; yet in the great pioneers of 
 science such opposite faculties have been united in a 
 most remarkable degree. They have been men of 
 ideals, but men whose vivid imaginations were regu- 
 lated by education, and chastened by wisdom. They 
 have been men of courage and perseverance, who fol- 
 lowed out their convictions through every discour- 
 agement. They have been men of entire truthfulness 
 who have never hesitated to submit their doctrines to 
 the test of crucial experiments and to abide by the 
 issue. They have been men of the most scrupulous 
 conscientiousness in attention to minute details, re- 
 garding themselves as responsible to the Giver of all 
 truth for accuracy in every observation, and for ex- 
 actness in every statement. Finally, they have been 
 men of modesty and of reserve in judgment, realizing, 
 as no other men ever have, how boundless is truth ; 
 how limited knowledge ; how intricate the problem 
 of nature ; how weak in comparison the intellect of 
 man. 
 
260 DICTATES OF EXPERIENCE. 
 
 LECTURE IX. 
 
 PREDOMINANT PRINCIPLES OF SCIENTIFIC 
 THOUGHT. 
 
 WE have already in the preceding lectures dis- 
 cussed at some length the validity and char- 
 acter both of the inductive and of the deductive forms 
 of scientific reasoning ; we have also studied the au- 
 thority and relations of the laws of nature, as well 
 as the warrant and use of scientific systems ; and in 
 order to complete my survey of the general methods 
 of science, I propose lastly to consider very briefly 
 certain general principles by which students of nature 
 have been greatly guided, and which, therefore, have 
 exerted a marked influence on the progress of knowl- 
 edge. As I have already said, the mental process of 
 induction is subject to no known laws that can be 
 accurately defined. It is a product of genius whose 
 antecedents we can rarely trace, and whose conditions 
 we can seldom analyze. Nevertheless, even genius is 
 guided by experience ; and there are two dictates of 
 experience so wide in their application, and so gen- 
 erally trustworthy, that they claim our notice in this 
 connection. I refer to the principles of analogy 
 and of continuity, which although often found deceit- 
 ful guides, yet when followed with caution and judg- 
 
ANALOGY. 26l 
 
 ment very seldom lead astray. Other suggestions 
 of experience, like the principles of least waste, of 
 the sufficient reason, of successive approach, of adap- 
 tation, and of intelligent plan, have been found at 
 times of great value in the study of science; but 
 they are not principles so generally accepted as 
 those first named, and are more restricted in their 
 application. 
 
 There can be no question that the suggestions of 
 analogy have led to more discoveries in science than 
 all other influences combined. 
 
 If the force of the earth's gravitation is not sensibly 
 diminished at the summits of the highest mountains, 
 why may it not reach to the moon? Since the phe- 
 nomena of light resemble in so many respects those 
 of sound, why may they not be, like these, the effects 
 of wave-motion? If there be in masses of matter an 
 internal molecular motion which produces thermal 
 changes, why should not these motions obey the well- 
 known laws which govern the motions of the masses 
 themselves? If, as Malthus has shown, the struggle 
 for existence has exerted such a marked influence on 
 the history of the human race, why should it not 
 produce far deeper and more lasting effects among 
 the lower animals, where the struggle is vastly more 
 intense? Thus it is through analogy that men have 
 been led to each of the great systems of science 
 now dominant in the intellectual world. So also 
 in unnumbered other instances analogy has given 
 the suggestion which observation or experiment has 
 verified. 
 
 The astronomer noticed through the telescope 
 
262 DECOMPOSITION OF THE ALKALIES. 
 
 patches of dazzling whiteness around the poles of 
 Mars; and since this planet moves around the sun 
 under relations similar to those of the earth, he in- 
 ferred that the greater brilliancy was caused by the 
 reflection of light from snow-caps like those which 
 render the earth's poles so inaccessible; and when on 
 watching the planet's disk from year to year, he ob- 
 served that these patches alternately increased and 
 diminished with the changing Martial seasons, he felt 
 assumed that this suggestion of analogy was correct. 
 
 Down to the beginning of this century the so-called 
 earths and alkalies, such as alumina, magnesia, lime, 
 soda, and potash, had been regarded as elementary 
 substances ; but towards the close of the last century 
 Lavoisier had shown that several materials closely 
 resembling the earths, such as iron-rust, litharge, 
 and tinstone, were compounds of metals with the 
 then newly discovered oxygen gas. Analogy at 
 once suggested that the earths and alkalies must also 
 contain metals united to oxygen ; but although the 
 analogy inspired a confident belief in this inference, 
 the chemists at the time did not succeed in decom- 
 posing the compounds, because the means at their 
 command were inadequate. But the discoveries of 
 Galvani and Volta gave the world a new agent in 
 voltaic electricity, which by the decomposition of 
 water proved to be a reducing force of wonderful 
 power; and the first moment he could command a 
 voltaic battery of sufficient strength Sir Humphry 
 Davy applied the new force to the alkalies, when out 
 at once the metals flowed. 
 
 In 1812 iodine was discovered by Courtois in the 
 
SPECIFIC FOR GOITRE. 263 
 
 crude soda-salt called kelp, which is prepared by- 
 burning wrack, and is simply the ashes of this sea- 
 weed. For a long time previously burnt sponge had 
 been used as a remedy in cases of goitre, which in 
 the mountainous regions of Switzerland produces 
 such wide-spread and distressing results. As sponge 
 in its habitat and relations resembles sea-weed, anal- 
 ogy suggested that the burnt sponge might contain 
 a minute amount of iodine, and that its efficacy 
 might be due to this new elementary substance ; and 
 in 1820 Dr. Coindet, a physician of Geneva, aided by 
 the young chemist Dumas, succeeded not only in 
 proving the presence of iodine in the sponge, but in 
 replacing a nauseous dose by preparations of iodine 
 which have proved almost a specific for the terrible 
 disease. 
 
 Such examples might be multiplied indefinitely; 
 but we have only time for one other, which is, how- 
 ever, very striking. As we have before said, the ele- 
 mentary rays of a beam of light must be regarded as 
 moving in a definite plane; and a beam all whose 
 rays are moving in the same plane is said to be po- 
 larized. By optical means we can readily determine 
 the position of this plane, which we call "the plane 
 of vibration," sometimes also " the plane of polariza- 
 tion." When a polarized beam of light passes through 
 a plate of quartz in the direction of the axis of the 
 well-known hexagonal crystals of this mineral the 
 plane of polarization suffers a rotation, to an extent 
 depending on the thickness of the plate. Now on 
 some of the hexagonal crystals .in which quartz crys- 
 tallizes there are to be found certain small planes, 
 is 
 
264 MAGNETIC STRAIN. 
 
 called " plagihedral," which are distributed after a 
 helioidal, or spiral-like, type of symmetry; and ac- 
 cording as the spiral ascends to the right or to the 
 left, the plane of polarization is rotated to one side or 
 to the other. Remember also that the effects of 
 crystals on light are referred by the undulatory 
 theory to their unequal elasticity in different direc- 
 tions, and that similar effects can be obtained with 
 homogeneous glass by subjecting this transparent 
 material to unequal strains, and thus developing un- 
 equal elasticity in different directions; add to all this 
 the further fact that when a current of electricity flows 
 through a spiral of copper wire wound round a bar 
 of iron, and renders it magnetic, a screw-like strain is 
 developed in the bar, — and you will then have the 
 basis from which Sir John Herschel, to whom these 
 facts and theories were very familiar, inferred by 
 analogy that if glass or other transparent material 
 could be subjected to a similar magnetic strain, we 
 might obtain under such conditions the same effect 
 of rotating the plane of polarization which is so 
 markedly exhibited by quartz; and further, that 
 possibly such a strain might be developed by a 
 powerful electro-magnet Herschel himself never 
 verified this suggestion of analogy; but the effect 
 was subsequently realized in a most striking manner 
 by Faraday. 
 
 The validity of analogical reasoning unquestionably 
 depends on the harmonies of nature. Since the uni- 
 verse has been made throughout on one. plan, and, 
 however varied the details, the same general patterns 
 reappear in all its parts, both great and small, we can 
 
VALIDITY OF ANALOGICAL REASONING. 265 
 
 safely infer from our very limited experience in a 
 narrow field what are the conditions and relations in 
 remote and inaccessible provinces which we can 
 never directly explore with our senses. Hence it is 
 that we can infer that molecules and atoms obey the 
 same laws of motion as suns and planets. It is 
 wholly conceivable that the microcosmos should 
 have been planned on a system entirely different 
 from that of the macrocosmos; but apparently the 
 very reverse is the truth; and a theory, which as- 
 sumes that within the masses of material bodies the 
 motions of suns and systems are reproduced on a 
 scale so minute as to task our power of imagination 
 to grasp the conception, is found to be in complete 
 accordance with all the facts which can be observed. 
 Moreover, whenever we have been able to obtain evi- 
 dence we have found our reliance on the unity of 
 nature fully justified. 
 
 Within a comparatively {ew years our confidence 
 in this regard has been very greatly strengthened by 
 the revelations of the spectroscope. If our globe 
 was once thrown off from the sun we might expect 
 that it would be a chip of the old block ; but we can 
 conceive of no necessity which requires that the ma- 
 terials of the fixed stars should be like that of our 
 earth. Still, the spectroscope tells us that in those 
 immensely distant bodies the same elementary sub- 
 stances are glowing with which we are so familiar in 
 our laboratories. And if anywhere in the depths of 
 space there revolves around one of those centres of 
 energy a globe which has been reduced to the cli- 
 matic conditions of our earth, we can infer with a 
 
266 VALIDITY OF ANALOGICAL REASONING. 
 
 confidence which approaches certainty that its rocks 
 contain the same minerals, and that its plants and 
 animals are fashioned after the same patterns with 
 which we are so familiar; and, if it has also become 
 the abode of intelligent beings, that they have been 
 discussing the same great problems which have per- 
 plexed man. 
 
 It is solely the unity and harmony of nature which 
 renders analogical reasoning valid. To this harmony 
 our own being answers, and it is only because we are 
 in unison with nature that we are able to interpret her 
 methods. Were our minds not in harmony with our 
 surroundings, or those surroundings not in harmony 
 with the rest of creation, our intelligences would have 
 been confounded, and all nature would have been to 
 us a sealed book. 
 
 Man cannot conceive in a concrete form of any- 
 thing he has not previously received through the 
 senses. No hypothesis can be so much as framed 
 in the mind which has not some semblance in pre- 
 vious experience ; and as through our senses we have 
 direct cognizance only of material things, we cannot 
 picture to ourselves any existences without associ- 
 ating with them some of the qualities of matter. The 
 most we can do is to alter the combinations of our 
 experience, or to change in degree the qualities we 
 have actually observed. This is all we have done in 
 forming the most subtile conception man has ever 
 grasped, — that of the luminiferous ether. We are 
 familiar with elasticity, and we can predicate an 
 elasticity a million or a billion times greater than 
 any that is known to us. We know what density 
 
FAILURES OF ANALOGY. 267 
 
 is, and we can at least in words describe a material 
 less dense than any known substance in a similar 
 extreme degree, and then in imagination combine 
 these extravagances. But what we reach is a con- 
 dition of matter, and all our calculations in regard 
 to it are based on its likeness to matter. We can, in 
 imagination, vary the known qualities of matter to 
 an unlimited degree. We can combine these quali- 
 ties in other than the accustomed relations. But, 
 however much we may think or talk about other 
 states of existence, we cannot actually picture to 
 ourselves any existence or mode of action of which 
 experience has not given us some semblance. Thus 
 all our science — that is, our knowledge of things — 
 rests on experience, and never could have been built 
 up had not the unknown been of a piece with the 
 known. 
 
 But while analogy is thus the guiding rule of sci- 
 entific thought, it is a rule which cannot be blindly 
 followed. The suggestions of analogy have often 
 proved delusive, — either because the resemblances 
 on which we counted were superficial and not real, 
 or because our scientific methods and appliances 
 were inadequate to establish the relations we sus- 
 pected. The history of science is full of examples 
 of misdirected efforts whose failure is to be attri- 
 buted to one or the other of these causes. Two 
 marked instances will serve as illustrations. 
 
 After the elder Herschel with his large telescope 
 had distinguished in several of the nebulas points of 
 light, and later Lord Rosse with a much larger re- 
 flector had resolved still more of these distant star- 
 
268 FAILURES OF ANALOGY. 
 
 clusters, it was inferred by astronomers that all the 
 nebulae were groups of stars, whose resolution was 
 only a question of telescopic power. But since the 
 application of the spectroscope to the problem it 
 has been found that there is a very large class of 
 these objects which are masses of luminous vapors ; 
 and it is evident that the astronomers were at first 
 deceived by a superficial resemblance. 
 
 Faraday, after he had investigated with such con- 
 summate skill the relations of electricity to mag- 
 netism, conceived that similar relations must exist 
 between these modes of energy and gravitation ; and 
 devoted a great deal of labor and thought to the in- 
 vestigation of the subject. He made several series 
 of laborious experiments in the clock-tower of the 
 Houses of Parliament and elsewhere, but with abso- 
 lutely no results. To use his own words, "The 
 experiments were well made, but the results are 
 negative; " but he adds, " I cannot accept them as 
 conclusive." So the question remains to the present 
 day ; and it is possible, as Faraday evidently believed, 
 that the failure arose from the want of appliances 
 sufficiently delicate to show the expected effects; 
 although, if the opinion previously expressed in 
 these lectures in regard to the nature of gravity be 
 correct, it was the seeming analogy which was at 
 fault, as Faraday himself at times suspected. 
 
 In his failures not less than in his successes, the 
 example of Faraday may teach us most important 
 lessons. A mind so subtile as his is apt to be capti- 
 vated by fanciful resemblances; but he never fol- 
 lowed vaguely the suggestions of analogy, inquiring 
 
GENERALIZATION. 269 
 
 diligently at every step whither they were leading, 
 and always submitting desire to the control of" ex- 
 perience. As thus curbed, analogy may be always 
 safely followed; and as Bishop Butler so tersely 
 wrote, " Analogy is the very guide of life." She 
 leads us when we are least aware of her guidance. 
 She colors all our language. She determines half 
 our thoughts. In submitting ourselves, as we must, 
 to her control, let us consider well the situation ; and 
 while we acknowledge our dependence, never part 
 with our more precious birthright. Our guide is 
 moulded of the same clay as ourselves; and there 
 may be things in earth, as well as in heaven, not 
 dreamt of in her philosophy. And, moreover, if 
 harmony with nature be a test of reality, then har- 
 mony with the spiritual life, then adaptation to the 
 needs of the soul, is also a mark of certitude, an 
 equally overpowering evidence of truth. 
 
 Generalization in science is only a form of ana- 
 logical reasoning. We are said to generalize when 
 we ascribe to a class of objects qualities or relations 
 which have been shown to be true of certain charac- 
 teristic members of the class. Thus a certain num- 
 ber of substances having a brilliant lustre, and to a 
 greater or less degree ductile or malleable, and at 
 the same time good conductors of heat and elec- 
 tricity, which we class under the general name of 
 metals, have been found after repeated trials to resist 
 every attempt to decompose them, and are therefore 
 regarded as elementary substances. Hence we con- 
 clude that all metals are elementary substances ; and 
 when a new one is discovered, as is not unfrequently 
 
2/0 
 
 GENERALIZATION. 
 
 the case, we never think of attempting to analyze it, 
 because experience with similar bodies assures us 
 that all such attempts would be fruitless. 
 
 Again, it has been shown by Davy, Wohler, and 
 others, that alumina, magnesia, and several of the simi- 
 lar earths are metallic oxides, and the metals of which 
 they consist have been extracted and studied; indeed 
 aluminum and magnesium are now articles of com- 
 merce and familiar to every one. Hence we con- 
 clude that all amorphous powders resembling alumina 
 and magnesia, and having like chemical properties 
 are also metalliferous; so that when, within a few 
 years, a large number of new earths were distinguished 
 the chemist accepted them at once as metallic oxides, 
 although in most cases the metal has not actually 
 been isolated. 
 
 Obviously, our assurance in all these cases rests on 
 our confidence in the unity of nature's plan and 
 method ; and the argument which convinces us dif- 
 fers from the ordinary argument from analogy only 
 in the extent of the ground covered. When Davy 
 inferred from analogy that potash must contain a 
 metal, and successfully followed out the suggestion, 
 he reasoned from a comparatively superficial resem- 
 blance between a few things to a deeper relationship. 
 When we conclude that the new earths are metallic 
 oxides, we reason from a wide knowledge of a class of 
 bodies that a new substance, which has been shown to 
 have the other qualities and relations of this class, 
 also has an additional character, — though as yet un- 
 observed, — which is common to all the other mem- 
 bers therein grouped. The reasoning in the last case 
 
ALL KNOWLEDGE RELATIVE. 2"Jl 
 
 is far more conclusive than in the first ; but evidently 
 it rests on the same assurance, the uniformity of nature. 
 Prior to experiment Davy's inference was only proba- 
 ble ; our conclusion is as certain as that the sun will 
 rise to-morrow. In either case, however, the argu- 
 ment is based on resemblances more or less remote, 
 and the difference is one of degree and not of kind ; 
 and so we may have every degree between the certi- 
 tude of a far-reaching generalization and the mere 
 suggestion of a feeble analogy. In science the merest 
 hint maybe of value; for when in an investigation 
 bewildered by complex conditions we are hesitating 
 which way to turn, or what to try first, the faintest 
 suggestion of analogy may decide us. On the other 
 hand, in the relations of the spiritual life we must 
 remember that even in our grandest generalizations 
 we cannot escape from the material clogs of our mor- 
 tal experience; that all our knowledge is necessarily 
 relative to our environment; and that though its 
 material forms are doubtless symbols of higher reali- 
 ties, yet these earth-born fancies can never be an 
 exact picture of things spiritual, or a precise measure 
 of things divine. 
 
 Man lives in time, and he cannot release his 
 thoughts from the fetters which this condition im- 
 poses. Continuous time and a corresponding con- 
 tinuous change or growth are so inseparable from 
 human experience that existence in time, with pro- 
 gressive change, is the only mode of being of which 
 the mind can form a concrete idea. We can reason 
 and talk about a Being who is the same yesterday, 
 to-day, and forever, and to whom a thousand years 
 
272 PRINCIPLE OF CONTINUITY. 
 
 are as one day and one day as a thousand years, — 
 we firmly believe in the reality of such a Being; but 
 we cannot picture the existence to our minds, as the 
 very imagery plainly shows. As we cannot escape 
 from the limitations of matter, so we cannot escape 
 from the limitations of time. As regards every event, 
 the mind demands an antecedent and a consequent. 
 The common axiom that " every event must have a 
 cause " is another phase of the necessity which the 
 conditions of our environment impose on our being. 
 The necessity is so interwoven in the complex web of 
 material existence that we cannot dissociate it if we 
 would. It is not a necessity of thought; for that 
 Being who is from eternity to eternity the same had 
 no antecedent and no cause. But it is a necessity of 
 the imagination, and therefore a necessity of scientific 
 knowledge. 
 
 In science we call this lesson of experience " the 
 principle of continuity," and it is a belief which 
 exerts a profound influence on all our reasoning about 
 material relations. It is this principle which alone 
 gives strength to the doctrine of evolution ; but it is 
 equally a controlling power in almost every depart- 
 ment of scientific inquiry ; indeed it controls the 
 very process of thought itself. 
 
 Examples of continuity of action are all around us, 
 and illustrations of the successful application of the 
 principle in scientific reasoning might readily be 
 cited. The science of geology is especially rich in 
 examples of this class ; and our knowledge of the 
 relative ages of strata, and of the succession of life on 
 the earth, is in very large measure the result of tracing 
 
BREAKS OF CONTINUITY. 273 
 
 out the evidences of continuous changes ; and in 
 physics we often reason from what we can see to 
 what we cannot see, through a chain of sequences 
 which connects the parts of a continuous series, and 
 thus exhibits relations which would be otherwise 
 obscure. The same principle underlies all classifica- 
 tion in natural history, and, as has been already 
 said, is the warrant of the theory of evolution. 
 Evolution is simply a wider growth, and is implied 
 in the only conception of being of which the mind 
 can frame a definite image. For our purpose, how- 
 ever, it is not necessary to multiply illustrations ; and 
 we turn next to some examples of the break of con- 
 tinuity which have a much more important bearing 
 on our subject ; for they indicate that beneath the 
 obvious material relations there may be other influ- 
 ences at work in determining the course of events. 
 
 While we can usually safely follow the indications 
 of continuity, yet, as in the case of analogy, we are 
 frequently deceived, and even more frequently than 
 in the application of the cognate principle ; and ex- 
 amples of break of continuity present a striking feat- 
 ure of nature which cannot be overlooked. Often 
 the break is only apparent, resulting from the inabil- 
 ity of our senses to follow changes succeeding each 
 other with more than a certain limited rapidity. 
 When a ball is fired from a rifled cannon it gains in 
 the two hundredth part of a second its full and fearful 
 velocity, and yet we know that while in the gun it 
 passed through every stage of motion from indefinite 
 slowness onwards. So also with molecular motions, 
 which may last only some thousand millionths of a 
 
274 CRYSTALLIZATION. 
 
 second ; between successive collisions all the phases 
 of the recoil, the free path, and the rebound, must 
 follow each other in due order. 
 
 We do however find in nature phenomena which, 
 after making every allowance for the imperfection of 
 our senses, appear to be absolute breaks of continuity. 
 One of the most striking of these is to be seen in 
 the process of crystallization. I confess that I never 
 witness the process without amazement. That out of a 
 perfectly homogeneous and structureless liquid there 
 should suddenly separate a perfect geometrical solid, 
 with all its sparkling facets grouped with mathemati- 
 cal exactness, is to me one of the greatest wonders in 
 this world of beauty. The structure of a crystal is of 
 course not so complex as that of a plant or an ani- 
 mal; but then it has no gradual genesis; it has no 
 antecedents ; it appears as a sudden break of con- 
 tinuity; its formation approaches as near to a sudden 
 creation as anything we ever behold. This may seem 
 to you inconsistent with what you have heard of the 
 slow growth of crystals. But such statements apply 
 only to the large, massive crystals, such as you may 
 see in our museums, — some of which have doubtless 
 been centuries in forming. I refer, on the contrary, 
 to the sudden production of the minute crystals of 
 which the larger crystals are gradually formed aggre- 
 gates. These small crystals, when examined with a 
 microscope, are seen to be as perfect as the larger 
 specimens ; indeed, they are often far more per- 
 fect; and they seem to drop out of the solution in- 
 stantaneously, — the creation of each one, if I may 
 dare to use the term, being in some cases attended 
 
DEFINITE PROPORTIONS. 275 
 
 with a flash of light as if to attest its mysterious 
 origin. 
 
 Another circumstance which sometimes attends on 
 crystallization is even more indicative of a break of 
 continuity than the facts I have mentioned. In the 
 liquid menstruum, as it is called, the constituents of 
 the future crystal are often mixed in variable propor- 
 tions ; but the crystals which form unite these ingre- 
 dients in absolutely definite proportions, conforming 
 to the great law of combining proportions of chem- 
 istry. This law in itself is probably the most general 
 and striking break of continuity in nature. You may 
 mix two substances, by solution or otherwise, in any 
 proportions whatever, and there appears to be a per- 
 fect interpenetration of the masses. Then when an 
 electric spark, or some other cause, determines chem- 
 ical union, these substances unite in certain constant, 
 definite, and calculable, proportions, excluding the 
 excess of one or the other ingredient; and this is 
 what takes place t in the example of crystallization 
 just referred to. In order to reconcile this striking 
 phenomenon with the principle of continuity, several 
 chemists have endeavored to show that these definite 
 proportions were merely a maximum effect of such 
 restricted range that we failed to recognize the grada- 
 tions ; and I have myself sought to test this sugges- 
 tion by experimenting, — thinking that the range must 
 be greater in proportion as the combining force was 
 feebler, and that possibly in cases of weak chemical 
 affinity it might be detected. But although at first I 
 thought I discovered an indication of such an effect, 
 my later experiments have proved that the propor- 
 
276 NATURAL AND SUPERNATURAL. 
 
 tions are just as definite in weak compounds as in 
 strong. I see therefore no escape from the conclu- 
 sion that this apparent break of continuity is a real- 
 ity; and should not such results teach us that the 
 preconceptions of our experience are not infallible? 
 Thus may even the study of science prepare us to 
 recognize other possibilities of being than those of 
 known material relations. 
 
 That mode of being not directly cognizable by our 
 senses we call the supernatural; and we often reason 
 as if it were something apart from and above nature. 
 But is it not the more consistent theory that the su- 
 pernatural and the natural are simply different phases 
 of one system ; and that while with our bodily senses 
 we apprehend only the material relations of this sys- 
 tem, we can with our spiritual sympathies and aspira- 
 tions reach out towards those higher associations 
 for which this life is a preparation? Or may we not 
 rather say that the supernatural embraces the natural, 
 modifying in numberless ways the more obvious ma- 
 terial relations, and thus constantly apprising us of 
 its omnipresence ; and do not such indications as we 
 have been studying ever remind us that the material 
 is not all of knowledge or all of life, and give us a 
 confident expectation of more life and ampler knowl- 
 edge behind the vail? 
 
 When we fully comprehend that the fundamental 
 conceptions comprised under the doctrine of con- 
 tinuity are simply a product of experience, and 
 dependent on material relations, we shall be able to 
 think and reason more justly about spiritual relations 
 in which the limitations of the material do not exist ; 
 
IDEA OF TIME. 277 
 
 and although difficulties of conception may by no 
 means be removed, yet a way is opened by which 
 the seeming contradictions of theological doctrines 
 with our experience may possibly be reconciled. 
 
 As has already been intimated, we have no expe- 
 rience, and therefore no actual knowledge, of any 
 state of existence, except of that in which continuous 
 change and growth constitute the invariable order 
 of being. Our idea of time is simply a conception 
 based on the succession of events. The fundamental 
 conception of duration arises unquestionably from 
 the succession of thoughts in our own minds. It is 
 thus that we reach an idea of short duration, as of 
 the swing of a pendulum; and it is only of such 
 durations that we can be said to have any direct 
 consciousness. Longer durations are to us simply 
 the multiples of such short intervals as we can di- 
 rectly perceive and appreciate ; or else have known 
 relations to the periods of events which we assume 
 as the standards of measure. The day is the period 
 of the rotation of the earth on its axis ; the hour is 
 one twenty-fourth part of a day, the minute the one 
 sixtieth part of an hour; the second the one sixtieth 
 part of a minute, and at any given place is the dura- 
 tion of the swing of a pendulum (about one meter 
 long), whose exact length is easily adjusted. It is 
 only this smallest unit of which we can be said to 
 have any direct perception. Our knowledge of much 
 larger periods, however exact, is purely formal. 
 When a boy learns that a year is the period of the 
 revolution of the earth around the sun, the most he 
 gains is the idea that this, to him already familiar 
 
278 TRUE MEASURE OF LIFE. 
 
 period ia human relations, during which the succes- 
 sion of seasons is completed, is the duration of a 
 continually recurring astronomical event. Nor does 
 his knowledge become any more real when he is 
 further informed that the year comprehends three 
 hundred and sixty-five days, five hours, forty-eight 
 minutes, forty-seven and seven tenths seconds. But 
 he can be thus impressed with the fact that the 
 durations of the events by which time is measured 
 bear a constant relation to each other, and hence, be 
 led to the conclusion that the quantity measured is 
 a real attribute of material relations, and hence, also 
 of material life. 
 
 A very few considerations, however, will show that 
 time is solely an attribute of material relations, and 
 no adequate measure, even of that phase of our 
 spiritual life which terminates with the death of the 
 mortal body. Conventionally, we measure man's life 
 in years ; but who does not recognize that Raphael, 
 dying at thirty-seven, or Pascal, dying at thirty-nine, 
 lived not only a richer, but a really longer life than 
 most of the Methuselahs and Nestors of history. He 
 lives longest who is able most fully — 
 
 " To crowd the narrow span of life, 
 With wise designs and glorious deeds." 
 
 Life should be measured not by years, but by 
 thoughts, events, and deeds. The succession of 
 thoughts in the mind is a far more accurate measure 
 of conscious duration than the beats of a pendulum; 
 although as compared with the standard of time, the 
 flow of thoughts is so variable, not only in the minds 
 
RAPIDITY OF THOUGHT. 
 
 279 
 
 of different men, but also in our own minds under 
 varying conditions. After some critical experience, 
 how often do we say that we have lived longer during 
 the past day or week than during months or years 
 before; and these words are no mere figure of speech, 
 but on the contrary express an important truth. 
 
 During our mortal lives, the rapidity of thought is 
 limited by our physical organization; but we can 
 easily conceive that it might be indefinitely in- 
 creased ; and such conceptions appear in part to be 
 realized both in the phenomena of dreams, and in 
 the experience of drowning men ; who, when subse- 
 quently resuscitated, often have said that, during the 
 brief interval before they became unconscious, the 
 whole course of their lives flashed through the mind. 
 Could we increase the rapidity of thought, we 
 should increase the conscious duration of life during 
 a given time ; and it is a perfectly rational concep- 
 tion, that with a finer organization the life of a cen- 
 tury might be crowded into a day. Obviously, we 
 can apply magnifying power to time as we can to 
 extension. As under our microscopes, an area 
 barely perceptible to the eye becomes spread out 
 into a broad plane, teeming, it may be, with life, so 
 we can conceive that a duration barely perceptible to 
 our senses may be to a more delicate organism a 
 period of vast activities. 
 
 " Alike in God's all-seeing eye, 
 The infant's day, the patriarch's age." 
 
 Magnify, now, duration indefinitely, not by extend- 
 ing time, but by crowding activities into the present, 
 T 9 
 
230 LIMITATIONS OF TIME AND SPACE. 
 
 and you annihilate time, — or rather, you eliminate 
 the element of time from the spiritual life; and such 
 considerations will lead the mind to recognize the 
 truth that eternity consists not in limitless time, 
 which would be unendurable, not in passionless con- 
 templation, which would be weariness, but in the 
 removal of the limitations of time from our mental 
 activities. Time, like space, is an attribute of material 
 relations ; and although in this life even our mental 
 processes are controlled by the limitations which 
 these relations impose, and although the imagination 
 can form no distinct image of a state of being freed 
 from the limitations of time and space, yet we are 
 able by such considerations as we have here imper- 
 fectly presented so far to dissociate in our thoughts 
 these conditions from our spiritual life as to recog- 
 nize the aptness of the imagery by which such a 
 state is prefigured in the Scriptures, and also to ad- 
 mit the possibility of spiritual relations which to our 
 material vision seem to be contradictory. We can- 
 not be said to have actual knowledge of any state of 
 being unconditioned by time and space ; but the 
 circumstance that we are able to recognize some of 
 the attributes of such a state is in itself weighty 
 evidence of its reality. 
 
 To a being freed from the limitations of time there 
 are no beginnings and no ends ; or rather, those tran- 
 sitions which to us appear as the beginnings or the 
 ends of events, are simply phases of the ever present 
 and the ever actual. God's prescience is not fore- 
 knowledge, but actual knowledge. He seeth the end 
 from the beginning, because both are ever present; 
 
FREE WILL. 28l 
 
 and His knowledge is not inconsistent with man's 
 free will, because that will is limited in its exercise 
 by the very conditions of time and space which the 
 Creator has imposed on the material universe. 
 
 In all material relations man's free will is a definite 
 factor, as much so as any other form of energy; and 
 the final attitude of man's mind towards his Maker is 
 equally within his own power of determination ; but 
 here man's prerogative stops. Man as a living creat- 
 ure has a subordinate power in the material creation. 
 Man as a living soul may regulate the attitude of his 
 mind to other living souls ; but however completely 
 he may control actions, he cannot force the wills even 
 of those nearest and dearest to himself. In a word, 
 his will has control only over material relations and 
 over himself; and to one who does not wait on re- 
 sults, but who sees at once every stage of our material 
 processes and of our mental conflicts, the foreknowl- 
 edge of events may be perfectly consistent with the 
 freedom of His subordinate actors in the drama of 
 human life. The architect, who in his imagination 
 sees his building completed in all its details, may be 
 said to have a foreknowledge which is compatible 
 with a large degree of freedom among the workmen 
 in their respective spheres ; and although this illus- 
 tration fails in essential details, it may serve to pre- 
 figure that fuller prescience when the limitations which 
 here exist are removed. 
 
 Such illustrations do not of course remove the diffi- 
 culty we have in conceiving of a being freed from the 
 limitations of time ; and, by dwelling on the thought 
 that it is impossible that we should be free if God 
 
UNREALIZED INFERENCES. 
 
 foresees all our actions, we can easily make the in- 
 compatibility appear as marked as ever. All that we 
 can hope is to recognize the possibility of conditions 
 which may make such relations intelligible, without 
 expecting to comprehend them. Free will is a fact 
 of consciousness, and such considerations as we have 
 advanced make God's foreknowledge a clear inference 
 of our intelligence from facts of consciousness; and 
 here as elsewhere we must be content to accept our 
 limitations, and wait for the clearer day when we shall 
 know even as we are known. 
 
 It is not solely in spiritual relations that our reason 
 leads us to inferences which lie beyond the powers of 
 conception. This is equally the case in the higher 
 forms of mathematics, where, as we have before said, 
 we often deal with relations, like the higher dimen- 
 sions of multiple algebra, of which it is impossi- 
 ble for the mind to form any distinct idea; and no 
 mathematician questions that these relations are re- 
 alities, yet he can only describe them by inadequate 
 and figurative language which deals with types and 
 symbols. 
 
 This power of the human mind of reaching out in 
 various directions beyond its own experience, to rela- 
 tions of which it can form no concrete and material 
 images, is to my own mind one of the strongest evi- 
 dences of the reality of a higher life in which these 
 dim visions shall be realized. 
 
 We do not, however, care to deal with theological 
 subtleties; but the overlooking of the distinction be- 
 tween the material and the immaterial, which we have 
 attempted to emphasize, has led to a fallacy in much 
 
MISTAKEN PRECONCEPTION. 283 
 
 of the reasoning about the genesis of nature which it 
 is important to expose. 
 
 We can form no clear conception of any act except 
 as taking place at a given time. The battle of Water- 
 loo was fought June 18, 181 5. America was discov- 
 ered on the 12th of October, 1492. Julius Caesar 
 was assassinated in the ides of March, 44 B. c. The 
 battle of Marathon was fought September 28 or 29 
 (according to somewhat uncertain computations), 
 490 B.C.; and the popular belief is that the world 
 was created at an equally definite date in the remote 
 past, which could be stated in equally precise chro- 
 nology if we only had the knowledge. At the basis 
 of this belief is a tacit assumption that all intelligence, 
 the Creator as well as the creature, must act under 
 the limitations of time. " God spake and it was 
 done; " and we assume that the word of the Creator, 
 like the word of man, was spoken at a definite mo- 
 ment in the succession of events which measure 
 time. But science shows that the genesis of the 
 world was a process of gradual growth ; and the in- 
 consistency of this conclusion in a great variety of 
 phases with man's preconception of the mode of 
 creation, has always been a hindrance to faith. 
 
 It is by no means perfectly clear how such a gen- 
 eral preconception arose. It certainly did not come 
 from the study of nature ; for, as has been said, the 
 whole scheme of nature, so far as we understand it, 
 is wholly at variance with such an idea. Growth is 
 the order of nature ; and although as yet no man has 
 been able to discover any distinct and unquestionable 
 traces of the first introduction of a new species into 
 
284 ORIGIN OF THE PRECONCEPTION. 
 
 the world, yet it cannot be seriously questioned that 
 the theory of the gradual development of organic 
 types is in harmony with all that we know of 
 biology. 
 
 Nor does it appear probable that the preconception 
 came from the Hebrew Scriptures ; for although in 
 Genesis it is distinctly declared that all things were 
 created by Jehovah, the great " I Am," the mode of 
 creation is described in such obviously figurative lan- 
 guage that no difficulty has been found in reconciling 
 it with any result of science when once clearly estab- 
 lished. Nevertheless, it is very generally assumed 
 that a creation " ex nihilo " at a definite moment of 
 time is expressly declared in the Bible, and on this 
 basis it is constantly urged, in answer to the appar- 
 ently irreconcilable evidence of science, that the 
 Almighty could instantly call a universe into being 
 out of nothing if He chose. Granting a clear revela- 
 tion, such a plea might be relevant. But there is no 
 such clear revelation ; for admitting whatever author- 
 ity the most extreme literalist may claim for the 
 Pentateuch, it must be conceded that the language 
 of these early books admits of the most diverse inter- 
 pretations ; and the mode of creation still remains an 
 open question for scientific investigation. The ques- 
 tion is not how to reconcile observation and revela- 
 tion, but to find out as far as possible what the facts 
 really were. 
 
 If, then, the preconception cannot be traced either 
 to a distinct revelation, or to the observation of na- 
 ture, must it not result from the normal action of the 
 human mind under its limitations? In all human 
 
god's creation not as man's creation. 285 
 
 relations creation, whether in art, in literature, or in 
 science, implies effort, often long-continued effort, 
 which taxes all the strength and all the perseverance 
 that the most gifted men can command. There are 
 obstacles to be overcome, and there is a conscious- 
 ness of weakness and inefficiency, which ever reminds 
 us of our limited powers. Moreover, at most our 
 creation consists in transforming old materials into 
 new shapes. The potter moulds the clay ; the sculp- 
 tor chisels the marble, and both clothe with beauty 
 the rude materials on which they work ; but all the 
 while they are painfully conscious of the limitations 
 which the material imposes on their art. It is nat- 
 ural, therefore, to think of the Almighty as a power 
 before which all obstacles yield without effort, and 
 which can call order and beauty not only out of chaos 
 but out of nothing. There is, however, an illusion 
 which vitiates this inference; and the old apho- 
 rism " Ex nihilo nihil fit " is much nearer the truth. 
 The error consists in overlooking the limitations of 
 time by which we are circumscribed, but which can- 
 not bound the Creator. Our times are in His hands; 
 but God himself does not work in time. " God work- 
 eth hitherto and I work," said the Saviour ; but He 
 worketh not as man worketh. " He seeth the end 
 from the beginning, and looketh under the whole 
 heavens ; " and what to us appear as consecutive and 
 consequent are to Him parts of a plan whose pur- 
 poses will be fully revealed only when time shall be 
 no more. 
 
 The view, therefore, that a theory of creation by 
 slow development derogates from the attributes of 
 
286 " ETERNAL GENERATION." 
 
 the Almighty is a pure illusion resulting from our 
 limitations. To Him who inhabiteth eternity pur- 
 poses are valued, not as they seem to ripen fast or 
 slowly to us, but according to their beneficent de- 
 sign. God, who is ever present throughout all time 
 both to will and to do of His good pleasure, compre- 
 hends our temporal relations in His all-embracing 
 Providence, and adopts methods in view of the uni- 
 versal, and not solely of a temporal good. 
 
 In all material relations we have every reason to 
 believe that the knowledge we have acquired is accu- 
 rate and trustworthy ; but in speculating about spirit- 
 ual relations, we must always remember that we are 
 liable to be deceived by the aberrations of our mate- 
 rial vision; and we cannot safely build a theory of 
 the universe on such treacherous foundations as our 
 preconceptions of the methods of the Divine govern- 
 ment can alone furnish. 
 
 The conception of the creative power as acting 
 through an indefinite time, or rather as independent 
 of time, was familiar to Origen and the other Nicene 
 fathers, and was embodied by them in the famous 
 doctrine of the " Eternal Generation," which, although 
 usually limited to the second person of the Trinity, 
 was by Origen, at least, extended to the material 
 creation. 
 
 The recognition of this doctrine as applicable in 
 some limited measure to the genesis of nature would 
 tend very greatly to reconcile the systems of theology 
 with the systems of science. For if the theologian 
 accepts the eternal generation of the Son as one of 
 the most fundamental of his tenets, how can he con- 
 
ALL KNOWLEDGE IN HARMONY. 287 
 
 sistently find fault with the analogous doctrine of 
 science which involves a similar idea? 
 
 We do not advance the doctrine of the eternal gen- 
 eration of matter as positive knowledge, or even as 
 a legitimate inference of science ; but we do claim 
 that it is a possible inference from the observed facts 
 of nature, and that it is in entire harmony with the 
 most profound dogmas of theology. 
 
 Such speculations may have little value towards 
 establishing truth ; but they at least show how foolish 
 it is to set theological dogmas in opposition to sys- 
 tems of science. All real knowledge must eventually 
 be found to be in harmony, and the only way to find 
 truth is to seek it with untiring effort, and to keep 
 the mind unbiassed by any theories during the search. 
 The path is difficult, the labor exhausting, and with- 
 out faith in eternal verities the investigator will soon 
 lose heart, and abandon the search. If, however, 
 with singleness of purpose the student keeps the one 
 great aim in view, and not only has faith in truth 
 but the courage to face it in whatsoever guise it 
 may appear, he will gather strength as he pro- 
 ceeds ; and, although his vision in this life may be 
 restricted, and he may not rid himself of earthly 
 clogs, yet in the end he will at least be satisfied 
 that throughout the universe of being One Mind 
 ruleth over all. 
 
 Moreover, such speculations may have this positive 
 result in so far as they show that time is not the 
 measure of spiritual being. There are often periods 
 in life when crowding opportunities demand more 
 time than we have to give. But taking life as a whole 
 
288 MORE LIFE. 
 
 there is time enough for all we are able to accomplish, 
 and it is more energy, and not more time, that we 
 really need : — 
 
 " 'T is life of which our nerves are scant ; 
 More life and fuller, that I want." 
 
THE TWO SYSTEMS. 2#g 
 
 LECTURE X. 
 
 THE SYSTEMS COMPARED, — RELIGION AND 
 SCIENCE. 
 
 TN the necessarily imperfect sketch of scientific 
 ■*■ methods which has been given in the previous 
 lectures, my main purpose has doubtless been obvi- 
 ous from the first; and I think it must have clearly 
 appeared that the speculative objections to Christian 
 belief which are so confidently set forth are no 
 greater than must be encountered in every depart- 
 ment of abstract thought, and are inseparable from 
 our material relations. The close resemblance in this 
 particular between the systems of science and the 
 systems of religion presents, as it seems to me, by 
 far the most cogent of the evidences of natural the- 
 ology; and after examining the features of the scien- 
 tific systems it remains to bring together the separate 
 threads of the discussion and present the opposite 
 side of this very striking analogy. 
 
 I enter, however, on this part of the task I have 
 undertaken with great diffidence. Thus far I have 
 been, for the most part, on my own ground ; now I 
 pass over on to yours. And at the same time I feel I 
 ought to change positions, and in this distinguished 
 school of theological learning to seek instruction, and 
 not attempt to teach. I feel, moreover, that my 
 
290 POSITION TAKEN. 
 
 education in great measure unfits me for the office 
 which I temporarily fill; and as it is impossible that 
 I should see the subject from your point of view, I 
 fear that I may weaken the force of my argument 
 by overlooking features which you deem important ; 
 or even involuntarily offend by ignoring doctrines 
 which you deem essential. While I feel the firmest 
 assurance of the underlying truths of Christianity, and 
 the deepest respect for every honest conviction, still 
 I must confess that my whole education has made it 
 impossible for me to attach the same importance to 
 details of doctrine, or forms of ceremonial, as do 
 those who have been trained in a different school, 
 though I would not by any hint of mine wound the 
 sensitive realist, or the conscientious ceremonialist. 
 I say this without the least assumption of greater 
 freedom, or suspicion of complacency, — freely ac- 
 knowledging that the judgment of those who minister 
 to spiritual needs is much better established, and not 
 questioning that their spiritual insight is far deeper 
 than mine. 
 
 In my own province of thought I know so well 
 how an exact knowledge of relations will often set 
 aside judgments which a superficial knowledge might 
 seem to justify, that I am fully sensible that the same 
 principle must hold in other departments of learning 
 equally ; and I therefore offer the argument I have to 
 make simply as a suggestion, — feeling sure that it 
 will receive your thoughtful consideration, and be 
 accepted for all it is worth. Nevertheless, I have 
 thought — otherwise I should not be here — that 
 a certain advantage might arise in presenting the 
 
THE ARGUMENT STATED. 29 1 
 
 subject from a point of view different from that in 
 which a theological student is accustomed to regard 
 it; and that the opinions of a student of science, who 
 had given much thought to such questions, however 
 crude his theology, might help you to meet similar 
 questions which sooner or later in your ministry will 
 be forced by thoughtful men on your attention. I 
 may overestimate the strength of my argument, — for 
 the force of an analogical argument depends very 
 greatly on the previous experience of those to whom 
 it appeals, — but it has come home with overpower- 
 ing force to my own mind; and I find it difficult to 
 conceive how any one who has felt the bewilderment 
 of scientific uncertainty, as well as of religious doubt, 
 can resist its cogency. Take out the elements of 
 feeling, affection, and faith, and the last is to me no 
 more oppressive than the first. 
 
 The argument itself may be stated in a few words. 
 As there are systems of science, so there are systems 
 of religion ; and among these, one both intellectually 
 and morally so far in advance of the others that 
 it alone claims the consideration of educated men. 
 Regard now the Christian religion simply as an 
 external fact, as an existing spiritual, moral, or in- 
 tellectual force, independently of all supernatural 
 sanctions, or superhuman obligations, and all must 
 admit that it is the greatest power in the world. 
 However originating, or however appointed, there is 
 no power over men's minds and hearts which can 
 for one moment be compared with it. Throughout 
 Christian lands this power is everywhere pervasive, 
 and even in lands not recognized as Christian its 
 
292 THE ARGUMENT STATED. 
 
 indirect influence has softened the asperities of bar- 
 barism, and mitigated the cruelties of savage life. 
 
 Compare, in its mere external or intellectual as- 
 pects, Christianity as a system with gravitation. 
 
 As the way was prepared for Newton, so was the way 
 prepared, and in a most remarkable manner, for the 
 Founder of Christianity. For centuries before His 
 coming all that was purest and noblest in the world's 
 thought was leading up to the expected Messiah. 
 Then as the greatest advance ever made in the 
 knowledge of material things came by one man, 
 who greatly raised the level of scientific thought, so 
 Christianity came like a great induction of spiritual 
 truth, which so greatly raised the level of spiritual 
 thought that after nearly two thousand years the 
 Christian world does not yet appreciate the elevation 
 that was reached. 
 
 As modern science dates from Newton, so all that 
 is noblest and best in man, all that is pure and lovely 
 in life, all unselfish morality, all heroic chivalry, all 
 holy charity, is dated Anno Domini. 
 
 The Founder of Christianity was no mythological 
 hero ; but, whatever views we may entertain of his 
 nature, he was in form and likeness a man, living at 
 one of the best known epochs of the world's history ; 
 and every account of his character is in perfect har- 
 mony with his elevated doctrines and momentous 
 declarations. 
 
 That doctrine and those declarations present diffi- 
 culties of conception. We cannot reconcile them 
 with our experience of natural relations; and in the 
 same way we cannot reconcile the system of gravi- 
 
THE ARGUMENT STATED. 293 
 
 tation with our knowledge of the mode of action of 
 the other forces of nature. 
 
 While, however, there are these difficulties of con- 
 ception, the practical application of Christian doc- 
 trine as a rule of life, like the use of the principle of 
 universal gravitation in astronomical computations, is 
 perfectly simple and definite. Indeed, Christianity 
 was revealed as a life, and has been handed down to 
 us pure and undenled in the lives of its disciples. 
 
 Like systems of science, Christianity deals with 
 symbols, which are obviously the signs of realities 
 in their essence incomprehensible by man ; and even 
 if — as does at times happen in both cases — the sign 
 is mistaken for the substance, still such symbols are 
 of the very greatest value in aiding the imagination 
 and guiding the thought. 
 
 Newton so greatly raised the level of astronomical 
 conceptions that since his time astronomers have 
 been fully occupied in deducing the consequences of 
 his great induction ; and so, since the Christian ages 
 began, apostles, saints, and fathers, with lowly and 
 learned men of every name and calling, have been 
 diligently unfolding the beauties, the marvels, and 
 the glories of the truth that was then revealed. No 
 wonder that the interpretations did not always agree, 
 that bitter controversies arose, and that men profess- 
 ing the faith used power and influence as instruments 
 of oppression and persecution ; for the same sad feat- 
 ures have disgraced the history of science, without 
 the excuse of intense feeling to inflame passion or of 
 blind fanaticism to obscure reason. But as in spite 
 of follies and quarrels astronomy has grown to be a 
 
294 THE ARGUMENT STATED. 
 
 noble science, worthy of the most gifted human in- 
 telligence, so in an immeasurably greater degree the 
 Christian Church through weakness has been made 
 strong, and has become a holy temple in which the 
 loftiest aspiration finds satisfaction, the purest affec- 
 tion repose, and unsullied charity its full reward. 
 
 Lastly, as the system of gravitation has been tested 
 and ratified by the complete accordance of natural 
 phenomena with the deductions that it involved, so 
 has a most commanding seal been set on Christianity 
 by the entire harmony of the system with the spir- 
 itual needs of man. It is in that harmony that all 
 its strength lies. It has been tested by the most 
 varied experience. The blood of the martyrs has 
 been the seed of the Church ; and the attestation of 
 the great army of its confessors rolls down the Chris- 
 tian centuries with ever louder shouts of rejoicing 
 and songs of thanksgiving and praise. 1 
 
 While thus wonderfully adapted to man's spiritual 
 needs, so just in proportion as our knowledge be- 
 comes enlarged, and our insight deepened, is Chris- 
 tianity found to be in harmony with all truth. The 
 most gifted minds and profoundest scholars the world 
 has known have not only confessed Christ before 
 men, and acknowledged Him to be the Lord, but have 
 also testified that increasing acquirements and widen- 
 
 1 This test of experience, so clearly recognized in science, is 
 also accepted in theology ; and even Roman Catholic doctors 
 admit that the decrees of Councils must be accepted by the pub- 
 lic mind of the Church before they can be declared the voice of 
 God. As early as the fifth century Vincentius Lirinensis laid 
 down as the test of authority: "Quod semper, quod ubique, 
 quod ab omnibus creditum est." 
 
CHRISTIANITY A FACT OF NATURE. 295 
 
 ing vision brought an ever deeper conviction of His 
 truth. 
 
 If, then, man can in any case rely on his experi- 
 ence as a test of truth ; if harmony with nature is 
 any evidence of participation in the scheme of na- 
 ture ; if this world is not wholly a phantom and a 
 deceit; if all knowledge is not equally delusive, — then 
 the essentials of Christianity must be true. Such is 
 the argument. You must have anticipated it as I 
 traced out the features of scientific systems ; and I 
 have only to add, before concluding this course of 
 lectures, some connected thoughts which may serve 
 to enforce or illustrate special points of this strik- 
 ingly close analogy. 
 
 Remember, in the first place, that we are here 
 treating Christianity as a fact of nature, as an exist- 
 ing system of religious truth, on the same plane as 
 any other system of knowledge ; and from this point 
 of view only do we compare it with systems of sci- 
 ence, like the system of gravitation. We all believe 
 that Christianity has other sanctions and attestations ; 
 but in a question of Natural Theology we leave all 
 this evidence on one side, and deal with Christianity 
 only as an external fact of nature, as an historical 
 phase in the development of humanity, as a system 
 of morals, as a system of philosophy, or as a guiding 
 and directing motive which controls large masses of 
 mankind. I trust that I am not misunderstood; 
 although there is an obvious rhetorical difficulty in 
 dealing with the subject in this way. My language 
 might very easily be misconstrued, although I have 
 earnestly endeavored to avoid the occasion. No one 
 
296 CHRISTIANITY A FACT OF NATURE. 
 
 who has deep religious feeling can associate even in 
 the most indirect way Christianity with a system of 
 science; or the Founder of Christianity with the 
 originator of such a system, however great and 
 worthy, without feeling the incongruity which the 
 comparison involves ; and it is difficult to find lan- 
 guage which shall convey my meaning without a 
 suggestion of irreverence. You will, I am sure, ap- 
 preciate the difficulty and pardon any infelicity. 
 
 We are dealing solely with the evidence of nature, 
 and we must treat Christianity as a part of nature, 
 just as gravitation is a part of nature, if we would 
 estimate the value of the evidence which nature alone 
 can give apart from all other sanctions. Of course 
 other evidences have their due place, and to most 
 minds have such a paramount authority as to wholly 
 hush the feeble voice of nature. But I am here to 
 show you, as far as I am able, how forcible the tes- 
 timony of nature is by itself, apart from any super- 
 natural credentials ; and I affirm that Christianity as 
 an external fact is a part of this evidence. Chris- 
 tianity is a definite force in the world, and is as 
 essential a factor in the development of humanity, 
 as steam-power, electricity, or natural selection. 
 The supernatural evidence of Christianity is wholly 
 additional to the sanctions we urge ; and the former 
 is rendered vastly more credible and persuasive by 
 the evidence of nature. If you can remove the ante- 
 cedent presumption against the miraculous, you 
 place at once the overwhelming historical evidences 
 of Christianity on the same basis as all other his- 
 torical testimony; and how can you accomplish this 
 
THE ULTIMATE TEST OF TRUTH. 297 
 
 so effectually as by showing that the resulting system 
 is in entire harmony with what are always regarded 
 as earth-born systems? 
 
 I must, however, myself protest against the last 
 term, while using it to point a distinction. I believe 
 most firmly that all truth is one and inseparable, 
 and that there is no real distinction between heaven- 
 born truth and earth-born truth. I believe that in 
 the strict sense of the term, gravitation was as much 
 a revelation to man as Christianity. I cannot, there- 
 fore, call one human and the other divine. Grant 
 the widest difference between the modes by which 
 the revelations were communicated. Grant that the 
 very diverse nature of the revelations required this 
 difference ; yet in either case the truth is God's 
 truth ; and in the last analysis, the ultimate test of 
 all truth must be its universal and perfect harmony. 
 To me the most weighty evidence of Christianity is 
 its supreme naturalness ; that intensely human life in 
 the past, that Holy Church ever since, in perfect 
 harmony with all my purest affections and loftiest 
 aspirations, is the strongest assurance of truth, — and 
 truth is always and everywhere divine. 
 
 Again, Christianity as a fact of nature involves all 
 prior questions as to the personality of the Godhead, 
 or the attributes of Deity. We have no occasion to 
 go back to questions of design, or plan in nature. 
 We deal with the most conspicuous design, the most 
 wonderful plan; and if these are shown to be of a 
 piece with the rest of nature, why need we further 
 testimony? In the first lecture of this course, we 
 endeavored to show that all arguments from adapta- 
 
298 ADAPTATION TO MAN'S WANTS. 
 
 tion or from general plan were inductions based on 
 analogy; and that like other inductions their force 
 depended on the fulness with which they harmonized 
 the facts of nature. We claim for our present argu- 
 ment the same validity ; and if the claim is allowed, 
 the argument has a far greater range than any pre- 
 vious argument of natural theology; for it secures 
 all that Christianity, as an external fact of nature, 
 can be justly claimed to include. And looking at 
 the question in its simplest aspect, why is not the 
 adaptation of Christianity to man's spiritual wants as 
 direct an evidence of design as the adaptation of 
 the eye to seeing, or the lungs to breathing? — and 
 regarding the plan of redemption simply as it was 
 first exhibited by the life and death of Christ, and as 
 it has been exemplified in the lives and deaths of 
 saints and martyrs ever since, as conclusive an evi- 
 dence of intelligence as the plan of the vertebrate 
 skeleton, or the spiral distribution of leaves on the 
 stems of plants? 
 
 We have in the most positive manner affirmed 
 that inductions based on analogy or otherwise are 
 not, and from the nature of the case cannot be, dem- 
 onstrations; and have shown that they may offer 
 every degree of conclusiveness depending on their 
 agreement with the phenomena of nature. We could 
 have no more perfect accordance than Christianity 
 offers. But however conclusive such evidence, there 
 is always room for speculative doubt; and we freely 
 admit that our argument is not a proof, but it affords 
 all the certainty we can have in natural theology. 
 
 As I have before said, it is a striking fact in regard 
 
THE WAY WAS PREPARED. 299 
 
 to all scientific inductions that they never come to 
 fruition until the time is ripe. If premature, they 
 fall on barren soil, and the numberless anticipations 
 of genius are well-known illustrations of this truth. 
 And when we consider the obvious law of progres- 
 sion which the development of knowledge obeys, we 
 are forced to recognize that individual men, however 
 great their genius, are not essential to the result. 
 Like the prophets of old, they are interpreters of a 
 preordained purpose. No one can question that the 
 law of gravitation would have been discovered within 
 half a century, if Newton had not lived ; and, great as 
 his influence has been, and greatly as he hastened 
 the progress at the time, astronomy would certainly 
 have been as far advanced to-day if the work had 
 been left for other hands. Since the time of Hippar- 
 chus the way had been preparing for the great in- 
 duction ; and Isaac Newton was the name given to 
 the faithful and gifted servant who was born into 
 the world when the time was ripe. 
 
 Again, how striking the analogy with the coming of 
 Christianity ! Here also the way was prepared. " But 
 when the fulness of the time was come God sent forth 
 his Son, made of a woman, made under the law ; " 
 and although the messenger was the Divine Son, and 
 the message was the redemption of man, yet the gos- 
 pel came in the same simple naturalness with which 
 every great truth has come to the world. Before 
 John came crying in the wilderness, how long, how 
 tedious, and how devious, had been the way, how 
 halting the progress ; yet from time to time seer and 
 prophet had caught glimpses of the coming truth as 
 
300 THE COMING. 
 
 they diligently toiled in the vineyard, and sought to 
 make ready for the vintage of the Lord. 
 
 As I ponder this sublime history I cannot resist 
 the impression that this conformity to natural methods 
 is an irresistible evidence of genuineness which we 
 cannot afford to overlook. God introduced Chris- 
 tianity into the world by the same methods by which 
 He has opened to us all knowledge, — in order that 
 He should not confuse the understanding, or confound 
 the intelligence, of His creatures ; and thus it is that 
 our expanding science becomes to us on a lower 
 scale a type and similitude of the methods of Divine 
 revelation ; and the certitude of the one gives us a 
 confident assurance of the certitude of the other. 
 
 It was because I wished to set forth this analogy 
 in a strong light that I dwelt at some length on the 
 prelude to the discoveries of Newton, — in order that 
 you might see that his way was prepared by methods 
 not always direct, and by servants not always worthy, 
 and yet that all conspired to ensure the final result ; 
 and that thus you yourselves might draw out the anal- 
 ogy with a power which I am unable to command. 
 
 In entire harmony with the perfect naturalness of 
 the whole dispensation was the coming itself. It was 
 not in an obscure period of human history, or in a 
 remote corner of the earth ; but in the midst of the 
 Roman Empire, and during the Augustan age of the 
 ancient civilization. The coming was not heralded 
 by signs and portents which inspired awe and com- 
 manded attention ; but in all the simplicity of child- 
 hood, and in all the naturalness of growth. What a 
 lesson is there in the simple statement that " the 
 
GRADUAL UNFOLDING. 30 1 
 
 child grew, and waxed strong in spirit." And so un- 
 obtrusive and unobserved was this growth, except 
 by a few humble peasants, that when the glory of His 
 mature powers broke upon the Jewish world it ex- 
 cited the wondering remark, " Whence hath this man 
 letters, having never learned?" 
 
 In respect only to this natural growth, but as a 
 further incidental illustration of the fact that the most 
 glorious of all advents came to the world with entire 
 conformity to natural methods, allow me in all rever- 
 ence again to call your attention to the striking cir- 
 cumstance in the life of Newton, upon which I have 
 before dwelt, — that we find him, while still a college- 
 student, in possession of mathematical power, and of 
 a new calculus, not only far in advance of his teachers 
 but also of his age. The advent of new truth has 
 always been by the same gradual unfolding ; and is 
 there not the strongest antecedent presumption that 
 He of whose fulness we all partake should in His 
 mediatorial office conform to the same methods He 
 had Himself ordained? And is not the harmony of 
 the result with this antecedent presumption the 
 strongest possible evidence of genuineness? Would 
 man's invention in a pre-Christian age ever have 
 conceived of such a method or pictured such a 
 likeness? 
 
 The feature which above all things else is most 
 striking in a great induction is that such an advent 
 raises the level of human thought. Therefore such 
 inductions mark epochs in science. Astronomy 
 points back to Newton; and no one can question 
 that for years to come natural history will point back 
 
302 ANCIENT AND MODERN CIVILIZATION. 
 
 to Darwin. How is it with religious thought? The 
 comparison may seem almost irreverent; and yet it is 
 highly instructive. Looking at Christian institutions 
 simply as outward facts, without regard to sanctions, 
 dogmas, doctrine, or creeds of any kind, what do we 
 see? No less than this : that everything in the world 
 which is loftiest and profoundest in thought, which 
 is most ennobling and heroic in character, which is 
 bravest and most unselfish in action, which is purest 
 and loveliest in art, which is most consoling or hope- 
 ful in philosophy, and above all this, every form of 
 beneficent charity, every movement for the amelior- 
 ation of mankind, every influence which sanctifies 
 family ties, dates from one conspicuous and definite 
 epoch of the world's history from which civilized 
 men began to count anew the revolving years. 
 
 I certainly need not in this place attempt to draw 
 a parallel between the ancient and the modern civili- 
 zation, to show how great a change was wrought, and 
 how great an elevation was reached in one short life. 
 But if in the interest of natural theology I can induce 
 you to look at the subject from my point of view, 
 and for the sake of argument to consider the claims 
 of Christianity as simply an external feature in human 
 society, I hope I may render a real service by giving 
 you the command of a very powerful argument which 
 can be pressed, not only without compromising or 
 invalidating any supernatural evidences, but on the 
 contrary, which will furnish a secure basis on which 
 such claims can be established. It must be that a 
 system which is so obviously a part of nature has the 
 same authenticity as the rest of nature; and then 
 
NATURE AND THE SUPERNATURAL. 303 
 
 comes home with redoubled force the old argument 
 that men unaided could not have raised themselves 
 by one leap to such an elevation. 
 
 Even in regard to scientific discoveries it inspires 
 confidence to know that the investigator was in full 
 relations with his subject, and in all respects equal to 
 his work; and we have shown how conspicuously 
 this was true in the case of Newton. But who can 
 " speak the matchless worth " of the Founder of 
 Christianity? Certainly not a layman in this place. 
 It is to be your great privilege to rehearse this story ; 
 and, as told by your lips, in simplicity and power, 
 may it bring consolation, comfort, and conviction to 
 many a weary and troubled soul. In seeking to 
 make evident that " Nature and the Supernatural," 
 are "The one System of God," a most gifted and 
 spiritually minded American clergyman, the late 
 Horace Bushnell, has sounded forth the glories of 
 that wondrous tale " in notes almost divine; " and in 
 following his chaste, beautiful, and effective presen- 
 tation of the character of Christ, the one feature that 
 most impresses the reader is its supreme naturalness. 
 The consciousness of power is all there ; the mystery 
 of personality is all there; the terror of justice is all 
 there ; the avvfulness of sacrifice is all there. But it 
 is the sweetness of affection, the tenderness of com- 
 passion, the earnestness of pity, the fervor of charity, 
 the ardor of zeal, the devotion to duty, the submission 
 to authority, the perfection of manhood, which rivets 
 our attention, which engages our sympathies, which 
 commands our reason. 
 
 All systems of science, as we have seen, present 
 
304 DIFFICULTIES OF CONCEPTION. 
 
 insuperable difficulties of conception, because mate- 
 rial relations are the measure of our experience and 
 therefore the measure of our positive knowledge. 
 Can we expect that the philosophy of religion will 
 be more intelligible? And the more we study, the 
 more plainly it will appear that in this respect also 
 the two orders of truth present a most striking anal- 
 ogy ; and that in either case the difficulties arise from 
 the impossibility on our part of picturing to the mind 
 any relations not realized in our own experience or 
 in that of our fellow-men. Even in regard to material 
 relations there is a great difference among educated 
 men in the power of realizing unseen conditions ; and 
 to rude, unimaginative folk nothing exists beyond the 
 range of their immediate perceptions. With those 
 whose imaginative faculties have been most cultivated, 
 the limit of power is soon reached ; and however 
 much the philosopher may speculate about trans- 
 mundane realities, and however firmly he may believe 
 in them, he can form no mental images of such beings 
 that are not painted in colors of clay. Hence it is 
 that I have dwelt so fully on the difficulties of con- 
 ception which the fundamental concepts of physical 
 science present, — in order that you might appreciate 
 how very close is the analogy which I am endeavoring 
 to enforce. 
 
 The incongruities and apparent inconsistencies 
 which the systems of science involve do not invali- 
 date their essential truth, but they do most conclu- 
 sively indicate that we are dealing with relations 
 beyond the range of our experience ; and our at- 
 tempts to represent these relations to our minds by 
 
NATURALNESS OF THE GOSPEL. 305 
 
 means of ethereal media or assumed attractions re- 
 semble the play of children with their dolls and toys. 
 
 In like manner it is no objection to a theological 
 system that it involves much that is incomprehensible 
 and seemingly contradictory. The question simply 
 should be, Does it give a faithful representation of 
 known facts and relations? and if so, the inconsis- 
 tencies indicate no more than this, that it deals 
 with forms of being beyond the range of human 
 experience. 
 
 It is to me a striking evidence of the truth, as well 
 as of the naturalness of the gospel narrative, that 
 throughout there should be such an accommodation 
 to the necessary limitations of human intelligence. 
 On all occasions the truth is presented in the simplest 
 material imagery, and the most tender regard is paid 
 to the Marthas and Thomases of every age, to whom 
 seeing could give to belief the only adequate certi- 
 tude ; and when it was necessary to certify to eternal 
 realities and to arouse men from their material leth- 
 argy, how unaffectedly it is done with a few simple 
 but grand sentences. How differently it would have 
 been, how differently it has been, with every human 
 teacher to whom has been opened a vision of things 
 eternal. How irresistible has always been the ten- 
 dency of the human mind, however enlightened, to 
 dwell on all that is anomalous, incongruous, or awe- 
 inspiring, in the situation described. We find this 
 most markedly in the elder dispensation. We find 
 it even in the vision of the Apocalypse. And is 
 there not a lesson in such facts which we may well 
 ponder? 
 
306 PARADOXES OF DOGMAS. 
 
 In teaching physical science it would be very un- 
 wise to give prominence to the difficulties of concep- 
 tion on which for a special purpose we have dwelt in 
 these lectures. These are real difficulties, and must 
 be met by every thoughtful student sooner or later ; 
 but they have no practical significance, and are 
 wholly ignored in the every-day work of the labo- 
 ratory. Of course no feeling is here involved, as in 
 religious questions ; but with all this difference is it 
 wise, in an age which is so much engrossed with ma- 
 terial interests, to give prominence to similar difficul- 
 ties of theological doctrine that have as little bearing 
 on Christian living? Is it not better that they should 
 be ignored than become hindrances to faith? and 
 does not all experience teach that a faith well- 
 grounded on personal experience and active benevo- 
 lence will accept any doctrine once delivered to the 
 saints whose holy lives it seeks to imitate? 
 
 Our Puritan forefathers delighted in theological 
 dialectics, and sought to exaggerate rather than to 
 reconcile the paradoxes and contradictions of dogmas. 
 They were thoughtful men of speculative dispositions, 
 whom both political circumstances and sensitive con- 
 sciences had debarred from the intellectual life of the 
 world, and who found the chief exercise of their in- 
 telligence in the discussion of theological dogmas. 
 But it may be doubted whether this at times morbid 
 exercise of their faculties induced any more humble 
 and loving lives than those of many a devoted saint 
 who never so much as heard of Foreknowledge or 
 Predestination. 
 
 In connection with the difficulties of conception 
 
CONTINUITY OF LIFE. 307 
 
 which the Christian system involves, the question of 
 the Christian miracles at once suggests itself; but 
 this is too large a subject to be discussed here. Two 
 principles, however, which we have sought to estab- 
 lish, have a bearing upon the matter. The first is 
 that, with certain obvious limitations, there can be no 
 prodigy in nature so wonderful that it may not be 
 accepted on adequate evidence; and the second is 
 that so far as our knowledge extends there is ample 
 room for the appearance of new forces in the chain 
 of causation. Obviously these principles, if estab- 
 lished, remove in very great measure the antecedent 
 presumption against miracles, and leave their authen- 
 ticity to be established in every case by the evidence 
 alone. In weighing evidence men will be guided by 
 the self-evident truth that it is more probable that a 
 witness should be deceived than that the usual order 
 of nature should be altered ; and if the evidence is in 
 question, the counter presumption thus created is 
 overwhelming. But in the presence of well-attested 
 fact all questions of probability scatter to the winds ; 
 and what better attestation of an historical fact can 
 you have than continuity of life? and I question if 
 any one who has fully partaken of that life ever 
 questioned the validity of the evidence. 
 
 Thus the continuous life of the Church from the 
 beginning becomes the most convincing evidence of 
 the Resurrection, that of all Christ's miracles the most 
 vital to the authority and influence of His Church ; 
 for " if Christ be not risen then is our preaching vain, 
 and your faith is also vain." Just as the religion of 
 Mahomet, as a power in history, dates from the 
 
308 THE RESURRECTION. 
 
 Hegira, and, however surprising the effects ulti- 
 mately produced by such gross materialism, presents 
 a perfect continuity from the first, each step of the 
 progress being natural and intelligible, — so Chris- 
 tianity, as a force in society, dates from the Resur- 
 rection, and shows an unbroken line of sequences 
 from that event. Granted, if you demand it, that the 
 Resurrection was a condescension to the conditions of 
 our material existence. Explain the outward aspects 
 of the event as you please. Still there remains the 
 fact of history that something occurred at that time 
 which produced conviction on the minds of the be- 
 holders, and to which the origin of the Christian 
 Church must be traced. 
 
 The high morality of Christ's teaching cannot 
 account for the founding of such a church. The 
 Crucifixion destroyed all hope even in the small 
 band of followers who were faithful to the last ; and 
 without some remarkable attestation, Christ's teach- 
 ing would have produced no more effect on the 
 world than that of Socrates, or of Plato, even if the 
 records had been preserved. Something must have 
 occurred which changed despondency to hope, and 
 which inspired the disciples with courage and enthu- 
 siasm. The gospel narrative gives an explanation 
 which accounts for the result. The wonderful event 
 which had been predicted took place. Man could 
 have no conviction except through experience, and 
 the experience was furnished. 
 
 We cannot suspect the founders of Christianity of 
 deliberate falsehood, any more than we can believe 
 that an event from which such great consequences 
 
THE RESURRECTION. 309 
 
 immediately flowed was a myth. The witnesses must 
 have believed that they saw what they described. 
 Explain away the facts as you please. Regard the 
 phenomena observed as purely subjective to the 
 minds of those present, and the outward appearances 
 as delusive, it still must be admitted that something 
 occurred, either outwardly or inwardly, which pro- 
 duced such a profound impression on the minds of 
 the beholders as to arouse the highest enthusiasm, 
 and the most unselfish devotion, the world has ever 
 known ; and from which a chain of consequences has 
 been forged link by link until all that is best and 
 noblest of the human race has been enchained in its 
 bonds of love. 
 
 Herein lies the great wonder. The miracle was not 
 wrought for us. Thank God ! we cannot investigate 
 the circumstances now, or analyze all the material 
 imagery that was accessory to that solemn scene. 
 But of this at least we may be sure : at that time a 
 new motive came into operation which changed the 
 whole order of society, and to this time history points 
 continuously back, as it does to Caesar crossing the 
 Rubicon, or to Luther nailing his theses to the door 
 of the Schlosskirche at Wittenberg. If there be such 
 a thing as order in the evolution of nature this event 
 was a part of that order. If there be an intelligent 
 Ruler of the world this event was ordained by Him ; 
 and whether He worked through methods intelligible 
 to us, or by means past our finding out, and which 
 with our limited knowledge and experience we call 
 supernatural, the event was no less miraculous in its 
 occurrence, no less wonderful in its result. 
 
310 THE SYMBOLISM OF CHRISTIANITY. 
 
 Turning now to the practical working of the Chris- 
 tian system, how simple are the principles of action, 
 how plain the duties ; and what Christian mother 
 watching over her sick child, what aged saint nearing 
 his rest, or what soldier of Christ in the midst of the 
 conflict were ever troubled by difficulties of concep- 
 tion? Our analogy here again is perfect. 
 
 I hope further that the analogy of the symbolism 
 of science may aid us to a better understanding of 
 the purport of the symbolism of Christianity. We 
 have endeavored to show that the symbols in 
 chemistry were something more than mere conven- 
 tionalism ; that although absurd and grotesque if 
 regarded as the exact patterns of realities, they were 
 obviously the signs of an underlying truth as yet 
 only dimly apprehended. How characteristic this is 
 also of all the legitimate symbols of Christianity, in- 
 cluding under this term much of the imagery both of 
 the Old and of the New Testaments. These are pro- 
 fessedly types, not likenesses of spiritual being; but 
 like the symbols of science, they are aids to the im- 
 agination, they give definiteness to thought, they 
 give substance to things unseen. Such types, how- 
 ever, must resemble in certain features their origi- 
 nal, inasmuch as they form a safe basis of inference, 
 and, like the symbols of science, guide the mind to 
 the discovery of truth. Like the ladder seen in vis- 
 ion by the patriarch at Bethel, they rest on earth, 
 but they lead upwards to where the material blends 
 with the spiritual in the effulgence of Divine glory. 
 On the other hand, as the conventional forms of 
 science often acquire an undue prominence, and be- 
 
GRADUAL UNFOLDING. 3 1 1 
 
 come invested with an imaginary concreteness in the 
 thoughts of those who are constantly occupied there- 
 with, so the symbolism of Christianity is also too 
 frequently materialized, and the spirit that giveth 
 life completely hidden by the letter that killeth. 
 
 In all great scientific inductions which have per- 
 manently raised the level of human knowledge, the 
 advantage gained has never been appreciated at the 
 time, and it has been the work of years to develop 
 the consequences of a single lofty intellectual con- 
 ception. Here again the parallelism is most striking 
 with the Christian revelation. How faintly did the 
 earlier disciples comprehend the work of their Mas- 
 ter; and, as century after century has passed since, 
 how slowly has the world come to a realization of the 
 truth ; and in proportion as man has become enlight- 
 ened, how steadily has the scope of the grand scheme 
 widened before his enraptured vision. So also if we 
 consider solely the intellectual aspects of the Chris- 
 tian system, where in literature shall we find a power 
 of deductive reasoning comparable with that of the 
 great apostle to the Gentiles, whose boast was " Not 
 as though I had already attained, either were already 
 perfect, but I follow after." Pressing this analogy 
 still further, we may not inaptly compare theological 
 systems with the deductions of science, and like the 
 last those also must abide the test of experience, and 
 be judged by the united voice of that great multitude 
 who have been redeemed to God " out of every 
 kindred and tongue and people and nation." 
 
 I have quite failed in one of my chief aims in these 
 
 lectures if I have not succeeded in impressing you 
 21 
 
312 SENSE OF LIMITATION. 
 
 with the strong sense which I feel of the uncertainties 
 and limitations which encompass the student of na- 
 ture on every side. I am well aware that such feel- 
 ings as I have expressed are in part a matter of tem- 
 perament, and that some men are more susceptible 
 to such impressions than others. Still, your own 
 knowledge of literature will sustain me in the asser- 
 tion that in all that I have said I am in sympathy 
 with the noblest thinkers the world has known. Un- 
 numbered scholars, of whose attainments the world 
 has been proud, and for whose contributions to knowl- 
 edge the human race will be ever grateful, — men like 
 Plato, Marcus Aurelius, Copernicus, Descartes, New- 
 ton, Faraday, — have left written evidence of a more 
 or less deep conviction that the intellectual life has a 
 nobler destiny than the life of the body ; that there 
 may be modes of existence of which 'the senses take 
 no cognizance ; and that, while the things which are 
 seen are temporal, the things that are unseen are 
 eternal. There has always been with such minds a 
 " reaching forth unto those things which are before," 
 and although they may not have recognized the goal, 
 a pressing "toward the mark for the prize of the 
 high calling of God in Christ Jesus, . . . who 
 shall change our vile body, that it may be fashioned 
 like unto His glorious body, according to the work- 
 ing whereby He is able to subdue all things unto 
 Himself." 
 
 How true it is now of our systems of theology as of 
 our systems of science that " we know in part, and 
 we prophesy in part. But when that which is per- 
 fect is come, then that which is in part shall be done 
 
man's place in nature. 313 
 
 away." And how obviously the recognition of such 
 limitations in our present life points beyond the veil. 
 The consciousness of limitation is an evidence of 
 things unseen, and thus our material hindrances 
 become educators of faith. They are a law in our 
 members " which is our schoolmaster to bring us 
 unto Christ." 
 
 The harmony of the Christian system with the 
 methods of nature, and the force of the argument 
 which rests on this analogy, nowhere appear more 
 conspicuously than when studied in relation to the 
 most recent of the great systems of science. Man as 
 an animal is weak as compared with many of the 
 higher vertebrates, and unfitted to cope with them in 
 the fight for existence. Place man naked, but in the 
 full command of his physical powers, in a jungle with 
 tigers, or even in a forest with wildcats, and he would 
 have no chance in the inevitable struggle that must 
 ensue. The element of intelligence, and that alone, 
 makes his superiority; and this mental endowment 
 has made a comparatively weak animal the lord of 
 creation. According to the new school of natural- 
 ists, man's development must have begun ages back, 
 when intelligence became an important factor in the 
 struggle for life. Remember, however, that, as I have 
 before shown, this factor may have been a preor- 
 dained condition then appearing for the first time in 
 the chain of causation ; and that as yet certainly we 
 have no knowledge whatever which would render 
 such an interference (if the preordained can be called 
 an interference) either impossible or improbable; 
 and further, recall the opinion then expressed that 
 
314 man's ancestors. 
 
 geological evidence indicates a marked break at the 
 advent of man. You may then without prejudice 
 accept the necessary inference from the theory that 
 man after the flesh was descended, not from any 
 species now existing, but from some species far less 
 fitted to cope with its surroundings than the monkey, 
 the ourang, or the gorilla have become. These an- 
 thropoids are not regarded as the ancestors of man ; 
 but both they and man are, according to the modern 
 hypothesis, descendants of a common ancestor. Man 
 has remained comparatively feeble in his physical 
 powers, but has gained supremacy through his in- 
 telligence. The animals most like him in outward 
 form and structure, not partaking of his intelligence, 
 have been developed in one or another direction 
 to a far higher degree ; because they have had to 
 wage the fight for existence with physical powers 
 alone. 
 
 In considering the influence of intelligence in the 
 struggle for existence, remember that it has led men 
 to combine in societies, and establish governments 
 so as to protect the weak. Under such conditions, 
 while man's collective power to cope with brute 
 forces has been greatly increased, his individual 
 power has been weakened ; and circumstances con- 
 stantly remind us what a weak, miserable animal man 
 is when left to his own resources. When you con- 
 sider what a delicate, helpless creature the human 
 infant is, it will require no aid of poetry or art to 
 show how soon the race would be extinguished if the 
 human mother were left to defend her offspring with 
 her own strength. The tales of the wilderness chiefly 
 
THE LEADERS OF MEN. 315 
 
 owe their interest, as it seems to me, to the vividness 
 with which they picture the features of that fierce 
 and terrible warfare from which civilized men are so 
 greatly protected through their institutions and their 
 inheritances ; and they show us that even in the sav- 
 age state the protection, such as it is, arising from 
 association and combination, is equally essential to 
 the continued life of the race ; thus plainly indicat- 
 ing that even the feeble intelligence of the savage 
 gives him an immense advantage over the brute in 
 the struggle for existence. 
 
 As intelligence has been the chief factor which has 
 given the race of man its pre-eminence, so it has been 
 that gift in a special degree which has given to indi- 
 vidual men the power of advancing their race. The 
 great men who have marked special epochs in history, 
 or to whom great movements may be traced, have 
 been men of great mental power in some phase or 
 other, or else men endowed with unusually clear 
 spiritual insight. Recall the great names of history, 
 the great conquerors, the great rulers, the great law- 
 givers, the great in literature, the great in art, the 
 great in science, the great in philosophy, the great 
 in theology, the founders of states, the founders of 
 religions, the heroes, the saints, and the prophets of 
 every age. Who of all these men whose names are 
 household words, remembered and cherished when 
 all other records of the past are forgotten, who, I say, 
 has exerted the greatest influence, and produced the 
 most lasting effect on the progress of mankind? 
 There can be but one answer. Theorize about the 
 matter as you please, explain the influence as you 
 
3 16 GROWTH THE METHOD OF CREATION. 
 
 may, by far the greatest effects ever produced in his- 
 tory can be traced directly to the teaching of the one 
 Man who was born of Mary in the manger at Bethle- 
 hem. Frame what theories you please about His 
 nature, He is, on the lowest view of His nature, the 
 greatest leader of humanity. It is the reasonable 
 course to accept His own theory of Himself, and to 
 act upon it; and men by acting upon it have raised 
 themselves and their fellows immeasurably in the 
 scale of being. 
 
 Let us not fail to remember also in this connection 
 that development, or slow growth, is plainly the 
 method of creation. Nothing is more distinctly 
 taught by nature than this. Every advance in knowl- 
 edge only makes this truth more plain. Before Dar- 
 win published his now famous work on " The Origin 
 of Species," an English poet wrote : — 
 
 " The solid earth whereon we tread 
 
 " In tracts of fluent heat began, 
 
 And grew to seeming random forms, 
 The seeming prey to cyclic storms, 
 Till at the last arose the man ; " 
 
 and this plain teaching of geology can be supported 
 by overwhelming facts from almost every department 
 of knowledge. If the Bible in some passages may 
 seem to imply otherwise, these passages must be in- 
 terpreted by the spirit of the writing, which through- 
 out enforces the reverse idea, and nowhere more 
 impressively than in the teaching of Christ Himself. 
 It is not, as some seem to think, a question of power 
 to create, but solely a question of method. One of 
 
PERFECTION THROUGH SUFFERING. 317 
 
 the most striking features in the life of Christ is His 
 submission to the slow, halting, and apparently cruel 
 methods of nature ; while all the time there is an evi- 
 dent consciousness of power to secure the end and 
 avoid the pain. When we are impatient with these 
 methods, and think that they derogate from the maj- 
 esty of the Almighty, let us remember that scene 
 under the olives of Gethsemane, the impatience of 
 the disciple, the calmness of the Master, and the 
 memorable words, " Thinkest thou that I cannot now 
 pray to my Father, and He shall presently give me 
 more than twelve legions of angels ? " 
 
 But although we may not without exaggeration 
 push our analogy further, yet we can catch glimpses 
 of a meaning still deeper than any we have as yet 
 grasped ; and I hope I shall be pardoned if with 
 deepest reverence I allude to this obscure and terri- 
 ble significance. We recognize the struggle for exist- 
 ence as an agency in nature, and the naturalists 
 discuss its effects as they would those of heat or 
 electricity. But do they, do we, realize what is im- 
 plied by these words ? They cannot ; for they would 
 be staggered by the thought, and overwhelmed by 
 the horror, and could not write or speak so coolly if 
 they did. " For we know the whole creation groaneth 
 and travaileth in pain together until now." Those 
 who minister in the slums of your cities know how 
 true this is ; and they will tell you that these impas- 
 sioned words of St. Paul convey no adequate con- 
 ception of the reality. Even fiction does not dare 
 to depict faithfully the terrible death struggle, and 
 art is powerless before it. If we turn pale at the 
 
3 IS PERFECTION THROUGH SUFFERING. 
 
 bare recital of the horrors of the siege of Jerusalem, 
 of the plague at Florence, of the hecatombs at Co- 
 massie, or of the battle-fields recorded on every page 
 of history, and also of the visitations of earthquake, 
 shipwreck, tornado, and pestilence, which at times 
 come near our own homes, and are stirred from the 
 inner depths of our souls by the distant roar of the 
 conflict, what must have been the ordeal through 
 which our race has passed, what the sorrow and 
 anguish through which every advance has been won ! 
 And do we ourselves realize that our civilization, 
 our education, our well-being, and all that consti- 
 tutes our birthright have been purchased with so 
 much blood? 
 
 If this be true of man, the most favored of creat- 
 ures, and through his intelligence the most capable 
 of protecting himself, we can readily believe the 
 declaration of naturalists that the destructiveness of 
 the internecine warfare among the lower animals is 
 wholly beyond the power of imagination to conceive. 
 Swift destruction is the rule, — life, however short, the 
 great exception ; and one is astonished by the enor- 
 mous productiveness of nature which can people the 
 earth in spite of such a drain. All naturalists are 
 agreed that it is this wholesale destructiveness which 
 alone gives efficacy to what is called natural selection. 
 As the animal is higher in the scale of being, the 
 destructiveness is less; but in the same proportion 
 the suffering is greater ; and among men the capa- 
 bility of suffering is almost a measure of intellectual 
 and spiritual growth. As then in the struggle for 
 existence perfection is reached through suffering, so 
 
THE MYSTERY OF PERSONALITY. 319 
 
 in the spiritual world men rise to higher things 
 through sorrow ; and though as they rise their power 
 of suffering is increased, yet in the beauty of holiness 
 their sorrow is at last turned into joy. " Blessed are 
 they that mourn, for they shall be comforted." Thus 
 the Cross becomes the type of perfect character, as 
 well as the type of deepest sorrow ; and as we pass 
 beneath its shadow, nature will help to teach us the 
 deep significance of those solemn words, " And if I 
 be lifted up I shall draw all men unto me." 
 
 On the quai which lines the banks of the Loire at 
 Tours stands a noble statue, erected in honor of the 
 greatest philosopher France has ever known; who, 
 although he thought and wrought elsewhere, and died 
 in a foreign land, was born in Touraine. On the 
 pedestal is engraved simply 
 
 " RENE DESCARTES ; " 
 
 but at the foot of the statue we read, as from the 
 great man's lips, 
 
 "COGITO, ERGO SUM." 
 
 Most beautifully has this famous aphorism been para- 
 phrased by the great English poet whose verses I 
 have several times quoted because nowhere else do 
 I find so forcible an expression of the overpowering 
 sense of natural phenomena which weighs on my 
 own soul, but which my feeble words are powerless 
 to reproduce : — 
 
 " The baby new to earth and sky, 
 
 What time his tender palm is pressed 
 
320 " C0GIT0, ERGO SUM." 
 
 Against the circle of the breast, 
 Has never thought that « This is I.' 
 
 " But as he grows he gathers much, 
 And learns the use of ' I ' and ' me ' ; 
 And finds ' I am not what I see, 
 And other than the things I touch.' " 
 
 The mystery of evil and the mystery of suffering 
 have their counterpart in the mystery of personality. 
 Science has not shed one single ray to lighten the 
 darkness of either mystery. We have faith "that 
 somehow good will be the final goal of ill." We 
 trust that Omniscience and Free Will, Omnipotence 
 and Sin, Beneficence and Suffering, will one day be 
 reconciled to our intelligences ; and we look for the 
 explanation to those awful necessities which an alli- 
 ance of the spiritual with the material implies. Still, 
 amidst all this darkness our analogy does not wholly 
 fail us, and we have clear indications that the pro- 
 visions of Grace are of a piece with the provisions 
 of material nature. 
 
 If there is one attribute of our being which more 
 than any other marks our individual existence, it is 
 the consciousness of personality ; and yet that entity 
 which thinks and wills is so blended with our material 
 nature that we cannot, except in thought, dissociate 
 the two. The conclusion of the profoundest analysis 
 which philosophy can make is still expressed in the 
 three words " COGITO, ERGO SUM." Nevertheless, 
 this personality is the most conspicuous fact in all 
 human history, and every attempt of false science or 
 of poetry to resolve or obscure it, has been wholly 
 
SPIRITUAL LIFE. 32 1 
 
 vain. Personality, with its free will, is, then, an ele- 
 mentary principle of nature ; and how wonderfully is 
 Christianity throughout in harmony with this funda- 
 mental truth. The great object of the Gospel is to 
 purify and sanctify the sources from which it pro- 
 ceeds, but the personal will is always left free and 
 inviolate. The recorded miracles all dealt with ma- 
 terial nature. Christ never constrained a human will. 
 When He knew that it was to betray Him, and a 
 single word would arrest the action, He allowed it 
 free course; and in the final passion — "then said 
 Jesus, ' Father forgive them, for they know not what 
 they do.' " 
 
 We have time for only one further thought. Man 
 knows nature because he is in harmony with it; man 
 knows spiritual truth in the same way; and certitude 
 in either case rests on similar evidence. Such are 
 the general propositions which I have sought to 
 maintain in these lectures. We have to thank the 
 evolutionists for a plausible explanation of the first 
 of the propositions, and they will not object if we 
 apply the same principles to the second. A simple 
 cell, at first only slightly sensitive to light, has devel- 
 oped into that organ of wonderful adaptations, the 
 eye. By the survival of the fittest, each advantage 
 gained has been held and handed down; and thus 
 the organ has been gradually adjusted to the environ- 
 ment, and fitted to give to the mind of man truthful 
 information about external objects and accurate im- 
 pressions of the beauties of the outer world. So 
 another cell, specially sensitive to the vibrations of 
 the atmosphere, by associating with itself other sen- 
 
322 CONCLUSION. 
 
 sitive cells and bequeathing every small gain by 
 which the resulting structure became more respon- 
 sive to the tremors of sound, has grown into that 
 other organ, not less wonderful, through which the 
 mind receives equally faithful impressions of har- 
 mony, melody, and articulate speech. The method 
 by which these results have been worked out is, 
 however, a question of no importance to our argu- 
 ment, so long as we all admit — as all do, evolu- 
 tionists with the rest — that the capacity of these 
 organs to give accurate information about the ex- 
 ternal world is wholly due to their adaptation to the 
 environment. 
 
 But if man's harmony with his environment physi- 
 cally is an evidence of truth, then his harmony with 
 his environment spiritually must be equally so. If a 
 sensitive nerve can be trusted, a sensitive conscience 
 is not less trustworthy; otherwise man's mind must 
 have grown into harmony with its environment in one 
 relation, and not in the other. If when man longs for 
 beauty and harmony the impressions which flow in 
 through the eye and ear are to be trusted, then it 
 must be that when in his higher moods he yearns for 
 purity and righteousness and holiness, the assurances 
 which come to him on his bended knees are equally 
 well-founded. 
 
 Finally, if there be any knowledge, if there be any 
 truth, if there be any certainty in this mortal state 
 of being, if there be any consolation in the past, any 
 satisfaction in the present, any hope in the future of 
 this world, it is only to be found in the spiritual life 
 
CONCLUSION. 323 
 
 of man. That alone is permanent amid ceaseless 
 change; that alone is satisfying amid constant sati- 
 ety; that alone is comforting amid constant disap- 
 pointments; that alone is sustaining amid constant 
 suffering ; that alone is consoling amid constant be- 
 reavement; that alone is assuring in the presence 
 of death ; that alone is triumphant in the confident 
 hope of immortality. And if I have been able, in 
 however imperfect a way, to make more evident to 
 your understanding that our power of apprehending 
 spiritual things, our discernment of righteousness, 
 our thirst for affection, our aspiration after purity, 
 our communion with holiness, are as truly evidences 
 of external realities as any impressions of our senses ; 
 and further, if it has appeared that the inductions 
 based on the experiences of our spiritual life are 
 just as authentic, and just as valid, as those drawn 
 from material phenomena, — then I have accomplished 
 the object at which alone I have aimed in these 
 lectures. 
 
 I am well aware that I have not sounded the key- 
 note of theology ; but this was not my office. I was 
 intrusted with the very subordinate task of sustaining 
 the harmony of the refrain in which alone nature can 
 join in the heavenly song; and I even fear that I 
 have made my part too prominent. 
 
 You will receive commission to preach the glad 
 tidings of a risen Lord, and no more noble service 
 can man render on earth. If I have in any measure 
 helped to prepare your way, it is all that I could 
 hope to accomplish. You are intrusted with a mes- 
 
324 CONCLUSION. 
 
 sage before which all the learning of the world must 
 bow. Proclaim it confidently and fearlessly, not in 
 " oppositions of science falsely so-called," but in 
 the name of Him who alone is " the Way, the Truth, 
 and the Life." 
 
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