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IDEALITY 
 
 IN THE 
 
 PHYSICAL SCIENCES 
 
 BY 
 
 BENJAMIN PEIRCE 
 
 BOSTON 
 LITTLE, BROWN, AND COMPANY 
 
 1881 
 
Copyright, 1881, 
 Bt S. M. Peirce. 
 
 University Press: 
 John Wilson and Son, Cambridge. 
 
K IBeBirate 
 
 THESE LECTURES 
 
 TO MY WIFE 
 
 WITH MT WHOLE HEART 
 
 BENJAMIN PEIECE 
 
 Cambridge, 790320 
 
EDITOR'S PREFACE. 
 
 In the winter of 1877-78, Mr. Augustus Lowell 
 proposed to my father to deliver a course of lectures 
 at the Lowell Institute in Boston, and suggested his 
 taking the occasion to express his views on the true 
 attitude of science towards religion, and to discuss 
 other subjects of wide interest, falling within the 
 range of his lifelong thought. My father was al- 
 ready sensible of the weakening and dispiriting influ- 
 ence of ill-healtL He was little accustomed to write 
 out his public addresses, or even his communications 
 to scientific societies, and he greatly shrank from 
 that labor ; while in this instance he was unwilling to 
 trust, in any considerable degree, to the utterance of 
 the moment. But he could not long hesitate to ac- 
 cept the opportunity — his last, as he expected it to 
 be, and as indeed it was — of appearing before the 
 general public, to advocate that high conception of 
 the functions of science which he always earnestly 
 
 ^ u 
 
iv PREFACE. 
 
 maintained, to offer his own contribution to the great 
 theory of evolution, and to testify his unwavering 
 faith in the ultimate advantage to religion of every 
 movement of scientific thought. 
 
 He limited himself to a course of six lectures, and 
 devoted his leisure during the year 1878 to preparing 
 the contents of the present volume. The lectures 
 were delivered in February and March, 1879. They 
 were also given, a year later, at the Peabody Institute 
 in Baltimore ; and two or three of them were read 
 occasionally in various private circles. It was a 
 great satisfaction to my father to have given this 
 final expression to some long-pondered views, for 
 which he felt, as he used to say, all the anxious 
 tenderness of a parent; and it is pleasant to re- 
 member that the kindness of his public towards 
 these children of his brain was a bright source of 
 happiness to him in his last years. 
 
 The plan of publishing the lectures was enter- 
 tained and abandoned at several different times. 
 Shortly before his death, my father thought of print- 
 ing separately the first, second, and sixth lectures ; 
 and he prepared them for the press with that view, so 
 far as any writing is prepared for the press before the 
 actual printing begins. He early concluded not to 
 publish the third, fourth, and fifth lectures till he had 
 worked out more fullj"- the form of the meteoric 
 
PREFACE. V 
 
 theory there broached, and its relation to the nebular 
 theory. He wished also to subject to careful revision 
 his criticism of other writers. But he left the ques- 
 tion of the pubKcation after his death of these, as 
 well as of the other, lectures to the discretion of his 
 family ; who feel that, — however some details of 
 statement or of argument may have been liable to 
 modification, if a final consideration had been given 
 to the work, — aU the lectures have too high an in- 
 terest in their relation to the mind of their author, 
 too much real value in the way of suggestion to 
 other students of the physical constitution of the 
 universe, and too excellent a quality as popular ex- 
 positions of the great theories with which they deal, 
 not to be invested with the permanent definiteness of 
 print. 
 
 In editing this volume, I have ventured on none 
 but unimportant alterations, chiefly slight verbal 
 changes in the three unre^ised lectures. I am re- 
 sponsible for the foot-notes, which undoubtedly, in 
 the main, name the authorities my father had in 
 mind, but perhaps in some instances err by excess or 
 defect. For the appendix, also, I am solely respon- 
 sible. Throughout, I must ask the indulgence of the 
 reader in view of the difficulty of the questions that 
 can hardly fail to arise in the case of a posthumous 
 publication. 
 
VI PREFACE. 
 
 The lectures, as originally delivered, were profusely 
 illustrated by diagrams and familiar explanations at 
 the blackboard. The words used in these parts of 
 the lectures were extemporary ; and the manuscript 
 is continuous and complete without them. Nor do I 
 greatly regret my inability to add to the scientific 
 and philosophical discussions here presented matters 
 which, though serviceable in the lecture-room, might 
 have appeared as intrusions in the printed form. 
 
 J. M. PEIECE. 
 
 HaBVAKD IlNrVBRSITT, 
 12 May 1881. 
 
CONTENTS. 
 
 LECTTTRE PAGE 
 
 I. Ideality in Science 9 
 
 n. Cosmogony 38 
 
 III. Feom Nebula to Stak 72 
 
 IV. Planet, Comet, and Meteor .... 99 
 V. The Cooling ov the Earth and the 
 
 Sun 133 
 
 VI. Potentlalitt 165 
 
 APPENDIX. 
 
 A 197 
 
 B 200 
 
IDEALITY IN THE PHYSICAL SCIENCES.' 
 
 IDEALITY IN SCIENCE. 
 
 Ladies and Gentlemen : 
 
 It would not be unjust in you to demand 
 an apology of your lecturer for the seem- 
 ing inconsistency between his customary 
 labors and the subject of his lectures. Enter 
 his workshop ; open either of the worn vol- 
 umes on his table. It is filled with figures. 
 From the beginning to the end it is a mass 
 of figures. Inspect his manuscript. Figures 
 everywhere ! nothing but figures ! Where 
 is the ideality in this monotonous repetition 
 of the nine digits 1 You might as well hope 
 to find it in the lawyer's plea, or in the doctor's 
 prescription, or in the balance sheet of the 
 merchant ; or statesmanship in the cobbler's 
 stall ; or charity in the miser's pocket ; or a 
 
10 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 sweet perfume pervading the laboratory of 
 the chemist. Nevertheless, you cannot think 
 ■ that any man, with a man's soul in his body, 
 could devote his life to the drudgery of addi- 
 tion, subtraction, multiplication, and division, 
 for the mere pleasure of the thing. To accu- 
 mulate coin, men have degraded themselves 
 lower than the beasts. But to accumiJate 
 useless figures is a martyrdom which is be- 
 neath man's lowest folly. 
 
 There are people whose habit it is to 
 count each night up to ten, or twenty, or even 
 to more than a hundred, in order to induce 
 drowsiness, — to quiet the ghosts of the day's 
 unburied cares and secure a healthful sleep. 
 An endless sleep would be the legitimate ter- 
 mination of an incessant, objectless, and fruit- 
 less counting. Computation is not barren 
 when it supplies subsistence ; it ceases to be an 
 unmitigated evil when it is dignified by min- 
 istering to the necessities of material life and 
 comfort. But the computation of the geom- 
 eter, however tedious it may be, has a loftier 
 aspiration. It provides spiritual nourish- 
 ment : hence it is life itself, and is the worthy 
 occupation of an immortal soul. The arith- 
 
IDEALITY IN SCIENCE. 11 
 
 metical formula, considered as an end, is the 
 embodiment of fact, and isolated fact is as 
 worthless as the idle gossip of the parlor 
 or the club; whereas facts combined into 
 formulae and formulae organized into the- 
 ory penetrate the whole domain of physical 
 science, and ascend to the very throne of 
 ideality. 
 
 A celebrated philosopher has advanced the 
 theory that every science has its three suc- 
 cessive stages, which he designates as the 
 theological stage, the metaphysical, and the 
 positive. In the theological stage, each phe- 
 nomenon is referred to the direct agency of 
 divinity ; in the metaphysical stage, abstrac- 
 tion takes the place of deity in the develop- 
 ment of phenomena ; but in the positive stage, 
 facts constitute the whole of science, with- 
 out regard to any question of theological 
 creation or of abstract generation. The theo- 
 logical stage becomes perfect when all the 
 gods are reduced to one God; the meta- 
 physical stage is perfect when all the abstrac- 
 tions are comprehended in the one abstraction 
 of Nature ; the positive stage will be perfect 
 when all facts are resolved into one fact 
 
12 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 Our philosopher regarded the positive stage 
 as the only one entitled to a profound and 
 philosophic study ; and such seems to be the 
 final verdict of physical science. We must 
 recognize the initial attraction to the human 
 mind of the theological form. Mind irresisti- 
 bly seeks in mind the primitive source of 
 power. Hence arise the gods created by 
 men, which are finally recognized as shadows. 
 Earth-bom, their images of clay are broken, 
 and they are at last dethroned. Their places 
 are occupied for a time by the equally 
 shadowy and inefficient, though it may be 
 high-sounding, nomenclature of metaphys- 
 ics. But the inevitable end of science is 
 pure fact, with its indisputable generaliza- 
 tions and irresistible laws. Where then is 
 the ideality? 
 
 What is this which we call fact ? It is not 
 a sound ; it is not a star. It is sound heard 
 by the ear ; it is a star seen by the eye. In 
 the simplest case, it is the spiritual recogni- 
 tion of material existence. One moiety of it 
 may be of the earth, earthy; but the other 
 moiety is essentially mental and dependent 
 upon the constitution of mind. There are 
 
IDEALITY IN SCIENCE. 13 
 
 even physical facts of which the knowledge 
 is wholly mental, and of which there is no 
 direct evidence to the senses. They are di- 
 rectly known only to the few who have the 
 logical training to follow the argument by 
 wlii(5h they are demonstrated; and indirectly 
 to those other few who have the loyal faith to 
 trust the testimony of the geometers. It is 
 undoubted that there are sounds which are 
 inaudible to some ears, and colors which are 
 invisible to certain eyes. It is equally un- 
 doubted that there are innumerable vibrations, 
 coursing through space, which make no "sen- 
 sible impression on any auditory or visual 
 organ or on any human nerve. Such facts, 
 known through our powers of reasoning, are 
 to us non-existent, except as pictures on the 
 imagination. 
 
 You remember that soul of Laura. Bridg- 
 man, almost hermetically sealed from external 
 impressions and the recognition of other 
 minds. You remember with what incredible 
 patience, untiring skill, and loving assiduity 
 of the great-hearted philosopher she was 
 educated into humanity. Observe the pe- 
 culiarity of her perceptions. They scarcely 
 
14 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 extend to the direct observation of outer 
 Nature, and are mostly restricted to the arti- 
 ficial signs addressed her by others. Yet 
 such is the constitution of her mind, so har- 
 monious is it with all our minds, that through 
 these narrow avenues intellectual intercourse 
 is possible. How different from that of the 
 dog, whose intelligence you applaud ! How 
 immeasurably superior to the horse, who 
 perceives and obeys the intention of your 
 finger! or to the bird, who imitates your 
 voice ! Their restricted brains exclude im- 
 aginative speculation and consecutive discus- 
 sion, and include no foundation for rational 
 conversation. The brute endowed with per- 
 fect senses is alive to all physical impressions, 
 but is subject to the monotonous limitations 
 incident to its want of ideality ; whereas the 
 poor girl, confined to the minimum of sensa- 
 tion, and awakened from her solitude by the 
 friendly taps which bring the only light to 
 her perpetual dungeon, can expand in a 
 spiritual universe as full of thought and 
 knowledge and poetry and religion as our 
 own. 
 
 Independent of this ideal element, which 
 
IDEALITY IN SCIENCE. 15 
 
 we see to be inseparable from fact, and addi- 
 tional to it, the classification and generaliza- 
 tion of facts, their combination and reduction 
 to fewer facts, and their arrangement in series 
 are processes which are not performed auto- 
 matically in the laboratory of Nature. They 
 are the intellectual result of profound thought, 
 enduring research, and fruitful imagination. 
 To translate a great poem demands months and 
 years of earnest devotion, coupled with poetic 
 inspiration. But to read the book of Nature 
 is the province and privilege of consummate 
 genius, submissive to unremitting discipline. 
 When Kepler undertook the investigation 
 of the motions and order of the planets, he 
 was under the influence of a species of super- 
 stition, which may have been a remnant of the 
 theological romance of the ancient science; 
 and he expected to find a reproduction or 
 image of some innate ideas in his own mind. 
 While this expectation partly emanated from 
 the gross astrology by which he computed 
 his almanacs and sought to read the story 
 of individual life and of national events 
 in the aspects of the stars, it also partook of 
 an exalted faith, anterior and superior to all 
 
16 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 science, in the existence of intimate relations 
 between the constitution of man's mind and 
 that of God's firmament. The study of the 
 geometric solids had fascinated him, and es- 
 pecially the doctrine of the spheres circum- 
 scribed and inscribed to polyhedrons. He 
 hoped to find in them indications of the ar- 
 rangements of the planets. His search was 
 vain. He found rude approximations to 
 the numerical ratios of the solar system. 
 They were such as might perchance have 
 satisfied the arithmetic aspirations of the weak 
 enthusiasts who are ever pestering science 
 with their delusive ciphers and visionary 
 hypotheses. But he honestly rejected them, 
 as giving no solid foundation for substantial 
 theory. His researches in the geometry of 
 cycles and epicycles were equally fruitless. 
 But when he turned to the conic sections, and 
 applied them to the astronomical measure- 
 ments, they immediately fitted the observa- 
 tions. He could have no doubt that the true 
 key was found, and that the rhythmic door of 
 the firmament was at length opened. His 
 faith and zeal had met their due reward. He 
 was enabled to reduce all the facts of planet- 
 
IDEALITY IN SCIENCE. 17 
 
 ary motion to the three great facts which are 
 familiar to men as The laws of Kepler. 
 This grand discovery required his unique 
 imagination. 
 
 But the task was not completed ; the three 
 facts were to be reduced to one, and the re- 
 duction was accomplished by an imagination 
 not less unique than his own, but as different 
 as intuition from prophecy. The one fact is 
 Newton's law op Univeesal Gravitation; 
 and it may never be equalled as a sublime 
 embodiment of all-embracing thought. 
 
 The whole domain of physical science is 
 equally permeated with ideality. You cannot 
 escape from it if you would. It illumines the 
 remotest star and the first-born of the nebulae. 
 There is no obscurity which it does not pen- 
 etrate, no resistance which it does not over- 
 come, and no magnitude which it does not 
 embrace. Call it by whatever name you 
 will, the spiritual eye recognizes its omni- 
 presence. "If you ascend up into heaven, 
 it is there ; if you make your bed in hell, 
 behold it is there. If you take the wings of 
 the morning and dwell in the uttermost parts 
 of the sea, even there shall its hand lead you. 
 
18 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 and its right hand shall hold you. If you say, 
 ' Surely, the darkness shall cover me,' even 
 the night shall be light about you." Yea, 
 spirit of ideality, "the darkness hideth not 
 from thee, but the night shineth as the day ; 
 and the darkness and the light are both alike 
 to thee." By what more satisfactory name 
 can we approach thee than by the awful 
 name of Jehovah! 
 
 There is nothing the eye can perceive 
 which is so small as not to contain a rich 
 mine of speculation. The drop of water rep- 
 resents infinite power, with its load of elec- 
 tricity, — enough to charge a thunder-cloud ; 
 it is the type of infinite beauty, as it trans- 
 forms sunlight into rainbow ; it is the embodi- 
 ment of infinite love, in its gentle descent 
 upon the grateful flower ; and by its curious 
 constitution it represents and stimulates an 
 inexhaustible knowledge. Is it not worthy 
 to be the vehicle of a divine baptism ? 
 
 Ascend from the infinitesimal to the infinite ; 
 pass from the elementary particle to the uni- 
 versal cosmos. With the increased grandeur 
 of dimension, the intellectual utterance is not 
 enfeebled. There is everywhere in Nature a 
 
IDEALITY IN SCIENCE. 19 
 
 • 
 
 voice audible to human ears, and a speech in- 
 telligible to human understanding. It is the 
 truth of science, the beauty of poetry, the 
 logic of philosophy, and the faith of religion. 
 Ignorance cannot hide it, nor deformity de- 
 grade it, nor superstition corrupt it, nor scep- 
 ticism conceal it. It vibrates in every soul ; 
 it is the consolation of the slave, and the con- 
 science of the king. It is the corner-stone 
 upon which sound government is built, and 
 the fulcrum by which eloquent speech moves 
 the world. 
 
 Mythology herself, however she may be 
 clothed in barbaric mystery, however she 
 may have been. born of the dread of the pow- 
 ers of Nature and of the ignorance of law, 
 attests the all-pervading ideality. The gods 
 of Egypt, whether worshipped as light or 
 sun, whether incarnated in bull, or hawk, or 
 cat, or beetle, or vulture, or ibis, or crocodile, 
 declare the presence, in the first source and 
 in every form of life, of a Nature imbued 
 with intelligible thought. The Chaldean, 
 Babylonian, and Arabian gods of the sun, 
 moon, and stars; of the planets, and the 
 months with their presiding triad ; of him 
 
20 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 who rules the day, and of him in whose hand 
 is the flaming sword, and who dispenses abun- 
 dance and wealth, — are the definite repre- 
 sentation of a real philosophy of Nature. 
 The gods of Greece and Rome, — Uranus 
 and Saturn, Jupiter and Juno; Neptune, 
 with his amphitrites, his tritons, sirens, ne- 
 reids, and naiads, his Scylla and Charybdis; 
 Apollo and Minerva, with the Muses; Pan 
 and Flora, with the fauns and nymphs ; Ve- 
 nus, with the graces and the saiyrs ; Ter- 
 minus and Vertumnus, with the lares and 
 penates ; Pluto and Proserpine, — what are 
 they all but human recognitions of the uni- 
 versal ideality f And what was the perpetual 
 intercourse between gods and men but the 
 perception by vivid minds of the amazing in- 
 tellectuality inwrought into the unconscious 
 material world ? 
 
 Remove the plurality of the deities, and 
 the absurdities vanish; the myth is trans- 
 formed into a glorious truth, and inestimable 
 is the gain to philosophy. The dragon no 
 longer guards the sacred fruit ; nor does the 
 serpent distribute it to the tempted sinner. 
 No Cerberus is in the path to the inner mys- 
 
IDEALITY IN SCIENCE. 21 
 
 teries; there is no danger in accepting the 
 invitations of Minerva, lest you may incur 
 the anger of Venus and Juno. In under- 
 taking the problems of the Sphinx, you need 
 not fear the ambiguities of a deceitful oracle 
 nor the inconsistent responses of rival gods 
 and capricious goddesses. The light of Na- 
 ture is henceforth single, and her heart puri- 
 fied from all malice and duplicity. However 
 strange the forms of phenomena may be, and 
 however complicated the combinations, there 
 remains no dark corner of hopeless obscur- 
 ity. Everywhere it is written, " Knock, and it 
 shall be opened unto you ; seek, and ye shall 
 find." Undertake the most intricate and pro- 
 found investigation which can be presented 
 to you ; pursue it with ardor, intrepidity, and 
 unswerving faith : you will surely secure 
 the prize, and accomplish the miracle prom- 
 ised to the faithful. It is the universal story 
 of invention and discovery, from Cadmus and 
 Pythagoras to Edison and Sylvester. 
 
 It is undeniable that some portion of the 
 ideality attributed to Nature has been the 
 product of man's fancy ; and its human aspect 
 is to that extent a subjective phenomenon. 
 
22 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 The images seen by the soothsayer in the 
 burning coals, in the lines of the hand, in 
 the flight of birds, in the configuration of the 
 stars, and in the dreams of imperfect sleep 
 are the weeds and spawn of a teeming super- 
 stition. Look at yonder cloud. It is backed 
 like a weasel, it is very like a whale, it is in 
 the shape of a camel, — in accordance with 
 the suggestions of frivolity and delusion. Go 
 where you will among the mountains — giants, 
 men, and animals present themselves to you 
 in the contours of all the hills ; but they are 
 the offspring of your own childish conceit, 
 and no thinking child regards them as truly 
 earth-born. How different is their insignifi- 
 cant tale from that of the lovely shadows ; of 
 the changing foliage ; of the grasshoppers, 
 the butterflies, and the humming-birds; of 
 the lightning, the rainbow, and the shooting 
 star ! The brilliant and majestic firmament 
 is studded with stars, distributed under no 
 order which can be deciphered, and with an 
 irregularity greater than that of the spots of 
 water on a floor, dashed from a dripping 
 brush. Nevertheless, the inventive imagina- 
 tion of the ancients combined them into 
 
IDEALITY IN SCIENCE. 23 
 
 constellations which have been a perennial 
 reservoir of beautiful poetry. The ideality 
 in this case is altogether a human artifice, 
 however real and divine may be the poesy ; 
 and it exhibits the cunning of man, where 
 Nature had declined to manifest any corre- 
 sponding intellectuality. 
 
 I have seen an ingenious artist who per- 
 mitted me to mark arbitrarily on a paper the 
 positions of the hands, feet, and head of some 
 proposed man ; and however impossible the 
 mutual relations might seem to be, it was' 
 curious how he always contrived to design a 
 natural figure engaged in some occupation 
 which admitted of the proposed positions. In 
 one case the positions were given for many 
 figures, scattered in the most bewildering con- 
 fusion. His corresponding picture was that of 
 a ship assaulted by pirates, in which the limbs 
 of the sailors were cut off" and thrown about 
 in the required places. With our unrestricted 
 play of fancy, how can we be sure that our in- 
 tellectual picture of the external world is not 
 a human creation, and the fabric of a vision 1 
 
 We will return to the starry heavens. 
 Amidst the constellations is a group of stars 
 
24 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 which cannot escape observation. The sweet 
 influence of the Pleiades may be rejected as 
 a baseless poetic myth, their supposed posi- 
 tion at the centre of the stellar world may be 
 a scientific error, the beauty of the constella- 
 tion may be set aside as having slight intel- 
 lectual significance ; but the reality of the 
 combination of at least five hundred stars in- 
 to one close family is indisputable and ab- 
 solutely independent of human recognition. 
 There is also the attractive cluster of the Hy- 
 ades, and that of the Coma Berenices. The 
 telescope has revealed a multitude of such 
 clusters, and the story which they compel 
 us to accept is irresistibly rich in ideality, 
 and of infinite comprehension. It reveals a 
 history of the sidereal universe which tran- 
 scends all possibility of human invention. 
 
 There is visible to every eye, whatever 
 may be the constitution of the mind of the 
 observer, a beautiful zone of small stars, cir- 
 cling the whole heavens, and which we call 
 the Milky Way. Even the brighter stars 
 have an evident connection with it, and it 
 again contributes an incontestible chapter to 
 the stellar history. 
 
IDEALITY IN SCIENCE. 25 
 
 There are some stars which move among 
 the others, distinguished at times by their 
 superior brilliancy. They are the planets ; 
 by their motions they have revealed the 
 chain of universal gravitation, and by their 
 harmonious system have a third time carried 
 us back to the origin of the stars. Even 
 here, then, where there has been through the 
 ages the most extraordinary accumulation of 
 fanciful suggestion ; where no strange meteor 
 can appear, but the nations are threatened 
 with war ; where the eclipse and the comet 
 are associated with the lightning and the tem- 
 pest as dragons of destruction, — in the very 
 stronghold of astrology, — we find the quiet 
 and indubitable evidence of the dominion of 
 intellectual order. 
 
 The conclusion in every department of 
 science is essentially the same. Whatever 
 may have been the play of fancy, or the 
 delusion of superstition, or the allurement of 
 profit, at the outset, the end has ever been a 
 congregation of facts, organized under law, 
 and disciplined by geometry. With the 
 transformation of astrology into astronomy 
 and of alchemy into chemistry, the planets, 
 
26 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 which were the lords of human fate, have be- 
 come the slaves of gravity ; the sublime devel- 
 opments of celestial mechanics have replaced 
 the puerile predictions of wealth and pros- 
 perity, of war and famine ; and instead of 
 the philosopher's stone and the elixir of life, 
 we are blessed with the golden laws of chem- 
 ical affinity and the profound philosophy of 
 physiology. The records of each science 
 justify its claim to the inheritance of ideality. 
 The wisest physical philosophers have ever 
 been the most rigid observers ; they have 
 penetrated through fact to the inmost soul 
 of Nature; and their proudest discoveries 
 have invariably been vast intellectual con- 
 ceptions exhumed from the recesses of the 
 material world. When the sculptor develops 
 his Apollo or his Venus from the quarried 
 marble, it is his own creation, and has his 
 image stamped upon it ; but the truth which 
 the man of science extracts has an abso- 
 lute character of its own, which no power of 
 genius can transform, and which is neither 
 attributable to accident nor bom of human 
 parentage. It pervades the meanest chips of 
 stone, which the artist rejects as superfluous. 
 
IDEALITY IN SCIENCE. 27 
 
 When we read the great poems and ora- 
 tions of former times and distant peoples, we 
 may often differ as to the intention of the 
 authors ; but we all agree that the works of 
 Homer and Virgil, of Dante, Voltaire, and 
 Goethe, of JEschylus and Sophocles, Aris- 
 tophanes, Moliere, and Shakspeare, the ser- 
 mons of. Massillon and Bossuet, of Taylor 
 and Channing, and the Vedas, and the Cid, 
 and Job, and the Psalms of David, and the 
 Song of Solomon, and the wise sayings of 
 Confucius and of Emerson are uninistaka- 
 ble productions of minds constituted like 
 our own, however surpassing they may be 
 in their beauty and sublimity. Is it other- 
 wise with the " books in the running brooks, 
 the sermons in stones, and the good in every- 
 thing " ! If there be any validity in logical 
 inference, if there be any soundness in the 
 argument from analogy, we must accept 
 the unanimous testimony of experience and 
 observation. There is no physical manifes- 
 tation which has not its ideal representation 
 in the mind of man. The humanity of Na- 
 ture is its clearest utterance and its surest 
 reality. 
 
28 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 There is a grand phenomenon in the his- 
 tory of science, by which the coincidence is 
 drawn still closer. Wild as are the flights 
 of unchained fancy, extravagant and even 
 monstrous as are the conceptions of un- 
 bridled imagination, we have reason to be- 
 lieve that there is no human thought, capable 
 of physical manifestation and consistent 
 with the stability of the material world, 
 which cannot be found incarnated in Na- 
 ture. The dreams of Pythagoras and Plato 
 upon the mysteries of number have been 
 surpassed in the numerical relations discov- 
 ered by modern science. The docti'ine of 
 the polyhedrons, which Kepler did not find in 
 the system of the planets, has as real a rela- 
 tion to Nature as it had to his generous mind. 
 It is found to be an essential feature of the 
 modem theory of crystallization, just as he 
 recognized in the paths of the planets and 
 comets, marked out by the Creator, the same 
 conic sections which were but ideal existences 
 with Euclid and ApoUonius. The imaginary 
 square root of algebra, from which the puzzled 
 analyst could not escape, has become tlie 
 simplest reality of Quaternions, which is the 
 
IDEALITY IN SCIENCE. 29 
 
 true algebra of space, and clearly elucidates 
 some of the darkest intricacies of mechanical 
 and physical philosophy. The highest re- 
 searches undertaken by the mathematicians 
 of each successive age have been especially 
 transcendental, in that they have passed the 
 actual bounds of contemporaneous physical 
 inquiry. But the time has ever arrived, 
 sooner or later, when the progress of obser- 
 vation has justified the prophetic inspiration 
 of the geometers, and identified their curi- 
 ous speculations with the actual workings 
 of Nature. Geometry had been projected 
 forward and onward into the free regions 
 of ideality by a force of imagination which 
 could not be restrained, although it always 
 submissively obeyed the logic of which it 
 was bom ; just as the jet of hydrogen which 
 is ejected from the surface of the sun hun- 
 dreds of thousands of miles into space never 
 escapes from the solar attraction, and in the 
 course of time returns to its controlling lu- 
 minary. 
 
 Identity of law, structure, or material is 
 indicative of community of origin. Such is 
 the nature of the evidence for the common 
 
30 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 origin of the snn and the stars, of the sun 
 and the planets, of the planets and the earth, 
 and all the other components of the solar 
 system, whether satellites, comets, or meteors. 
 A few lines of the spectrum, seen in the gas 
 thrown from the sun, prove it to be hydro- 
 gen, because the same lines are found in the 
 hydrogen upon the earth. In the same way, 
 the identity between the laws of mind and 
 matter may justly be virged as an evidence 
 of their common origin. But is this a suffi- 
 cientl)'- solid basis for the hypothesis that 
 either of the two has originated the other? 
 The speculation that the mind of man first 
 constructed the world with its great harmo- 
 nies, and then shrank to its present stature, 
 may excite a derisive smile. But is it not as 
 worthy of serious consideration as the oppo- 
 site fiible, that the mind has grown out of 
 this brute matter, which is now utterly un- 
 conscious and incapable of intellectual argu- 
 ment or spiritual emotion? 
 
 I have read an attempted explanation of 
 the process by which consciousness could be 
 evoked out of the unconscious. It miirht 
 have been written in some prehistoric San- 
 
IDEALITY IN SCIENCE. 31 
 
 skrit, or in lunar hieroglyphics, for all my ca- 
 pacity to understand it. I cannot, therefore, 
 presume to criticise it. But it seems to be a 
 gross violation of the principle of the necessity 
 of an adequate cause for the production of an 
 effect. Without some more lucid expdsition, 
 notwithstanding my sincere respect for the 
 high authority from which it emanated, I must 
 place it in the same category with demonstra- 
 tions which I have in vain striven to imder- 
 stand, of the possibility of perpetual motion, 
 and of the falsity of the law of gravitation, 
 or of the earth's curvature. It leaves us 
 at the mercy of vague speculation, and de- 
 prives philosophy of its soundest instrument 
 of research. 
 
 If the common origin of mind and matter is 
 conceded to reside in the decree of a Creator, 
 the identity ceases to be a mystery. The 
 divine image, photographed upon the soul of 
 man from the centre of light, is everywhere 
 reflected from the works of creation. The 
 origin is as distinctly imprinted upon the 
 records of philosophy and the laws of Nature 
 as are the lines of the sun upon every solar 
 spectrum. How could it be otherwise ? Is 
 
32 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 it not a vagary of philosophy which erects 
 one part of creation, and that the least, into 
 the authorship of the whole f — which ignores 
 the Deity, because he is materially invisible 
 except in his works, wherein is his only 
 possible mode of material manifestation ? 
 We might better assert that the star, which is 
 only known by its light, consists of mere 
 rays; that the picture is a product of self- 
 controlled color, and the anthem the offspring 
 of unconscious sound. 
 
 That the perfection of theology requires 
 that all the gods should be reduced to one 
 God, will be admitted. But let us consider 
 where the proposition lands us, that all science 
 can be reduced to one fact. Among the facts 
 to be embodied, are the facts of omnipresent 
 ideality, the intelligible cosmos, and the all- 
 comprehending intellect. The law of univer- 
 sal gi'avitation must be incorporated in it, and 
 the laws of rest and motion, of chemistry and 
 heat and electricity, of sound and light, and of 
 all vibrations audible and inaudible, visible 
 and invisible, and of all forms of sensation 
 actual or possible. All the laws of the ma- 
 terial woi'ld must be included, and they will 
 
IDEALITY IN SCIENCE. 33 
 
 constitute its least part. The mind of man 
 must be in it, with its philosophy, its emo- 
 tions, and its infinite capacity of develop- 
 ment. It must contain the law of love, the 
 Sermon on the Mount, and the Lord's Prayer. 
 What can this mighty fact be but God him- 
 self? Where is the man who will not accept 
 this fact, as the one fact which comprehends 
 all others ? And where is he who will accept 
 less than this f 
 
 But will science receive this doctrine I 
 Physical science has long outgrown its theo- 
 logical stage. The manufacture of human 
 gods is a lost art, which superstition and 
 priestcraft cannot revive, even with the aid 
 of animal magnetism, legerdemain, and spir- 
 itualism. Science is rapidly emerging, if it 
 has not already emerged, from its metaphysi- 
 cal stage. Nature no longer abhors a vacuum ; 
 abstract and final causes have lost their 
 power; grass does not grow, trees do not 
 bear fruit, fish do not swim, birds do not fly, 
 beasts do not walk the earth, for the purpose 
 of supplying food to man. Events and beings 
 are because they cannot help it ; they obey a 
 law which they cannot resist. The struggle 
 
 3 
 
34 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 for existence is an instinctive battle, which 
 has no more voHtion or sentiment in it than 
 the fall of the forest pine struck by the thun- 
 derbolt; than the frosts of winter, or the 
 showers of spring, or the heats of summer, 
 or the autumn's harvest moon. The primi- 
 tive nebulosity has condensed into definite 
 nebulae; the nebula has concentrated into 
 stars ; each star has surrounded itself with its 
 solar system ; each planet has cooled from a 
 gaseous to a liquid form, and thence to solid- 
 ity, till it became a fit residence for plants 
 and animals and man, warmed and nour- 
 ished by the heat and light of the central 
 sun ; and every step in the progress of evo- 
 lution has been the unconscious yielding to 
 irresistible force. 
 
 In the midst of this vast series of trans- 
 formations, science has humbly submitted to 
 the task of observation. It has devoted itself 
 to bringing together and co-ordinating facts ; 
 it has collected museums, founded labora- 
 tories, and built observatories. It has in- 
 vented microscopes and telescopes, polari- 
 scopes and spectroscopes, and all forms of 
 instruments for enlarging the realm of the 
 
IDEALITY IN SCIENCE. . 35 
 
 senses. It has ascended mountains, risen in 
 balloons, sounded the depths of the sea; it 
 has gone to the uttermost parts of the earth 
 to watch the eclipse and the transit ; and it 
 has faithfully and humbly recorded its watch- 
 ings. But is there no tinge of condescend- 
 ing pretension under its humility? It has 
 nowhere seen the divine hand, and therefore 
 it does not recognize deity. It sees evolution 
 and the magnificent harmonies everywhere 
 evolved. Is there not reason to apprehend 
 that it is placing this very evolution upon the 
 throne which can be occupied by no created 
 power or any metaphysical abstraction? 
 The force of evolution is as brute and un- 
 conscious as that of fire ; there is no more 
 royalty in it than in the log which Jupiter 
 threw down to the frogs. In its descent it 
 has made a frightful splash in the pool of 
 science ; but the world will recover from it, 
 as it did from the dangerous doctrine of the 
 earth's motion. 
 
 Science, in its positive stage, devoted to 
 rigid observation, has nowhere seen the divine 
 hand. "With all its power of prediction, with 
 all its keen capacity to penetrate the past and 
 
36 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the future, we are as far from the end of the 
 world as is science from the one final fact, 
 which must also be the primal fact, — the first 
 and the last, the alpha and the omega of fact. 
 But notwithstanding the short-sightedness of 
 scientists, we may not forget that there have 
 been wise philosophers, who in the beginning 
 have seen the end. Call it wisdom, call it 
 inspiration, call it what you will ; it was di- 
 vine truth which the great lawgiver of Judea 
 uttered, when he dethroned all the heathen 
 gods with the declaration that " In the begia- 
 ning God created the heavens and the earth." 
 Without this treasure of faith, the omni- 
 present ideality of science terminates in an 
 impoverished and powerless pantheism. With 
 it, the observed ideality is the divine thought, 
 and the book of Nature is the divine record. 
 At the turning of each new leaf the page may 
 seem dark ; but if you will persevere in its 
 perusal with the docility, faith, and patience 
 of the child, it will become luminous. 
 
 Men of science ! do not forget the lessons 
 of piety and reverence taught to youth. 
 Your logic of induction may be as pellucid 
 as .ice; but beware lest you be bound in its 
 
IDEALITY IN SCIENCE. 37 
 
 frigid and rigid bonds, till you become as 
 immovable and incapable of progress as those 
 who were seen by the Florentine prophet, 
 condemned to the lowest depths of Tartarus. 
 Retrace your steps upwards, through the 
 narrow avenue of ideality, out of this threat- 
 ened darkness, to the grateful warmth and 
 light of the surface, where you can see the 
 stars again. Your science will recover the 
 perception of the central luminary, which is 
 the unfailing fountain of pure knowledge, 
 and will be restored to the praise and worship 
 of the almighty, onmiscient, and all-loving 
 God. 
 
38 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 II. 
 
 COSMOGONY. 
 
 How came we here, in this physical world, 
 so curiously adapted to our material and 
 spiritual nourishment! This is one of the. 
 first questions proposed by thinking man, as 
 soon as he begins to reason. The inquiry 
 into the origin of the world is, almost in- 
 stinctively, the beginning of scientific specu- 
 lation ; whereas the complete solution of the 
 question can be achieved only at the very 
 close. So long as a scientific doubt remains, 
 the story of cosmogony is partially untold. 
 
 At the commencement, the short-sighted 
 observer has nothing to guide him but the 
 obvious phenomena in his immediate vicinity. 
 He cannot see the distant path, with its diffi- 
 culties and dangers. But, fortunately. Nature 
 is God's messenger ; and her clew, faithfully 
 followed, will, after innumerable turnings and 
 
COSMOGONY. 39 
 
 windings, lead out of the labyrinth. Each 
 observer starts from his own peculiar position, 
 which may be far removed from others. In 
 the dim and uncertain light, he pursues crude 
 theories, imbued with the minimum of fact 
 and the maximum of fancy. He is easily 
 diverted from his course by some delusive 
 ignis fatuus or some glittering generality. 
 When the causes are obscure and the visible 
 agents fail, he constructs fairies and genii, 
 demons and gods, to work out the mysteries 
 which he perceives, but cannot understand. 
 
 He whose home is in the plains, where the 
 strata of the earth are nearly horizontal and 
 have an almost uniform thickness, finds in the 
 evaporation of aqueous solutions a natural 
 and sufficient explanation of the phenomena 
 of geology. He, on the contrary, who lives 
 in mountainous countries, where the evidences 
 of volcanic action are apparent to the most 
 superficial observation, is impelled to adopt 
 fire as the primary earth-building agent. The 
 various observers, justly confiding in the 
 soundness of their own observations, unjustly 
 oppose the apparently inconsistent views em- 
 anating from other localities. Human pas- 
 
40 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 sions, swift to vindicate opinion, are aroused 
 on either side. 
 
 Under the banners of Neptune and Vul- 
 can, scientific armies were arrayed against 
 each other about a century ago, and a bitter 
 war was waged for many years. So long 
 as victory, and not truth, was the leading 
 incentive, the contest endured, with virulent 
 onslaught of words and impassioned demo- 
 lition of reputations. The excited combatants 
 accumulated immense stores of fact to sustain 
 their respective hypotheses of the formation 
 of strata and the origin of the successive ter- 
 restrial inequalities. The collected facts had 
 in themselves a mighty power of instruction ; 
 when warmed into life, their teachings were 
 irresistible, and the warlike attitude of those 
 who marshalled them yielded before their en- 
 lightening influence. The controversy had 
 done its work in stimulating study ; and the 
 field was left to the legitimate operations of 
 the searchers after truth. Without formal sur- 
 render or articles of treaty, the strongholds 
 of faithful record were abandoned by their 
 partisan garrisons, and became the common 
 property of the science of the world. 
 
COSMOGONY. 41 
 
 In earlier times, to which the light of 
 history has scarcely penetrated, but where 
 human nature was the same as to-day and 
 yesterday, and as it will be to-morrow:, there 
 must have been going on the same uncon- 
 scious induction from the processes of Nature. 
 The muddy deposits of the Nile, laden with 
 untold fertility of production, must have 
 suggested a primitive formless chaos to the 
 Egyptian sage. The association of the over- 
 flowing of the great river with the rising of 
 Sirius, the most brilliant star of the firma- 
 ment, was nearly as inevitable as the asso- 
 ciation of the sun with the light and heat of 
 the day ; and the absence of this alliance 
 from the cosmogony of Egypt would not 
 be less strange than that of the solar influ- 
 ence itself, or than the failure of the Egyp- 
 tian astronomer to associate the pole-star 
 with the pole. On the other hand, it would 
 have been far from creditable to northern 
 philosophers, if the annual concurrent effects 
 of the winter frosts and the summer heats, 
 in tearing the rocks to pieces and converting 
 them into fruitful soil, had not become a 
 fundamental principle in their speculations 
 
42 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 upon the earth's origin. May it not also 
 have induced them to recognize the beneficial 
 influence of the battles of the gods ? 
 
 All nations capable of making profound 
 and thoughtful observation, wherever situa- 
 ted, whether in Phcenicia or Egypt, in India 
 or China, in Polynesia or Finland, must have 
 perceived in the egg the primitive idea of an 
 incipient world. The egg was not more cer- 
 tain to be transformed into a bird, whether 
 buzzard or eagle, — or into a reptile, whether 
 tortoise or crocodile, — than this universal 
 fact to be developed into some theory of 
 evolution. Manifold must have been the 
 forms through which theory groped its way 
 duiing the long centuries which preceded the 
 definite records of history. At the outset 
 they must have been as gross and deformed 
 as the early residences of man, and, like his 
 temples and divinities, overlaid with super- 
 stition and mythological monstrosity. But 
 intellect has its laws, which are as undevi- 
 ating as those of the physical world. Man's 
 conceit, stupidity, and obstinacy cannot re- 
 sist them ; and in the end they will prevail. 
 He cannot escape the constant observation of 
 
COSMOGONY. 43 
 
 phenomena, succeeding each other by invari- 
 able laws. He is forced to the discovery of 
 regions of the universe whence the arbitrary 
 is banished, and where there remains no evi- 
 dence of choice, or consciousness associated 
 with power. The quiet and silent force here 
 manifested is all the more permanent that it 
 is not subject to the caprices of will ; and its 
 unchangeableness may have extended back 
 to the very beginning. There are every- 
 where opposing forces, violent action, and 
 vigorous resistance; but the result of the 
 struggle seems to be uniformly harmonious 
 with some preconceived plan. The furious 
 hurricane and the roaring and destroying 
 tempest rage for a day and a night ; and, in 
 the morning, the ocean and the atmosphere 
 subside to the serenity and rest of the peace- 
 ful and well-rounded spheroid. 
 
 There have recently been uncovered at 
 Nineveh tablets four thousand years old, con- 
 taining an account of the Babylonian cos- 
 mogony. In the first tablet are placed, side 
 by side, the two primitive sources of crea- 
 tion, — Chaos and Ideality. They stand si- 
 lent and immovable, — imperturbable med- 
 
44 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 itation and inactive mass, — like the sphinx 
 by the pyramid. There they might have 
 remained eternally unproductive. But the 
 tablet's next record is the birth of Motion. 
 Motion is the divine energy of creation ; it 
 signifies change and phenomena, and the 
 genesis of the powers of evolution, with the 
 controlling, planning, and warring gods. 
 How this creative energy could itself have 
 been born is of all mysteries the most in- 
 comprehensible. It is the inevitable impos- 
 sibility inherent in any speculation which 
 would develop everything out of nothing. 
 
 The subsequent tablets coincide quite well 
 with the Mosaic cosmogony. There is the 
 birth of Thoth, the god of light, previous to 
 the sun ; and there is the conspiration of the 
 divinities of the sun, moon, and stars in the 
 establishment of the measures of time ; and 
 the order of events is nearly the same as that 
 of the first chapter of Glenesis. But it seems 
 not to be the accepted doctrine of the learned 
 Biblical archaeologists that the Mosaic account 
 was derived from the Babylonian specula- 
 tions. It is maintained, on the contrary, 
 that the Mosaic simplicity indicates a greater 
 
COSMOGONY. 45 
 
 antiquity, or at least a more archaic source, 
 but that each may have been the sponta- 
 neous growth of human thought. 
 
 The Mosaic record is delivered from the 
 grossness and superstition of the pagan tab- 
 lets. The finite gods — finite in time, power, 
 and wisdom — are annihilated in the presence 
 of the one God, who is eternal, almighty, and 
 omniscient. He can himself declare that the 
 light which he has created is good. 
 
 The coincidences of the successive steps of 
 this creation with the established theories of 
 evolution do not indicate the previous knowl- 
 edge of those theories, but are the conclusions 
 of a sound philosophy, which is ever consist- 
 ent with itself and with undpng truth. The 
 preservation of the cosmological form of sci- 
 ence is evidence of the antiquity of this ac- 
 count. Its brevity is accordant with the 
 wisdom which restricted the creative action 
 by no finite limitations. The long periods 
 of time requisite for the action of finite 
 gods, or of laws of development, would 
 have been unpardonable restrictions of al- 
 mighty power. The creator of time requires 
 no time for his grandest work. The least 
 
46 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 measured interval, the single day, is the 
 equivalent of myriads of centuries with 
 him who, like science itself, has neither 
 beginning nor end. The first chapter of 
 Genesis is the sublime termination of the 
 most magnificent example of evolution which 
 the history of mind has exhibited. It was 
 the inevitable outgrowth of free and untram- 
 melled philosophy. 
 
 As a cosmogony, the Mosaic account does 
 not undertake to manufacture the details of 
 a fanciful record, and supersede that which 
 man, with labor and study and faith, must 
 read where the Creator himself has written 
 it. It is the simple declaration that no finite 
 agent can accomplish an infinite production ; 
 and that the King of kings has placed be- 
 tween himself and his children no other god, 
 to whom the work of creation has been en- 
 trusted, and to whom we are to bend the 
 knee. 
 
 The cosmogony is the least portion of the 
 wonderful entrance to the book of our re- 
 ligion. It is the mere frame of the door-way. 
 Above it is written the name of Jehovah, the 
 only true king of the Jew fii-st and also of 
 
COSMOGONY. 47 
 
 the Gentile, the source of all power, and the 
 object of all obedience and of all worship. 
 Upon the panels of the door are inscribed 
 the powers of Nature, each of which might 
 seem to claim independent homage ; and each 
 is declared to be no god, but a created thing, 
 without proper title to the worship of man- 
 kind. The abolition of the heathen poly- 
 theism and the charter of the king of Israel 
 to sovereign power are proclaimed with a 
 simplicity and sublimity of language worthy 
 of the great law-giver and statesman to 
 whom they are attributed. 
 
 The Mosaic philosophy deserves to be 
 studied as a classification of power. It is 
 complete without redundancy. No source 
 of power is omitted, and each in succession 
 is declared to be a created agent and a ser- 
 vant of the sovereign ruler. First of all, 
 physical force is typified, under the name 
 of light. And God said, " Let there be 
 light," and light was. The work of the 
 day was one instant of thought. What 
 grander type of power has modem science 
 discovered? Next comes the heavenly fir- 
 mament, the home of Jupiter, the council 
 
48 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 chamber of the gods of the Gentiles, the 
 central residence of the regulating spiritual 
 forces, separating the infinite below from the 
 infinite above. God made this firmament, 
 and called it Heaven. Worship him, and 
 not his creatures ! And then comes the gath- 
 ering together of the infinite below into dry 
 land, with its inherent capacity for the pro- 
 duction of grass, herb, and tree. God cre- 
 ated the earth, and endowed it with its 
 exhaustless power of development. Shall 
 we, scientists of to-day, erect this created 
 evolution into an original divine power, and 
 honor it as a god ? We might as well go 
 back to the worship of light and the sun. 
 The infinite above was also concentrated in- 
 to sun, moon, and stars, which illumined the 
 earth and gave it the divisions of time. The 
 beneficence of Nature, here typified, is not 
 its own intention : God was the author, and 
 he saw that it was good. And whence arise 
 the monsters of the deep, and the winged 
 fowl that fly above the earth in the open 
 firmament of heaven ? Whale has been born 
 of whale, and eagle of eagle, back to the 
 very beginning of observation : it is an end- 
 
COSMOGONY. 49 
 
 less birth of like from like, as if it were 
 the manifestation of an eternal, independent 
 power. But the record declares that it was 
 an act of Grod's volition, and was marked 
 upon its front by his blessing. And so it is 
 with the origin of every living creatm-e on 
 the earth, whether beast, or cattle, or creep- 
 ing thing, and even of man himself. Let not 
 man boast that he is in the image of the 
 Creator, and that the ideality of the universe 
 is fully represented in his intellect and im- 
 agination ; let him not wonder at the infinity 
 of his own capacity, nor contemplate his 
 likeness to the Father, until he at length 
 persuades himself that he is a god, and be- 
 comes his own worshipper. Like the atom 
 of dust, he was created out of dust, and the 
 divine image was stamped upon him, that 
 he might humbly study and wisely under- 
 stand the works of creation, and contribute 
 to Grod's glory, while growing to the mea- 
 sure of the vast cosmos and of the divine 
 plan. 
 
 The Mosaic record is, finally, the consum- 
 mation of the philosophical study of the 
 phenomena of thought, design, and harmony, 
 
50 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 everywhere manifested. An all-pervading 
 unity is discovered, of which the only satis- 
 factory explanation is one God. We are 
 not now to consider the importance of this 
 doctrine to every human soul. It is the 
 foundation and hope of science as well as 
 of religion. It assures us that facts and laws 
 are born of God; that in all fact there is 
 law, and that the law is ascertained by the 
 study of the fact. The facts of to-day reveal 
 the law ; and the law, applied to the remote 
 facts, completes the imperfect and obscure 
 history of the past, and predicts the future. 
 In this sense, the first chapter of Genesis is 
 a profound cosmogony. It may not be the 
 revelation of an actual past, but it teaches 
 where that revelation is to be found ; that it 
 is engraved on stonei by the all-wise Author ; 
 that it is written in the sun, moon, and plan- 
 ets ; that it is inscribed on the sidereal uni- 
 verse, and that every star is an oracle of 
 God. Such is the Mosaic doctrine, rightly 
 interpreted. The most sublime production 
 of human language is the grandest embodi- 
 ment of human thought. The lips of man, 
 through the soul's craving for ideality, have 
 
COSMOGONY. 51 
 
 involuntarily given voice to God's inspira- 
 tion. 
 
 We may now undertake the consideration 
 of the latest form to which cosmogony has 
 grown, under the sunshine of modem sci- 
 ence. The trunk of the tree is the Nebular 
 Theory ; and upon its soundness depend the 
 vigor, height, spread, and endurance of the 
 subsequent development. Astronomers are 
 frequently asked whether they believe the 
 nebular theory. The question is logically 
 preposterous. An hypothesis may be be- 
 lieved or disbelieved ; but a theory is an 
 organized system of observed phenomena, 
 which may be accepted as good and com- 
 plete, or discarded on account of its defects, 
 but of which belief or disbelief cannot prop- 
 erly be predicated. 
 
 The nebular theory is, pre-eminently, a 
 grand ideal organization of all the phenomena 
 of the celestial universe, and embraces a 
 complete ideal history of the inorganic world. 
 The universe, according to that theory, com- 
 mences with an all-pervading substance, in 
 which there is no apparent structure nor 
 division into parts, but the same monotonous 
 
52 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 uniformity throughout. Passing through in- 
 numerable transformations, it terminates in 
 a system, whence disorganization has been 
 wholly eliminated, and where vast multitudes 
 of indi\dduals, each a perfect organism in 
 itself, are combined in indestructible har- 
 mony. In the beginning, it has the unity 
 of monotony ; in the end, it has the unity of 
 complete organization. In the beginning, it 
 is crude material, without form, and void ; 
 in the end, it displays the wonderful plan of 
 an unbounded imagination. 
 
 No grander conception of the physical 
 universe has ever been presented to philo- 
 sophical discussion. "While there is nothing 
 vaster in the wide realm of physical science, 
 there is no theory which is more plentifully 
 fraught with rich and varied suggestion. The 
 more the great masters of thought have been 
 penetrated by it, the more searching and 
 profound have been their investigations, and 
 the more exalted and harmonious have been 
 their conclusions. It has proved a curious 
 and unfailing guide amidst the mazes of 
 Nature, and it seemingly stretches through- 
 out the labyrinthic windings of intricate 
 
COSMOGONY. 53 
 
 investigation. It enables the magi of sci- 
 ence to read the stars, to decipher the lines 
 on Nature's palm, and to divine the past and 
 future history of worlds and races. From 
 time to time, it must ,be submitted to rigid 
 scrutiny and analysis, so as to extend its 
 comprehension, enlarge its domain, correct 
 its doctrine, and prepare it for the researches 
 of the next age. It must be liberated from 
 needless hypothesis, which may unguardedly 
 have been allowed to enter it, be closer fitted 
 to fact, and become more and more the in- 
 corporation of ideality with strict and exact 
 observation. 
 
 Certain wise and good men, jealous of 
 their religious faith, have feared that the 
 nebular theory is liable to the reproach of 
 being an invention to relieve the Almighty 
 from the incessant care of his creation. We 
 cannot deny that some eyes have been daz- 
 zled by it, so as to become insensible to the 
 more needed light of spiritual faith. But 
 how could there be such brilliancy, except 
 in an emanation from divine light? The 
 intellectual force of the conception is conse- 
 quent upon its verity. Any harm which it 
 
54 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 may have done is due, not to the impurity 
 or dimness of the light, but to the weakness 
 or disease of the eye. 
 
 An undeviating succession of events has 
 been observed. Such a phenomenon is in- 
 separable from uniformity of law and plan, 
 and is the only possible expression of an 
 unchangeable will, which is subject to no ca- 
 price. It is the mode of growth adopted by 
 the Creator to accomphsh the plan of creation. 
 The universe is a book written for man's 
 reading. If it were destitute of strict logical 
 connection, it would fail of its purpose, and 
 be unintelligible. The luminous order of 
 the pages and the successive introduction 
 of new and strange truths are marvellously 
 adapted to the development and expansion of 
 the created intellect. It is a glorious mani- 
 festation of the all-pervading affection and 
 of the fostering care of divine wisdom. 
 Facility of execution was no motive to the 
 Omnipotent, nor transparency of conception 
 to the Omniscient. Our weakness has been 
 consulted in the spiritual food presented to 
 our nutriment. 
 
 The divine presence only at the beginning. 
 
COSMOGONY. 55 
 
 and the seeming absence of Deity from the 
 actual course of natural events, is a human 
 misconception not easy to be eradicated, for 
 it is one which is incident to our finite nature. 
 Man lives in time and space. It is only 
 through media that he is cognizant of the 
 near and the remote, of the past and the fu- 
 ture. Standing on the earth, he sees the dis- 
 tant star by the light which strikes his eye ; 
 and, by the aid of the telescope, can see one 
 still more remote. Guided by the law of 
 cause and effect, he traces back events into 
 the past and prophesies the future. 
 
 This is man's mode of seeing ; but it can- 
 not be God's. The Omniscient and Omni- 
 present needs neither created light nor human 
 telescope to penetrate space, nor our logic to 
 connect events. "With him there is nothing 
 distant; all objects, celestial and terrestrial, 
 are in immediate proximity, and the past and 
 the future are forever present. Deity does 
 not exist in time and space ; but they are in 
 him, — they are his inward conceptions, his 
 created conditions, to which man by his will 
 is subject. 
 
 This wonderful riddle is at present be- 
 
56 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 yond human conception ; it is faintly rep- 
 resented in the mystery of the dream. But 
 it is vain for the finite to strive to com- 
 prehend the infinite. We are permitted to 
 know all that we require. The universal 
 plan is apparent to every mind which yields 
 itself to logical induction. The links of the 
 all-embracing chain are in open sight. We 
 need not search the obscure past to find out 
 God. It is not in the first appearance of 
 animal life or of man himself that he need be 
 sought, any more than in the whirlwind or 
 the earthquake. His dwelling is not where 
 the law of continuity is broken. There 
 would be the proper home of some heathen 
 deity, who rejoiced in lawlessness. But our 
 God proclaims himself in the silent law of 
 universal gravitation; he is forever present 
 in the quiet grandeur and intellectual sim- 
 plicity of the processes of the nebular the- 
 ory, and in the soul of man, which is fitted 
 to understand the divine harmony. The 
 Creator is not ruled out of the universe 
 by our theory of evolution. That which 
 we call evolution is but the mode in which 
 he is present on whom mortal cannot look 
 
COSMOGONY. 57 
 
 with physical eyes and live. It is the man- 
 ifestation of his paternity. He becomes 
 through it, more legibly than ever, the be- 
 ginning and the end, the Alpha and the 
 Omega, the eternal I am, the omnipresent 
 Father, the breath of whose nostrils' is wis- 
 dom and power and love. 
 
 The Nebulae Theory. 
 
 Naturalists sometimes divide the history 
 of the animal organism into the successive 
 periods of germ, youth, maturity, and old age. 
 Similarly, the nebular history can be divided 
 into the periods of Chaos, Nebula, Star, and 
 Planet. The division has the advantage of 
 promoting precision and distinctness of dis- 
 cussion. The successive stages of actual pro- 
 gress are not well defined, nor bounded by 
 clearly marked outlines. This is a signifi- 
 cant fact in the history ; it shows the exist- 
 ence of those imperceptible gradations of 
 transformation to which forms of growth are 
 necessarily subject. 
 
 We begin with Chaos. If we venture back 
 to the primeval chaos, we are to regard it as 
 
58 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 presenting the uniformly monotonous appear- 
 ance already indicated. But the uniformity 
 must be an illusion. Complete monotony 
 can be its own only offspring. Where there 
 is a perfectly uniform distribution of material 
 and force, there is no internal cause which 
 could introduce variety. Whatever dissimil- 
 itude may have become subsequently visible 
 must have had its corresponding existence in 
 the chaos from which it originated. However 
 dormant and concealed in the outset, its pres- 
 ence in the inscrutable darkness is revealed 
 by the occurrence of the subsequent changes. 
 The plan of the coming universe must have 
 resided in the initial chaos, as surely as the 
 eagle is in the e^g, or the leviathan in its 
 primitive germ. The musical instruments of 
 Nature must have included in their structure 
 the psalm of life and the music of the spheres. 
 The organ must have been tuned, the ma- 
 chinery contrived, and the stops arranged, 
 before the descending weight could evolve 
 the symphony. 
 
 Subsequent to the original chaos, innu- 
 merable chaotic periods may have inter- 
 vened, some of which may have been par- 
 
COSMOGONY. 59 
 
 tial, while others were universal. These 
 periods involve an enlargement of the idea 
 of chaos. It no longer necessarily implies 
 an exceedingly attenuate matter, universally 
 diffused. Inactivity of condition is now the 
 only essential attribute. The chaotic type 
 is as truly found in the sand of the desert 
 or the slag of the furnace as in the isolated 
 particles of a gas. A perfect chaos could not 
 be visible even as nebulosity ; for luminous- 
 ness, however feeble, is the result of active 
 force. It may be that wholly inert matter is 
 nowhere to be found. Its actual non-exist- 
 ence does not invalidate the ideal theory, to 
 which it is essential as a conception. The 
 masses of chaos may even include the ex- 
 ^ hausted remains of a previous universe ; so 
 that they might then retain the systems of 
 motion which they had already acquired. A 
 harmony of motion, once introduced, would 
 thus be perpetuated through successively 
 alternated periods of chaos and cosmos, 
 through world after world, to countless 
 ages. 
 
 The light of the Nebula is the first visible 
 signal that the creative power has begun to 
 
60 IDEALITY IN- THE PHYSICAL SCIENCES. 
 
 act. The uniform distribution of heat is 
 inseparable from the quiescent condition 
 of chaos. But as soon as motion starts, 
 and material atoms begin to aggregate and 
 press upon each other, or to strike each 
 other in their paths, heat and light are 
 developed, and the morning of creation has 
 ' dawned. 
 
 That great astronomer and philosopher, 
 Sir William Herschel, devoted his life to the 
 study of the sidereal universe. He attempted 
 to apply to celestial objects the methods of 
 classification which naturalists had found 
 most instructive in the study of the animal 
 and vegetable kingdoms. He undertook to 
 arrange the nebulae and stars into groups ; 
 and, if we will consent to follow him in his , 
 essays and inquiries, we shall appreciate the 
 rich harvest of truth which he gathered into 
 the stores of science. The principal divisions 
 which we shall adopt are: Nebtdosity, Nebula 
 proper, Cluster, Milky Way, Magellanic Cloud, 
 Annular Nebula, and Spiral Nebula. Very 
 many subdivisions, considered by Herschel 
 and suggested by his immensely extended 
 observations, may be omitted from our dis- 
 
COSMOGONY. 61 
 
 cussion, with the statement that they con- 
 cur in the same mighty testimony. 
 
 A Nebulosity is a faint, indistinct lumi- 
 nousness, without definite boundaries. It is 
 doubtful whether there be any portion of the 
 firmament free from nebulosity, and whether 
 in the darkest spaces there be not a luminous 
 background. If the visible sidereal universe 
 is unlimited, there must be luminousness in 
 every direction, equal to the average intensity 
 of the light of the celestial objects visible in 
 that direction ; and there can be no such 
 phenomenon as absolute darkness. The dis- 
 turbance which such a condition would in- 
 troduce into the classification of the fainter 
 nebulae and stars has not been demonstrated; 
 and it may be safer, for the present, to re- 
 gard the celestial world as having a limited 
 extent. 
 
 The Nebula proper is a stellar mist, with 
 greater or less distinctness of outline, irregu- 
 larity of shape, and brightness of light, and 
 even not without resolvability into stars 
 upon the application of sufficient telescopic 
 powef. On the one side, it is hard to define 
 where nebulosity ends and nebula begins; 
 
62 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 and, on the other side, the limits between 
 nebula and cluster are equally uncertain, 
 and there is no intermediate line of dis- 
 tinct demarcation. The shape is in some 
 cases exceedingly irregular, while in others 
 it is a well-draAvn oval ; and there are instan- 
 ces of an almost exact circle. The variety 
 far exceeds that of the pebbles on the sea- 
 shore; and there is scarcely a conceivable 
 form which has not its representative. Some- 
 times the light is uniform over the entire 
 surface, while in other cases it is concentrated 
 into regular or irregular patches. Here, it is 
 collected at the centre of a regular figure; 
 and, there, it is dispersed without regard to 
 symmetry. The accumulation of light is 
 often limited to a single bright spot, and 
 as often, perhaps, there are many luminous 
 centres. There are sometimes two or three 
 nebulae distinctly separated from each other, 
 but whose proximity and constellation indi- 
 cate that they belong to the same nebulous 
 aggregation, and constitute a double, triple, 
 or even quadruple nebula. 
 
 The Cluster has the same variety in shape, 
 brightness, and mode of concentration as 
 
COSMOGONY. 63 
 
 the nebula, and is sometimes so filled with 
 nebulous matter that it is doubtful where it 
 should be classed. With a little more con- 
 centration, the nebula is transformed to clus- 
 ter ; and, with a Uttle less, the cluster reverts 
 to nebula. For many a cluster you can 
 select a nebula to which it corresponds, as 
 a child to its parent ; there can be no doubt 
 as to the closeness of the relationship. 
 
 A powerful telescope frequently illustrates 
 the effect of concentration, and brings out a 
 cluster, where an inferior telescope had seen 
 only a nebula. Sir William Herschel at one 
 time thought that there were peculiarities by 
 which he could distinguish the resolvable 
 nebulae, and that all the nehulce proper are 
 really clusters. But after some errors of judg- 
 ment he frankly acknowledged his mistake, 
 and became convinced of the actual existence 
 of irresolvable, and of partly irresolvable, 
 nebulse. The discovery of the spectroscope 
 is held to have established this view, and to 
 have furnished a test for distinguishing the 
 genuine from the apparent nebulse. It is 
 found that the spectrum of a star is con- 
 tinuous, like that of the sun ; while that of 
 
64 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the luminous mist is discontinuous, and con- 
 sists of a few isolated lines, like that of a 
 gas. It is even possible to identify the gas 
 of the true nebula. But this remarkable 
 observation does not wholly separate the 
 two forms of matter. They are often found 
 united in the same nebulous star or cluster. 
 There seems to be a series of these doubly 
 constituted bodies, diflfering in the propor- 
 tion of their constituents from one extreme 
 to the other, and offering little opportunity 
 for sharp and definite classification. 
 
 The Milky Way, or Galaxy, is familiar to 
 all. To the naked eye it bears a nebulous 
 aspect ; but the slightest telescopic power 
 resolves it into a cluster. It girdles the 
 whole sphere of the firmament ; and " this 
 remarkable belt," says Sir John Herschel, 
 "has maintained from the earliest ages the 
 same relative situation among the stars ; and, 
 when examined tlirough powerful telescopes, 
 is found — wonderful to relate ! — to consist 
 entirely of stars scattered by millions, like glit- 
 tering dust, on the black ground of the gen- 
 eral heavens." The constitution of the galaxy 
 has been subjected to special investigation by 
 
COSMOGONY. 65 
 
 the two Herscliels ; it has been gauged in 
 every direction and mapped with extreme 
 care. It is a stratum of stars, of which the 
 thickness is small, as compared with its other 
 dimensions. But it is thick enough to include 
 all the stars visible to the naked eye; .and 
 their apparent removal from the common zone 
 of the Milky Way is a simple visual con- 
 sequence of their proximity. The distance 
 of the farthest star is not greater than light 
 traverses in two or three thousand years ; 
 and the thickness of the stratum is not far 
 from one thirtieth of its longest diagonal. 
 Its bifurcation and its branching and diverg- 
 ing streams afford opportunity for curious 
 speculation, and correspond to the structure 
 of many of the nebulae and clusters. It is 
 concentrated symmetrically above and below 
 its central plane, which is that of the greatest 
 .density. It presents an embodiment of the 
 historic idea which pervades the celestial uni- 
 verse. But it has advanced to such a period 
 that the regular oval nebulae and the glob- 
 ular clusters have disappeared from its inner 
 structure. The cosmical spring-time and 
 summer, with their nebular buds and flow- 
 
 5 
 
66 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 ers, have passed away ; and the ripe harvest 
 of suns and planets is maturing. 
 
 The two Magellanic Clouds are conspicuous 
 displays of stellar light, which are unseen 
 by the northern astronomer. They resemble 
 portions of the Milky Way in their general 
 aspect and brightness. When examined 
 through the telescope, their constitution is 
 found to be astonishingly complex. Accord- 
 ing to Sir John Herschel, they combine 
 patches of nebulosity of every degree of 
 resolvability " nebulae in abundance, both 
 regular and irregular; globular clusters in 
 every state of condensation ; and objects of 
 a nebulous character quite' peculiar, and 
 which have no analogue in any other region 
 of the heavens." They are celestial mu- 
 seums, in which examples of all sidereal 
 forms are collected. Not only do they con- 
 tain every variety of nebula and cluster, 
 but even the monsters have their represent- 
 atives. 
 
 The Annular Nebulae are sidereal rings, 
 which exhibit a peculiar mode of develop- 
 ment. Unlike the ordinary nebulae, they 
 manifest a centrifugal rather than a centri- 
 
COSMOGONY. 67 
 
 petal class of aggregation ; they do not in- 
 dicate statical, but dynamic, equilibrium. 
 They suggest an approach to organic con- 
 stitution. 
 
 The ring furnishes an ideal connection 
 between the most immense and the minutest 
 phenomena of the physical world. It is found 
 among the stars and planets, as well as with 
 the nebulae. It adorns Saturn, making it the 
 most beautiful of the stars ; and Laplace saw 
 in it the remnant of the process by which 
 the solar system was developed. It is quite 
 probable, as indicated by Mr. Charles S. 
 Peirce of the Coast Survey, that our galaxy 
 should be classed as a stellar ring. The ring 
 is conspicuous among the typical forms of 
 the animal kingdom, and is essential to the 
 elemental vortex theory. In the intellectual 
 world it is not restricted to geometry; it 
 has wound its way into art as the type of 
 infinity, into law as the symbol of authority, 
 and into religion as the pledge of faith. The 
 geometric idea does not expand with the 
 magnitude of the circle, nor dwindle with 
 its contraction. It is equally perfect in the 
 molecule and in the sidereal cluster ; and no 
 
68 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 complication of appearance can obscure the 
 simplicity of the conception. 
 
 The annular nebula demands careful study 
 on account of the variety of aspect under 
 which it may be presented. Its circular 
 form may be foreshortened into an ellipse, 
 or an elliptical form into a circle. When 
 viewed from the side, it may be undistin- 
 guishable from a dumb-bell nebula ; and 
 since it cannot be taken in the hand, and 
 turned around for inspection, the actual fig- 
 ure can be recognized only by refined and 
 thoughtful observation. 
 
 The Spiral Nebula, first exhibited by the 
 telescope of Lord Rosse, is the visible repre- 
 sentative of a peculiar process of evolution. 
 It tells of mighty explosions, of a rotating 
 mass, and of a resisting medium. Behold it, 
 and wonder if geometry will ever penetrate 
 its mystery and explore the secret of its for- 
 mation ! Its suggestions are obvious to the 
 simplest understanding ; but the profoundest 
 philosopher may exhaust his wisdom in ex- 
 ploring its ideality. There is evidence of sim- 
 ilar action in the streaming outskirts of a large 
 number of nebulae and of the galaxy itself. 
 
COSMOGONY. 69 
 
 I have attempted to give a simple descrip- 
 tion of the various classes of nebulae. Typ- 
 ical forms can be selected, but they are never 
 sharply isolated from other forms. We have 
 always a continuous series, and an uninter- 
 rupted succession of apparent transforma- 
 tions. There are not distinct species and 
 genera and families and classes, as in the 
 organic world ; but each division seems to 
 be a temporary and transitional stage. 
 
 When you enter a grove of oak, and see 
 trees of every size surrounding you, you do 
 not hesitate to arrange them in a mental 
 series, according to their seeming age ; and 
 you read, in the succession, the history of 
 each individual, as correctly as if you had 
 seen it grow. When the botanist inspects 
 his herbarium, with its specimens of seed, 
 germ, early shoot, and plant in flower, in 
 fruit, and in seed, he is enabled to study 
 each growth, without awaiting the long course 
 of development. In the same spirit of phi- 
 losophy, Sir William Herschel interpreted 
 the unbroken law of succession in the celes- 
 tial forms. They constitute an illustrated 
 history. If he could have prolonged his 
 
70 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 life for the immense period necessary to 
 watch the change of a nebula from nebu- 
 losity to cluster, he would have found the 
 forms intermediate to those which he act- 
 ually observed. But what was his magnifi- 
 cent discussion of his observations but a 
 prolongation of life ? In becoming pene- 
 trated with the truth of Nature, he had 
 drunk the veritable elixir. 
 
 We can see the changes of these lower 
 clouds which give us rain and hail and snow, 
 and are laden with thunder and lightning, 
 and associated with wind and rainbow. We 
 can study them as thunder-storm, or water- 
 spout, or cyclone, and trace their path across 
 the continent. But their history is not more 
 clearly legible than that of the sidereal 
 clouds with their innumerable varieties and 
 modes of transformation. 
 
 O ye of little faith ! Accept the divine 
 record of the sidereal universe, or ye would 
 not believe in God if his name were written 
 in letters of fire upon the firmament ! To 
 reject the ideal history is to strengthen the 
 stronghold of scepticism. It is to deny the 
 celestial doctrine written upon the heavens 
 
COSMOGONY. 71 
 
 and the earth. It is to reject the law of the 
 Lord, which is perfect, converting the soul. 
 Let the children be faithful to the Father, and 
 loyally receive the declaration that he made 
 the light with which he shines through the 
 stars, and that it is good. ' 
 
72 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 III. 
 
 FEOM NEBULA TO STAR. 
 
 In the last lecture, the nebulae were dis- 
 cussed. Plain description was offered, with 
 no varnish of hypothesis. There was an 
 attempt at classification, which was only 
 roughly successful, because no definite lines 
 of demarcation could be found from one end 
 of the series of forms to the other. But 
 there was spontaneously developed a pro- 
 found history, an extraordinary tale of con- 
 tinuous transformation, indicative of growth 
 and evolution. The changes testified to the 
 forces by which they were accomplished. 
 We may now proceed to investigate the nature 
 of these forces, and their modes of action. * 
 
 Force, regarded as cause, is an ideal phe- 
 nomenon, suggested to recognition by the ef- 
 fort which we make to perform work. In- 
 visible as the mind of man, it can be known 
 
FROM NEBULA TO STAR. . 73 
 
 only by its effects. The mechanical philo- 
 sopher can discover nothing in it but a phe- 
 nomenon of motion and a transfer of action 
 from one mass of matter to another. Even 
 when a man performs a work, there is no ex- 
 ternal evidence that any exertion of the power 
 of mind was involved. All the physical effects 
 are fully accounted for by the known con- 
 sumption of muscular material. The mind, 
 undoubtedly, has a controlling influence, just 
 as the engineer controls the steam engine, or 
 the sovereign his subjects ; but the work which 
 is done is the exact equivalent of the expendi- 
 ture of material. How it is that the control- 
 ling power of the mind is exerted, cannot be 
 explained. When philosophy strives to give 
 an account of the inexplicable, she finds her- 
 self hemmed in, on all sides, with impenetra- 
 ble mystery. But when she is content with the 
 legitimate search for the laws of operation, 
 the mystery vanishes, like the cloud before 
 the rising sun. When work is done, the 
 requisite amount of physical strength is 
 manifestly consumed. Less is not sufficient, 
 and more is not required, whatever may be 
 the mode of operation. This is the law of 
 
74 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 power ; it is so simple that it is almost an 
 axiom, and it cannot be explained by other 
 independent laws. 
 
 Again, when a man wills, his brain is heated, 
 and his arms and feet obey the intention of 
 his will ; they have no innate power of resist- 
 ance. This is the law of harmonious action. 
 It is sufficient to itself and to all the demands 
 of healthy work and inquiry. The laws of 
 power and of harmony are both pre-estab- 
 lished, and I am not aware that the bold- 
 est evolutionist has ever regarded them as 
 the results of evolution. 
 
 In almost every natural phenomenon, there 
 is a combination of two or more forces inces- 
 santly occurring, and indispensable to any 
 variety of appearance. The mode of combi- 
 nation, at each instant of time, is exceedingly 
 simple. A mass to which a force is applied 
 must, in consequence of its inertia, yield un- 
 resistingly. To decline to receive the offered 
 force would be an evidence of volition, and 
 directly antagonistic to inertia. The mass, 
 if it starts from the state of rest, moves in 
 the first instant in the direction of the force, 
 and in a straight line, to a distance propor- 
 
FROM NEBULA TO STAR. 75 
 
 tioned to the magnitude of the force. The 
 body to which the force has thus been applied, 
 and in which it may be considered as deposi- 
 ted, continues to move uniformly in its initial 
 direction and with its initial velocity, until 
 some new force is applied to it. Upon the 
 application of a new force, the body moves 
 in a second straight line, with the velocity 
 corresponding to this second force, while at 
 the same time it preserves the velocity pre- 
 viously imparted to it. The combined eflPect 
 is one which might have been produced by a 
 single force, called the resultant. If, instead of 
 acting at successive instants, the forces act si- 
 multaneously, the resultant is the same. The 
 components being represented by two straight 
 lines starting from a point, the resultant is 
 the geometric sum of these lines ; it is the 
 diagonal of the parallelogram constructed 
 upon the component lines ; it is the third 
 side of the triangle of which the compo- 
 nents are, successively, the other two sides. 
 This proposition admits of generalization : 
 any number of forces may be added together 
 by the construction of a polygon, of which 
 each side, in succession, represents one of the 
 
76 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 forces; and the closing side of the polygon, 
 drawn from the initial to the final point, ex- 
 presses the resultant of the given forces.. This 
 mode of combining forces constitutes the fun- 
 damental idea of Analytic Mechanics and the 
 substance of the doctrine of that science. 
 
 If, instead of one body, there is a system 
 of bodies, connected by however complicated 
 relations, the mathematical conditions of the 
 problem are susceptible of simple algebraic 
 expression. An equation, first written by the 
 illustrious Lagrange, consisting of only six 
 
 symbols, 
 
 IPSp = 0, 
 
 is the universal type by wliich every problem 
 of mechanics is subjected to analytic discus- 
 sion. All that remains is for the mathematician 
 to pass the equation through his ideal alembics, 
 and give it the just interpretation. All physi- 
 cal forces and phenomena, possible as well as 
 actual, ideal as well as real, are condensed into 
 this foi-mula and subject to its magical power. 
 It embraces the complete history of the ma- 
 terial universe from the beginning to the end. 
 Man has been permitted to write it. What 
 a marvellous proof of his ideality ! Could 
 
FROM NEBULA TO STAR. 77 
 
 he read all that is contained in it, he would 
 be greater than one made in the image of his 
 Creator ; he would himself be omniscient. 
 
 The system of which the forces balance 
 each other is in equilibrium. There are two 
 forms of equilibrium, — the stable and the un- 
 stable. The stable equilibrium is spontaneous- 
 ly maintained ; and when it is disturbed the 
 system tends to revert to its original position, 
 and oscillates within narrow limits about its 
 normal state of rest. A system in unstable 
 equilibrium, on the contrary, not only yields 
 to a slight effort of - displacement, but con- 
 stantly tends away from the state of rest, from 
 which it may recede to some very great 
 amount. The simplest example is that of 
 the rod which hangs down from a point of 
 support, and is then in stable equilibriixm ; 
 whereas, when it is skilfuly balanced in 
 the reversed position, above the supporting 
 point, it is in unstable equilibrium. 
 
 The only possible position in which an 
 inorganic system can remain at rest, is that 
 of stable equilibrium. But positions of un- 
 stable equilibrium are essential to organic 
 structures. "Where there is life, there must 
 
78 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 be motion as well as rest ; and those are the 
 conditions best adapted to life in which there 
 is the greatest facility both for rest and for 
 motion. Perhaps the most striking charac- 
 teristic of an organism is its power of main- 
 taining unstable equilibrium, either in its ele- 
 ments or in its whole mass. The philosophy of 
 instability is profoundly connected with the 
 variety of organic condition and the preserva- 
 tion and development of its ideality. All the 
 chemical compounds essential to vitality are 
 unstable, as is evident from their ready decom- 
 position when life ceases. Men walk, birds fly, 
 fishes swim, through a constantly recurring se- 
 ries of unstable positions of equilibrium. In- 
 stability is a necessary element of spontaneous 
 action, and intimately connected with the uni- 
 versal pre-established harmony. Without it, 
 the germs of being could not be developed, the 
 egg could not begin to grow, nor chaos take 
 its first step towards cosmos. The equilib- 
 rium of chaos must be the unstable equi- 
 librium of organic life ; and its legitimate 
 type is, — where the slightest motion of heat 
 may originate action, and where all philos- 
 ophy has sought it, through Plato and Aris- 
 
FROM NEBULA TO STAR. 79 
 
 totle, from the most ancient Egyptian, Chal- 
 dean, and Judaic speculations, — in the egg. 
 In most of the processes of art, instability- 
 is the habitual and necessary resort of the 
 engineer. When the sexton goes to toll the 
 church bell, he finds it hanging by its wheel, 
 in a stable position, with its weight below the 
 axis of suspension, and not at all disposed 
 to move at an imbecile bidding. He is not 
 strong enough nor heavy enough to reverse 
 it immediately. He skilfully vibrates it from 
 side to side, gradually increasing the height 
 of oscillation ; until he brings it up to rest, 
 and " sets " it, above the axis, in the unstable 
 position of equilibrium. Happy is the bell- 
 ringer who can accomplish his feat in fewer 
 vibrations than his fellow ; the bell itself 
 rings out the story of his triumph, and all the 
 village, which understands his art, applauds 
 him ! Have you not seen the grim smile with 
 which he contemplates his achievement? The 
 bell is now placed so that the gentlest impulse 
 will start it oflF upon the complete circuit of a 
 maximum oscillation, and the sexton's artful 
 touch readily carries it up on the other side, 
 and restores it to its unstable rest. 
 
80 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 Were there no friction, no resistance of the 
 air, and no impediment of any kind to the 
 motion of the wheel, an infinitesimal distur- 
 bance would suffice to give the initial start. 
 But if only such a disturbance were appHed, 
 an infinite time would be required to start 
 the bell sensibly from its place of rest, or to 
 communicate to it a finite and visible mo- 
 tion. The sexton would have been buried 
 and forgotten, although his force would 
 remain alive. The interval of the visible 
 vibration, when it came at length, would 
 endure a few instants ; and after another in- 
 finity, the perfect equilibrium would be again 
 attained. We will not be diverted to discuss 
 the philosophical significance of this ideal 
 geometric infinity. But as we know that for 
 any phase of oscillation of the bell and the 
 wheel there is a definite velocity of easy 
 computation, which belongs to this infinite 
 duration of vibration, we claim that it cannot 
 be rejected as a baseless vagary. In the con- 
 stant approach to the unstable equilibrium, 
 which is never reached, and the constant 
 diminution of velocity, which never vanishes, 
 we may struggle in vain to form a distinct 
 
FROM NEBULA TO STAR. 81 
 
 conception. It is one of the problems with 
 which the sphinx delights to feast on man's 
 intelligence. It is a hieroglyph, which no 
 power of figures can enable the mathemati- 
 cian to decipher, so long as he is no less rig- 
 idly subject to the trammels of time than 
 the unpretending ignoramus. 
 
 We will resume the consideration of the 
 nebular theory, within the due limits of scien- 
 tific research. The active forces of the nebulae 
 may be considered, relatively to their effects, 
 as concentrative or diffusive. In most nebulae 
 there are regions of concentration, and in- 
 deed every visible nebula is a concentrating 
 mass. The purely gaseous nebula would be 
 diffused, if it were not held together by a suf- 
 ficient attraction towards its interior. It 
 would gradually grow faint and disappear, if 
 it were not constantly giving out light and 
 heat by compression and condensation. It 
 must, then, be that the attraction is more 
 powerful than the internal elasticity. It would 
 be extraordinary if this were not the case, 
 considering the extreme tenuity of the nebu- 
 lous substance. In all probability, the con- 
 densation would advance so rapidly as to 
 
82 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 be perceptible, within a few years of obser- 
 vation, if the elasticity were the only force 
 opposed to the attraction. But the most de- 
 licate scrutiny of astronomers has not yet 
 established an instance of increasing ag- 
 gregation. The extreme slowness of the 
 process indicates internal motion as the most 
 powerful, and probably the chief, antagonist 
 of the attraction. 
 
 The simplest form of motion, and that 
 which it is most reasonable to suppose, con- 
 sists in a rotation of the nebula about an 
 axis. In a balanced condition, the centrifu- 
 gal force arising from rotation is everywhere 
 equal and opposite to the attraction. But 
 such a dynamic equilibrium could only be 
 partial and temporary. There would be no 
 centrifugal force in the direction of the axis 
 of rotation; while there must be attraction 
 in that direction, on each side of a medial 
 plane, which may be called the equatorial 
 plane, and towards that plane. This at- 
 traction, unresisted by centrifugal force, will 
 condense the nebula towards the plane, until 
 the elasticity developed by the condensation 
 shall balance the attraction. The centrifugal 
 
FROM NEBULA TO STAR. 83 
 
 force may, in some regions and for some 
 periods of time, prevail over the attraction, 
 and a diflfusive process be introduced. But 
 it does not follow that, in this case, aggre- 
 gation and the development of light and 
 heat will be excluded. The annular nebu- 
 lae are fine exhibitions of this phenomenon; 
 and their light, when they are purely gase- 
 ous, must arise from condensation occurring 
 in the body of the ring. The mathematical 
 formulae which would express the possible 
 constitution of one of these nebular rings 
 have not yet been written. But if I held 
 them in my hand, you would not thank me 
 to display them. They would dazzle more 
 than they would illumine you. The most sci- . 
 entific audiences refuse to listen to the awk-. 
 ward ostentation of algebraic demonstration ; 
 they would rather rend their indiscreet lec- 
 turer than be choked by the pearls of his 
 pedantry. I submit to the inevitable judg- 
 ment, and proceed with the nebular history. 
 
 We have reached the period of the transition 
 from Nebula to Star; which may be considered 
 under the heads of Bound Nebula, Nebulous 
 Star, Star, Double Star, and Solar System. 
 
84 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 The Bound Nebula is the natural and obvi- 
 ous result of symmetrical aggregation. In- 
 creasing aggregation and density are invari- 
 ably accompanied by the development and 
 emission of light and heat. But the emitted 
 heat of a gaseous body is always less than 
 that which is generated. It cannot be other- 
 wise. A higher temperature is required to 
 balance the increased mutual attraction of the 
 particles, arising from their greater proximity. 
 The increase of density and elasticity is never 
 sufficient. The nebulae present, then, the 
 astonishing paradox of cooling bodies which 
 are always growing hotter. The opposite 
 paradox of bodies which are absorbing heat 
 and thereby growing colder is equally ad- 
 missible ; and, strange to say, seems to have 
 been actually observed. As the atoms of a 
 contracting body approach each other, they 
 may, in the course of time, come into so close 
 proximity as to induce chemical action, not- 
 withstanding the increase of heat. Com- 
 pounds will then be formed, which will be 
 gaseous, liquid, or solid, conformably to their 
 temperatures of liquefaction and solidifica- 
 tion, in comparison with the temperature at 
 
FROM NEBULA TO STAR. 85 
 
 which they are generated. The spectroscope, 
 in its discrimination between solid and gas, 
 indicates the progress of change in either 
 direction. In the solidifying nebula, the 
 spectrum will mostly change from a con- 
 stitution of individual lines to one of con- 
 tinuity, modified however by the conditions 
 of temperature ; but the reversed order of 
 change may be manifested in the expanding 
 nebula. Contraction corresponds to the di- 
 rect law of sidereal progress. But several 
 years ago I ventured to indicate that expan- 
 sion was not only a possible phenomenon, 
 but a necessary and unavoidable complement, 
 of direct progress. The interchange of heat 
 between the celestial bodies should produce 
 it ; and it has now been unmistakably ob- 
 served. 
 
 The light radiated from the heated gas is 
 not only different in the character of its spec- 
 trum from that of the solid or liquid, it also 
 seems to be less intense, and thereby sup- 
 plies the characteristic distinction between 
 the rotind nebula and the Nebulous Star. The 
 feebler brilliancy of the nebulse is not to be 
 attributed to their greater distance, but to 
 
86 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 their actual deficiency of light. It is, indeed, 
 a reason for supposing them to be nearer 
 than the stars of small magnitude, at least 
 when they retain any visible portion of gase- 
 ous light. Their natural position in the side- 
 real constitution is not where the progress of 
 condensation is most advanced, but upon the 
 outskirts of our galaxy, where it has but just 
 begun. We should look for them in that 
 part of this region which is nearest to us ; 
 that is, in the direction perpendicular to the 
 plane of the Milky Way. Hence it is that 
 we find them clustering in the vicinity of the 
 galactic poles. 
 
 If the nebulae were as remote as they have 
 sometimes been assumed to be, their apparent 
 changes in position or structure' would be 
 proportionably slow, and require long peri- 
 ods of time to be detected. But skilful and 
 indefatigable observers, especially those at 
 Washington, have succeeded in discovering 
 some interesting nebular motions and trans- 
 formations. If these observations tend to 
 contract our ideas of the dimensions of the 
 visible sidereal universe, there is the greater 
 necessity of an unlimited ideal space com- 
 
FROM NEBULA TO STAR. 87 
 
 mensurate witli tlie expansibility of the human 
 intellect. ' 
 
 After the nebula has advanced to the stage of 
 cluster, the brightness must be less, in propor- 
 tion to the small size of the constituent stars. 
 The stellar structure will increase the distance 
 at which the nebula may be seen ; but the 
 relations of brightness and proximity will not 
 be greatly modified by the resolvability. 
 
 The continued condensation of the nebu- 
 lous star will be accompanied by an increase 
 of brightness and distinctness and an absorp- 
 tion of nebulosity, until it appears quite as a 
 true Star. Liquefaction or partial consolida- 
 tion will occur near the surface ; the higher 
 the temperature, the closer the particles are 
 pressed together. But the body remains 
 gaseous throughout its general mass, with 
 only a superficial flaming photosphere. The 
 surface must be in perpetual ebullition ; and, 
 when shaken by the frozen meteors which are 
 on all sides dashing in upon it with a veloc- 
 ity of many hundred miles a second, may 
 throw up its gases as high as we are from the 
 moon. Disturbed by its own colder planets,- 
 it is liable to terrific storms. Hurricanes may 
 
88 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 whirl apart the luminous masses, and produce 
 breaks in the photosphere, tlrrough which the 
 telescope may be able to penetrate into the 
 dark abyss below ; and the Very darkness may 
 be light to the human mind. It may reveal to 
 the philosopher the probable absence of an in- 
 terior nucleus ; for any such nucleus would be 
 heated up under the pressure of the stellar 
 atmosphere and the blows of the meteors, till 
 it exceeded the photosphere and the surround- 
 ing gas in brightness. Bright spots would then 
 seem to be possible, but not the dark ones 
 with which we are familiar, and which have 
 been studied with the greatest success by the 
 American astronomer. Professor Langley. 
 
 When there are several points of conden- 
 sation in a nebula, making it a double, triple, 
 or multiple nebula, it naturally terminates in 
 the corresponding evolution of a Double, 
 Triple, or Multiple Star. Various internal 
 motions might produce peculiar combinations 
 of nebula and star, which might be retained 
 in the resulting stellar group, and would de- 
 serve delicate observation and critical analy- 
 sis. The path of star about star obeys the 
 law of universal gravitation, and tends to 
 
FROM NEBULA TO STAR. 89 
 
 the conic section as naturally as did the studies 
 of the Greek geometers. Its determination 
 demands of the observer consummate skill and 
 the exercise of extreme patience. Near the 
 close of the last century, and at the beginning 
 of the present one, Sir William Herschel, 
 guided by his masterly astronomical insight, 
 perceived that there were too many stars in 
 close apparent proximity to be accounted for 
 on the mere optical ground of an accidental 
 nearness of direction, without supposing a 
 physical relation. He undertook to measiire 
 their relative positions, with all the accuracy 
 in his power. Since his time, for more than 
 fifty years, the finest instruments and the 
 greatest observing skill have been devoted 
 systematically to the measurement of the 
 double stars. Many thousands of pairs have 
 been observed, and more than a hundred 
 thousand measurements have been made ; 
 and, as the result, we have only about a 
 dozen good orbits. In most cases the change 
 of position has been imperceptible, so that 
 one man's life cannot avail to ascertain the 
 duration of the period of revolution, which, 
 in the large proportion of unknown orbits, 
 
90 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 must exceed fifteen centuries. Hence arises 
 a new and serious obstruction, in the neces- 
 sity for combining together the observations 
 of different astronmers, each affected by his 
 own personal peculiarities. 
 
 The frequent difference of color between 
 the constituent stars of a binary system is an 
 interesting and suggestive phenomenon. It is 
 an evidence that, during the transition from 
 nebula to star, there is a tendency to a pro- 
 cess of differentiation, by which the material 
 collected in one centre differs from that col- 
 lected in the other. This might arise from 
 the union of various causes, — from the law 
 of diffusion, by which, in equilibrium, each 
 gas is a vacuum to the others ; from the dif- 
 ferent temperatures and pressures at which 
 they liquefy or solidify ; and from the pecu- 
 liar conditions of each chemical combination. 
 "Without undertaking to discuss the mode of 
 operation, it is obvious that here is sufficient 
 suggestion for the origin of the individual 
 color and the diverse glory of the twin stars. 
 
 The binary constituents are often of equal 
 brilliancy, and probably, therefore, of equal 
 magnitude. But, in a multiple system, one 
 
FROM NEBULA TO STAR. 91 
 
 star is frequently of superior magnitude to 
 the others, which move around it as if they 
 did it homage. Our own Solar System is the 
 famihar example of such a sidereal constitu- 
 tion. The non-luminousness of some of its 
 members is a secondary and relative pheno- 
 menon, which does not impair the value of 
 the record. No planet or satellite can have 
 lost all its primitive heat, and the general 
 character of motion must have been trans- 
 mitted from the stellar condition. 
 
 We have eight primary planets, all of 
 which revolve about the central sun in the 
 same direction, which is that of the sun's 
 rotation about its axis, and nearly in the 
 plane of the solar equator. Six of these 
 planets rotate upon their axes in the same 
 direction, and with their axes nearly parallel 
 to the solar axis. About two hundred aste- 
 roids are now known. How many more will 
 be discovered, after the visual orbs of Peters 
 and Watson have gone to sleep, we cannot 
 foretell. But we can predict, with a high 
 degree of certainty, that they will all revolve 
 in the company of their brethren, in the same 
 common direction. There are twenty-two 
 
92 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 satellites, including Saturn's ring, all of which 
 revolve about their primaries, in the direction 
 of their rotation, and nearly in the planes of 
 their equators. Whence comes this common 
 motion ? I might carry you into the vague 
 regions of probability, and compute the 
 chances, greater than the number of sands 
 upon the sea-shore, against this concurrence 
 of events as an accidental phenomenon. But 
 this is not a case to be decided by the rules 
 of chance. It must be presented to the tri- 
 bunal of good sense and sound judgment. 
 We have here the unanimous declaration of 
 a community of origin. Every philosopher 
 must approve the conclusion reached by the 
 great geometer Laplace, that this grand phe- 
 nomenon, so precisely corresponding to the 
 nebular theory, is an independent confirma- 
 tion of its validity. 
 
 The successive steps of the planetary de- 
 velopment are necessarily obscure. What is 
 now the solar system was probably once a 
 round, rotating nebula, which might have 
 been early transformed into a nebulous star. 
 The nebulous gas, surrounding the nucleus, 
 would take the form of a thin disk, similar 
 
FROM NEBULA TO STAR. 93 
 
 to Saturn's ring, perpendicular to tlie axis of 
 rotation. The disk might be divided ideally 
 into concentric circular rings, each of which 
 would have its distinct velocity of rotation, 
 sufficient to generate the centrifugal force 
 necessary to balance the attraction towards 
 the centre. Each particle of the nebula 
 might, indeed, be regarded as a small planet, 
 revolving in its proper time about the nu- 
 cleus. The outer rings would, consequently, 
 rotate more slowly than the inner ones, and 
 would tend to retard them by some species 
 of attrition, while they themselves would be 
 accelerated. The outermost ring would thus 
 be accelerated, and its centrifugal force in- 
 creased, until it actually separated from the 
 inner mass, and formed a ring around it 
 similar to Saturn's ring. 
 
 But such a ring could not long be retained 
 in its position. It would soon move bodily 
 in some direction in its own plane, until 
 it was brought into collision with the in- 
 cluded mass, and so broken up. Why does 
 not this happen with the ring of Saturn? 
 Because it is sustained by the near satellites ; 
 or perhaps because its condensation has ad- 
 
94 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 vanced so far that its nebular continuity is 
 destroyed, and it has become a cluster of 
 meteors; or perhaps because it preserves 
 an atmospheric connection with the planet 
 through the medium of the dusky ring. 
 But the supposed ring about the sun has 
 neither of these forms of support. It might 
 be actually formed, but would almost imme- 
 diately be destroyed. The temporary form- 
 ation and destniction could hardly fail to 
 introduce inequality of density and a con- 
 centrating tendency, which might continue 
 to draw in the nebular substance, until chem- 
 ical action was induced, and a planet was 
 formed. 
 
 By the same process, new planets might 
 be formed from the remaining nebula. Each 
 planet, when formed, would exert an influence 
 upon the nebula within its orbit and on its 
 subsequent condensation. Although we may 
 not to-day possess the geometric skill to de- 
 fine the nature of this influence, we may infer 
 it from the actual order of the solar system. 
 The nearly circular orbits of the two outer 
 planets, and especially of Neptune, corre- 
 spond to the small disturbing influence to 
 
FROM NEBULA TO STAR. 95 
 
 which they were subjected from exterior 
 bodies. The larger mass and eccentricity 
 of the next planet, Saturn, and the prepon- 
 derating mass of Jupiter, indicate the con- 
 centrating tendency of the outer planets. 
 The greatly diminished size of the four inner 
 planets is a probable consequence of the 
 undue proportion of material absorbed into 
 the four outer planets and the small remnant 
 of nebulous gas left for their construction. 
 Jupiter, the king of the planets, had appro- 
 priated the lion's share. His excessive influ- 
 ence had caused the great eccentricity of the 
 orbit of Mars. The same royal power had 
 induced repeated condensation, at point after 
 point, in the nebula immediately within his or- 
 bit ; in consequence of which the system has 
 lost a primary planet, and gained nobody 
 knows how many insignificant asteroids. 
 The largest of these little planets has per- 
 haps no greater superficial area than that 
 contained by the State of Texas, while the 
 smallest that we know has a diameter of 
 only some twelve or fifteen miles. But it 
 were better to freeze on the least of the as- 
 teroids, in the full sight of Grod's firmament, 
 
96 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 than to roast upon the fiery surface of Jupi- 
 ter, beneath an impenetrable atmosphere of 
 clouds. 
 
 The distribution of the planets has been 
 thought to obey a law pointed out by Bode, 
 which is that the mean distance of each or- 
 bit from the next exterior one is twice as 
 great as from the next interior orbit. The 
 law does not extend to the planet Neptune ; 
 but the existence of this planet was unknown 
 in the time of Bode. It was known, how- 
 ever, that the law fails in the interval from 
 Mars to Jupiter. Hence Bode surmised that 
 there might be an iindiscovered planet in 
 that interval. The subsequent discovery of 
 four asteroids astonished astronomers ; and 
 the cluster of which these four bodies were 
 but the first known members is now large 
 enough to satisfy the demands of the ideal 
 law. But the. unwarranted extension of 
 Bode's law misled Leverrier in determining 
 the limits within which the mean distance of 
 Neptune could lie. It is fortunate for ce- 
 lestial mechanics that there is no such un- 
 certainty about the universality of the law 
 of gravitation. 
 
FROM NEBULA TO STAR. 97 
 
 The commensurability of the mean mo- 
 tions of the planets is a more important 
 phenomenon in the theory of their mutual 
 perturbations. It may easily have arisen from 
 the perturbative action exerted during the 
 period of concentration, especially if it be 
 admitted that the orbital eccentricities were 
 larger at the beginning than they are at pres- 
 ent. The system is filled with examples of 
 commensurability of mean motions. The year 
 of Uranus is just about one half that of Nep- 
 tune ; and we here have a case of the occur- 
 rence of the simplest of ratios. The year 
 of Saturn is one third of that of Uranus, 
 giving the next ratio in the order of sim- 
 plicity. In the other annual ratios there is a 
 frequent approximation to the ratios of one 
 half and one third, not unlike that which bot- 
 anists have found in the arrangement of the 
 leaves of plants. Thus the year of Jupiter 
 is nearly two fifths of that of Saturn, which 
 introduces the third fraction of the law of 
 phyllotaxis. All astronomers are aware of the 
 vast importance of this fraction in the theo- 
 ries of these two planets. The year of our 
 earth is about three halves of that of Venus 
 
 7 
 
98 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 and one half that of Mars, and the year of 
 Mercury is about two fifths of that of Venus. 
 In the three inner satellites of Jupiter, and 
 the four inner satelhtes of Saturn, the frac- 
 tion one half occurs four times in the ratios 
 of their mean motions. 
 
 These appear to be small facts ; but they 
 bind together the origin and growth of plan- 
 ets and satellites into one harmonious history. 
 The still smaller facts of the spectroscope 
 show the presence throughout the stellar 
 world of the same elementary substances 
 which we find to be necessary for organic 
 structure on this earth. The same nitrogen 
 and hydrogen are found in the youngest of 
 the gaseous nebulae, and foretell future solar 
 systems, with their habitable planets, when 
 ours shall have passed away. 
 
 Can this vast speculation of the Nebular 
 Theory be a reality ? Can man, with his 
 diminutive stature, measure this great world ? 
 With his threescore years and ten, can he 
 read this stupendous history? "Whence comes 
 so sublime a power, if it is not God's gift, 
 bestowed with his blessing? 
 
PLANET, COMET, AND METEOR. 99 
 
 IV. 
 
 PLANET, COMET, AND METEOE. 
 
 The final stage of the nebular history is 
 the Congealed Star ; which may have its In- 
 organic and Organic Period ; of which Planet, 
 Satellite, Comet, and Meteor are special forms ; 
 and which is destined to become again, at 
 last, a Chaotic Mass. 
 
 Through some process of condensation, the 
 star may begin at the surface to liquefy per- 
 manently, and may after a time become liquid 
 throughout. But a solid surface may always 
 require the presence of an incumbent atmos- 
 phere ; and there may be solid portions dis- 
 tributed through the mass of a gaseous or 
 liquid star, under laws which have not yet 
 been sufficiently explored. 
 
 The difference between the gaseous and 
 liquid states is strikingly manifested in the 
 conditions of temperature and density. The 
 
100 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 contraction and heat resulting from compres- 
 sion are large in the gas and small in the 
 liquid. "We have seen how, notwithstanding 
 its radiation of heat, the gaseous nebiJa 
 grows hotter and denser and smaller ; where- 
 as the congealed star is constantly cooling at 
 its surface. It may be in a liquid state, and 
 still be classed as a Congealed Star. The sub- 
 sequent solidification is a physical phenom- 
 enon, which is reserved for later discussion. 
 Should a rigid surface be early formed over 
 an included liquid, it must continue to cool, 
 contract, and undergo innumerable forms of 
 flexure from the gases within, from the war 
 ters falling from the atmosphere, and from 
 other external causes. It will pass through 
 the geologic Inorganic Period, the epochs of 
 which, studied by philosophers, are replete 
 with grand ideal speculation. 
 
 The surface will, at length, become cool 
 enough for Organic Life. At the same time, 
 life will make its appearance, — plants first, 
 and then in their proper order the difi"erent 
 branches of the animal kingdom, concluding 
 with fish, bird, beast, and man. Whence did 
 they come ? Were they latent in the womb 
 
PLANET, COMET, AND METEOR. 101 
 
 of creation ; or did they exist only in the in- 
 tention of the creator, and demand a new- 
 creative act ? What is the difference to sci- 
 ence, which only studies the laws of change 1 
 What the difference to religion, which sees 
 the divine hand as plainly in the nebula as in 
 the star; in the inorganic period as visibly 
 as in the organic ; in the growth of planets 
 from the formless chaos, through the nutri- 
 ment of the falling meteors, as distinctly as 
 in the development of a Shakspeare from a 
 helpless, thoughtless infant ! What difference 
 can it make to man's faith in a creator, if he 
 does not think of him as -a pagan Jupiter, 
 the slave of some power of fate, which sub- 
 jects the destiny of to-morrow to the acci- 
 dents of yesterday, but as the source of all 
 intelligence, whose works are the products 
 of law and the result of deliberate intention 1 
 With the infinite wisdom of such a being 
 would it not be incompatible to construct a 
 habitable world, and never provide for it its 
 appropriate inhabitants 1 The pre-established 
 harmony is essential to the plan. 
 
 The Planet, Satellite, Comet, and Meteor 
 are different forms of the congealed star. 
 
102 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 They are simultaneous in existence, and not 
 belonging to successive stages of the his- 
 tory. Starting from a common origin, they 
 have passed through a process of differentia- 
 tion, and are fitted for different functions. 
 They may all be regarded as bolides; and 
 they fill the celestial spaces with every con- 
 ceivable variety of magnitude, motion, and 
 physical aspect. 
 
 I shall begin with the Comet. From the 
 strangeness of its appearance in the inacces- 
 sible firmament, the comet has been the im- 
 memorial wonder and dread of mankind. It 
 has been the beard or tail of some invisible 
 monster. It has been the sword of some 
 angry god. It has been the pen of the furies, 
 writing in the book of fate the death of kings, 
 the fall of empires, the speedy coming of fam- 
 ines and pestilences and destructive wars. 
 It has been a light which has filled the souls 
 of philosophers with darkness. Even the 
 great Aristotle, with liis clear belief in Na- 
 ture and his contempt for superstition, could 
 propose no theory which was not a tissue 
 of gratuitous and inconsequent hypotheses. 
 He thought the comet, with its regular mo- 
 
PLANET, COMET, AND METEOR. 103 
 
 tions, to be a phenomenon like the flitting 
 and uncertain ignis fatuus, an exhalation 
 from the earth. But, before presuming to 
 reproach him, listen to what the generous 
 Pingr^ says in his learned cometography : 
 "Little minds may be elated when they can 
 cast some malicious sarcasm upon the most 
 solid reputations of all tirde. But they do 
 not perceive that their mean words defile 
 the mouth which utters them, more than they 
 tarnish the glory against which they are 
 breathed." Observe, also, the modesty with 
 which the Greek philosopher propounded his 
 cometic explanation : "If any man can 
 give one that is more satisfactory, and more 
 in accordance with natural principles, he will 
 establish a legitimate claim to our gratitude." 
 Nevertheless, even in cometology, where 
 modern progress has been so essentially 
 aided by the discovery of gravitation and the 
 invention of the telescope, the instinct of the 
 ancient thinkers achieved some memorable 
 results. Passing by the researches of the 
 Pythagoreans, we need only refer to the 
 writings of Seneca in the first century of 
 the Christian era. " I know," writes Seneca, 
 
104 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 " no nobler research, nor a more useful sci- 
 ence, than that which undertakes the study of 
 the stars ; but to perfect this science, is it not 
 expedient to examine whether the nature of 
 the comets differs from that of the other celes- 
 tial bodies ? If. we reflect on their motions, 
 on their vicissitudes of rising and setting, on 
 their light and brilliancy, we shall be struck 
 with the analogy which we perceive between 
 them and these other bodies. We need an 
 exact history of the comets which have 
 hitherto appeared ; for it is their rarity of ap- 
 pearance Avhich prevents our deciding upon 
 the regularity of their movement. We are 
 ignorant whether, describing fixed orbits, they 
 do not reappear at periodic and determinate 
 intervals of time." This was the prediction of 
 thoughtful genius. Modern astronomy, prof- 
 iting by the ancient suggestion, has demon- 
 strated this, like many other truths. The 
 dwarf of to-day who stands on the shoul- 
 ders of the giant of yesterday can see a 
 greater distance than the giant. Let him 
 copy the ancient modesty, and not plume 
 himself upon his height, as though it were 
 due to his taller stature. 
 
PLANET, COMET, AND METEOR. 105 
 
 The perfect comet combines nucleus and 
 train. The beauty belongs to the train, 
 which is unsubstantial and temporary ; while 
 the mass and density reside in the almost in- 
 visible but permanent nuclieus. The solid 
 nucleus moves about the sun in a nearly 
 parabolic orbit, obedient to the same law of 
 attraction which governs the motions of any 
 one of the planets ; whereas each particle of 
 the train moves in its own hyperbolic orbit, 
 in consequence of a repulsion from the sun, 
 often two or three times as great as the or- 
 dinary solar attraction, — or as Hooke, the 
 antagonist of Newton, might have claimed, of 
 a principle of levity, which he believed to be 
 as universal as gravity. 
 
 These particles of the train are electrified 
 bodies, and have the same electricity as that of 
 the sun ; the particles which are most highly 
 electrified advance to the front edge of the 
 tail, while those which are the least electrified 
 fall back to the rear. Each particle seems to 
 retain an undiminished electricity during the 
 whole period of visibility. Some of the par- 
 ticles are electrified just enough to balance 
 the solar gravitation ; so that, after separat- 
 
106 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 ing from the nucleus, they become neu- 
 tral to the sun's action and move uni- 
 formly in straight lines, but without ceasing 
 to be part of the tail. The particles which 
 are less highly electrified remain attracted 
 by the sun, but move in hyperbolic or- 
 bits, — in the opposite branch of the hyper- 
 bola, however, to that in which the repelled 
 particles move. These hyperbolic orbits are 
 as real a phenomenon, and subject to as cer- 
 tain, and definite a geometry, as the planetary 
 ellipses themselves. Their mathematical re- 
 lation to the parabolic orbit of the nucleus is 
 singularly simple to him who can read the 
 formulae of algebra. They conform to Kep- 
 ler's first two laws, and beautifully illustrate 
 the dynamic principle of the preservation of 
 areas. 
 
 This theory, in an imperfect state, was 
 rudely applied by Bessel to the tail of Hal- 
 ley's comet, in 1835. But the comet dis- 
 covered by Donati in 1858 offered as fine an 
 opportunity as can be desired for its full 
 verification. How grand was the beauty of 
 that comet ! All the world stopped in the 
 street, when it became visible after twilight, 
 
PLANET, COMET, AND METEOR. 107 
 
 and wondered at it with bated breath. A few 
 centuries ago it would have caused universal 
 dismay, and men would have paled at the 
 frightful portent. But the Christian of to-day- 
 beholds it as the loveliest messenger of divine 
 wisdom. A multitude of observations were 
 made upon the train as well as the head, in 
 all civilized countries, and the theory of the 
 train was sustained in every detail. The ele- 
 gance of the shape strictly conformed to the 
 ideal constructions of the geometer.'^ 
 
 But some, allied phenomena of a different 
 nature presented themselves. There was ex- 
 hibited another class of tail perfectly straight, 
 quite indistinct, and having a direction ex- 
 actly opposite to that of the sun from the 
 comet. It resembled the lines of hght and 
 shadow which we often see thrown upon the 
 terrestrial clouds, especially near sunrise or 
 sunset, and which are famiharly but ignor- 
 antly named "the sun drawing water." It 
 does not seem unreasonable to accept the 
 obvious suggestion, and to regard these false 
 tails as similar shadowy phenomena. 
 
 If the nucleus of a comet were taken 
 
 1 Gould's Asironomkdl Journal, v. 186 ; vi. 50. — Editor. 
 
108 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 away, the train would continue to move 
 oiF through space, undisturbed by the loss 
 of its head. Singular as this phenomenon 
 may seem, it has been actually observed. 
 At midday on the 28th of February, 1843, 
 groups of people in many of the towns of 
 New England, especially at Portland, col- 
 lected at the corners of the streets, gazing 
 up towards the sun. Protecting their eyes 
 in the shadows of the houses, they saw a 
 brilliant object a few degrees from the sun. 
 Such a marvellous spectacle had never before 
 been beheld. A thoughtful ship captain, Mr. 
 F. G. Clarke, brought out his sextant, and 
 carefully measured the distance of the strange 
 body from the sun's limb. These unique ob- 
 servations are on record; and, submitted to 
 rigid criticism, attest the accuracy of the 
 observer.'^ The same remarkable phenome- 
 non was seen on the same day, also, in 
 Mexico, in various cities of Italy, and at the 
 Cape of Good Hope. On the 27th it was 
 seen by Captain Ray at Conception in South 
 America ; and he then estimated — though 
 he did not measure — the distance of the 
 
 ' American Journal of Science, xliv. 412-417; xlv. 229, 
 230. — Editor. 
 
PLANET, COMET, AND METEOR. 109 
 
 strange body -from tlie sun at five minutes 
 of arc, or one sixth of the sun's apparent 
 diameter. 
 
 A few days later, a wonderfully brilliant 
 tail of a comet was seen skirting the horizon 
 soon after sunset, and reaching more than 
 one third of the way round the sky. What 
 we now saw was tail without head, as we 
 had before seen head almost destitute of tail. 
 But head and tail were members of the same 
 comet. 
 
 Many mathematicians in America and Eu- 
 rope busied themselves in determining the 
 path of this remarkable qomet. One of the 
 most noted orbits was that computed by 
 Sears C Walker, the brightest and most sug- 
 gestive of intellects, the gayest and warmest 
 of hearts, and the most ponderous and John- 
 sonian of bodies among American astrono- 
 mers, filled to the brim with wit, learning, 
 and profound science. At the comet's peri- 
 helion, it passed nearer to the sun than any 
 known comet, with the single exception of 
 that of 1680, computed by Sir Isaac Newton ; 
 in the discussion of which, in the Principia, he 
 broached the first approximation to the true 
 
110 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 theory of the cometary tail. These two com- 
 ets approached the sun so closely that it would 
 seem quite possible that they touched its sur- 
 face, or at least swept in within the corona. 
 
 It would not have been an absurd hypo- 
 thesis to suppose that these two comets were 
 ejected from the sun at the time of perihe- 
 lion, if it had not been for the fact that the 
 comet of 1680 was seen on its way down to 
 the sun, and for the remarkable phenomenon 
 which we are about to describe in the case of 
 the comet of 1843. It may be claimed as an 
 admissible supposition that each of them was, 
 at some former time, the product of a solar 
 eruption, according to Buffon's theory of the 
 origin of comets. This would require only a 
 force sufficient to double the greatest observed 
 velocity given to the solar jets of hydrogen ; 
 but a juster interpretation of the last-named 
 phenomenon than that which involves an 
 extravagant volcanic action, is that it is 
 simply the splash of the falling meteor. 
 
 In about two horn's, the comet of 1843, 
 like that of 1680, went round the sun, from 
 one side to the other. "What could have be- 
 come of the tail, which was reaching out 
 
PLANET, COMET, AND METEOR. Ill 
 
 about a hundred millions of miles from the 
 sun as far as to the earth's orbit ? There have 
 been those who have actually adopted the 
 incredible — I may say the impossible — 
 hypothesis that the tail rotated through this 
 immense circuit, developing a centrifugal 
 force which all the united powers of the 
 universe could not have sustained. But, no ! 
 The comet practically left its tail behind it, 
 and began to grow a new tail as it receded 
 from the sun. There were thus two tails, 
 nearly side by side, stretching from opposite 
 sides of the sun iti nearly the same direction. 
 The new tail began at the head of the comet ; 
 whereas the old deserted tail began without 
 any head at some distance from the nucleus, 
 and extended further from the sun than the 
 new tail. 
 
 That such a phenomenon should be pre- 
 sented by this comet was suggested by a 
 geometer, before he knew that it had been 
 actually seen ; and it was as veritable a pre- 
 diction as if it had been made before the 
 observation. On several nights at the begin- 
 ning of March, and before the comet had been 
 observed by European astronomers, a double 
 
112 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 tail was seen in Chili, by M. Charles Darlu, 
 and at Monte Video by Dr. Martin de Moussy. 
 M. Darlu describes the second tail as begin- 
 ning near a point about one third of the length 
 of the first from the nucleus, and extending 
 much further than the first. Dr. de Moussy 
 describes the second tail as by the side of the 
 principal tail, but of less dimensions, and not 
 attached to it at any point. A similar phe- 
 nomenon was seen, early in March, at various 
 other places at which the comet could then 
 be observed.^ But the visible separation of 
 the two tails lasted for only a few days, 
 because the earth passed, almost at once, 
 through the plane of the comet's orbit, so 
 that one tail eclipsed the other. 
 
 The nucleus of the comet is surrounded 
 by a mist, which is called the coma, or hair ; 
 the name comet signifying a hairy star. The 
 height of the coma above the nucleus de- 
 
 1 Comptes Bendvts, xvii. 362; xxi. 774. Royal Astro- 
 nomical Society Notices, v. 297, 303, 303 ; and Memoirs, xv. 
 231. Astronomische Nachrichten, xxi. 199. Herschel's Out- 
 lines (589). Tor further information concerning this comet, 
 see Royal Astronomical Society Notices, vols, v, vi ; Comptes 
 Rendus, vol. xvi ; Astronomische Nachrichten, vols, xx, xxi ; 
 G-ould's Astronomical Jowrnal, vols, i, ii; Cooper's Cometic 
 OrUts (Markree Catalogue), pp. 159-163. — Editor. 
 
PLANET, COMET, AND METEOR. 113 
 
 pends on the mass of the nucleus, and gives 
 the measure of its weight ; or, more exactly, 
 the least limit of weight which will suffice to 
 maintain such a height of atmosphere. 
 
 The nucleus is usually so closely sur- 
 rouftded by the dense mist that its diameter 
 cannot be measured; but at times the mist 
 rises, uncovers the nucleus, and leaves it with 
 a sharp stellar aspect. The least diameter 
 determined at such times may be larger than 
 the actual one, but cannot be smaller. From 
 the combination of mass and diameter, the 
 density of the nucleus can be computed. In 
 the case of Donati's comet, the diameter of the 
 nucleus was perhaps not more than a hundred 
 miles, while the height of the atmosphere ex- 
 tended to eighteen thousand miles. You may 
 be surprised to learn that the corresponding 
 density of the nucleus was at least equal to 
 that of iron. What an unexpected contrast 
 is here presented to the prevalent notions 
 concerning the sun and the comets ! The 
 solid sun is reduced by science to the state 
 of gas, while the substance of the ethereal 
 comet is a solid and heavy metal. 
 
 In its approach to the sun, the surface of 
 
114 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the nucleus is rapidly heated; it is melted 
 and vaporized and subjected to frequent 
 explosions ; the vapor rises in its atmosphere 
 with a well defined upper surface, which is 
 known to observers as an envelope. Various 
 envelopes, including each other, are often 
 observed. Mr. Bond, then director of the 
 Harvard College Observatory, measured the 
 envelopes for the Donati comet repeatedly and 
 carefully. The uniformity of the law of ascent 
 (about nine hundred miles a day) was re- 
 markable ; it is altogether inconsistent with 
 the acceleration or retardation of freely mov- 
 ing matter. But it is the characteristic mode 
 of ascent of a mist rising in an atmosphere. 
 The electrification of the cometary mist is 
 analogous to that of our own thunder-cloud. 
 Any portion of the coma which has received 
 the opposite kind of electricity to the sun and 
 to the repelled tail will be attracted. This 
 gives a simple explanation of the negative 
 tails which have been sometimes seen, di- 
 rected towards the sun. In cases of violent 
 explosion, the whole nucleus might be broken 
 to pieces, and the coma dashed around so as to 
 give varieties of tail, and even multiple tails. 
 
PLANET, COMET, AND METEOR. 115 
 
 There seems indeed to be no observed phe- 
 nomenon of the tail or the coma, which is 
 not consistent with a reasonable modification 
 of the theory which has been presented. 
 
 A vibration of the nucleus, corresponding 
 to a rotation upon the axis, combined per- 
 haps with the motion of a magnet attracted 
 by the sun, was observed by Bessel, in the 
 case of Halley's comet in 1835 ; and an anal- 
 ogous phenomenon was observed in the case 
 of Donati's comet. 
 
 The relations of the comets to the solar 
 system present an interesting and instructive 
 study. With very few exceptions, their visi- 
 ble paths are so nearly parabolic, and the po- 
 sitions of their nuclei and centres of gravity 
 so uncertain in the midst of their comae, that 
 it is quite out of the question to obtain nice 
 enough data to measure exactly the extent of 
 their orbits, and ascertain how great may be 
 their deviations from exact parabolas, and 
 whether the deviations are such as to make 
 them ellipses or hyperbolas. If an orbit is 
 actually parabolic or hyperbolic, and if there 
 is no decrease in the central attractive force 
 as the comet approaches the sun, it must have 
 
116 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 entered the solar system from outer space, 
 and cannot be one of our permanent partners. 
 It will leave the system again, and we may 
 never expect its return ; unless, indeed, having 
 passed through the circuit of other suns, after 
 myriads of years, it reappears in an orbit 
 entirely different from its former one, so as to 
 afford no evidence through which it may be 
 recognized. But if it moves in an ellipse, 
 and does not leave our system, it will return 
 in a sensibly unchanged orbit, through which 
 it may be detected. 
 
 The astronomer is often asked, upon the 
 announcement of a comet: "Is it a new 
 one 1 " and the tone of inquiry usually im- 
 plies a feeling of satisfaction in witnessing the 
 discovery of a new star. But it is just the 
 reverse with the astronomer himself. He ran- 
 sacks the records, hoping against hope that 
 he may enjoy the good fortune of ascertain- 
 ing that the new comet is an old one, — old, at 
 least, in the sense that it has been observed 
 once before, but not twice. On its first re- 
 appearance, a comet is certain to be loaded 
 with the name of the geometric discoverer of 
 its path. Its theory is computed ; its future 
 
PLANET, COMET, AND METEOR. 117 
 
 returns are rigidly predicted ; its social posi- 
 tion is definitely established, and it takes its 
 place among the registered members of our 
 constellation. But a comet may belong to 
 our system, and yet go so far from the sun 
 that the intervals between its periods of visi- 
 bility may be as long as three hundred* 
 thousand centuries. Of the three hundred 
 comets which appear in a century, we must 
 not, then, lose patience, if we do not recover 
 one into the catalogue of elliptic orbits. 
 
 There are a few comets of which the non- 
 parabolic character is evident at once. Their 
 orbits are decidedly elliptical ; their periods do 
 not exceed a baker's dozen of years ; and they 
 are intimately related to the planets in their 
 positions and directions of motion. Professor 
 Newton, of Yale College, has given a distinct 
 and satisfactory explanation of the mode in 
 which these comets were probably diverted 
 from their original parabolic paths by the 
 action of the planet Jupiter.^ It was a royal 
 sport, and the final character of the comet- 
 ary orbit was the natural termination of the 
 
 1 American Journal of Science [III.] xvi. 165; British 
 Association Beport for 1879, p. 272. — Editor. 
 
118 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 game. These comets must be excluded from 
 our general discussion. 
 
 Omitting them, we find nothing in the 
 position of the other orbits which indicates 
 relation to the solar axis of rotation or to the 
 planetary planes of revolution. They are as 
 'uniformly distributed as if they had entered 
 our system indijfferently from every direction, 
 and without reference to the prevailing mo- 
 tion of the planets or to their mutual organ- 
 ization. They are simply the largest of an 
 immense swarm of Meteors which are floating 
 all around us, — a swarm of which by far the 
 greater portion consists of bodies too small 
 to be seen by th^ light thrown upon them 
 from the sun ; and this invisible portion 
 greatly surpasses, in number and even in 
 combined mass, all the visible components of 
 our constellation. 
 
 The invisible meteors become visible when 
 they come into collision with the earth's at- 
 mosphere. They are known as Shooting Stars, 
 when seen flying through the sky ; while their 
 metallic remains, found upon the earth, and 
 having a peculiar iron constitution, are called 
 Meteorites. But there is sufficient reason for 
 
PLANET, COMET, AND METEOR. 119 
 
 regarding the chemical constitution of active 
 meteors as not limited to that which has been 
 found in the dead meteorites. There are 
 problems of ^geology which admit of their 
 most satisfactory solution by attributing to 
 the meteors varieties of constitution, and in- 
 deed any composition which has ever been 
 observed among inorganic substances. 
 
 The heat derived from the collision of me- 
 teors with the sun, earth, and planets is. of 
 fundamental importance in the cosmical dis- 
 cussions in which we are most directly in- 
 terested. The whole collection of meteors in 
 the vicinity of the sun may be called the 
 Solar Nebula; and the sun itself, with the at- 
 tendant planets, may be regarded as included 
 in this comprehensive term. It would be 
 vain to undertake the exact determination of 
 the distribution of material in our nebula. It 
 is almost certain, indeed, that it is an irregu- 
 lar collection ; but there are indications that 
 there is a sufficient approximation to a law of 
 distribution to justify the attempt at its dis- 
 covery. The nan-ow deviations from uni- 
 formity of the solar heat and of the terrestrial 
 seasons show that there can be no extravagant 
 
120 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 variation in the meteoric collisions. More- 
 over, the nearly parabolic paths of the comets 
 correspond to a constant law of velocity and 
 to a fall from a very great distance. 
 
 Imagine a paraboloid of revolution with the 
 sun in its focus; and imagine all the para- 
 bolic orbits of the comets to be turned into 
 such a position as to have all their axis coin- 
 cide in direction and position with the axes of 
 the supposed paraboloid. All orbits which 
 have a less perihelion distance than the para- 
 boloid will be included within it ; and their 
 number will, if they are evenly distributed 
 through space, be proportional to the area of 
 the section of the paraboloid, made by any 
 fixed plane perpendicular to its axis. The 
 area of this section will be itself proportional 
 to the perihelion distance of the paraboloid ; 
 whence it follows that the comets ought to be 
 uniformly distributed in reference to perihelion 
 distance. This simple law, applied to all the 
 observed comets, is verified with as great an 
 accuracy as ca^p. be demanded in such an in- 
 vestigation. It is reasonable to extend the 
 same law of distribution to all the smaller me- 
 teors which are not too remote from the sun. 
 
PLANET, COMET, AND METEOR. 121 
 
 If the comets are cosmical and enter the 
 solar system from outer space, they must 
 take about eight milHon years to come so 
 near the sun as to be visible from the earth. 
 Now there are rather more than three comets 
 of parabolic orbit seen each year; so that 
 there must be, on the hypothesis of their 
 cosmical origin, as many as fifty millions 
 of such comets at any one time, — say the 
 present moment, — contained within the so- 
 lar sphere. 
 
 The mass is, however, more important than 
 the number. We may assume each comet to 
 be as heavy as those which have been approxi- 
 mately weighed ; that is, to have a mass which 
 exceeds, on the average, a sphere of a hun- 
 dred miles in diameter, with a density equal 
 to that of the earth. Such a mass is about 
 one five-hundred-thousandth part of the 
 earth's mass. The aggregate mass of the 
 comets just enumerated may be estimated, 
 then, as one hundred times that of the earth. 
 
 If the perihelion distance is extended so 
 as to embrace the comets which approach 
 the sun as near as Neptune, the mass is in- 
 creased to three thousand times as great as 
 
122 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the earth ; and the perihelion distance may be 
 extended much further, and still remain well 
 within the sun's legitimate radius of control. 
 Without resorting to the meteors, which 
 might easily increase our estimate a million 
 fold, it is easy to see that the hypothesis of 
 the cosmical origin of the comets refutes it- 
 self. The velocity of a comet which ap- 
 proached the sun under so enormous an 
 increase of attraction as would arise from 
 this immense aggregation of meteors, could 
 not fail of manifestation, and would exceed 
 any that has been exhibited in the comet- 
 ary motions. 
 
 In the approach of the comets to the sun, 
 they have been seen to burst asunder, prob- 
 ably in consequence of the solar heat. If we 
 reflect upon the immense variations of heat 
 of the unprotected moon, we cannot be sur- 
 prised at this phenomenon. When we find 
 by computation that the heat to which the 
 Great Comet of 1843 was exposed was sixty 
 thousand times as great as that of the hot- 
 test equatorial noon-day sun upon our earth, 
 we may wonder that any portion of it re- 
 mained as nucleus. In some cases debris of 
 
PLANET, COMET, AND METEOR. 123 
 
 comets are distributed all along a cometary 
 path. These debris are meteorites, and when 
 they enter our atmosphere are visible as shoot- 
 ing' stars, diverging from some fixed point in 
 the heavens. They may, like other meteor- 
 ites, be deflected and pass out again into space ; 
 they may be burned up by the heat arising 
 from their concussion and rapid motion, and 
 portions of them may fall upon the earth as 
 meteoric stones. Pursuing their paths in 
 groups, they give us the celebrated meteoric 
 showers of August and November. Their 
 theory has been luminously discussed by 
 Professor Newton.^ ■ 
 
 The sun's corona, which is evidently sep- 
 arated from its body by a vacant space, in 
 which the gaseous jets are free to move above 
 the solar atmosphere, seems to be composed 
 of meteorites. They probably have an inde- 
 pendent history, and may consist of a com- 
 bination of rings, corresponding to that of 
 Saturn. The heat to which they are sub- 
 jected must fill their spaces with gas; and 
 thus may be explained the spectroscopic phe- 
 nomena of the corona. 
 
 1 Am. Jour. Sci. [II.] xxxvi. 300 ; xxxvii. 377 ; xxxviii. 
 53; XXX jx. 193; xliii. 285. Nature, xix. 315. — Editor. 
 
124 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 The principal body of the meteors seem to 
 discharge an important function in the solar 
 economy. The sun's light and heat may 
 have been derived, in the outset, from gas- 
 eous compression ; and some astronomers are 
 still disposed to regard this as their source. 
 Combustion, or any form of chemical action, 
 has been abandoned by physicists. The rival 
 theory to the theory of gaseous compression 
 is that of the derivation of heat from the 
 concussion of meteors which are constantly 
 falling into the sun. It is not as fuel that 
 they are supposed to act, supplying heat by 
 combustion ; but they are congealed masses, 
 which have an energy exhibited under the 
 form of rapid motion. When they are stopped 
 by striking the sun, the energy is taken out 
 of them, and passes from them into the sun, 
 where it is exhibited as heat, and radiated in- 
 to space to warm our earth and the other plan- 
 ets. This theory was proposed by Mayer,^ 
 and has been ably developed by that ad- 
 mirable physical philosopher. Sir William 
 
 1 Beitrage zur Dynamik des Eimmels, Seilbronn, 1848. 
 American Journal of Science, xxxvi, 261; xxxvii, 187; 
 xxxviii, 239, 397. Youman's Correlation and Conservation 
 of Forces, p. 259. — Editor. 
 
PLANET, COMET, AND METEOR. 125 
 
 Thomson,^ to whose scientific investigations 
 the nations are largely indebted for their 
 modes of telegraphic communication. But 
 there are some important additions to Thom- 
 son's theory, which it is my purpose to sub- 
 mit to you. 
 
 Our own sun may be assumed to have been, 
 in the outset of its present history, a round 
 nebula, and then a nebulous star. In an 
 early stage, it was condensed into meteors, 
 intermingled with gas ; and it is not unlikely 
 that the corona was formed at that period, 
 which was as early as the development of the 
 planets and of the solar system from the cen- 
 tral denser portion of the nebula. 
 
 The meteors, or bolides, may be assumed 
 to move, like the larger comets, in parabolic 
 orbits, and to partake of the cometary law of 
 distribution. They must strike the sun in 
 sufficient quantity to replace the heat con- 
 stantly given off by radiation. The amount 
 of that heat, although it has no especial 
 bearing upon our present argument, has been 
 measured and may be stated. It is of such a 
 
 ^ Comptes Bendus, xxxix. 682. Edinburgh Transactions, 
 xxi.63. Phihsophicdl Magazine, [IV. '\-<n.\\.^(^-,\x.QQ. Brit- 
 ish Association Report for 1861, sections, p. 27. — Editor. 
 
126 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 measure that it requires a mass of our bolides 
 equal to about one one-hundred-and-fiftieth 
 part of the earth's mass to fall annually into 
 the sun. The corresponding mass of bolides 
 which annually enter the sphere of which the 
 earth's orbit is a circumference must, in ac- 
 cordance with the law of distribution which 
 has already been brought to view, exceed this 
 amount in the ratio of the earth's distance 
 from the sun to the sun's semi-diameter ; that 
 is, it must be more than two hundred times 
 as great, or nearly three halves of the weight 
 of the earth. Each meteor, however, when 
 it strikes the sun, will Iiave an energy much 
 greater than that which it had when it was at 
 the earth's distance from the sun, — greater 
 in the inverse ratio of the distance from 
 the sun, and therefore greater in exactly the 
 same ratio as that in which the whole mass 
 of meteors is diminished. The aggregate 
 meteoric energy, therefore, which passes in 
 through the spherical surface of which the 
 radius is the earth's distance and the centre 
 the sun's centre, is precisely the same with 
 that which is thrown into the sun. But each 
 meteor which does not strike the sun will 
 
PLANET, COMET, AND METEOR. 127 
 
 again pass off ; so that there will be nearly 
 the same amount of meteoric energy passing 
 out through our spherical surface. Thus 
 the whole amount of meteoric energy which 
 passes through this supposed spherical sur- 
 face, in both directions, will be nearly twice 
 that which is communicated to the sun. 
 
 Some of these meteors will strike the earth ; 
 and we will strive to ascertain the relative 
 amount of the heat thus communicated to the 
 earth directly by the collision of the bolides, 
 and that which it receives from the sun by 
 radiation. The radiant heat of the sun, being 
 supposed to be diffused uniformly, will com- 
 municate to the earth that minute portion 
 which the earth will intercept. The measure 
 of this is not necessary for our argument ; but 
 we may state that it is rather less than one 
 half of one thousandth of one millionth of 
 the heat emitted by the sun. Now, of all 
 the energy communicated to the earth by the 
 collision of meteors, one half is restored to 
 the striking body in the form of planetary 
 velocity; for the meteor passes, in conse- 
 quence of the collision, from the velocity 
 of a body moving in a parabolic orbit to 
 
128 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 that of the earth into which it is absorbed ; 
 and the energy which belongs to the lat- 
 ter velocity is one half of that which be- 
 longs to the former. The remaining half 
 of the energy of the meteor is destroyed in 
 the form of visible motion, and converted into 
 heat. But the mass of bolides intercepted by 
 the earth must bear to the whole mass which 
 passes through the spherical surface of which 
 the earth's orbit is a great circle the same 
 minute ratio which the solar heat, intercepted 
 by the earth, bears to the heat emitted from 
 the sun. Thus we are brought to the start- 
 ling conclusion, that the heat which the 
 earth receives directly from the collision of 
 meteors is the same in amount as that which 
 it derives from the sun by radiation. It is 
 remarkable that this strange result is sup- 
 ported by accurate observations, made long 
 ago by a most eminent and trustworthy 
 authority, but which have never been dis- 
 cussed in relation to their significance, though 
 they have never been invalidated. 
 
 Every one knows that at sunset there is a 
 rapid fall of the thermometer, which of course 
 proceeds from the sudden cutting off of the 
 
PLANET, COMET, AND METEOR. 129 
 
 direct rays of the sun. The thermometer 
 continues to sink during- the night, at a 
 rate which was submitted to careful anal- 
 ysis by Pouillet. From this analysis, ac- 
 companied by ingenious observations, he 
 discovered that heat must come to the earth 
 from some other source than the sun. Pouil- 
 let called this heat the heat of space. He 
 carefully measured it, and found it to be only 
 a little less than that derived from the sun.^ 
 Whence can it come! Not from the earth 
 itself, for the earth would not give out a 
 thousandth part of this amount. Not from 
 vacant space : no physicist would hold so 
 untenable a doctrine. It is unreasonable to 
 assign it to the stars, as Pouillet appears to 
 have done ; such an hj^pothesis involves too 
 vast a diflference between the ratio of stellar 
 to solar light, and the ratio of stellar to solar 
 heat. Those of you who have witnessed a 
 total eclipse of the sun know how the small- 
 est portion of the sun puts out the light of 
 all the stars; how unreasonable is it, then, 
 to suppose that the combined heat of the stars 
 
 1 Comptes Bendus, vii. 24-65. Poggendorff, Annalen, xlv. 
 25-56, 481-500. Taylor's Scientific Memoirs, iv. 44-90. — Ed. 
 
130 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 is as great as the heat of the sun ! But the 
 meteoric theory fully explains the phenom- 
 enon. The doubt, indeed, is reversed, and 
 the question arises, why did Pouillet's ob- 
 servation make the meteoric heat less than 
 the solar? The difference would seem to 
 be partly due to the penetrability of the 
 earth's atmosphere to the solar rays, where- 
 as a large portion of the meteoric heat must 
 be absorbed into the upper atmosphere and 
 radiated into space, before it can reach the 
 surface of the earth. Again, it is possible 
 that five sixths of the sun's heat is derived 
 from the meteors, and the remainder from 
 the sun's continued compression. Pouillet's 
 observations may be claimed as strongly 
 supporting the meteoric theory of the solar 
 heat. 
 
 The constant dashing in of cold bolides 
 upon the sun would occasion the mighty dis- 
 turbance of its surface and the vast gaseous 
 jets of which we have spoken. The mass of 
 the sun would be increased, but at so slow a 
 rate that many decades of centuries of nice 
 observation will be required to perceive the 
 effect. But there are modes in which it is 
 
PLANET, COMET, AND METEOR. 131 
 
 not impossible that the increase of mass may- 
 be detected, through the revelations of geom- 
 etry. The constant increase of the solar mass 
 would have an influence on the planetary- 
 orbits. It -vrould diminish their eccentrici- 
 ties, according to a law of easy computation. 
 Hence it is possible that the orbits of the 
 planets may have been originally very eccen- 
 tric, almost like those of comets; and their 
 present freedom from eccentricity may have 
 resulted from the growing mass of the sun. 
 What modification of the nebular theory 
 may be involved in this supposition cannot 
 easily be imagined, without the guidance of 
 some indication from Nature. 
 
 Returning to the original round nebula, 
 from which the solar system was formed, we 
 must suppose that it has gone through 
 changes which are represented in many of 
 the nebulae. A central spherical portion 
 seems to have concentrated into the sun and 
 planets, leaving an outer spherical envelope, 
 which was much slower in the process of 
 condensation, and finally became an envelope 
 of bolides. The natural orbits of the bolides 
 were nearly circular paths, of which the sun 
 
132 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 was at the centre. The variety of directions 
 of the planes of the orbits was so great that 
 they constituted a nearly uniform system, 
 constantly approaching each other, and by 
 their mutual heat producing explosions. 
 They were thus broken up into an increased 
 number of smaller irregular masses, such as 
 we are familiar with in the meteoric stones. 
 Thus we find all the varieties that exist among 
 the bodies of the solar system harmoniously 
 explained. Would it not be stranger than 
 any fiction, — would it not violate all physi- 
 cal analogies, — if this ideal hypothesis of the 
 meteoric structure of our system, sustained 
 by such a variety of observation, were not a 
 close representation of its actual history I 
 
COOLING OF THE EARTH AND SUN. 133 
 
 V. 
 
 THE COOLING OF THE EAETH AND THE 
 
 SUN. 
 
 The geological and paleontological records 
 of tlie earth's history demand a long con- 
 tinued supply of heat from the sun, and an 
 equally enduring solidity at the earth's sur- 
 face. Is the nebular theory competent to 
 meet this demand; or does it require serious 
 modification ? Whatever may be the answer 
 to these questions, we may rest assured that 
 Nature is harmonious with herself, and that 
 the inconsistencies by which science may be 
 embarrassed are temporary clouds in the in- 
 tellectual atmosphere. They will be swept 
 away by the besom of the true wizard. 
 
 In attempting to penetrate the past obscur- 
 ity, we may fail to arrive at satisfactory 
 results ; but our investigation will not be a 
 barren one. The expected treasure may not 
 
134 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 be unearthed; but there will be a harvest 
 of knowledge commensurate with the labor 
 of the tilling, and an inheritance of truth 
 which will manifest the wisdom and divinity 
 of the testament whence we have derived 
 such stimulus to inquiry. 
 
 We shall find the conservative opinion con- 
 firmed, that all the phenomena on scientific 
 record are within the legitimate powers of 
 the agents now in operation, and require the 
 introduction of no extravagant and unknown 
 force. The various stages of the investigation 
 will carry us over a wide range of real and 
 positive science, but nowhere shall we escape 
 the dominion of ideality. 
 
 The attempt has been made by Darwin 
 and other naturalists, and by various geol- 
 ogists, to estimate the length of time neces- 
 sary for the evolution of the different forms 
 of life and for the accomplishment of the 
 geological transmutations. The rate at which 
 erosion proceeds and the whole thickness 
 of the eroded surface of the earth have 
 been subjected to careful examination. A 
 vast series of organisms has been traced 
 back to an apparent commencement, which 
 
COOLING OF THE EARTH AND SUN. 135 
 
 occurred with the Cambrian rocks. There 
 was a previous independent history, more 
 indistinct in its evidence, possibly as long as 
 all that follows. But, from the Cambrian 
 period on, there has been an unbroken se- 
 ries of development, down to the present day. 
 Even those very great naturalists who have 
 been averse to the doctrine of evolution have 
 been profound behevers in the laws of the 
 succession of species. Lamarck and Dar- 
 win have not been abler expositors and 
 discoverers of these laws than Cuvier and 
 Agassiz.. The difference of doctrine is one 
 of form rather than of substance It is not 
 unlike that between Newton, who carefully 
 declared gravitation to be simply the ex- 
 pression of the laT^ by which the planets 
 tended towards the sun, and the Newtonians, 
 whp speak of the sun's attraction for the 
 planets, as if it were the product of some 
 power of volition. 
 
 Disciples are ever dangerous to the doc- 
 trine of the masters. Pythagoras was not a 
 Pythagorean, nor Plato a Platonist, nor Aris- 
 totle an Aristotelian, nor is Darwin a Darwin- 
 ite. The scholar most honors his master 
 
136 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 when, instead of accepting his doctrine on his 
 authority, he imitates him in going directly 
 to the source of truth, and submitting the 
 master's teachings to severe criticism, adopt- 
 ing . what he finds to be true, amending the 
 defective, and rejecting the erroneous. May 
 this ever be the quality of American disciple- 
 ship ! and then our science will remain worthy 
 of the atmosphere of freedom. 
 
 The succession of organisms has been natu- 
 rally exhibited in geologic periods, which are 
 of uncertain length. The order of succession 
 has been accurately defined by the relative 
 position of fossil remains in different localities. 
 The more thorough the researches of geologists 
 have been, the greater has been the harmony 
 of their conclusions concerning this order. 
 The subsequent attempt to present the esti- 
 mate of the duration of successive periods in 
 numbers of years has introduced a vague 
 element, which is foreign to the science. It 
 is obvious that each geological period is 
 long ; but how long, is a matter of uncertain 
 definition. 
 
 We shall find that the estimates in years of 
 the duration of the con-esponding changes 
 
COOLING OF THE EARTH AND SUN. 137 
 
 which, have taken place in the physical con- 
 dition of the earth are hardly more distinct 
 and accurate, notwithstanding the aid fur- 
 nished by the mathematician. No power of 
 computation can give precision to that which 
 is inherently inexact. Nevertheless, no other 
 medium than that of years has been hitherto 
 proposed for the comparison of the estimates 
 made by the different sciences. It performs 
 the ofl&ce of money in the exchange of values 
 in the market. It is not impossible that a 
 way may be found by which the amount of 
 energy absorbed in the various processes of 
 change may take the place of time, in form- 
 ing the estimates. Thus, if at some period 
 less heat is required and slower evolution 
 manifested, there may during that same pe- 
 riod occur a diminished production of heat ; 
 so that the work may correspond to the power 
 available for its production. 
 
 The amount of time needed for the geolog- 
 ical history has been rated by geologists and 
 zoologists as high as three hundred millions 
 of years. In later estimates the demand has 
 been greatly reduced, so that a period of fifty 
 millions of years may not now appear to be 
 
138 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 too great a restriction. How does this estimate 
 compare with the limitations of time from the 
 physical point of view ! Sir William Thom- 
 son has profoundly discussed them ; and no 
 philosopher is more competent than he to 
 avail himself of all the resources of physics 
 and geometry. He has been aided by Pro- 
 fessor Tait, the eminent mathematician and 
 skilful expounder of Quaternions. 
 
 "We may first question the earth, and con- 
 sider its testimony. Where and how does it 
 hold its power of bringing forth grass and 
 the herb yielding seed ? The power does 
 not extend over those portions of the surface 
 which are covered with ice and snow ; and it 
 is equally deficient in large extents of parched 
 deserts. It requires certain intermediate con- 
 ditions of superficial temperature. Heat is 
 essential to growth, whatever else maybe need- 
 ed ; but excess of heat is destructive to life. 
 
 How do we know that the required heat does 
 not come up from the earth's interior, whence 
 the hot geysers and the molten lava arise ? 
 There is heat enough within. The tempera- 
 ture increases, the further we penetrate into 
 the earth. The rate of increase near the sur- 
 
COOLING OF THE EARTH AND SUN. 139 
 
 face may be roughly stated to be, on the 
 average, about one degree of Fahrenheit for 
 every fifty-five feet of descent. Consider 
 how few feet of earth are a complete pro- 
 tection from the coldest frosts of winter, and 
 you will require no weight of authority to 
 demonstrate to you that the daily ascent of 
 heat through these fifty-five feet of earth is 
 quite imperceptible. Were it wholly taken 
 away you would never miss it. 
 
 None the less, the decrease of heat in 
 ascending from the interior is a vital fact in 
 the history of our planet. Its story cannot 
 be impeached. At the depth of about two 
 miles the heat equals that of boiling water, 
 which involves the death of all living things. 
 With your permission, I will pass for an in- 
 stant from the consideration of these grand 
 phenomena of Nature to a trivial and homely, 
 but instructive example. Two days in each 
 week I am wont to find upon my breakfast- 
 table a loaf of Boston brown bread. I have 
 observed a systematic difference between 
 these loaves. That of the first day is hotter in 
 the interior than at the surface ; while the re- 
 verse is the case with the second day's loaf. 
 
140 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 My cook, though no physical philosopher, can 
 explain to you the simple cause of this differ- 
 ence. The loaf of the first day is fresh from 
 the baker's oven, and is undergoing the pro- 
 cess of cooling ; while that of the second day, 
 having been put back into the oven after it 
 was cooled; and being placed on the table be- 
 fore it was equally heated throughout, hon- 
 estly reveals its history. In the same man- 
 ner the earth tells us that, like the loaf of 
 the first day, it is in the process of cooling ; 
 and that, at some past time, its surface must 
 have had about as great a temperature as it 
 now has in its hottest interior. 
 
 In the liquid state of the earth, its temper- 
 ature would be subject to the law of convec- 
 tive equilibrium. The convective equilibrium 
 of a gas or liquid is that condition of pressure, 
 density, and temperature by which any por- 
 tion of the mass, when conveyed from one 
 position to another within the mass, imme- 
 diately assumes the density and temperature 
 of its new locality, in consequence of the 
 change of the pressure. In a gas, the 
 changes of density and temperature are 
 great; while they are small in the case of 
 
COOLING OF THE EARTH AND SUN. 141 
 
 the almost incompressible liquid. The law 
 of temperature in the solid and intermediate 
 states depends on the order of solidification. 
 There is a deficiency of observation concern- 
 ing the solidifying process. Hence there is 
 room for variety of opinion and of hypoth- 
 esis, for legitimate suggestion regarding the 
 direction of future inquiry, and for faith in 
 the power of scientific investigation to de- 
 velop the truth. 
 
 You aU know how and why water solidi- 
 fies first at its surface, — that it expands near 
 the point of crystallization, and that this 
 causes it to become lighter and therefore to 
 rise, and appear as ice at the surface. But 
 this is regarded by physicists as an ex- 
 ceptional phenomenon. Most metals are 
 thought to have the opposite property, and 
 to become heavier as they solidify, so as 
 naturally to sink to the bottom, throughout 
 the process of cooling into solidity. Hence 
 it is plausibly maintained that the solidifi- 
 cation of the earth began at the centre, and 
 extended upward to the surface; so that 
 when the surface became solid, the globe 
 was solid throughout. 
 
142 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 This doctrine is not only adopted on phy- 
 sical grounds by Sir William Thomson, but 
 he has undertaken to demonstrate that the 
 supposed fluidity of the earth's interior is 
 inconsistent with astronomical phenomena. 
 His argument deserves careful analysis, as 
 a profound scientific discussion of undeni- 
 able facts. 
 
 Thomson first considers the tides, the exact 
 knowledge of which is so essential to naviga- 
 tion. They depend upon the attractions of 
 the sun and the moon on the different por- 
 tions of the terrestrial ocean, causing it to 
 rise in one place and fall in another; while 
 the land remains stationary, and is the basis 
 from which the height of the water is meas- 
 ured. Were the body of the earth quite 
 destitute of rigidity, the land would rise 
 and fall with the sea, and there would be 
 no tidal variation of depth. Even in the 
 Grulf of Maine, where we have now a change 
 of depth of sixty feet in six hours, from high 
 to low tide, there would be neither tide nor 
 tidal current nor inward rush of ocean over 
 the bottom of the sea, which would rise just 
 as fast as the upper surface. With an 
 
COOLING OF THE EARTH AND SUN. 143 
 
 exceedingly small rigidity, such as there 
 would be if the earth's surface were a thin 
 crust, the tides would be proportionally 
 small. 
 
 Theory is incompetent to ascertain what 
 would be the precise magnitudes of the tides 
 on a perfectly rigid earth. The dynamical 
 conditions of the problem present almost in- 
 superable difficulties. Were it a question of 
 pure equilibrium, or of so slight a motion as 
 to render inertia an unimportant element, the 
 solution would not be difficult. But the in- 
 ertia involves the consideration of conserva- 
 tion of force, of meeting currents, of the ve- 
 locity of the tide-wave, of depths of the sea 
 varying in time and space, of vibrating sur- 
 faces and nodal lines, and of special laws 
 peculiar to each of the three great classes of 
 tides, — the diurnal, the semi-diurnal, and the 
 fortnightly. There is too great complication 
 for the clearest and strongest mind to un- 
 ravel, without the aid of fuller observation. 
 Until, then, we have obtained better means 
 for the comparison of theoretical with ob- 
 served tides, we must submit to be governed 
 by the opinion of the wisest, with such ap- 
 
144 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 proximation to theory as can be derived from 
 legitimate argument. 
 
 Sir "William Thomson's exact computations 
 have undoubtedly shown that " if the rigidity 
 [of the earth, on the whole,] were as great as 
 that of steel, the relative rise and fall of the 
 water would be reduced by elastic yielding to 
 two thirds, or if the rigidity were only that 
 of glass, the relative rise and fall would be ac- 
 tually reduced to two fifths, of what it would 
 be were the rigidity perfect." I suppose, 
 therefore, that we may safely, for the present 
 time, adopt the opinion of this philosopher 
 that "the tidal effective rigidity of the 
 earth must be greater than that of glass ;" 
 and that, instead of living "on a mere thin 
 shell of solid substance, inclosing a fluid mass 
 of melted rocks or metals," the tidal phe- 
 nomena indicate "that the earth as a whole 
 is much more rigid than any of the rocks that 
 constitute its upper crust." * But as there is 
 no historical record to tell us of the tides of 
 past geological ages, we cannot carry back 
 this argument to any distant past. 
 
 Thomson has sought to corroborate the 
 
 1 Thomson and Tait's Natural Philosophy, i. 55 832-846. 
 
COOLING OF THE EARTH AND SUN. 145 
 
 evidence of the tides by that which is 
 fm-nished by a far more accurately deter- 
 mined phenomenon, the precession of the equi- 
 noxes. His discussion of this subject is 
 too profound, original, and suggestive not 
 to be presented here. But I must begin by 
 recalling to your memory the phenomenon 
 to which the discussion relates.-^ 
 
 The earth's equator and axis of revolution, 
 though fixed in the earth, are constantly 
 moving in space ; and their changes of posi- 
 tion are recognized by astronomers in the 
 daily reduction of their observations. The 
 equinoxes are the directions in which the 
 plane of the earth's orbit, called the ecliptic, 
 cuts the plane of the equator. When, in its 
 seeming annual path, the sun arrives at either 
 of these directions from the earth, the days 
 and nights are equal throughout our globe ; 
 and it is from this circumstance that the name 
 of the equinoxes is derived. The plane of 
 the ecliptic is nearly stationary, but the equi- 
 noxes retrograde ; that is, they move in a 
 
 ^ Sir W. Thomson has withdrawn, or seriously modified, 
 the part of his argument here criticised, in view of the 
 " quaai-rigidity induced in a liquid by vortex motion." Brit. 
 Assoc. Bep. for 1876, sections, p. 5. — Editor. 
 
 10 
 
146 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 direction opposite to that of the suns 
 apparent yearly motion among- the stars. 
 This motion, called the precession of the 
 equinoxes, has been known for two thousand 
 years, or since the time of Hipparchus, the 
 father of mathematical astronomy. Its an- 
 nual amount is about fifty seconds of arc ; so 
 that either equinox will pass through the 
 whole circuit of the ecliptic, and return to its 
 present position in the firmament, in a little 
 less than twenty-six thousand years. There 
 is a corresponding motion of the earth's axis 
 among the stars; the pole of the equator 
 describing a circle about the nearly station- 
 ary pole of the ecliptic. 
 
 An essentially similar phenomenon to pre- 
 cession is to be found, where you would per- 
 haps little expect it, in the spinning of a boy's 
 top ; so that the geometer recognizes the same 
 idea in the plaything of the child and in the 
 vast object of astronomic study. Before the top 
 has reached what the lad significantly styles 
 its state of sleep, you must have observed how 
 the axis rotates swiftly around a vertical line. 
 This motion tj^pifies the precession of the 
 equinoxes. But in a fraction of a second it 
 
COOLING OF TEE EARTH AND SUN. 147 
 
 completes a circuit for which the observer 
 of the terrestrial axis must wait twenty-six 
 thousand years. There is the same ideal 
 connection with another plaything known 
 as the " devil-on-two-sticks," and also with 
 the scientific toy called the " gyroscope." 
 There has been no mystery in these mo- 
 tions for the past seventy years, notwith- 
 standing that astonishing discoveries of eluci- 
 dation are still occasionally heralded to the 
 world in the public journals. 
 
 Not only is there a resemblance in certain 
 phenomena of the axial motions of the top and 
 the earth ; there is also a similarity of causa- 
 tion. But it is too involved a problem of 
 analytic mechanics for present discussion. I 
 may, however, venture to call your attention 
 to a few leading facts. The direct tendency of 
 the earth's attraction upon the top is to make 
 it fall; and it would fall if it were not for its 
 rotation upon its axis. In the same way the 
 boy's hoop, when rolling forward with speed, 
 cannot be forced to fall, imtil it is nearly 
 stopped, and its velocity of rotation greatly 
 reduced ; and so also the rapid rotation of the 
 wheel of the bicycle tends to keep it erect, 
 
148 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 and also to preserve its onward direction of 
 motion. Geometrical analysis develops the 
 fact that this is merely a manifestation of the 
 simplest law of motion, by which each par- 
 ticle of matter, in consequence of its inertia, 
 tends to preserve its rectihnear and uniform 
 velocity. On the same principle, the sun and 
 the moon always conspire to bring the equa- 
 tor into coincidence with the ecliptic ; and the 
 earth would yield to their attractions if it 
 were not for its rapid rotation upon its axis. 
 But the force, applied in the one case to the 
 top, and in the other to the earth, cannot be 
 nullified by inertia. Neither mass has any 
 power of volition, by which the offered force 
 can be rejected ; it must be accepted in strict 
 obedience to the laws of mechanics, and 
 logically combined with the force that has 
 been previously imparted. 
 
 For reasons which are plain enough to 
 him who will go through with the studies 
 necessary to apprehend them, the motion of 
 rotation imparted to the axis in either case is 
 perpendicular to that which would be im- 
 parted if the body were at rest. Take a 
 common globe, mounted on a stand ; rotate 
 
COOLING OF THE EARTH AND SUN. 149 
 
 it swiftly upon its axis, and then try to turn 
 the axis in any direction : you will instantly 
 perceive a strong tendency to turn in a per- 
 pendicular direction ; that is, you will wit- 
 ness a phenomenon similar to precession. 
 The greater the applied force, or the less 
 the mass of the moving body, the greater 
 must be the precession. 
 
 Now, with the earth, the protuberance at its 
 equator constitutes, as it were, a handle, by 
 which the sun and the moon strive to turn 
 it; and the consequence of their action is 
 that the earth's axis is made to rotate about 
 a line perpendicular to the plane of the eclip- 
 tic. This constitutes the precession of the 
 equinoxes. 
 
 The magnitude of the earth's protuber- 
 ance has been measured in various ways, — 
 by the length of the degree in different lat- 
 itudes ; by the swinging of the pendulum in 
 many places ; and by a peculiar phenomenon 
 of the lunar theory. Supposing the earth to 
 be solid throughout and perfectly rigid, the 
 corresponding precession has been computed, 
 and it agrees with observation. Were the 
 earth deficient in rigidity, its form would 
 
150 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 partially- yield to the solar and lunar attrac- 
 tions, and a portion of the force would be 
 consumed in distorting the earth's figure ; so 
 that the remaining force, effective for the 
 production of precession, would be dimin- 
 ished, and give a result less than the actual 
 observation. On the other hand, if the 
 earth's interior were fluid, the solid mass to 
 be rotated would be diminished, so that the 
 actual precession would be too small. 
 
 Here are two nearly allied phenomena 
 which may exist simultaneously and pro- 
 duce opposite effects. It is not impossible 
 that they may exactly balance each other, 
 by reason of numerical relations between 
 the imperfect rigidity of the earth and its 
 partial solidity. We should then still have 
 the same precession as that due to perfect 
 rigidity and complete solidity. Thomson 
 regards such an accidental agreement as 
 quite improbable, especially with the thin 
 shell which would be required for the as- 
 sumed geological phenomena and the great 
 accompanying deformation of the earth. 
 Such improbable accidents are nevertheless 
 constantly occurring. 
 
COOLING OF THE EARTH AND SUN. 151 
 
 There is, however, a feature of the case 
 which Sir Wilham Thomson seems origi- 
 nally to have overlooked. If the enclosed 
 fluid did not partake of the change of axis 
 of the external solid, it would continue to 
 rotate on its original axis, while the axis of 
 rotation of the external shell was turning 
 into a different position. Th'ese axes would 
 thus be ever separating, and a resisting 
 friction would be developed, which would 
 tend to diminish the excessive precession. 
 Thus, if they came to be separated as far 
 as twenty degrees, for instance, and if the 
 shell were quite thin, the difference between 
 the velocities of the contiguous points of the 
 outer surface of the interior fluid, and of 
 the inner surface of the solid shell, would ex- 
 ceed three hundred miles an hour through- 
 out great regions of the two surfaces. The 
 friction thus developed would act as a resist- 
 ance to the separation of the axes. If, at 
 any instant, the influences on which pre- 
 cession depends were to be removed,' the 
 friction would soon restore the axes to co- 
 incidence. It must, in the course of time, 
 become sufficient to prevent any further sep- 
 
152 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 aration ; and when this stage is reached, the 
 axial motion pervades the whole globe, and 
 is the same in amount as if the solidity were 
 complete. The effect of want of rigidity will 
 remain, but be diminished in amount; and 
 this appears to be accordant with actual 
 observation. 
 
 There remains for our consideration the 
 argument for the solidity of the earth which 
 Thomson has derived from the increasing den- 
 sity of the cooling metals, in regard to which 
 another class of objections will soon be pre- 
 sented for your criticism. But these you will 
 more readily appreciate, after you have lis- 
 tened to the exposition of Thomson's profound 
 researches on the cooling of a solid earth. 
 
 His determination of the corresponding 
 time which must be assigned, from the ac- 
 complishment of the earth's solidification to 
 its present condition of temperature near the 
 surface, is undeniably correct in principle, 
 and his allowance for the numerical uncer- 
 tainty of the data is more than ample. The 
 principal elements of the investigation are : 
 
 (1) The initial temperature of the earth; 
 
 (2) The average conductivity of the earth's 
 
COOLING OF THE EARTH AND SUN. 153 
 
 crust; and (3) The law by whicli the tem- 
 perature of cooling solids increases with the 
 depth below the surface. 
 
 The initial temperature is that at which 
 the rocks would melt, and which is assumed 
 by Thomson, from the best physical experi- 
 ments, as seven thousand degrees of Fahren- 
 heit. The conductivity of the earth's crust, 
 derived from various extensive investigations, 
 is considered by him to be, on the average, 
 at the rate of four hundred degrees of Fah- 
 renheit a year, through a stratum in which 
 the temperature increases by one degree for 
 each foot of thickness. This datum is the 
 least certain, and demands renewed exami- 
 nation. Finally, the mathematical theory of 
 the cooling is adopted from the admirable 
 treatise upon Heat by the great French ge- 
 ometer, Fourier. It is simple, and presents 
 the law of temperature in a form which is 
 readily adapted to the proposed problem. 
 An exceedingly short time, probably not 
 more than a single year, will be required to 
 reduce the superficial temperature from seven 
 thousand degrees to a temperature which 
 may be assumed to be sensibly that of the 
 
154 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 present day. Hence, there would be no 
 physical obstacle to the immediate intro- 
 duction of simple organic forms upon the 
 earth's surface. Then Thomson finds that 
 the rate at which the temperature of the 
 earth would increase for every foot of de- 
 scent below its surface would become 
 
 in 10,000 years 2° 
 
 40,000 " 1° 
 
 160,000 " 1° 
 
 " 4,000,000 " ^° 
 
 " 100,000,000 " ^° 
 
 The present rate of increase of temperature 
 corresponds, then, to an interval of a hun- 
 dred millions of years from the possible 
 commencement of organic life. 
 
 Do these great numbers embarrass you, 
 and interfere with your reception of the 
 truth which lies buried beneath them f We 
 can lessen the numbers by changing our 
 unit of time. To the inhabitant of the 
 planet Neptune, this vast period of a hun- 
 dred million years is only about six thou- 
 sand of his centuries. If we call the period 
 of the equinoctial circuit an ceon, it is only 
 forty centuries of seons. You must not be 
 
COOLING OF THE EARTH AND SUN. 155 
 
 surprised, therefore, if I cannot sympathize 
 with the weakness of your numerical ideahty. 
 
 "Whenever a contribution of numbers shall 
 be taken up, the generosity of the mathe- 
 maticians will be found to be inexhaustible. 
 Archimedes wrote a treatise, which he dedi- 
 cated to Gelo, Prince of Syracuse, in order 
 to exhibit to him the human capacity for 
 number. He showed the prince how he 
 could express in numbers the sands upon 
 the seashore of Syracuse, and those around 
 the whole island of Sicily : nay, much more 
 than that ; how, if the volume of the seashore 
 were of such immensity as to embrace all the 
 visible world, and if the sands were finer than 
 the finest dust blown by the gentlest wind, 
 the number of particles would be far below 
 his power of expression. He devised the 
 most ingenious system of numeration which 
 ever entered the imagination of science. He 
 condensed a universe of number, vaster than 
 creation, into a single phrase, and laid it at 
 the feet of the son of Hiero. 
 
 The million of centuries assigned by 
 Thomson for the geological history appears 
 like an infinity to him who is accustomed 
 
156 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 to measure time by the standard of human 
 events. The geologist of yesterday may 
 have been content with it. But science has 
 not educated him out of humanity ; and his 
 insatiate appetite for time seems to grow 
 with what it feeds on. Now we hear a 
 murmuring demand for six hundred millions 
 of years as required for the formation of the 
 geological strata ! ^ 
 
 Notwithstanding my faith in Sir William 
 Thomson, who is justly regarded as the high- 
 est living authority in questions of cosmi- 
 cal j)hysics, I cannot accept his process of the 
 earth's solidification, with its corresponding 
 limitation of the geologic ages. Were our 
 planet, when liquid, thoroughly homogene- 
 ous, and did it remain so as it crystallized, 
 I could offer no reasonable objection to his 
 hypothesis. But it has become too obviously 
 heterogeneous for the maintenance of such a 
 belief. The excessive radiation at the sur- 
 face, when it was at the primitive temper- 
 ature of seven thousand degrees, must have 
 induced the beginning of crystallization as 
 a superficial phenomenon. It is probable 
 
 » Proceedings of the Boy al Society, xxviii. 281-283. — Ed. 
 
COOLING OF THE EARTH AND SUN. 157 
 
 that the solidified portions, from their su- 
 perior weight, descended, at the outset, as 
 Thomson supposes, into the interior. Up to 
 this point, then, his doctrine is admirable; 
 except that, at the instant of crystallization, 
 the various materials combined in the liquid 
 are likely to have separated from each other. 
 Certain of them may have remained as slag 
 at the surface, and formed the commence- 
 ment of an outer crust. This is so usual a 
 phenomenon in all processes of art that the 
 only question would seem to be, how much 
 it may amount to. It also appears to be in- 
 dicated by the various geologic strata and by 
 upheavals, that the earth's interior is formed 
 of much purer metal than its surface. 
 
 Even though the slag were not separated 
 at the outset, the rocks, combined into solid 
 form too soon to resist the internal heat, 
 would be melted in their descent. Whether 
 the portions first melted would be the denser 
 or the lighter parts must depend upon their 
 relative fusibility. But the result would not 
 be essentially modified in either case. If 
 the denser constituents were the most fluid, 
 they would be melted out, and leave the 
 
158 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 lighter constituents to ascend and become 
 annexed to the surface. If, on the contrary, 
 the lighter parts were the most fluid, they 
 would, when melted, reascend to the surface 
 and be frozen again. In any case, therefore, 
 it seems undeniable that there is a permanent 
 superficial solidification at an exceedingly 
 early stage of the history, even if, at the 
 same time, there is the formation of an in- 
 terior solid nucleus. This process must con- 
 tinue to the end, the thickness of the crust, 
 and also the volume of the central nucleus, 
 constantly increasing. These interior and 
 exterior solid portions will be separated by a 
 liquid stratum, which is ever decreasing in 
 thickness, to supply the increasing solidity 
 above and below it. 
 
 What must be the effect of this interior 
 fluid and thickening outer crust upon the 
 rate of cooling, and on the length of time 
 required for physical changes of tempera- 
 ture? According to Thomson's hypothesis, 
 the greater part of the heat which passes 
 through the surface comes from a depth of 
 less than eighty miles ; and the whole body 
 of the earth beyond that depth remains at the 
 
COOLING OF THE EARTH AND SUN. 159 
 
 original temperature of solidification. In 
 other words, the external cooling has pene- 
 trated, at the farthest, to a depth of only 
 eighty miles, and at that depth its effect is 
 scarcely perceptible. The average depth of 
 the cooling of the earth's crust is about 
 twenty miles; so that these upper twenty 
 miles afford an ample supply for all the 
 heat which comes from the interior in a 
 thousand centm-ies. 
 
 Now, the hj^othesis of the liquid interior 
 adds immensely to the reservoir of supply, 
 without increasing the rate of exhaustion. 
 Every degree of heat communicated to the 
 surface of the liquid is raj)idly distributed 
 through its whole mass by convection ; so 
 that the temperature of the liquid surface 
 cannot be lowered by a single degree without 
 a corresponding diminution of the tempera- 
 ture of all the inner mass. Hence, in place 
 of the superficial reservoir of twenty miles in 
 depth, we shall have all the body of our 
 globe to draw upon. The supply of heat 
 will thus be more than sixty-fold augmented ; 
 and no physical obstacle can mathematically 
 be interposed to embarrass the researches of 
 
160 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 geologists, to interfere with the extension of 
 their ages of erosion, and to diminish the pos- 
 sibiHty of an increased duration of organic 
 life.^ 
 
 We may now turn from the Earth to the 
 more brilliant testimony of the Sun. 
 
 How long can this luminary have contin- 
 ued to give out its present great amount of 
 heat? Some distinguished astronomers and 
 physicists have contended, for not more than 
 twenty millions of years. But it is not diffi- 
 cult to show, that, on the very principles 
 justly adopted in the computation, the period 
 may be increased to at least five hundred 
 millions of years. 
 
 It has been correctly assumed that the 
 amount of heat radiated from the sun is to be 
 measured by the energy which the sun itself 
 has received from the accumulation of mate- 
 rial near its centre. This is simply the trans- 
 
 1 For Sir W. Thomson's views on tlie subject of the Cool- 
 ing of the Earth and of its Rigidity, the leading references are 
 as follows: Philosophical Transactions, vol. cliii. pp. 573- 
 582; Transactions of the, Boyal Society of Edinburgh, vol. 
 xxiii. pp. 157-169 ; Thomson and Tait, Treatise on Natural 
 Philosophy, vol. i, §5 832-849, and Appendix (D) ; British 
 Association Beport for 1876, Sections, pp. 3-12. See also Tait's 
 Becent Advances in Physical Science. — Editor. 
 
COOLING OF THE EARTH AND SUN. 161 
 
 mutation of energy from the form of swift 
 motion to that of intense heat. If the com- 
 putations are correctly performed, it makes 
 no difference whether the increase of ma- 
 terial energy was derived from new matter 
 falling into the sun in the form of meteors, 
 or from the compression of the mass of the 
 sun itself into a smaller space, combined with 
 an increasing density at the solar centre. 
 There are phenomena, however, in which the 
 difference is visibly manifest, and by which 
 we are enabled to distinguish the character 
 of the augmentation of energy. The addi- 
 tion of new matter to the sun involves a 
 shortening of the year of every planet, and 
 cannot reach an amount which would be 
 inconsistent with astronomical phenomena, 
 and especially with the observed precession 
 of the equinoxes at the time of Hipparchus. 
 The mass supposed to be required for the 
 maintenance of the sun's heat, and adopted 
 in the computations above referred to, can be 
 shown to be twenty-five times as great as is 
 necessary. The actual distribution of the 
 solar material was not properly considered. 
 
 It is from this element that I derive the vast 
 
 11 
 
162 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 increase of the sun's possible duration, even 
 if it had always given out heat at the same 
 rate as at the present time. 
 
 But we have reason to believe that the 
 heat radiated from the sun is greater now 
 than it has ever been before. The increase 
 of mass which has occurred can hardly fail to 
 be exhibited in the number and augmented 
 energy of the meteors which fall into it ; and 
 this increase will continue, until there is a 
 corresponding diminution of the nebulous 
 cloud from which the comets and meteors 
 are falling. It is therefore possible, and even 
 probable, that the sun has given out less heat 
 in past ages than it is now radiating. The ap- 
 parent inference is that the earth was cooler 
 then than it is at present. But this inference 
 would not seem to confoi'm to the earlier phe- 
 nomena of our geologic history ; and there 
 are sufficient reasons for its rejection. 
 
 In a former lecture, I told you of the me- 
 teors striking the earth and thereby heating 
 it. I told you that the heat derived from 
 the meteors might be as great as that re- 
 ceived from the sun. You may have thought 
 that the meteors struck the solid earth; 
 
COOLING OF TEE EARTH AND SUN. 163 
 
 which would have been a more terrific phe- 
 nomenon than the severest hailstorm or than 
 a bombardment by artillery. But fortunately 
 we are protected from them by the cushion 
 of the earth's atmosphere. It is on this that 
 the immediate blows fall, and the heat is 
 mostly deposited in the upper regions of the 
 atmosphere, — though a few of the larger 
 meteors have penetrated the atmosphere, and 
 exhibited their powers of destruction upon 
 the inhabitants of the earth. In the same 
 way, a large part of the sun's heat is at first 
 communicated to the upper atmosphere ; and, 
 finally, that portion which is not radiated 
 from the atmosphere descends to the surface 
 of the solid earth, partly by radiation and 
 partly by convection. 
 
 It is in this wise that the earth's surface is 
 heated up. It is, at the same time, emitting 
 heat by radiation ; and the heat must in- 
 crease until the radiation is sufficient to throw 
 off all the external heat received from the 
 sun and the meteors. Consequently, the 
 more the radiation is retarded by the sur- 
 rounding atmosphere, the greater will be the 
 heat attained by the surface of the earth ; 
 
164 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 unless there be a corresponding diminution 
 in the heat communicated to the earth. If the 
 height of the atmosphere in past times had 
 been twice what it is now, or if, by the addi- 
 tion of aqueous vapor or carbonic acid, the 
 resistance to radiation had been doubled, the 
 heat of the sui-face upon which we live must 
 have been likewise doubled. In that case, 
 our present sun would have been too power- 
 ful for organic life ; animals and vegetables 
 would have been scorched out of existence. 
 We should have been better off witliout this 
 sun, which we now bless for its beneficent 
 light and heat: the meteors would have 
 given us the needed temperature. 
 
 How such a state of things would in- 
 crease our respect for these almost invisible 
 bodies ! and how it would destroy the admi- 
 ration and the worship of the sun ! But we 
 have come to the knowledge of the benefi- 
 cence of the unseen meteors through the 
 visible meteors and the stars. To the wise 
 man, it strengthens his faith in the divine 
 harmony and the omnipresent ideality. 
 
POTENTIALITY. 165 
 
 VI. 
 
 POTENTIALITY. 
 
 Ideality is pre-eminently the foundation of 
 the mathematics. Observation suppHes fact. 
 Induction ascends from fact to law. Deduc- 
 tion, applying the pure logic of mathematics, 
 reverses the process and descends from law 
 to fact. The facts of observation are liable to 
 the uncertainties and inaccuracies of the hu- 
 man senses ; and the first inductions of law 
 are rough approximations to the truth. The 
 law is freed from the defects of observation 
 and converted by the speculations of the ge- 
 ometer into exact form. But it has ceased 
 to be pure induction, and has become ideal 
 hypothesis. Deductions are made from it 
 with syllogistic precision, and consequent 
 facts are logically evolved without immediate 
 reference to the actual events of Nature. If 
 the results of computation coincide, not 
 
166 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 merely qualitatively but quantitatively, with 
 observation, tbe law is established as a 
 reality, and is restored to the domain of in- 
 duction. 
 
 If, on the contrary, there is some inexpli- 
 cable divergency between the computed and 
 the observed facts, the law must be rejected. 
 It cannot be accepted as an expression of the 
 rigid theory embodied in Nature. There is 
 nevertheless a truth at its foundation, — as 
 surely as there is a base to a mountain, or a 
 bottom to a well. It includes some mathe- 
 matical conception, which remains as un- 
 deniable a phenomenon as Nature herself 
 It is her spiritual child, of as legitimate a 
 birth as her recognized material offspring. 
 It is an ideal potentiality, which may include 
 the actual ; and is loyally submissive to the 
 inflexible laws which control the human 
 mind. Its fixed seat in the soul is not to be 
 disturbed by the blindness of the body. It 
 is a criterion to discriminate between the ac- 
 curacy of theory and observation. It is a 
 judge, having power to decide upon the juris- 
 diction of his own tribunal. 
 
 In the studio of the painter, the sculptor, 
 
• POTENTIALITY. 167 
 
 and the poet, ideal art is prone to conceal its 
 natural figure under the garb of reality. But 
 in the frozen cave of geometry, the thoughts 
 which may trickle in from the actual world 
 are crystallized into glittering, passionless, 
 and unsympathizing stalactites; and the 
 mathematical sage cares not whence they 
 came, — whether they fell as dew from the 
 quiet sky, or as rain from the clouds driven 
 by the wind. Whatever be their origin, they 
 are ideal truth. 
 
 The laws of planetary motion, which Kep- 
 ler deduced from the observations made by 
 Tycho Brahe, are more exact embodiments 
 of fact than the observations themselves. 
 But their defect is their want of elasticity. 
 They give a precise, unchanged orbit, in 
 which each planet moves with a fixed law of 
 velocity. There is no recognition of the 
 disturbing influence of other planets. There 
 is no suggestion of such influence, in their 
 simple statement of the forms of motion. 
 
 Obedient to intellectual instinct, man in- 
 quires into the cause of these motions. He 
 subjects them to elementary analysis ; con- 
 siders the instantaneous tendencies to motion, 
 
168 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 and finds them to be direct manifestations 
 of a simple law of gravitation. The planet 
 gravitates to the sun, the satellite gravitates 
 to the planet. The comprehensive mind of 
 Newton asks : Why should there be limita- 
 tion in the attractive force ? Why should 
 not planet gravitate to planet ? Why should 
 not every particle of matter in the universe 
 gravitate to every other particle 1 Thus was 
 born the simple potentiality which has 
 opened the way to all the problems of celes- 
 tial mechanics, to the study of the motions 
 and figures of the stars and of their tidal 
 chanofes of fiofure. 
 
 How simple the fundamental idea; and 
 how complicated the details of theory to be 
 elaborated ! They have absorbed the labors 
 of astronomers for the last two centuries, in 
 the observatory at night, and in the study by 
 night and day. Statistics do not inform us 
 how many computers have been engaged in 
 the task, how many volumes of logarithms 
 have been consumed, how many thousands 
 of figures have been written down, how 
 many pens of goose and gold have been used 
 up. But if each pen were worth a gold mine ; 
 
POTENTIALITY. 169 
 
 if each figure were a golden thought ; if each 
 volume were the life of a philosopher ; if each 
 computer were a man of genius, — the whole 
 expenditure of material and brain would he in- 
 significant in comparison with the unbounded 
 domain subjected to the authority of ideality. 
 
 The work has not, however, been accom- 
 plished without intellectual perplexity and 
 frequent trial of faith. The universality of 
 the law of attraction, in so unexampled an 
 harmonious accord with the sunplicity of the 
 human spiritual longing, was not established 
 without the striking of some false notes. 
 Strong minds have doubted whence the dis- 
 cord came, — whether it was in the instru- 
 ment or in Nature's intention ; whether the 
 geometer might not have erred, or whether 
 there might not be some obscure complica- 
 tion of law awaiting his discovery. Feeble 
 scientists may be alarmed at the breath of the 
 wind among the leaves, and may exclaim, in 
 their terror, that the heavens are falling. But 
 the doubts of genius are the foresight of the 
 lofty soul which perceives some celestial truth 
 just rising above his extended horizon. 
 
 During the first century after the discovery 
 
170 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 of universal gravitation, six ^planets were 
 known, whose masses and normal orbits 
 were to be determined, and wbOse irregu- 
 larities of motion were to be reconciled with 
 their mutual perturbations. If their theories 
 had been established with ultimate precision, 
 and submitted to the critical comparison 
 with observation which is practised to-day, 
 the exterior planet Saturn would have pre- 
 sented inexplicable deviations from its proper 
 theory. What would have been the conse- 
 quence ? Recent experience has sufficiently 
 informed us. There would have been scepti- 
 cism respecting the validity and accuracy 
 of the Newtonian law. The repulsive force 
 manifested in the tail of the comet, the 
 resisting medium adopted by an eminent 
 authority to explain his comet's diminish- 
 ing years, would have been food enough for 
 the intellectual nourishment of many a stand- 
 ing doubter. Nevertheless, there would have 
 been stout hearts which would not have 
 yielded to unreasonable scepticism. They 
 would have faithfully and exhaustively ex- 
 plored the region of legitimate research, 
 to discover some possible cause of the 
 
POTENTIALITY. 171 
 
 anomalous ii-regularities. If the telescope 
 had failed, the pen of the geometer would 
 have detected the disturbing planet. But 
 Herschel, with his great telescope, antici- 
 pated the mathematical computations. Ura- 
 nus was discovered ; and the theories of the 
 seven planets were ere long presented to as- 
 tronomy by the untiring genius of Laplace, 
 accompanied by astronomical developments, 
 grander than new planets. 
 
 In the subsequent attempt to construct 
 tables which should serve for the prediction 
 of the places of the planets, it was ascer- 
 tained that the irregular motions of the new 
 outer planet still required the intervention of 
 some unseen power. Two great geometers, 
 independently of each other, computed the 
 elements of a planet which should reconcile 
 the discrepancies. They coincided in its orbit 
 and position. In the very direction predicted 
 by them the planet Neptune was found, in 
 consequence of their predictions, and ap- 
 parently in full confirmation of them. Nep- 
 tune completely accounts for the previous 
 defects of the theory of Uranus, and leaves 
 no apparent indication of the further exten- 
 
172 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 sion of the solar system. The discovery- 
 was an extraordinary achievement, and de- 
 serves the wreath of immortality which has 
 been awarded to Adams and Leverrier. 
 
 But there is a supplement to the story, 
 which seems incredible. The statement is 
 one which violates popular prejudice ; it has 
 been wrongfully attributed to contemporary 
 jealousy; it would not be introduced here, 
 but it is too pertinent an example of geo- 
 metric potentiality to be omitted. The ob- 
 served planet is quite distinct, in orbit and 
 theory, from that which was predicted ; and 
 the theory of prediction throws no light upon 
 the actual theory, nor has it any but an 
 accidental connection with it. 
 
 It is not rare that there are several differ- 
 ent possible causes of an event, and through 
 the influence of incomplete evidence or pre- 
 judice the wrong cause has been selected. 
 Under the wisest administration of justice, 
 there has been so skilful an array of circum- 
 stantial evidence that the innocent man has 
 been punished even to the loss of life. To 
 the present case I have given a critical and 
 laborious investigation. My examination has 
 
POTENTIALITY. 173 
 
 covered a far wider range of theory than that 
 included in the original researches. I have 
 carefully revised the computations of Adams 
 and Leverrier. I find in them no error, no 
 lact of judgment, and no failure in respect to 
 any legitimate mode of investigation. Never- 
 theless, I strictly adhere to the correctness of 
 my early statement. I am aware that there 
 are great names opposed to me; but their 
 opposition has arisen from the mistaken con- 
 clusions of ill-digested argument. The time 
 must come when personality will disappear, 
 and nationality sink into oblivion ; and you 
 must await the fi:nal rendering of the verdict 
 of astronomy. 
 
 My position is that there were two possible 
 planets, either of which might have caused 
 the observed irregular motions of Uranus. 
 Each planet excluded the other ; so that, if 
 one was, the other was not. They coincided 
 in direction from the earth at certain epochs, 
 once in six hundred and fifty years. It was 
 at one of these epochs that the prediction 
 was made ; and at no other time for six cen- 
 turies could the prediction of one planet have 
 revealed the other. The observed planet was 
 
174 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 not the predicted one. It was excluded 
 through the Hmitations which had been de- 
 termined by Leverrier himself, after a pro- 
 digious outlay of profound and ingenious 
 research. He had proclaimed the investiga- 
 tion of the limits as essential to the full so- 
 lution of the problem. It was certainly its 
 larger moiety, and most intricate portion ; 
 and he had worthily solved it. It is incon- 
 ceivable how the great master can have con- 
 sented to abandon his choicest production 
 and most brilliant jewel to popular applause 
 and its ignoble bribery. The potential planet 
 is as splendid a reality as the true planet, and 
 as marvellous a discovery. 
 
 Physical potentiality is Protean in its 
 forms. Work done is the representative 
 and equivalent of the energy by which it 
 was accomplished ; if it could undo itself or 
 be undone, it would set at liberty the same 
 amount of energy, and this could be applied 
 to the performance of other work. The en- 
 ergy which is used in performing work, and 
 which is buried in the work, may be consid- 
 ered as latent energy ; and, in reference to its 
 possible development and transformation, may 
 
POTENTIALITY. 175 
 
 be designated as potentiality. All mechanical 
 philosophers recognize this potentiality, and 
 agree that the aggregate energy of the ma- 
 terial world, including the potential as well 
 as the actual, has never suffered increase or 
 decrease. Man's will has no power over it ; 
 not so much as it may have to add a cubit 
 to his stature, or to change the color of his 
 hair. 
 
 A profound analysis of the operations of 
 Nature has led Sir William Thomson to the 
 conclusion that there are paths of work 
 which cannot be retraced, and in which there 
 is-an absorption of energy which cannot be 
 recovered. If this be so, there is energy 
 which is practically lost ; or, in other words, 
 there is a continual diminution of the avail- 
 able energy of the physical world. 
 
 Wlien, ^ in the winding of a clock, the 
 weight is raised, it represents in its position 
 the power of gravity which resisted its ele- 
 vation. There is potentiality in its position. 
 As the weight descends and turns the ma- 
 chinery, overcoming the friction which re- 
 tards the descent, the potential energy of the 
 position decreases, and is transformed into 
 
176 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 work and thence into heat. In the same way, 
 the planet which has ascended to its great- 
 est distance from the sun has acquired its 
 position of maximum potential energy. At 
 the same time, it has lost an equal amount 
 of actual energy, which is manifest in de- 
 creased velocity. If a stone were to fall from 
 the top of a monument, it would, on reach- 
 ing the ground, acquire a velocity which, 
 reversed in direction, would be the exact 
 amount required to carry it up again to the 
 point from which it fell. But if it were 
 permitted to strike the ground, the power 
 would be again transformed, and would be 
 represented in the heating, bending, and 
 breaking of itself and of the surface upon 
 which it fell. 
 
 Heat is but a name for the energy of the 
 motion of vibration of the particles of a body. 
 When water is heated to a certain temper- 
 ature, it passes into the form of steam ; and a 
 large amount of heat is absorbed in the pro- 
 cess of transition. Upon the reversal of the 
 process, the steam cools, retui-ns to the form of 
 water, and develops the power needed for the. 
 steam engine. In this case, potential energy 
 
POTENTIALITY. 177 
 
 is represented by the form of steam. Again, 
 in the passage from ice to water there is a 
 similar absorption of heat ; so that the liquid 
 represents potentiality in comparison with 
 the solid form of water. There is no chem- 
 ical transformation in which there is not a 
 corresponding exhibition of potentiality. It 
 extends even to the organic world. When 
 the tree grows, it absorbs the solar heat, 
 which is treasured up as potentiality in the 
 form of wood or coal. 
 
 The coal of the geological strata, formed 
 ages before the birth of man, was from the 
 beginning designed for his use, as certainly 
 as the charcoal which is brought to market, 
 or as to-day's sunlight. The supply of mate- 
 rial essential to man's civilization, so long an- 
 terior to the demand, — how can you explain 
 it? It could have had no influence in the 
 production of man ; but it is the evidence of 
 the plan of his coming, inwrought into the 
 course of evolution, — in the same way as the 
 openings in the frame-work of a building de- 
 monstrate the future stairs and chimneys. If 
 you were to travel to another planet, and there 
 behold a similar deposit of coal, occurring 
 
 13 
 
178 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 where man was absent, would you not justly 
 infer that that planet was intended at some 
 time to be peopled by civilized beings like 
 ourselves ? Whether you believe in the law 
 of development or in the law of design, what 
 other conclusion is consistent with your doc- 
 trine ? There is a spiritual potentiality of plan, 
 as visible to the penetrating eye of the seer as 
 any physical potentiality. 
 
 The past and the future are equally ideal. 
 The present is, alas ! the only reality. The 
 past is irrecoverably lost as an actuality ; but, 
 restored by history, it is an ever-living in- 
 structor. The future, inferred from the in- 
 structions of the past, is soon to become the 
 present, and its approach is watched for with 
 intense interest. In the market it means 
 failure or it means untold wealth ; in politics 
 it means ambition rewarded or punished ; in 
 religion it means heaven or eternal suffering 
 or absolute death. To be able to foretell an 
 eclipse or a comet or the place of the plan- 
 ets or the aspects of the stars was to endow 
 the race with a higher sense ; it was giving 
 to civilized humanity authority over those 
 powers of darkness which the superstitious 
 
POTENTIALITY. 179 
 
 barbarian worshipped. There is a singular 
 charm in prediction, even when one cannot be 
 present at its verification. But to verify pre- 
 diction is to receive the homage of Nature. 
 
 Is spiritual prediction a hopeless impos- 
 sibility, like that of the storms of the next 
 century! What is to be each individual's 
 future ; and what the future of all man- 
 kind % Science has banished the prophetic 
 rule of the stars. But the continuity of law 
 has taken possession of the throne of augury 
 vacated by astrology. It is not unreasonable 
 to hope that honest and reverent inquiry will 
 have its due and promised reward, even when 
 it seeks to penetrate the mysteries of the spir- 
 itual future. 
 
 There was once an age of stone upon the 
 earth. Its records are found in all lands. 
 Though it had not a simultaneous existence 
 over the whole earth, its history is one and 
 the same everywhere. Man was scarcely ele- 
 vated above the beasts, and used no imple- 
 ments of peace or war but those formed most 
 inartificially of earth or stone. His dwelling 
 was a cave or a wretched hut of wood and 
 mud, of similar architectural merit to that of 
 
180 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the bird's nest or tbe beaver's dam. He was 
 destitute of written language. From that 
 inferior stage, the lord of creation has gradu- 
 ally and naturally risen to his present posses- 
 sion of arts, science, and literature, and with 
 a constantly increasing rate of progress. If 
 the stone age was an advance upon a still 
 earlier unknown condition, how low that con- 
 dition must have been! Lower perchance 
 than that of the apes and monkeys of to-day, 
 from which proud man, in his foolishness, so 
 dreads being forced by the doctrines of evo- 
 lution to trace his descent. 
 
 On the other hand, is the story already 
 completed? Have we reached the last act, 
 and are we suddenly brought to a stop upon 
 the very threshold of the divine temple 1 No 
 miracle has accomplished the past progress. 
 Is the end to be a destructive work worthy 
 of a demon ? Such a conclusion is not more 
 disheartening than it is unphilosophical. It 
 is contrary to analogy and experience, not 
 less than to hope and faith. To religion it is 
 falsehood, and to evolution it is absurdity. 
 Each new invention and discovery in the arts 
 and sciences has hitherto opened the way to 
 
POTENTIALITY. 181 
 
 many others, still more surprising. The law 
 of progress will not be suddenly interrupted ; 
 it cannot cease without previous indication 
 and some evident diminution in the rate of 
 advance. We have a just and abiding faith 
 that our planet will endure for the develop-' 
 ment of our children and our children's chil- 
 dren, to the latest generation. Our trust is 
 founded upon the eternal laws which govern 
 the universe, and upon the rock of ages, that 
 the promise of creation will be fulfilled, and 
 that the end will not come without unmis- 
 takable signs and warnings. 
 
 But while the race may last, may not the 
 individual be sacrificed ? How many mill- 
 ions of germs of plants and animals are de- 
 stroyed, for one which escapes destruction and 
 becomes fruitful ! How many children die, 
 while so few arrive in health at maturity ! It 
 seems to be the law of life that individuals 
 should be produced in numbers sufficient to 
 insure the permanence of the race. When 
 the supply has been deficient, the race has 
 died out. Such has been the case with fam- 
 ilies of plants and animals, and with the ab- 
 origines of many countries ; and such is the 
 
182 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 inevitable destiny of our own aborigines. It 
 is the law of material life. 
 
 But tbe law of spiritual life demands otber 
 evidence and principles of investigation. In 
 tbe material world one atom can replace 
 another without prejudice to the system. 
 Tree can ever be substituted for tree, and 
 beast for beast, each in its kind ; so that 
 species is everything, and individual notliing. 
 But it is quite the reverse in the spiritual 
 world. An individual cannot hold the place 
 of another, as father, mother, or child ; as hus- 
 band or wife ; as king, or warrior, or states- 
 man, or judge, or trusted friend, or beloved 
 pastor. The spiritual individual is every- 
 thing. The desti-uction of any soul would 
 be an irreparable loss ; nothing can be con- 
 ceived more utterly at variance with the har- 
 mony of creation. It is an absolute impossi- 
 bility ; and we may hold it, not irreverently, 
 to be a limitation even of Almighty Will. A 
 man can tell a lie, and thereby demonstrate 
 his feebleness ; the pagan god can deceive, be- 
 cause he is weak and limited. But our God, 
 for the reason of his infinite strength and of 
 his eternal omniscience, must forever coincide 
 
POTENTIALITY. 183 
 
 •with Hmself. Otherwise, instead of being an 
 infinite and necessary reality, he would be an 
 infinite impossibility. At one and the same 
 instant, he would be and not be Grod. We 
 may dismiss the argument for the ideality of 
 physical science as an unreal fable, when we 
 set aside our assurance of the immortality of 
 the spirit as a delusive promise. 
 
 But how is it with the immense apparent 
 failure of spiritual intention ? If we may 
 interpret the actual facts of experience, with 
 what judgment shall we judge 1 Each day 
 solves some riddle of the past, but there 
 will always be riddles to be solved. Na- 
 ture's riddles are man's intellectual nourish- 
 ment : they are the bread and wine of his 
 science and his ideality. To shrink from 
 them is cowardice and want of faith. To 
 solve them is to bring light into the world, 
 and to drive out ignorance and superstition : 
 it is the anticipation of futurity, the beginning 
 of immortality, and salvation from intellec- 
 tual death. 
 
 What shall we say concerning the suflFer- 
 ing with which this world is afflicted ? What 
 of sin ! These awful topics are above my 
 
184 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 sphere, and it is with extreme diffidence that 
 I venture to throw my small light into their 
 dark mysteries. If you reject my specula- 
 tions as idle and illogical fancies, I hope that 
 you will find them neither rash nor irrev- 
 erent. 
 
 What is man ? What a strange union of 
 matter and mind ! A machine for converting 
 material into spiritual force ! A soul impris- 
 oned in a body ! Is not the body a dun- 
 geon, — a tenement of decay, from which the 
 soul will rejoice to free itself, and wing its 
 flight to the perennial spring-time of heaven 
 and to perpetual rest in the bosom of the 
 Father ? Perpetual rest ! — for an immortal 
 soul, whose only life is action ! Why not re- 
 main in the sleep of the grave, and never be 
 awakened by the last trump ? Such a doc- 
 trine may satisfy the wisdom of Confucius, 
 or delight the Buddhists, but has no place in 
 Christian philosophy.. 
 
 The body is the vocal instrimient through 
 which the soul communicates with other 
 souls, with its past self, and even, perhaps, 
 with its God. Were the communication be- 
 tween soul and soul direct and immediate, 
 
POTENTIALITY. 185 
 
 there would be no protection for thought; 
 each man would take full possession of the 
 thoughts of every other man, and there would 
 be no such thing as personality and individu- 
 ality. The body is needed to hold souls 
 apart and to preserve their independence, as 
 well as for conversation and mutual sympa- 
 thy. Hence body and matter are essential 
 to man's true existence. Without them, he 
 must, as is supposed in the Chinese theology, 
 be instantly absorbed into the infinite spirit. 
 In this case, creation would be a false and 
 unmeaning tragedy. The soul which leaves 
 this earthly body still requires incorporation. 
 The grandest philosopher who has ever spec- 
 ulated upon this theme has told us in his sub- 
 lime epistle that there are celestial bodies as 
 well as bodies terrestrial. It may not be vain 
 to strive at some insight into the possible 
 nature of the celestial bodies ; and it may per- 
 chance furnish us with some grounds of con- 
 solation for the seeming evils of man's lot. 
 
 Our present bodies are admirably adapted 
 to the demands of this life ; and the forces, as 
 well as the construction, of the material world 
 are fitted to the interchange of thought, and 
 
186 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 as a vehicle of tlie divine truths required for 
 the beginning of our education. The inertia 
 of matter is indispensable for a trustworthy- 
 medium. Matter must transmit thought pre- 
 cisely as it is received, without suspicion of 
 transformation. It must be competent to re- 
 ceive all forms of thought, and incapable of 
 resistance to any. 
 
 Above all other intellectual appetites is the 
 soul's passionate love of unity. It is a con- 
 trolling principle of material phenomena, and 
 of every form of human art and poetry. By 
 the attraction of gravitation, masses are held 
 together in one system, or combined into a 
 single body. By the chemical forces, discrete 
 portions of matter are drawn together in an 
 endless variety of new forms ; each of which 
 endures till it has discharged its appropriate 
 function, whether for an instant or for an age. 
 In these forms, it is curious how the mathe- 
 matical formula of the compound indicates 
 its attributes : it is as if the union had been 
 effected by some ideal geometer. Every- 
 where there is a texture of substance, fitted 
 to the health, comfort, and adornment of hu- 
 manity. Can we fear lest the celestial bodies 
 
POTENTIALITY. 187 
 
 will be less adapted to the souls which they 
 are to clothe % Is it not a fair and just infer- 
 ence that each body will be nicely fitted to 
 its soul, as if organized and crystallized under 
 a controlling influence from within ? 
 
 What better suggestion can be made, which 
 shall give us the full benefit of the discipline, 
 education, ties, and sympathies of this life ? 
 We shall be known as we are. Soul will 
 recognize soul through its external covering, 
 with unerring certainty. The stature of each 
 body will correspond to the magnitude of the 
 soul. The intellectual supremacy and con- 
 summate beauty of a Shakspeare will be 
 more apparent in his celestial body than in 
 his ideal statue. The countenance of the 
 great law-giver of Judaea will shine as when 
 he descended from Mount Sinai. No crown 
 will be needed to designate legitimate royal- 
 ty, nor any celestial aureole, encircling the 
 head, to mark the loving and majestic pres- 
 ence of the apostles and the true saints. 
 
 On the other hand, we may justly appre- 
 hend that the deformity of our future body 
 will conform to our spiritual errors in the 
 present life. Would not such be the natural 
 
188 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 and legitimate punisliment for sin? It is a 
 punishment we can endure, in humble trust 
 in the infinite mercy as well as the supreme 
 justice, before which we stand. But, sur- 
 rounded by love and sympathy, who would 
 not speedily repent and hasten to be restored 
 to his intended excellence, and fill heaven 
 with joy at his recovery I We then might 
 recognize how suffering and sin are short- 
 lived violations of material and spiritual law, 
 and essential to free agency ; how they are 
 the evidence of unlimited potentiality, and 
 how they are amply compensated by the free- 
 dom and the pardon with which they are 
 associated. 
 
 The diversity of mind is hardly less note- 
 worthy than the uniformity of body and .the 
 fixedness of spiritual and natural laws. It 
 would be a detraction from creative fertility 
 to conceive a possible character which did not 
 exist. Nevertheless, we must admit that 
 there are limits to spiritual possibility. Cer- 
 tain general principles of human nature must 
 be diffused through all souls which are in- 
 tended for mutual intercourse. Such is 
 mathematical truth, which all men accept as 
 
POTENTIALITY. 189 
 
 absolute. But shades of opinion are as many 
 as there are men, as justifiable in their vari- 
 ety as flowers and fruit, as season and song ; 
 and they are essential to a well-organized 
 society, in which mind may grow and ex- 
 pand. The graces of ideality may not be 
 cramped by the narrowness and bigotry of 
 one mind or of a multitude. 
 
 Two exactly twin souls would be dull and 
 useless companions, and they are more un- 
 known to Nature than two undistinguishable 
 faces. The wildest conflicts of opinion which 
 arise from the diversity of mind are needed 
 for the purification of the atmosphere of 
 thought. Two similar souls may start from 
 the same neighborhood, in close and intimate 
 friendship, and keep along together, side by 
 side, for months and years, subject to the 
 same influences. However little their paths 
 may diverge, their distance apart will at 
 length become perceptible, and, like that of 
 two straight lines, drawn from the same point, 
 will at length exceed any proposed magni- 
 tude. But, at the same time, the sphere of 
 each mind's sympathies is likely to enlarge 
 even more rapidly, so that the circle of co- 
 
190 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 incident thouglit and affection may always 
 increase in extent, while each, by his aug- 
 mented diversity, will be a worthier friend of 
 the other. 
 
 Experience justifies the assertion that all 
 forms of mind required in this world are 
 here to be found. How will it be with the 
 greater demands of the future world ? Whence 
 is the supply to come? Mostly, we may be- 
 lieve, from other worlds ; but why not in part 
 from those immature spirits which began 
 their existence here, where there are marriage 
 and offspring, and are ready for a different 
 training, partly perhaps under our own guid- 
 ance, in the different circumstances of the 
 celestial life ? 
 
 There may hereafter be a wide and ever- 
 widening enlargement in the avenues of sen- 
 sation, and in the speculations and oppor- 
 tunities offered for discussion. How many 
 new problems came with the discovery of 
 America ! And how there has been a cor- 
 responding increase in the dimensions and 
 variety of intellect ! The birth of Christian- 
 ity changed the whole firmament of thought. 
 It was a new spiritual world into which the 
 
POTENTIALITY. 191 
 
 race was transported. Centuries of profound 
 brooding were required, ere mankind could 
 shake off the torpor of the ancient darkness 
 and awake to the morning light of the gospel. 
 But when at last the eyes were fully opened, 
 the natural world was revealed in a new 
 light, learning revived in grander aspects, 
 and science was transformed from speciality 
 to generality. 
 
 "We have here five imperfect senses, and 
 they are as many as we can control in this 
 terrestrial imbecility. A lifetime is required 
 for most of us to become journeymen in the 
 use of any one of them, and no man has 
 yet been known who was a master of them 
 all. Their wide range of perception in diff- 
 erent persons and their great capacity for 
 education give us undoubted intimation of 
 how much they may be extended in a more 
 delicate and sensitive organization. That 
 the immense extent of unheard and unseen 
 vibrations with which the universe is palpi- 
 tating should never become available to the 
 soul, is contrary to the analogies of Nature. 
 It is far from unreasonable to suppose that 
 there will be a corresponding variety of. ways 
 
192 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 of knowledge, and of opportunities for scien- 
 tific study, for the development of strange 
 inventions for reinforcing the senses, and for 
 the creation of wonderful, grand, and lovely 
 forms of fancy and imagination. In the ex- 
 quisite organization of the celestial substance, 
 the range of sensible vibrations may be in- 
 creased immeasurably ; and the ultimate 
 limits to which future perception and educa- 
 tion may advance is possibly a mystery, 
 transcending the powers of research even of 
 the archangels. 
 
 The increased possibilities of future in- 
 quiry may not only arise from increased 
 capacities of sensation, but also from bet- 
 ter conditions for exact and delicate obser- 
 vation. No quickening of the senses can re- 
 lieve the astronomer from our flittering and 
 obscuring atmosphere ; nor can the carpet 
 of the good fairy lift him above its influence ; 
 nor can he, by any art, sweep the skies clear 
 or quiet their ceaseless twinkle. Why have 
 such curious and intricate celestial problems 
 been presented to man's appetite for know- 
 ledge 1 Why have the seers of the stars been 
 treated to this Barmecide feast? Have as- 
 
POTENTIALITY. 193 
 
 tronomers committed the unpardonable sin 
 of Tantalus ? Have they ventured too near 
 the heavenly throne, where the heathen gods 
 still hold their rule, and regard with jealous 
 eyes the spiritual Babel of our modern sci- 
 ence, aspiring to the highest heaven ; or have 
 we been granted a true sight of the promised 
 land ? The changing surface of the sun and 
 his planets ; the wonderful system of Sat- 
 urn with his mysterious ring and his many 
 satellites ; the intricate maze of the cluster 
 of Hercules and of the Pleiades ; the im- 
 mense nebular and stellar transformations, — 
 are a stimulus to research, presented by the 
 divine teacher, and a promise, surer than the 
 rainbow, that we shall be delivered from this 
 deep flood of ignorance. 
 
 Do we need a nearer approach to the 
 planets and stars ? There is Halley's comet, 
 upon which we might be conveyed through 
 the whole extent of the solar system; and 
 there are other comets, which might carry us 
 out to the home of the meteors, or to the 
 most distant regions of space. 
 
 Such is the glory and majesty of the in- 
 tellectual future life, naturally suggested to 
 
 13 
 
194 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the faith of the Christian philosopher. How 
 infinitely grand, in comparison with the sen- 
 sual joys promised by other forms of re- 
 ligion ! It is a daring flight upon the wings 
 of pure logic by which the modern geome- 
 ter has soared away from the realities of 
 the ancients into the strange ideality of the 
 fourth dimension of space, with its impossible 
 triangles and its inconceivable metamor- 
 phoses. But this future and this present are 
 the natural and reasonable expansion of the 
 ideal development which began with the 
 nebular theory. 
 
 Judge the tree by its fruit. Is this magni- 
 ficent display of ideality a human delusion ; 
 or is it a divine record ? The heavens and 
 the earth have spoken to declare the glory of 
 God. It is not a tale told by an idiot, signi- 
 fying nothing. It is the poem of an infinite 
 imagination, signifying immortality. 
 
APPENDIX. 
 
APPENDIX. 
 
 The questions of cosmical physics which are dis- 
 cussed in the third, fourth, and fifth lectures were the 
 leading object of Professor Peiree's study during his 
 last years, — a study which was by no means com- 
 pleted at his death. The views here expressed must, 
 therefore, be regarded only as representing a stage in 
 the progress of his thought, and as affording a gene- 
 ral sketch of the full theory which he was seeking to 
 develop. In regard to these three lectures, he had 
 made up his mind not to print them until he had been 
 able to bring them into a form more completely sat- 
 isfactory to himself, and to supply them with notes 
 addressed to the technically scientific reader. 
 
 In the mean time, he continued a series of com- 
 munications which he had already begun, to the 
 American Academy of Arts and Sciences. On March 
 14 and April 11, 1877, he presented communications 
 on " An Application of Lane's Law of the Accumula- 
 tion of Solar Heat," and on " The Temperature of a 
 Perfect Gas which is in Convective Equilibrium." 
 {Proc. Amer. Acad., xii. 286, 287.) On March 13, 
 1878, he " made some remarks on the internal struc- 
 
198 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 ture of the earth mth reference to Lipswich's results 
 in regard to its density, and to the theory of Sir 
 "William Thomson." {Hid., xiii. 433.) On April 9, 
 1879, he made a communication on " The Meteoric 
 Constitution of the Solar System." {Ibid., xiv. 329.) 
 On June 11, 1879, he made a communication on " The 
 Meteoric Constitution of the Universe." (Ibid., xv. 
 370.) On October 8, 1879, he presented the follow- 
 ing " Propositions in Cosmical Physics " : — 
 
 " 1. All stellar light emanates from super-heated gas. 
 Hence the sun and stars are gaseous bodies. 
 
 " 2. Gaseous bodies, in the process of radiating light 
 and heat, condense, and become hotter throughout their 
 mass. 
 
 " 3. It is probable that their surfaces would become 
 colder if there were not an external supply of heat from 
 the collision of meteors. 
 
 " 4. Large celestial bodies are constantly deriving su- 
 perficial heat from the collision of meteors, till at length 
 the surface becomes super-heated gas, which constitution 
 must finally extend through the mass. 
 
 " 5. Small celestial bodies are constantly cooling till 
 they become invisible solid meteors. 
 
 " 6. The heat of space consists of two parts : first, that 
 of radiation principally from the stars, which is small, ex- 
 cept in the immediate vicinity of the stai's ; the second 
 portion is derived from the velocity with which the meteors 
 strike the planet at which the observation is taken ; and 
 this velocity partly depends upon the mass of the star by 
 which the orbit of the planet is defined, and partly upon 
 the mass of the planet itself 
 
 " 7. If the planets were originally formed by the colli- 
 
APPENDIX. 199 
 
 eion of meteors, it is difficult to account for an initial heat 
 sufficient to liquefy them, and at the same time to account 
 for their subsequent cooling, without a great change in 
 the number and nature of the meteors ; and any such 
 hypothesis seems to invalidate the meteoric theory. 
 
 "8. If the planets were not originally formed by the 
 collision of meteors, their common direction of rotation 
 becomes difficult of explanation." {Ibid., xv. 201.) 
 
 He also submitted the same propositions, for criti- 
 cism and as a basis of discussion, at the first of a series 
 of informal scientific meetings held at Harvard Uni- 
 versity during the academic year 1879-80 ; and, a few 
 weeks later, he read at one of these meetings the fol- 
 lowing additional propositions, which, however, he did 
 not publish, except so far as they may have been vir- 
 tually contained in previous communications to the 
 Academy : — 
 
 " 9. Space is filled with invisible meteors, which by 
 their collision supply the heat and light of the sun and 
 stars, and are the principal source of the heat of the 
 planets, partly by direct collision. 
 
 " 10. Their collision with the sun causes the vast jets 
 of gas and the violent commotions of the sun's surface. 
 
 " 11. The meteors are the source of the star-dust ob- 
 served on the earth, and also supply carbon and other 
 substances foreign to our planet, or of which there is a 
 deficiency. 
 
 " 12. The collisions with Jupiter and Saturn occasion 
 the heat of those planets. 
 
 " 1 3. The nebulous stars and the stars in the nebulso 
 correspond to this meteoric constitution of the sidereal 
 universe." 
 
200 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 B. 
 
 As Professor Peirce refers in his sixth lecture to 
 the view he maintained respecting the discovery of 
 Neptune, and as his position in this matter has not 
 always been precisely noted, or treated with careful 
 justice, it seems advisable to add here a brief ac- 
 count of the leading facts of the case, with a citation 
 of the words which he actually used in the original 
 discussion. 
 
 The problem of determining the elements of an un- 
 known planet, which should account for the observed 
 perturbations of Uranus, was taken up independently 
 by Mr. Adams in England and by M. Leverrier in 
 France. Both geometers began from the hypothesis 
 that the mean distance of the new planet from the 
 sun could not be far from satisfying Bode's law. That 
 law gave for the mean distance of the required planet 
 38.8, that of the earth being taken as unity. Adams 
 at first assumed a mean distance of 38.4, but, in his 
 second hypothesis, assumed 37.6. Leverrier assigned 
 to his predicted planet a mean distance of 36.154. 
 He also undertook to determine limits between which 
 the mean distance must lie ; and he found as these 
 limits, 35.04 and 37.90. The part of M. Leverrier's 
 work which was involved in these determinations was 
 undoubtedly one of the most remarkable portions of 
 his investigation. 
 
 On Sept. 23, 1846, Neptune was observed by 
 Dr. Galle at Berlin, in consequence of a letter to 
 
APPENDIX. 201 
 
 him from M. Leverrier, and within one degree of the 
 place in the heavens assigned by the latter. The an- 
 nouncement created an intense excitement through- 
 out the civilized world. The prediction thus so brill- 
 iantly verified was deemed to surpass any previous 
 triumph of mathematical astronomy; and the error 
 which was afterward found to be involved in it does 
 not materially lessen its glory. Such, at least, was 
 the judgment of Professor Peirce, to whom the skill, 
 power, and thought shown in the mathematical in- 
 vestigation were the true ground of admiration for 
 the exploit. It is to be regretted that the correction 
 of* the error was not received, on the part of the 
 French astronomer, with the magnanimity and fair- 
 ness which it is always painful not to find associated 
 with high intellectual power. 
 
 The elements of the new planet were computed 
 from observation, and it was then found that the 
 mean distance was, in fact, only 30. This surprising 
 result was communicated to the American Academy 
 by Mr. Sears C. Walker on 16 March 1847. At thei 
 same meeting of the Academy, Professor Peirce re- 
 marked, " That the orbits given by Mr. Walker differ 
 so widely from the predictions, that he has been in- 
 duced to make a careful re-examination of the observa- 
 tions. He has not only himself verified Mr. Walker's 
 distance of 30, and the consequent angular motion ; 
 but Mr. George P. Bond, of the Cambridge Observa- 
 tory, has also, at his request, verified this distance 
 and motion from the Cambridge observations alone. 
 From these data, without any hypothesis in regard to 
 
202 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 the character of the orbit, he has arrived at the con- 
 clusion, that THE PLANET NePTUNE IS NOT THE PLANET 
 TO WHICH GEOMETRICAL ANALYSIS HAD DIRECTED THE 
 
 TELESCOPE ; that its orbit is not contained within the 
 limits of space which have been explored by geometers 
 searching for the source of the disturbances of Uranus ; 
 and that its discovery by Galle must be regarded as a 
 happy accident." He continued : — 
 
 " Mr. Adams, in his Explanation of the Observed Irreg- 
 ularities of Uranus, considered two hypothetical orbits, 
 in one of which the mean distance is 38.4, or just double 
 that of Uranus, and in the other it is 37.6; while M. 
 Leverrier, in his Researches into the Motions of the Planet 
 Herschel, called Uranus, after deriving some rough approxi- 
 mations from the consideration of the mean distance 38.4, 
 proceeds to the accurate examination of the three dis- 
 tances 39.1, 37.6, and 36.2. The extension of the inves- 
 tigations to any other mean distances can be made only 
 by assuming a continuous law to pervade the subject of 
 inquiry, and that there is no important change in the 
 character of the resulting perturbations. Guided by this 
 principle, well established, and legitimate, if confined with- 
 in proper limits, M. Leverrier narrowed with consummate 
 skill the field of research, and arrived at two fundamental 
 propositions ; namely, — 
 
 " 1. That the mean distance of the planet cannot be 
 less than 35, or more than 37.9. The corresponding 
 limits of the time of sidereal revolution are about 207 
 and 233 years. 
 
 " 2. That there is only one region iu which the dis- 
 turbing planet can be placed, in order to account for the 
 motions of Uranus ; that the mean longitude of this 
 
APPENDIX. 203 
 
 planet must have been, on Jan. 1, 1800, between 243° 
 and 252°. 
 
 " Neither of these propositions is of itself necessarily 
 opposed to the observations which have been made upon 
 Neptune, but the two combined are decidedly inconsistent 
 with observation. It is impossible to find an orbit which, 
 satisfying the observed distance *and motion, is subject at 
 the same time to both of these propositions, or even ap- 
 proximately subject to them. If, for instance, a mean 
 longitude and time of revolution are adopted according 
 with the first, the corresponding mean longitude in 1800 
 must have been at least 40° distant from the limits of the 
 second proposition. And again, if the planet is assumed 
 to have had in 1800 a mean longitude near the limits of 
 the second proposition, the corresponding time of revolu- 
 tion with which its motions satisfy the present observa- 
 tions cannot exceed 170 years; and must therefore be 
 about 40 years less than the limits of the first proposi- 
 tion. Neptune cannot, then, be the planet of M. Le- 
 verrier's theory, and cannot account for the observed 
 perturbations of Uranus under the form of the inequali- 
 ties involved in his analysis. 
 
 " It is not, however, a necessary conclusion that Nep- 
 tune will not account for the perturbations of Uranus, for 
 its probable mean distance of about 30 is so much less than 
 the limits of the previous researches, that no inference from 
 them can be safely extended to it. An important change, 
 indeed, in the character of the perturbations takes place 
 near the distance 35.3 ; so that the continuous law by 
 which such inferences are justified is abruptly broken 
 at this point, and it was hence an oversight in M. Le- 
 verrier to extend his inner limit to the distance 35. A 
 planet at the distance 35.3 would revolve about the sun 
 
204 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 in 210 years, which is exactly two and a half times the 
 period of the revolution of Uranus. Now, if the times of 
 revolution of two planets were exactly as 2 to 5, the effects 
 of their mutual influence would be peculiar and compli- 
 cated ; and even a near approach to this ratio gives rise 
 to those remarkable irregularities of motion which are 
 exhibited in Jupiter and Saturn, and which greatly per- 
 plexed geometers until they were traced to their origin by 
 Laplace. This distance of 35.3, then, is a complete bar- 
 rier to any logical deduction, and the investigations with 
 regard to the outer space cannot be extended to the in- 
 terior. . . ." {Proc. Amer. Acad., i. 65-67.) 
 
 On this occasion, Mr. Peirce expressed no opinion 
 on the question whether the actual planet, as well as 
 the predicted one, would account for the perturba- 
 tions of Uranus. It was necessary that that question 
 should remain altogether unanswered, until the test 
 of computation had been applied to it; since the 
 mathematical theory of the predicted planet was not 
 the mathematical theory of the planet which had been 
 discovered. It is, however, noticeable that M. Lever- 
 rier said, less cautiously, 29 March 1847^ that " the 
 smallness of the eccentricity which resulted from Mr. 
 Walker's calculations would be incompatible with the 
 nature of the perturbations of the planet Herschel." 
 {Comptes Rendus, xxiv. 531.) 
 
 At the meeting of the Academy held on the 4th of 
 May Professor Peirce stated that he was strongly of 
 the opinion, that the irregularities of motion exhibited 
 by Uranus were not due to the influence of Neptune. 
 {Proc. Amer. Acad., i. 144.) On 4 April 1848, how- 
 
APPENDIX. 205 
 
 ever, he retracted this expression of opinion, and an- 
 nounced that, having completed his investigation, he 
 had ascertained that Neptune would completely ac- 
 count for the perturbations of Uranus ; and that " the 
 theory of Uranus is now perfect,'' "provided that 
 mass of Neptune be adopted which is- derived from 
 Mr. Bond's observations of LasseU's satellite." {Ihid., 
 p. 332.) 
 
 At the same meeting of the Academy, Mr. Peirce 
 remarked, " that his original views were unchanged 
 in regard to the importance to be attached to the vast 
 discrepancies between the predicted and observed 
 orbits of the planet which disturbs the motions of 
 Uranus." He said : — 
 
 " Neptune is not the planet designated by geometry, 
 although it is a perfect solution of the problem -which 
 analysis had undertaken to investigate, and had really 
 solved, but in a form radically different from the actual 
 solution of nature. This is not a personal question ; it 
 is certainly not one in which the reputations of Adams 
 and Leverrier are concerned. The accuracy of their inves- 
 tigations is not assailed ; but it is expressly admitted that 
 they announced the correct results of most profound ana- 
 lytical researches. 
 
 " The fair consideration of this question cannot be 
 made without recalling the true office and position of 
 geometry in science, which alone entitles it to the appel- 
 lation of the key to the physical world. Mathematics is 
 the science of exact measurement ; accuracy is its sole 
 aim and object, and it is this which places it in harmony 
 with a creation which is subject to perfect law and un- 
 deviating order. An inaccurate result cannot be a geo- 
 
206 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 metrical one ; a result, inaccurate beyond certain well- 
 defined limits, does not belong to the exact science ; 
 an inconsistency which exceeds a certain amount may 
 not be neglected by him who deals with nothing but 
 more or less, without disturbing the very foundations 
 of his faith. 
 
 " The geometrical statement was distinctly made, that' 
 the planet which disturbed Uranus could not be at a less 
 mean distance from the sun than thirty-five times the 
 earth's mean distance from the sun; that is, that no planet 
 which was within this distance could cause the observed 
 irregularities in the motions of Uranus. Neptune's mean 
 distance from the sun is only thirty times the earth's 
 mean distance, and yet Neptune does account for the 
 perturbations of Uranus. It is five hundred millions of 
 miles nearer the sun than it was distinctly stated by 
 geometry that it possibly could be, in order to be capable 
 of producing the effect which it actually does produce. 
 The spirit of mathematical accuracy cannot be supposed 
 to be sufficiently elastic to embrace so great an inconsis- 
 tency, amounting to one sixth part of Neptune's distance 
 from the sun, and to one half of the distance of his orbit 
 from that of Uranus. 
 
 " Whence comes this enormous difference between the 
 theoretical and observed planets? Had it been quite 
 small, it might have been regarded as an excusable numer- 
 ical error. Had it even amounted to once or twice the 
 radius of the earth's orbit, it might have been deemed an' 
 error, although it would then have been a grievous one, 
 and would have seriously marred the beauty of the result. 
 But, as it is, it cannot be assumed to be a mere error, with- 
 out admitting that such an one radically vitiates the whole 
 theory. Whoever adopts this opinion, be it the author of 
 
APPENDIX. 207 
 
 the theory himself, is bound to show where the error is, 
 and how far it extends. Such an opinion has never been 
 advanced by me, and I am not responsible for it. I admit, 
 however, that I have not fully investigated this point, but 
 maintain that the profound geometry of M. Leverrier is 
 not to be set aside without proof, or even argument. M. 
 Leverrier found that the planet which would best account 
 for the disturbed motion of Uranus was at the mean dis- 
 tance 36 from the sun ; and that, by increasing or de- 
 creasing the mean distance of the hypothetical disturber, 
 the want of coincidence between the observed and com- 
 puted motions of Uranus increased until, at the mean dis- 
 tances of 38 on the increase and 35 on the decrease, the 
 residual differences between theory and observation be- 
 came so great as to be wholly inadmissible. He therefore 
 came to the natural conclusion, from such a result, that 
 the mean distance of the required planet from the sun 
 could not be less than 35, or more than 38 ; and he con- 
 tented himself with this conclusion, without extending his 
 inquiries to still smaller mean distances ; and any facts in 
 regard to these inner distances which are at variance with 
 this result are certainly not to be included under his 
 theory. I have confined my remarks to M. Leverrier's 
 researches, but nothing in Mr. Adams's less comprehensive 
 investigations, in which there is no attempt to ascertain 
 the limits, is opposed to these conclusions. 
 
 " It has been intimated, that too rigorous an agreement 
 ' with observation was insisted upon in the original in- 
 quiries, and that the limits might have been extended to 
 include Neptune, by a more liberal concession to other 
 unknown planets, or to an error in the mass of Saturn. 
 The inspection of the preceding table completely refutes 
 such a suggestion, for it now appears that Neptune satis- 
 
208 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 fies the observations of Urauus more perfectly than the 
 best planet of previous theory. If Leverrier was, as I 
 have supposed, correct in his former computations, he 
 must have found by extending them, that, although the 
 action of his hypothetical planet agreed less perfectly 
 with observation by the contraction of the radius of its 
 orbit from 36 to 35, and that this disagreement would 
 have still further increased by a still further contraction, 
 there was a distance at which the disagreement ceased to 
 increase, and would on the contrary begin to diminish, 
 until at the distance 30 it would have vanished, and the 
 disturbed motions of Urauus would have been wholly ex- 
 plained. But this singular change in the character of the 
 disturbing force, if it really occurs, — and the only doubt 
 in regard to it is derived from a supposed but unproved 
 inaccuracy in Leverrier's investigations, — was excluded 
 from the range of this geometer's investigations ; and now 
 that observation has led to its discovery, geometry cannot 
 claim it as one of its predictions. The defect of the theory 
 must be as frankly admitted, as the more serious charge of 
 error is boldly repelled. 
 
 " From some indistinct remarks which have been 
 thrown out in regard to the mass of Neptune, which is 
 not too small to be excluded from the limits of the theory, 
 there seems to be an indisposition to confess this defect. 
 But on turning to the original formulae, it will be found 
 that, although this small mass is not positively excluded, 
 its adoption does not contribute to advance the claim of 
 geometry upon the planet. It shows, on the contrary, 
 most decisively, that the orbits of theory are aU of them 
 fundamentally different from those of Neptune. For 
 the mean distance which corresponds to this mass in the 
 theory is about 35^, and the eccentricity very much 
 
APPENDIX. 209 
 
 greater than in the best hypothetical orbit, while the dis- 
 crepancy between the theoretical and observed action on 
 Uranus is increased beyond the admitted limits. 
 
 " The case might safely rest there ; but I desire to 
 dwell upon the essential and radical diiference between 
 Neptune's action upon Uranus and that of the planets of 
 theory. For this purpose, I will read an extract from a 
 report made by me last September to the honorable com- 
 mittee of the Overseers of Harvard University who visited 
 the Observatory : — 
 
 " ' The differences are not accidental, but inherent in 
 the very nature of the case, while the points of resem- 
 blance are purely accidental. The solutions of Adams 
 and Leverrier are perfectly correct for the assumption to 
 which they are limited, and must be classed with the bold- 
 est and most brilliant attempts at analytical investigation, 
 richly entitling their authors to all the eclat which has 
 been lavished upon them on account of the singular suc- 
 cess with which they are thought to have been crowned. 
 But their investigations are nevertheless wholly inappli- 
 cable to the theory of the mutual perturbations of Uranus 
 and Neptune. The successive periods of conjunction and 
 opposition, occurring at intervals of eighty-four years, — 
 that is, in about the time of revolution of Uranus, — this 
 planet is always at the same part of its orbit when it is most 
 affected by the action of Neptune. The action of Neptune, 
 consequently, assumes a fixed, permanent, undisturbed 
 character, so that it can hardly be recognized as pertur- 
 bation by the practical observer. It is far otherwise with 
 the ordinary class of perturbations, where the place of 
 greatest disturbance varies from point to point of the 
 orbit ; thus the place of greatest disturbance in the case of 
 the theoretical planet would not have remained stationary, 
 14 
 
210 IDEALITY IN THE PHYSICAL SCIENCES. 
 
 but have varied 80° upon the orbit of Uranus at each 
 successive conjunction and opposition; so that the dis- 
 turbance could not in this case be disguised to any great 
 extent under the fixed laws of ordinary elliptic motion. 
 In the case of Neptiine, its action on Uranus is to be 
 detected in the comparatively small diiferences between 
 its character and that of an elliptic motion, and the differ- 
 ence between the influence at opposition and that at con- 
 junction. In undertaking, therefore, anew the solution of 
 the problem of the perturbations of Uranus, with the 
 assumption of the actual period of Neptune, instead of 
 that adopted in the former theories, I found at once that 
 I could not profit by the previous researches of Adams 
 and Leverrier. The problem now presented, instead of 
 being of the usual character, assumed a differential form 
 by the disguise of the primary perturbations imder the 
 aspect of elliptic motions, and the whole question now 
 rested upon the secondary perturbations, which were com- 
 paratively unimportant in the previous theories.' ..." 
 (Ibid., pp. 338-341.) 
 
 The full list of references in this matter is as fol- 
 lows : Proceedings of the American Academy, i. 41, 
 57-68, 144-149, 285-295, 332-342. 
 
 The view which was maintained by M. Leverrier 
 will be found in the Comptes Bendus, xxvii. 273-279, 
 325-333. 
 
 It has sometimes been urged that M. Leverrier's 
 problem was simply to point out the place of the new 
 planet ia the heavens ; and that problem he undoubt- 
 edly successfully solved. But this by no means des- 
 cribes the scope of his endeavor. His contention 
 was — and it was this which gave the, true ^cZa^to his 
 
APPENDIX. 211 
 
 prediction — that he had accomplished his result by 
 first calculating the elements of the unknown body; 
 as is emphatically shown by the remarks of M. Arago, 
 made at the Academy of Sciences in Paris, 19 Oc- 
 tober 1846. {Comptes Bendus, xxiii. 746.) 
 
 Many years later. Professor Peirce resumed the 
 consideration of this question, and made an investi- 
 gation, which occupied him for several months, of the 
 whole range of space in which it would have been 
 possible to find a planet, having an orbit of small 
 eccentricity, and accounting for the observed irregu- 
 larities in the motion of Uranus. The results of this 
 computation were very curious, and confirmed Pro- 
 fessor Peirce, as he has stated in his sixth lecture, in 
 the views above cited ; but they were never reduced 
 to a publishable form. 
 
 THE END. 
 

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