自然哲学的数学原理-6

when it went frpm it; that he could not say when this cometwould drop into the sun ;it might perhaps have five or six revolutions more first, but whenever it did it would so much increasethe heat of the sun that this earth would be burned, and no animals in it could live. That he took the three phenomena, seenby Hipparchus, Tycho Brahe, and Kepler s disciples, to have beenof this kind, for he could not otherwise account for an extraordinary light, as those were, appearing, all at once, among thethe fixed stars (all which he took to be suns, enlightening otherplanets, as our sun does ours), as big as Mercury or Venus seemsto us, and gradually diminishing, for sixteen months, and thensinking into nothing. He seemed to doubt whether there werenot intelligent beings, superior to us, who superintended theserevolutions of the heavenly bodies, by the direction of the SupremeBeing. He appeared also to be very clearly of opinion that theinhabitants of this world were of short date, and alledged, as onereason for that opinion, that all arts, as letters, ships, printing,needle, &c., were discovered within the memory of history, whichcould not have happened if the world had been eternal; and thatthere were visible marks of ruin upon it which could not beeffected by flood only. When I asked him how this earth couldhave been repeopled if ever it had undergone the same fateit was threatened with hereafter, by the comet of 1680, heanswered, that required the power of a Creator. He said hetook all the planets to be composed of the same matter with thisearth, viz. : earth, water, stones, &c.3 but variously concocted. JLIFE OP SIR ISAAC NEWTON. 55asked him why he would not publish his conjectures, as conjectures, and instanced that Kepler had communicated his; andthough he had not gone near so far as Kepler, yet Kepler sguesses were so just and happy that they had been proved anddemonstrated by him. His answer was, " I do not deal in conjectures." But, on my talking to him about the four observationsthat had been made of the comet of 1680, at 574 years distance,and asking him the particular times, he opened his Principia,which laid on the table, and showed me the particular periods,viz.: 1st. The Julium Sidus, in the time of Justinian, in 1106,in 1680." And I, observing that he said there of that comet, incidetin corpus solis, and in the next paragraph adds, stellae fixaerefici possunt, told him I thought he owned there what we hadbeen talking about, viz. : that the comet would drop into the sun,and that fixed stars were recruited and replenished by cometswhen they dropped into them ; and, consequently, that the sunwould be recruited too ; and asked him why he would not own asfully what he thought of the sun as well as what he thought ofthe fixed stars. He said, that concerned us more; and, laughing, added, that he had said enough for people to know hismeaning."In the summer of 1725, a French translation of the chronological MS., of which the Abbe Conti had been permitted, sometime previous, to have a copy, was published at Paris, in violationof all good faith. The Punic Abbe had continued true to hispromise of secrecy while he remained in England ; but no soonerdid he reach Paris than he placed the manuscript into the handsof M. Freret, a learned antiquarian, who translated the work, andaccompanied it with an attempted refutation of the leading pointsof the system. In November, of the same year, Newton receiveda presentation copy of this publication, which bore the title ofABREGE DE CHRONOLOGIE DE M. LE CHEVALIER NEWTON, FAITPAR LUI-MEME, ET TRADUIT SUR LE MANUSCRIPT ANGLAIS. Soonafterward a paper entitled, REMARKS ON TFE OBERVATIONS MADEON A CHRONOLOGICAL INDEX OF SIR ISAAC NE.WTON, TRANSLATEDINTO FRENCH BY THE OBSERVATOR, ANL PUBLISHED AT PARIS,56 LIFE OF SIR ISAAC NEWTON,was drawn up by our author, and printed in the PhilosophicalTransactions for 1725. It contained a history of the wholematter, and a triumphant reply to the objections of M. Freret.This answer called into the field a fresh antagonist, Father Soueiet,whose five dissertations on this subject were chiefly remarkablefor the want of knowledge and want of decorum, which theydisplayed. In consequence of these discussions, Newton was induced to prepare his larger work for the press, and had nearlycompleted it at the time of his death. It was published in 1728,under the title of THE CHRONOLOGY OF THE ANCIENT KINGDOMSAMENDED, TO WHICH is PREFIXED A SHORT CHRONICLE FROM THEFIRST MEMORY OF THINGS IN EUROPE TO THE CONQUEST OFPERSIA BY ALEXANDER THE GREAT. It consists of six chapters: 1. On the Chronology of the Greeks; according to Whiston,our author wrote out eighteen copies of this chapter with hisown hand, differing little from one another. 2. Of the Empireof Egypt; 3. Of the Assyrian Empire; 4. Of the two contemporary Empires of the Babylonians and Medes ;5. A Descriptionof the Temple of Solomon ;6. Of the Empire of the Persians ;this chapter was not found copied with the other five, but as itwas discovered among his papers, arid appeared to be a continuation of the same work, the Editor thought proper to add itthereto. Newton s LETTER TO A PERSON OF DISTINCTION WHOHAD DESIRED HIS OPINION OF THE LEARNED BlSHO^ LLOYD SHYPOTHESIS CONCERNING THE FORM OF THE MOST ANCIENT^EAR, closes this enumeration of his Chronological Writings.A ihird edition of the PRINCIPIA appeared in 1726, with manychanges and additions. About four years were consumed in itspreparation and publication, which were under the superintendanceof Dr. Henry Pemberton, an accomplished mathematician,and the author of "A VIEW OF SIR ISAAC NEWTON S PHILOSOPHY." 1728. This gentleman enjoyed numerous opportunitiesof conversing with the aged and illustrious author. " I found,"says Pemberton, " he had read fewer of the modern mathematicians than one could have expected; but his own prodigiousinvention readily supplied him with what he might have an occasion for in the pursuit of any subject he undertook. I have oftenLIFE OF SIR ISAAC NEWTON. 57heard him censure the handling geometrical subjects ly algebraiccalculations ; and his book of Algebra he called by the name ofUniversal Arithmetic, in opposition to the injudicious title ofGeometry, which Descartes had given to the treatise, wherein heshows how the geometer may assist his invention by such kindof computations. He thought Huygens the most elegant of anymathematical writer of modern times, and the most just imitatorof the ancients. Of their taste and form of demonstration, SirIsaac always professed himself a great admirer. I have heardhim even censure himself for not following them yet more closelythan he did ; and speak with regret of his mistake at the beginning of his mathematical studies, in applying himself to the worksof Descartes and other algebraic writers, before he had consideredthe elements of Euclid with that attention which so excellent awriter deserves."" Though his memory was much decayed," continues Dr. Pemberton,"he perfectly understood his own writings." And eventhis failure of memory, we would suggest, might have been moreapparent than real, or, in medical terms, more the result of functional weakness than organic decay. Newton seems never tohave confided largely to his memory : and as this faculty manifests the most susceptibility to cultivation ; so, in the neglect ofdue exercise, it more readily and plainly shows a diminution ofits powers.Equanimity and temperance had, indeed, preserved Newtonsingularly free from all mental and bodily ailment. His hair was,to the last, quite thick, though as white as silver. He nevermade use of spectacles, and lost but one tooth to the day of hisdeath. He was of middle stature, well-knit, and, in the latterpart of his life, somewhat inclined to be corpulent. Mr. Conduitsays," he had a very lively and piercing eye, a comely and gracious aspect, with a fine head of hair, white as silver, without anybaldness, and when his peruke was off was a venerable sight."According to Bishop Atterbury, "in the whole air of his face andmake there was nothing of that penetrating sagacity whichappears in his compositions. He had something rather languidin his look and manner which did not raise any great expectation58 LIFE OF SIR ISAAC NEWTON.in those who did not know him." Hearne remarks, " Sir Isaacwas a man of no very promising aspect. He was a short, wellsetman. He was full of thought, and spoke very little in company, so that his conversation was not agreeable. When he rodein his coach, one arm would be out of his coach on one side andthe other on the other." These different accounts we deemeasily reconcilable. In the rooms of the Royal Society, in thestreet, or in mixed assemblages, Newton s demeanour alwayscourteous, unassuming and kindly still had in it the overawingsof a profound repose and reticency, out of which the communicative spirit, and the "lively and piercing eye" would only gleamin the quiet and unrestrained freedom of his own fire-side." But this I immediately discovered in him," adds Pemberton,still further, "which at once both surprised and charmed me.Neither his extreme great age, nor his universal reputation hadrendered him stiff in opinion, or in any degree elated. Of this Ihad occasion to have almost daily experience. The remarks Icontinually sent him by letters on his Principia, were receivedwith the utmost goodness. These were so far from being anyways displeasing to him, that, on the contrary, it occasioned himto speak many kind things of me to my friends, and to honour mewith a public testimony of his good opinion." A modesty, openness, and generosity, peculiar to the noble and comprehensivespirit of Newton. " Full of wisdom and perfect inbeauty," yetnot lifted up by pride nor corrupted by ambition. None, however, knew so well as himself the stupendousness of his discoveriesin comparison with all that had been previously achieved ; andnone realized so thoroughly as himself the littleness thereof incomparison with the vast region still unexplored. A short timebefore his death he uttered this memorable sentiment: " I do notknow what I may appear to the world ; but to myself I seem tohave been only like a boy playing on the sea-shore, and divertingmyself in now and then finding a smoother pebble or a prettiershell than ordinary, while the great ocean of truth lay all undiscovered before me." How few ever reach the shore even, muchless find "a smoother pebble or a prettier shell!"Newton had now resided about two years at Kensington ; andLIFE OF SIR ISAAC NEWTON. 59the air which he enjoyed there, and the state of absolute rest,proved of great benefit to him. Nevertheless he would occasionally go to town. And on Tuesday, the 28th of February, 1727,he proceeded to London, for the purpose of presiding at a meetingof the Royal Society. At this time his health was considered,by Mr. Conduit, better than it had been for many years. Butthe unusual fatigue he was obliged to suffer, in attending themeeting, and in paying and receiving visits, speedily produced aviolent return of the affection in the bladder. He returned toKensington on Saturday, the 4th of March. Dr. Mead and Dr.Cheselden attended him ; they pronounced his disease to be thestone, and held out no hopes of recovery. On Wednesday, the15th of March, he seemed a little better; and slight, thoughgroundless, encouragement was felt that he might survive theattack. From the very first of it, his sufferings had been intense.Paroxysm followed paroxysm, in quick succession : large drops)f sweat rolled down his face ; but not a groan, not a complaint,not the least mark of peevishness or impatience escaped him :and during the short intervals of relief, he even smiled and conversed with his usual composure and cheerfulness. The fleshquivered, but the heart quaked not ; the impenetrable gloom wassettling down : the Destroyer near ; the portals of the tombopening, still, arnid this utter wreck and dissolution of the mortal,the immortal remained serene, unconquerable : the radiant lightbroke through the gathering darkness ; and Death yielded up itssting, and the grave its victory. On Saturday morning, 18th,he read the newspapers, and carried on a pretty long conversationwith Dr. Mead. His senses and faculties were then strong andvigorous ; but at six o clock, the same evening, he became insensible ; and in this state he continued during the whole of Sunday,and till Monday, the 20th, when he expired, between one andtwo o clock in the morning, in the eighty-fifth year of his age.And these were the last days of Isaac Newton. Thus closedthe career of one of earth s greatest and best men. His missionwas fulfilled. Unto the Giver, in many-fold addition, the talentswere returned. While it was yet day he had worked ; and forthe night that quickly cometh he was not unprepared. Full of60 LIFE OF SIR ISAAC NEWTON.years, ind full of honours, the heaven-sent was recalled ; and, inthe confidence of a " certain hope," peacefully he passed awa}into the silent depths of Eternity.His body was placed in Westminster Abbey, with the stateand ceremonial that usually attended the interment of the mostdistinguished. In 1731, his relatives, the inheritors of his personalestate, erected a monument to his memory in the most conspicuous part of the Abbey, which had often been refused by the deanand chapter to the greatest of England s nobility. During thesame year a medal was struck at the Tower in his honour ; arid,in 1755, a full-length statue of him, in white marble, admirablyexecuted, by Roubiliac, at the expense of Dr. Robert Smith, waserected in the ante-chamber of Trinity College, Cambridge.There is a painting executed in the glass of one of the windowsof the same college, made pursuant to the will of Dr. Smith, wholeft five hundred pounds for that purpose.Newton left a personal estate of about thirty-two thousandpounds. It was divided among his four nephews and four niecesof the half blood, the grand-children of his mother, by the Reverend Mr. Smith. The family estates of Woolsthorpe arid Susternfell to John Newton, the heir-at-law, whose great grand-fatherwas Sir Isaac s uncle. Before his death he made an equitabledistribution of his two other estates : the one in Berkshire to thesons and daughter of a brother of Mrs. Conduit ; and the other,at Kensington, to Catharine, the only daughter of Mr. Conduit,and who afterward became Viscountess Lymington. Mr. Conduit succeeded to the offices of the Mint, the duties of which hehad discharged during the last two years of Sir Isaac s life.Our author s works are found in the collection of Castilion,Berlin, 1744, 4to. 8 torn.; in Bishop Horsley s Edition, London,1779, 4to. 5 vol.; in the Biographia Brittannica, &c. Newtonalso published Bern. Varcnii Geographia, &c., 1681, 8vo.There are, however, numerous manuscripts, letters, and otherpapers, which have never been given to the world: these arepreserved, in various collections, namely, in the library of TrinityCollege, Cambridge ;in the library of Corpus Christi College,Oxford ;in the library of Lord Macclesfield : and, lastly aridLIFE OF SIR ISAAC NEWTON. 61chiefly, in the possession of the family of the Earl of Portsmouth,through the Viscountess Lymington.Everything appertaining to Newton has been kept and cherished with peculiar veneration. Different memorials of him arepreserved in Trinity College, Cambridge ;in the rooms of theRoyal Society, of London : and in the Museum of the RoyalSociety of Edinburgh.The manor-house, at Woolsthorpe, was visited by Dr. Stukeley, in October, 1721, who, in a letter to Dr. Mead, written in1727, gave the following description of it: " Tis built of stone,as is the way of the country hereabouts, and a reasonably goodone. They led me up stairs and showed me Sir Isaac s stud}-,where I supposed he studied, when in the country, in his youngerdays, or perhaps when he visited his mother from the University.I observed the shelves were of his own making, being pieces ofdeal boxes, which probably he sent his books and clothes downin on those occasions. There were, some years ago, two or threrhundred books in it of his father-in-law, Mr. Smith, which SirIsaac gave to Dr. Newton, of our town." The celebrated appletree,the fall of one of the apples of which is said to have turnedthe attention of Newton to the subject of gravity, was destroyedby the wind about twenty years ago ; but it has been preservedin the form of a chair. The house itself has been protected withreligious care. It was repaired in 1798, and a tablet of whitemarble put up in the room where our author was born, with thefollow, ng inscription :" Sir Isaac Newton, son of John Newton, Lord of the Manorof Woolsthorpe, was born in this room, on the 25th of December,1642."Nature and Nature s Laws wei-e hid in night,God said, " Let NEWTON be," and all was light.THE PEINCIPIA.THE AUTHOR S PREFACESINCE the ancients (as we are told by Pappus), made great account oithe science of mechanics in the investigation of natural things : and themoderns, laying aside substantial forms and occult qualities, have endeavoured to subject the phenomena of nature to the laws of mathematics, Ihave in this treatise cultivated mathematics so far as it regards philosophy.The ancients considered mechanics in a twofold respect ; as rational, whichproceeds accurately by demonstration ; and practical. To practical mechanics all the manual arts belong, from which mechanics took its name.Rut as artificers do not work with perfect accuracy, it comes to pass thatmechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical , what is less so, is called mechanical. But theerrors are not in the art, but in the artificers. He that works with lessaccuracy is an imperfect mechanic ; and if any could work with perfectaccuracy, he would be the most perfect mechanic of all; for the descriptionif right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requiresthem to be drawn ;for it requires that the learner should t be taughtto describe these accurately, before he enters upon geometry ; then it showshow by these operations problems may be solved. To describe right linesand circles are problems, but not geometrical problems. The solution ofthese problems is required from mechanics ; and by geometry the use ofthem, when so solved, is shown ; and it is the glory of geometry that fromthose few principles, brought from without, it is able to produce so manythings. Therefore geometry is founded in mechanical practice, and isnothing but that part of universal mechanics which accurately proposesand demonstrates the art of measuring. But since the manual arts arechiefly conversant in the moving of bodies, it comes to pass that geometryis commonly referred to their magnitudes, and mechanics to their motion.In this sense rational mechanics will be the science of motions resultingfrom any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. This part of mechanics wasi:;vm THE AUTHOR & PREFACE.cultivated by the ancients in the five powers which relate to manual arts,who considered gravity (it not being a manual power), ho Otherwise thanas it moved weights by those powers. Our design not respecting arts, butphilosophy, and our subject not manual but natural powers, we considerchiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive ; andtherefore we offer this work as the mathematical principles :f philosophy ;forall the difficulty of philosophy seems to consist in this from the phenomena of motions to investigate the forces of nature, and then from theseforces to demonstrate the other phenomena ; and to this end the generalpropositions in the first and second book are directed. In the third bookwe give an example of this in the explication of the System of the World :for by the propositions mathematically demonstrated in the former books,we in the third derive from the celestial phenomena the forces of gravitywith which bodies tend to the sun and the several planets. Then from theseforces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could dorivethe rest of the phenomena of nature by the same kind of reasoning frommechanical principles; for I am induced by many reasons to suspect thatthey may all depend upon certain forces by which the particles of bodies.by some causes hitherto unknown, are either mutually impelled towardseach other, and cohere in regular figures, or are repelled and recede fromeach other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain ; but I hope the principles here laiddown will afford some light either to this or some truer method of philosophy.In the publication of this work the most acute and universally learnedMr. Edmund Halley not only assisted me with his pains in correcting thepress and taking care of the schemes, but it was to his solicitations that itsbecoming public is owing ; for when he had obtained of me my demonstrations of the figure of the celestial orbits, he continually pressed me to communicate the same to the Royal Societ//, who afterwards, by their kind encouragement and entreaties, engaged me to think of publishing them. Butafter I had begun to consider the inequalities of the lunar motions, andhad entered upon some other things relating to the laws and measures oigravity, and other forces : and the figures that would be described by bodiesattracted according to given laws ; and the motion of several bodies movingamong themselves; the motion of bodies in resisting mediums; the forces,densities, and motions, of rn( Hums ; the orbits of the comets, and such like ;Ixixdeferred that publication till I had made a searcli into those matters, andcould put forth the whole together. What relates to the lunar motions (being imperfect), I have put all together in the corollaries of Prop. 66, toavoid being obliged to propose and distinctly demonstrate the several thingsthere contained in a method more prolix than the subject deserved, and interrupt the series of the several propositions. Some things, found out afterthe rest, I chose to insert in places less suitable, rather than change thenumber of the propositions and the citations. I heartily beg that what 1have here done may be read with candour; and that the defects in asubject so difficult be not so much reprehended as kindly supplied, and investigated by new endeavours of mv readers.ISAAC NEWTON.Cambridge, Trinity Coupge May 8, liHB.In the second edition the second section of the first book was enlarged.In the seventh section of the second book the theory of the resistances of fluidswas more accurately investigated, and confirmed by new experiments. In