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## CHAPTER XII.

THE FIRST IDEA OF GRAVITY OCCURS TO NEWTON IN 1665 — HIS FIRST SPECULATIONS UPON IT — HE ABANDONS THE SUBJECT FROM HAVING EMPLOYED AN ERRONEOUS MEASURE OF THE EARTH'S RADIUS — HE RESUMES THE SUBJECT IN CONSEQUENCE OF A DISCUSSION WITH DR. HOOKE, BUT LAYS IT ASIDE, BEING OCCUPIED WITH HIS OPTICAL EXPERIMENTS — BY ADOPTING PICARD'S MEASURE OF THE EARTH HE DISCOVERS THE LAW OF GRAVITY, AND THE CAUSE OF THE PLANETARY MOTIONS — DR. HALLEY GOES TO CAMBRIDGE, AND URGES HIM TO PUBLISH HIS TREATISE ON MOTION — THE GERM OF THE PRINCIPIA WHICH WAS COMPOSED IN 1685 AND 1686 — CORRESPONDENCE WITH FLAMSTEED — MANUSCRIPT OF PRINCIPIA SENT TO THE ROYAL SOCIETY — HALLEY UNDERTAKES TO PUBLISH IT AT HIS OWN EXPENSE — DISPUTE WITH HOOKE, WHO CLAIMS THE DISCOVERY OF THE LAW OF GRAVITY — THE PRINCIPIA PUBLISHED IN 1687 — THE NEW EDITION OF IT BY COTES BEGUN IN 1709, AND PUBLISHED IN 1713 — CHARACTER AND CONTENTS OF THE WORK — GENERAL ACCOUNT OF THE DISCOVERIES IT CONTAINS — THEY MEET WITH OPPOSITION FROM THE FOLLOWERS OF DESCARTES — THEIR RECEPTION IN FOREIGN COUNTRIES — PROGRESS OF THE NEWTONIAN PHILOSOPIIY IN ENGLAND AND SCOTLAND.

Such is a brief and general view of the labours and lives of those illustrious men who prepared the science of Astronomy for the application of Newton's genius. Copernicus had determined the form of the Solar System, and the relative position and movements of the bodies that composed it. Kepler had proved that the planets revolve in elliptical orbits; that their radii vectores describe areas proportional to the times; and that the squares of their periodic times are as the cubes of their distances from the sun. Galileo had added to the universe a whole <290> system of secondary planets. Huygens had given to Saturn a satellite, and the strange appendage of a ring; and, while some astronomers had maintained the doctrine of universal gravitation, others had referred the motions to an attractive force, diminishing with the square of the distance, and producing a curvilineal motion from one in a straight line.[1]

We have already seen that, in the autumn of 1665, Newton was led to the opinion that the same power by which an apple falls from a tree extends to the moon, and retains her in her orbit; but upon making the calculation, he found such a discrepancy between the two forces that he abandoned the subject, suspecting that the power which retained the moon in her orbit might be partly that of gravity, and partly that of the vortices of Descartes.[2] This discrepancy arose from the adoption of an erroneous measure of the semi-diameter of the earth, of which the moon's distance was taken as a multiple. Unacquainted with the more accurate determinations of Snellius[3] and Norwood,[4] the last of which would have given Newton the exact quantity which he required, he adopted the measure of sixty miles for a degree of latitude, which had been employed by the old geographers and seamen, and in which, as Mr. Rigaud conjectures, he may have placed the more confidence, as it agreed with the result of the observations which Edward Wright, a Cambridge mathematician, had published in 1610.

It does not distinctly appear at what time Newton became acquainted with the more accurate measurement <291> of the earth, executed by Picard in 1670, and was thus led to resume his investigations. Picard's method of measuring his degree, and the precise result which he obtained, were communicated to the Royal Society on the 11th January 1672,[5] and the results of his observations and calculations were published in the Philosophical Transactions for 1675. But whatever was the time when Newton became acquainted with Picard's measurement, it seems to be quite certain that he did not "resume his former thoughts concerning the moon" till 1684. Pemberton tells us, that "some years after he laid aside" his former thoughts, "a letter from Dr. Hooke put him on inquiring what was the real figure in which a body, let fall from any high place, descends, taking the motion of the earth round its axis into consideration;" and that this gave occasion to his resuming his former thoughts concerning the moon, and determining, from Picard's recent measures, that "the moon appeared to be kept in her orbit purely by the power of gravity."[6] But though <292> Hooke's letter of 1679 was the occasion of Newton's resuming his inquiries, it does not fix the time when he employed the measures of Picard. In a letter from Newton to Halley in 1686, he tells him that Hooke's letters in 1679 were the cause of his "finding the method of determining the figures, which, when I had tried in the ellipsis, I threw the calculations by, being upon other studies; and so it rested for about five years, till, upon your request, I sought for the papers." Hence Mr. Rigaud considers it clear, that the figures here alluded to were the paths of bodies acted upon by a central force, and that the same occasion induced him to resume his former thoughts concerning the moon, and to avail himself o Picard's measures to correct his calculations. It was, therefore, in 1684, that Newton discovered that the moon's deflexion in a minute was sixteen feet, the same as that of bodies at the earth's surface. As his calculations drew to a close, he is said to have been so much agitated tha he was obliged to desire a friend to finish them.[7]

<293>

Sir Christopher Wren and Hooke and Halley had each of them, from independent considerations, concluded that "the centripetal force decreased in the proportion of the squares of the distances reciprocally."[8] Halley had in 1683-4 derived this law "from the consideration of the sesquialterate proportion of Kepler," but was unsuccessful in his attempts to demonstrate by it the laws of the celestial motions. Sir Christopher Wren had "very many years" before 1686, attempted by the same law "to make out the planet's motion by a descent towards the sun, and an impressed motion," but had "given it over, not finding the means of doing it;" and Dr. Hooke, as we have already seen, though he adopted the law of the squares, never fulfilled his promise of proving that it could be applied to the motions of the planets.[9] It is therefore to Newton <294> alone that we owe the demonstration of the great truth, that the moon is kept in her orbit by the same power by which bodies fall on the earth's surface.

The influence of such a result upon such a mind, may be more easily conceived than described. If the force of the earth's gravity bends the moon into her orbit, the satellites of the other planets must be guided by the same power in their primaries, and the attractive force of the sun must in like manner control the movements of the comets and the planets which surround him. In the application of this grand truth to the motions of the Solar System, and to the perturbations arising from the mutual action of the bodies that compose it, Newton must have rejoiced in the privilege of laying the foundation of so magnificent a work, while he could not fail to see that the completion of it would be the achievement of other minds, and the glory of another age. But, however fascinating must have been the picture thus presented to his mind, it was still one of limited extent. He knew not of the existence of binary and multiple systems of stars, to which the theory of universal gravitation would be extended. He could not have anticipated that Adams and Leverrier would have tracked an unseen planet to its place by the perturbations it occasioned : Nor could he have conjectured that his own theory of gravitation might detect the origin and history of nearly thirty planetary bodies, revolving within a sphere apparently destined for one. It was enough for one man to see what Newton saw. The service in the Temple of Science must be performed by many priests; and fortunate is he who is called to the humblest task at its altar. The revelations of infinite wisdom are not vouchsafed to man in a day. A light so effulgent would paralyze the noblest intellect. It must <295> break in upon it by degrees; and even each separate ray must be submitted to the ordeal of various minds, — to the apprentice skill of one age, and to the master genius of another.

It is not easy to determine the exact time when Newton first adopted the great truth, "that the forces of the planets from the sun are reciprocally duplicate of their distances from him," but there is sufficient evidence to shew that it must have been as early as 1666, and therefore contemporaneous with his speculations on Gravity in his garden at Woolsthorpe. "In one of my papers," says he,[10] "writ, (I cannot say in what year,) but I am sure some time before I had any correspondence with Oldenburg,[11] and that's above fifteen years ago, (1671,) the proportion of the forces of the planets from the sun, reciprocally duplicate of their distances from him, is expressed, and the proportion of our gravity to the moon's conatus recedendi a centro terræ, is calculated, though not accurately enough. That when Hugenius put out his Horologium Oscillatorium, a copy being presented to me, in my letter of thanks to him I gave those rules in the end thereof a particular commendation for their usefulness in philosophy, and added, out of my aforesaid paper, an instance of their usefulness in comparing the forces of the moon from the earth, and the earth from the sun; in determining a problem about the moon's phase, and putting a limit to the sun's parallax, which shews that I had then my eye upon comparing the forces of the planets arising from their circular motion, and understood it; so that a while after when Mr. Hooke propounded the problem solemnly <296> in the end of his attempt to prove the motion of the earth, if I had not known the duplicate proportion before, I could not but have found it now." In another letter to Halley, written about three weeks afterwards,[12] he distinctly states, that "for the duplicate proportion I can affirm that I gathered it from Kepler's theorem about twenty years ago," that is, in 1666. Hence it is obvious that the written paper referred to by Newton was, as Mr. Rigaud says, "the result of his early speculations at Woolsthorpe," and that "the deduction from Kepler, which is said to have preceded the calculation[13] by a twelvemonth, took place in 1665."

Such was the state of Newton's knowledge regarding the law of gravity, when, in January 1684, Halley, Wren, and Hooke were discussing together the subject in London. Halley had learned from this interview that neither of his friends possessed a "convincing demonstration" of this law, and finding, after a delay of some months, that Hooke "had not been so good as his word," in shewing his demonstration to Wren, he set out for Cambridge in the month of August 1684, to consult Newton on the subject.[14] Without mentioning either his own specula <297> tions, or those of Hooke and Wren, he at once indicated the object of his visit by asking Newton what would be the curve described by the planets on the supposition that gravity diminished at the square of the distance. Newton immediately answered, an Ellipse. Struck with joy and amazement, Halley asked him how he knew it ? Why, replied he, I have calculated it; and being asked for the calculation, he could not find it, but promised to send it to him. After Halley left Cambridge, Newton endeavoured to reproduce the calculation, but did not succeed in obtaining the same result. Upon examining carefully his diagram and calculation, he found that in describing an ellipse coarsely with his own hand, he had drawn the two axes of the curve instead of two conjugate diameters somewhat inclined to one another. When this mistake was corrected he obtained the result which he had announced to Halley.[15]

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That Halley and Paget would, without delay, remind Newton of his promise, and that Newton would fulfil it there can be no doubt; and we accordingly find that about the middle of February he had sent to Mr. Aston, one of the Secretaries of the Royal Society, his "notions about motion." Mr. Aston, as a matter of course, would thank Newton for the communication, and mention the fact of its being registered; and that all this was done, appears from a letter of Newton's to Aston of the 23d February, 1685, written on another subject, but thanking him for "having entered on the register his notions about motion." Newton added, "I designed them for you before now, but the examining several things has taken a greater part of my time than I expected, and a great deal of it to no purpose. And now I am to go into Lincolnshire for a month or six weeks. Afterwards I intend to finish it as soon as I can conveniently."

The treatise De Motu, thus registered in the books of the Royal Society, was the germ of the Principia, and was obviously intended to be a brief exposition of the system which that work was to establish. It occupies twenty-four octavo pages, and consists of four theorems and seven problems, four of the theorems and four of the problems containing the more important truths which are demonstrated in the second and third sections of the First Book of the Principia.[18]

<300>

The years 1685 and 1686 will ever be memorable in the life of Newton, and in the history of science. It was in these two years, and in the early months of 1687, that he composed the Principia and gave it to the world, and all the details connected with this great event have been carefully preserved for the instruction and gratification of posterity. The personal history of the philosopher, therefore, during this period, the nature of his correspondence and inquiries, and all the mechanical and even commercial circumstances under which his great work <301> was written, and printed and published, are subjects which cannot be overlooked in any extended account of his life and writings. Although Newton had identified the law of gravity on the earth with the same law at the moon, yet he required the aid of the practical astronomer in enabling him to apply his theory to the motions of the planets and comets of the system. Fortunately for Newton, Flamsteed was the Astronomer-Royal at Greenwich.

In November and December 1680, when the great comet appeared, Flamsteed observed it with peculiar care, and, before it had ceased to be visible, he put all its observed places into a little table, which, with his thoughts on the subject of comets, he communicated to Mr. Crompton, Fellow of Jesus College, Cambridge. In this letter, Flamsteed asserted that "the two comets (as they were generally thought) were only one and the same; and he described the line of their motions before and after it passed the sun." Mr. Crompton shewed this letter to Newton, who, in return, addressed a long letter to him, to be sent to Flamsteed, containing observations on Flamsteed's "hypothetical notions," and endeavouring to prove "that the comets of November and December were different comets." The commencement of Newton's letter is very characteristic, and though it is intended to be kind in its expressions, we can conceive a mind like that of Flamsteed regarding it, as he did many years afterwards, as "magisterially ridiculing the opinion for which he thought the arguments convincing and unanswerable."[19] "I thank Mr. Flamsteed," says Newton, "for this kind mention of me in his letters to Mr. Crompton, and, as I commend his wisdom in deferring to publish his hypothetical notions till they have been well consi <302> dered both by his friends and himself, so I shall act the part of a friend in this paper, not objecting against it by way of opposition, but in describing what I imagine might be objected by others, and so leaving it to his consideration. If hereafter he shall please to publish his theory, and think any of the objections I propound need an answer, to prevent their being objected by others, he may describe the objections as raised by himself or his friends in general, without taking any notice of me." After this kind introduction, Newton proceeds, in a long and elaborate letter, to controvert Flamsteed's opinions, and, from the evidence of several Cambridge scholars, to shew that there were two comets, and not one; and also in opposition to Flamsteed, that "more comets go northward than southward." Flamsteed replied to this letter in March 1681,[20] in such complimentary terms, that he could not have taken any offence at Newton's remarks upon his views.[21] He seems to have answered several of Newton's objections, and removed some of his difficulties, but to have failed in satisfying him that there was only one comet in 1680. Newton had been on a visit in the country during almost the whole of March, and, after his return to Cambridge, was prevented, "by some indisposition and other impediments," from replying to Flamsteed till the 16th of April. In this letter "he forbears to urge further" any objections to Flamsteed's hypothesis, and confines himself "to the question of two comets," <303> which he discusses at great length, pertinaciously maintaining an opinion, which, a few years afterwards, he was obliged to abandon.[22]

When, after his return from Lincolnshire to Cambridge, Newton was occupied with the composition of the Principia, he renewed his correspondence with Flamsteed. Many of their letters are lost;[23] but it is obvious, from one of Newton's, dated September 19, 1685, that he had received many useful communications from Flamsteed, and especially regarding Saturn, "whose orbit, as defined by Kepler," Newton "found too little for the sesquialterate proportions." In the other letters written in 1685 and 1686, he applies to Flamsteed for information respecting the orbits of the satellites of Jupiter and Sa <304> turn; — respecting the rise and fall of the spring and neap tides at the solstices and the equinoxes; — respecting the flattening of Jupiter at the poles, which, if certain, he says, would conduce much to the stating the reasons of the precession of the equinoxes; — and respecting the differences between the observed places of Saturn and those computed from Kepler's tables about the time of his conjunction with Jupiter. On this last point the information supplied by Flamsteed was peculiarly gratifying to Newton; and it is obvious from the language of this part of his letter, that he had still doubts of the universal application of the sesquialteral proportion. "Your information," says he, "about the errors of Kepler's tables for Jupiter and Saturn, has eased me of several scruples. I was apt to suspect there might be some cause or other unknown to me which might disturb the sesquialteral proportions, for the influences of the planets one upon another seemed not great enough, though I imagined Jupiter's influence greater than your numbers determine it. It would add to my satisfaction if you would be pleased to let me know the long diameters of the orbits of Jupiter and Saturn, assigned by yourself and Mr. Halley in your new tables, that I may see how the sesquialteral proportion fills the heavens, together with another small proportion which must be allowed for."[24]

In order to explain to Newton the cause of the delay, Halley, in his letter of the 22d May, alleges that it arose from "the President's attendance upon the King, and the absence of the Vice-Presidents, whom the good weather had drawn out of town;" but there is reason to believe that this was not the real cause, and that the delay arose from the unwillingness of the Council to undertake the publication in the present state of their finances.[27]

Such was the emergency in which Halley undertook the labour of editing, and the expense of printing, the <307> Principia, and thus earned the gratitude of Newton and of posterity. We cannot admit that the low state of their funds was any apology for the conduct of the Council in refusing to carry into effect the resolution of a general meeting of the Society. Why did they not borrow the necessary sum on the security of their future income, or subscribe individually to fulfil an honourable obligation, and discharge an important duty? If the nobility and gentry who then composed the Royal Society devolved upon their secretary the payment of expenses which, as a body, they had agreed to defray, let it not be said that it was to the Royal Society that we are indebted for the publication of the Principia. It is to Halley alone that science owes this debt of gratitude : It was he who tracked Newton to his College, who drew from him his great discoveries, and who generously gave them to the world.

Newton's reply to Halley,[28] written after a month's delay, is a remarkable production. He acknowledges that Hooke told him of the duplicate proportion, but that his <309> views were erroneous, as he conceived it "to reach down from hence to the centre of the earth." He confesses "that he himself had never extended the duplicate proportion lower than to the superficies of the earth," and that " before a certain demonstration he found last year (1685) he suspected it did not reach accurately enough down so low." In the rest of the letter he shews very satisfactorily, from letters to Oldenburg and Huygens, and even from this theory of gravity, that he must have been acquainted with the duplicate proportion before his conversation with Hooke.

When Newton had finished this letter, he was informed "by one who had it from another lately present at one of the Society's meetings, that Mr. Hooke had there made a great stir, pretending that Newton had all from him, and desiring they would see that he had justice done him." Roused by what he considered "a very strange and undeserved carriage towards him," he writes an angry postscript to his letter, putting forward the claims of Borelli and Bullialdus to the duplicate proportion, and ungenerously charging Hooke with having derived his knowledge of it from them, and even with having been led to it by perusing his own letter to Huygens, which might have come into his possession after the death of Oldenburg. "My letter," says he, "to Huygens was directed to Mr. Oldenburg, who used to keep the originals. His papers came into Mr. Hooke's possession. Mr. Hooke knowing my hand, might have the curiosity to look into that letter, and thence take the notion of comparing the forces of the planets from their circular motion; and so what he wrote to me afterwards about the rate of gravity might be nothing but the fruit of my own garden. And it's more than I can affirm, that the duplicate proportion <310> was not expressed in that letter."[29] This reasoning is certainly far from being sound. If Hooke had the law of gravity from Borelli and Bullialdus, Newton might have had it from them also; and if Hooke obtained it by the process indicated in the letter to Huygens, which he probably never saw, it follows that Hooke's views were as sound as those expressed in that letter, and that he then knew as much about the law as Newton did. But there is no evidence whatever that Hooke saw the letter.

Halley was much annoyed with the contents of this postscript, and lost no time in replying to it. He gives Newton an account of the interview between Hooke, Wren, and himself, previously described, and which led him to go to Cambridge. He tells him that Hooke's manner of claiming the discovery has been represented in worse colours than it ought, "for he neither made application to the Society for justice, nor pretended you had all from him ;" and he gives "the truth," by telling what really happened at the meeting of the Society, and of the little quarrel between Hooke and his friend Sir John Hoskyns. Halley concludes his letter by begging Newton "not to let his resentments run so high" as to deprive the world of his Third Book, on the theory of comets.

Though ruffled for a moment, Newton's excellent temper soon recovered its serenity. When he understood from Halley that Hooke had been in some respects misrepresented to him, he "wished that he had spared the postscript in his last ;" and he goes on to acknowledge that Hooke's "letters occasioned his finding the method of determining figures which he tried in the ellipsis ;" — that Hooke told him of the experiment with "Halley's <311> pendulum clock at St. Helena, as an argument that gravity was lessened at the equator by the diurnal motion ;" — and that he also told him a third thing which was new to him, and which he would acknowledge if he made use of it, namely, "the deflexion of fallen bodies to the south-east in our latitude." Having thus sincerely told Mr. Halley the case between him and Mr. Hooke, "he considered how best to compose the present dispute," which he thought might be done by the enclosed scholium to the fourth proposition. "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen, Wren, Hooke, and Halley."

On the 30th June, the President was desired by the Council to license Mr. Newton's book, entitled Philosophiæ Naturalis Principia Mathematica, and after Halley had obtained the author's leave about the middle of July to substitute wooden cuts for copperplates, the printing of it was commenced and went on with considerable regularity. The Second Book, though ready for the press in autumn, was not sent till March 1687. The Third Book was presented to the Society on the 6th of April, and the whole work published about midsummer of 1687.[30] It was dedicated to the Royal Society as flourishing under his <312> august Majesty James VII.,[31] and there was prefixed to it a set of beautiful Latin hexameters, addressed by Halley to its immortal author.[32] They began thus —

En tibi norma poli, et divæ libramina molis,

Computus atque Jovis; quas, dum primordia rerum

Pangeret, omniparens leges violare creator

Noluit, æternique operis fundamina fixit,

and ended with the following lines —

Talia monstrantem mecum celebrate camœnis,

Vos qui cœlesti gaudetis nectare vesci,

Newtonum clausi reserantem scrinia veri;

Newtonum Musis charum, cui pectore puro

Phœbus adest, totoque incessit numine mentem,

Nec fas est propius mortali attingere divos.

This great work, as might have been expected, excited a warm interest in every part of Europe. The impression was quickly sold.[33] A copy of the Principia could scarcely be procured in 1691, and at that time an improved edition was in contemplation. Newton himself, though pressed by his friends, had refused to undertake it, and M. Facio D'Huillier, who had studied it with the most minute attention, had intimated to Huygens his design of publishing a new edition.[34] In 1694 Newton resumed the study of the lunar and planetary theories, with the view of rendering more perfect a new edition of his Book; but the difficulty which he experienced in getting the neces <313> sary observations from the Astronomer-Royal, interfered with his investigations, and contributed more than any other cause to prevent him from bringing them to a close. Flamsteed did not sufficiently appreciate the importance of Newton's labours; but while we deeply regret that he should have treated so ungraciously the importunities of his friend, we are disposed to find some apology for his conduct in the infirmities of his health and of his temper.

Mr. Edleston has stated, with much appearance of truth, that the steps taken by Newton's friends at the close of 1695, may have interfered as much as the infirmities of Flamsteed with the completion of the lunar theory ;[35] but whether or not this was the case, there can be no doubt that his appointment to the Wardenship of the Mint in 1696, and to the Mastership in 1699, deferred to a distant day the appearance of a new edition of the Principia. Even in November 1702, when he was visited by Bd. Greves, who saw in his hands an interleaved and corrected copy of the Principia, he would not acknowledge that he had any intention to reprint it.[36] The preparation of his Optics, which was published in April 1704, must have interfered with his revision of the Principia, and it appears, from his letter to Flamsteed, in November 1694, that he was then occupied in preparing a new edition of his great work.[37] His duties at the Mint allowed him but little time for the performance of so laborious a task ; and when his consent was at last obtained to put the work to press, they greatly interrupted its progress.

Dr. Bentley, the distinguished Master of Trinity College, had for a long time solicited and even urged Newton to <314> give his consent to the re-publication of the Principia.[38] In the middle of 1708 he succeeded in removing his scruples, but it was not till the spring of 1709 that he prevailed upon him to entrust the superintendence of it to a young mathematician of great promise, Roger Cotes, Fellow of Trinity College, who had been recently appointed Professor of Astronomy and Experimental Philosophy. On the 21st May 1709, after having been that day with Newton, Bentley announced this arrangement to Cotes. "Sir Isaac Newton," he said, "will be glad to see you in June, and then put into your hands one part of his Book corrected for the press." About the middle of July Cotes went to London, in the expectation doubtless to bring down with him to Cambridge the corrected portion of the Principia. Newton, however, had some farther improvements to make upon it, and promised to send it down in about a fortnight. Cotes was impatient to begin his work, and when a whole month had passed without any intelligence from Newton, he addressed to him the following letter : —

"Cambridge, August 18th, 1709.

" SR, — The earnest desire I have to see a new Edition of yr Princip. makes me somewhat impatient till we receive your Copy of it which You was pleased to promise me about the middle of the last Month, You would send down in about a Fourtnights time. I hope you will pardon me for this uneasiness from which I cannot free myself & for giving You this Trouble to let You know it. I have <315> been so much obliged to You by Yrself & by Yr Book yt (I desire you to believe me) I think myself bound in gratitude to take all the Care I possibly can that it shall be correct . . . . . I take this Opportunity to return You my most hearty thanks for Yr many Favours and Civilitys to me who am

Roger Cotes.

" For Sir Isaac Newton at His House in Jermin Street near St. James's Church Westminster."

No answer was returned to this letter from Cotes, and a long month had passed away when one evening his next-door neighbour, William Whiston, about the end of September, put into his hands "the greatest part of the copy of the Principia," ending with the thirty-second Proposition of the Second Book. In a letter dated October 11, Newton intimated to Cotes that he had sent him by Mr. Whiston "the greatest part of the copy of his Principia, in order to a new edition," thanked him for his letter of the 18th of August, and requested him not to be at the trouble of examining all the Demonstrations, but "to print by the copy sent him, correcting only such faults as occur in reading over the sheets," which would entail upon him "more labour than it was fit to give him." These were the two first letters of that celebrated correspondence between Newton and Cotes, which has lain in Trinity College Library for nearly a century and a half, in spite of the wishes expressed by Dr. Monk,[39] and felt by other admirers of the Principia, "that one of the many accomplished Newtonians who are resident in that society would favour the world by publishing the whole collec <316> tion." Through the liberality of the present Master and Seniors of Trinity College, this has at last been done, and in a manner highly creditable to the learning and talents of Mr. Edleston, by whom the Correspondence is edited.[40] The printing of the Principia went on very slowly, and was not finished till the first week of March 1713. Cotes expressed a wish that Dr. Bentley should write the preface to it, but it was the opinion of Sir Isaac and the Master of Trinity, that the preface should come from the pen of Cotes himself. This he readily undertook, but previous to writing it he addressed the following letter to Dr. Bentley, in order to learn "with what view he thought proper to have it written."

TO DR. BENTLEY.

"March 10th, 1712-13.

Immediately after the arrival of this letter on the 12th, Sir Isaac happened to call upon Dr. Bentley, and they agreed to meet in the evening at Sir Isaac's house, to write a reply to it. They objected to any joint preface "to be fathered by Cotes :" they suggested as the subject of the Preface an account of the work itself, and of the improvements of the new edition, and they answered that he has Sir Isaac's consent "to add what he thought proper about the controversy of the first invention, you yourself being full master of it, and want no hints to be given you." Cotes was also instructed "to spare the name of M. Leibnitz, and abstain from all words and epithets of reproach." In reply to this letter on the 18th March, Cotes sketched the plan of the Preface in conformity with the directions already given him, and asks Newton for permission to appeal to the judgment of the Society in the Commercium Epistolicum. To this Newton answers, that if any farther Preface is written, "he must not see it, as he finds he shall be examined about it." The plan of the Preface is therefore altered, and the proposed notice of the dispute respecting the discovery of <318> fluxions is abandoned. Cotes confines himself to an exposition of "the manner of philosophizing made use of" in the Principia, and to an examination of the objections of Leibnitz and of the theory of vortices.

The general Preface thus drawn up by Cotes, is dated 13th May 1713, and in a subsidiary Preface, dated March 2d, Sir Isaac himself mentions the leading alterations which have been made in the New Edition. "In the second section of the First Book," he says, "the determination of the force by which bodies may revolve in given orbits, is simplified and enlarged. In the seventh section of the Second Book, the theory of the resistance of fluids is more accurately investigated, and confirmed by new experiments; and in the Third Book the theory of the moon, and the precession of the equinoxes, are more fully deduced from their principles, and the theory of comets is confirmed by several examples, and their orbits more accurately computed."

On the 25th of June, Cotes announces to its author, through Dr. Samuel Clark, "that the book is finished,"[42] and on the 27th of July, Newton waited on the Queen to present a copy of the Principia to her Majesty.[43]

Such is a brief notice of the composition and printing of the first and second editions of a work which will be memorable not only in the annals of one science or of one <319> country, but which will form an epoch in the history of the world, and will ever be regarded as the brightest page in the records of human reason, — a work, may we not add, which would be read with delight in every planet of our system, — in every system of the universe. What a glorious privilege was it to have been the author of the Principia! There was but one earth upon whose form and tides and movements the philosopher could exercise his genius, — one moon, whose perturbations and inequalities and actions he could study, — one sun, whose controlling force and apparent motions he could calculate and determine, — one system of planets, whose mutual disturbances could tax his highest reason,[44] — one system of comets, whose eccentric paths he could explore and rectify, — and one universe of stars, to whose binary and multiple combinations he could extend the law of terrestrial gravity. To have been the chosen sage summoned to the study of that earth, these systems, and that universe, — the favoured lawgiver to worlds unnumbered, the high-priest in the temple of boundless space, — was a privilege that could be granted but to one member of the human family ; — and to have executed the task was an achievement which in its magnitude can be measured only by the infinite in space, and in the duration of its triumphs by the infinite in time. That Sage — that Lawgiver — that High-priest was Newton. Let us endeavour to convey to the reader some idea of the revelations which he made, and of the brilliant discoveries to which they conducted his successors.

The Principia consists of three Books. The First and <320> Second, which occupy three-fourths of the work, are entitled, On the Motion of Bodies ; the First treating of their motions in free space, and the Second of their motions in a resisting medium. The Third bears the title, On the System of the World.

The First Book, besides the definition and axioms, or laws of motion, with which it begins, consists of fourteen sections, in the first of which the author explains the method of prime and ultimate ratios, used in his investigations, and which is similar to the method of fluxions, more fully explained in the Second Book. The other sections treat of centripetal forces, and motions in fixed and moveable orbits.

The Second Book consists of nine sections, and treats of bodies moving in resisting media, or oscillating as pendulums.

The Third Book is introduced by the "Rules of Philosophizing." It consists of five sections on the Causes of the System of the World, — on the Quantity of Lunar Errors, — on the Quantity of the Tides, — on the Precession of the Equinoxes, — and on Comets; and it concludes with a general scholium, containing reflections on the constitution of the universe, and on the "Eternal, Infinite, and perfect Being" by whom it is governed.

The great discovery which characterizes the Principia, is that of the principle of universal gravitation, that every particle of matter in the universe is attracted by, or gravitates to every other particle of matter, with a force inversely proportional to the squares of their distances. In order to establish this principle, Newton begins by considering the curves, which are generated by the composition of a direct impressed motion with a gravitation or tendency towards a centre; and having demonstrated, that in all cases the <321> areas described by the revolving body are proportional to the times of their description, he shows how to find, from the curves described, the law of the force. In the case of a circular orbit passing through the centre of tendency, the force or tendency towards the centre will be in every point as the fifth power of the distance. If the orbit is the proportional spiral, the force will be reciprocally as the cube of the distance. If it is an ellipse, the force towards the centre of it will be directly as the distance. If it is any of the conic sections, the centripetal force, or tendency towards the focus, will, in all points, be reciprocally as the square of the distance from the focus. If the velocity of the impressed motion is of a certain magnitude, the curve described will be a hyperbola, — if different to a certain degree, it will be a parabola, — and if slower, an ellipse, or a circle in one case.

In order to determine whether the force of gravity resided in the centres of the sun and planets, or in each individual particle of which they are composed, Newton demonstrated, that if a spherical body acts upon a distant body with a force varying as the distance of this body from the centre of the sphere, the same effect will be produced as if each of its particles acted upon the distant body according to the same law. And hence it follows, that the spheres, whether they are of uniform density, or consist of concentric layers, with densities varying according to any law whatever, will act upon each other in the same manner as if their force resided in their centre alone. But as the bodies of the solar system are very nearly spherical, they will all act upon one another, and upon bodies placed on their surface, as if they were so many centres of attraction; and therefore we obtain the law of gravity which subsists between spherical bodies, namely, <322> that one sphere will act upon another with a force directly proportional to their quantities of matter, and inversely, as the square of the distance between the centres of the spheres. From the equality of action and reaction, to which no exception can be found, Newton concluded that the sun gravitated to the planets, and the planets to their satellites, and the earth itself to the stone which falls upon its surface; and consequently that the two mutually gravitating bodies approached to one another with velocities inversely proportional to their quantities of matter.

Having established this universal law, Newton was enabled not only to determine the weight which the same body would have at the surface of the sun and the planets, but even to calculate the quantity of matter in the sun and in all the planets that had satellites, and even to determine the density or specific gravity of the matter of which they were composed, — results which Adam Smith pronounced to be "above the reach of human reason and experience." In this way he found that the weight of the same body would be twenty-three times greater at the surface of the sun than at the surface of the earth, and that the density of the earth was four times greater than that of the sun, the planets increasing in density as they are nearer the centre of the system.

If the peculiar genius of Newton has been displayed in his investigation of the law of universal gravitation, it shines with no less lustre in the patience and sagacity with which he traced the consequences of this fertile principle.

The discovery of the spheroidal form of Jupiter by Cassini had probably directed the attention of Newton to the determination of its cause, and consequently to the investigation of the true figure of the earth. The spheri <323> cal form of the planets had been ascribed by Copernicus to the gravity or natural appetency of their parts; but upon considering the earth as a body revolving upon its axis, Newton quickly saw that the figure arising from the mutual attraction of its parts must be modified by another force arising from its rotation. When a body revolves upon an axis, the velocity of rotation increases from the poles where it is nothing, to the equator where it is a maximum. In consequence of this velocity the bodies on the earth's surface have a tendency to fly off from it, and this tendency increases with the velocity. Hence arises a centrifugal force, which acts in combination with the force of gravity, and which Newton found to be the 289th part of the force of gravity at the equator, and decreasing as the cosine of the latitude, from the equator to the poles. The great predominance of gravity over the centrifugal force prevents the latter from carrying off any bodies from the earth's surface, but the weight of all bodies is diminished by the centrifugal force, so that the weight of any body is greater at the poles than it is at the equator. If we now suppose the waters at the pole to communicate with those at the equator by means of a canal, one branch of which goes from the pole to the centre of the earth, and the other from the centre of the earth to the equator, then the polar branch of the canal will be heavier than the equatorial branch, in consequence of its weight not being diminished by the centrifugal force; and, therefore, in order that the two columns may be in equilibrio, the equatorial one must be lengthened. Newton found that the length of the polar must be to that of the equatorial canal as 229 to 230, or that the earth's polar radius must be seventeen miles less than its equatorial radius; <324> that is, that the figure of the earth is an oblate spheroid, formed by the revolution of an ellipse round its lesser axis. Hence it follows, that the intensity of gravity at any point of the earth's surface is in the inverse ratio of the distance of that point from the centre, and consequently that it diminishes from the equator to the poles, — a result which he confirmed by the fact, that clocks required to have their pendulums shortened, in order to beat true time, when carried from Europe towards the equator.[45]

The next subject to which Newton applied the principle of gravity, was the tides of the ocean. The philosophers of all ages had recognised the connexion between the phenomena of the tides and the position of the moon. The College of Jesuits at Coimbra, and subsequently Antonio de Dominis and Kepler, distinctly referred the tides to the attraction of the waters of the earth by the moon, but so imperfect was the explanation which was thus given of the phenomena, that Galileo ridiculed the idea of lunar attraction, and substituted for it a fallacious explanation of his own. That the moon is the principal cause of the tides is obvious from the well-known fact, that it is high water at any given place a short time after she is in the meridian of that place; and that the sun performs a secondary part in their production, may be proved from the circumstance, that the highest tides take place when the sun, the moon, and the earth are in the same straight line, — that is, when the force of the sun conspires with that of the moon; and that the lowest tides take place when the lines drawn from the sun and moon to the earth are at right angles to each other, — that is, when the force <325> of the sun acts in opposition to that of the moon. The most perplexing phenomenon in the tides of the ocean, and one which is still a stumbling-block to persons slightly acquainted with the theory of attraction, is the existence of high water on the side of the earth opposite to the moon, as well as on the side next the earth. To maintain that the attraction of the moon at the same instant draws the waters of the ocean towards herself, and also draws them from the earth in an opposite direction, seems at first sight paradoxical; but the difficulty vanishes when we consider the earth, or rather the centre of the earth, and the water on each side of it, as three distinct bodies, placed at different distances from the moon, and consequently attracted with forces inversely proportional to the squares of their distances. The water nearest the moon will be much more powerfully attracted than the centre of the earth, and the centre of the earth more powerfully than the water farthest from the moon. The consequence of this must be, that the waters nearest the moon will be drawn away from the centre of the earth, and will consequently rise from their level, while the centre of the earth will be drawn away from the waters opposite the moon, which will, as it were, be left behind, and consequently be in the same situation as if they were raised from the earth in a direction opposite to that in which they are attracted by the moon. Hence the effect of the moon's action upon the earth is to draw its fluid parts into the form of an oblong spheroid, the axis of which passes through the moon. As the action of the sun will produce the very same effect, though in a smaller degree, the tide at any place will depend on the relative position of these two spheroids, and will be always equal either to the sum, or to the difference of the effects of the <326> two luminaries. At the time of new and full moon, the two spheroids will have their axes coincident; and the height of the tide, which then will be a spring one, will be equal to the sum of the elevations produced in each spheroid considered separately, while at the first and third quarters the axes of the spheroids will be at right angles to each other, and the height of the tide, which will then be a neap one, will be equal to the difference of the elevations produced in each separate spheroid. By comparing the spring and neap tides, Newton found that the force with which the moon acted upon the waters of the earth, was to that with which the sun acted upon them as 4.48 to 1 ; — that the force of the moon produced a tide of 8.63 feet ; — that of the sun one of 1.93 feet ; — and both combined, one of $10\frac{1}{2}$ feet, — a result which, in the open sea, does not deviate much from observation. Having thus ascertained the force of the moon on the waters of our globe, he found that the quantity of water in the moon was to that in the earth as 1 to 40, and the density of the moon to that of the earth as 11 to 9.

The motions of the moon, so much within the reach of our own observation, presented a fine field for the application of the theory of universal gravitation. The irregularities exhibited in the lunar motions had been known in the time of Hipparchus and Ptolemy. Tycho had discovered the great inequality called the variation, amounting to 37′, and depending on the alternate acceleration and retardation of the moon by the action of the sun in every quarter of a revolution ; and he had also ascertained the existence of the annual equation. Of these two inequalities, Newton gave a most satisfactory explanation, making the first 36′ 10″, and the other 11′ 51″, differing only a few seconds from the numbers adopted by Tobias <327> Mayer in his celebrated Lunar Tables. The force exerted by the sun upon the moon may be always resolved into two forces, one acting in the direction of the line joining the moon and the earth, and consequently tending to increase or diminish the moon's gravity to the earth ; and the other in a direction at right angles to this, and consequently tending to accelerate or retard the motion in her orbit. Now, it was found by Newton that this last force was reduced to nothing, or vanished at the syzygies or quadratures, so that at these four points the described areas are proportional to the times. The instant, however, that the moon quits these positions, the force under consideration, which we may call the tangential force, begins, and it reaches its maximum in the four octants. The force, therefore, compounded of these two elements of the solar force, or the diagonal of the parallelogram which they form, is no longer directed to the earth's centre, but deviates from it at a maximum about thirty minutes, and therefore affects the angular motion of the moon, the motion being accelerated in passing from the quadratures to the syzygies, and retarded in passing from the syzygies to the quadratures. Hence the velocity is, in its mean state, in the octants, a maximum in the syzygies, and a minimum in the quadratures.

Upon considering the influence of the solar force in diminishing or increasing the moon's gravity to the earth, Newton saw that her distance and periodic time must, from this cause, be subject to change, and in this way he accounted for the annual equation observed by Tycho. By the application of similar principles, he explained the cause of the motion of the apsides, or of the greater axis of the moon's orbit, which was an angular progressive motion of 3° 4′ nearly in the course of one luna <328> tion ;[46] and he showed that the retrogradation of the nodes, amounting to 3′ 10″ daily, arose from one of the elements of the solar force being exerted in the plane of the ecliptic, and not in the plane of the moon's orbit, — the effect of which was to draw the moon down to the plane of the ecliptic, and thus cause the line of the nodes, or the intersection of these two planes, to move in a direction opposite to that of the moon.

The lunar theory thus sketched by Newton, requited for its completion the labours of another century. The imperfections of the fluxionary calculus prevented him from explaining the other inequalities of the moon's motions, and it was reserved to Euler, D'Alembert, Clairaut, Mayer, and Laplace, to bring the lunar tables to a high degree of perfection, and to enable the navigator to determine his longitude at sea with a degree of precision which the most sanguine astronomer could scarcely have anticipated.

By the consideration of the retrograde motion of the moon's nodes, Newton was led to one of the most striking of all his discoveries, namely, the cause of the remarkable phenomenon of the precession of the equinoctial points, which moved 50″ annually, and completed the circuit of the heavens in 25,920 years. Kepler had declared himself incapable of assigning any cause for this motion, and we do not believe that any other astronomer ever made the attempt. From the spheroidal form of the earth, it may be regarded as a sphere with a spheroidal ring surrounding its equator, one half of the ring being above the plane of the ecliptic, and the other half below it. Considering this excess of matter as a system of satellites <329> adhering to the earth's surface, Newton now saw that the combined actions of the sun and the moon upon these satellites tended to produce a retrogradation in the nodes of the circles which they described in their diurnal rotation, and that the sum of all the tendencies being communicated to the whole mass of the planet, ought to produce a slow retrogradation of the equinoctial points. The effect produced by the motion of the sun he found to be forty seconds, and that produced by the action of the moon ten seconds.

Although there could be little doubt that the comets were retained in their orbits by the same laws which regulated the motions of the planets, yet it was not easy to put this opinion to the test of observation. The visibility of comets only in a small part of their orbits rendered it difficult to ascertain their distance and periodic times, and as their periods were probably of great length, it was impossible to obtain approximate results by repeated observation. Newton, however, though he at first imagined that comets moved in straight lines, removed this difficulty, by showing how to determine the orbit of a comet, namely, the form and position of the orbit, and the periodic time, by three observations. This method consists of an easy geometrical construction, founded on the supposition that the paths of comets are so nearly parabolic, that the parabola may be used without any sensible error, although he considers it more probable that their orbits are elliptical, and that after a long period they may return. By applying this method to the comet of 1680, he calculated the elements of its orbit, and from the agreement of the computed places with those which were observed, he justly inferred that the motions of comets were regulated by the same laws as those of the <330> planetary bodies. This result was one of great importance ; for as the comets enter our system in every possible direction, and at all angles with the ecliptic, and as a great part of their orbits extends far beyond the limits of the solar system, it demonstrated the existence of gravity in spaces beyond the planets, and proved that the law of the inverse ratio of the squares of the distance was true in every possible direction, and at very remote distances from the centre of our system.

Such is a brief view of the leading discoveries which the Principia first announced to the world. The grandeur of the subjects of which it treats, — the beautiful simplicity of the system which it unfolds, — the clear and concise reasoning by which that system is explained, — and the irresistible evidence by which it is supported, might have insured it the warmest admiration of contemporary mathematicians, and the most welcome reception in all the schools of philosophy throughout Europe. This, however, is not the way in which great truths are generally received. Though the astronomical discoveries of Newton were not assailed by the class of ignorant pretenders who attacked his optical writings, yet they were everywhere resisted by the errors and prejudices which had taken a deep hold even of the strongest minds. The philosophy of Descartes was predominant throughout Europe. Appealing to the imagination more than to reason, it was quickly received into popular favour, and the same causes which facilitated its introduction, extended its influence, and completed its dominion over the human mind. In explaining all the movements of the heavenly bodies by a system of vortices in a fluid medium diffused through the universe, Descartes had seized upon an analogy of the most alluring and deceitful kind. Those who had seen <331> heavy bodies revolving in the eddies of a whirlpool, or in the gyrations of a vessel of water thrown into a circular motion, had no difficulty in conceiving how the planets might revolve round the sun by analogous movements. The mind instantly grasped at an explanation of so palpable a character, and which required for its development neither the exercise of patient thought, nor the aid of mathematical skill. The talent and perspicuity with which the Cartesian system was expounded, and the show of experiments with which it was sustained, contributed powerfully to its adoption, while it derived a still higher sanction from the excellent character and the unaffected piety of its author.

Thus entrenched as the Cartesian system was, in the strongholds of the human mind, and fortified by its most obstinate prejudices, it was not to be wondered at that the pure and sublime doctrines of the Principia were distrustfully received, and perseveringly resisted. The uninstructed mind could not readily admit the idea, that the great masses of the planets were suspended in empty space, and retained in their orbits by an invisible influence residing in the sun; and even those philosophers who had been accustomed to the rigour of true scientific research, and who possessed sufficient mathematical skill for the examination of the Newtonian doctrines, viewed them at first as reviving the occult qualities of the ancient physics, and resisted their introduction with a pertinacity which it is not easy to explain. Prejudiced, no doubt, in favour of his own metaphysical views, Leibnitz himself misapprehended the principles of the Newtonian philosophy, and endeavoured to demonstrate the truths in the Principia by the application of different principles. Even two years after the publication of the Principia, he published a dissertation <332> in which he explained the motions of the planets by an ethereal fluid. Huygens, who above all other men was qualified to appreciate the new philosophy, rejected the doctrine of gravitation as existing between the individual particles of matter, and received it only as an attribute of the planetary masses. John Bernouilli, also, one of the first mathematicians of the age, opposed the philosophy of Newton. Mairan, in the early part of his life, was a strenuous defender of the system of vortices. Cassini and Maraldi were quite ignorant of the Principia, and occupied themselves with the most absurd methods of calculating the orbits of the comets long after the Newtonian method had been established on the most impregnable basis ; and even Fontenelle, a man of liberal views and extensive information, continued throughout the whole of his life to maintain the doctrines of Descartes.

<334>

"The Universities of St. Andrews and Edinburgh were, I believe, the first in Britain where the Newtonian philosophy was made the subject of the academical prelections. For this distinction they are indebted to James and David Gregory, the first in some respects the rival, but both the friends of Newton. Whiston bewails, in the anguish of his heart, the difference in this respect between those universities and his own. David Gregory taught in Edinburgh for several years prior to 1690, when he removed to Oxford; and Whiston says,[49] ' he had already caused several of his scholars to keep Acts, as we call them, upon several branches of the Newtonian philosophy, while we at Cambridge, poor wretches, were ignominiously studying the fictitious hypotheses of the Cartesians."[50] I do not, <335> however, mean to say, that from this date the Cartesian philosophy was expelled from those universities; the Physics of Rohault were still in use as a text-book, — at least occasionally, to a much later period than this, and a great deal, no doubt, depended on the character of the individual. Professor Keill introduced the Newtonian philosophy in his lectures at Oxford in 1697; but the instructions of the tutors, which constitute the real and efficient system of the University, were not cast in that mould till long afterwards." Adopting the same view of the subject, Mr. Dugald Stewart has stated, "that the philosophy of Newton was taught by David Gregory at Edinburgh, and by his brother, James Gregory, at St. Andrews,[51] before it was able to supplant the vortices of Descartes in that very university of which Newton was a member. It was in the Scottish universities that the philosophy of Locke, as well as that of Newton, was first adopted as a branch of academical education."

Anxious as we should have been to have awarded to Scotland the honour of having first adopted the Newtonian philosophy, yet a regard for historical truth compels us to take a different view of the subject. It is well known that Sir Isaac Newton delivered lectures on his own philosophy from the Lucasian chair before the publication of the Principia; and in the very page of Whiston's life, quoted by Professor Playfair, he informs us that he had heard him read such lectures in the public schools, though at that time he did not at all understand them. Newton <336> continued to lecture till 1699, and occasionally, we presume, till 1703, when Whiston became his successor, having been appointed his deputy in 1699, In both of these capacities, Whiston delivered in the public schools a course of lectures on astronomy, and a course of physicomathematical lectures, in which the mathematical philosophy of Newton was explained and demonstrated, and both these courses were published, — the one in 1707, and the other in 1710, — for the use of the young men in the University. In 1707, the celebrated blind mathematician, Nicholas Saunderson, took up his residence in Christ's College, without being admitted a member of that body. The society not only allotted to him apartments, but gave him the free use of their library. With the concurrence of Whiston, he delivered a course "On the Principia, Optics, and Universal Arithmetic of Newton," and the popularity of these lectures was so great, that Sir Isaac corresponded on the subject of them with their author; and on the ejection of Whiston from the Lucasian chair in 1711, Saunderson was appointed his successor. In this important office he continued to teach the Newtonian philosophy till the time of his death, which took place in 1739.

But while the mathematical principles of the Newtonian system were ably expounded in our seats of learning, its <339> physical truths had been studied by some of the most distinguished scholars and philosophers of the times, and were subsequently explained and communicated to the public by various lecturers on experimental philosophy. The celebrated Locke, who was incapable of understanding the Principia from his want of geometrical knowledge, inquired of Huygens if all the mathematical propositions in that work were true. When he was assured that he might depend upon their certainty, he took them for granted, and carefully examined the reasonings and corollaries deduced from them. In this manner he acquired a knowledge of the physical truths in the Principia, and became a firm believer in the discoveries which it contained. In the same manner he studied the treatise on Optics, and made himself master of every part of it which was not mathematical.[55] From a manuscript of Sir Isaac Newton's, entitled, "A Demonstration that the Planets, by their gravity towards the Sun, may move in Ellipses,[56] found among the papers of Mr. Locke, and published by Lord King," it would appear that he himself had been at considerable trouble in explaining to his friend that interesting proposition. This manuscript is endorsed, "Mr. Newton, March, 1689." It begins with three hypotheses, (the two first being the two laws of motion, and the third the parallelogram of motion,) which introduce the proposition of the proportionality of the areas to the times in motions round an immovable centre of attraction.[57] Three lemmas, containing the properties of the ellipse, then prepare the reader for the celebrated <340> proposition, that when a body moves in an ellipse,[58] the attraction is reciprocally as the square of the distance of the body from the focus to which it is attracted. These propositions are demonstrated in a more popular manner than in the Principia, but there can be no doubt that, even in their present modified form, they were beyond the capacity of Mr. Locke.

Among the learned men who were desirous of understanding the truths revealed in the Principia, Richard Bentley was one of the most distinguished. In 1691, when only thirty years of age, he applied to John Craige, a mathematician of some eminence, and a friend of Newton, for a list of works which would enable him to study the Principia. Alarmed at the list which Craige sent him, he was induced to apply to Newton himself, who drew up the directions which, along with those of Craige, we have given in the Appendix.[59] When Bentley was appointed, in 1692, the first Lecturer on Robert Boyle's Foundation, he chose as the subject of his discourse, "A Confutation of Atheism." The insidious doctrines of Spinoza and Hobbes had at that time made considerable progress among the upper ranks of society, and as these authors denied a Divine Providence, and considered the existence of the universe as the result of necessity, Bentley proposed to conclude his course of lectures with the demonstration of a Divine Providence from the physical constitution of the universe, as demonstrated by Newton. Before printing his discourses, he consulted Newton on some points which required elucidation, and it was in <341> reply to the Queries thus addressed to him, that Newton wrote the five remarkable letters already alluded to. By this means some of the great truths of the Newtonian Philosophy were promulgated among a class of readers who would not otherwise have heard of them.[60]

About the year 1718, Isaac Watts speaks of the exploded Physics of Descartes, and the noble inventions of Sir Isaac Newton, in his "hypotheses of the heavenly bodies and their motions;" and he refers to previous writers who have explained Nature and its operations in a more sensible and geometrical manner than Aristotle, especially those who have followed the principles of that wonder of our age and nation, Sir Isaac Newton.[61]

Dr. John Keill was the first person who publicly taught natural philosophy, "by experiments in a mathematical manner." Desaguliers informs us, that this author "laid down very simple propositions, which he proved by experiments, and from these he deduced others more compound, which he still confirmed by experiments, till he had instructed his auditors in the laws of motion, the principles of hydrostatics and optics, and some of the chief propositions of Sir Isaac Newton, concerning light <342> and colours. He began these courses in Oxford about the year 1704 or 1705, and in that way introduced the love of the Newtonian philosophy."[62] When Dr. Keill left the University, Desaguliers began to teach the new philosophy by experiments. He commenced his lectures at Harthall, in Oxford, in 1710, and delivered more than a hundred and twenty discourses ; and when he went to settle in London in 1713, he informs us that he found "the Newtonian philosophy generally received among persons of all ranks and professions, and even among the ladies by the help of experiments."[63]

Such were the steps by which the philosophy of Newton was established in Great Britain. From the time of the publication of the Principia, its mathematical doctrines formed a regular part of academical education, and before twenty years had elapsed, its physical truths were communicated to the public in popular lectures, illustrated by experiments, and accommodated to the capacities of those who were not versed in mathematical knowledge. The Cartesian system, though it may have lingered for a while in the recesses of our universities, was soon overturned; and long before his death, Newton enjoyed the high satisfaction of seeing his philosophy triumphant in his native land.

In closing our account of the Principia, and in justification of the high eulogium we have pronounced upon it, we may quote the opinions of two of the most distinguished men of the past or the present age. "It may be justly said," observes Halley, "that so many and so valu <343> able philosophical truths, as are herein discovered, and put past dispute, were never yet owing to the capacity and industry of any one man."[64] "The importance and generality of the discoveries," says Laplace, "and the immense number of original and profound views which has been the germ of the most brilliant theories of the philosophers of this century, and all presented with much elegance, will ensure to the work, on the Mathematical Principles of Natural Philosophy, a pre-eminence above all the other productions of human genius."[65]

[1] In 1673, Huygens had announced the relations between attractive force and velocity in circular motion.

[2] Whiston's Memoirs of his own Life, p. 37.

[3] Eratosthenes Batavus, 1617.

[4] Seaman's Practice, 1636.

[5] Mr. Rigaud remarks, that "we do not know when Norwood's determination became known to Newton, but we are certain that he was well aware of Snellius's measures quite as soon as he was of Picard's, — probably much sooner, since the specific mention of them is made in Varenius's Geography, (cap. iv., pp. 24-26, 1672,) of which he edited a new edition at Cambridge in 1672." — Historical Essay, p. 12. "Had he adopted," as Mr. Rigaud adds, "28,500 Rhinland perches, the length of a degree given by Snellius, he would have obtained for the moon's deflexion, in a minute, 15.5 feet."

[6]

Among the manuscripts of Conduit, we found the following statement regarding Newton's "resuming his former thoughts concerning the moon:" —

"In 1673, Dr. Hooke wrote to him to send him something new for the Transactions, whereupon he sent him a little dissertation to confute the common objection, that if it were true that the earth moved from east to west, all falling bodies would be left to the west; and maintained that, on the contrary, they would fall a little eastward, and, having described a curve with his hand to represent the motion of a falling body, he drew a negligent stroke with his pen, from whence Dr. Hooke took occasion to imagine that he meant the curve would be a spiral, whereupon the Doctor wrote to him that the curve would be an ellipsis, and that the body would move according to Kepler's notion, which gave Sir. Isaac Newton an occasion to <292> examine the thing thoroughly; and for the foundation of the calculus he intended, he laid down this proposition, that the areas described in equal times were equal, which, though assumed by Kepler, was not by him demonstrated, of which demonstration the first glory is due to Newton."

Immediately after this statement, Conduit adds, — " Pemberton, in his preface, mentions this in another manner," and he quotes part of that preface.

The above extraordinary story of Hooke's having considered a negligent stroke of Newton's pen as a spiral, and on that ground having charged him with maintaining that falling bodies would describe such a curve, could not have been given on Newton's authority, but must have been invented by an enemy of Hooke's. Newton himself admits, in his letter to Halley, July 27, 1686, that Hooke's "correcting his spiral occasioned his finding the theorem by which he afterwards examined the ellipsis."

In the preceding extract, the date 1673 is obviously erroneous. The document was copied for me by the late Henry Arthur Wallop Fellowes, the elder brother of the present Earl of Portsmouth, who kindly assisted me in the examination of Newton's papers, and who placed at the top of the document the words, (P. 49 in Jones,) which I cannot explain.

[7] Robison's Works, vol. ii. p. 94, 1822. Tradition is, we believe, the only authority for this anecdote. It is not supported by what is known of Newton's character.

[8] Principia, lib. i., Prop. iv., Schol.

[9] These various facts are stated in a letter from Halley to Newton, dated June 29, 1686. "According to your desire in your former, I waited upon Sir Christopher Wren, to inquire of him if he hid the first notion of the reciprocal duplicate proportion from Mr. Hooke. His answer was, that he himself very many years since had had his thoughts upon making out the planet's motions by a composition of a descent towards the sun and an impressed motion; but that at length he gave over, not finding the means of doing it. Since which time Mr. Hooke had frequently told him that he had done it, and attempted to make it out to him, but that he never was satisfied that his demonstrations were cogent. And this I know to be true, that in January 1683-4, I, having from the consideration of the sesquialterate proportion of Kepler, concluded that the centripetal force decreased in the proportion of the squares of the distances reciprocally, came on Wednesday to town (from Islington) where I met with Sir Christopher Wren and Mr. Hooke, and falling in discourse about it, Mr. Hooke affirmed that upon that principle all the laws of the celestial motions were to be demonstrated, and that he himself had done it. I declared the ill success of my attempts, and Sir Christopher to encourage the inquiry, said that he would give Mr. Hooke some two months' time to bring him a convincing demonstration thereof, and besides the honour, he of us that did it should have from him the present of a book of forty shillings. Mr. Hooke then said he had it, but that he would conceal it for some time, that others trying and failing might know how to value it when he should make it public. However, I remember that Sir Christopher was little satisfied that he could do it, and though Mr. Hooke then promised to shew it him, I do not find that in that particular he has been so good as his word."

[10] Letter to Halley, June 20, 1686. See also Rigaud's Hist. Essay, pp. 51, 52.

[11] It appears from Birch, in his Hist. of the Royal Society, vol. iii. p. 1, that Newton had written to Oldenburg a letter, dated January 6, 1673.

[12] July 14, 1686. Rigaud's Hist. Ess., App. pp. 39, 40.

[13] The erroneous calculations from his having used an incorrect measure of the earth's diameter.

[14]

In both the editions of the Commercium Epistolicum, drawn up by a committee of Newton's best friends, there occurs the following passage, which has misled several of Newton's biographers. "Anno . . . 1683, in . . . Actis Lipsicis pro mense Octobri, calculi differentialis elementa primum edidit D. Leibnitius, literis A. G. L. designatus. Anno autem 1683 ad finem vergente, D. Newtonus propositiones principales, earum quæ in Philosophiæ Principiis Mathematicis habentur Londinum misit," &c., No. LXXI. It is certain that 1684 should have been substituted for 1683. Mr. Rigaud, who justly remarks that this could not have been an error of the press, as "the argument with reference to Leibnitz would fall to the ground if 1684 were substituted for it," has endeavoured successfully to find out the cause of the mistake. In the Macclesfield Collection he found two Memoranda on the first communication of the Principia to the Royal Society, said to be "from <297> an original paper of Newton," which we presume means in Newton's handwriting. In the first the date 1683 is given, and in the second the correct date of 1684, "the 3 having been evidently altered to 4," by Newton himself, so that the editors of the Commercium Epistolicum made a grave mistake in adopting the date 1683.

Since the publication of Mr. Rigaud's Historical Essay, Mr. Edleston has thrown a new light on this subject. The two Memoranda mentioned by Mr. Rigaud are the commencement of a critique by Newton himself on three papers by Leibnitz, in the Leipsic Acts for January and February 1689. The critique, which Mr. Edleston thinks was probably written in 1712, occupied nearly six pages, and is preserved among the Lucasian Papers. The first sentence is given in four different forms. In the two first the date 1684 is used, and in the two last 1683. "Newton," says Mr. Edleston, "first of all clearly wrote 1684, then altered the 4 to a 3, afterwards crossed all the figures out, and wrote distinctly 1683 . . . . Newton, therefore, after endeavouring to recollect the exact year in which he sent up the fundamental proposition of the Principia to London, antedated the event by a twelvemonth," so that no blame can be cast upon the editors of the Commercium Epistolicum, for the erroneous date which they adopted. The critique is given by Mr. Edleston in his Appendix, p. 307. See Rigaud's Hist. Essay, pp. 16-18, and his Appendix, No. xix.

[15] We have given this account of Halley's interview with Newton, nearly as we find it in Conduit's manuscript, in which May is erroneously mentioned as the time of Halley's visit. Halley's own account is more brief: — "The August following <298> when I did myself the honour to visit you, I then learned the good news that you had brought the demonstration to perfection, and you were pleased to promise me a copy thereof, which I received with a great deal of satisfaction from Mr. Paget." — Letter to Newton, June 29, 1686.

[16] " Dr. Halley has often valued himself to me," says Conduit, "for being the Ulysses which produced this Achilles."

[17] Mr. Paget was Mathematical Master in Christ's Hospital. He was a friend of Newton's, and was recommended by him to Flamsteed on the 3d April, 1682, as a competitor for the Mastership. Flamsteed joined in the recommendation, and after his appointment found him "an able mathematician." He gave such satisfaction to the Governors indeed, that they sent Flamsteed "a staff," and made him one of their number. Flamsteed has left it on record that this accomplished young man, before seven years had expired, became a drunkard, neglected his duties, lost his character, and banished himself to India. What a lesson to the young who are accidentally associated with great men after whom posterity inquire! As the bearer of the germ of the Principia to Halley, Paget's name has for nearly two centuries been mentioned with honour. As a protégé of Newton and Flamsteed, who failed in justifying their recommendation, a blot has been left upon his name, which but for that honour would never have been known. See Baily's Flamsteed, p. 125.

[19] See Baily's Flamsteed, p. 50, note.

[20] This letter is not extant, but its date and character appear from Newton's answer.

[21] Mr. Baily, whose views respecting the quarrel which subsequently arose between Newton and Flamsteed, we shall afterwards have occasion to controvert, acknowledges that he cannot find in these two letters of Newton "any foundation for Flamsteed's censure." It is very obvious, indeed, from the highly complimentary terms in which Flamsteed at this time wrote to Newton, that he did not consider Newton as "magisterially ridiculing his opinions."

[22] At this time, and even in 1684, when he wrote his treatise De Motu, Newton had very erroneous views regarding the motions of comets; and it was not till September 19, 1685, that he acknowledged, in a letter to Flamsteed, that "it seemed very probable that the comets of November and December were the same comet." In the first edition of the Principia, p. 494, he went farther, and acknowledged that Flamsteed was right. In giving an account of the treatise De Motu, Mr. Rigaud thus speaks of Newton's views respecting the motions of comets: — " He certainly at this time had not resolved the difficult question of the paths of comets. In the Arithmetica Universalis, (Prob. 56,), he had proceeded on their supposed uniform rectilinear motion, and, in the present case, he still holds expressly to that earlier theory. How, under such conditions, (if strictly adhered to,) they could return, is not easy to understand; but waving this question, his reasoning seems to show that if they did, they might be recognised by a similarity in their motions. To determine this, he proposes to reduce the places of the comet to analogous points in an imaginary ellipse, of which the focus is occupied by the sun; and these places having been calculated by means of the auxiliary curve, were to be verified by their application to the rectilinear path. It seems wonderful, when we consider his extraordinary acuteness, that such an hypothesis did not immediately lead him to the truth; but as he so repeatedly and so distinctly describes the supposed motion of the comet to be in a straight line, it is impossible not to conclude, that even his most powerful mind required the assistance of time to emancipate itself from preconceived opinions." — Rigaud's Hist. Essay, p. 29.

[23] The dates of these letters, which are published in the General Dictionary, vol. vii. pp. 793-797, are, September 19, 1685; September 25, 1685; October 14, 1685; December 30, 1685 (?); January (?) 1686; September 3, 1686. Excepting the second, which is from Flamsteed, they are all from Newton.

[24] This letter has no date, but Flamsteed says that it was written about 1685, or January 1685-86.

[25] Edleston's Correspondence, &c., p. xxix.; and Newton's letter to Halley, June 20, 1686.

[26] Phil. Trans., 1686, pp. 6-8.

[27] We here express the opinion of Mr. Rigaud, who, after a careful and repeated examination of the Royal Society's minutes, from 1686 to 1699, "ventures to say," that "there is no notice of any pecuniary aid having been extended to the Principia." Halley was a married man with a family, and at "a considerable pecuniary risk provided for the disbursement, precisely at that period of his life when he could least afford it." — Rigaud's Hist. Essay, pp. 33-37.

[28] June 20,1686. Appendix, No. IX.

[29] It was not expressed in the letter, as Newton afterwards admits. See Appendix, No. X. Letter, July 27, 1686.

[30] The manuscript of the Principia, without the preface, bound in one volume, is in the possession of the Royal Society. Mr. Edleston is of opinion that the manuscript is not in Newton's autograph, and he believes it to be by the same hand as the first draught of the Principia in the University library, the author's own handwriting being easily recognised in the additions and alterations in both manuscripts. Edleston's Correspondence, &c{.}, pp. lvii. lviii. In a very interesting letter from Dr. Humphrey Newton to Conduitt, which is printed in our second volume, p. 91, he informs him, that "he copied out the Principia before it went to press." Pemberton states that the Principia was written in a year and a half. "Sir Isaac Newton says in one of his papers, that he wrote the Principia in seventeen or eighteen months, beginning the end of December 1684, and sending it to the Society in May 1686, except about ten or twelve of the propositions, which were composed before, viz., two in 1679, and the rest in June and July 1684." — Conduitt's MS. See p. 471.

[31] A copy of the Principia was presented to the King by Halley, accompanied with a paper giving a general account of the Book, and more especially an explanation of the notes, a subject in which the King was likely to take a deep interest, from his having as Lord High Admiral commanded the British fleet in the war with the United Provinces. See Phil. Trans., vol. xix. p. 445, and Rigaud's Hist. Essay, App. p. 77.

[32] See Appendix, No. XI.

[33] The number of copies printed is not known. The original price seems to have been ten shillings.

[34] See Rigaud's Hist. Essay, pp. 89-95.

[35] Correspondence, &c., Præf. p. xi.

[36] Ibid. Præf. p. xiv.

[37] Baily's Flamsteed, p. 138.

[38] It would appear from a conversation between Sir Isaac and Conduitt, that Bentley was at the expense of printing the second edition of the Principia, and received the profits of the work. "I asking him, (Newton,") says Conduitt, "how he came to let Bentley print his Principia, which he did not understand — 'Why,' said he, 'he was covetous, and I let him do it to get money.' " — Conduitt's MS. See vol. ii. pp. 248-254.

[39] Monk's Life of Bentley, p, 180.

[40] These letters, relating to questions connected with the new edition of the Principia, are seventy-two in number, and extend from May 21, 1709, to March 31, 1713. Mr. Edleston has added other fifty, connected with the Principia, from Newton, Cotes, Keill, Jones, Brook Taylor, and others, and in an Appendix he has published thirty-four letters, chiefly from Newton, and collected principally from original sources. Mr. Edleston has enriched this valuable work with an excellent synoptical view of Newton's life, and a large number of notes of the highest interest.

[41] The critique by Newton, already mentioned, bore upon this paper by Leibnitz, see p. 296, Note.

[42] Some account of this interesting and distinguished person, whose name is so indissolubly associated with that of Newton, and with the Principia, will be found in Appendix, No. XII.

[43] A third edition of the Principia was published in 1726, by Dr. Henry Pemberton, from materials furnished by Newton himself. Pemberton tells us that he had much personal intercourse with Newton, and that "a great number of letters passed between them on this account." This correspondence, however, has been lost. It is stated in Conduit's manuscript, that Sir Isaac "gave Pemberton two hundred guineas for printing his Principia," and that he had 3000 subscriptions at a guinea each for his "View of Sir Isaac Newton's Philosophy," published in 1728.

[44] The celebrated Lagrange, who frequently asserted that Newton was the greatest genius that ever existed, used to add — and the most fortunate, for we cannot find more than once a system of the world to establish. — Delambre, Notice sur la Vie de Lagrange, Mém. de l'Institut. 1812, p. xlv.

[45] This was first observed by Richer, who found that a clock regulated to mean time at Paris lost 2′28″ daily at Cayenne.

[46] Newton made it only 1° 31′ 28″, just one-half of its real value. Clairaut obtained the same result, but afterwards, by a more accurate calculation, found it to be 3° 4′, agreeing exactly with observation.

[48] In 1738 Voltaire published a popular exposition of Newton's discoveries, which contributed greatly to their reception on the Continent.

[49] Whiston's Memoirs of his own Life," p. 36.

[50]

It does not appear at what time the Newtonian Philosophy was received at Oxford. Judging from Addison's "Oration in Defence of the New Philosophy," spoken in the Theatre at Oxford, July 7, 1693, six years after the publication of the Principia, we have no doubt that the Cartesian Philosophy, which is obviously the "New Philosophy," defended by Addison, was in full force at that date. This oration, "done from the Latin original," is appended to the English translation of Fontenelle on the Plurality of Worlds ; and on the title-page to that work it is called "Mr. Addison's Defence on the Newtonian Philosophy." Our readers will decide from the following extract whether the New Philosophy means the Newtonian or the Cartesian Philosophy : —

"How long, gentlemen of the University, shall we slavishly tread in the steps of the ancients, and be afraid of being wiser than our ancestors? How long shall we religiously worship the triflings of antiquity as some do old wives' stories? It is indeed shameful, when we survey the great ornament of the present age, (Newton,) to transfer our applauses to the ancients, and to take pains to search into ages past for persons fit for panegyrick." So far the New Philosophy may mean that of Newton, but the following passage contradicts any such inference : — "The ancient philosophy has had more allowed than it could reasonably pretend to; how often has Sheldon's Theatre rung with encomia on the Stagyrite, who, greater than his own Alexander, has long, unopposed, triumphed in our school desks, and had the whole world for his pupils? At length rose Cartesius, a happier genius, who has bravely asserted the truth against the united force of all opposers, and has brought on the stage a new method of philosophizing. But shall we stigmatize with the name of novelty, that philosophy which, though but lately revived, is more ancient than the peripatetic, and as old as the mother from whence it is derived ? A great man <335> indeed he was, and the only one we envy France, (Descartes.) He solved the difficulties of the universe almost as well as if he had been its architect." The name of Newton or his philosophy is never again mentioned. — Author.

[51] Dr. Reid states, that James Gregory, Professor of Philosophy at St. Andrews, printed a Thesis at Edinburgh in 1690, containing twenty-five positions, of which twenty-two were a compend of Newton's Principia.

[52] Cotes states in his preface to the second edition of the Principia, that copies of the first edition were scarce, and could only be obtained at an immense price. Sir William Brown, when at college, gave more than two guineas for a copy, and owing to the difficulty of procuring one at a reasonable price, the father of Dr. John Moore of Glasgow transcribed the whole work with his own bind. See Nichol's Literary Anecdotes, vol. iii. p. 322, and Encyc. Brit., Art. Moore.

[53] See the Museum Criticum, vol. ii. p. 514.

[55] Preface to Desaguliers' Course of Experimental Philosophy, vol. i. p. viii. Dr. Desaguliers says that he was told this anecdote several times by Sir Isaac Newton himself.

[56] The Life of John Locke. Edit. 1830, vol. i. pp. 389-400.

[57] Principia, lib. i. prop. i.

[58] Principia, lib. i. prop. xi.

[59] See Appendix, No. XIII. The original of these directions was given by Richard Cumberland, the relation of Bentley, to Trinity College, along with the originals of the five celebrated letters from Newton to Bentley, to which our attention will be afterwards directed.

[60] Lord Aston, "a great lover of the mathematics, who would gladly be satisfied in a difficulty or two on that science," requested Mr. Greves and Sir E. Southcote to submit these difficulties to Sir Isaac Newton. Mr. Greves accordingly went on Monday, the 30th November 1702, and gives the following account of the conversation. "He owns there are a great many faults in his book, and has crossed it and interleaved it, and writ in the margin of it, in a great many places. It is talked he designs to reprint it, though he would not own it. I asked him about his proof of a vacuum, and said that if there is such a matter as escapes through the pores of all sensible bodies, this could not be weighed ….. I find he design to alter that part, for he has writ on the margin, Materia sensibilis; perceiving his reasons do not conclude in all matter whatsoever." — Edleston's Correspondence, Pref. p. xiv., and Tixall's Letters, II. 152, quoted there.

[61] Improvement of the mind, Part I. chap. xx. Art. vi. and xvi., or his Works, vol. v. pp. 301, 306.

[62] These lectures were first published in Latin in 1718, and afterwards in English in 1721 and 1739, under the title of An Introduction to the true Astronomy, or Astronomical Lectures, read in the Astronomical School of the University of Oxford. by John Keill, M.D., F.R.S.

[63] Desauglier's, ut supra, Preface, pp. viii, x.

[64] Phil. Trans. vol. xvi. p. 296.

[65] Systéme du Monde, Edit. 2de, 1799, p. 336.