Catalogue Entry: OTHE00128

Chapter XII

Author: David Brewster

Source: Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, vol. 1 (Edinburgh: 1855).

[Normalized Text] [Diplomatic Text]

[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."


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.


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.

[18] Mr. Rigaud has published it in his Historical Essay. He is of opinion that it is not the same paper, a copy of which was brought to Halley by Mr. Paget in November 1684, on the ground that that paper was never mentioned to the Royal Society by Halley, and that Halley did not see the "curious treatise De Motu till his second visit to Cambridge, in November or December 1684." Mr. Edleston, <300> however, is of opinion that the treatise De Motu was part of the lectures delivered by Newton as Lucasian Professor, which commenced in October 1684, and a copy of which is preserved in the University library; and that the paper sent to Halley in November was the germ of this treatise, and the one registered by Mr. Aston. In a letter from Cotes to Jones, published in Edleston's Correspondence, p. 209, it is stated that the manuscript at Cambridge was "the first draught of the Principia," as Newton read it in his lectures, — a statement to which Mr. Edleston refers in support of his opinion. There are certainly expressions in the letters both of Newton and Halley unfavourable to both these opinions, but we think that the following view of the question is the most probable. Halley went to Cambridge to learn if Newton had a demonstration of the proposition that a force varying reciprocally with the square of the distance would produce a motion in an ellipsis. Newton told him that he "had brought this demonstration to perfection," but that having mislaid it, he would send him "a copy thereof." This copy was sent to Halley in November obviously for his own information. Halley does not lay it before the Society, but is so pleased with it, that he goes again to Cambridge in order to "confer with Newton about it." He now saw the treatise De Motu which Newton promised to send to the Society, and which was registered. Now when Halley says (letter to Newton, June 29, 1686) that he went to Newton to confer with him about it, that is, the demonstration, and adds immediately, "since which time it has been entered upon the register books of the Society," he can only mean that the demonstration was entered as part of the treatise De Motu, of which it was certainly the leading feature. If the two its mean the same thing, then Halley received in November the same treatise that was afterwards sent to Aston in the following February, which is scarcely admissible even upon Mr. Edleston's conjecture that Halley did produce the paper on the 10th December, though the fact is not recorded in the journal book. In Newton's letter to Halley, July 14, 1686, he says, that having tried the calculation in the Ellipsis, he had thrown them by for about five years, till upon Dr. Halley's request "he sought for that paper, (namely, the calculation in the Ellipsis,) and not finding it, did it again, and reduced it into the propositions (we read proposition) showed you by Mr. Paget." — See Rigaud's Hist. Essay, p. 14, and Edleston's Correspondance, pp. lv. and 209.

[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.

[47] Mém. Acad. Par. 1720.

[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.


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.

[54] The following passage in Whiston's Life of Dr. Clarke, is not in accordance with some of the preceding statements. "About the year 1697, while I was chaplain to Dr. John Moor, then Bishop of Norwich, I met at one of the coffee-houses in the market-place at Norwich, a young man, to me then wholly unknown ; his name was Clarke, pupil to that eminent and careful tutor, Mr. Ellis, of Gonvil and Caius College in Cambridge. Mr. Clarke knew me so far at the university, I being about eight years elder than himself, and so far knew the nature and success of my studies, as to enter into a conversation with me about that system of Cartesian philosophy his tutor had put him to translate, — I mean Rohault's Physics; and to ask my opinion about the fitness of such a translation. I well remember the answer I made him, that, 'since the youth of the university must have, at present, some system of Natural Philosophy for their studies and exercises; and since the true system of Sir Isaac Newton's was not yet made easy enough for the purpose; it was not improper, for their sakes, yet to translate and use the system of Rohault, (who was esteemed the best expositor of Descartes,) but that as soon as Sir Isaac Newton's philosophy came to be better known, that only ought to be taught, and the other dropped.' Which last part of my advice, by the way, has not been followed, as it ought to have been, in that university: But, as Bishop Hoadley truly observes, Dr. Clarke's Rohault is still the principal book for the young students there. Though such an observation be no way to the honour of the tutors in that university, who, in reading Rohault, do only read a philosophical romance to their pupils, almost perpetually contradicted by the better notes thereto belonging. And certainly to use Cartesian fictitious hypotheses at this time of day, after the principal parts of Sir Isaac Newton's certain system have been made easy enough for the understanding of ordinary mathematicians, is like the continuing to eat old acorns after the discovery of new wheat, for the food of mankind. However, upon this occasion, Mr. Clarke and I fell into a discourse about the wonderful discoveries made in Sir Isaac Newton's philosophy ; — and the result of that discourse was, that I was greatly surprised that so young a man as Mr. Clarke then was, not much I think above twenty-two years of age, should know so much of those sublime discoveries which were then almost a secret to all, but to a few particular mathematicians."

[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.

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