That the composition occupied a year and a half is repeated by Newton* in the following note: "The book of the Principles was writ in about seventeen or eighteen months, whereof "about two were taken up with journeys, and the MS. was "sent to the R. S. in spring 1686; and the shortness of the time, in which I wrote it, makes me not ashamed of having "committed some faults." 66 Of the breaks which altogether are said to have occupied about two months, one occurred in March, 1685, and probably the only other one in June or July of the same years. It should be remarked, however, that although during the year 1685 Newton worked steadily at the composition of the Principia, he did not devote the whole of his attention to it, and his note-books show that his chemical researches were carried on simultaneously, and occupied in all a considerable time during this year. As might be expected, he chose the subject-matter of the Principia for his lectures in the Michaelmas Term, 1685. These lectures are ten in number, and are written in the same manuscript as those for 1684. The first lecture is on what is printed in the Principia as props. 22-25 (inclusive), and lemma 22; the second is on props. 26-28, and lemmas 23-26; the third is * In the Macclesfield Collection, quoted by Rigaud, p. 92. The fact was well known, and is mentioned by Pemberton, see above, p. 11. + The time of the first break is indicated by Newton in his letter to Aston (see above, p. 32). A record of the residence of fellows of the College was kept, as they were entitled during residence to 3s. 4d. a week "pro pane et potu," namely, 10 loaves of bread at 1d. each, 10 quarts of small beer at 1d. a quart, and 10 quarts of strong beer at 2d. a quart. The only period during the years 1685 and 1686 in which Newton is entered in this record as having been absent from College is from March 27 to April 11, 1685, and from June 11 to June 20, 1685, but as one day's residence may have covered some days on each side of it, this may indicate an absence in all of some six or seven weeks. The College Buttery books would be a more conclusive test as to his continuous residence, but the volume for the period immediately previous to Oct. 9, 1686, is missing. See the Cotes Correspondence, pp. lxxxiv-lxxxvi. on props. 29, 30, and lemmas 27, 28; the fourth is on prop. 31; the fifth is on the seventh section, namely, props. 32-39; the sixth is on the eighth section, props. 40-42; the seventh is on props. 43, 44; the eighth is on prop. 45; the ninth is on props. 46–51; and the tenth lecture is on props. 52–54. His lectures in 1686 are lost, but it would seem most likely that they were on the results given in the fifty-fifth and following propositions of book i. Those in 1687 are a popular exposition of the results of the third book. The considerable mechanical labour involved in writing out the manuscript of the Principia for the press was lightened by the employment of an amanuensis, named Humphrey Newton but apparently no relation of Sir Isaac's. Humphrey Newton commenced his work "in the last year of King Charles II.,” and as the King died on Feb. 2, 1685, we may reasonably suppose that Sir Isaac first employed his amanuensis when he began the composition of the Principia*. Humphrey Newton left Cambridge in 1689, thus serving Sir Isaac, says he, "for "about five years. In such time he wrote his Principia "Mathematica, which stupendous work, by his order, I copied "out before it went to the press." The same fact is mentioned by Newton in the memorandum from which an extract is quoted above on p. 58, where, after noting a mistake in book ii. prop. 10 of the first edition, he says: "there may have been some other mistakes occasioned by the shortness of the time "in which the book was written, and by its being copied by an amanuensis, who understood not what he copied, besides "the press faults." It would serve no useful purpose to go here into minute details relating to the preparation of the Principia. Early drafts of the commencement and other parts of it are in the Portsmouth Collection. In a few cases where these notes are fuller or differ materially from the corresponding propositions. * Brewster, vol. ii. p. 50. Brewster's remark that H. Newton was engaged from 1683 to 1689 must be a slip. as printed in the first edition, they might be added to a critical edition of the work, but their production here would only overload this essay. It may be interesting, however, to note the dates at which the various parts of the work were completed. Newton's lectures in the Michaelmas Term of 1684, and his tract De Motu, contain the substance of sections ii and iii of book i; it was not until 1685*-probably early in the spring-that he determined the attraction of a spherical body on any external point. 'No sooner," to quote from Dr. Glaisher's address on the bicentenary of the publication of the Principia, "had "Newton proved this superb theorem-and we know from his own words that he had no expectation of so beautiful a result "till it emerged from his mathematical investigation—than all "the mechanism of the universe at once lay spread before him. "When he discovered the theorems that form the first three "sections of book i., when he gave them in his lectures of "1684, he was unaware that the sun and earth exerted their "attractions as if they were but points. How different must "these propositions have seemed to Newton's eyes when he "realised that these results, which he had believed to be only approximately true when applied to the solar system, were really exact! Hitherto they had been true only in so far as "he could regard the sun as a point compared to the distance "of the planets or the earth as a point compared to the distance "of the moon—a distance amounting to only about sixty times "the earth's radius-but now they were mathematically true, excepting only for the slight deviation from a perfectly "spherical form of the sun, earth, and planets. We can "imagine the effect of this sudden transition from approxima"tion to exactitude in stimulating Newton's mind to still "greater efforts. It was now in his power to apply mathe"matical analysis with absolute precision to the actual problems. "of astronomy." *Newton's letter of June 20, 1686, printed below, p. 157. It is most likely that the manuscript of the first book was finished by about Easter, 1685, though certain corrections and additions were made* in the following winter. At the meeting of the Royal Society on April 21, 1686, Halley read a discourse concerning gravity wherein† it is stated that his "worthy countryman Mr. Isaac Newton has an "incomparable Treatise of Motion almost ready for the press," and that the law of inverse squares "is the principle on which "Mr. Newton has made out all the phenomena of the celestial "motions so easily and naturally that its truth is past "dispute." At the meeting of the Society on April 28, 1686, "Dr. "Vincent presented to the Society a manuscript treatise intitled. "Philosophiae Naturalis principia mathematica, and dedicated "to the Society by Mr. Isaac Newton, wherein he gives a "mathematical demonstration of the Copernican hypothesis as proposed by Kepler, and makes out all the phaenomena of the "celestial motions by the only supposition of a gravitation "towards the center of the sun decreasing as the squares of the "distances therefrom reciprocally. It was ordered that a letter "of thanks be written to Mr. Newton; and that the printing "of his book be referred to the consideration of the council; "and that in the mean time the book be put into the hands of "Mr. Halley, to make a report thereof to the council." The preface was added later, and in the first edition bears no date, but in the second edition the date May 8, 1686, was inserted. At the meetings of the Royal Society on May 19, 1686, it was ordered "that Mr. Newton's Philosophiae naturalis principia mathematica be printed forthwith in quarto in a fair "letter; and that a letter be written to him to signify the "Society's resolution, and to desire his opinion as to the print, * Newton's letter of June 20, 1686, printed below, p. 158. + Philosophical Transactions, No. 179, 1686, pp. 6–8. ‡ Birch, History of Royal Society, London, 1757, vol. iv. pp. 479–480. § Ibid, p. 484. "volume, cuts, &c." To this was appended the following note: "Mr. Halley wrote accordingly to Mr. Newton the 22d "of May the following letter," and then follows the letter printed below on pp. 154-155. At the meeting of the Council of the Society on June 2, 1686, "it was ordered, that Mr. Newton's book be printed, and "that Mr. Halley undertake the business of looking after it, "and printing it at his own charge; which he engaged to do.” The extant correspondence of Newton and Halley in connection with the printing of the work is printed below in chapter viii. The manuscript of the first book went to presst before June 7, 1686; and in the records of the meeting of the Royal Society on June 30, 1686, there is a minute, "Ordered. "that the president be desired to license Mr. Newton's book "intitled Philosophiae naturalis Principia mathematica, and "dedicated to the Society." The consequent imprimatur of Pepys, the then president, is dated July 5. This first book is given up to the consideration of the motion of particles or bodies in free space either in known orbits, or under the action of known forces, or under their mutual attraction. In it Newton generalised the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density. The rough manuscript of the second book was finished in the summer of 1685, but was not written out as a clean copy $ till after June 20, 1686; whether it was formally communicated to the Royal Society is doubtful, and I am not aware of any minute on the subject; at any rate the Society seem to Birch, History of Royal Society, London, 1757, vol. iv. p. 486. Birch, vol. iv. p. 491. § Newton's letter of June 20, 1686, printed below, p. 158. |