these thoughts I was forced from Cambridge by the intervening plague, and it was more than two years before I proceeded further.’ The college was dismissed in consequence of the plague on 8 Aug. 1665; but Newton appears from the books to have left Cambridge before that date. The plague reappeared in 1666; the college was again dismissed 22 June 1666. It seems probable, therefore, that Newton was in Cambridge for some time between these two dates, and this is confirmed by the statement due to Conduitt that the prism was bought at Stourbridge fair. A paper in Newton's handwriting, in the possession of the Earl of Macclesfield, printed in the Appendix to Rigaud's ‘Essay,’ p. 20, shows that on 13 Nov. 1665 he wrote a ‘Discourse on Fluxions,’ and the notebooks among the ‘Portsmouth Collection of Papers’ have references to the same subject, dated 20 May 1665, and also May, October, and November 1666.
It was in the autumn of 1665, at Woolsthorpe, in enforced absence from Cambridge, that the idea of universal gravitation occurred to him. ‘As he sat alone in a garden,’ says Pemberton, his intimate friend of later years, and the editor in 1726 of the third edition of the ‘Principia,’ in his preface to ‘A View of Sir Isaac Newton's Philosophy’ (1728), ‘he fell into a speculation on the power of gravity, that as this power is not found sensibly diminished at the remotest distance from the centre of the earth to which we can rise … it appeared to him reasonable to conclude that this power must extend much farther than is usually thought. Why not as high as the moon? said he to himself, and, if so, her motion must be influenced by it: perhaps she is retained in her orbit thereby.’ The story that this train of thought was aroused by seeing an apple fall is due to Voltaire, and is given in his ‘Philosophie de Newton,’ 3me partie, chap. iii. Voltaire had it from Newton's step-niece, Mrs. Conduitt. For many years tradition marked the tree in the garden at Woolsthorpe; it was shown to Sir D. Brewster in 1814, and was taken down in 1820.
Now Newton knew at this time, by a simple deduction from Kepler's third law, that if the moon were kept in an orbit approximately circular by a force directed to the centre of the earth, that force must be inversely proportional to the square of the distance between the moon and the earth. He tells us this in the paper in the Portsmouth MSS., of which part has already been quoted, and he proceeded therefore to compare the consequences of his theory with the observed motion of the moon, ‘and found them,’ to use his words, ‘answer pretty nearly.’ Still the matter was laid aside, and nothing more came of it for nearly twenty years.
To make the calculation a knowledge of the earth's radius was required. Now, the common estimate in use among geographers before Newton's time was based on the supposition that there were sixty miles to a degree of latitude, and Pemberton states that Newton took this common estimate, but he added: ‘As this is a very faulty supposition, each degree containing about sixty-nine and a half of our miles, his computation did not answer expectation, whence he concluded that some other cause must at least join with the power of gravity on the moon.’ It seems, however, impossible that Newton continued long unacquainted with the fact that the estimate he had used was exceedingly rough. Norwood's ‘Seaman's Practice,’ published in 1636, contained the much more correct measure of sixty-nine and a half miles to a degree, and this was a well-known work, a sixth edition having appeared in 1667, and a seventh in 1668. Snell had given nearly the same result, 28,500 Rhineland perches, in 1617, and this was referred to in Varenius's ‘Geography,’ an edition of which was prepared in 1672 by Newton himself. Picard made a very elaborate series of measures, published in Paris in 1671, giving sixty-nine and one-tenth miles to the degree. This was mentioned at the Royal Society on 11 Jan. and 1 Feb. 1672 (Birch, History of Roy. Soc. iii. 3, 8). Newton had been elected a fellow a month previously, and his telescope was discussed at the meeting at which Picard's measurement was announced. It was referred to at Royal Society meetings on other later occasions, and was discussed on 7 June 1682 at a meeting at which Newton was again present. But although Newton thus learned within a few years that his calculations of 1665 were founded on erroneous numbers, he deferred undertaking a recalculation till some time after 1682—probably in 1685—when he repeated his work with Picard's numbers, and found exact agreement between the theory and the facts. His delay in beginning the recalculation was probably due, as Professor Adams suggested, to the fact that he was unable till about 1685 to calculate the attraction of a large spherical body on a point near its surface; it was in his ‘Principia’ that Newton first publicly divulged the solution of that problem.
Newton returned to Cambridge in 1667, and on 1 Oct. was elected, with eight others, a fellow of Trinity College. There had been no election in 1665 and 1666, probably in consequence of the plague. During the next