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 respondence with him in 1679. Hooke in 1671 (ib. App. p. 53; letter to A. Wood, ib. p. 37) had written on the attraction of gravitating power which all bodies have ‘to their own centres, whereby they attract not only their own parts,’ but ‘all the other celestial bodies which are within the sphere of their activity.’ In his ‘Discourse on the Nature of Comets,’ read to the Royal Society in the autumn of 1682, and printed among his posthumous works, Hooke, moreover, spoke of a gravitation by which the planets and comets are attracted to the sun, and he gave (p. 184) an ingenious hypothesis as to the cause of gravity: he supposed it due to pulsations set up in the ether by gravitating bodies, and attempted to show that on this hypothesis the law of the inverse square would follow; but all his ideas were vague and uncertain. Hooke's ingenuity was great, but he was quite incapable of conducting a piece of strict reasoning; the idea of the inverse square law had occurred to him as it had to Newton, Wren, and Halley, but he had given no proof of its truth. Hence Newton, when he received Halley's letter of 22 May, felt that Hooke's claims were small, and wrote at once, 27 May, giving his version of the events of 1679–80. This letter, which is of great importance, has only recently been printed (, Essay on Newton's Principia, 1893, p. 155). A manuscript copy, in Hooke's handwriting, was purchased among a number of papers of Hooke by Trinity College in May 1888. Newton, in this newly recovered reply of 27 May 1686, wrote: ‘I thank you for what you write concerning Mr. Hooke, for I desire a good understanding may be kept between us. In the papers in your hands there is no proposition to which he can pretend, for I had no proper occasion of mentioning him there. In those behind, where I state the system of the world, I mention him and others. But now we are upon this business, I desire it may be understood. The sum of what passed between Mr. Hooke and me, to the best of my remembrance, was this. He soliciting me for some philosophical communication or other, I sent him this notion, that a falling body ought, by reason of the earth's diurnal motion, to advance eastwards, and not fall to the west, as the vulgar opinion is; and in the scheme wherein I proposed this I carelessly described the descent of the falling body in a spiral to the centre of the earth, which is true in a resisting medium such as our air is. Mr. Hooke replied that it would not descend to the centre, but at a certain limit turn up again. I then made the simplest case for computation, which was that of gravity uniform in a medium non-resisting, imagining that he had learnt the limit from some computation, and for that end had considered the simplest case first, and in this case I granted what he contended for, and stated the limit as nearly as I could. He replied that gravity was not uniform, but increased in the descent to the centre in a reciprocal duplicate proportion of the distance from it, and that the limit would be otherwise than I had stated, namely, at the end of every entire revolution, and added that, according to his duplicate proportion, the motions of the planets might be explained and their orbs defined. This is the sum of what I remember; if there be anything more material or anything otherwise, I desire that Mr. Hooke would help my memory. Further, that I remember about nine years since Sir Christopher Wren, upon a visit Dr. Done and I gave him at his lodgings, discoursed of this problem of determining the Heavenly Motions upon philosophical principles. This was about a year or two before I received Mr. Hooke's letters. You are acquainted with Sir Christopher: pray know when and where he first learnt the decrease of the force in the duplicate ratio of the distance from the centre.’ Halley called on Sir Christopher Wren, who replied that ‘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’ (Halley to Newton, 29 June 1686;, Essay on the First Publication of the Principia, App. p. 36; , Essay on Newton's Principia, p. 162).

Writing on 20 June 1686 (, App. p. 30), Newton stated that the second book of his great work was nearly ready for press; ‘the third I now design to suppress. Philosophy is such an impertinently litigious lady that a man had as good be engaged in lawsuits as have to do with her.’ Fortunately for posterity, Halley prevented this. A letter announcing that the second book had been sent was read to the society on 2 March, and on 6 April 1687 the ‘third book of Mr. Newton's treatise “De Systemate Mundi” was presented.’

The ‘Principia’ was published, but without a date, about midsummer 1687. The manuscript is kept at the Royal Society, but it is not in Newton's handwriting. For the completion and publication of the work the world owes, it should be explicitly acknowledged, an enormous debt to Halley. ‘In Brewster's words, “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 never