THE ENGLISH PRECURSORS OF NEWTON. 791 



too was divined by him divined, not demonstrated. In 1079 he wrote 

 to Newton, suggesting the law of inverse squares, or "reciprocal du- 

 plicate proportion," and it was this letter which led the Cambridge 

 philosopher to " resume his former thoughts concerning the moon." * 

 He first, as is well known, attempted the problem of assimilating the 

 force of gravity at the earth's surface to the deflecting power exerted 

 on the moon's orbital motion, in 1665, when he "gathered" the dupli- 

 cate proportion from Kepler's third law ; but the defective data then 

 at his command obliged him to suspend his speculations. Now, with 

 the results of Picard's improved degree measurement in his hands, he 

 once more set his gigantic powers to their equally gigantic task. Hav- 

 ing made some progress with the calculations, he, however, again 

 " threw them by, being upon other studies " f ; and it required a further 

 fillip to induce him to complete them. It was given thus . 



One January day in 1684, Edmund Halley, a young and rising as- 

 tronomer, having independently worked out the great problem so far 

 as to perceive the necessity for the ratio of inverse squares, came to 

 town from Islington, and, falling into discourse with Wren and Hooke 

 on the subject, the latter "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," continues Halley,J " the ill-success 

 of my attempts, and Sir Christopher, to encourage the enquiry, 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 a present of a book of forty shillings. 

 Mr. Hooke then said he had it, but should 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 show it him, I do not find that in that particular he has 

 been so good as his word." 



The two months' interval allowed by Wren for the production of 

 the desired solution elapsed four times over, and Hooke made no sign. 

 Then, at last, Halley started for Cambridge, and laid the difficulty be- 

 fore Newton. In after-life he was accustomed to boast that " he had 

 been the Ulysses who produced this Achilles." For the result of his 

 visit was the "Principia." 



The most painful passage in Hooke's life now comes before us. 

 When the first book of his rival's immortal work was, on April 28, 

 1686, received by the Royal Society with the applause which it de- 

 served, he was unable to restrain his jealous disappointment within 

 the bounds of moderation or decency. He quarreled with the Presi- 



* Brewster, " Life of Newton," vol. i., p. 291. 



\ Letter to Ealley, quoted by Brewster, vol. i., p. 292. 



% Letter to Newton, quoted by Brewster, vol. i., p. 293, note. 



Brewster, " Life of Newton," vol. i., p. 298. 



