INDUCTIVE EPOCH OF NEWTON. 163 



laws concerning the elliptical motion, was a pro- 

 blem quite different from the preceding, and much 

 more difficult; but the dispute with respect to 

 priority in the two propositions was intermingled. 

 Borelli, in 1666, had, as we have seen, endeavoured 

 to reconcile the general form of the orbit with the 

 notion of a central attractive force, by taking cen- 

 trifugal force into the account; and Hooke, in 1679* 

 had asserted that the result of the law of the inverse 

 square in the force of the earth would be an ellipse 2 , 

 or a curve like an ellipse 3 . But it does not appear 

 that this was anything more than a conjecture. 

 Halley says 4 that " Hooke, in 1683, told him he had 

 demonstrated all the laws of the celestial motions 

 by the reciprocally duplicate proportion of the force 

 of gravity ; but that, being offered forty shillings by 

 Sir Christopher Wren to produce such a demonstra- 

 tion, his answer was, that he had it, but would con- 

 ceal it for some time, that others, trying and failing, 

 might know how to value it when he should make 

 it public." Halley, however, truly observes, that 

 after the publication of the demonstration in the 

 Principia, this reason no longer held ; and adds, 

 "I have plainly told him, that unless he produce 

 another differing demonstration, and let the world 

 judge of it, neither I nor any one else can be- 

 lieve it." 



3 Newton's Letter, Biog. Brit., Hooke, p 2660. 



3 Birch's Hist. R. ., Wallis's Life. 



4 Enc. Brit., Hooke, p. 2660. 



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