INDUCTIVE EPOCH OF NEWTON. 401 



a conjecture. Bailey says 4 that " Hooke, in 1683, told him he had 

 demonstiated all the laws of the celestial motions by the recipro- 

 cally duplicate proportion of the force of gravity ; but that, being 

 offered forty shillings by Sir Christopher Wren to produce such a de- 

 monstration, his answer was, that he had it, but would conceal 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 Princ'qna, 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 believe it." 



Newton allows that Hooke's assertions in 1679 gave occasion to his 

 investigation on this point of the theory. His demonstration is con- 

 tained in the second and third Sections of the Princijria. He first 

 treats of the general law of central forces in any curve ; and then, on 

 account, as he states, of the application to the motion of the heavenly 

 bodies, he treats of the case of force varying inversely as the square 

 of the distance, in a more diffuse manner. 



In this, as in the former portion of his discovery, the two steps were, 

 the proposing the heavenly motions as a mechanical problem, and the 

 solving this problem. Borelli and Hooke had certainly made the 

 former step, with considerable distinctness ; but the mathematical solu- 

 tion required no common inventive power. 



Newton seems to have been much ruffled by Hooke's speaking 

 slightly of the value of this second step ; and is moved in return to 

 deny Hooke's pretensions with some asperity, and to assert his own. 

 He says, in a letter to Halley, " Borelli did something in it, and wrote 

 modestly ; he (Hooke) has done nothing ; and yet written in such a 

 way as if he knew, and had sufficiently hinted all but what remained 

 to be determined by the drudgery of calculations and observations ; 

 excusing himself from that labor by reason of his other business; 

 whereas he should rather have excused himself by reason of his in- 

 ability ; for it is very plain, by his words, he knew not how to go 

 about it. Now is not this very fine ? Mathematicians that find out, 

 settle, and do all the business, must content themselves with being 

 nothing but dry calculators and drudges ; and another that does 

 nothing but pretend and grasp at all things, must carry away all the 

 inventions, as well of those that were to follow him as of those that 



4 Em. Brit. Hooke, p. 2660. 

 Vol. I.— 26 



