400 HISTORY OF PHYSICAL ASTRONOMY. 



least nearly true, before he visited Newton. Hooke was reported to 

 Newton at Cambridge, as having applied to the Royal Society to do 

 him justice with regard to his claims ; but when Halley wrote and in- 

 formed Newton (in a letter dated June 29, 1086), that Hooke's con- 

 duct " had been represented in worse colors than it ought," Newton 

 inserted in his book a notice of these his predecessors, in order, as he 

 said, "to compose the dispute." 1 This notice appears in a Scholium 

 to the fourth Proposition of the Principia, which states the general 

 law of revolutions in circles. "The case of the sixth corollary," New- 

 ton there says, " obtains in the celestial bodies, as has been separately 

 inferred by our countrymen, Wren, Hooke, and Halley ;" he soon after 

 names Huyghens, " who, in his excellent treatise De Horologio Oscil- 

 latorio, compares the force of gravity with the centrifugal forces of re- 

 volving bodies." 



The two steps requisite for this discovery were, to propose the mo- 

 tions of the planets as simply a mechanical problem, and to apply 

 mathematical reasoning so as to solve this problem, with reference to 

 Kepler's third law considered as a fact. The former step was a conse- 

 quence of the mechanical discoveries of Galileo and his school ; the 

 result of the firm and clear place which these gradually obtained in 

 men's mind, and of the utter abolition of all the notions of solid spheres 

 by Kepler. The mathematical step required no small mathematical 

 powers ; as appears, when we consider that this was the first example 

 of such a problem, and that the method of limits, under all its forms, 

 was at this time in its infancy, or rather, at its birth. Accordingly, 

 even this step, though much the easiest in the path of deduction, no 

 one before Newton completely executed. 



2. Force in diferent Points of an Orbit. The inference of the law 

 of the force from Kepler's two laws concerning the elliptical motion, 

 was a problem quite different from the preceding, and much more dif- 

 ficult ; but the dispute with respect to priority in the two propositions 

 was intermingled. Borelli, in 1666, had, as we have seen, endeavored 

 to reconcile the general form of the orbit with the notion of a central 

 attractive force, by taking centrifugal 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 any thing more than 



1 Blog. Brit, folio, art. Hooke. 2 Newton's Letter, Blotf. Brit., Hooke, p. 2660. 



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



