162 HISTORY OF PHYSICAL ASTRONOMY. 



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," Newton there says, " obtains 

 in the celestial bodies, as has been separately infer- 

 red by our countrymen, Wren, Hooke, and Halley;" 

 he soon after names Huyghens, " who, in his excel- 

 lent treatise De Horologio Oscillatorio, compares 

 the force of gravity with the centrifugal forces of 

 revolving bodies." 



The two steps requisite for this discovery were, 

 to propose the motions of the planets as simply a 

 mechanical problem, and to apply mathematical rea- 

 soning so as to solve this problem, with reference to 

 Kepler's third law considered as a fact. The former 

 step was a consequence of the mechanical discoveries 

 of Galileo and his school ; the result of the firm and 

 clear place which these gradually obtained in men's 

 minds, 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 different Points of an Orbit. The 

 inference of the law of the force from Kepler's two 



1 Biog. Brit, folio, art. Hooke. 



