400 HISTORY OF PHYSICAL ASTRONOMY. 



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

 Newton at Cambridge, as baving applied to tbe Royal Society to do 

 bim justice witb regard to bis claims ; but wben Halley wrote and in- 

 formed Newton (in a letter dated June 29, 1686), tbat Hooke's con- 

 duct " bad been represented in w T orse colors tban it ougbt," Newton 

 inserted in bis book a notice of tbese bis predecessors, in order, as be 

 said, "to compose tbe dispute." 1 Tbis notice appears in a Scbolium 

 to tbe fourtb Proposition of tbe Principia, wbicb states tbe general 

 law of revolutions in circles. " Tbe case of the sixtb corollary," New- 

 ton tbere says, " obtains in tbe celestial bodies, as bas been separately 

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

 names Huygbens, " wbo, in bis excellent treatise De Horologio Oscil- 

 latorio, compares tbe force of gravity witb tbe centrifugal forces of re- 

 volving bodies." 



Tbe two steps requisite for tbis discovery were, to propose tbe mo- 

 tions of tbe 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 different 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 



T.rit. folio, art. Boole. * Newton's Letter, Biog. Brit., Hooke, p. 2660. 



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



