LAW OF THE UNIVERSE. 



237 



point through S to V, then the measure of the central force 

 will be ^-^ p-^r. By finding the value of those solids in 



O X s\ -t V 



Fig. 6. 



any given curve, we can determine the centripetal force in 

 terms of the radius vector S P ; that is, we can find the pro- 

 portion which the force must bear to the distance, in order to 

 retain the body in the given orbit or trajectory ; and con- 

 versely, the force being given, we can determine the tra- 

 jectory's form. 



This proposition, then, with its corollaries, is the founda- 

 tion of all the doctrine of centripetal forces, whether direct or 

 inverse ; that is, whether we regard the method of finding, 

 from the given orbit, the force and its proportion to the 

 distance, or the method of finding the orbit from the given 

 force. We must, therefore, state it more in detail, and in the 

 analytical manner, Sir Isaac Newton having delivered it syn- 

 thetically, geometrically, and with the utmost brevity. 



