Chap. XXI.] THE HEAVENS. 241 



gravitation, then the force of astral gravitation which 

 resists the sun's motive action along the orbit is as 

 the square of the velocity of motion. 



Corollary 2. — By the above and Proposition VIII. 

 the resistance of astral gravitation is as the square of 

 the velocity it opposes, whether it be a velocity of 

 revolution or a velocity of motion. 



This is to be inferred also from the centrifugal 

 force being equal to the centripetal, and therefore 

 inversely as the square of the distance from the sun ; 

 so that the remainder of the retarding force which 

 opposes the sun's revolving force is inversely as 

 the distance. 



PEOPOSITION XVI. 



Theorem. — The ratio which the motive force of gravi- 

 tation, acting along the orbits of the planets, bears 

 to the relative vis-inerti^e of the planets in respect 

 to the sun's direct force is as the sixth power of 

 the distance. 



Because the one is inversely as the distance (Pro- 

 position XV.), and the other directly as the fifth 

 power of the distance (Proposition XIV.) 



E 



