Chap. XXI.] THE HEAVENS. 239 



(Pro2:)osition XIT.) ; for the revolving force is in- 

 versely as the cube of the distance from the sun 

 (Proposition IV.) 



PEOPOSITION XIV. 



Tlieorem. — The ratio which the vis-inertijB of the 

 planets bears to the combined action of the direct 

 and revolving forces of the sun's gravitation is as 

 the fifth power of the distance from the sun. 



Because the normal ratio of the square of the 

 distance which vis-inertite bears to the sun's direct 

 force is increased as the cube of the distance by the 

 existence of the revolving force. 



PROPOSITION XV. 



Theorem. — The combined action of the direct force and 

 the revolving force of the sun's gravitation makes 

 its motive action along the orbits of the planets 

 inversely as the relative distances. 



Because the sun's revolving force is inversely as 

 the cube of the distance from the sun (Proposition 



