238 THE OCEAN. [Book X. 



PROPOSITION XII. 



Theorem. — The ratio which the vis-inertia3 of the 

 planets bears to the direct force of the sun's 

 gravitation is as the square of the distance from 

 the sun. 



Because vis-inertite is the source of every force 

 of gravitation, or the whole action of the gravitation 

 of the universe (Book III.) : -^ 



And the direct force of the sun's gravitation is 

 inversely as the square of the distance from the sun : 



Therefore the ratio which vis-inertias bears to the 

 direct force of the sun's gravitation is as the square 

 of the distance from the sun. 



PROPOSITION XIII. 



llieovem. — The ratio which the vis -inertias of the 

 planets bears to the sun's revolving force is as 

 the cube of the distance from the sun. 



By the same argument which makes the ratio it 

 bears the direct force as the square of the distance 



1 See Proposition XXXII. 



