232 THE OCEAN. [Book X, 



of the distances (Prop, IV.) ; therefore the squares of 

 the velocities are directly as the revolving force. 



Definition. —The velocity of revolution must not 

 be confounded with the velocity of motion. 



The former applies to the relative number of 

 revolutions, and the latter to the relative velocities 

 of the motions by which the revolutions are effected. 

 So that the relative velocities of revolution must be 

 multiplied by the relative distances to give the relative 

 velocities of motion. 



PROPOSITION VII. 



Theorem. — If vis-inertite, or a force of inertion in- 

 herent in matter, be the cause of gravitation, the 

 moon must have both an apparent lagging motion 

 and an orbital motion. 



Because vis-inertite, being the cause of the entire 

 force of gravitation acting at any point ; when any 

 part of that force of gravitation tends to give a body 

 at that point a new position, it is evident that the 

 position to which the body is moved under its action 

 must be intermediate between that to which the 

 motive force of gravitation tends to carry it and 

 that in which the remaining force tends to retain it j 



