224 



THE OCEAN. 



[Book X. 



PBOI'. 



gravitation is as tlie fifth power of the distance from 

 the Sun. 

 XV. The combined action of the direct force and the revolving- 

 force of the Sun's gravitation make its motive action 

 along the orbits of the planets inversely as the relative 

 distances. 

 XVI. The ratio which the motive force of gravitation, acting 

 along the orbits of the planets, bears to the vis-inertise 

 of the planets is as the sixth power of the distance. 



XVII. The velocities with which the Sun's revolving force endea- 

 vours to move the planets along their respective orbits 

 are decreased as the square roots of the revolving forces 

 in the respective orbits decrease. 

 XVIII. To determine the normal period in which the force which 

 causes the Sun's rotation endeavours to revolve the 

 planets, as indicated by the actual relative periods in 

 which they perform their orbital revolutions. 

 XIX. The revohing force of the Sun's gravitation in the orbits of 

 the planets is directly as the ratio which the velocities 

 of the orbital and lagging motions bear to each other in 

 each orbit respectively. 

 XX. The relative velocities of the lagging motions of the planets 

 are as the square roots of the ratio which vis-inertise 

 bears to the direct and revolving force of the Sun's 

 gravitation in their respective orbits. 

 XXI. The relative velocities of absolute motion with which the 

 planets move along their orbits are to each other 

 directly as the square roots of the fractions of the Sun's 

 force of gravitation which act as revolving forces in 

 each orbit respectively. 



XXII. The ratio of the relative velocities of orbital and apparent 

 motions is as the square root of the ratio of the forces of 

 gravitation by which they are caused. 



XXIII. The orbital motions of the planets are caused by the revolv- 



ing action of the Sun's gravitation, and the apparent 

 motions by the retarding action of astral gravitation. 



XXIV. The revolving force of the Sun's gravitation, decreasing in- 



versely as the cube of the distance, makes the relative 

 velocities with which the planets perform their orbital 

 revolutions round the Sun to be as the cubes of the 

 velocities of the motion along the respective orbits in 

 which the revolutions are made. 

 XXV. The distances of the planets from the Sun are regulated by 



the action of astral gravitation. 

 XXVI. To apply Proposition XXV. to the motion of a spinning- 

 top. 



