234 THE OCEAN. [Book X. 



onwards, and the opposing action of astral gravita- 

 tion, then the force of astral gravitation increases 

 as the square of the velocity of revolution which 

 it opposes. 



Because, being in equilibrium, the force of astral 

 gravitation is equal to the revolving force ; 



But the revolving force is as the square of the 

 velocity of revolution (Proposition VI.) : 



Therefore the force of astral gravitation increases 

 as the square of the velocity of revolution which it 

 resists. 



Note. — The action of astral gravitation which 

 opposes the revolving force is a centrifugal force ; 

 because, acting in exactly the opposite direction to 

 that in which the revolving force acts, it tends to 

 draw the revolving body backwards out of its orbit, 

 as shown by the diagram on p. 88. 



PEOPOSITION IX. 



Theorem. — The direct force of the sun's gravitation 

 acts as a retarding force, opposing its revolving 

 force along the orbits of the planets. 



Because the planets move along their orbits with 

 such velocities of absolute motion as to make the 



