252 THE OCEAN. [Book X. 



Because the opposing action of solar and astral 

 gravitation tends to give the planets both orbital and 

 apparent motions (Proposition VII.) ; 



And the actual relative velocities of the opposite 

 motions in each orbit are neither greater nor less 

 than would result from the free action of those forces 

 (Propositions XIX. to XXII.) ; 



Therefore those motions are not dependent on the 

 action of any other forces than those stated in the 

 above theorem. 



Note. — Extraneous forces, acting from other 

 centres of rotation, may revolve the whole solar 

 system jointly, and cause perturbations in the 

 motions of the planets under consideration in this 

 Proposition ; but the acceleration in one part of the 

 orbit being compensated by the retardation in the 

 opposite part, the mean velocities will not be 

 affected. 



PEOPOSITION XXIV. 



Theorem. — The revolving force of the sun's gravita- 

 tion, decreasmg inversely as the cube of the dis- 

 tance, 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 

 motions along the orbits in which the orbital 

 revolutions are made. 



