27() THE OCEAN. [Book X. 



Because the eartli's perihelion has a motion of 

 revolution similar to that of the moon's perigee ; and 

 therefore the arguments of this Proposition indicate 

 the existence of a central force of rotation, bearing 

 the same relation to the sun and earth as the sun 

 Joes to the earth and moon. 



The action of this force on the motion of the 

 moon's perigee will be less than on that of the earth's 

 perihelion, in proportion as the diameter of the moon's 

 orbit about the earth is less than that of the earth 

 about the sun. For its effect depends on the differ- 

 ence in the force of its action in opposite parts of 

 the orbit. 



PEOPOSITION XXXVI. 



Problem. — To apply Propositions XXXIV. and 

 XXXV. to the disturbing action of the earth 

 on the moon's orbital motion round the sun. 



The earth's revolving force accelerates the orbital 

 motion of the moon round the sun when the moon is 

 outside the earth's orbit ; the force of astral gravita- 

 tion, drawing it from its orbit, then increases as the 

 square of the increase of the velocity of the motion, 

 and carries it farther and farther from the sun, until 

 the decrease in the revolving force of the latter, and 



