250 THE OCEAN. [Book X. 



The fractions of the sun's dnect force which act 

 as revolving forces are inversely as the distance 

 (Proposition III., Corollary). 



But Mercury makes 683 orbital revolutions whilst 

 Neptune makes one ; and the length of Neptune's 

 orbit being 77 times greater than that of Mercury, 

 the velocity of Mercury's orbital motion is 8'8 times 

 greater than Neptune's. The square of this iacreased 

 velocity is 7 7 '44, which is, approximately, inversely 

 as the difference of the relative distances. 



Note. — The above is demonstrated also by the 

 table on p. 82, which shows that the fraction of 

 the sun's force which at any distance acts as a 

 revolving force is inversely as the distance, and 

 directly as the squares of the velocities of motion in 

 the planetary orbits. 



PROPOSITION XXII. 



Theorem. — The ratio which the motive force of gravi- 

 tation bears to the vis-mertia3 of the planets in 

 each orbit is as the square of the ratio which the 

 velocities of the orbital and lagging motions bear 

 to each other. 



For the velocity of Mercury's orbital motion is 

 8*8 times greater than Neptune's ; and the velocity 



