Chap. XXL] THE HEAVENS. 253 



For the foregoing Propositions show the sun's 

 revolvins: force to be the cause of the orbital revolu- 

 tions of the planets ; and Plate XVII. shows the 

 existence of that ratio of real and apparent velocities 

 of orbital motion as regards Mercury and the earth ; 

 and the same ratio exists as regards all the planets. 



Thus, the relative velocities of the orbital motions 

 of Mercury and Neptune are as 8*8 is to 1 ; the cubes 

 of those velocities are as 681 is to 1 ; which re- 

 presents approximately the relative number of their 

 orbital revolutions. 



Also, because the revolving force is inversely as 

 the cube of the distance (Proposition TV.) and the 

 motive force acting along the orbit is inversely as 

 the distance (Proposition XV.) ; therefore the rela- 

 tive number of revolutions are as the cubes of the 

 relative velocities of motion. 



PEOPOSITION XXY. 



2 heor em.— The distances from the sun at which the 

 planets are revolved in their orbits are determined 

 by the action of astral gravitation. 



Data. — The planets are revolved in their orbits 

 in equilibrium between opposing forces of solar and 

 astral gravitation. 



