CiiAP. XXI.] THE HEAVENS. 251 



of Neptune's lagging motion is 52,591 times greater 

 than Mercury's : 



Therefore the ratio which the orbital bears to the 

 lagging motion is 463,350 times greater in the orbit 

 of Mercury than in that of Neptune. 



The square of that ratio of velocities is 

 214,693,222,500 — which is approximately the sixth 

 power of the distance, and therefore represents the 

 relative ratio of forces (Proposition XYI.) 



PEOPOSITION XXIII. 



Data. — The sun rotates from west to east, and the 

 planets revolve in their orbits in the same direc- 

 tion ; but the periods of their revolution are 

 greater than that of the sun's rotation, so that 

 they have apparent motions over the surface of 

 the sun from east to west. 



Theorem. — The motions by which the planets are 

 revolved in their orbits from west to east round the 

 sun are caused by the revolving force of the gravita- 

 tion of the latter, tending as it rotates to carry the 

 planets round with it in the same motion of rotation ; 

 and the apparent motions from east to west, in rela- 

 tion to the surface of the sun, are caused by astral 

 gravitation. 



