Chap. XXI.] THE HEAVENS. 265 



santly exchanging their positions as the ratio of the 

 conflictmg forces varies at different depths or in 

 different parts of the ocean. 



PROPOSITION XXX. 



Theorem. — -If the revolving force of a sphere be greater 

 than its direct force, nothing can rest loosely on 

 its surface. 



Because the centrifugal force of astral gravita- 

 tion is equal to the revolving force (Proposition 

 VIII.) ; 



Therefore objects placed on the surface are carried 

 from it by astral gravitation sufficiently far to bring 

 this into equilibrium with the direct force (Propo- 

 sition XXV.) 



PROPOSITION XXXI. 



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

 tion, and the force of astral gravitation Avhich 

 resists the direct force of the earth's gravitation 

 in the absence of any revolving force, are together 

 less than the direct force of the earth's gravitation 



