268 THE OCEAN. [Book X. 



The distance at whicli they are equal forms the 

 normal line of the equilibrium of vis-inertise. 



This normal line of equilibrium is destroyed by 

 the force of astral gravitation which opposes the 

 sun's revolving force (Proposition XXV.) 



But as this force of astral gravitation decreases 

 inversely as the cube of the distance from the sun 

 (Proposition XXV.) ; 



Whilst the direct force of the sun's gravitation 

 decreases inversely as the square ; 



Therefore the line of equilibrium will be reached 

 at some greater distance from the sun, as already 

 shown in Proposition XXV. 



PEOPOSITION XXXIII. 



Theorem. — An indefinite number of successive lines 

 of equilibrium separated by spaces, in which the 

 forces of gravitation drawing towards and from 

 the earth are unequal, might be formed in the 

 same manner as that shown in the preceding 

 Proposition. 



Because bodies in the first line of equilibrium 



entire extension of space. And yet to us these comparatively 

 infinitesimal portions of power, of time, and of space are equally 

 all-important. — The Elevients : Longmans, Green & Co, London, 

 1866, vol. i. p. 89. 



