Chap. XXL] THE HEAVENS. 260 



and therefore the revolving force being at the equator 

 1,000,000, it is on the 45th parallel 581,000. 



There is therefore a relative excess of revolving 

 action on the 45th parallel ; for the normal amount 

 of retarding force on the 45 th parallel is '504, and the 

 revolving force "581 of the same forces respectively 

 on the equator if the source of the revolving force be 

 as given in the foregoing section. 



PROPOSITION XXVIII. 



Theorem. — If any force inherent in a j)lanet, or any 

 extraneous force continuously acting on it, tended 

 to give it a faster motion in its orbit than that 

 imparted by the revolving force of the sun's 

 gravitation, that planet could not remain in the 

 solar system. 



Data. — Proposition XXV. 



Pro^?/.— Because, however slight the increase of 

 velocity, the equilibrium in the orbit is destroyed by 

 the centrifugal force increasing as the square of the 

 velocity : and as the planet, whilst increasing the 

 velocity of its onward motion, recedes from the 

 centre under the action of the opposing force, the 

 opposing forces become more and more unequal ; for 



