Chap. XXI.] THE HEAVENS. 2o5 



on p. 88. In consequence of the increase of the re- 

 tarding force of astral gravitation the planet at a is 

 carried to c in the orbit c d e, instead of moving from 

 a to ^ in its former orbit, a bf. The increased force 

 of astral gravitation thus lifts the planet into an orbit 

 farther from the sun at x. 



Note. — The planet having been held in equilibrium 

 by vis-inertise, the whole of that force, except the 

 force of astral gravitation created by the action of 

 the revolving force, tends to keep it at its normal 

 distance of equilibrium. 



Corollary. — Therefore the action of a revolving 

 sphere on other bodies in positions of normal equi- 

 librium may be considered as exerting a centripetal 

 force decreasing as the square of the distance, and a 

 revolving force decreasing as the cube of the distance 

 and of necessity resisted by a retarding and centrifugal 

 force also decreasing in the latter proportion. 



PROPOSITION XXVI. 



Problem. — To apply Proposition XXV. to the motion 

 of a spinning-top. 



Suppose the velocity of rotation be, say, 8 in the 

 direction abed (Plate XVIII.) ; if the resisting 



