OUTLINES OF NATURAL PHILOSOPHY. 



The gravitation of one planet to another, is express- 

 ed by the quantity of matter in each, divided by 

 the square of the distance > and therefore the two 

 bodies tend to come together with a force that is 

 as the sum of their masses divided by the square 

 of the distance ; so that when the motion of both 

 is referred to one only, the force must be express- 

 ed by the sum of the masses divided by the square 

 of the distance* 



The disturbances produced by the action of the pri- 

 mary planets on one another, are of more difficult 

 investigation than those produced by the Sun on 

 the motions of the Moon, because the disturbing 

 body is not at an immense distance, as in the lat- 

 ter case. The only sure way of subjecting them 

 to calculation, is by a direct solution of the Pro- 

 blem of the Three Bodies ; the part of which that 

 may be accounted quite elementary is now to be 

 considered. 



;fo 



vlt 



264. The forces which act upon a body, to 

 however many centres they tend, and whatever 

 law they may obey, may be resolved into the 

 directions of three lines or axes, given in po- 

 sition, at right angles to one another. 



This is evident from Dynamics, vol. i. 70. 



The advantage of this resolution of forces for deter- 

 mining the motion of a body attracted to several 



centres. 



