PHYSICAL ASTRONOMY. 



force parallel to SM or #, that affects the rela- 

 tive motion of P to S, is 



(1 -f- m)x , jg^g' i m' q 

 r^ r /J a* x' 



For the action of the Sun on P being resolved as 

 above, the part of it that is in a direction parallel 



to x or to SM is ; and the action of P' on P 



being resolved in like manner, the part of it paral- 



m f (x - x*} 

 lei to x is - '. Now, supposing x to 



vary by the momentary increment or fluxion x 9 x f 

 remaining constant, the increment of q, or q will, 



be such that -- = x x . , and therefore 

 x f 



m (x-x) = m q ^ ^jgjj^ therefore, is the force 



by which P' acts directly on P ; and if to this be 

 added the Sun's force in the same direction, viz. 



, the amount of the direct action of S and P' 



x -' 



on P, in a line parallel to SM, is - + 



* 



Now, 



