250 OUTLINES OF NATURAL PHILOSOPHY* 



The mean quantity of the force (1 3 sin .r*}, 



for an entire revolution, is found by multiplying it 

 by x y when it becomes (# 3 x sin 2 #), the flu- 

 ent of which, or the sum of the disturbing forces = 



mr . 3 , 3 . 



(* -* +-sm^Xcosjr); 



and this, when x is an entire circumference, be- 



comes X-^ . This must be divided by , 



and it gives ~ ? for the mean disturbing force 



acting on the Moon, in the direction of the radius 



vector. 



250. Hence, at the quadratures, the gravity 

 of the Moon to the Earth is increased by a 

 quantity equal to the mass of the Sun multi- 

 plied into the radius of the Moon's orbit, and di- 

 vided by the cube of the Sun's distance from the 

 Earth ; at the opposition and conjunction it is 

 diminished by twice this quantity 5 and the ef- 

 fect 



