PHYSICAL ASTRONOMY. 249 



orbit = ^ ; also the Sun's force on M in the di- 





rection SM = , -. rj nearly, and hence the 



(a *~~ T sin x j 



force HK, or MN, is found = -^ . 3 r sin x. 



Therefore, MO = 3 . 3 r sin* x 9 and 



NO ==. 



Also MF = ~ 



In all this the terms involving powers of r greater than 

 the first are rejected ; and hence also, MF MO, 

 pr the whole force with which the gravity of the 

 Moon to the Earth is increased or diminished, 



is- (i 3 sin* x}. This last force is 0, when 

 a 3 v 



3 sin* x = 1, or sin % = -- , that is, when 



x =; 35. 15/5"; at the quadratures the same force 



7)1 T 



is + - , and at the opposition and conjunc- 



2 mr 

 tion . 



Tho 



