THE ELEMENTS OF THE ORBIT OF A SATELLITE. 775 
refer to the moon, therefore make r and / interchange their meanings, and drop the 
accents to N' and \J>'. Thus as far as important 
d W 0 It V -r , . . . 
~ff j— =& sm ( A sin 2g.(138) 
This gives the whole effect of the solar tides on the moon. 
Then collecting results from (137-8), we have by (14) 
P . AN 
=ii sin ( N—xjj) 
- (sin 4fj—sin 2g x +sin 2g) + — 
sin 
2 gJ 
(139) 
This gives the required additional terms due to bodily tides in the equation for 
dN/dt, viz. : the second of (133). 
If the viscosity be small 
sin 4^ — sin 2g 1 +sin 2g“ sin 4f 
sin 2 ^ 
O 
= ^sin 4f 
(140) 
Next take the secular change of inclination of the lunar orbit. 
For this purpose we have to find dW/j'dN'-\-^j'dW/de , and may drop terms in 
i sin (N — xfi). 
First take the case (i.), where the tide-raiser is the moon. 
From (129) 
1 dW /t 3 
/ -^7 g = ^ Fll ' sin { N — ^+2^=11 cos (N-xp) sin 4 :^ . . . (141) 
, ,,dW. /t 3 , „ . . ~ 
h / sm2f i 
_i 
sin 4f x .(14f 
From (130) 
1 dW /t 3 
/ dN'/ g =- 2 G i{^ sin (dv r -V/+g ] )+i sin gl ] = —\{j+i cos {N—$)) sin 2g x (143) 
.,dW It 2 
^j'~dd 1 / Q = ^ P resen ^ orL ^ er °f approximation 
• (144) 
From (131) 
1 dW A 3 
j'dfr/ % — sin sin g}={(j+i cos (N— iff)) sin 2g . (145) 
V /r 2 
2 / 7-= 0 absolutely.(146) 
5 G 2 
