922] 
NOTE ON THE LUNAR THEORY. 
The following intermediate results may be recorded; 
= 1 +X> 
r = 
— log r = 
dv 
dt 
it™ 4 
i™ 2 - Iff™ 4 
1 
Cos 2D 
+ |-m 4 
m 2 + 
jn m 2-f |5 m 3 + 43£, 
Cos 4D 
+ 
■|m 4 
2 01 -yyo 4 
Cos G 
+ \em 2 
e ( 1 — f to 2 ) 
e(2 — § m 2 ) 
Cos 2D + G 
4- em 2 
e (j^m 2 ) 
e ( f< g-m 2 ) 
Cos 2D — G 
+ em 2 , 
e (Jg 5 -m + J/^m 2 ), 
e Gfm + \\ 3 -m 2 ), 
1 c?r 
r 
Sin 2D 
2m 3 + Jj 3 -m 3 + ^-m 4 
Sin 4>D 
fw 4 
Sin G 
e (1 — f m 2 ) 
Sin (2D + G) 
e (if m 2 ) 
Sin (2D - G) 
e (-^-m + f|-ra 2 ). 
These were, in fact, made use of for finding the foregoing values of r, 
C. XIII. 
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