479] 
FUNCTION IN THE LUNAR AND PLANETARY THEORIES. 
525 
terms which experience an alteration in passing from the development of the reciprocal 
of the distance to those of the disturbing functions m' upon m, and m upon mf 
respectively. 
We have 
Disturbing Function m upon m 
= m 
r cos H 1 
r' 2 p 
Disturbing Function m upon mf 
r cos H 1 
= m i — + - 
r 2 p 
The expressions of — rco ~— and _ } developed to the third order in the 
eccentricities and inclination, are given, Leverrier, pp. 272 and 274 Expressed in the 
terms of the foregoing arguments L — ®', &c., and in terms of a, a' in place of a 
and a, these are as follows : 
r cos H a . 
, 2 = / 2 mt0 
r a 
L'-& 
H 
l 
L — © 
L-n 
- 1 + -| (e 2 + e' 2 ) + rf 
cos 
1 
0 
-1 
0 
— ed 
>5 
+ 1 
+ 1 
-1 
- 1 
+ §e — § ee' 2 — § erf 
+ 1 
0 
-1 
+ 1 
- i e + 4 ee' 2 + § e 3 + L erf 
55 
+ 1 
0 
-1 
- 1 
— 2e' + e 2 e' + §e' 3 + 2 erf 
„ 
+ 1 
+1 
- 1 
0 
- £ e 2 d 
55 
+ 1 
+1 
-1 
-2 
+ & ee' 2 
55 
- 1 
+ 2 
+ 1 
-1 
tÍt ee 2 
„ 
+ 1 
+ 2 
- 1 
"I 
+ # 6rf 
55 
+ 1 
0 
+ 1 
-1