[479 
479] 
FUNCTION IN THE LUNAR AND PLANETARY THEORIES. 
527 
r' cos H a . 
IS = “2 mt0 
•r a 1 
L'- 
-0' 
L'-W 
L- 
-0 
H 
1 
© 
— 
1 e' 2 
cos 
+ 
1 
+ 2 
— 
1 
0 
- 
rf 
5) 
+ 
1 
0 
+ 
1 
0 
- 
1 ,>3 
¥ e 
+ 
1 
0 
- 
1 
+ 3 
- 
-V 6 - e3 
)> 
+ 
1 
0 
- 
1 
- 3 
+ 
f i e “ e 
- 
1 
+1 
4» 
1 
+ 2 
- 
T6 ere 
>> 
+ 
1 
+1 
- 
1 
+ 2 
- 
i ee' 2 
- 
1 
+ 2 
+ 
1 
+ 1 
- 
2T e ' 3 
5) 
- 
1 
+ 3 
+ 
1 
0 
- 
i *' S 
JJ 
1 
+ 3 
- 
1 
0 
- 
2 erf 
JJ 
+ 
1 
0 
+ 
1 
+1 
- 
h e 'i 2 
+ 
1 
+1 
+ 
1 
0 
It is hardly necessary to observe that, to obtain the expressions of the Disturbing 
Functions, these additional terms are to be combined with the corresponding terms 
in the expression of the reciprocal of the distance: thus, in the Disturbing Function 
il (to' upon to), the entire term depending on cos [L' — ©' — (L — 0)] is 
= to' |2(1, ... 20) i=1 + ^(-l+i(e 2 + e 2 ) + t/ 2 )} cos [(£' - ©') - (L - ©)], 
where, however, the supplemental term is taken to the third order only.