IN PHYSICAL ASTRONOMY. 
271 
s = - _ nearly, 
r 
f e 2 e 2 "1 
= | 2 h 6 + -j Ziso + -J z u9j ysmy 
{■ 
e- 
+ <t Z U7 + ~2 Z 131 + -~2 “153 
6 2 1 
— *153 j y sin (2 t — y) 
+ | Z 148 + ~2 2 152 + ~2 *154 J - 7 S i n (2 t + y) + &C. 
- J 7 + J ^+ *f* R + r (df) = 0 
d- . r- 
2 . d «'* 
d t- r 3 
{r 2 — 2 r r cos (X — X) + r, 2 } 2 
(££)<!*' 
Neglecting the square of the disturbing force 
"d^ - • — + 2/d B + r (/) = 0 
— d a . r 3 S . 
d 2 2 j u, z m t z , 3m t zr r cos (X' — X) q 
d i 2 r 3 r, 3 r , 5 
d 2 . $ z 
3 /x s 8 . — 
+’ 
r u.S .z m, z 3 /j., z r r cos (X' — X) 
+ z — *r — r + — U 
d t* r i° r 
d X' _ h(] + s 2 ) (1 + s 2 ) /*/ d R\ 
d t r 2 r 2 J \d X/ 
d t 
r (—\ = a ( dR \ dR = ( 
\ d r / \d 
R\ dR 
a )’ dX' 
d t 
, ( t being used for n t — n i t) . 
Integrating the equation of p. 270, line 9, by the method of indeterminate 
coefficients, neglecting the cubes and higher powers of e in order to ob- 
tain a first approximation, m being equal to ^ as in the notation of M. Da - 
moiseau ; 
m, a 3 f , 3 ~ . 3 „ 3 , 1 
-’■»-t]Tvi 1+ T c + - T y ) = 0 
4(1- m) 2 | (1 + 3 e 2 ) r, — ^ {r 3 + r + } j - r v 
2 N 
MDCCCXXXI. 
