370 
SECOND NOTE ON THE LUNAR THEORY. 
[466 
Writing a + 8a, e + 8e, &c., in place of a, e, &c., and observing that the divisor for 
the integration of the term in 2c — 2g is 2 (c — g), = — 3m 2 , the first five equations 
give respectively 
8 a = 0, 
8e = — f y 2 e cos 2c — 2g, 
By = +17 e ' 2 » 2c - 2 g, 
8c = + § y 2 sin 2c — 2g, 
Bg = + f C 2 „ 2c - 2g. 
The constant term in il is 
= m 2 n 2 a 2 (i + § e 2 — f y 2 ), 
and this gives in 
dl _ cWl , dil 1 d£l 
It’ da + ie Te + ^ cb’ 
a term 
which is 
m 2 (— 1 — § e 2 + f y 2 
+ f e 2 - f y% 
= m 2 (— 1 — f e 2 + f y 2 ). 
di 
the term 
which is 
Substituting for e, y, their correct values e + Be, y + 8y, it appears that contains 
m 2 (— | eSe +f y&y), 
= m 2 (|| + |f =) e 2 y 2 cos 2c — 2g, 
= ffm 2 e 2 y 2 „ 2c — 2g, 
and joining to this the before-mentioned term 
= — m 2 e 2 y 2 „ 
we find 
dd 
dt 
/45 15 15 m S/>SU£ 
— VTÏÏ S / Tf> m e 7 
2c - 2g, 
2c - 2g, 
whence, writing as above l + 81 for l, and integrating, we have 
81 = 
— j 5 g e 2 y 2 sin 2c — 2g, 
and it thus appears that the values of 8a, 8e, 8y, 8c, 8g, 81, agree with those obtained 
in my former Note.