466] 
SECOND NOTE ON THE LUNAR THEORY. 
369 
cin | (1 +7 2 ) (1 - Vl +7 2 ) dn 
dg no? Vl — e 2 7 dl 
dil 
de ’ 
dg _ 2 dil 1 — e 2 — Vl — e 2 dO 1 + 7 2 dil 
d£ iia da ?ia 2 e de na 2 Vl —V 2 7 t/7 ’ 
d£ _ 2 ciO 1 — e 2 — Vl + e" dn (1 + 7 2 ) (1 — Vl -f 7 s ) dL2 
d£ ?ia c?a wa 2 e de na ? Vl — V 7 ¿7' 
The disturbing function contains the term 
ndrdcd (+ y| e 2 7 2 ) cos 2c — 2¿7. 
If after the differentiations we write for greater simplicity a = 1, n = 1, we have 
c¿7 1 7 2 
?ia 2 Vl — e 2 7 
dc _ 2 dii 1 — e 2 
dt na da na 2 e 
dn 
da 
dn 
de 
dn 
dry 
dn 
dc 
dn 
dg 
= + Li m-e-ry 2 
COS 
2c - 2g, 
= + Li m 2 e y 2 
55 
2c - 2g, 
= + - 1 jj- m 2 e 2 7 
55 
2c - 2g, 
= — Li m-e'ry 2 
sin 
2c — 2gr, 
= — Li m 2 e 2 7 2 
55 
2c — 2<7, 
and the formulae for the variations give 
da 
dt 
2 
/dn 
V dc 
dn\ 
+ dg) 
= 0 
de 
dt 
1 
e 
dn 
dc 
= — V' ^dery 1 
sin 
2c - 2^, 
II 
1 so 
1 
7 
dn 
dg 
= — ^ m 2 e 2 7 
55 
2c - 2g, 
dc 
dt 
1 
e 
dn 
de 
= m2 7 2 
COS 
2c - 2g, 
II 
1 
7 
dn 
dy 
= — m 2 e 2 
55 
2c - 2^, 
aj a. 
cs. 1 O* 
II 
-2 
dn 
da 
, dn 
+ i e is 
+ i7^ = (-¥+«+«=)-¥ 
55 
2c - 2$r, 
but this value of is, as will presently be seen, incomplete. 
C. VII. 
47