376 
ADDITION TO SECOND NOTE ON THE LUNAR THEORY. 
and longitude. I wish to notice that the results, to the very limited extent to which 
they go, agree with those obtained by M. Delaunay in his “ Theorie du Mouvement 
de la Lune,” from his 49th operation, the object of which is to take away the term 
(63) of R, that is the term involving cos (2c— 2^). The formulae (see vol. I. p. 788), 
taken only to the necessary degree of approximation are 
a replaced by a, 
e- 
V 
e 2 
— 5 7 2 e 2 
COS 
%9> 
r 
>> 
7 2 
+ f 7 2 e 2 
29, 
l 
„ 
l 
-f 7 2 
sin 
2g, 
h + g + 1 
>, 
h+g + 1 
+ f 7 2 e 2 
V 
2g, 
h 
„ 
h 
+ f e 2 
}} 
2 9, 
which, observing that 
y (Del.) = ^ 7 (for present purpose), 
l = c, 
9 + l =9> 
h -f- g + l = l, 
and therefore g = — (c — g), 
become 
a replaced by a, 
c- 
„ e 2 - 1 re 1 
cos 
2c - 2g, 
7 2 
„ 7 2 + 1 y-e 2 
2c - 2g, 
c 
» c + 1 7 2 
sin 
2c - 2g, 
l 
» 1 ~ fk 7 2ß2 
2c - 2g, 
l-g 
>> L 9 7s ® 
2c - 2g, 
the last of which may be changed into 
9 » 9 + I« 2 
2c - 2g, 
or if the new values of a, e, 7, c, g, l, are called a + 8a, e + 8e, 7 + ¿>7, c + 8c, g + 8g, 1 + 81, 
then the increments 8a, 8e, 8y, 8c, 8g, 81, have the values given above. The process of 
my Second Note, taken as a first transformation, has in fact the object of removing 
the term cos (2c — 2g), and to the degree of approximation regarded, the result is not 
affected by the previous transformations, or by the substitution, t. 11. p. 800, introducing 
for a, e, 7, their standard elliptic values.