ADDITION TO SECOND NOTE ON THE LUNAR THEORY. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxvn. (1866—1867), 
pp. 267—269.] 
Writing as in my Second Note, Monthly Notices, Yol. xxv., pp. 203—207 (May 
1865), [466], for the Moon, 
a, the mean distance, 
e, the excentricity, 
y, the tangent of the inclination, 
l, the mean longitude, 
c, the mean anomaly, 
g, the mean distance from node, 
I obtained by the ordinary method of the variation of the elements, from the constant 
term of R and the term involving cos (2c — 2g), the following expressions of the 
variations, 
Sa = 0, 
Se = — ■§ y 2 e 
COS 
2c - 2g, 
S 7= + 1 V e ' 
2c - 2g, 
Sc = +if 
sin 
2c - 2g, 
= + 1 & 
» 
2c - 2g, 
Si= + *y* 
» 
2c - 2g, 
viz. if in the elliptic expressions of the radius vector, longitude, and latitude, we 
apply to a, e, y, c, g, l, the foregoing increments, we obtain to the fourth order in 
(e, y) the portions independent of m in the expressions of the radius vector, latitude,