\ 
465] 
361 
465. 
NOTE ON THE LUNAR, THEORY. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxv. (1864—1865), 
pp. 182—189.] 
I attend, in the expressions for the lunar coordinates, only to the coefficients 
independent of m. Planas values, taken to the fourth order only, are as follows; for 
greater simplicity I write a = 1 ; and, instead of nt + constant, cnt + constant, gnt + con 
stant, I write l, c, g respectively ; viz., I is the mean longitude, c the mean anomaly, 
g the mean distance from node : this being so, then r, v, y, denoting the radius vector 
longitude and latitude respectively, we have 
- (Plana) = 
r 
(but I omit Plana’s term 
e — 
ïï e 3 ' 
- 1 fe 
cos 
c 
+ 
e 2 - 
i* 4 
~ \ fe 2 
33 
2c 
+ 
§ e 3 
33 
3c 
+ 
Î 
33 
4c 
- 
Î fe 2 
>3 
2<7 
— 
1 f e 
33 
o 
1 
+ 
i 
COS 
2c + 2g which should be = 0). 
1+ 
+ 
2 e - 
ì e 3 
- h fe 
sin 
c 
+ 
Î e 2 - 
ii pi 
2 4 e 
~ if fè 1 
3 3 
2c 
+ 
13 p3 
T2 e 
33 
3c 
+ 
103 (A 
_ 9(T 6 
33 
4c 
- 
Ì f~ 
ÄTV + 4 f 
33 
2<7 
+ 
f fe 
33 
cs 
1 
r fcO 
C. VII. 
46