NOTE ON THE LUNAR THEORY. 
re 
D = (1 — m)t, G = (l — §m 2 )£, (v =mt). 
The verification for the first equation is 
and the verification is thus completed. 
[922 
1 d 2 r 
r dt 2 
II 
r_l IT. 
II 
TT+O 
3I3 
1 
to 2 {—(cos2r— 2ri)} = 
Const. 
-1 +1 
= 0 
+ f ?n 2 
— £m 2 
= 0 
4- 2to 4 
- -W mi - & m * 
— |f m 4 
= 0 
Cos 2D 
4- 4 m 2 
— J^-m 2 4- 3m 2 
— fm 2 
= 0 
4- L4 m 3 
— f£m 3 4- - 1 fm 3 
= 0 
4-^-TO 4 
- MJt m 4 + 1|1 m 4 
= 0 
Cos 4D 
4- 8?h 4 
— f^-m 4 4-' à §-m i 
33 qil ^ 
16 ni 
= 0 
Cos G 
e 
— 4e 3e 
= 0 
— few 2 
4-3em 2 — f end 
= 0 
Cos (2D + G) 
e fffm 2 
e (- if m 2 ) e (\% 7 -m 2 ) 
e (— 3m 2 ) 
= 0 
Cos (2 D-G) 
em (ff) 
em (- ff-) em (±g-) 
= 0 
em 2 (- &) 
em 2 (— if-) em 2 (f 5 f-) 
em 2 (3) 
= 0. 
The verification for the second equation is 
2 dr dv 
r dt' dt 
d 2 v 
+ dt? ~ 
4- f m 2 sin (2v — 2ri) = 
Sin 2D 
4- 4?n. 2 
— if m 2 
4- f m 2 
= 0 
4- 2£-m 3 
— 5 s 6 -m 3 
= 0 
4- if^m 4 
— J-jp-ra 4 
= 0 
Sin 4 D 
4- ^-m 4 
2 01 />•>-! 4 
16 " L 
+ |f m 4 
= 0 
Sin G 
e. 2 
4- e . - 2 
= 0 
e. 3m 2 
4- e. 3m 2 
= 0 
Sin (2D +G) e. if^m 2 
e. — ifm 2 
e. 3m 2 
= 0 
Sin (2D — 
Cr) e. J^m 
e. - Jfm 
= 0 
e. ffm 2 
e. — |f m 2 
e. — 3?n 2 
= 0