OF THE moon’s MEAN MOTION. 
403 
12 . Hence we obtain 
1 1 , 1 /' T ,3 
„'o„\ IQ y 4^ a^ ' 
a tti 2 a^ K 
9 
4 a. 
9 , 495 , 27 
64 < 7 , 
^ ^ 16 fit; 
16 a, 
3 m' 
147 
3 Wl’ 
+5^(l-5e«) + Y-e»+5.-e«- 
8 «, 
285 m'^ 
e" 
8 a, 
' 2 n 441 9 ,2 
4 ^ '' 16 flj 16 ’ 
or 
1 1 
0=-— --j 1 — ~ 7 Tf—- mV^+3inM 
3153 
64 
-/we 
7/i 
Now in Plana’s notation, or (substituting the value ofjo given in Plana, 
vol. ii. p. 855 ). 
= nearly. 
1 1 
13 
=d 1 — t/wVM 
3201 
and 
a a 
«'=«/{ 
64 
me 
1 I 2 4 t ^ 2/2 3129 j 
1 -|-m — ~m-\-^me 
13 . Again, by substitution in the equation for we obtain 
dt \ V 3 ,27 147 3 
I ^ 2^ 
+5 ^7 
— 2 ^^^) — 2 m(i)-l- |e' sin (21/ — 2 w/v — e'rm) 
-pC' sin ( 2 i' — 2 w/t'-l-c'my) 
— — -e'^^ sin ( 2 v — 2 mv) + |e'sin (2v — 2 /wj' — c'mv) 
— -xe' sin {2v — 2mv-^c'mv) 
~6 J (2/1 — 2 mi')-l-^e' sin ( 2 t' — 2 mj'— c'w?f') 
— ^e' sin (2v — 2mv-{-c'mv) 
ahu 
,27 
+ 8 - “‘It 
^ 1 — sin {2v — 2 wv) 4 -d ®in ( 2 * 1 — 2mv — c'mv) 
Jij 
— 2e' sin ( 2 i/— 2 wit' 4 -c'wiv) 
14 . Develope this equation as before, retaining m* only when it occurs in the 
non-periodic part, and we have 
