24 
Consequently 
T = 
on hansen’s lunar theory. 
p 2 d_ m 2 V( 1—e 2 ) 2pe sin <£ dX 
na 2 \/(l—e 2 ) rfi p 2 + a(l-e 2 )df 
[163 
= — 2 -5 
dip 2pe sin 0 dA 
2pe sin 0 _P^ Tj'iP /f 
a( 1 - e 2 ) u 'rca 2 V(1 - e 2 ) ' (i ’ } 
d 
dX 
dt ’ 
om ^ u,/v X ^2 //1 o\ 
dt a (1 — e 2 ) dt na 2 V( 1 — e 2 ) äi >ia ^ e 
2pesin $ n /v p- 
H/ a t} ~ ^v(i - o n; ( ^’ ‘>5’ 
»_ ^ pe sin $ d\ pe sin 
A ¿(T-» a(1 - e 2 ) H/ & *> “ F '& *>' 
and substituting in these equations the values of 
dip pesinó d\ , d ... . 
■®-"S(W) dt aud s m 
we find 
T= ¡2 -cos(v — A) — 1 + 
2p 
a(l — e 2 ) 
cos (?;, — A) — 1 
na dfl 
V(1 — e 2 ) dv t i 
+ 2- sin(v — A) 
na dii 
r 
V(1 — e 2 ) c?r 
— 211 ('¿T t) P es i n< fr n//>» x\ P 2 
' } a (1 - e 2 ) A1 ' ( n«V(l - e 2 ) di 
wa rfn p 
B ~~ |r cos - x > - 1 +;^fh) ( cos “ x) ~ *)} V(T^) f - r sin <*' - X) V(T^j r § 
+ n,(f, of^-r (?, 0, 
ciA 
which are Hansen’s values, except that in the coefficient of n' (£, t) has been re 
placed by its value. 
2, Stone Buildings, 31 si March, 1855.