IN PHYSICAL ASTRONOMY. 
381 
This gives for the coefficient of sin (i + z) in the expression for the longitude 
f 5 a _ 3 m, a 4 \ 
12 a, 8 p a* J 6 ‘ 
which in sexagesimal seconds is 2i"'7, according to M. Damoiseau it should 
be 17"'56. 
Finally, 
a , , m. a 3 , f, 7 m, a 3 } , 5 a ,, , . 
r 6(1.0, 3 l 12y,a / 3 J 4 a, 1 y ' 
, , n • . f 5 a 3ra,a 4 l • \ 
X = n< + 2esinx+{ — — b ■■ } e, sin (t + 2 ) 
L 2 a, 8 [A a* J 
Substituting for b 31 , b 3 „ their values in series 
, 3a 3.3.5 a 3 - 
* 3,1 =-—+ o , , + &C - 
2.4a, 3 
, 3.5a* 3.3.5.7a 4 ' 
Oo.o = ——— + - ■ , v —r- + &c - 
. 3 m, a 3 
— I- 1 — 
4(l a, 3 
C/ = 1 - 
'3,2 
3 ma- 
4 a, 2 
2.4.6a, 4 
I have shown, Phil. Trans. 1832, p. 38, that when a < a, 
S [A la, 3 3,0 4a, 3 3,1 J 
, m.a~ , l 
1 + wM 
Similarly it may be shown that 
1 . 7)1 f T 3 # 7 1 
g,_l+-[6 w -—S,.,} 
m a 
4M 
b 
3,1 
} 
The arguments 
nt — v, nt — v ,, nt, — v, and n,t — v 
occupy the same place in the expression for the latitude as 
nt — ra, nt — ra,, re, t — ra, and re, £ — ra¬ 
in the expression for the radius vector. Similar methods may be employed to 
determine the arbitrary quantities, so that no other angles occur in the ex¬ 
pression for s except the quantities t, x , z, y, and if the quantities c and g are 
rational, no imaginary angles can be introduced. 
3 D 
MDCCCXXXII. 
