IN PHYSICAL ASTRONOMY. 
381 
This gives for the coefficient of sin (/ + z ) in the expression for the longitude 
, /5o_ _ 3m,a* \ 
L 2 a t 8[x .a* ) 1 
which in sexagesimal seconds is 21 "'7, according to M. Damoiseau it should 
be 17"’56. 
Finally, 
a . . m, a 3 , f, 7 m, a 3 ' 1 ,5a , 
r 6 pa, 3 L 1 2 [A a 3 J 4 a, 
X = n< + 2esinx+< — — — ' ■ ^ e, sin (t + z) 
1 2 a t 8 [a a* J 
Substituting for b 3 l , b 3 2 their values in series 
3 a . 3.3.5 a 3 
& 3,1 = + 
} n 
c = 1 
a t 2.4 a, 3 
3 m , a 3 
+ &c. 
c, = 1 “ 
, 3.5a 2 , 3.3.5.7a 4 „ 
2,4.6./ +&C - 
3 ma 2 
4 [a a 3 4 j^a, 2 
I have shown, Phil. Trans. 1832, p. 38, that when a < a, 
Similarly it may be shown that 
i . 7H f i 3 Ct / 1 
& 
{ . , ma , 1 
l+ 4m'>') 
The arguments 
nt — v, nt — v lt nt t — v t and n k t—v 
occupy the same place in the expression for the latitude as 
nt — ct, nt — n t t— and < — ■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. 
