IN PHYSICAL ASTRONOMY. 
25 
Supposing <p o = 0 // = 0, c 0 = 0, c 0 being in fact imperceptible to observa- 
tion, and neglecting cos 2 n't, sin 2 n't, in order to find the constant part 
of 
d^o 
dt’ 
dec, _ _ 3 (A C) g j n w CQS w CQS C ^ 
dt 2n A a' 3 A 
c dy — _ s (A c) j^i g j n u cos w s j n c n ' t 
dt 2 nAa' s A 
1^2 = 3(C — A) M , cQs _ 3 (C-A ) n , s cog 
dt 2 nCa' 3 2 nC 
This result agrees with that given in the Mec. Cel. vol. ii. p. 318, and with 
that given by M. Poisson, Memoires de l’Academie, vol. vii. p. 24/. In La- 
place’s notation u — h, m = n'. In M. Poisson’s notation co = Q, m — n'. 
p. 35 7. 
From the general equations given in the Mec. C61. vol. i. p. 268, the fol- 
lowing may be inferred. 
3 a A , 
a 
5 a a 
_ 2 (a* + a, 2 ) A 3 
a 6 
2 a, 1,8 
a , 2 1,1 a t 1,u 
2 a, 1 ' 3 
a/ 2 1,8 2 
47 1, 1 
a i 
7 “ & ]4 
— 3 (a 2 + a, 2 ) , 5 a. 
9 a A - 
_ 4 (a 2 + a, 3 ) A 7 
a b 
2 a i * 
a* I>3 2 a, 1)2 
2 a ( 1,5 
a/ 3 2 
a t 1,3 
a A 
2 hS* 
_ (a- + a,-) /, 3 a h 
a ,' 3 3,1 a t 3,0 
3a, 
2 (a- + a/ 3 ) , 5 
a, 2 3,2 2 
a A 
—•^3,1 
«/ 
5a, 
2 
_3(a 2 + a 2 ), 7a, 
7 a A , 
_ 4 (a 3 + a, 2 ) A 9 
a 6 
a? 3,3 2 a, 3 ’- 
2 a ( ° 3 ’ 5 
a/ 3 J ’" 2 
a, 3,3 
-~b i0 
-(*+a?) b 5a b 
a & 
_ 2 (a 2 + a, 2 ) j 7 
a b 
2 a, ’ 
a t ~ ’ a, 
2a ( 5,3 
a* 2 
Ur J,\ 
a i 
3 a , 
2T, h » 
_ 3 («■ + «,«), 9 a,, 
5 5 
_ 4 (a 2 + a/ 3 ) A 1 1 
a A 
— " 5,3 
a, , 
a* 5 ’ 3 2 a, 52 
2 a, 5,5 
a y 2 3,4 2 
^1,0 ■ 
— a- + a? b a , 
a* b *‘° a, 3 ’ 1 
*i.i 
a 2 + a, 2 , 2 a 7 
- , «... — 
a A 
— b 3 
a, 
MDCCCXXXI. 
E 
