IN PHYSICAL ASTRONOMY. 
35 
According 1 to the value of the parallax given by M. Damoiseau, p. 573, 
r, = -00834, r 3 = '18350, r 4 = -01625, r 5 = -00547, r 6 = -03342, r 7 = -004525, &c. nearly. 
From the preceding values it appears that several of the quantities X which 
correspond to arguments in the longitude depending on the cubes and fourth 
powers of the eccentricities are of the same order as those which correspond 
to the arguments 1, 3, &c. : hence in order to carry the development of h R 
d R 
and S &c. to the terms depending on the cubes of the eccentricities, X 21 , X^, 
X 24 , &c. cannot be neglected when extreme accuracy is sought ; and if the 
method which I have employed should be adopted, it will be necessary to extend 
very considerably the Table II. so as to embrace these quantities. 
The advantages of this method appear to me by no means confined to the 
condition of taking into account all sensible quantities ; a few lines of calcu- 
lation suffice to obtain approximate results. 
Thus neglecting the squares of the eccentricities, 
fl=„,{_A_^-|^ cos 2f + ^ c os*+ y^co S ( 2 i — *)-f-£«o.(S< + *) 
- T $ e ‘ cos * - I' $ e ' cos (2 ‘- 2) + T $ e ‘ cos ( 2 ‘ + } 
' -.Q 
= 0 
2 m af 
3 m. a 3 I 
' l 
. 1 
- r i — -H- — — - 1 
+ 
1=0 
2 pa 3 1 
. 1 — m 
/ 
1 
+ 
1 10 
|3 
,1® 
11 
0 
p a . 
3 1 
9 m, a 3 f 
1 
3 ~ Y ri / ~ r * + 
2 /x a 3 l 
1 — 2 m 
3 1 
3 m, a 3 
/ 3 
r *” T r ‘J- r <- 
13 — 27 n 
+ 1 
}- 
3 m, a 3 
? n 2 r 5 - r 5 - — -1 — = 0 
2 [L a 3 
/o <3 ™\o 21 m, a 3 f 2 1 
(2-*)*r.-r,+ 1 !lf!{ 2 +1 j =0 
4 p a 3 L 2 — m J 
F 2 
