a Problem in physical Astronomy .< 
539 
— 3 
?rA=(tf-|-6) 2 X < 
+ 
2 \/(l — CC ) 
CC 
8 
2 CC 
C6 
8 — 5 cc 
+ Av/(l-Cf) — ^^) + ^ + v /(l — C^j; 
and thence, by a more commodious arrangement of the terms, 
and dividing both sides by tt, 
A = 
f 8 — 2 c c 
w {a -f- b) 
1 X «< 
5 cc 
a. 
t_ ~1~ ( 1 ^0 -h ^ ~f" y 6 '^ “f - ^ 
io. The value of A, when » = 1, being now found, let us 
next investigate the value of it when » = £ ; which, for the 
sake of distinction, in a use to be made of it in a subsequent 
article, I denote by A'.* 
By writing £ for n in the fluxionary expression obtained in 
Art. 4, we have (a + bp' x -7 2 -^-~- 4 which bv 
converting the radical quantity y/(i — vv) into series, becomes 
/ „ f L\ 4 2 < ct / 4 I . V V . ^ 17 4 j 3 . 5 Z / 6 » » - —8 t 
(<* + * X 
— 5 
^/{yv _ cc) 
f~ 2 4 
1 + ^ + i^ + 
* 2 1 2./i 1 
24 
4. i±ZA!. ^ ] 
24.6 1 24.6.8’ 
— [a -j- b) * x< 
— cc) 
+ 
— a 
I -j : 
L v[yv 
V (ctz _ cc) 
I 4 tyz + i±ui 1 3±c9i 6 ^ ) 
41 4.6 1 4 .6,8 T 4.6.8.10’ ^ C,/ 
Now, the fluents of these terms, without their coefficients, 
are as follows : 
/ 
/ 
/ 
f\ 
•v V 
— 4 
•/ (vv — cc) 
is = v' i vv — cc) 2 \/(vv — cc) 
<V v 
\/{w __ cc) 
*v 
V{ vv — cc) 
’VV 2 
2 CC V 3 
V[yv — cc) 
3 c 4 c 
C C V 
H. L. t’ + W^-cc) 
c 
y( p p — eg) v + cc* 
CK 
V'T'*' — cc) 
as they are exhibited in Art. 5. 
3 Z 2 
£; and the rest 
