a Problem in physical Astronomy. 
5 k 1 
3-5 
4.6. 2 
3-S-7-3 
4.6. 8.4.2 
+ 
* + 
3-5-7 
4.6. 8. 4 
3-5-7~9-5 
4.6.8.10.6.4 
, , 3 - 5 - 7 - 9 .;. ^ is 
* 4 . 6 . 8 . xo. 6 1 4 . 6 . 8 . 10 . 12 . 8 ’ 
— 4-j-Xh.L. sax'; 
16 1 4 
_L .. 3»5-7-9- ll -7 • 
^ 4 . 6 . 8 . 10 . 12 . 8 , 6 ’ 1S 
= rr + ^H. L. 2 = «'; 
_ 3-5-7-9 5-3 r , 3-5-7-9-H-7-5 , 3 -5-7-9-n-i3-9-7 a?,, • 
4 . 6 , 8 . 10 . 6 . 4.2 * 4 . 6 . 8 . 10 . 12 . 8 . 6.4 ‘ 4 . 6 . 8 . 10 . 12 . 14 . 10 . 8 , 6 ’ ^ 
= i-° 67 4 - H L 2 — «' * 
12288 I 5 i 2 rt *' L '* 2 — 
We therefore now have « +* V (1 — cc) + y!cc^ ( 1 —cc) 
+ ^V(i — f° r a near value of the infinite series -2- a 4. 
4 ‘ 
-M. £ 4- l- 5 ' 7 V A?/; 
4.6 ^ ^ 4 . 6.8 ° 6 * 
13. Having thus obtained a sufficiently near value of the in- 
finite series which entered into the fluent, in Art. 10, we have 
only to add to it the three radical terms there found, v being 
put = 1, and to multiply the whole by (a+b)~ 4 , and we shall 
have 
~ 2 y/(X— CC) . 4^/(1 —CC) x/(l—CC) 
3 cc • ic* 1 
7rA'=(a + 61 1 9 5 - z t« 
v ' I + ITs-s uc * 
CC 
j 1 1 28 — S4CC 
— cc) -pp'cc (1 — Cc)-\-v'c 4 s /( 1 — cc 
which equation being more concisely expressed, and dividet 
by 7 r, gives 
96—23 CC 
A' = 
cc 
128 — 840; 
1 +✓(.,_«) (i ±p+*'+p’cc+,' e >). 
* See the Appendix. 
