•284 PROFESSOK G. H. DARWIN ON THE STABILITY OF THE PEAR-SH.VPED 
PAliT II. 
Numerical Calculation. 
§ 15. Determination of Certain Integrals. 
The integrals w/, p/, depend on certain others, namely— 
— 
- 
WTT do 1 
0 Ad“A 
cos-« <i ,, I 
Tam — iy2»r j 
>■ 
(33). 
After a large part of the work had been done, I found that these Integrals tend to 
ive the required results in the form of the difference between two large numbers, 
c 
1 
and tliat it would have been more advantageous to consider the integrals 
A: 
i: = ^ cw 
Jo Ap" 
Op 
*A 
rDsiir"(i ,, 
)„ Tpr 
!» 
(34). 
It will be sliown hereafter how the group (34) may easily be found from the group 
(33), and it inay be mentioned that most of the results were determined in dujilicate 
from both forms. 
I proceed then to consider the H, T integrals. 
Since Aj = 1 — k“ sin* y siir 6, r'l = cos“ y + k '' sin“ y cos’ (f), sin“ /3 = k ' siir y, we 
have 
1 ..‘J 0 \ ^ 
TT/Vl - 
" siff/3 
/Ti2ii-2 _ t^2,i-2\ 
(35). 
= - ^ cor y T|;r'^ + 3 sin y t: 
2 /r—2 
J 
I now write 
// = f*" 
Jo A ’ 
rhir 
F 
rD 
J 0 \ 
t(b 
Q f {1 — k'^ cos" 0 
V de 
a: = [^ A cie 
J 0 
iff = [ (1 — C0S'’(^) d<^ 
J 0 
A(y)= Pa id 
. . (36). 
