PEOFESSOE G. H. DAEWIN ON ELLIPSOIDAL HAEM ON IC ANALYSIS. 531 
For brevity write 
J — 'i' 
io=s’i(/^4y+6). 
yi=A6(/-12y+68). 
Then we have seen in ( 73 ) and ( 75 ) that 
(1 —/3 cos 
(l-yScOS 30)" 
{<Eif _ 
[ 1 —^ cos 20)’ 
= ^ ”[1 + 8^ COS 24 >], 
= cos 2(f)\, 
= (l+y8Vo) {1—1^(./-1) cos 2(/)]b 
Therefore 
i 
Jo 
2/3 /5(1 —co82^) 
(S.^)^#=:7(l-i^+y8^ii) {cos-^^+P+-A-;SMy-h20)}, 
(1 —/S cos 20)" 
[. —{cos" ^4-2)5+iV/3'(j + 4)}, 
f.(®i)"c^^ = 27r (l+^yo) {cos^^+^ + i/S"^ (^ + 3)j 
0 
(78). 
Now pick out the parts of 'pdcr and of these integrals (78) which are independent 
of 9, and write 
F=.M (1 
= {1 -1 2-b fi- (r-127+ 388)}, 
G=.M(i-«»(}^y(i+i^+^o'.) ^ , („), 
= 7 rM| l+f/ 3 +-^-^g |S^(^" —12^ + 68)1, 
H = 2=rM(l-^)i('4|)*(l + /30,) 
= 27rM l_f^+-3lj^X7'-‘-4;'+S4)} 
A.lso write 
/ ( 1 4-^/3/ +f/3), 
^=1 +i/Sj + |A 
1 — 
«:'^= !—«" = -—SO that /c^=2/:J+2/S“-|- . . . 
. ( 80 ). 
3 Y 2 
