526 
l>EOFP:SSOIi G. H. DAinVIX OX ellipsoidal HAILMOXIC AXALYSIS. 
§16. Portion of the Integration in the case of s = 1 
'I’lie preceding method may Ije used for hndiug the four integrals 
and 
There will then remain four integrals of the type jp (P/)' dcr to evaluate. 
The first jjair of our integrals are clearly to be treated Ijy putting Ifj = 0, 
t/s—: — <l-\ — t), qs—i. — q ~3 = t), and then determining jPpid. The condition for tlie 
second pair only ditfers in the accentuation of the q s which vanish, and in the use 
of 
The vanishing of IIq makes 
T\ cos -hbl.. cos d ], 
y,=l3n, cos 0+^-^ H-Pi cos 0j . 
In the first of these 
n ,=: -2r/3TfPA ID=:273PT^+ {Y 8 )'(PP' i 
and in the second the form is the same with accented </s. 
. I , , jML(/(l 
Also since k- ~aa = i),^yo iuive -;^ = 6. 
J cn.s a 
Hence 
Jz ^’ + f • 
kx+1 i-i: 
■{2/3qfi~l){i^2) + 2^%{i-l){i-2){i~-S)[{~i) 
and F.;,c/d is the same with accented ^’s. 
It is only necessary to pursue the cases jp and jp since the 
other pair of integrals may lie determined by means of multiplication by the 
ap|)ro})riate factors, determined in § 9. 
