716 
PEOEESSOE CAYLEY ON PEEPOTENTIALS. 
of the first factor (see Annex I.) is = 4 2 ' ; and writings, x in place of r, w respectively, 
I 2 s 
2(TiV . 
the integral is =■ pjf ■ into 
k 
y s ~ l dxdy 
or we have 
J{(a?->c ) 2 + j / 2 } is+2 
over the circle x*-\-y‘ 2 =f‘ 2 ; viz. this last expression (without the factor r ^J is the disk- 
integral discussed in the present Annex. 
67. We find for the value in regard to an internal point x<f, 
Y = r( is | r |^ w) /,+ 'JW- 
which in the particular case q— — is 
ere 
It may be added that in regard to an external point a >f, the value is 
v =r<p^lS ; i¥=?) ■ 2C '' + ’ - JJ 
which in the same case q= — 1 is 
where the ^-integral is 
o V — s + 1 v — 8 — 1 v~ s +l 
and the value of V is therefore 
(pip+l fs + 1 
_ r (*«+*) x®- 1 * 
d 2 d? d* 
Recurring to the case of the internal point; then writing V=^... an< ^ 
observing that V(;s 2 )=4(^s+A), we have 
VY=- 
4(ri) sH 
T&s-i 
(in particular for ordinary space s+l = 3 , or the value is — 7 ^, = — 4r, which is right). 
v w 
