PROFESSOR CATLET ON PEEPOTENTIALS. 
729 
85. But the forms nevertheless belong to a system of four ; from the formulae 
n(a, j3, y, v ) 
r « r /3 t x 
= r 7 r ( a +/ B - y ) a > v ) 
= (1— vy~ y 11(0, a, a-}-|3— 7 , v ) 
= (l — v) 13 y p^ a + ( 8 — y)r y n(a+^ — y, y, 0 , v ), 
writing therein a=^-s+g', 0 =-^— y= — 1 +g 1 , we deduce 
n(is +^ 5 \ — q, —\+q, v ) 
r ( - 1 + gfr (is- 1 + i ) n ( - i+^ j+1, t>) 
n(|— q, is+q, &—q+ 1, v) 
-*+& W, *); 
and the last-mentioned values of the disk-integral may thus be written in the four forms: 
rd-^rjl i+g) / 1_2? n (i s +^ I-?, -term in s, 
-r**r£ 
r(i+s)r(i*-?+i) ^ 2? n (~2+^ \s-q-\-l, 2 «+ 2 »/*) 
W + j ) - „ , 
r ( i + ff ) r ( V - ff + i )(^“/) - i + 2 . W » 7 *) “ ” ; 
and since the last of these is in fact the second of the original forms, it is clear that if 
instead of the first we had taken the second of the original forms, we should have 
obtained again the same system of four forms. 
86 . Writing as before x=~ -L — &c., the forms are 
° t+J~ — K- ’ 
nsTi 
T{i-q)T^s + q) 
■ ri*ri 
( Z 2 -* 2 ) 1 
lP+i-'(t+f a —x*j-*+*' l (t+f *)-*-' dt — term in s, 
riK^rtV-g+i) /" 1 ^ 2 -^ 1 - 2 ! r?+? ( t+r-*?T * (*+/ 2 )-^ „ 
JV*“* (£+/ 2 -* 2 )-* + i (i5+/ 3 )-i s+ ^ 1 ^- „ 
( # s " ? (^-f/ 2 -^ 2 )- Js - 2 (^-f/ 2 )“ i+? — 
r(|-g)r(i s +g) J 
-ri*r* 
r(i S -g+i)r(i+ ? ) 
