of Edinburgh, Session 1885-86. 
with m- 1 like results for the other minors, we have 
829 
P m in | aW . . . h m ~ 3 kT | 
= P W in | cdtyfi . . . k m ~H n | multiplied by the product of the 
cofactor of Piped . . . T) last written and m - 1 like expressions 
with b, c, d, ... I respectively in the first row instead of a ; and 
thus we have 
m - 2 I 1 Gj 
p = r 2 (abe . . . 1 ) . II / x / , 0 \ , 
m b v ' | (z-m + 1) (z-m + 2) j , 
where II consists of m factors from a to l inclusive. 
Again, in 
a°b l e 2 
■w 
since the minor 
| b°cM 2 . . . h m -W | = Piped . . . 1) 
(z -m+ 2)' (z -m + 3) ; 
(y-m + 2)' (y-m + 3)' 
which by § 1 
= piped . . . 1) 
1 a a 2 
(z-m + 1), (z-m + 2), (z-m- 1-3) 
(y-m + 1), (y-m + 2), (y-m + 3) 
with m - 1 like results for the other minors, we have 
P m in | a°b 1 c 2 . . . g™~% y k z l n \ 
= P m in la®^ 2 .... & TO_2 Z ra | multiplied by the product of the 
cofactor of piped . . . T) last written and m - 1 like expressions 
with b, c, d, ... I respectively in the first row instead of a ; and 
thus we have 
P„ = £ 22 (afc...Z).n 
l a a 2 
(z-m+l), (z-m + 2), (z-m+ 3) 
(y-m+ 1), (y-m + 2), (y-m + 3) 
And in like manner it may be shown that in 
| aW . . . f m - 5 g*hm n | 
P <>wi — 2 
m = 4— (abe.. .1). n 
l a a 2 a 3 
(z-m+l), (z-m + 2), (z-m + 3), (z-m + 4) 
(y-m + 1), (y-m + 2), (y-m + 3), (y-m + i) 
(x-m+1), (x-m + 2), (x-m + 3), (x-m + 4) 
