136 
MAJOR P. A. MACMAHON ON A CERTAIN CLASS OF 
Multiply 
column by 
/^13 
and 
row by 
1 
3 rd 
; 5 
1 
^23 
33 
qrd 
33 
/^23* 
(5 - 1)“^ 
1 
3 3 
(s - 1 )“ .. 
^2, s- !• 
(s + 1)“ 
1 
(« + ir 
ys-1,5 +1 
7s-l,s + l ^2,8 + 1 
35 
(s + 2)‘'' 
1 
(s + 2 )“ „ 
ys - i,s + 1 , 
53 
7s-l,s + l ^2,3 + 2 
33 
^th 
’ 3 
1 
Ts—l,s + l ^2,u 
53 
ys- i,s +1 
Art. 38. To represent the result conveniently, suppose the determinant divided 
into four compartments by the lines of deletion, thus— 
I. 
11 . 
III. 
IV. 
We then obtain- 
