134 
MAJOR P. A. MACiMAHON ON A CERTAIN CLASS OF 
f Tl 1'' 
are ( ) in number; it will be shown that the quantities yx,y those to which 
reference has been made in the above statement of theorem. 
Art. 35, 
With the new 
symbols the deteroiinant may 
be w'ritten :— 
1 
As yi3 
^14 714 
A,'/!-i7i,k-i 
Am 7i-i 
1 
A 2 
1 
^■23. 
Ar 724 
A2,'rt-i 72 , M-l 
Asn 7'2a 
1 
As 7i3 
1 
/^23 
1 
Ar 
• A, n-l73,n-l 
Asii 73« 
1 
A 4 714 
1 
Ai 724 
1 
Ai 
1 
A,n-l74.!i-l 
A4ii 74'/! 
1 
1 
1 
1 
1 
An-1,'-! 
/3l, n- l7l, » 
-1 A, «-i 72, «-l 
Ai,« — 1 7s, K — 1 
^4,7?—1 y i, 77 —1 
1 
1 
1 
1 
1 
1 
An 7l« 
/S'ln 7‘ln 
Asn 73n 
and may be transformed, without alteration of value, by the following operations 
performed successively. 
Multiply 
column by 
1 
3 ''^ column ~ 
P<iZ 
„ row ^23 
4 ^^ column 
„ I’OW ^24 
5? ?? J3 
column ^ 
P 23 
„ row ySog 
?? ?5 3? 
n‘'' column 7^ 
