214 
Transactions of the Boyal Society of South Africa. 
in determinants, however, which concerns the multipHcation of an %-line 
determinant by an expression of n terms has a close analogue in Pfaffians, 
namely. The product of an n-line Pfaffian by an expression of n terms 
is equal to the sum of n Pfaffians the xth of ivhich is got from the given 
Pfaffian by multiplying the elements of the rth line by the terms of the 
given expression deprived of its rth term. For example 
^3 a^\ X (x^ + x^ + x^ + x^) 
I X 2a2 "^3^3 ^4^4 
^, b. 
a. a^ 
x-,a. 
a. 
x^b. xj)^ 
xjj^ 
\ 
x^c^ 
+ \ct2 
a^ 
x-^a^ 
xjj^ 
to look for the cofactor 
of X 
on the 
right-hand side. 
