200 
Transactions of the Royal Society of South Africa. 
a^ 
a^ 
a^ 
^3 
a^ 
«'0 
ai 
ag 
a.. 
aj . 
\ 
h 
\ 
ho 
h 
h ■ 
\ 
h 
h 
h 
\ 
h 
and that the most convenient way of specifying any minor of this eliminant 
is by giving the numbers of the rows and columns from which the minor is 
taken ; for example, 
237 
357 
standing for 
aQ 
h 
a^ 
(3) The adjugate of Bezoufs eliminant of 
+ ^4 = O, + + 
O 
where 
H 
234567 I 
345678 
f^4 
^5 
I 234567 I 
I 245678 I 
the row-numhers of /x,. being 234567 and the column-numbers being obtained 
hy deleting the digit r + 1 from 2345678. 
To prove the identity of any one of the /x's with the appropriate primary 
minor, we may follow the procedure laid down by Le Paige in 1880 
(' Comptes Eendus ' .... Paris, xc, pp. 1210-1212), namely, multiply the 
ji in question by such another form of itself as will give the square of the 
desired equivalent ; for example, 
0 ^ _ I 234567 f ^ _ I 234567 
^^'^ 1 345678 1 345678 
567234 
678345 
I 234567 
I 345678 
567234 I 
678345 I 
where the minus above a row-number indicates change of sign in the row ; 
and columnwise multiplication now gives 
as desired. 
\a^b^\ + \a^h^\ \a^^\ + 
\ajb^\ 
1^264! 
\a.^^\ 
