438 
Proceedings of Boyal Society of Edinburgh. [sess. 
we find the identity to be 
\af 2 d^gff\af. 2 d^g b h & \ - \af 2 d^fi s \.\af 2 d^gfi^ 
+ = 0 , 
a glance at which suffices to show that it is nothing more than the 
extensional of 
\gjh[\9jh\ - \9A\Wh\ + \9<sH\vJh\ = °> 
the very identity of Bezoufc which was taken as a basis for it. As 
the same extensional has already been found among those of 
Desnanot, any new interest in it is due to the peculiar way in 
which Jacobi obtained it. By the same method, viz., by substitu- 
ting for secondary minors an expression (4) involving primary 
minors and the primitive determinant, he shows that 
+ Axt = o. 
(xxm. 12) 
This being translated in the same manner as the preceding, becom'es 
| a i^2^3 e 4 f&9f& 1*1 ^1^2^3 e 4^5^8 I I a f >i A$A i f b9f% I’ I a f > 2 ( ^'Z e ^9 
+ KVs^/^'sl^Ms^AI = 
and is thus seen to be another of Desnanot’s results, viz., the exten- 
sional of 
l/e0Vks - \frth\-9s + I fsffelto = °- ( XXIIL 12 ) 
The deduction 
9 A? 
‘A? 
a®a; : :. 
Af 
"A? 
CD 
II 
AfAf ’ 
8 a ( g 
(<") 
A *’ i 
k’ 
(0 
is made from it by substituting appropriate differential coefficients 
for the primary and secondary minors involved in it. (lviii.) 
The eleventh section is devoted to the establishment of the 
general theorem which includes the theorem 
«-AA = AfA<f>-A?Af 
of the preceding section, and which, as we have seen, Jacobi had 
first enunciated in 1833. To start with it is repeated that the 
system of equations • 
