185 
1901-2.] Dr Muir on the Theory of Jacobians. 
it occurs multiplied by 
/ _ + ^ .... tyn-l 
" “ tom+l d%m+ 2 ?x ' 
The desired result thus is 
which Jacobi formerly enunciates as follows : 
d/»-i 
“E Determinante 
]) — X? + jL 'bf n — \ 
^ ~dx 0Xj 0X w _x 
deducantur (??i+l) 2 alia Determinants, uni cuilibet dif- 
ferentialium Jpsarum x , x 1 , . . . , respectu sumtorum 
substituendo successive differentialia ipsarum x n , £e w+1 , . . . , x n+m 
respectu sumta : illarum (m + 1) 2 quantitatum Determinans 
aequatur expressioni 
/ _ -|\(m+l)(»i+l)g>»Y + 1 .... ^«~1 . ” 
J—-L a)/V» fW S')* 
‘ - v/i+1 2 
From equating cofactors of 
tyn m bfn+j ...... d fn+m 
dx 0aq dx m ’ 
Jacobi proceeds to equate cofactors of 
¥n + 1 ty n+m 
dx 
in the same fundamental identity, the resulting theorem now being 
2 ± »aa ■■■■ /c a = ( - • lr 
and then he adds, 
3/n 
dx n+m ’ 
u Eodem modo obtinetur generaliter 
[m- 1 ) 
= ± ^ ± 
0a*., 
^4 
