1903 - 4 .] Dr Muir on General Determinants. 71 
— a statement differing from Jacobi’s in having r’s and -s’s on the 
right-hand side where he has s’s and r’s respectively. The over- 
sight was probably not noticed by reason of the fact that in the 
special instances considered by him the values of any r and the 
corresponding s are the same. 
In the first of these instances he puts 
= r 2 = • • • = r n = - 1 
S 1 = s 2 = • • • = s n = - 1 , 
and obtains 
VlVi "'Vn 
thus arriving at Cauchy’s theorem regarding the adjugate, viz., 
B = A n ~ 1 . 
In the second instance, he puts 
r l — r 2 — * ' ' — r m — ~ 1 > r m + 1 — r m + 2 _ * ' * _ T n ~ 0 , 
S l ~ S 2 ~ ' ‘ ' = S m ~ ~ 1 ) S m + 1 = S m+‘l ~ * * * = 8 n = 0 ) 
and obtains 
f 1 ] 
= 
[w-ij 
Ms ‘"Vn 
He then recalls the fact that by the conditions attaching to the 
expansion of the expressions enclosed in rectangular brackets the 
powers of x 1 , x 2 -. . . x m contained in the one and the powers of 
Um+ j Vm+ 2 , • • • , y n contained in the other are all positive ; and 
argues that as we are concerned only with terms that do not 
involve these variables, it is quite allowable to put them all equal 
to 0. This being done it is seen that 
X 
1 
m+ 2 
1 
1 
+ aWaL m +n 2) • • . ai n * 
