1899-1900.] Dr Muir on the Theory of Skew Determinants. 183 
and the common denominator 
(0,1)(3,2) + (0,3)(2,1) + (0,2)(1,3), 
or, as he thereafter writes it 
(0, 1,3,2). 
When the similar set of six equations came to he dealt with, the 
devising of the multipliers requisite for elimination would neces- 
sarily be harder ; hut keeping in view the analogous mode of 
arriving at the solution of 
-H a 2 x 2 = ^ ) 
b + b 2 x 2 = ^ f 
and then proceeding to the solution of 
apr x + a 2 x 2 + a 3 x 3 = £ 4 
bpx x + b 2 x 2 -I- b 3 x s = £ 2 
c i x i + e 2 x 2 + cpc 3 = £ 3 J , 
where, it will be remembered, the multipliers requisite for elimina- 
tion are of the same form as the common denominator of the values 
of the unknowns in the preceding case, Jacobi would have little 
real difficulty in finding that corresponding to the four multipliers 
requisite for eliminating dx x fix 2 , bx 3 in his first case, viz., — 
0, (2,3), (3,1), (1,2) 
he would now require to have the six multipliers 
0, (2345), (3451), (4512), (5123), (1234). 
As a matter of fact, he gives for the numerator of the first un- 
known 
mx{ * +(2345)X 1 + (3451)X 2 + (4512)X 3 + (5123)X 4 + (1234)X 5 }, 
the others being 
mr{(3245)X + * + (4350)X 2 + (5402)X 3 + (0523)X 4 + (2034)X 5 } 
The common denominator is not mentioned ; we should have ex- 
pected him to say that it was 
(10)(2345) + (20)(3451) + (30)(4512) + (40)(5123) + (50)(1234) 
or -(012345). 
