553 
1902 - 8 .] 
Dr Muir on a Special Girculant. 
and the next two operations, which combined do not alter the 
sign, give 
1 
1 
— a determinant which is got from G(3 , 2) by reversing the order 
of the rows and reversing the order of the elements in each row, 
and which therefore is known to be equal to G(3 , 2). 
In the last place there .is the equally interesting result 
G(/x,/x + p) = G(p,,p). (4) 
This is established by showing that the determinant on the left 
is, after slight modifications in form, resolvable into two factors, 
one of which is G(//, , p ) and the other a determinant whose main 
diagonal consists of units and whose elements on one side of the 
said diagonal are all zeros. The modifications referred to are made 
by the last row being added to the row which has only one zero on 
the right of the diagonal, the second row from the end being added 
to the row which has only two zeros on the right of the diagonal, 
and so on. Thus 
G(3 , 4) = 
1 1 
11111 
11... 
1 . . 
1 1 . 
1 1 1 
1 1 
. 1 
1 1 
. 1 
1111 
.111 
1.11 
11.1 
1 . . . 
11.. 
- G(3 , 1) . 
PROC. ROY. SOC. EDIN. 
1 
1 . 
1 1 
111111 
111.. . 
.111 
1 1 
. 1 
1 . . . 
11.. 
11111 
1 1 1 
1 1 
1 1 
1 1 
1 1 
. 1 
1 1 
. 1 
1 1 1 
. 1 1 
. . 1 
1 1 1 ! 
.ii 
. . i I 
— VOL. XXIV. 
36 
