143 
1809—1900. 
Dr Muir on Determinant Minors. 
vanish in the case of axisymmetric determinants of the 4 th , 6 th , 
8 th , . . . orders respectively. Removing, then, the restriction as 
11 2 3 4 5 6 
|1 2 3 4 5 6 
expanding each of the specified minors in terms of the elements of 
the last row and their cofactors, we have 
to the form of the parent determinant, 
say, and 
1 23 
45 6 
1 2 4 
356 
+ 
1 2 5 
346 
1 2 6 
345 
1 2 3 
45 
1 2 
46 
1 2 
3 5 
+ 
1 2 
5 6 
1 2 
3 6 
1 2 
34 
1 2 
5 6 
1 2 
I 3 6 
1 2 
4 6 
1 21 
6 
. + 
! 2 
6 
1 2 
6 
3 4; 
5 
35 
*4 “ 
45 
*3 
Now the twelve minors of the second order which occur here are 
not all different, the real state of matters being that we have two 
appearances of each of the six minors formable from the two 
curtailed rows 
1111 
3 , 4 , 5 , 6 , 
2 2 2 2 
3, 4, 5, 6. 
Taking advantage of this we find our aggregate equal to 
1 2 
4 5 
1 21 
I 4 6.J 
1 2 
3 5 
+ 
+ 
+ 
1 2 
( s q 
5 6 
\4 3/ 
1 2 
3 6 
\5 i) 
12 
1/5 6\ 
34 
\6 5/ 
where the cofactor of every two-lined minor is the difference 
between a pair of conjugate elements of the parent determinant. 
