150 
Proceedings of Eoyal Society of Edinburgh. [sess. 
the second side of which, as before, manifestly vanishes when the 
parent determinant is axisymmetric, and becomes 
1 1 
4 5 
2 2 
4 5 
3 3 
4 5 
4 
5 
1 1 
6 7 
2 2 
6 7 
3 3 
6 7 
4 4 
6 7 
5 5 
6 7 
6 
7 
when the parent determinant is skew. 
1 
8 
2 
8 
3 
8 
4 
8 
5 
8 
6 
8 
7 
8 
(9) Leaving now this subject — which has been led up to by a 
consideration of Kronecker’s theorem — let us turn to a similar 
inquiry connected with my analogous theorem of 1888. 
The latter is to the effect that the aggregates 
3 1 
34 
124 
+ I 
34 
3 1 
3 4 
45 1 
456 
456 
45 1 
426 
456 
14 5 6 
356 
4 2 6 
+ 
456 
5 6 7 1 
5 6 2 8; 
5378] 
|4678j| 
5 6 7 8 
+ 5 6 7 8 j + 
5 67 8 
5 6 7 8] 1 
5 6 7 8 
5 67 8 
5 6 7 8 
5 6 78; i 
5 6 7 1 
15 6 2 8 
5378 
4678 J 
4 5 6; 
3 5 6 ^ 
vanish in the case of centro-symmetric determinants of the 4 th , 
6 th 8 th , . , . orders respectively. 
