40 Proceedings of the Koyal Society of Edinburgh. [Sess. 
wanted than has already been used : and in dealing with each theorem, 
only one instance need be considered, the others following from it by 
reason of the fact that the determinant is invariant to the circular sub- 
stitution of the full set of variables ; thus, if it be shown that © vanishes 
.when c=g — l i it follows that the same happens when d — h = a. 
Rondebosch, S.A., 
1st December 1918. 
{Issued separately May 16, 1919.) 
