358 
Proceedings of Royal Society of Edinburgh. [sess. 
and subtracting from row 7, the first six elements in row 7 are 
reduced to zero and the seventh element becomes S. Hence the 
determinant (8) is S times the determinant 
a 
a - h 
g -h b 
h 
-g h 
f -g 
f 
b -f g 
~f c 
and this is found to be abcS. Hence as before the eliminant of 
(7) is abcfghS 2 . 
