The Product of Any Determinant and its Bordered Derivative. 93 
x, y, z, u, v, w are given the values which they hold in our theorem above. 
Now, even where the basic determinant is not axisymmetric but is 
| aJ> 2 c. £ d A | , as at the close of §4 above, we have 
xw — yv -f zu 
= I a A c b d & I I a \ h -> c :A I - I a h c A I I a A c A I + I a A c b d Q I I a A c A ! » 
and this being an extensional of 
I a :h I I a A I - I a 2 b 4 I I a A I + I a A I I a i h 4 I 
must vanish identically as the latter is known to do. 
RONDBBOSCH, S.A. ; 
27 April, 1921. 
