142 
Transactions of the Boyal Society of South Africa. 
and consequently each of the three determinants is partitionable into two 
determinants. These six, however, may be combined into two triads, one 
being representable by 
4?'" 
and the other by 
t)?/2 
A further step is then suggested, the former triad being, by the above- 
mentioned theorem of Jacobi, the equivalent of the first part of (a), 
namely, 
and the latter triad being condensable into the four-line determinant which 
is the second part. 
The theorem is thus established. 
