334 
Transactions of the Boyal Society of South Africa. 
Similarly P, Q, E, S being the co-factors of the elements {dd'), {dc'), 
{cd'), (cc') in the four-line determinant we have 
(aa') 
(ah') 
(ac') 
(ad') 
(ba') 
(hh') 
(he') 
(hd') 
P Q 
(aa') 
(ah') 
{ca') 
(ch') 
(cc') 
(cd') 
E S 
(ba') 
(hh') 
(da') 
(dh') 
(dc') 
(dd') 
■■ by (I.) 
•■■ by (II.) 
:|> 
and again by (I.) 
And so generally. 
^P- PS- 
(aa') (ah') 
(ba') (bb') 
(aa') 
(ha') 
(ah') 
(bb') 
(aa') 
(ca') 
(ac') 
(cc') 
( 
aa 
) 
.(aa')(bb')(dd') 
(aa') (ah') 
(ha') (bb') 
> (aa')(bb')(cc')(dd'). 
