100 
Transaotions of the Boyal Society of South Africa. 
got by changing the suffix 4 everywhere into 3. It is seen to concern the 
elements of a 4 — by — 3 array, and to have its left member conveniently 
symbolisable by 
i h h 
^ j Co Cg 
where the first two rows have a double link of connection and the other two 
a single link. With the first two still doubly connected, but with different 
single ends, there is the diagram 
I I ^ ^2 ^3 
d^ d^ ds 
giving us the equality 
so that we have 
IV3I 
124! 
1125 
124| 
134 
As the double-ends might also be at a^c^, a-^d-^, h^c^, b^d^, c^d^ ; and as the 
number of 4-by-3 arrays is 4 ; and as there is as many 3-by-4 arrays 
equally fruitful ; the full number of three-line minors resolvable in this 
particular way is 
2 X 6 X 4 X 2 i.e. 96. 
(7) Changing the cZ's of the foregoing into c's, we obtain the familiar 
equality regarding the adjugate of \a-fic^c.^\ 
f f CK'l 0-2 Cis 
^1 ^2 ^3 
la^hc^l la^fegl \a2\\ 
[a^Col lajCgl koCgl 
IfcjCgl \h^c^\ I60C3I 
Of this there must be sixteen instances, one corresponding to every primary 
minor of {a^hoC^d^]. 
(8) An example of the next type of resolvable minors is ^^^^^^ 
equality connected with which is 
, the 
