192 Transactions of the Boyal Society of South Africa. 
Next we see that in this the cofactor of 
^345 
-^45 
-^35 
-^34 
^ ^5 
^235 
-^25 
-^24 
-^23 
^245 
^^235 
^1245 
ds 
c, c, 
^T235 
-^23 
ei 
^234 
64 
-C145 
-d. 
5 
-C14 
~dj. 
- ^134 
— 61 
4 
:234 
— that is to say, is equal to a determinant of the form We thus learn 
not only that is unisignant, but that the number of its terms is 4 times 
the number in 
In exactly similar fashion it is found that 
^6 = ^[^2 X determinant hke ^'J 
(XIL) 
where 
(X2 
a^ 
- K50 
^3450 
- C2450 
— ^^2350 
~ ^450 
~ ^350 
~ ^^250 
— 62340 
- 6340 
^240 
I' 
«5 
-^340 
^250 
~ ^^240 
d. 
— (^230 
^230 
61 
The unisignancy of ^„ is thus established ; and, as we have seen, this 
carries with it the unisignancy of T„. 
10. The number of the terms is most readily got, when we have 
reached this stage, by putting each of the variables equal to 1 in the 
original form of the two determinants. Thus, the number of terms 
in ^3 
1 
= i.8.34: 
4.3^ 
and the number of terms in T^ is (5 + 4).4't. Generally, the mmiher in 
^„ is 
{n-1) {n-2Y-\ 
and the nuinher in T„ is 
(2n - 1) {n - If-' (XIII.) 
Similarly, we find the number in to be 
(n-l)-, 
and we can thus verify the statement made above that the number in 
^„ is n - 1 times the number in 
