100 
Transactions of the Royal Society of South Africa. 
where it will be seen that the only steady sequence occurs in the subscripts 
0, 1, 2, . . ., Jc—1, the row of non-subscripts having h — 2 duplicated and pre- 
ceded by — , A; — 8 duplicated and preceded by +? ^ — 4 duplicated and pre- 
ceded by — , and so on. The m^^ row of the other determinant is also best 
read from right to left, but is of simpler construction, namely, 
, 0^^-1)2. (^^^-1)2' i'^n-l)^, (m-l)i, (w-l)o, (m-l)o, 
duplication occurring in the case of each combinatory number as a whole. 
EONDEBOSCH, 
January 1, 1919. 
