102 
Transactions of the Royal Societij of South Africa. 
the former showing affinity with the symbol of § 8 and the latter with that 
of § 6. Using either symbol, we readily infer that the number of vanishing 
minors is thirty-two. 
(11) There thus results the following census : 
Irresolvable .... 144 
Resolvable, type 33 . . .96 
type 114 . . . 96 
type 32 . . .16 
type 124 ... 16 
Vanishing .32 
giving the requisite total of 400. As in the first three groups each minor 
has an equivalent companion, there are altogether 168 such pairs of equals 
Capetown, South Africa, 
Ajpril \lth, 1917. 
