1917-18.] Note on the Construction of an Orthogonant. 153 
and in form closely resembles the result got by self- multiplication, it is not 
identical with the said result. In the second place its adjugate is peculiar, 
the complementary minor of p rs being p rs .(f L and the complementary minor 
% 
of p rr being (M - 
As for Q, the most interesting point about it is its value, namely, 
(2C 2 • 
that is to say, tlce product of the square of the sum of five squares by the 
sum of ten squares. It is scarcely likely that there is any very simple 
mode of effecting the evaluation of so cumbersome a determinant. 
Certainly the mode by which the value was first reached cannot he so 
styled. It consists in multiplying by F? in the form 
• 
«o 
a 3 
a 4 
a 5 
— a 2 
• 
ft 3 
ft 4 
ft 
~a 3 
-ft 
• 
74 
75 
~ a 4 
ft 
-74 
. 
S 5 
partitioning the product into two determinants one of which vanishes and 
the other is a bordered zero-axial skew determinant, and then evaluating 
the two pfaffians into which the latter breaks up, namely, 
and 
f 5 . • n ■ 
Rondebosch, S.A., 
Dec. 27, 1917. 
( Issued separately August 22. 1918.) 
