1904 - 5 .] Signed Primary Minors of a Determinant. 373 
The sum of the signed primary minors of a zero-axial skew deter- 
minant is equal to a similar determinant of the next higher order , 
and therefore is zero if the order of the original determinant he even , 
and is the square of a Pfaffian if the order he odd. (Ill) 
(3) By the application of the second fundamental result (B) 
the case of a centro-symmetric determinant can he equally easily 
dealt with, the result being — 
The sum of the signed primary minors of a centrosymmetric 
determinant is equal to a similar determinant of the next lower 
order , and therefore is resolvable into two factors. (IV) 
Thus, the sum of the signed primary minors of 
a b c 
d e d 
c h a 
a — h — d + e 
d-e-c+h 
h — c — e + d 
e— d—h+ a 
(a - b - d + e) 2 - (h - c- e + d) 2 , 
= (a - c)(a - Zb - c - 2d + 2e) . 
(4) The case of a continuant requires and is worthy of a little 
more consideration. Restricting ourselves, merely for shortness’ 
sake, to the six-line continuant 
/ \ \ K b 6 \ 
I Oj a 2 a % a i a b a 6 I 
\ C \ ^2 C 3 C 4 C 5 / J 
and denoting the sum of its signed primary minors by prefixing to 
it an M, we know to begin with that this sum equals 
-.111111 
1 a 1 b Y . 
1 Cj a 2 b <2 
1 • C 2 #8 h ' ■ 
1 . . C, <J 4 J 4 . 
1 ... a 5 b 5 
\ .... c 5 a 6 . 
Fixing the attention on the last column and last row, the non- 
