The theory of determinants in the historical order of development, by Sir Thomas Muir.

SKEW DETERMINANTS (CAYLEY, 1854) 269
+ a/31234.1234*
+ al ~31 ~ 22 * 33 44
+a2. /2.11.33.44
+a3. 3.11.2244
+a4./4 11 22 33
+a123./ 123.44
+a124./124 33
+a134 /3134 22
+a234 /3234 11 J."
Naturally enough it is noted by Cayley that the writing of
a=3= 5 gives us the less general theorem with which he
started; but he does not explain why a third way of arranging
the terms of the development is adopted. Stranger still, he does
not remark on the fact that by making 11, 22, 33, 44 all vanish
there is obtained the identity
a1234 /31234 = a,1234234234,
's= -s', ''=O
which is the twin theorem to one given in his previous paper
regarding a bordered skew symmetrical determinant of even
order. It will be remembered, however, that in the statement of
this latter theorem, the peculiar narrow use of the word 'bord '
did not occur.
Although what may be called Part Second of the paper (pp.
301, 302) may seem at first sight to concern something else, it
really only draws attention to the fact that the minors (by which
he means those afterwards named primary minors) of a skew
determignant are themselves skew, being "gauches ordinaires " when
their cofactor in the original determinant is of the form rr, and
"cgauches bordes " when their cofactor is of the formn rs. Considerable space is occupied in verifying by two examples that the
same result will be reached whether we apply the theorem of
Part First directly to
12:3... 123... n
or to the primary minors in its equivalent
11.23... n 23... n- 12 23...n 13... n +.....
* A serious misprint in the original is here corrected.