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

DETERMINANTS IN GENERAL (TERQUEM, 1846)

41

unknowns. Continuing, he says that if we are to have z = w = 0,
we must have
a b2 c3 5 I a b b2 4 5 I = ~0, (d8)
and that therefore these two equations are "les deux equations
de condition pour que 4 equations entre 2 inconnues puissent
etre satisfaites par les memes valeurs." The words "et ainsi de
suite" are added to draw attention to the general theorem.
On this we can only remark that the giving of the equations
of condition in the form (3) in the second case, even although
the real equations of condition
al b1 ce d1
a2 bo c2 12 = 0
a5 b5 C, d5
are thence deducible, seems quite inexcusable, especially in an
exposition meant to be elementary.
CAYLEY, A. (1847).
[Sur les determinants gauches. Cqrelle's Journ., xxxviii. pp.
93-96; or Collected Math. Papers, i. pp. 410-413.]
As the title implies, the subject of this paper is not general
determinants. Part of the purpose, however, which the author
had in view necessitated reflection on the definition of such
determinants, and the outcome was a suggestion which it would
be a serious mistake to pass over. In explaining the character of
the functions known afterwards as Pfaffians, and which he was
-about to show were closely connected with skew determinants, it
was natural that he should be struck with certain points of
resemblance between them and general determinants, and that in
consequence he should seek a genera] definition which would
include both. The new definition given is
".... en exprimant par (1 2... n) une fonction quelconque dans
laquelle entrent les nombres symboliques 1, 2,..., n, et par + le signe
*The second determinant is incorrectly printed in the original.