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

492 HISTORY OF THE THEORY OF DETERMINANTS

STUDNICKA, F. J. (1878).
v
[Poznamka k nauce o determinantech. Casopis pro pestovdni math.
afys., vii. pp. 31-33.]
This paper is not quite in keeping with its title, the subject being
the expression for double the area of a triangle whose vertices are
(x1, Y1), (x2, Y2) (x3, Y3). (There are similar papers in Casopis, ii.
pp. 69-82, etc.)
PAIGE, C. LE (1878).
[Sur une transformation de determinants. Nouv. Corresp. Math.,
iv. pp. 79-82.]
This is the transformation of T into (a' —a)Y already familiar
from Cayley (1858) when dealing with the geometric theories of
involution and homography. (Hist., ii. pp. 453-455.)*
PRATT, 0. (1878).
[Problem 231. Analyst, v. p. 190; vi. p. 25.]
The assertion here made is in effect that if
0(x) -= x(x-1)m - x(x-2),
the determinant
0(1).... (n)
0(n+l).... ~(2n)
~........,
o(n2-n+1).... (^n2)
vanishes for all values of n above 3. The reason is that
+q(x) - 2q(x-1) + 0(x-2) = m-2.
* We might have noted somewhat earlier a distantly related identity dealt with
by J. J. Walker in Proceed. London MIath. Soc., iv. p. 413. Cayley's result is
A( \ 1 a+oa' aca'
i}a- = -(a'-a) 1 +ef' t3/ '
6 '=a 1 7+y7' Y7