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

SYMMETRIC DETEIRMINANTS (WOLSTENHOLME, 18'70) 127
from which Woistenholme's form * is 'readily derived. The merit
of Roberts' result is that it is true for any value of s and is easily
generalizable, the corresponding expression for the three-line
determinant being
s2. (8-2t)Qs-2b)(s-2c) ( s + + sti
which, when s stands for a+b+c, is easily reducible to 2s3 abc.
J. J. Walker's procedure, on the other hand, is to start with the
more general but self-evident result
+ 3
=ABOT) + ZB8
'y l c+y 'y A.
1 8 a D+8
and then make the requisite substitution.
Mollame's process at the outset resembles that of Roberts, but is
not an improvement.
GUNTHER, S. (1873, 1876).
[Ueber einige Determinantensaltze. Sitzungsb.... Soc. zu Erlangen, v. pp. 85-95.]
[Ueber aufsteigende Ketteubrtiche. Zei'tschrifl f. lia/h1. a. Plhys.,
xxi. pp. 178-191.]
What is here established, in two different ways, is Lucas' special
result of 1870.
In the paper of 1876 GUnther incidentally returns to the subject
(Q 5, pp. 183-184), the penultimate form of his development, however, being the same as Albeggiani's of the year preceding.
"Wolstenhiolme's form of development seems oddly chosen; for it manifestly
2s~.4.2abc 8s- abcd = 284 (S. ]"abc - 4abcd)
2 90. ia2bc,
The corresponding determinant of thc fifth order, when s =a ~b+ c ~d ~e,
is equal to
2s91(s. Ya2bC ~- 12abcde),
from which the preceding result is got by putting e =0.