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

LESS COMMON SPECIAL FORMS (CLEBSCH, 1859) 451

CLEBSCH, A. (1859).
[Theorie der circularpolarisirenden Medien. Crelle's Journ., lvii.
pp. 319-358.]
In ~ 3 (pp. 324-330) Clebsch is led to consider the nature of
the roots of the equation dealt with by Hermite in 1855, not
knowing, apparently, what the latter had done. Unfortunately
the proof given of the reality of the roots is not effected without
the use of a set of unessential equations of which the determinant
is the eliminant.
The interesting fact is noted that when n= 3 the equation can
be changed into
b23 - b13 b12
all-x a$ 2 al 0.
all - a12 a13 23
(I612 a22-x a23 a a a -
212 (22 X 23 - 13
CL13 (C23 a33-x a 3 - b
13 C23 33 — ~ 2
(7y) DETERMINANTS CONNECTED WITH ANHARMONIC
RATIOS.
CAYLEY, A. (1854, February).
[On some integral transformations. Quart. Jou7rn. of Math.,
i. pp. 4-6; or Collected Math. Papers, iii. pp. 1-4.]
This paper opens with two statements in reference to the
determinant
1 a a aa
1 /3 /3 /3/3 '
1,~, or P say.
17 y y 7yy
1 86 ' 86',
The first is to the effect that the equation
0 = 0

asserts the equality of the anharmonic ratios of a, /, y, 6 and