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

320 HISTORY OF THE THEORY OF DETERMINANTS

McKENZIE, J. L. (1874).
[Question 4526. Educ. Times, xxvii. p. 166; solution by R. F.
Scott in Math. from Educ. Times, xxv. pp. 106-107.]
The theorem brought forward by McKenzie is Joachimsthal's
of 1854 (Hist., ii. pp. 169-170). In Scott's proof the determinant
concerned appears as the result of eliminating the coefficients of
the related equation.
GUNTHER, S. (1875): MUIR, T. (1876).
[LEHRBUCH DER DETERMINANTEN-THEORIE,... iii+236 pp.
Erlangen.]
[New general formulae for the transformation of infinite series into
continued fractions. Transac. R. Soc. Edinburgh, xxvii.
pp. 467-471.]
Giinther's contribution (p. 88) is that when the series of distinct
elements in a persymmetric determinant are in equirational progression the determinant vanishes; and Muir's result, involving
persymmetric determinants, is a rediscovery.
McKENZIE, J. L. (1878).
[Question 5622. Educ. Times, xxxi. p. 114; solution by R. F.
Scott and others in Math. from Educ. Times, xxxviii.
pp. 86-87.]
The ' question ' here concerns the primary minors of
S0 S1 8... n
S1 S2 S3 ' ' S,+1
S2 83 84... +2
I n Si+1 8n+2 ~ * * * 82n
in which s,. stands for the sum of the rth powers of the roots of an
equation of the nt" degree, and the value of which is identically 0
(Hist., ii. p. 353).