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

118 HISTORY OF THE THEORY OF DETERMINANTS

TRZASKA, W. (1876): FERRERS, N. M. (1876).
[Question 201. Nouv. Corresp. Math., ii. p. 401. Solution by
Even, iii. pp. 91-92.]
[AN ELEMENTARY TREATISE ON TRILINEAR COORDINATES, 3'r ed.
(pp. 59-73, 172, 179). xiv+184 pp. London.]
Exactly in Cayley's manner it is shown that higher-order determinants formed like his third of 1841 (Hist., ii. p. 110) vanish also.
The result intended to be given by Ferrers (p. 72, ex. 8) is
(b+c)2 c2 b2
c2 (c+a)2 a2 2 (bc-+ca+ab)3.
b2 a2 (a+b)2
JAMET, V. (1877): LONGCHAMPS, G. DE (1877).
PAIGE, C. LE (1879): WOLSTENHOLME, J. (1879).
[Sur une application des determinants. Nouv. Annales de Math.,
(2) xvi. pp. 372-373.]
[Des fractions etagees (p. 325). Giornale di Mat., xv. pp. 299-328.]
[Question 514. Nouv. Corresp. Math., v. p. 452. Solution by Jamet,
vi. pp. 92-93.]
[Question 6038. Educ. Times, xxxii. pp. 243, 315; or Math. from
Educ. Times, xxxii. p. 91.]
None of these is of any moment, the first and third being but
instances of the square of an oblong array, the fourth a simple
instance of the multiplication of two determinants, and the second
a reproduction of Ferrers' first result of 1855.
MANSION, P. (1877).
[On an arithmetical theorem of Professor Smith's. Messenger of
Math., vii. pp. 81-82.]
[Generalisation d'un theoreme de M. H.-J.-S. Smith. Annales...
Soc. Sci.... Bruxelles, ii. (B), pp. 211-224; or as ~iii. of
pamphlet "Sur la theorie des nombres." 16 pp. Gand, 1878.]
Mansion, recognising not only that Smith's determinant is axisymmetric but that it also has the element in the place (r, s) equal