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

DETERMINANTS IN GENERAL (SYLVESTER, 1851) 63

SYLVESTER, J. J. (1851, Oct.).
[On a remarkable discovery in the theory of canonical forms and
of hyperdeterminants. Philos. Magazine (4), ii. pp. 391 -410; Collected Math. Papers, i. pp. 265-283.]
Here, amid matter of great algebraical importance, there is
incidentally suggested the discarding of the use of the term
'determinant' as connected with a single function,-that is to
say, Gauss' original use of the term,-and the, substitution of the
term 'discriminant' in its place. The introduction of a new
word, it is explained, is for the purpose of avoiding the obscurity
and confusion which arises from employing the same word in
two different senses, and "'discriminant' because it affords the
discrimen or test for ascertaining whether or not equal factors
enter into a function of two variables, or more generally of the
existence or otherwise of multiple points in the locus represented
or characterised by any algebraical function." *
CAYLEY, A. (1851, end).
[On the theory of permutants. Cambridge and Dubl. Math.
Journ., vii. pp. 40-51; Collected Math. Papers, ii. pp. 16-26.]
The second part of his paper of 1843, as we have seen, Cayley
devoted to the consideration of a class of functions obtainable
from the use of m sets of n indices in the way in which a determinant is obtainable from only two sets. The general symbol
used for such a function was
* Apropos of this happy coinage, Sylvester adds in a footnote the general
remark:-" Progress in these researches is impossible without the aid of clear
expression; and the first condition of a good nomenclature is that different
things shall be called by different names. The innovations in mathematical
language here and elsewhere (not without high sanction) introduced by the
author, have been never adopted except under actual experience of the embarrassment arising from the want of them, and will require no vindication to
those who have reached that point where the necessity of some such additions
becomes felt." The truth of the remark is not appreciably diminished by the
occurrence of the word 'meso-catalecticism 'in another footnote two pages
further on. The year of the paper (1851) was for Cayley and Sylvester a year
teeming with fresh ideas as well as with fresh words.