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

:388 HISTORY OF THE THEORY OF DETERMINANTS

The rest of the paper is occupied with the converse theorem;
but as the author himself came to be dissatisfied with his attempt
at a proof and returned to the subject seven years later, it need
not be entered on here.
SYLVESTER, J. J. (1851, April).
[Sketch of a memoir on elimination, transformation, and canonical
forms. Cctmbridge and Dub. Math. Journ., vi. pp. 186-200;
or Collected Math. Papers, i. pp. 184-197.]
The expression " determinant of a function " or, more definitely,
"determinant of a function in respect to certain variables"
occurs repeatedly in Sylvester's writings of the year 1850, the
accompanying notation being*
D2(u);
for example, when dealing with ternary quadrics U and V,
expressions like
_ l __ | (XU+ vT)
X/a Xyz
are in constant use by him. It is clear, however, that the
determinant which he had in mind was not Hesse's, but that
which the year following he named the " discriminant." t
The interest of the present paper lies in the fact that, amid
much other matter, not only are the said two determinants
clearly defined and distinguished, but are shown to be viewable
as having a common parentage, being indeed two extreme
members of a family group. In the first place, the determinant
of any homogeneous integral function is incidentally defined as
the resultant of the first partial differential coefficients of the
function, when drawing attention to Boole's proposition (1843)
that the said determinant " is unaltered by any linear transformation of the variables, except so far as regards the introduction of
0 D was used by Cayley in 1846 as the symbol of hyperdeterminant derivation.
See Collected lMath. Papers, i. p. 97.
t See Philos. Magazine, ii. (1851), p. 406, and Cambridge and Dub. MIath. Journ.,
vii. (1852), p. 52; or Sylvester's Collected MIath. Papers, i. pp. 280, 284.