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

338 HISTORY OF THE THEORY OF DETERMINANTS

SYLVESTER, J. J. (1852, April).
[On the principles of the calculus of forms. Cambridge and Dub.
Math. Journ., vii. pp. 52-97, 179-217; or Collected Math.
Papers, i. pp. 284-327, 328-363.]
Here the same subjects and the same special determinants
are dealt with as in the preceding; and the determinant
whose vanishing has been seen to be the condition for "meiocatalecticism" is denominated (p. 62) the catalecticant* of the
even-degreed function in question, while the determinant whose
resolution into linear factors furnishes Sylvester's canonical form
of an odd-degreed function is called the canonizant t of the said
function. As the former is an invariant of its function, so the
latter is a covariant.
BRUNO, F. FAA DI (1852, May).
[Demonstration d'un theoreme relatif a la reduction des fonctions
homogenes a deux lettres a leur forme canonique. Journ.
(de Liouville) de Math.... xvii. pp. 193-201.]
The subject of the whole of this paper is simply the solution
of the set of equations dealt with in Sylvester's paper of 1851
(October). The process is lengthy and uninviting, the sole point
of interest being that the equation in X comes out in the form
aoX - a, a(1\ - a2.... aX - a+ooX2 - a2 aX,2 - a3..... aX2 - a+2 =
(to1n+ - an+1 an+l -- n+2... aXn+l- 2n+l
where the determinant is easily shown to be the same as one of
Sylvester's forms by diminishing each row in order, beginning
with the last, by X times the row immediately preceding.
' "Meicatalecticizant," Sylvester truly says, would have been the more correct
word, but even he took alarm sometimes.
t The name would have been equally appropriate for the determinants of the
preceding paper which have v in their diagonal.