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

CHAPTER XVI.

THE LESS COMMON SPECIAL FORMS, UP TO 1860.
THERE now only remain for consideration those special forms
which, prior to 1860, had not received any noteworthy attention.
These will be found to include: (a) permanents, which are
touched on by three authors; (P3) determinants with the typical
element ars + b.si, which are referred to in four memoirs; (y) two
other forms, which are each dealt with in two papers; and
(8) nine others, which make their appearance only once. It will
also be appropriate to collect in a note (e) the facts ascertained
up to 1860 regarding the census of terms in special forms of
determinants.
(a) PERMANENTS.
As we have already seen, Cauchy, in his memoir of 1812,
widened the ordinary meaning of the term " symmetric function,"
and was consequently led to call such expressions as
acb2 + a2bl, alb2 + 2b3 + aCbl + acb3 + a2bl + 3b2,...
"fonctions symetriques permanentes," denoting them by S2(acb2),
S3(ab2),....
In the same year, as we have also noted, Binet gave the
identities
Eab' = acb - Eab,
Eab'c" = Ea2Ebc + 27abc - cEabc - Ibeca - Ec~ab,