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

CHAPTER X.

SKEW DETERMINANTS AND PFAFFIANS, FROM 1861 TO 1880.
THE corresponding chapter in the preceding volume did not end
with 1860, but brought the record up to 1865. There ought therefore to have been included in it a note of Sylvester's of 1861; the
omission is herewith rectified. To the same longer period belongs
Clebsch's memoir, " Ueber das Pfaff'sche Problem " (Crelle's Journ.,
lx. pp. 193-251, lxi. pp. 146-179). In this case, however, the
omission was intentional, as Clebsch, unlike Frobenius the author
of an equally long memoir with the same title, does not devote any
special attention to the determinants which he uses.
SYLVESTER, J. J. (1861).
[Generalization of a theorem of Cauchy on arrangements. Philos.
Magazine, xxii. pp. 378-382; or Collected Math. Papers, ii.
pp. 290-293.]
In the third footnote Sylvester incidentally states that 'polar'
would in his opinion be a better name than 'skew,' and he defines
a Pfaffian as a "sum of quantities typifiable completely, both as
to sign and magnitude, by a duadic syntheme of 2n elements."
NATANI, L. (1867).
[Substitution, lineare. Hoffmann's Math. Worterbuch, vi. pp.
605-685.]
Natani's ~5 (pp. 618-621) concerns "symmetrische und symmetrale Determinanten," the latter adjective (symmetral) being