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

17() HISTORY OF THE THEORY OF DETERMINANTS

of the variables. As, however, previous to printing, the main part
of the paper was found to be covered by Garbieri's of the preceding
year the manuscript was withheld (Proceed. R. Soc. Edinburgh,
xiv. p. 433).
[The word 'alternant' appears here for the first time as the
designation of a special form of determinant. Having been told
that I had been forestalled in the usage by Sylvester, I called it
from the outset "Sylvester's word." My informant, however, was
probably in error, as some years afterwards I found Sylvester
employing it to denote a peculiar form of operator in the theory
of reciprocants. (American Journ. of Math., ix. pp. 130-132,*
published in January 1887.)]
HAHN, J. (1879).
[Untersuchung der Kegelschnittnetze deren Jacobi'sche oder
Hermite'sche Form identisch verschwindet. Math. Annalen,
xv. pp. 111-121.]
One of the identities here used (p. 117), which may be written
I~2 I2 a a12 I ay alz2V
'2 1a2 1 b1c2 I I Cla2 I. 1Y2 I I y 2 1z 1 2 1Z = I b1x2 i I bxy2 12 bz2 12
IC1I21 IcY212 1 C1Z2 2
it is best to view as a simple case of Zehfuss' theorem of 1859
regarding a double alternant (Hist., ii. p. 190), the product
1 ab2 * I bl2 1 I Ca2 I
being equal to
b2 2
J2 (~162 al
b7,2.2 b2 1 'I
c 2 1
C2 C1C2 C1
i 2 IC2 bIj\C.i.e. ac,, [,, [,,c2
as we have seen above (p. 132).
* Collected Math. Papers, iv. pp. 415-417.