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

252 HISTOR.Y OF THE THEORY OF ]DETERMINANTS
and thence proceeds to establish generally that
- '\T W~~,..W (u,, vj,...1..., mV v2),... I XVP).. UL
This, we may pause to remark, is viewable even in the simplest
case as the resolution of a special compound W~ronskian into factors,
and is thus comparable with the series of identities given at the
close of Christoffel's paper (Hist., ii. p. 227).
The case where v is 2 is considered of special interest, and thereon.
the remainder of the investigation is based. It is first stated in
the form
\Y yi y-i,, Yi~ tn Yk)'VV(Y Yii)T~ n
but this is readily seen to be the same as
AV XVi -,yj,1, *. * I, y, -) y) y YJ)
_ W (y' Yi.?fr-i' Yi,,~i' * i)
ax W (y1,.* y.)
and the three important quotients here being denoted- not merely,
for shortness' sake —by
we are free to put it in. the form

A study of the z's then follows (~~ 2, 3, pp. 248-252).
the determinant

Developing

i/i Y2... tim
tlij Y2,1.. *~"
Y1,v-2 Y2, - 2. * Yn, - 2
tWX Y2,X l~nX
where y,.,, stands for 'ay.1x3 and which therefore is W (yl,.. ),
when X = n-1, in terms of the elements of the last row and their