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

250 HISTORY OF THE THEORY OF DETERMINANTS

where the conditions are the same save that (x-a)f (x) is put for
b (x). As the first development of F(x) must be identical with the
second, he is thus face to face with unverified evaluations of the
Wronskians in the former of the two, and he sets himself the task
of supplying the want. The procedure followed, however, is not
at all attractive.
It is impossible not to note the irony involved in Cayley's use of
Lagrange when we recall the object of Wronski's Refutation.
FROBENIUS, G. (1873).
[Ueber den Begriff der Irreductibilitat in der Theorie der linearen
Differentialgleichungen. Crelle's Journ., lxxvi. pp. 236-270.]
[Ueber die Determinante mehrerer Functionen einer Variabeln.
Crelle's Journ., lxxvii. pp. 245-257.]
For the discussion of the subject of the first of these papers, the
theorem regarding the vanishing of a Wronskian is found by
Frobenius to be a requisite, and he consequently devotes ~ 1 (pp.
238-240) to the consideration of it. It would seem that he was
thus led to the investigation of AVronskians in general, and apart
from their relation to differential equations, for, after a brief interval,
the second paper, a short methodically arranged exposition, was
written.
Immediately following the definition comes Christoffel's theorem
of 1857, namely,
W(yyI, YY2,..., yy)= yn W(yl, Y2,..., yn)
the proof consisting in writing for yn in the right-hand member the
determinant
y.
y y..
y" 2yg y..
y(n-i) (-l)y() W(n-l)(n-2) y(-3) y