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

WIRONSKIANS (FUCHS, 1865)

-949

FUCHS, L. (1865).
[Zur Theorie der linearen Differentialgleichungen mit veriinderlichen
Coefficienten. Cirelle's Journ., lxvi. pp. 121-460.]
The second section of this (pp. 126-131) deals with the Wronskian,
but not in any fresh connection.
ZMURKO, W. (1871).
[Dow6od na twierdzenie Hesse'go o wyznaczniku ftinkcyjnym,.
Pamietnik Towarzystwva Nauk Scislych w Parytu, i. pp. 89-92.]
The theorem here proved and spoken of as Hesse's is the first of
the two theorems of fiesse's which had been previously reached by
Christoffel (Hist., ii. p. 228). Zmu-rko had already dealt with the
subject in 1866 (see above, p. 16).
CAYLEY, A. (1872).
[On Wrouski's theorem. Quart. Journ. f Matlz., xii. pp. 221-228
or Collected Math. Papers, ix. pp. 96-102.]
Cayley first shows that in Wronski's own form of development
the loi supreme is not more general than
Ni NI 1 1
F(x) F - %F' + 4' JT'
1.2 f'2
X3
(2) (fF)" (' F,1I2
123 (kk)// ff3F' T
+.
where F,, F '..... stand for F(a), f (a), FY(a),..., and a is a root
of the equation 7(x) = 0, and therefore also of ~(x)+Xf(x) = 0.
He then obtains, by the use of Lagrange's theorem, the alternative
form
N f N~/2 fF/2f
F(M) F- -F' + 2) F I
1 1
N~23 J'J-5'.~ I