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

256 HISTORY OF THE THEORY OF DETERMINANTS

Connected with this application the interesting fact is brought
forward that when yi, Y2,..., y, are binary quantics of one and the
same degree, Rosanes' determinant (1872) may be utilized instead of
the Wronskian, the relation between the two being
~'aI-lul 11 —lul ail-1]Dxl-1 ax -2y ' ' ' ' y-1
nX — 1 x y ' ' ' ay~-l
U-112 -lu2 "-lu2
-n(n- 1)
y_( I_ 1)' (in 2)..... (M W(Um, UQ,....IU )
where the u's are binary m-thics. By way of proof it is only necessary
to multiply the determinant on the left by y~"(')-~) in the form
yn-1 (n-1),Xyn-2 (n —)2yn-.... x-1|
y1-2 (n- 2),xy-.... x-2. *. yn-:y....
go
y~ ~~"j