1910—11.] 
The Theory of Wronskians. 
297 
Malmsten, C. J. (1849). 
[Moyens pour trouver l’expression de la w-ieme int^grale particuliere 
de l’equation y {n) + ~Py {n ~ 1) + • • . + Sy {1) + Ty = 0 a l’aide des 
n — 1 valeurs y v y 2 , . . . , y n _ x qui satisfont a celle equation. 
Crelles Journ., xxxix. pp. 9 L— 98 : or abstract in Cambridge and 
Bub. Math. Journ., iv. pp. 286-288.] 
The result obtained, after an introductory note on Determinants, is 
^=^ 1 +^ 2 + • • * + Z n-lVn-l, 
where 
«r = ( - 1 ) n ~ l [ ^= 2 ) * e ~^ dX(]x , and E = 1 / ^ ± ViV'A • • • Vn - 1 • 
J dy r i 
Only one special property of the Wronskian is used, namely, that regard- 
ing its differential-quotient. 
Puiseux, V. (1851). 
[Sur la ligne dont les deux courbures ont entre elles un rapport 
constant. Journ. (de Liouville) de Math., vi. pp. 208-211.] 
At the close of his paper Puiseux remarks that his proof would have 
been shortened by using the theorem, “ Les lettres t, u, v, . . . , w designant 
n variables, si le determinant du systeme de n quantities. 
t 
u . . 
. . w 
dt 
du . . 
. . dw 
dH 
d^u . . 
. . dho 
d n ~H 
d n ~ l u . . 
. . d n ~ho 
est egal a zero, on a necessairement V equation 
at + bu + cv- f- . . . + gw '= 0 
oil a, b, c, . . . , g sont des constantes ” The theorem is spoken of as known, 
but no reference is given. 
Tissot, A. (1852). 
[Sur un determinant d’integrales definies. Journ. (de Liouville) de 
Math., xvii. pp. 177-185.] 
Tissot incidentally asserts that if y, y v y 2 , ... , y n all satisfy a linear 
differential equation similar to that dealt with by Malmsten above, then 
^(±yy'iyl ■ ■ ■ si"’) = yt- frdx 
where y is independent of x. It is further stated that Liouville proved this 
