1904-5.] Dr Muir on the Theory of Continuants. 
suggests the finding (pp. 80, 81) of the results 
663 
i b, 
-ii \ 
■ -i i-\ 
n + 1 
1, 
and 
1-&! \ = 
“1 i — ^2 ^3 
"I 1-&3 
| n ) 
1 — &]_ + ^1^2 — ^1^2 ^3 d* • • • • 
the latter of which may be compared with a result obtained by 
Nachreiner when under the same influence. 
In an appendix there appears as a “ personliche Mittheilung von 
Hrn Professor Dr Stem ” the statement that “ auch Sylvester sich 
der Kettenbruch-determinanten bedient hat.’ 5 
Gunther, S. (1873, March). 
[Ueber die allgemeine Auflosung von Gleichungen durch Ketten- 
briiche. Math. Annalen , vii. pp. 262-268.] 
The starting-point here is a result of Furstenaii’s,* viz., that the 
smallest root of the equation 
x n + a n _ 1 x W_1 + . . . . + a 2 x 2 + a x x + a Q = 0 
is]P/R, where E, is the persymmetric determinant 
% a n - 1 i 
Uq a j a 2 a n _2 a n _ ^ 1 
. $0 cq a n _ 3 ^n— 2 Q"n-\ 1 
• • a 0 a n - 4 a n - 3 ®n - 2 ®n-\ 
of infinite order, and P is the determinant got from it by altering 
a 1 , a 0 in the first column into — a 0 , 0 . All that is of interest in 
* Furstenau, E. Darstellung der reellen Wurzeln algebraisclier Gleich- 
ungen durch Determinanten der Koefficienten. 35 pp., Marburg, 1860. A 
short but clear account of the essential parts of this pamphlet will be found 
in the Zeitschrift f. Math. u. Phys., vi. Liter. Zeitung, pp. 9-11. 
