1904 - 5 .] Dr Muir on the Theory of Continuants. 
649 
Studnicka, F. J. (1872, March). 
[Ueber eine besondere Art yon symmetralen Determinanten und 
deren Yerwendung in der Theorie der Kettenbriiche. Sitz- 
ungsb bohm. Ges. d. Wiss. (Prag), Jahrg. 1872, pp. 
74-78.] 
The determinant referred to in the title is 
a 1 - 1 . 
1 a 2 - 1 
1 a 3 
a n 
and the fact of its skewness is what Studnicka utilises in finding 
the ordinary expansion of it. Using the general theorem which 
gives an expression for any determinant in the form of an aggre- 
gate of terms each consisting of two parts, viz., (1) a product of 
diagonal elements, and (2) the cofactor of this product in the 
determinant, he notes that the said cofactors are either zero-axial 
skew determinants of odd order and therefore vanish, or are of 
even order and have sometimes the value 0 and sometimes the 
value 1. This last statement, though correct so far as it goes, is 
not in any way attempted to he justified. In illustration of it and 
of the inappositeness of the procedure We may take the case of the 
4th order, viz. 
a 1 - 1 
1 a 2 -1 
1 % - 1 
1 a 4 
for which would be obtained 
+ a 1 a 2 \ 
. - 1 + a x a 3 
1 1 • 
+ a Y a 4 \ 
. - 1 | + a 2 a 3 
1 . 1 
+ a 2 a 4 
5 . • + a 3 a 4 \ 
. -1 
■ J 
1 . 
