666 Proceedings of Royal Society of Edinburgh. 
[sess. 
Gunther, S. (1873, Oct.?). 
[Beitrage zur Theorie der Kettenbriiche. Arcliiv d. Math. u. Phys., 
lv. pp. 392-404.] 
Only one of the sections of this paper — the third (pp. 397-401) 
— is connected with continued-fraction determinants, the subject 
dealt with being practically an extension of the result given in the 
immediately preceding paper by the same writer. Instead of the 
special persymmetric determinant which there forms the denomi- 
nator of the fraction proposed for transformation, we have now a 
perfectly general determinant; that is to say, the given fraction 
now is 
1 
a 2 
a B 
<h 
a 2 
a B 
h 
\ 

C, 
C B 
c i 
C 2 
C B 
The procedure followed is the same as before, a double application 
of it, however, being necessary. Strange to say, the illustrative 
example chosen is not quite general, being that in which the 
denominator is 
1 1 
Xq x \ 
Vo Vi 
z o 
This is first changed into 
z i ~ z o z 2 ~ z i 1 
H x x z 2 - .v 2 z 1 x 2 
- v&i V2 
i i 
x 2 a? 3 
V2 Vs 
1 
X B 
Vb 
• z \ z 2(y\ z 2 y 2 ^ 1 ) j 
where Id is written for 
( x o z i ~ x i z o) (vi z 2 ~ y^i) ~ ( x i z 2 “ x 2 z i ) (yo z i ~ yi z o) • 
The operations for effecting the second change are then specified, 
and the resulting continued fraction is stated to be 
