658 
Proceedings of Royal Society of Edinburgh. [sess. 
Nachreiner, V. (1872, Dec.). 
[Beziehungen zwischen Determinanten und Kettenbrtichen. 
(Dissert.) 24 pp. Miinchen.] 
The starting-point here is Spottiswoode’s short statement given 
on p. 374 of the 51st volume of Crelle’s Journal. This having 
been quoted, pains are then taken to establish a so-called 
“generalisation,” viz. 
where 
- u r+l 7 , 
a r -\- . °r+ 
^ OL . 1 H 
+ 
a r 
b r + 1 
-1 
a r+ 1 
b r+2 
-1 
a r+ 2 
«»- 1 
b n 
-1 
a n 
but unfortunately the left-hand side of the identity is not given as 
here, a r + being incorrectly put * instead of its reciprocal. 
a r + 1 + • • • 
The identity 
<*i b i ■ 
c 1 a 2 b 2 
C 2 a 3 
a Y 1 
V 1 a 2 
1 
• ^2^2 
a 3 
is next demonstrated, the procedure involving the division of the 
2nd, 3rd, 4th, .... columns by b x , b Y b 2 , bfbfb*, respectively, 
and thereafter the multiplication of the corresponding rows by the 
same. This is used to deduce some variants of the above 
“generalisation,” and then the results thus far obtained are 
* This oversight runs through Sect. I., and should be corrected in the 
results marked (3), (4), (6), (7), (8). 
