1904 - 5 .] Dr Muir on the Theory of Continuants. 675 
the two sets of operations necessary to establish it being 
roWj + r row 2 , row 2 + r row 3 , 
and 
col 2 - r colj , col 3 — r col 2 , 
The case previously announced is that where 
Cj = c 2 = c 3 =....=== 1 and 8 - r = (3 . 
Bauer’s result regarding the product of two continued fractions 
having been noted in reviewing his paper, the generalisation of 
it here obtained may also be shortly alluded to. Denoting by F 
the continued fraction 
h(b 2 _a) | bJ , bt _ a) 
fi 
+ - a) 
P 
the author first shows, with the help of his theorem in continu- 
ants, that 
(3 + a 
2 
b 2 + 
HhzT 1' 
P + b 2 -b 3 + 
^3(^3 a ) 
/3 + b 2 -b i + 
a — [3 F — b 1 # 
’ Y+lf ; 
+ K(K- a) 
P + b n - a 
thence, by merely changing the sign of a and the signs of all the 
b’s, that 
- a — (3 F + b T . 
'F^~bf 
f3 ~ 5 n + a 
and therefore by multiplication, that the product of the two con- 
tinued fractions on the left is equal to 
/F-a 2 
p - a 0 2 {0 2 - a) 
2 +v "a j -V', *,+/„+ 
- a ) 
4 
