1904 - 5 .] Dr Muir on the Theory of Continuants. 
of Brouncker, viz., that the product of 
653 
2(a - 1 + 
3 2 and a + 1 + 
is a 2 . The two things are linked together in the title because 
the main feature of the paper is the establishment of a relation 
between a continued fraction of Euler’s type and a continued 
fraction of the very different type which appears in Wallis’ 
theorem. If we denote by S the continued fraction 
n + a 9 
+ - 2 
a 3 + 
+ 
n + a r _ i 
which includes Euler’s, and by T the fraction 
the relation in question is 
w(S + l) 
S + n ~ 
or as Bauer puts it, 
«(P r +Q r ) 
P r + nQ r ’ 
where 
Qr — 
a, 
1 
a. 
l 3 
1 
- n - a r _ x 
a, 
