•380 Proceedings of Royal Society of Edinburgh. [skss. 
Not© on Pure Periodic Continued Fractions. 
By Thomas Muir, LL.D. 
(MS. received October 27, 1902. Read November 17, 1902.) 
(1) There is a short paper* in a recent volume of the Comptes 
Rendus of the French Academy of Sciences which deserves notice 
if only in order that the attention of the author and others may 
he drawn to previous work on the same subject and to more 
effective methods of treatment. 
(2) It is well known that by the solution of a quadratic equation 
we can show that the periodic continued fraction 
, 1 1 1 
CL -, + — — 
* Ct% + Cfc 3 + • • + O n + • • • 
* 
\/ { ( a l> • • • , a n) ~ (®2 > • l) j 2 * + 4(<Xj , . ..,a n — l)(c&2s . . .,®w) + j (%, . • ^n) ~ 1) } 
2 
tinuants explained by the example, 
(^i » ^ 2 > > a ±) = 
etc., 
on 
the right are con- 
1 
1 
-1 
«8 
1 
-1 
a 4 
$2 , . 
• • ) 
a n in the reverse 
order we have 
1 1_ 1_ 
+ ••••+ a 2 + + • • • 
* 
V{(a, l ,-M%|^Can-i,...,a2)} 2 + 4(a M ,...,a 2 )(a w _i 5 ...,ai)+{(a n ,...,a 1 )-(a„_i,...,a 2 )} 
• 2(as»-i,... l a 1 ) 
the numerator here being the same as before because of the fact 
* Ceelier, Sur le developpement de certaines irrationelles en fraction con- 
tinue. Comptes Rendus . . (Paris), cxxviii. pp. 229-231 (year 1899). 
