96 Proceedings of the Poyal Society of Edinburgh. [Sess. 
Now multiply by xf{x)l{irih), integrate from a to h, and let ix tend 
to infinity. Then, from (10), (6), and (4) we see, using the theory of 
Dirichlet Integrals, that, if a<r<b, 
2 A,R(«,) = + 0) +/(»• - 0) } • 
.t=l 
When r — a or h, the sum is obviously zero. 
(Issued separately May 1 , 1922 .) 
