Purser — Apj)iicaf/on8 of Bossel's Ftoic/ious to F/if/.sir.s. HO 



To determine K we have, multiplying by /•, and integrating from 

 r = to /• = R, 



To determine co, we have now 



fxam't 



Via' r' 1 " 



0)^^ = ^ • - + :S2(r„. — rJ, {a,,r)e P . 

 If Z a„, 



This satisfies the condition w = 0, for r = R, more and more 

 closely as R increases indefinitely. In this case, which is that of 

 vortex spreading from a uniform value inside an internal cylinder 

 into infinite space, we may express the S terms as definite integrals. 

 Let X = ttf^r, then q. p, 



\x x-t 



ni 



or writing x, = . 



a 



li.r 



(T1l\ 

 ^ j their values in series 



we shall obtain a scries 



(i* = ii:iA,, [ P"' (it. 



J 



K.l.A. PROC, VOL. XXVI., SIX'. A.] F 



