Purser — Applications of Vessel's Funcfions to Pltt/.^ics. 49 



Our boundary equations, then, between inner cylindrical space and 

 sheath, give 



B.,KlnR) + 2a 1 + P„ = A„ (F.(«i?) - ir„(«JJ)), (62) 



B„K,{nR) = A„ ( Y,{nR-) - JgJJ K,{nR) j ; (63) 



.-. B.JnR = (P„ + 2a//«=) (ggJ-J ir,(«i2) - y.(«if)) . (64) 



Let us suppose, now, R not < l\ then we may write for K^^ Yx their 

 exponential values, viz., 



Y,{nR') 3 



1 ^"-^ / 

 K,{nR) = -— -7= 1 

 ^27r ^7iR^ 



3 



.-. coefficient of (^P,^ + 2a/l?i^) = q. p. 



V2V / V 8 nR 



Neglecting the term in P„ as before, we have 

 1 llrR 



i.e. B,^ is small compared with — 



The kinetic energy of the fluid will then be given by 

 i.e. as disk descends, 



1 



oc 



