for Differential Equations of Mathematical Physics. 603 



conditions can easily be obtained. " The result can then be 

 compared with that obtained by the ordinary methods. 



Consider the case of a circular cylinder of radius a spinning 

 with uniform angular velocity co, and coaxial with another 

 cylinder of radius b, the region between being filled with a 

 viscous fluid. 



The boundary conditions are then, writing C= - — . and 

 . . v ' 



using non-dimensional quantities, 



( ^o = +1 = • • • = °> 

 Along r — 1 ] d^o _ . ch/^ _ __ ft m 



L dr or 



b J ^r ~ > U > 



along r = - i r 



The equations for yjr etc. are : 



V 4 to = o. 



and the equations for ty 1 etc. all reduce to the same, the 

 right side vanishing in virtue of the fact that 



= ?&tB4.W)-g|(W)]=0. 



Hence the expansion in C consists of the terms in yfr only. 

 The solution of (17) is 



f = Ar 2 log r + Br 2 + C log r + D, . . (18) 



where the four constants are to be derived from ^ = 0, 



cW^c 

 Br 

 and 



1 at r = 1. 



c£= < j>| n (V s fo) = Oatr = 6/, 



