430 Prof. E. M. Wellisch : Experiments on 



the steady state 



fB 2 ^ l"dn o 2 n~\ 



where n is the number of particles per c.c. at (V, z). 

 The boundary conditions are 



w ==0 when r = b for all values of z ; 

 91 = when z= ztl for all values of r. 



r = 01 

 At the point 0, i. e. at ^ > we must also have 



~bn ~ftn 



^— =0 and ^- =0. 

 or dz 



Let N = ^+^(r 2 -6 2 ), (2) 



(1) becomes 



^ + i^ + P =0 , (3) 



Or 2 r or o^ 



with the conditions 



N = when r = b for all values of s . . (i.) 

 N= jyt {r 2 — b' 2 ) when £ = ±Z for all values of r . (ii.) 



a. r = (Tl BN n , BN ..... 



At n ^ ^r— =0, and ^— =0 (m.) 



The function ~N = AJ {oir) {e a " -\-e~ a ), using the usual 

 notation of the Bessel functions, is a solution of (3) which 

 satisfies the condition (iii.). We have the constants A and « 

 at our disposal. (i.) will be satisfied if a be a root of 

 J (Xb)~0. This equation has an infinite number of real 

 positive roots, X^ X 2 , X n , 



Now if we can^expand — L (r 2 — b 2 ) as a series 



SA.(/* , +«- w )J &,r), 



it is easy to see that 



N=a,(^ + r x *)j,M .... (4) 



n = l 



will be the solution of (3) which will satisfy all the condi- 

 tions of the problem. 



