Wellisch — Experiments on Active Deposit of Radium. 295 



Coefficient of Diffusion of the Active Deposit of Radium. 



6. An expression was given in Section 3 for the amount of 

 active deposit present in the gas contained in a cylindrical 

 vessel when a steady state is es- 

 tablished, such that the produc- 

 tion of fresh deposit from the 

 emanation is balanced by diffusion 



to the surface. This expression is, A | | ' ] B 



however, only approximate, as it 

 neglects the diffusion to the top 

 and bottom of the cylinder ; inas- 

 much as the exact expression 

 comes out with surprising sim- 

 plicity, it seems desirable to pre- 

 sent here the exact theory. 



Let ABCD represent a longitu- 

 dinal section of the closed cylin- 

 der (without any central elec- 

 trode). Let q be the number of 

 active deposit particles produced 

 per cc. per second from the ema- 

 nation. 



Let the axis of the cylinder be 

 taken as the axis of z, and let the 

 origin be midway between top 

 and bottom. 



Let 21 be the height of the cylinder, and b its radius. 



Using cylindrical co-ordinates we have as the equation of 

 the steady state 



\ 



Fig 



. 2. 



, k — * 



\ 



z 

 z 







=-1 



D 







(9r* 



9n 



w 



9z 2 



(1) 



where n is the number of particles per cc. at (r, z). 

 The boundary conditions are n — when r=b for all values of z 



n=0v?hen z = ±1 for all values 

 of r, - 



„ ~ n I we must also have =- = and 

 z — u l $ r 



At the point O, i. e. at 



9n 

 9z 







Let 



N = «+-| ) (, 



2 ~N" 

 (1) becomes + 



9r r 9r 



a 5 N 



9z' 



(2) 

 (3) 



