432 Prof. E. M. Wellisch : Experiments on 



Now the total number of active particles in the gas is- 

 given bv 



S J £r=b£z=l 



G = 47r I I nrdrdz. 



o Jo 



Using (7) and also the integral 



C b o 



I rJ (k n r)dr= — Ji(\ n b), 



Jo A n 



we deduce as the expression for the total number of active 

 particles in the gas contained within a cylinder of height 21 

 and radius b when the steady state is established, 



P _ ^qbH __ 87T<7 s 1 e^nl — e—^nl 



ID W^XJeM + e-W ' * W 



where Ai, ^2> are the roots of J (\6) = 0. 



So far no approximation at all has been made, so that the 

 series (8) is the exact solution of the problem ; the first 

 term was obtained in Section 3 as the approximate solution 

 when the diffusion to the top and bottom was neglected. 



The cylinder used in the present experiment had a height 

 of 14 cm. and a radius of 2*9 cm. So that we have Z = 7*0 

 and 6 = 2-9. 



Using Gray and Mathews' Tables the following are the 

 first five values of X n : 



A* = '829; X 2 = l-93; X s = 2'98 ; X 4 = 4«07 ; X 5 = 5*15 : 



— Xnl 



A I a. -A £ * s P rac tit- >a lly indistinguishable from unity, and 

 S A = 2-592. 



From (8) we obtain for the number of active particles in 

 the gas in the steady state : 



G = 103-1 ^ (9) 



Without the correction for vertical diffusion we obtain 



123'8 ^y, L e. 20 per cent, in excess. Let Q be the number 



of particles produced per minute in the gas contained in the- 

 cylinder, 



.-. Q = UOirbHq, 



G 103-1 1 -0146 



Q~" 120 b 2 W~ D 



9 



G* 



so that D=-0146^ (10) 



