238 Mr. A. A. Robb on the Conduction of Electricity 

 takes a soluble form, we shall write it 



d 2 y 2 __ b c dy 2 



dv 2 y 2 y 2 d 



where 



3 = 



v 2y 2 [dv) ' ' ' W 



Sttoc 



C ~ eR^^R.+R,)' 



€ 47re(R 1 H-R 2 )' 



It is to be observed here that e is the same quantity as that 

 introduced by Langevin (Recherches sur les Gaz ionises. 

 University of Paris, 1902), and denoted by the same letter. 



It follows from the physical meaning which he gives it 

 that e must be a positive fraction. 



In order to reduce equation (4) we make the following 



series of substitutions : 1st. Putting -j- = ~~ and y e =-. 



^ dv e z J z 



we get 



dw be ae i-i 



10 V; ~ CW+ *X Z =--t Z . ' ( 5 ) 



2nd. Putting w= jr~f, where K is a constant to be after- 

 wards determined, we get 



d 2 z , ,„ T ^ dz , be^„ «e T ™ i-? 



' s2 ds 2 



+ (1- cK)s ~+^ K 2 z= - ~ KV 7 . . (6) 



- as 2 2 v J 



3rd. Putting Q = zs n , we have 



i d 2 e 2 d 2 z^ dz , f r 



■ 3-7-9 =s -=-« + Ins-r -\-n(n—±)z. 



s n ~ 2 ds 2 ds 2 ds v ; 



If, therefore, K and n be determined by the equations 



1-cK = 2m, 



and oe w 1 ^\ 



-K a = n(?-1); 



