260 Mr Wilson, On the Hall Effect in Gases 



in the positive direction along % tends to move, then Z is positive 

 when the velocity of the negative ions is greater than that of the 

 positive ions. That is, Z helps on the positive ions in the positive 

 direction of z but retards the negative ions. 

 When a steady state is reached evidently 



nA (Z + hXH) -K x ^= 0, 



where K x is a coefficient of diffusion of the positive ions. Simi- 

 larly 



nJc 2 (-Z + hXH)-K 2 ^ = 0. 



But n 1 = n 2 = n (say) so that 



^.^ = n(-Z + k 2 XH). 

 k 2 dz 



But -r? = ~ according to the kinetic theory of gases, so that 



Z + k 1 XH=-Z+k 2 XH; 



.'. Z = \HX{k 2 -k x ). 



In this expression for Z the change in the transverse distribution 

 of the discharge produced by the magnetic field is taken into 

 account so that no error is introduced into this investigation by 

 this effect. 



In the above calculation the influence of the walls of the 

 discharge tube is left out of account and it is possible that this 

 influence may not be unimportant in some cases, especially at low 

 pressures. It is well known that when a gaseous ion strikes a 

 solid body such as glass it remains stuck to it (or at least its 

 charge remains stuck), thus for example it is easy to remove all 

 the ions from a gas by passing it through a glass wool plug. 

 Consequently when a discharge is passing through a glass tube 

 the walls of the tube ought to be regarded as perfect absorbers 

 of the ions so that close to the glass ?^ 1 = and n 2 = 0. 



The glass must therefore get charged up sufficiently to make 

 the number of negative ions striking it in any time equal to the 

 number of positive ions. Since the negative ions diffuse quicker 

 than the positive ions the glass will get a negative charge. 



In the same way the electrodes E and E' ought to be regarded 



