Experiments on Residual Ionization. 401 



indications of a small number of: ions per c.c. per second 

 produced by the collisions of thermal agitation, but more 

 refined experiments are required to confirm this point. In 

 addition a formula has been derived for the number of thermal 

 collisions in a gas per c.c. per second producing ionization 

 which agrees with the experimental results if the number of 

 such collisions is small. 



Theory. — The question of ionization by the collisions of 

 thermal agitation has been investigated theoretically by 

 Langevin and Rev *. In this paper the authors obtained an 

 expression for the number of collisions in a gas per c.c. 

 per second for which the relative velocity of the colliding 

 molecules normal to the sphere of shock was greater than an 

 arbitrary standard. If we denote the number of these 

 '" effective " collisions by K, then 



K = ve-* hmv ' 2 , 

 where */ = total number of collisions per c.c. per second, 



h= -^ and e = 2V2xlQ- l \ 

 4el 



v = arbitrary minimum velocity. 



According to this formula K would vary very rapidly 

 with the temperature, a prediction which is contradicted by 

 experiment. 



Exception was taken to Langevin's work bj r Wolfke t, 

 who suggested that the potent factor in producing ionization 

 at the collision of two molecules was not their relative 

 velocity normal to the sphere of shock, but rather their 

 relative velocity tangential to it. Indeed he suggested that 

 the normal component would rather prevent ionization by 

 pushing the electron further into the atom, although it is 

 difficult to judge of the value of this suggestion on account 

 of the very conjectural nature of our knowledge of the 

 mechanism of an atom. However, on this ground Wolfke 

 suggested that the number of effective collisions would 

 depend on the relative velocity of the molecules normal to 

 the sphere of collision being less than a certain value, v. 

 The formula obtained for the number of effective shocks is 



v(l — e-" hmv2 ), 



where the symbols have the same meaning as before. From 

 this Wolfke calculated that if the collisions in air produce 



* LaDgevin and Rev, Le Radium, x. p. 142 (1913). 

 t Wolfke, Le Radium, x. p. 265 (1913). 



Phil. Mag. S. 6. Vol. 32. No. 190. Oct. 1916. 2 E 



