84 THE THEORY OF IONIZATION OF GASES 



supply of the latter is supposed to be generated at the 

 cathode by the impact against it of positive ions. The 

 expression for the sparking potential V as found on this 

 hypothesis is 



v -v 0.1 w ( 1 + feV o g ) C < 1 + M7 ) 1 .fr+rc) d 

 V(rf > g * k\e A ^ pe A' 



where V is the cathode fall of potential, /3, w t and k 

 are constants, y the ratio of the number of collisions in 

 which corpuscles remain attached to the molecule to the 

 total number of collisions, A the mean free path of a 

 corpuscle, c the thickness of the Crookes layer, and e the 

 charge on an ion. 



It is difficult to understand the reason for many of the 

 assumptions that are made in obtaining this formula 

 For instance, it is supposed that the positive ions all 

 traverse the Crookes layer, impinging on the cathode with 

 a kinetic energy eVo, a supposition which involves the 

 assumption that they make no collisions with the molecules 

 of the gas, although the length c is much longer than the 

 mean free path of the positive ions. This view is said to 

 be supported by experiments which show that solid 

 obstacles placed in the cathode dark space cast a shadow 

 on the electrode. But it must be remembered that the 

 solid obstacle which is placed near the cathode would 

 presumably take up a potential less than the cathode 

 fall of potential. The potential difference between the 

 cathode and the obstacle in question would therefore be less 

 than the minimum sparking potential, and no current 

 could be maintained between the cathode and the obstacle. 

 This should hold for any theory of the discharge, and 

 the fact that the gas is not luminous in the space between 

 the cathode and the obstacle supports equally all theories 

 that account for the minimum sparking potential. 



