THEOKY OF ELECTRIC DISCHARGES 77 



property of ionizing the gas. 1 A radiation of this kind 

 would obviously affect the potential required to maintain 

 a current, but if the intensity of the radiation is pro- 

 portional to the square of the number of ions per cubic 

 centimetre of the discharge, as Professor H. A. Wilson's 2 

 investigations on the ionization in the positive column 

 seem to indicate, the rays would be inappreciable with 

 small currents, and would not affect sparking potentials. 



33. Cathode fall of potential; ionization in the space 

 near the cathode when the cathode fall of potential 

 is established. 



In gases above the critical pressure the currents 

 when large are accompanied by the phenomena known 

 as the cathode fall of potential. The polarization in the 

 gas as measured by this fall does not vary with the 1 1 

 current, and the potential difference between the 

 electrodes also remains approximately constant. At 

 this stage the effects which take place in the gas are 

 so complicated, involving recombination and various 

 changes in the velocities of the ions, that no theory has 

 been proposed which explains the distribution of force in 

 the path of the discharge and accounts for the remarkable 

 fact that certain potentials are almost independent of the 

 current. It is, however, easy to show in a general way 

 that the ionization arising from collisions in these cases 

 may be sufficient to maintain the current. 



The condition which must be satisfied by the values 

 of a and /3 along the path of the discharge between 

 electrodes at a distance I apart may be written in the form 



1 J. J. Thomson, Proceedings Cambridge Philosophical Society, 

 Vol. x., Pt. ii., p. 74. 



3 Philosophical Magazine, July, 1903. 



