THEORY OF THE ELECTRIC ARC 167 



is the accumulation in its neighborhood of positive ions 

 which have been drawn from the_yapor of the arc but have 

 not yet reached the cathode. This accumulation can not 

 become indefinitely great, for, when it increases, the current 

 flowing from the cathode increases, and this soon causes 

 the drop in potential through the remainder of the circuit 

 to become as great as it is possible to have it with the given 

 E.M.F. On the other hand the cathode drop can not fall 

 below a certain value, for it must be great enough both 

 to cause negative ions to be formed at the cathode and to 

 cause these to produce positive ions by their impact on 

 the molecules of the gas. Whichever of these is the greater 

 will determine how great the cathode drop must be. 



One can not at present say with certainty which of these 

 is the greater. The cathode drop in some cases is not only 

 much smaller than that needed to produce electrons by 

 the impact of the positive ions on a cold cathode, but also 

 much smaller than that needed to produce positive ions by 

 the impact of electrons on the molecules of a gas. 1 Appar- 

 ently at high temperatures both forms of ionization occur 

 much more easily than at low. Since we do not know the 

 exact relation between the temperature and the potential 

 difference needed for ionization with either the positive 

 or negative ions, we can not state definitely which is the 

 lower at high temperatures. 



There are, however, reasons for believing that in all cases 

 the potential difference needed, for ionization by the posi- 

 tive ions is the greater. We shall find, for example, when 

 we examine the drop in potential through the gas of the 

 arc, that in some way the ionization of the arc is kept up, 

 though the mean free path of the electrons in some cases 



1 Phys. Rev., 24, 93; 1907. 



