A _ 

 + I 



1 60 THE ELECTRIC ARC 



formula 7 = Ae, where / is the current passing from the 

 metal, the absolute temperature, and A and Q are con- 

 stants, depending on the kind of metal used. There are 

 somewhat serious objections to the assumptions made by 

 Richardson in deriving this formula, 1 but the formula itself 

 has been found to be approximately true for several of the 

 metals and will give an idea of the rapidity with which the 

 current increases when the temperature is raised. 



Fall of Potential through the Arc. To pass then to 

 the arc, we have found that it may be divided into three 



parts, the part near the 

 anode, A, Fig. 57. at which 

 there is a sudden drop in 

 potential, as is shown in 

 the diagram; that through 

 the arc, where the fall in 

 potential is gradual and 

 nearly uniform, as ac; and 



that very near the cathode, C, at which the drop is again 

 sudden. 



To understand these peculiarities we may begin with the 

 case where ionization is produced in the gas between the 

 two electrodes, but not in their immediate neighborhood; 

 we may next consider the phenomena introduced by the 

 impact of the ions on the electrodes, and finally may pass 

 to the case where the electrodes are incandescent. 



An example of the first will be found when two plates 

 are placed on opposite sides of a flame and at some distance 

 from it. For example, let ac, in Fig. 58, be a space where 

 ionization occurs. This space will then contain both posi- 



1 Wilson, Phil. Trans., 202 A, 243; 1904. 

 Horton, Phil. Trans., 207 A, 163; 1908. 



