upon the Poles of the Electric Arc. 979 



and K the dielectric constant of! the gas. The term inside 

 tjie bracket represents the effect of the charge upon the 

 mean free path. 



Wellisch showed that, given that the ion is a single 

 molecule, the formula is in agreement with the experi- 

 mental values of mobility obtained at ordinary temperatures. 

 In applying it to the case of the arc at a temperature of, let 

 us say, 3500° C, certain approximations are necessary. We 

 may assume the arc to be filled with carbon vapour, for 

 which, however, K and a are unknown. K may be taken 

 to be proportional to density but otherwise independent 

 of temperature ; or may be corrected lor temperature by 



Sutherland's formula, a 2 y. 



K> 



Two sets of calculations are included, the first using the 

 values of K and a for the diatomic gas oxygen and the other 

 for the monatomic gas helium. The other constants are 

 known for carbon, and are therefore the same in both 

 calculations. In each case the values of \ are worked out 

 (1) assuming the ion to be a carbon atom, (2) assuming it 

 to be an electron. 



The table shows the corresponding values for \. 



(K- 



(2) 



i)xio 5 . 



m. 



aXJ0 s . 



XX 10 s . 



59 



carbon atom. 



3-1 



9-6 



7~4 



do. 



1-86 



26 



59 



electron. 



1-5 



9-2 



7-4 



do. 



0-93 



35 



Now, the number of grammes leaving one of the electrodes 



per second is — , where u z" is that part of the current 



carried by the ions starting at that electrode. Hence 



the force on that electrode due to them is P = — . v=i J X. 



e U 



If the carriers are electrons, the fact that there is no 



appreciable wind from the body of the are, i.e. that the 



space-charges of positive and negative electricity in it are 



equal, requires that the current carried by positive ions 



shall be to that carried by negative ions in the proportion 



of their respective mobilities. In other words, the negative 



ions will carry practically the whole current in the arc. On 



the other hand, if the carriers are molecules the mobilities 



will be roughly the same for each sign. In either case we 



