32 THE ELECTRIC ARC 



Firth and Rogers 1 superimposed an alternating current 

 on the direct current through the arc, and the resistance of 

 the arc to this alternating current was taken as its resist- 

 ance. Frequencies between 7 and 250 complete alterna- 

 tions per second gave the same resistance. They, there- 

 fore, believed that the changes in the current were so 

 rapid that there were no corresponding changes in the 

 arc. The value of the resistance which they found varied 

 much with different carbons and with different currents. 

 Values ranging from 2 to 2 ohms are given by them. 

 The corresponding values of the counter E.M.F. were in 

 the neighborhood of 40 volts. 



Following the investigation of Firth and Rogers was a 

 careful examination of the counter E.M.F. and resistance 

 by Duddell. 2 His principal advance over the work of 

 others consisted first in devising a method by which one 

 could test whether the arc remained constant during the 

 change in current or not, and secondly, in using much 

 higher frequencies than those which had previously been 

 used. 



To decide whether the arc changed any or not he im- 

 posed a small alternating current on the direct current 

 which was passing through the arc, and determined whether 

 this alternating current was in phase with its E.M.F. or 

 not. Ordinarily, when an alternating current is thus 

 used, it lags behind its E.M.F. Duddell assumed that if 

 the two were in phase the condition of the arc had not 

 changed during the change in current. He found that for 

 low frequencies with solid carbons the oscillations were 

 1 80 degrees out of phase, and that to have the two 



1 Phil. Mag., (5), 42, 407; 1896. 



2 Phil. Trans., 203, A, 305; 1904. 



