28 THE ELECTRIC ARC 



Meaning of " Resistance of the Arc." We find, how- 

 ever, that "resistance of the arc" has meant four different 

 things with different experimenters, and with these differ- 

 ent meanings there are corresponding differences in what 

 is meant by counter E.M.F. 



First of all it has been used to mean the ratio between 

 the potential difference at the terminals and the current. 

 This, however, has usually been called the " apparent re- 

 sistance." 



Secondly, it has been used to mean the term nl in the 

 expression r = m -\- nl, which was used by Edlund, namely, 

 the part of the apparent resistance which was proportional 

 to the length of the arc. This Edlund called the " true 

 resistance." 



At a later time it was used to mean the ratio between a 

 small increase in E and the corresponding increase in /, or 

 what we may call dE/dl. An approximation to this was 

 made by those who used some modification of the Wheat- 

 stone bridge. 



Finally, it was pointed out by Luggin 1 that any change 

 in the current through the arc produced a corresponding 

 change in both the vapor of the arc and the shape of the 

 carbon, so that one does not have the same arc after the 

 current has been increased as before. The methods which 

 are modifications of the Wheatstone bridge do not cor- 

 rectly measure either the resistance of the arc in its first 

 condition, nor its resistance after the current has been in- 

 creased. This difficulty has been clearly stated by Mrs. 

 Ayr ton, 2 Duddell 3 and others. They have, therefore, de- 



1 Centralbl. f. Elektrot., 10, 567; 1888. 



2 Mrs. Ayrton's " Electric Arc," p. 400. 



3 Phil. Trans., 203, A, 306, 1904. 



