ARC IN AIR BETWEEN CARBON ELECTRODES 29 



fined the true resistance of the arc as the ratio between a 

 small change in potential difference and the corresponding 

 change in the current, when the change is made so small, or 

 for so short a time, that the condition of the arc itself does 

 not vary. In other words the resistance as thus defined is 

 the partial derivative of the potential difference with re- 

 spect to the current which we shall indicate by dE/dl. 



This would undoubtedly be the correct way of defining 

 the resistance, if it were not for the doubt which must 

 exist in one's mind as to whether it is possible to have a 

 change in current without having a change in the con- 

 dition of the arc. If the current in the arc is carried by 

 ions, as we have reason to believe, it is not possible to 

 change the current without changing either the number of 

 the ions or their velocity. In either case there would be a 

 change in the condition of the gas. However, this defi- 

 nition may properly be considered as giving a limiting con- 

 dition toward which a close approximation may be made, 

 although it would be better to avoid the use of the word 

 " resistance " entirely when speaking of the arc. It is com- 

 monly avoided when speaking of the discharge of elec- 

 tricity through vacuum tubes, and there is the same reason 

 for avoiding it here. 



If we pass to other methods of attacking the problem 

 we find that Swendler 1 gave the value of the counter 

 E.M.F. as 2 volts, but since he did not divulge his method 

 of arriving at this conclusion, we are unable to judge of 

 the importance of his work. 



As far as we know the first experimenter to use a method 

 different from that of Edlund's was von Lang 2 who en- 



1 Lond. Elec., 2, 107 and 117; 1879. 



* Centralbl. f. Elektrot., 7, 443; 1885. Wied. Ann., 26, 145; 1885. 



