The "Back Electromotive Forced 149 



and hence E may be found by 



E = e-4 6 . . . ■, (3) 



a/i 



This method of determining the electromotive force 

 included in a circuit by means of measurements taken at 

 the terminal points gives correct results as long as Ohm's 

 law holds for all parts of the conducting system. But 

 although we cannot speak of Ohm's law when the electric 

 current passes through a gas, it is yet assumed in all 

 discussions of this so-called back electromotive force that 

 equation (2) gives what is called the "true" resistance. 

 We need only analyse the various devices which have 

 been adopted to separate resistance and electromotive force 

 in the arc to see that they all depend on defining the resist- 

 ance as the ratio of an increase of electromotive force to an 

 increase of current. Generally the arc is maintained by an 

 independent battery, and is increased or diminished by a 

 small additional current ; the change produced is then 

 made to affect the measuring instruments. The difficulty 

 is inherent, and I do not see how it can be overcome by 

 any measurements made outside the arc. A special case 

 will shew that the objection raised is a serious one. I will 

 imagine that an experimenter wishes to decide whether 

 there is a " back electromotive force " in a vacuum tube and 

 in order to do so adopts such methods as have been assumed 

 to give correct results for the voltaic arc. A series of 

 measurements supplied by Hittorf* will allow us to 

 calculate the results he would get. 



In the following table the first column gives the 

 number of the experiment, the second the measured 

 difference of potential between the ends of a vacuum tube, 

 and the third the corresponding current in micro-amperes. 



• Wied. Ann., Vol. XX. p. 727. 



