THEOEY OP ELECTEIC DISCHAEGES 71 



Thus the sparking potential between A and B was 

 lowered by 150 volts by concentrating the force near the 

 cathode. 



The essential points on which this theory of the 

 diminution of the potential required to maintain a 

 current below the sparking potential is based may be 

 stated briefly as follows : 



The supply of ions by which the current is maintained 

 depends chiefly on the negative ions, and of these the 

 most efficient are those generated near the negative 

 electrode, since they travel nearly the whole length of 

 the discharge. When the force is increased near that 

 electrode and the total fall of potential between the 

 electrodes is diminished, two effects are produced : the 

 number of ions generated by one of the negative ions in 

 travelling between the electrodes is diminished, and the 

 number of ions generated by a positive ion near the nega- 

 tive electrode is increased, thus increasing the number of 

 the most active negative ions. Now the rate of increase 

 of /3 with the force X bears to /3 a much greater 

 ratio than the corresponding rate of increase of a bears 



f 1 d(B 1 da~| . ... , 

 to a or^ j>- 5^ an( * on this depends the mam- 

 p aX aaXJ 



tenance of the current in spite of the large diminution 

 which takes place in the potential difference between the 

 electrodes. When this potential is reduced the average 

 value of a along the path of the discharge is diminished, 

 and the effect of the negative ions, which depends on an 



exponential term (such as N e a ), is greatly reduced; 

 but, owing to the large increase in the value of /3, a 

 compensating effect of the same order is introduced (in 



