THEORY OF ELECTRIC DISCHARGES 73 



corresponding value of /3 2 may be neglected. If X 2 be 

 on the side of the negative electrode, the condition for the 

 maintenance of a current is 



which shows that ai fte^ 1 ^ a =0, or that the 

 potential fall in the distance a on the positive side must 

 be the sparking potential V a for parallel plates at the 



distance a apart. Hence the potential difference between 

 the electrodes is in this case 



If the forces are reversed so that X 2 is on the side of the 

 positive electrode, the condition for the maintenance of a 

 current reduces to 



, (ai /3i) a 



ai-ft^ , -a 2 b 



~ -- or ~r e -I, 



"i Pi 



which shows that ai must exceed fte^* 1 * , and con- 

 sequently the potential fall along the distance a is less 

 than the sparking potential V a , so that the potential 



difference between the electrodes must be less than 



The most familiar examples of phenomena which may 

 be explained on this principle are point discharges. 

 When the point is negative, the strong field is near the 

 negative electrode, so that the potential required to 

 produce a discharge is less than when the point is 

 positive. The same result is obtained when a gas is 

 contained between two concentric cylinders : the lower 



