74 THE THEOEY OF IONIZATION OP GASES 



sparking potential corresponds to the case in which the 

 inner cylinder is negative. 



The theory thus gives a satisfactory explanation of the 

 variation of the potential with the current for parallel plate 

 electrodes and also of the difference between the sparking 

 potentials for point discharges when the direction of the 

 force is reversed. 



31. Phenomena at pressures below the critical pressure. 



The preceding results can only be considered to 

 hold for pressures above the critical pressure, as the 

 experiments by which the values of a and /3 were 

 determined show that for these pressures the ionization 

 of the gas is completely accounted for by the action of 

 the positive and negative ions in generating others by 

 collisions with molecules. The curves which have been 

 obtained for the values of a and /3 show that a/p does 

 not vary much with the force for large values of X/p, so 

 that a diminishes nearly in direct proportion to the 

 pressure when the force is large and the pressure is below 

 the critical pressure. The question then arises whether 

 the quantity /3 increases sufficiently rapidly to account 

 for the sparking potentials obtained experimentally for 

 the low pressures. It is easy to calculate roughly 

 the values of /3 which are necessary, and they do not 

 appear to be greater than the numbers that might be 

 expected to correspond to points on continuations of the 

 curves for /3/jp, but the question cannot be decided in this 

 way, as it is difficult to apply the theory of collisions 

 accurately when the free paths of the ions become con- 

 siderable fractions of the distance between the plates. 

 Some evidence of the processes which influence the 

 sparking at the low pressures may, however, be obtained 



