THEORY OF ELECTRIC DISCHARGES 79 



value of the potential may be taken as 260 volts for any 

 of the currents. 



If, therefore, the plates are at a large distance apart 

 and the fall of potential along a layer of thickness b near 

 the negative electrode has attained the value of 260 

 volts, b being the distance between electrodes for which 

 the pressure in the gas is the critical pressure, the 

 current will be maintained by the ions generated in 

 that layer, even when the force in the rest of the dis- 

 charge is not sufficient to cause ions to be generated by 

 collision. The experiment quoted shows that the 

 potential fall along the distance b need not vary much 

 with the current. 



Thus the cathode fall at a given pressure p should 

 be independent of the current and of the distance 

 between the electrodes, should be equal to the minimum 

 sparking potential, and should extend over a distance b, 

 where p X b is a measure of the amount of gas corre- 

 sponding to the minimum sparking potential, and b should 

 consequently vary inversely as p. These conclusions 

 are in general agreement with experiment. 



The cathode fall of potential as determined experimen- 

 tally is independent of the length of the discharge and 

 the intensity of the current, and has been shown by 

 Strutt 1 to be practically the same as the minimum 

 sparking potential. Experiments also show that the 

 thickness bi of the layer of gas across which the fall of 

 potential takes place increases as the pressure diminishes, 

 though it cannot be found very accurately as the force is 

 very small at a short distance from the cathode. The 

 product pbi, as given by most observers, is less than pb, 



1 Hon. E. J, Strutt, Philosophical Transactions, Vol. cxciii., 

 p. 377, 1900. 



