78 THE THEORY OF IONIZATION OF GASES 



and if the values of a and ft are very small in the column 

 of gas of length I b in contact with the positive electrode, 

 the quantity on the right of the above equation becomes 

 very small, and the integral 



rJ>- 



Jo 



a)dx 



dx 



becomes nearly equal to unity, so that the potential 

 fall along the distance b (from-o;=0 to x=b) at the 

 negative electrode is nearly the same as the potential 

 that would maintain the same current between electrodes 

 at a distance b apart, the pressure of the gas being 

 unchanged. 



It is possible to show the connection between the 

 cathode fall of potential and the minimum sparking 

 potential by using the above investigation in connection 

 with the following experimental results. 



The sparking potential has a minimum value corre- 

 sponding to a certain amount of gas between the plates, 

 which may be measured by the product pb, where p m 

 is the pressure and b the critical distance between the 

 plates for the pressure p. In this case the sparking 

 potential does not differ much from the potential required 

 to maintain a discharge in the gas. Thus in a set of 

 experiments with hydrogen at a pressure of 2'55 milli- 

 metres, the following potentials were obtained between 

 electrodes '44 centimetres apart : 273 volts for a 

 very small current and 272, 255, and 250 volts for 



currents of 2xlO,~ 5 2XlO,~ 4 and 4'6xlO~ 3 amperes 

 respectively. Within an error of about 4 per cent, the 



