THEOKY OF ELECTRIC DISCHARGES 87 



in obtaining which it is supposed that ions are generated 

 by the collisions of positive and negative ions with 

 molecules of the gas, and also that negative ions are set 

 free from the negative electrode when the positive ions 

 collide with it. For large distances between the electrodes 

 greater than the distance corresponding to the minimum 

 sparking potential the condition for sparking becomes 



y=ae~~ , y representing the effect of the positive 

 ions per centimetre in ionizing the gas. This equation is 



nearly the same as the equation o,=$c~~^' (section 23), 

 since ft is small compared with a, and it has been seen 

 that this gives the correct expression for sparking. 



With regard to the general expression for the con- 

 dition for sparking given above, it is difficult to use the 

 equation in order to make calculations of the potential, as 

 the numerical values of the effects involved are not 

 determined. From general principles, however, it 

 appears obvious that it could not be very accurate for 

 pressures or distances between the electrodes for which 

 the product p X d is less than the critical value, as it fails 

 to take into consideration processes of ionization which 

 would account for experimental results with electrodes of 

 various shapes and which would explain the variation of 

 the potential with the current between parallel plates. 



As has already been explained in section 28, the 

 potential required to spark or maintain a current in 

 a gas diminishes as the force becomes concentrated at 

 the cathode, when the ions are produced by the action 

 of positive and negative ions in the gas. In the general 

 formula quoted above the system of ionization considered 

 consists of the ions generated by positive and negative 

 ions from molecules of the gas and in addition ions set 



