290 Prof. Townsend on the Variation of the Potential 



The present investigation deals with the field of force which 

 is required to maintain a continuous current in a gas. From 

 the results of the experiments that have been made on the 

 effects of the collisions between ions and molecules of a gas, 

 it is easy to show that the sparking potential is greater than 

 the potential required to maintain a discharge, that the latter 

 potential diminishes as the current increases, and that a fall 

 of potential in a certain layer of gas near the cathode 

 approaches the value of the minimum sparking potential *. 

 The same analysis which shows that the potential required to 

 maintain a discharge is less than the sparking potential also 

 shows that the potential required to produce a discharge from 

 an electrified point is smaller when the point is, negatively 

 charged than when it is positively charged. 



The effects produced by various disturbing influences such 

 as the heating of the gas and the recombination of the ions 

 would be very small, and may be neglected when dealing with 

 small currents which are not accompanied by the normal 

 cathode-fall of potential. 



When the ordinary cathode-fall of potential is developed, 

 the effect of heating would introduce a complication in the 

 calculations when the currents are large; but in these cases 

 a method of treating the problem may be used which with 

 the aid of some simple experimental results will lead to an 

 explanation of some of the phenomena which accompany the 

 ordinary vacuum-tube discharge. In addition, the radiation, 

 from the electrodes and luminous portions of the discharge, 

 produces ionization to a small extent in the conducting gas. 

 Thus a small amount of ionization may be produced near the 

 positive electrode due to Rontgen rays, but the effects would 

 most probably be inappreciable except at very low pressures, 

 to which this investigation is not intended to apply. 



2. It is evident that a continuous steady current would be 

 maintained if the positive and negative ions produced ions in 

 sufficient quantities by their motion through the gas. . It is 

 possible to find the exact extent to which ionization must be 

 produced in the gas when the field of force is not uniform, 

 and it is possible to decide whether the currents which are 

 obtained in practice could be maintained by the process of 

 ionization by collision. 



Let the current pass between two parallel plate-electrodes 

 at a distance (a) apart, and let x be the distance of any 

 point in the gas from the negative electrode. Let u be the 

 velocity of the negative ions, a the number of molecules 



* A brief account of the results thus obtained is given in a note on 

 this subject: Phil. Mag. December 1904. 



