298 Potential required to maintain a Current in a Gas. 



metre apart and the gas at 2 \55 millimetres pressure gave 

 the following results : — 



Sparking potential, 273 volts. 



Potential required to maintain a current of 2 10~ 5 ampere, 272 volts. 

 „ „ „ 2 10- 4 „ 255 „ 



4-6 10-3 „ 250 „ 



Let these potentials be represented by v, so that within an 

 error of about 4 per cent, the value of u may be taken as 

 260 volts for hydrogen for any current. 



The cases in which the product p x a is greater than m may 

 now be considered. Let b be determined so that px b = m. 



When the value of a becomes very small in the column of 

 gas of thickness (a—b) near the positive electrode, the fol- 

 lowing condition is satisfied approximately, 



( J b J X (£-a)rfx 



ax e dx. 



^ o 



This is the condition that the fall of potential from # = to 

 x = b, should maintain the same current between two plates 

 separated by the distance b, so that this fall of potential must 

 be equal to u. Consequently the fall of potential in the layer 

 of gas m near the negative electrode will in general attain a 

 value nearly equal to the minimum sparking potential, and 

 will remain constant for the larger currents. 



Experiment on the cathode-tall of potential show that this 

 phenomenon connected with the discharge has the general 

 properties which have been found theoretically for the fall of 

 potential across the layer m near the cathode. The cathode- 

 fall of potential is independent of the pressure, the distance 

 between the plates, and the current, and in addition it has 

 been shown * that the cathode-fall of potential is practically 

 the same as the minimum sparking potential. Also when the 

 normal cathode-fall of potential is developed, the electric 

 force in those parts of the gas which are remote from the 

 cathode is comparatively small. 



The cathode-fall of potential as determined experimentally 

 is the fall of potential between the negative electrode and a 

 point at a certain short distance C from the electiode. The 

 electric force is very high near the electrode, and at a short 

 distance (C) from the electrode the force becomes very small, 

 so that the fall of potential across the layer of thickness 



b = — will also be equal to the cathode-fall of potential, 

 * Hon. R. J. Strutt, Phil. Trans, vol. exciii. p. 377 (1900). 



