required to maintain a Current in a Gas. 207 



electrode cannot exceed a certain fixed value which is equal to 

 the minimum sparking potential. The condition which has 

 been given may be expressed in the form 



dx. 



1 — I ae ace = 1 ae 



Jo J b 



If the value of a is very small in the column of gas of 

 thickness a — b in contact with the positive electrode, then 

 the quantity on the right of the above equation becomes very 

 small. This implies that nearly all the ionization takes place 

 in the layer of thickness b near the negative electrode. Also 

 since the quantity 



c 



\ X (/3-a)*r 

 Jo 



1—1 ae da 



Jo 



becomes very small in this case, the potential fall along the 

 distance from x = to x = b is practically the same as would 

 maintain the same current between electrodes at a distance 6 

 apart, the pressure of the gas being unchanged. 



The theory shows that the current could be maintained in 

 the gas even when the value of a vanishes in the positive 

 column, and in this case the potential fall in tbe layer near 

 the negative electrode would be determined accurately by the 

 condition 



1-1 ae d.r = 0. 



-i: 



It is possible to show the connexion between the cathode- 

 fall of potential and the minimum sparking potential by using 

 the above investigation in connexion with the following 

 experimental results. 



The sparking potential for parallel plate-electrodes has a 

 minimum value corresponding to a certain amount of gas 

 between the plates. Let m be the product of the distance 

 between the plates and the pressure p which corresponds to 

 the minimum sparking potential. When the product exceeds 

 the value m the potential required to maintain a discharge is 

 less than the sparking potential, but when the product 

 approaches the value m the potential required to maintain a 

 discharge does not differ much from the sparking potential. 

 For hydrogen wi=l'l, the distance between the plates being 

 measured in centimetres and the pressure in millimetres of 

 mercury. A =et of experiments with the plates *44 centi- 



