required to maintain a Current in a Gas. 293 



3. Some interesting results may be obtained from equation 

 (1), as it may be put into forms which are suggested by the 

 experimental investigations. 



Let the current be very small so that the field of force is 

 uniform. The quantities a and (S are then independent of 

 the distance .r, so that the equation 



Jo 



J o J 03-a)<£r 



e" x a x d.v reduces to 



i=^( e «->--i), 



0f a-^-** = 0. 



This is the condition which, as has been already shown, 

 determines the sparking potential. Hence the sparking 

 iotential may be defined as the potential which is required 

 to maintain a very small current in the gas. 



This result has also been established experimentally. When 

 the sparking potential is obtained by increasing the number 

 of cells in a battery connected to the electrodes through a 

 high resistance and a galvanometer, it was found that the 

 potential difference at the electrodes did not drop appreciably 

 below the sparking potential during the passage of a very 

 small current which was accompanied by a faint glow 

 in the gas. 



4. The difference of potential between the electrodes 

 required to maintain a current diminishes as the current 

 increases when the pressure of the gas is greater than that 

 which corresponds to the minimum sparking potential. It is 

 easy to show that this result is in accordance with the theory. 



AVhen new ions are generated in the gas by the colli- 

 sions of ions with molecules, the negative ions which are 

 formed are of much smaller mass than the positive ions. 

 The latter would therefore move more slowly so that a 

 resultant positive* charge would accumulate in the gas, and 

 the electric force near the negative electrode would in con- 

 sequence become greater than the force near the positive 

 electrode. Since all the positive ions must pass through the 

 gas in the neighbourhood of the negative electrode, the positive 

 charge would be greatest near that electrode, unless the 

 velocity of the ions becomes much greater near the cathode 

 than at other parts of the discharge owing to the increase of 



* This explanation of the positive charge near the negative electrode 

 was first suggested bv Professor Schuster (Bakerian Lecture, Proc. Koval 

 Soc. xlvii. 1890, p. 541). 



