Conducting Gases on the Direction of the Electric Field. 223 



ionization near the surface of the plate A. Suppose the plate 

 A is positive and charged to a potential V, and the plate B to 

 earth. 



Let d = distance between the plates ; at all points between 

 the parallel plates a short distance from the surface the ions 

 are positive in sign. 



Using the same notation as on p. 218, the current i y per 

 sq. cm. through the gas is given by 



where n x is the number of + ions per c. c. Also 



d*V . 

 — =4™^. 



From these two equations we obtain 



dY ^V_4 7 n 1 

 dx ' d.v 2 K x ' 



If x is measured from the plate A, 



( 



rfV\«_frrt> A , 



dx J Kj ' 



where A is the value of ( -y— J at the surface of the plate A. 



Now the value of A can be made as small as we please, by 

 making the ionization very intense near the surface of the 

 plate, since the potential-gradient, which will remove a suf- 

 ficient number of positive ions from the ionized layer to 

 carry the current, decreases with increase of the intensity of 

 ionization. 



Let 8m, 



Then rfV 



asr-Ca.+A*)*. 



Integrating between the limits and d, 



