66 THE THEORY OF IONIZATION OF GASES 



Jx 

 o ; thei 



may be expressed in the form 



f* l 



fiiii=AZ()-HcZ(0)| [ZO)] ftdx, 



Jo 



and similarly 



Since all the ions are produced in the gas, the folio 

 conditions hold at the electrodes : 



At the negative electrode x=0, ni=Q, and n^v=c. 



At the positive electrode x=l, n 2 =0, and HIU=C. 



The first two conditions give A=0 and B=c, am 

 second two give 



l=Z(9f[Z(*)]- ^jS&t and 



Jo 



Z(x)]~ Xadx, 



which are not independent, since 



so that the equation 



ci - a )dx. 

 ' dx 



ci 

 =\ 



Jo 



represents the condition which must be satisfied b) 

 values of a and /3 along the path from the negi 

 electrode x= to the positive electrode x=l in c 

 that a continuous current should be maintained. 



When the current is very small, so that the fiel 

 force between the plates is uniform, a and ft are consl 

 and the above condition reduces to 



- 



|3-a 



