40 THE THEORY OF IONIZATION OF GASES 



let r r be produced in the layer between this plane and 

 the positive electrode. 



Then n=no+r+r'. 



Let a be the number of ions produced by a negative 

 ion in moving through one centimetre of the gas. 

 Let /3 be the corresponding number for a positive ion. 



x 



The number of ions dr generated between the two 

 planes at distances x and x-\-dx is given by the 

 expression dr=a(nQ-\-r)dx-\-fir'dx, since the number of 

 negative ions travelling through the length dx is fto+ r 

 and these produce a(nQ+r)dx, and the number of positive 

 ions passing through the same element of length dx is 

 r', and they produce fir'dx. Substituting n n r for r' 

 the equation for r becomes 



which on integration gives 



The constant c is determined by the condition 

 when x=0. 



Hence the value of r is given by the equation 



