4 THE THEORY OF IONIZATION OF GASES 



no ions. In passing through a path of length dx 

 these ions produce nadx new ions by collisions, so 

 that dn=nadx. This equation on integration gives 



log n= ax -{-constant, or n=n a since UQ is the value 

 of n corresponding to x=0. 



The quantity a depends only on the electric force and 

 pressure of the gas, and if these are constant the charges 

 wi, w 2j etc., acquired by the positive plate for different 

 distances l\, 1%, etc., between the plates will be 



ttli din , 



m=nQ 1 ;?z 2 =n e J ; etc. 



Hence for equal increments of the distance the ratios of 

 the successive charges will be the same, viz. 



The conditions specified above are easily realized in 

 practice, and experiments show that this simple expo- 

 nential law 1 for the increase of the current with the 

 distance I is accurately true for small distances between 

 the plates ; for larger distances the conductivity rises 

 more rapidly owing, as will be explained later, to the 

 effect of positive ions; but for simplicity the currents 

 between plates separated by short distances will be 

 considered first. 



1 These results showed definitely that it was necessary to abandon 

 the older theories of surface layers by which these phenomena were 

 formerly explained. Such theories provided, it is true, a possible 

 explanation of the increase of current with increase of force, as it 

 is conceivable that the greater the force the greater the number of 

 ions drawn from the plate. But it is clear that if the force at the 

 surface is kept constant an increase in the distance between the 

 plates should not affect the current, and this is quite contrary to the 

 experimental results. 



