Saturation Currents in Ionization. 651 
theory of ionization by saying that all the ions reach the 
plates before they have had time to recombine. This view, 
although it agrees with the general feature, does not explain 
the numerous cases where the current continues to increase, 
although slowly, even when considerable potential-difterences 
are used. There are cases in which it is unlikely that this 
ean be ascribed to the action of the field in producing new 
ions in the gas, or in altering the rate of recombination. 
Now if ‘ saturation,” practical or absolute, is obtained, the 
general equations + which represent the motion of ions, and 
which appear to have a wide range of applicability, ought to 
throw some light on this question ; but I have not seen any 
formal proof from the equations that “ saturation ? must be 
reached under given conditions. 
For this purpose it is necessary to obtain exact solutions of 
the equations. In the general case these are too complicated 
to deal with ; but it seemed to me that consideration of even 
a particular case in which the equations could be integrated 
might reveal the conditions under which saturation could be 
obtained. 
Let us take two infinite parallel plates at distances 2/ 
apart, and at potentials + V and —V. 
Let m;=number of positive ions per unit volume at any point. 
ny J) negative oP) 29 oy) oe) 
e =charge of an ion. 
t=eroup velocity of the ions per unit electric force, 
supposed to be the same for both positive and 
negative ions. 
q =rate of production of ions per unit volume. 
a =coeflicient of recombination. 
X=electrical force at any point. 
Then, if we measure 2 perpendicularly to the plates and 
take the origin as the point midway between the plates, 
we get 
AX 
ae Saget, —Fio),, 3 sey ee 
dite 1 
Te a ate ot 
Ing X& 1 . 
ae — p67 anans) 2 luca beeen 
In these we suppose g, 2, and R to be constant throughout 
the field. 
* See J. J. Thomson, ‘Conduction of Electricity through Gases,’ 
eh, lil. 
