658 Saturation Currents in Ionization. 
for large values of X, both (n,), and (n); vary inversely as 
X;, so that will vary inversely as X2 and we shall have a 
true saturation current. But it is conceivable that the 
supply may increase with X,, so as to make @ constant, or 
even increase with X,; and, as we have seen, even small values 
20 
of ef suffice to produce very profound modification of the 
curve *, 
We have taken oe small and less than unity, but cases 
¢ 
may arise in which this is not so. If —becomes greater than 
7 
unity the solution of (10) has to be expressed in ordinary 
circular functions instead of hyperbolic functions. I do not 
propose to discuss this at present. | 
a > . 
Although I have selected the case ae =2 for dis- 
cussion, there are several other cases in which the integration 
a 
can be effected, e.g. aR =4, 4, i. 
I have not had time to examine these very completely, but 
as far as I have gone they indicate the same general features 
a 
Smeh 
break down at exceedingly low pressures, we may take 
as in the case 
=2. Although the equations probably 
a . ° ° ° 
——__ moderately small and obtain a solution in series. For 
S7ehR 
large values of X>, the force at 2=0, I find that approximately 
pa GAN e 2, Smge (RD beter 
Ce oe yee sie Bate Set 3 f 
Loe 
A Ye ea 
This indicates the same kind of effect, viz., if @ is zero the 
saturation current is 2gel, while if @ is not zero a complete 
modification of the curve for large voltages may be produced. 
These considerations show that the supposition of even a 
small supply of ions from the plates readily explains the - 
observed facts. At the same time it raises a somewhat serious 
difficulty as to the interpretation to be put on the results 
ae 2V= 21K} TE 
* Although 20 i. small, it is obvious that when the current exceeds 
7 
2Qgel, the rate of supply by the plates must make up the excess. 
