656 Mr. G. W. Walker on 
In case (2), using the same value of R, I took g= 108 which 
‘is about the value due to radium chloride of moderate 
strength. The corresponding values of the current in amperes 
are got by multiplying the values of fby 2x10-"4. The 
values of f show that if no ions are supplied by the plates, 
theoretical saturation is only obtained at an infinite P.D, 
Nevertheless the current attains to 99 per cent of the satura- 
tion value for *72 volt between the plates when g= = and 
for 720 volts between the plates when g=10*%. (Fig. 2.) 
The effect of supposing that @ is not zero is very interesting. 
ibs Ee is small and constant as X, is varied, the initial portion 
of the curve showing the relation between P.D. and current is 
not sensibly altered, but instead of attaining saturation the 
current continues to increase as the P.D. increases. For 
very small values of X, we get from (12) and (13) 
e =, (qRet, 
a 24eXi(a5-) i ier) a 
and 2V = 1-414 Xie 
while for very large values of X1 we get 
i BR? yoRexas 
imdge.  -Xi(ge) = (ye 
and By a eae, | 
Thus for very large and very small P.D.’s the current is 
proportional to the P.D., but the slope of the curve showing 
the relation between current and P.D, at the higher voltages 
is 2 (“)’ of the slope for small voltages. We may further 
( 
note that, other things being equal, the value X, required for 
a given fraction of the true saturation current is proportional 
to l. 
The general agreement between these results and experi- 
ments on ionization, e.g. in flames*, is exceedingly close, 
although of course the pressure in the case we are consideri ing 
is much greater than in the experiments. 
‘¢ 
We have seen that 0=5 (nn2), so that — = = 
In order that @ should not be zero, positive ions must be 
supplied at the positive plate, and negative ions at the 
negative plate, by the plates themselves at a rate (nz): RXy. 
* See Thomson, ‘Conduction of Electricity,’ pp. 197-203. 
