276 MR. J. S. TOWNSEND ON THE DIFFUSION OF IONS PRODUCED IN AIR 
We shall first examine the relative values of the charges on the ions in the 
different cases. For this purpose a knowledge of the velocities of the ions through 
air, when acted on by a known electric force, is required. 
If N is the number of molecules per c.c. of a gas at atmospheric pressure (10 6 dynes 
per square centim.), e the charge on the ion of the gas in electrostatic units, u the 
velocity of the ion in a field of 1 volt, per centim., and K the coefficient of diffusion 
of ions into the gas ; then— 
N X e = 
3 x 10% 
K 
If E is the charge on a hydrogen ion in a liquid electrolyte, then N X E = 1 '22 
X 10 10 , E being expressed in electrostatic units. 
From these formulas we see that when u and K are known, we can find e in terms 
of E. 
It has already been shown in this manner, in the case of Rontgen rays, that the 
charge carried by the positive and negative ions is in all cases very nearly the same 
as the charge E, the differences not being greater than possible experimental errors. 
In order to make a similar investigation for ions produced by other methods, a 
complete knowledge of the velocities u would be necessary, hut it is only in a few 
cases that these velocities have been found. 
The value of u for ions produced by ultra-violet light given by Professor Ruther¬ 
ford is I ‘5 centims. per second in air at atmospheric pressure.* If we take the 
mean of the two values of K which we have found for dry and moist air, we find 
that in this case N<? = 1T2 X 10 10 . The effect of moisture on the velocity under 
an electric force has not been examined, so that we cannot expect to obtain a nearer 
agreement with the electrolytic value of NE. 
The velocities of the ions produced by point discharges have been investigated by 
Professor Chattock. t The values given for the positive and negative ions are 1'37 
and 1'80 (centims. per second in a field of 1 volt per centim.) respectively. Other 
values were also obtained smaller than these, which would agree better with the 
observed coefficients of diffusion, hut Professor Chattock is of opinion that the low 
values he obtained for the velocities are less reliable, owing to experimental errors. 
The arrangement of the apparatus for the determination of the velocities was such 
that the point was not surrounded by a narrow tube, so that the larger values 
obtained for the coefficient of diffusion may be taken in conjunction with the above 
values of the velocities. The numbers so obtained for Ne are 1'66 X 10 10 and 1*46 
X 10 10 for the positive and negative ions respectively. 
These results would seem to show that some of the ions carried a double charge, 
but we cannot attach much importance to the above numbers, since the coefficients of 
* E. Rutherford, ‘Cambridge Philosophical Society Proc.,’ vol. 9, Part VIII., 1898. 
t A. P. Chattock, ‘Phil. Mag.,’Nov., 1899. 
