BY THE ACTION OF A RADIO-ACTIVE SUBSTANCE, ETC. 2G1 
positive and negative ions appear simultaneously in the gas. From the results of the 
experiments on diffusion, we are led to conclude that the ions thus produced resemble 
very closely those produced by Rontgen rays, and carry the same charge. We will 
therefore assume that the laws governing the recombination will not be much different 
in the two cases. The method of finding the correction for recombination has been 
explained in the previous paper.^ It was there shown that for small conductivities 
the loss due to recombination was about 4 per cent, of the loss due to diffusion to the 
sides. 
The time, Z 1 /Y, in the experiments made with Rontgen rays was about ypth of a 
second, the radius of the tubing being 1'5 millims. A new apparatus was made with 
finer tubing (a = ’5 milliin.), so that without altering KZpbdV, the value of ZJY is 
reduced to gV The number, N, of ions which recombine is similarly reduced from 
N to N/9. 
The radio-active substance was contained in a sealed glass tube, which cut down 
the radiation proceeding from it so as to produce densities of ionisation less than the 
smallest that was used in the' experiments made with Rontgen rays. We may 
therefore assume that in the present experiments the process of recombination does 
not affect the value of y to the extent of '5 per cent. 
Mutual Repulsion. 
W1 len a gas contains ions of one sign (as in the case of ions produced by the action 
of ultra-violet light on a metal plate, or by a point discharge), the electrostatic field 
arising from the electric density is sometimes sufficient to exert a considerable force. 
It would be difficult to find the exact amount that this effect contributes to the loss 
of ions in a tube while diffusion is taking place, but it is easy to find an upper limit 
to the error it introduces. 
Let us consider the case of a charged gas in a metal tube losing its electrification 
owing to the motion of the ions along lines of force from the axis to the surface. If 
we suppose that no diffusion is taking place, it is easy to sliowf that the density of 
electrification at any point is given by the formula — 
' 1 + 47 TUp 0 t ’ 
p 0 being the initial density, supposed uniform, u the velocity of an ion when acted on 
by unit electrostatic force, and t the time during which the density falls from 
Po to p. 
The proportion of ions lost, -- P , is practically 47 rp 0 ut when the loss is small. 
P<) 
* Lor. cit., stqirci, p. 144. 
t John S. Townsend, ‘ Phil. Mag.,’ June, 1898. 
