688 Mr. C. T. R. Wilson on the Condensation Method 
that 40 ions of either sign are produced per second in each 
c.c. This is the rate of ionization deduced from leakage 
experiments ina small vessel of silvered glass*. (The number 
20, given in the original paper, was deduced from the experi- 
ments by using J. J. Thomson’s first value for the ionic 
charge, since shown by him and by H. A. Wilson to be about 
twice too larget.) If q be the rate of production of ions per 
c.c. per second, then the number of ions of either sign in each 
c.c., if loss by diffusion be ignored, will be given by 
N= w/a, 
where « is the coefficient of recombination. Putting g=40, 
a=3°3 x 10° e (where e is the ionic charge) and e=3 x 10~¥” 
we have N=6x10?. If, on the other hand, we neglect the 
loss by recombination and consider only the loss by diffusion, 
then ina column of one sq. cm. in cross section extending 
from plate to plate and perpendicular to the plates, the number 
of ions when a steady state is reached is equal to cd T 7B, 
3 
where 2/ is the distance between the plates and D is the 
coefficient of diffusion of the ions through the gas (J. J. 
Thomson, ‘Electrical Properties of Gases,’ p. 21). The 
average number for every c.c. of air between the plates 
will be 
Dieci le 
itr 3 D 
For negative ions in moist air D is equal to 0°035t. Thus 
when g is 40, N=4x10?/. In an apparatus with plates 
less than a centimetre apart, as in many of the older experi- 
ments, so that / is less than 4, N is less than 100 per c.c. 
instead of the 6 x 10° obtained when only Joss by recombina- 
tion is considered : thus in this case the final number of ions 
is determined by diffusion, the loss by recombination being 
negligible. With the larger apparatus of the present paper 
27=5ems:., N=4 x 10? x 2'5?=2°5 x 10? when we consider only 
the loss of ions by diffusion. The loss by recombination is 
now no longer negligible, but the loss by diffusion is the more 
important factor ; the total number of ions when a steady 
condition is reached will be less than the value obtained when 
either recombination or diffusion is ignored, it must be some- 
what less than 2°5 x 10° per c.c. 
* C. T. R. Wilson, Roy. Soc. Proc. vol. Ixviii. p. 161. 
+ J. J. Thomson, Phil. Mag. vol. v. p. 846; H. A. Wilson, Phil. Mag. 
vol. v. p. 429 (1903). 
t Townsend, Phil. Trans. A. cxcy. p. 259 (1900). 
te 
