Mr Kleeman, The Unstable Nature of the Ion in a Gas. 277 
This was principally due to the fact that the values of fe required, 
where 8 denotes the coefficient of collision for the positive ions, 
could not be obtained from Townsend’s curves for small values of 
—. There is good reason to believe, however, from other experi- 
ments, that the period of life of a positive cluster is greater than 
that of a negative. The behaviour of the positive and negative 
rays in a discharge tube, which has been studied in great detail 
by Sir J. J. Thomson, Wien, and others, is evidence in support of 
this. Obviously we should obtain evidence of those clusters only 
whose period of life is greater than the time it takes them to 
travel the length of the tube under the electric field. The number 
of different clusters obtained would in that case depend on the 
pressure of the gas in the tube, its dimensions, etc., and this has 
been found in practice. Now as a rule the number of different 
negative clusters obtained is much smaller than the number of 
positive clusters, and may be explained by a difference in the 
period of the clusters. It will be of interest, however, to give the 
formula here by means of which the period of life of a positive 
cluster could be calculated. The production of dark and luminous 
spaces in a discharge tube under certain conditions must be in 
part regulated by the fact that the proportion of free ions to 
clusters increases as the ions pass into a stronger field. The 
principles involved will be brought out in deducing the formula 
in question. 
Let K denote the number of positive ions drawn through 
the gauze when at a positive potential, of which #, are in the 
elementary state and k, clusters, so that K =k,+k,. The ionisation 
current c, produced by the free ions /, is given by 
k,(8—a) e#-* | 
(= Base Sen tea nteruccaoeaee (3), 
where 8 denotes the number of new ions made by a positive 
ion per cm. of its path. This formula is obtained by inter- 
changing a and 8 in the formula used by Townsend in his 
investigations of the ionisation by collision of positive ions. 
The ionisation produced indirectly by the clusters will be 
considered separately. Let S denote the number of clusters that 
cross per second a plane parallel to the plate at a distance «, and 
6 the fraction of the number of clusters becoming elementary 
ions per second. We then have ee S6, which on integrating 
dt 
hes 
becomes S=/,e-t. Now t=——, where V, denotes the average 
VE 
