272 Mr Kleeman, The Unstable Nature of the Ion in a Gas. 
The fraction of clusters drawn through the gauze that become 
elementary ions on their passage from gauze to plate must be 
small if the calculated fraction is small of the ions drawn through 
the gauze that must be in the elementary state to account for the 
total current observed due to ionisation by collision. If all the 
clusters were to become elementary ions before reaching the plate 
the current obtained would be very nearly equal to that obtained 
on the supposition that all the ions drawn through the gauze are 
in the elementary state. Since only a small fraction of the ions 
are in the elementary state it follows that the life of a cluster in 
the gases under consideration is greater than the time the cluster 
takes to pass from gauze to plate. If the velocity of a cluster is 
taken equal to the velocity of an ion measured in the usual way 
(strictly it must be less) the time of passage of a cluster in the 
experiments just mentioned is for CO, eee = 00735 sec. and 
oy up DoS US ; ‘ ; ; 
for air 187x760 7 00554 sec. Thus the average periods of life 
of the clusters must be greater than these values, and the values 
of 7 consequently less than 66°45 and 90:2 respectively. 
The values of V,a in the cases under consideration are 1047 
and 1150 respectively, and thus the values of » are small in 
comparison with the values of V,a. Equation (2) may therefore 
be used to calculate the values of y, if ae is not small in com- - 
1 
parison with &,. 
Thus for example in the case of air a current of 172 and 80 
was obtained corresponding to a field of 1440 and 1320 volts 
respectively. The values of < corresponding to the values of a | 
are ‘85 and ‘715 respectively. The positive leaks corresponding — 
to the above voltages were 20 and 18°5 respectively. If k, denote 
the number of free ions and &, the number of clusters corre-_ 
sponding to the leak 20, the number corresponding to the leak 
18°5 are k, a and k, — The two simultaneous equations 
obtained from equation (2) and the equations k,+4,=20 and 
t:n=1 then give k,='196, k,=19°8, n=11384, and t,='89 sec. 
Thus about 1 7% of the ions in equilibrium in air are in the 
elementary state; and the period of life of a cluster at a pressure 
of 15 mm. of mercury is of the order of one second. The value of 
y is 115, and the corresponding period of life ¢ of an elementary 
ion therefore ‘00872 sec. Since ¢, and ¢, are inversely proportional 
to the pressure, their values at atmospheric pressure are ‘0176 and 
‘000172 second respectively. 
