270 Mr Kleeman, The Unstable Nature of the Ion in a Gas. : 
' 
dissociation of the clusters is equivalent to an additional number 
of free ions equal to =: being drawn through the gauze. 
V, 
In the paper on clustering of ions quoted it is shown that 
tn =c, where c denotes the concentration of the clusters per c.c., 
n the number changing into other clusters and elementary ions 
per second, and ¢ the life of a cluster. If the clusters are con- 
sidered in a body so that ¢ denotes the average life of a cluster, 
nc =n, and therefore ¢ = 7 
It appears also that the dissociation of a cluster takes place 
after it has undergone a certain average number of collisions, and 
the time required for these collisions therefore varies inversely as 
the pressure of the gas, or 7 increases with increase of pressure 
of the gas. But the value of 7 probably also depends on the 
electric field applied to the gas when of great intensity. The 
field increases the violence of collision of the cluster with other 
molecules and consequently decreases its period of life. Since the 
kinetic energy given to a cluster between two consecutive collisions 
is proportional to the electric field and inversely proportional to 
the “mean free path” of the cluster, the effect of the field on the 
value of 7 may be expressed as a function of za We may there- 
fore write n=p.¢, (=) , where the value of ¢, CG} increases with | 
an increase of X, and consequently decreases with an increase of p. 
If y denote the fraction of elementary ions becoming clusters 
per second of a number of ions in equilibrium we have yk, = nkp, 
since the number of elementary ions becoming clusters per second 
must be equal to the number of clusters becoming elementary 
ious. The ratio of k, to k, is independent of the pressure of the 
gas when the ions are not subject to any external force such as an 
electric field. The effect of the electric field may as before be 
expressed in terms of = or do eh It follows therefore 
2 
that we may write y=p. 4; (=) : 
The foregoing considerations will now be applied to some of — 
the experimental results obtained. Let us first calculate the 
fraction of elementary ions drawn through the gauze that would 
have to be in the elementary state to account for the current due 
to ionisation by collision on the supposition that no clusters be- 
come elementary during their passage from gauze to plate. Thus 
in the case of CO, at a pressure of 9°5 mm. of mercury a current 
of 187 in arbitrary units was obtained corresponding to a field of — 
