Mr Kleeman, The Unstable Nature of the Ion in a Gas. 269 
gauze of which k, are elementary negative ions and hk, clusters of 
various complexities, and thus K=k,+h,. The quantity K can 
be measured directly. The elementary ions give rise to a current 
k,e by collision with neutral molecules*, where / denotes the 
distance between gauze and plate, and a the number of fresh ions 
produced by a negative ion per cm. of its path. 
There is an additional current produced by some of the clusters 
becoming elementary ions during their passage from gauze to 
plate. Let WV denote the number of clusters in a c.c. at a distance 
« from the plate. We then have de=— dn. e, where de 
denotes the current from a strip of gas of thickness dw and unit 
:, aN 
area in which ——.d« clusters become elementary ions per second. 
dt 
Now ee N. where 7» denotes the fraction of clusters be- 
dt 
coming elementary ions per second. Integrating this equation 
we have WV = — e—, where ¢ denotes the time the clusters take 
V 
1 
to pass over the distance (J—«), and V, the average velocity of 
a cluster. The value of ¢ is given by t= _ Therefore 
1 
dN k,  -%# 
V, 
GB Va 
we =) 
and thus dc = mee LI 
1 
Integrating this equation between the limits =/ and «=0 we 
obtain 
ae {ele — ei 
Viat+n 
The total current C is therefore given by the equation 
s kon d 
= Ge ae VEN ICIEG! cosssoacaoa: 1 
eee | (1) 
: : : Ue : 
If » is small in comparison with V,a, 7 => is small in com- 
V, 
parison with Ja, and the equation becomes 
ae kon la 
Cc a + i Chee Wenn sat cict cha on bs (2). 
It will be seen that in the latter case the effect produced by the 
* The Theory of Ionisation by Collision, p. 4. By Prof. J. S. Townsend. 
VOL. XVII. PT. IIl. 18 
