Cluster in a Gas under Influence of an Electric Field. 939 

 Previous Experiments on Negative Ion Clusters. 



In a previous paper the writer has studied the currents 

 when negative ions were drawn through the gauze for fields 

 of different strengths using a large number of different 

 gases. It was found that for the larger number of gases the 

 current, when the effect of ionization by collision became 

 appreciable, could be accounted for by supposing a small 

 fraction only of the ions drawn through the gauze in the 

 free state. The clusters in these gases would thus require, 

 generally speaking, a large field to disintegrate them. The 

 gases which appeared to be exceptional were CC1 4 , C 6 H 6 , 

 and CS 2 , and the clusters in these gases are thus either dis- 

 integrated by a comparatively weak field, or the proportion 

 of free ions to clusters in a number of ions in equilibrium is 

 larger than in the other gases. 



A Formula for the Mean Free Path of Disintegration 

 of an Ion Cluster. 



It will be of interest to obtain a formula for the mean free 

 path of disintegration of an ion cluster. Let n x denote the 

 number of chances per cm. of path an ion cluster would 

 have to break up when moving under the action of an electric 

 field, due to being bombarded by neutral molecules. If V 

 denote the velocity of a cluster under unit electric field, and 

 ti its period of life under ordinary conditions, the value of 

 n l5 if the electric field applied be denoted by X, is given by 



h n i = vrr . Now U= — * * and V = — - , where p denotes 

 aV p p r 



the pressure of the gas and M x and M 2 are constants which 



depend only on its nature, and hence n, = ^Hnririi • Next 



r J 1 XM^M.2 



let n 2 denote the number of chances an ion cluster would 

 have per cm. of its path of breaking up due to the action of 

 the electric field. A cluster probably breaks up when the 

 kinetic energy imparted to it by the electric field exceeds a 

 certain maximum value E. An ion will thus acquire the 

 requisite velocity to disintegrate under the force X when it 

 travels freely along a distance x such that &X#>E, or when 

 X# exceeds a certain potential P. The quantity n 2 then 

 denotes the number of free paths per cm. which exceed the 

 distance x. In going through the element d.v of these paths 

 the number of chances of disintegration will be proportional 

 to n 2 \ dx, hence —dn 2 = kn 2 .dx, where h is a constant. On 



* Loc. tit. 



