Mobility of the Positive Ion in Flames. 785 



then 



where M L = mutual potential energy of ion and molecule at 

 collision, 

 M 2 = kinetic energy of molecule. 



K — 1 e 2 



Langevin shows that M, = — ,-r, 



where K = specific inductive capacity of the gas, 

 n = number of molecules per c.c, 

 r — distance apart of ion and molecule at collision. 



The difficulty in applying this correction is the uncertainty 

 a* to the value of r; since M x varies as the fourth power 

 of r, any error in the value of r is quadrupled in the result. 

 To illustrate the matter, let us take the case of air at normal 

 pressure and temperature. We find that Mi/M 2 = 3*3 if the 

 ion is a single molecule, i. e. if the distance apart at collision 

 is put equal to one molecular diameter. In this case electric 

 attraction decreases the free path 4*3 times. If, however, 

 the ion consists of a single layer of molecules grouped round 

 a central molecule, i. e. (27r4-l) molecules in all, the value 

 of Mx is reduced 16 times, and is only 02; so that the free 

 path is reduced only 20 per cent. If we calculate the 

 mobility in each case, we find it approximately the same for 

 both. In the first case the mobility 



mv\4:'6J 

 and in the second case 



v \Dniy 



the slight change in the ratio (X/v) due to the size of the 

 cluster being of a much smaller order than the other 

 correction. This ambiguity in the interpretation of mobility 

 experiments seems inevitable. A single molecule ion has its 

 free path diminished by electric induction to such an extent 

 that it behaves like a cluster ion which, on account of its 

 large size, is scarcely affected by induction. Wellisch * has 

 interpreted his mobility experiments as supporting the idea 

 that the ion is a single molecule. At ordinary temperatures 

 the agreement between experiment and such a theory is very 



* Wellisch, Phil, Trans. A. (1909). 



