[ 177 ] 



XX. The Structure of Ions formed in Gases at High Pressure?, 

 By (X W. Richardson, M.A., D.Sc* 



M. LANGEVIN has recently pointed out f that the slowness 

 of diffusion of ions in gases cannot be explained simply by 

 the increase of collision -frequency caused by the attraction 

 of neutral molecules polarized by the electric field surrounding 

 the ions. He finds that, even when this effect is taken into 

 account, it is necessary to assign to the positive and negative 

 ions diameters equal respectively to thrice and twice that of 

 an uncharged molecule, in -order to obtain the values of the 

 coefficient of diffusion actually found. The object of the 

 present note is to indicate some further considerations which 

 seem to shed light on the structure of ions in gases. 



As is well known, by making use of the kinetic theory of 

 gases we can obtain an expression for the drift velocity v ! 

 of an ion, whose charge is e and mass ???, under an electric 

 field of intensity X. in the form 



1 e \ 



i — 



--X 



2 m c 



where A, is the mean free path and c the mean speed. In 

 deducing this formula, the statistical assumption is made that 

 the effect of a collision is to wipe out the previous history of 



the molecules concerned ; it is also assumed that -. — s- is 



4 mc z 



small compared with unity. This condition is satisfied if 



the ratio of the electric intensity to the pressure is small 



enough. 



If we assume that the ions at pressures near atmospheric 

 consist of two or three molecules held together by an electric 

 charge, and substitute the probable values of e, m, and c in 

 the above formula, we obtain values of v somewhat less than 

 that found experimentally but of the same order of magnitude. 

 Several reasons might be assigned for the discrepancy, but 

 we shall not enter into them here. The fact that the correct 

 order of magnitude is attained indicates that the theory is not 

 altogether wide of the mark. 



Admitting this, we see that if the nature of the ions 

 remains unaltered, ?//X, the velocity under unit field, will be 

 directly proportional toX, that is, inversely proportional to the 

 pressure p. This result has been established experimentally 

 by Langevin J, who found that at pressures sufficiently 



* Communicated by the Author, 

 t Comptes JRendus, torn. cxl. p. 35 (1905). 



% Theses de V Universite de Paris, A. 481, p. 190. Gauthier Villars, 

 Paris, 1902. 



Phil. Ma,g. S. 6. Vol 10. No. 55. July 1905. N 



