IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 275 



We deduce the expression for the mobility in the form : 



AT? /-/mY' 3 /! .MY- 1 */. . V 8 J . 4(K-l)e 2 



'- -- ~ -- -- 



T? /-m! .. . . -e 



= '- 4\/2 hey 1H -- 1 + ~ lH -- jT7 -- mf 



l \M/ \ m/ \ */ I 7mmv 2 s+s') J 



When the mass and dimensions of the ion are the same as those of a molecule, we 

 have M = m, s' = s, and the expression for the mobility becomes 



This expression can be transformed into 



(J 



Consider the expression (a) which has been found for the velocity of an ion, 

 regarded as a molecule carrying a charge equal to that associated with the monovalent 

 ion in electrolysis, moving under unit electric intensity in a gaseous medium at a 

 pressure p dynes per square centimetre and a temperature of C. 



For a given medium K^, p lf and p^ are constant ; whence k varies inversely as p, 

 provided ? is constant. Now, by MAXWELL'S law,* the coefficient of viscosity of a 

 gas is independent of its density ; consequently over the range of pressures for which 

 this law holds good we should expect the ionic mobility to vary inversely as the 

 pressure, a conclusion which has been verified experimentally. 



The expression (a) involves only known physical constants of the gas and is 

 therefore directly comparable with the results of experimental observation. The 

 results obtained by substituting the observed experimental values of the quantities 

 involved are given in Table III. The values of the viscosity coefficients and of the 

 dielectric constants have been taken from LANDOLT and BORNSTEIN'S Tables (3rd 

 edition) ; the constant p l was taken as 1,013,610 (dynes per square centimetre). 



The sixth column in the table affords an indication of the effect on the mobility of 

 the electric polarisation of the molecules due to the ionic charge ; it will be seen that 

 the effect is quite considerable. Column seven gives the values of the mobilities 

 under a potential gradient of 1 volt per centimetre, which would be possessed by a 

 molecule carrying a charge E if there were no retarding effect due to this polarisation. 

 The remaining columns give the values of the mobilities as deduced from the 

 expression (a) together with the observed experimental values of the positive and 

 negative ionic mobilities ; these values correspond to. a real or hypothetical pressure 

 of 760 mm. of mercury. 



Unfortunately the values of K have been determined experimentally for only a 

 very limited number of gases and vapours ; in consequence, several vapours whose 

 mobilities have been ascertained do not appear in the table. 



* Vide JEANS, ' Dynamical Theory of Gases,' p. 252. 

 2 N 2 



