378 Prof. Thomson, On the theory of the motion 



The mobility of an ion, i.e. the speed with which it moves 

 through the gas under unit electric force, is connected with the 

 rate of diffusion of the ion by the equation 



Ne 



where tt is the pressure due to iV" molecules per cubic centimetre. 

 Hence 



\ mi ma Vyu,2— lilt's 



We see from this that the mass of a heavy ion has not much 

 effect on its mobility; the mobility of an ion consisting of a charged 

 molecule of the gas through which it is moving is \/2 times the 

 mobility of one whose mass is very much greater than that of a 

 molecule of the gas ; the mobility does not however depend on the 

 charge on the ion. The velocity, through hydrogen, of an ion made 

 of a molecule of hydrogen charged with electricity, would be about 

 half as much again as that of a charged molecule of methyl iodide 

 through hydrogen and so would easily be distinguished from it. 



Mobility of an ion through a mixture of gases. 



If we have a small number of charged molecules A diffusing 

 through a mixture of gases B and G we can readily prove by 

 Maxwell's method that i), the coefficient of diffusion oi A through 

 the mixed gases, is given by the equation 



D^-l 1 



2hA^ / mim.2 lyb^—Y.e^ I niiWis I \x^—\.e^ 



""'V m, + m,\/ SttN '^ "' V m, + m,V irN ' 



where Vq, and v^ are respectively the number of molecules of 

 B and G present per unit volume, m^, m^ the masses of the 

 molecules of these gases, /ig and fis the indices of refraction 

 of these gases when there are N of their molecules per unit 

 volume. 



The mobility k of the ion through these gases is given by 



1 / mjma /fx„—l I vfi-jn-i I ix^ — \ 



Let us consider the application of this equation to the experi- 

 ments lately made by Mr Wellisch on the mobilities of the ions 

 through mixed gases and calculate the difference between the 

 mobilities through the mixture of charged molecules of B and 



