MR. J. S. TOWNSEND ON THE DIFFUSION OF IONS INTO GASES. 131 



SECTION I. 



M vniKMATH'Ai, INVKSTK. \IIN. 



1. In a conducting gas we have two distinct sets of bodies to deal with : the ions, 

 which are charged, and whose motion under an electromotive force constitutes 

 conduction, and the uncharged molecules, the number of which is very much greater 

 than the number of ions [the latter number multiplied by 10 12 gives about the order 

 of the number of molecules]. The ions, which for the present we will suppose to 

 consist of an equal number of positively and negatively charged carriers, may be con- 

 sidered as a distinct gas, A, and the rest of the molecules through which they move 

 as another gas, B, the two together constituting a conducting gas. When the 

 carriers come into contact with a metal surface, they either give up their charge to 

 the metal or remain in contact with the surface, so that the metal behaves like 

 a perfect absorber of the ions. 



In a paper On the Dynamical Theory of Gases,* MAXWELL has given the general 

 equations of motion of two gases diffusing into each other. 



The equations are of the form : 



Ot ~r - 



dt d*r 



where p\ and p t are the densities of the gases ; p l and p 2 their partial pressures ; 

 HI and 2 their mean velocities in the x direction ; /'A a constant for the two gases 

 which depends upon the temperature ; and X the force acting on unit mass. 



The first and last terms in the above equation may be omitted, as they are small 

 compared with the other two, but in dealing with a gas which is made up of small 

 charged bodies a new term must be introduced when electric forces are acting. 



Thus the term /a,X arising from the force of gravity/for example, is 981 X fn,n, ; 

 'where n, is the number of molecules of the first gas per cub. centim. and m, the mass 

 of each (m l expressed in grammes is of the order 10~ M ). 



In order to estimate dp t /dx roughly, we will suppose that the gases are contained 



in a tube of '15 centim. radius, and that p t = at the surface. In this case -r- 1 will 



be of the order ^ , where ', is the value of p t at the centre. Letting , rj, and , 

 *lo 



denote the mean velocities of agitation in the directions x, y, and 2, p\ = m\ n\ \ , 



/' ')il 71 f* 



and we obtain ' *- - ' , which is large compared with 981 X wij n',, since f, is 

 'lo '15 



of the order 10 4 . 



The first term m^dui/df is small compared with dpjdx, since the resistance to 

 the motion is so great ; the acceleration in the cases with which we are concerned 



* J. C. MAXWELL, ' Phil. Trans.,' vol. 157, 1866. 

 s 2 



