﻿4 Mr. William Sutherland on the 



plane from the side of increasing density than from that of 

 decreasing density, and diffusion results. Thus if n x is the 

 number of molecules per unit volume at the plane, that at a 

 small distance x from it will be n 1 + xdn 1 /dx. The number 

 of molecules leaving an element dx after encounter in it to 

 cross the plane before the next encounter must be proportional 

 to n x + xdn^dx, to dx, to the mean number of collisions per 

 second ^i/A-i, where X x is the mean free path of the molecules 

 of the first set near x, and finally to e~ x ^ the probability of 

 a path greater than x, so that the number of molecules of 

 the first set which cross the plane from one side in unit time 

 is proportional to 



1 



n (wi + xdn x \dx) e~ x ^ dxj\ Y 



(although x was stipulated to be small to justify the expres- 

 sion n x + xdn^dx, no harm can come of integrating to go , 

 because the value of the integral becomes negligible for all 

 values of x greater than a few times X x ). The number of 

 molecules crossing from the other side is proportional to 



f 



Jo 



v i ( n i — % dn-Jdx) e~ x ^ dx[X^ 



so that the excess accumulating in unit time on one side 

 is proportional to 



2^1 xe~ x ^dxdn x ldx\i, 



that is to 2v 1 \idn 1 /dx. The number of molecules of the 

 other set crossing in the opposite direction is proportional to 

 2v 2 \ 2 dn 2 /dx. As these two expressions are not equal, there 

 is a gain of molecules on one side of the plane and a loss on 

 the other proportional to 



2(v 1 \ 1 dn 1 /dx — v 2 \dn 2 /dx) ; 



and to preserve the uniformity of pressure Meyer supposes a 

 bodily motion of the mixed gases to take place so as to carry 

 this number of molecules in the opposite direction, of which 

 the fraction n^fjix -f- n 2 ) belongs to the first set and w 2 /(n 1 + w 2 ) 

 to the second : thus the diffusion-stream of the first gas is 

 proportional to 



dn Y 2n 1 / dn Y dn 2 \ 



2v ^lx~ - ,M^A Vl ^ - V ^dx)> 



that of the other being equal and opposite. On account 

 of the uniformity of pressure, dn l /dx=dn 2 /dx and the diffusion- 



