in the Kinetic Theory of Gases. 309 



Let N be the number per unit of volume of molecules of 

 gas M, a the number for gas m, at any point in the tube. 

 By Avogadro's law N + n is constant throughout, or taking 

 the axis of the tube for that of x\ 



dN _ dn 

 dx dx' 



The stream velocity is assumed to be very small compared 

 with the molecular velocity of mean square. The problem of 

 diffusion is to find the stream velocity. 



Take as an element of volume in the tube a cylinder of 

 length Sx, and whose base is unit area parallel to yz. 



Let N be the number per unit of volume of molecules M 

 at the left-hand face (towards A) of that cylinder. Then the 

 number at its right-hand face is 



N + &4^, that is N- 8xp. 



ax ax 



The number of M molecules of the class Xfjuvco 2 doodS which 

 enter the cylinder through its left-hand face in unit of time is 



XN 



'AM 



(")■«- 



M»2 



The number of the same class which pass out of the cylinder 

 through its right-hand-face in unit of time is 



and therefore, but for encounters, the number of molecules M 

 of the class X ja v go? da> dS within our cylinder would be in- 

 creased in unit of time by the quantity 



\ it J dx 

 or the number per unit of volume would be increased by 



lM\Un 



(")■ 



e -*M»V<fodS. 



ax 



Therefore 



BF = x (hM.Vdn 



^t \ 7T / dx 



This is a zonal harmonic function of the first order about 

 the axis of x. In this case we shall assume 



