d.r, 



24 Prof. Maxwell on the Process of Diffusion of two or 



there is no mean motion of translation, and then consider the 

 effect of such motion separately. 



Let a stratum whose thickness is a (a small 

 quantity compared with /), and area unity, 

 be taken at the origin, perpendicular to the 

 axis of x ; and let another stratum, of thick- 

 ness dx, and area unity, be taken at a distance 

 x from the first. 



If M, be the mass of a particle, N the number in unit of 

 volume, v the velocity of agitation, / the mean length of path, 

 then the number of collisions which take place in the stratum 

 dx is 



- *$*. 



The proportion of these which reach a distance between nl and 

 (n-f fl?n)/is 



e~ n dn. 



The proportion of these which have the extremities of their paths 

 in the stratum a is 



The velocity of these particles, resolved in the direction of x, is 



vx 

 ~"n~V 



and the mass is M ; so that multiplying all these terms together, 

 we get 



2n*/ 3 6 ~ (30) 



for the momentum of the particles fulfilling the above conditions. 

 To get the whole momentum, we must first integrate with 

 respect to x from #= — nl to x= +nl, remembering that / may 

 be a function of x, and is a very small quantity. The result is 



d /NMiA - 



Tx\-^-r mdn ' 



Integrating with respect to n from n=0 to n= oo, the result is 



-"di\—) =ttXp • • • • (31 



as the whole resultant force on the stratum a arising from these 



NMv 2 

 collisions. Now — jr- =p by Prop. XII., and therefore we 



