Prof. Maxwell on the Process of Diffusion of two or 



mm of this definite motion of agitation, combined with the general 

 motion of translation. 



When two gases are in communication, streams of the two 

 gases might run freely in opposite directions, if it were not for 

 the collisions which take place between the particles. The rate 

 at which they actually interpenetrate each other must be investi- 

 gated. The diffusion is due partly to the spreading of the par- 

 ticles by the molecular agitation, and partly to the actual motion 

 of the two opposite currents in mass, produced by the pressure 

 behind, and resisted by the collisions of the opposite stream. 

 When the densities are equal, the diffusions due to these two 

 causes respectively are as 2 to 3. 



Prop. XIV. In a system of particles whose density, velocity, 

 fyc. are functions of x, to find the quantity of matter transferred 

 across the plane of yz, due to the motion of agitation alone. 



If the number of particles, their velocity, or their length of 

 path is greater on one side of this plane than on the other, then 

 more particles will cross the plane in one direction than in the 

 other; and there will be a transference of matter across the 

 plane, the amount of which may be calculated. 



Let there be taken a stratum whose thick- 

 ness is doc, and area unity, at a distance x from 

 the origin. The number of collisions taking 

 place in this stratum in unit of time will be 



Njdx. 



The proportion of these which reach a distance between nl and 

 (n-\-dn)l before they strike another particle is 



e~ n dn. 



The proportion of these which pass through the plane yz is 



nl+x 



2nl 

 and nl— x 



when x is between — nl and 0, 

 when x is between and -f nl ; 



2nl 



the sign being negative in the latter case, because the particles 

 cross the plane in the negative direction. The mass of each 

 particle is M ; so that the quantity of matter which is projected 

 from the stratum dx, crosses the plane yz in a positive direction, 

 and strikes other particles at distances between w/and (n + dn)l is 



2yt/ r ' dxe~*dn, (26) 



where x must be between ±nl, and the upper or lower sign is 

 to' be taken according as x is positive or negative. 



