ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 393 



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, &c. 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 thickness is dx, and 

 area unity, at a distance x from the origin. The nuniber of 

 collisions taking place in this stratum in unit of time will be 



N V 7 dx. ** 







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 



=- when x is between nl and 0, 

 Ml 



nl ^~ x 



and -- y- when x is between and + nl ; 



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 nl and 

 (n + dn) I is 



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

 according as x is positive or negative. 



In integrating this expression, we must remember that N, v, and I are 

 functions of x, not vanishing with x, and of which the variations ate very 

 small between the limits x= nl and x= +nl. , 



VOL. i. 50 



