more kinds of Moving Particles among one another. 27 



Prop. XIX. To find the law of diffusion in the case of two gases 

 diffusing into each other through a plug made of a porous material ', 

 as in the case of the experiments of Graham. 



The pressure on each side of the plug being equal, it was 

 found by Graham that the quantities of the gases which passed 

 in opposite directions through the plug in the same time were 

 directly as the square roots of their specific gravities. 



We may suppose the action of the porous material to be similar 

 to that of a number of particles fixed in space, and obstructing 

 the motion of the particles of the moving systems. If L, is the 

 mean distance a particle of the first kind would have to go before 

 striking a fixed particle, and L 2 the distance for a particle of the 

 second kind, then the mean paths of particles of each kind will 

 be given by the equations 



l=A Pl + B^+i -L=Cp 1+ Dp 2 +i-. . (38) 



The mechanical effect upon the plug of the pressures of the gases 

 on each side, and of the percolation of the gases through it, may 

 be found by Props. XVII. and XVIII. to be 



1^ * L 2 dx L, dx L 2 ' ' W 



and this must be zero, if the pressures are equal on each side of 

 the plug. Now if Q w Q 2 be the quantities transferred through 

 the plug by the mean motion of translation, Q, ^pjfj = MjN,Vj ; 

 and since by Graham's law 



Q 2 ~ " V M s " ~V 



we shall have 



M l N 1 v,V l = — M 2 N 2 v 2 V 2 = U suppose ; 



and since the pressures on the two sides are equal, ■— = — ■—, 



and the only way in which the equation of equilibrium of the 

 plug can generally subsist is when Lj = L 2 and l x — l^ This 

 implies that A=C and B = D. Now we know that v 1 3 B=v 2 3 C 



A 



Let K=3— o, then we shall have 

 v? 



A=C=4KV, B=D = |Ki; 2 3 , . . . (40) 



and 



y- = y- ^Kfa^+tW^+jj. > • • (41) 



The diffusion is due partly to the motion of translation, and 

 partly to that of agitation. Let us find the part due to the 

 motion of translation. 



