398 ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 



PROP. XVIII. To find the -mechanical effect of a difference in tJie mean 

 velocity of translation of two systems of moving particles. 



Let F,, V t be the mean velocities of translation of the two systems 

 respectively, then ., ' 2, (V l F,) is the mean momentum lost by a particle 



Jjl j T~ Ixl g 



of the first, and gained by a particle of the second at collision. The number 

 of such collisions in unit of volume is 



e lt or tpa; 

 therefore the whole effect of the collisions is to produce a force 



on 



<>>f t > 



the first system, and an equal and opposite force 



on unit of volume of the second system. 



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 ., is the mean distance a particle of the 

 first kind would have to go before striking a fixed particle, and Z, the distance 

 for a particle of the second kind, then the mean paths of particles of each 

 kind will be given by the equations 



, j 1 , ................... (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 



MJTJQ.V. d Pl I, dp, I, 

 ~ZT " ^ A ~ dx L, ~ 



