DIFFUSION. 629 



gases will encounter each other, and every encounter will act as a check to 

 the process of equalization of the density of each gas throughout the mixture. 



The interdiffusion of two gases in a vessel is therefore a much slower 

 process than that by which the density of a single gas becomes equalized, 

 though it appears from the theory that the final result is the same, and that 

 each gas is distributed through the vessel in precisely the same way as if no 

 other gas had been present, and this even when we take into account the 

 effect of gravity. 



If we apply the ordinary language about fluids to a single gas of the 

 mixture, we may distinguish the forces which act on an element of volume 

 as follows : 



1st. Any external force, such as gravity or electricity. 



2nd. The difference of the pressure of the particular gas on opposite sides 

 of the element of volume. [The pressure due to other gases is to be con- 

 sidered of no account.] 



3rd. The resistance arising from the percolation of the gas through the 

 other gases which are moving with different velocity. 



The resistance due to encounters with the molecules of any other gas is 

 proportional to the velocity of the first gas relative to the second, to the 

 product of their densities, and to a coefficient which depends on the nature 

 of the gases and on the temperature. The equations of motion of one gas of 

 a mixture are therefore of the form 



- u. 3 ) + &c. = 0, 



where the symbol of operation ^ prefixed to any quantity denotes the time- 



variation of that quantity at a point which moves along with that medium 

 which is distinguished by the suffix (,), or more explicitly 



8, d d d d 

 cr-= -r + u,-j- + v 1 -j- + w 1 -j-. 

 8t at dx dy l dz 



In the state of ultimate equilibrium it l = u t = &c. = Q, and the equation is 

 reduced to 



which is the ordinary form of the equations of equilibrium of a single fluid. 



