CHAPTER XIV. 



FEEE PATH PHENOMENA (CONTINUED). 

 DIFFUSION. 



Elementary Theory. 



322. THE difficulties in the way of an exact mathematical treatment of 

 diffusion are similar to those which occurred in the problems of viscosity 

 and heat conduction. Following the method adopted in discussing these 

 earlier problems, we shall begin by giving a simple, but mathematically 

 inaccurate, treatment of the question. 



We imagine two gases diffusing through one another in a direction 

 parallel to the axis of z, the motion being the same at all points in a plane 

 perpendicular to the axis of z. The arrangement of the gases is accordingly 

 in layers perpendicular to the axis of z. Let us denote the mass velocity of 

 the whole gas in the direction of z increasing by w , and the molecular 

 densities of the two gases by v 1} z> 2 - Then z/,, v 2 and w are functions of 

 z only. 



We assume that as far as the order of approximation required in the 

 problem, the mass-velocity of the gas is small compared with its molecular- 

 velocity, and we also assume that the linear scale of variation of either 

 gas is great compared with the average mean free path of a molecule. 



We may, therefore, to a first approximation, assume that Maxwell's law 

 of distribution of velocities obtains at every point, and that h is the same for 

 the two gases. 



Since the mass velocities are small quantities of the first order, and their 

 squares are therefore small quantities of the second order, it follows that, as 

 far as the first order of small quantities, the pressure p is constant throughout 

 the gas. 



