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L. Theoretical Considerations respecting the Separation of 

 Gases by Diffusion and similar Processes. By Lord 

 Rayleigh, Sec. R.S.* 



THE larger part of the calculations which follow were 

 made in connexion with experiments upon the concen- 

 tration of argon from the atmosphere by the method of 

 atmolysis f. When the supply of gas is limited, or when it 

 is desired to concentrate the lighter ingredient, the conditions 

 of the question are materially altered ; but it will be con- 

 venient to take first the problem which then presented itself 

 of the simple diffusion of a gaseous mixture into a vacuum, 

 with special regard to the composition of the residue. The 

 diffusion tends to alter this composition in the first instance 

 only in the neighbourhood of the porous walls ; but it will be 

 assumed that the forces promoting mixture are powerful 

 enough to allow of our considering the composition to be 

 uniform throughout the whole volume of the residue, and 

 variable only with time, on account of the unequal escape of 

 the constituent gases. 



Let x, y denote the quantities of the two constituents of the 

 residue at any time, so that — da, —dy are the quantities 

 diffused out in time dt. The values of dx/dt, dy/dt will 

 depend upon the character of the porous partition and upon 

 the actual pressure ; but for our present purpose it will 

 suffice to express dy/dx, and this clearly involves only the 

 ratios of the constituents and of their diffusion rates. Calling 

 the diffusion rates fi f v, we have 



£ = '-2. • • • (1) 



dX fJLX v y 



In this equation x, y may be measured on any consistent 

 system that may be convenient. The simplest case would be 

 that in which the residue is maintained at a constant volume, 

 when x, y might be taken to represent the partial pressures 

 of the two gases. But the equation applies equally well 

 when the volume changes, for example in such a way as to 

 maintain the total pressure constant. 



The integral of (1) is 



y l "=Q^, (2) 



where is an arbitrary constant, or 



ylx=Cx- l +*'» (3) 



* Communicated by the Author. 



t Rayleigh and Ramsay, Phil. Trans, clxxxvi. p. 206 (1895). 



