494 Lord Rayleigh on the Separation of Gases 



If X, Y be simultaneous values of x, y, regarded as initial, 



$ -©"""• « 



so that 



-*m » 



In like manner 



»= Y (m) ^ 



If we write 



y/x 



Y/X = r > (7) 



r represents the enrichment of the residue as regards the 

 second constituent, and we have from (5), (C), 



XfY~X + Y + X + Y ' * ' * y) 



an equation which exhibits the relation between the enrich- 

 ment and the ratio of the initial and final tolal quantities of 

 the mixture. 



From (8), or more simply from (4), we see that as x 

 diminishes with time the enrichment tends to zero or infinity, 

 indicating that the residue becomes purer without limit, and 

 this whatever may be the original proportions. Thus if the 

 first gas (x) be the more diffusive (/u, > v), the exponent on the 

 right of (4) is negative ; and this indicates that r becomes 

 infinite, or that the first gas is ultimately eliminated from the 

 residue. When the degree of enrichment required is specified, 

 an easy calculation from (8) gives the degree to which the 

 diffusion must be carried. 



In Graham's atmolyser the gaseous mixture is caused to 

 travel along a tobacco-pipe on the outside of which a vacuum 

 is maintained. If the passage be sufficiently rapid to 

 preclude sensible diffusion along the length of the pipe, the 

 circumstances correspond to the above calculation ; but the 

 agreement with Graham's numbers is not good. Thus in one 

 case given by him * of the atmolysis of a mixture containing 

 equal volumes of oxygen and hydrogen, we have 



Y/X = l, ylx= 92-78/7-22, . 



so that r= 13 nearly. Thus, if in accordance with the view 



* Phil. Trans, vol. cliii. p. 403 (1863). 



