by Diffusion and similar Processes, 495 



usually held fjb/v=4, we should have from (8) 



|±^=i x 13 _f + i X 13~ § = '229 ; 



so that a reduction of the residue to '229 of the initial quantity 

 should have effected the observed enrichment. The initial 

 and final volumes given by Graham are, however, 7*5 litres 

 and *45 litre, whose ratio is *06. The inferior efficiency of 

 the apparatus may have been due to imperfections in the walls 

 or joints of the pipes. Such an explanation appears to be 

 more probable than a failure of the law of independent 

 diffusion of the component gases upon which the theoretical 

 investigation is founded. 



In the concentration of argon from a mixture of argon and 

 nitrogen we have conditions much less favourable. In this 



case 



/i/v=S20/y/U = '077. 



If an enrichment of 2 : 1 is required and if the original 

 mixture is derived from the atmosphere by removal of oxygen, 

 the equation is 



,,.,, -6-13 -5-13 



^%=-99x2 +-01X-2 



= •0142 + -0029 = -0171, 



expressing the reduction needed. The results obtained 

 experimentally (loc. cit.) were inferior in this case also. 



When the object is the most effective separation of the 

 components of a mixture, it is best, as supposed in the above 

 theory, to maintain a vacuum on the further side of the porous 

 wall. But we have sometimes to consider cases where the 

 vacuum is replaced by an atmosphere of fixed composition, as 

 in the well-known experiment of the diffusion of hydrogen 

 into air through a porous plug. We will suppose that there 

 are only two gases concerned and that the volume inside is 

 given. The symbols x, y will then denote the partial 

 pressures within the given volume, the constant partial 

 pressures outside being a, /3. Our equations may be written 



dx = /i{a — a:)dt\ 



dy = v(P-y)dt J> GO 



or on integration 



x = a + Ce-*\ y = j3 + De- vf , . . . (10) 



C, D being arbitrary constants. 



After a sufficient time a?, y reduce themselves respectively 

 to a, /3, as was to be expected. 



