496 Lord Rayleigh on the Separation of Gases 



The constants /jl, v are not known beforehand, depending 

 as they do upon the specialities of the apparatus as well as 

 upon the quality of the gases. If we eliminate t 3 we get 



y-^=E(*-«)->, (11) 



in which only the ratio v//jl is involved. 



As a particular case suppose that initially the inside volume 

 is occupied by one pure gas and the outside by another, the 

 initial pressures being unity. Then in (10) 



«=0, 0=1, C = l, D = -lj 



we have 



x = e-' xt , y = l—e- vt , .... (12) 

 and 



s.+y — 1 + e-v*— e -vt (13) 



gives the total internal pressure. When this is a maximum 

 or minimum, e^~ v)t =fi/v ) and the corresponding value is 



■■♦■'-"er^ 1 -?}- • • • <"» 



Thus in the case of hydrogen escaping into oxygen, /*/v = 4, 

 and #+y=l-3x4-£=-528, 



the minimum being about half the initial pressure *. 



Returning now to the separation of gases by diffusion into 

 a vacuum, let us suppose that the difference between the 

 gases is small, so that (v—^) //* = #, a small quantity, and that 

 at each operation one-half the total volume of the mixture is 

 allowed to pass. In this case (8) becomes 



"V" i \r *"*~* i 



so that r=-g=(i)" (15) 



This gives the effect of the operation in question upon the 

 composition of the residual gas. If s denote the corres- 

 ponding symbol for the transmitted gas, we have 



(Y-y)/Y _ l-y/Y _ l-r*/X 

 '-(X-aO/X-1-tf/X 1-x/X 



= 1 -f _ ,/v ' = 2 — r approximately, 



* The most striking effects of this kind are when nitrous oxide, or dry 

 ammonia gas, diffuse into the air through indiarubber. I have observed 

 suctions amounting respectively to 53 and 64 centimetres of mercury. 



