1 6 THE DIFFUSION OF GASES THROUGH 



Between the variables belonging to II and II' respectively there is an imme- 

 diate relation, since on mere expansion for flotation 



PjPn = p'jp'n (24) 



at any time, from which p' may be reduced to p; or, for instance, in case 

 of equation (18) 



w= -( — + — ) — ;etc. (25) 

 t \R a R h / p h 



Finally, the initial mass, m , of hydrogen imprisoned must be given, 

 corresponding to the initial volume v = v , not expanded like v' for flotation; 

 v is variable while v' is constant. Hence 



m = v U/R h T (26) 



and at any subsequent time 



v (Ph ,Pa\ ( v 



m = m a -f w» = - ^— + jr) (27) 



which reduces to 



p =-\r-r)^K (29) 



p being the density of the mixture undergoing transpiration at t seconds 

 and p the density of the pure hydrogen at / = seconds. 



The value of p h given in equation (29) may now be inserted into equation 

 (n), whereupon this becomes 



m i-R a p/R h Po k h -k a h"p w g . . 



a i-RjRn ~h" + 2h'"~ r a h"+2h'" K3 } 



which is perhaps the most acceptable form of the equation for m; but, as 

 stated above, it can not be integrated, because p = p a -\-p n = m/v, both of 

 which (m and v) are variable in the lapse of time. Since m' = mp /p is 

 observed, the equation is advantageously referred to volume. If the mean 

 temperature and pressure are assumed constant throughout, implying 



R a P/RhPo = R a /R 

 where R the gas constant of the mixture, 



a i-R a /R h h"+2h'"^ a h"+2ti" {3V 



If m or v is constant, a result which eventually appears in all the experi- 

 ments, it follows that p is constant, i. e., a gas mixture of definite composi- 

 tion or density eventually diffuses, since 



k h~ K R a P 



m = all 



h"+2h"' R a -R» Po 



