m 



1 6 the; diffusion of gases through 



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

 diate relation, since on mere expansion for flotation 



PjPn^p'jp'r. (24) 



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

 of equation (18) 



'^' ( Pa , Ph\Ph , .^ f . 



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

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

 V is variable while v' is constant. Hence 



'mQ = VQU/Rj^T (26) 



and at any subsequent time 



^h 



which reduces to 



p,(i i\ R^ 



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

 and Po the density of the pure hydrogen at / = o seconds. 



The value of pf^ given in equation (29) may now be inserted into equation 

 (11), whereupon this becomes 



m _„ i-Rap/R„Po h-K |T ^"Pwg / X 



a i-RJRn h" + 2h"'~^'^''h"+2h"' ^^^^ 



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

 stated above, it can not be integrated, because p = pa-\-pj^ = m/v, both of 

 which {m and v) are variable in the lapse of time. Since m' = mp^lp is 

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

 temperature and pressure are assumed constant throughout, implying 



where R the gas constant of the mixture, 



a ~ I-RJR^ h"+2h"' ^ ''h"+2h"' ^^^ 



li 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 



m = aVi 



K], K„ Jx, 



a 



h"-\-2h"' R,-R, p. 



