58 THE DIFFUSION OF GASES THROUGH 



In equation (3) tc h can not be found even when K a is given, unless p h is 

 also given, which is not generally the case in a phenomenon so complicated. 

 If equation (3) is expressed in terms of p a 



- 2k '"+ h " g » (B-Tr-p tt +h"p w g)(K h -K a )+K a h" Pu> g (8) 



a 



Hence, since at the beginning p a = o, 



-(2h" , +h")i> Q /o=(B-ir+h"p„g)K h -(B-7r)K tt (9) 



so that for given ;.„, i< h may be found from the slope of the initial tangent of 

 the time graph. 

 If p a =h"p„g, 



- J *0=&-*)K n -(B-TT-h"p w g)K a (TO) 



so that K h can again be found if this stage of diffusion can be recognized, 

 which is not generally the case. When v = o, 



Ph('<h-Ka)= K ah"p ie g (") 



which still contains the two unknown quantities, p h and k 1p for known K a . 



If the gases within and without the diver are initially identical, but in 

 multiple as in the case of air, the quantities being limited within and un- 

 limited without, 



2 h'"+h" ■ t f 



— a \ = Ka(Pa-pa)+ K h(Ph-Ph) ( J 2 ) 



Since B — tt = p h -{-p a and B — k"p w g—ir=p H — p a , the equation may be written 

 2h'"-\-h" • / 



- - — l 'o=^a- K ? t )Pa- ( K a- K h)Pa+ K h h "Pv,g ( r 3) 



If n a and i; h are not the same, the term involving p a is variable and hence 

 v is not constant. Theoretically this is an objection against the use of air 

 as a standard gas. In practice, however, v is, apart from temperature 

 discrepancies, very nearly constant, i. e., the departure of the time graph 

 from a straight line throughout a sufficiently long interval of observation 

 can not be detected (see transpiration figures, Chapter II). Hence the two 

 diffusion coefficients are nearly enough the same to justify equation (5) in 

 most cases if sufficient time has elapsed to establish the equilibrium condi- 

 tions. The extreme difficulty of using any other gas and the special errors 

 introduced by the necessity of an artificial atmosphere more than counter- 

 balance the theoretical preference suggested. 



39. Diffusion of Air into Air Through Water. — The apparatus used 

 was of the double-tube type of fig. 16 and its dimensions are given at the 

 head of table 16. The float fitted the tube somewhat too snugly, so that 

 observation was very slow, owing to the thin sheet of water between diver 



