270 PROFESSOR TAIT ON THE 



If we now suppose that our arrangement is a tube of length I and section S, 

 connecting two infinite vessels filled with the two gases respectively; and, 

 farther, assume that the diffusion has become steady, the equation (10) 

 becomes 



dt dx 2, 



where the left-hand member is constant. Also, it is clear that, since dQJdx 

 must thus be a linear function of x, we have 



S^-K 1 -?)' 



so that the mass of either gas which passes, per second, across any section of 

 the tube is 



where p is the common density of the two gases. 



For comparison with the corresponding formulas in the other cases treated 

 below, we may now write our result as 



Also, to justify our assumption as to the order of the translatory speed, we 



find by (3) 



1-38X 



\l-x)Jh 



Hence, except where l—x is of the order of one thousandth of an inch or less, 

 this is very small compared with h~ l . And it may safely be taken as impossible 

 that n x can (experimentally) be kept at at the section x = l. 



If the vessels be of finite size, and if we suppose the contents of each to be 

 always thoroughly mixed, we can approximate to the law of mixture as follows. 

 On looking back at the last result, we see that for p we must now substitute 

 the difference of densities of the first gas at the ends of the connecting tube. 

 Let g v g 2 be the quantities of the two gases which originally filled the vessels 

 respectively ; and neglect, in comparison with them, the quantity of either gas 

 which would fill the tube. Then, obviously, 



r/G 1= SDp/Gt fl-GA 

 dt " I \f/ 1 g 2 J' 



whence 



G = -71.72 Hl + £ i 9l9t { 



This shows the steps by which the initial state (g lt 0) tends asymptotically to 



