272 Free Path Phenomena [CH. xiv 



^\ 



The coefficient of ~ on the right-hand side is the coefficient of diffusion 



vz 



for the two gases in question. If we write 



2 



\7rhm 2 



so that GI, c 2 are the mean velocities in the gases in question, this assumes 

 the form 



(P^ 1 XiCi^i" K-%C%V\ /CQK\ 



3 !>! + v% 



325. If we consider diffusion between two gases in which the molecules 

 are approximately of equal size and weight, and agree to neglect the 

 differences in size and weight, we may take X and c to be the same for 

 each gas, and so obtain 



< = |Xc (636). 



Comparing this with the value of the coefficient of viscosity (equation (573)) 



(637), 



if 



we obtain the relation 2) = (638). 



P 



Correction when Molecules are Elastic Spheres. 



326. This equation of course requires correction by multiplication by a 

 numerical factor, and this we shall now try to estimate. As in the case of 

 viscosity, there are two sources of error, the first arising from our inaccurate 

 evaluation of X, and the second from neglect of the persistence of velocities. 



As regards the first, it is clear that in expression (624), X must be 

 replaced by X c and taken under the sign of integration. Hence instead of X 

 in the final result, we must have I, where 



f 



JO 



/ 



Jo 



(639). 



This however is exactly the same as the I of the viscosity formula, of 

 which the value was found in 304 to be 



1-051 



V27TZ/0- 2 ' 



Hence this correction affects 2) and K exactly similarly, multiplying each by 

 T051, but does not affect equation (638). 



