53* DIFFUSION 459 



53*. Coefficient of Diffusion 



This result enables us also to express in terms of the free path 

 the number of molecules, represented by the last formula in 51*, 

 which pass over unit area in unit time in the direction of increasing 

 x : for this we have 



In the opposite direction flows an equal number with changed 

 sign, so that 



more particles cross in the positive direction than in the negative. 

 If now we introduce the necessary subscripts for the two 



gases, 



particles of the first kind and 



particles of the second kind pass through unit area in unit time 

 in the positive direction. By repeating the procedure employed 

 in 95, and remembering that 



tf i + N 2 = N 



is a constant independent of x, we obtain for the constant of 

 diffusion the expression 



which agrees with the former one. We have to substitute in this 

 the values of the free paths as in 98 ; and we then obtain 



where for shortness are put 



54*. Differential Equations 

 If this value of D were constant, the differential equations 



tit dx*' dt dx 2 ' 



