300 Free Path Phenomena [OH. xv 



If there are no external forces, we can put X l = X 2 = 0, and obtain 



= _^-- = / _ K 



dx 



where u 2 , i^ are now mass-velocities. Since the temperature is constant 

 throughout the gas, we may take 



__ ^ v l 



de ~ dx 



^.P? JL 

 dx ~ dx 



Hence we have 



(722). 



The total flow of molecules of the first kind per unit area per unit time 

 :learly 

 we have 



^\ 



is clearly z/jWj, and is also 5) la - , if 3) 12 is the coefficient of diffusion. Hence 



so that equation (722) becomes 



From this we obtain as the value of > 12 , 



ON _ 1 _ /m! + m 2 

 12 2Aw 1 m a A 1 (i/! + i/ a ) V ^ 



For diffusion of a single gas into itself, this becomes 



and if from equation (709) we introduce rj, given by 

 this value of 2) becomes 



Introducing the value of the coefficient of viscosity, 



rjv 



