323, 324] Diffusion 271 



If the similar quantity for the second kind of gas is denoted by F 2 , 



- 2 X 2 



/Gar\\ 



(629). 



324. The increase per unit time of molecules of the first kind per unit 



volume at z = z is clearly ~ , so that 



. ...(630), 



at 



. ...(631). 



at 



Hence l + T = ~ 



This quantity is in any case independent of z, since Vi + v 2 is constant 

 throughout the gas, and vanishes in the steady state. Hence in the steady 

 state F! + F 2 is constant throughout the gas. Clearly Fj + F 2 measures the 

 net flow of gas per unit area across any plane perpendicular to the axis of z. 

 If there is no steady current of this kind, 



................................. (632). 



We have also the relation (equation (619)) 



v\ + v<2, = constant, 

 whence, by differentiation, 



dvA fdv a \ _ 



^-1+^-) = U ........ - .................... (Odd). 



dz/ \dzj 



If we add together equations (628) and (629), simplifying by means of 

 the equation just obtained, we get 



/ \ 



2 = W ( Vl + i/ 9 ) - 



,-=. - ~ 

 \/ 7r hm 1 



and since Fj + F 2 = 0, this gives the value of W Q in the form 



Vl + 1 



Substituting this value in equations (628) and (629) we obtain 



