Diffusion of Gases. 477 



of CP is cos QCP cos (j> ; that is, zero, since cos cj> = 0. There- 

 fore molecules of gas I. issuing from encounter with molecules 

 of gas II. with velocity v have no average translation-velocity ; 

 that is, « 2 / = 0. 



15. Our equation (2) is thus reduced to 



or 



1 dn q v 2 , , , 



where a/ is the mean projection on x of the velocity v of a 

 molecule of gas I. as it comes with that velocity out of an 

 encounter with another molecule of gas I. Now there can he 

 no gain or loss of x velocity to gas I. as a whole from encoun- 

 ters between its own molecules, although some classes may 

 gain and others lose. It follows that if we integrate for all 

 values of v from go to 0, 



or 



j/W Budv =§f(v) B*/ dv. 



But the effect of these encounters is to 'equalize wholly or 

 partially the translation-velocities of the different classes ; so 

 that a/ is less than a for high, greater than a for low, values 

 of v. Also B increases with v. Therefore, since 



f /(»)B«<fo= f /(»)B«/<fo, 

 i f(v)*idv must be greater than I f{y) dv. 



16. We have then 



dn? v 



^ _ _L 



dn l dx B 



a o y TT + 9 "1 J 



Therefore, taking mean values, n Y is the stream of gas I., and 



2 dn 2 v 9 



