35 MAXWELL'S LAW 71 



molecules through the surface F in unit time, and these 

 carry back the oppositely directed momentum 



NmF(G - a) 2 . 



The two halves into which the gaseous mass is separated 

 by the surface F, therefore, both gain and lose momentum, 

 and the question is, What variation in the law of distribu- 

 tion results ? If we call that side the right towards which 

 the flow is directed, we can say that the right side gains 

 an amount of momentum directed towards the right which 

 is equal to 



while it loses momentum directed towards the left equal to 



The right half thereby obtains an amount of right-directed 

 momentum which exceeds the left-directed momentum, and 

 this excess is equal to 



NmF{(G + a) 2 + (G - a) 2 }. 



The excess of left-directed over right-directed momentum 

 which arises in the left half is of equal amount; for this 

 half gains left-directed momentum equal to 



NmF(G - aY, 

 and loses right-directed momentum equal to 



so that the left-directed momentum in the left half will 

 exceed the right-directed momentum in the left half by the 

 amount 



a)* + (G + a) 2 }. 



These formulae, however, do not account for the whole 

 changes that occur. In the case of a flowing gas the other 

 two-thirds of the molecules come also into account; for 

 these, too, take part in the flow, and therefore possess the 

 velocity a in the direction perpendicular to the surface F. 

 In this direction, therefore, there pass 



