7-2 MOLECULAR MOTION AND ITS ENEKGY 35 



molecules from the left half to the right in the unit of time, 

 and these carry with them the momentum 



The total excess, therefore, of right-directed over left- 

 directed momentum which is produced in unit time in the 

 right half is given by 



$NmF{(G + a) 2 + (G - a) 2 } + %NmFa 2 



= NmF(G* + a 2 ). 



Just as large is the excess of left-directed over right- 

 directed momentum which occurs in the left half in unit 

 time ; for the former increases by 



NmF(G - a) 2 , 

 while the latter diminishes by 



Now, according to the kinetic theory of gases, the pressure 

 is nothing else than the momentum carried across unit 

 area in unit time ; consequently the pressure is expressed by 

 the formula 



p = JVm(JG 2 + a 2 ), 



and this formula holds good equally well for the direction 

 in which the gas flows and for the opposite direction. As 

 for the former direction, the added term 



Nma 2 = pa 2 



expresses the stress exerted by the stream, so for the oppo- 

 site direction it represents the equal reaction-stress 

 which is exerted by the flowing gas on the containing 

 vessel. 



For a direction at right angles to the stream the pres- 

 sure will be expressed by the formula 



p = $NmG\ 



which holds good for all directions in a gas at rest. An 

 essential difference, however, consists in the magnitude G 

 not having the same value for a flowing gas as it has in a 

 gas at rest. This is, at least, the case when the gas is not 

 brought into a state of motion by the application of energy 



