7* PRESSURE AND ENERGY 363 



Further, when the gas has no progressive motion as a whole 

 we shall have \y 



u 2 = v 2 = w 2 . *M\ 



The value of these three equal means is easily found ; for if w is 

 the actual velocity of a particle 



and therefore w 2 = u 2 + v 2 + 



and consequently y? =~ 



In this special case then 



that is, the pressure in a gas which is in equilibrium and at rest 

 as a whole is the same in all directions, and acts always normally 

 to the surface on which it acts. 



If the gas possesses a progressive motion in which its whole 

 mass takes part, the magnitudes of the mean values are just 

 as easily found. Let a be the velocity with which the gas 

 as a whole moves in the direction of the component u] then, if 

 we put 



u = Ui + a, 



Ui is the component of the molecular motion which is perceptible 

 not as causing change of position, but as producing heat and 

 pressure in the gas, and, by 33, the relations 



hold good, if we now represent the pure molecular velocity freed 

 from that of the flow by where 



Wl 2 = V + tf + w*. 



We have in this case also, just as before, expressions of the form 



for the components of pressure at right angles to the direction of 

 flow. On the contrary, for the pressure in the direction of flow 

 we have _ 



X t = p (u, + a) 2 = P ?7? + ,oa 2 , 



