156 Physical Properties [CH. vn 



It will now be clear that all the analysis of the present chapter will hold, 

 even after allowing for the finite size of the molecules, if we take v to be the 

 density everywhere except at the boundary, provided that, in considering an 



element of surface at distance ^ from the boundary, we replace v by v^. 



A 



In calculating the pressure, it will be remembered, we assumed the 

 element of volume so great that intermolecular forces could not act across it. 

 At the same time we assume it so small that the density is approximately 

 constant throughout. These assumptions become inconsistent at the 

 boundary, because the density, as is clear from 134, varies over a range 

 across which intermolecular forces can and do act. In this case, however, we 

 can abandon the supposition that the density will be approximately constant 

 throughout. All that is required is a knowledge of the mean density in the 

 element of volume, and this, on account of the thinness of the layer near the 

 surface in which the mean density differs perceptibly from v, may still be 

 taken to be v. 



Gas in Equilibrium. 



177. We now examine the form assumed by our equations, when the 

 /gas is in equilibrium. In this case we can clearly take the law of distri- 

 bution of velocities to be Maxwell's law at every point, so that 



V 



p(j- = pu = vmu = ^- 



by equation (161), and 



uv = vw = WU = 0. 



Thus of the system of pressures specified by equations (363), that part 

 which arises from molecular agitation reduces to a simple hydrostatical 



pressure of amount ^y- . Clearly also the w system of pressures, arising 



from the intermolecular forces, will reduce to a simple hydrostatical pressure, 

 and we shall therefore have 



PXX = Pyy = PZZ = Vr+ 2h> 



P P _ P _ n 



* xy - 1 xz -* yz v 



The total pressure at the point oc, y, z is therefore a simple hydrostatical 

 pressure of amount P given by 



P = 1S + ^h ' (370)> 



178. The equations of equilibrium become 



pH = x- etc (371). 



ox 



