26, 27] 



The Statistical Method 



25 



Gas in a closed vessel. 



27. This completes the determination of the steady states of an infinite 

 mass of gas. We have next to consider the modifications introduced when 

 the gas is confined in a closed vessel. Supposing the walls of this vessel to 

 be absolutely rigid and elastic, we shall shew that the law of distribution 

 already found in equation (25), namely 



f = 



will still represent a steady state, independently of the shape of the containing 

 vessel, provided that this vessel is moving with a velocity U Q> v , w . 



To prove this we consider the collisions of molecules with a single small 

 element of the wall of the containing vessel. Let this element be of area da 

 and let the direction -cosines of a line drawn perpendicular to it be I, m, n. 

 Consider the class of collisions such that the components of velocity of the 

 colliding molecule before impact lie between 



u and u + du, v and v + dv, w and w + dw ............... (34). 



As before, let us call all such molecules, molecules of class A. Let us, as 

 on a former occasion ( 13), take a fixed point as origin and represent the 

 velocities of the different molecules in magnitude and direction, by a system 

 of lines drawn from this point. All the molecules of class A will be repre- 

 sented by lines having their representative points inside a certain small 

 rectangular parallelepiped the rectangular parallelepiped of which the ortho- 

 gonal coordinates lie within the limits (34). 



FIG. 2. 



