supposed Irreversible Processes* 485 



no such tendency. A priori and directly that problem would 

 not be easy to attack. Indirectly and a posteriori it can be 

 shown that this tendency does exist. It follows, namely, from 

 the fact that our molecules, if elastic spheres have finite radius, 

 if centres of repulsive force have finite sphere of action, that 

 a certain stream motion (defined post) must exist beyond the 

 accidental stream which in Maxwell's distribution would exist 

 if the molecules were mere material points. 



And this tendency becomes inappreciable only when the 

 density becomes inappreciable. Further this property holds 

 for an infinite system, that is if our space S (Art. 8) is infinite, 

 but the density, or aggregate volume of all molecules in unit 

 of volume, is finite. 



26. I define stream motion at a point thus : — Let P be the 

 point, r the distance of any other point from P. Let f be a 

 function of r which is everywhere positive, finite, and continu- 

 ous, is equal to unity when r<za (a very small quantity), is of 

 negative degree when r>c, and such that 



i47JT 2 i/r dr is finite. 

 Jo 



And yfr being so defined, then let 



f at P=2wi|r/S^, 

 7j at F=^vyfr/%yjr, 

 £atP=St<^/2^, 



in which u, v, w are the component velocities of a sphere, and 

 the summation includes all our spheres. And I now define 

 f , rj, £ to be the components of stream motion at P. 



27. Now consider two cases : case (1) the spheres, each of 

 finite mass, have infinitely small diameters, so that no collisions 

 occur. This system will be in stationary motion, if Maxwell's 

 law of distribution prevails. Other laws may be possible, but I 

 assume Maxwell's to exist. On this assumption we calculate 

 the values of f ? , rf, £ 2 . Case (2) the spheres have finite 

 diameter. It can be proved, as I have shown in Chapter V. 

 of a work recently published on the Kinetic Theory of Gases, 

 that in this case the motion is not stationary if £ 2 &c. have 

 the same values as before. To make it stationary f 2 &c. must 

 have greater values than they have in Maxwell's distribution. 

 This means, by the definition of £ &c, that spheres near to each 

 other have a tendency to move in the same direction. And 

 this again requires that the law of distribution of velocities 

 shall be e~ AQ , in which Q is not the sum of squares only, but 



