G2 Mr. S. H. Burbury on the Second Law of Thermodynamics 



of the second particle between oc 2 and # 9 + dx^ 



Hi and pi + dyv 



of the Xth particle between .i\ and ^ + tfofy 



2? A and ~ A +</~ A , 

 may, when dk&j, <///,, . . . dz K are very small, be considered as 

 having the same value of % for ergal, notwithstanding any va- 

 riations of position within those limits. 



Let all such positions be deemed to constitute one configu- 

 ration, which we may call configuration M. Then, as Boltz- 

 man has shown, the time during which on the average of any 

 very long time the system will be within configuration M is 

 proportional to 



?*#*, di/ l . . .dgfy, 



Its actual value is therefore 



€ hx dx } dy x . . .dz k 



the integration extending over all possible configurations.. 

 The mean value of any function, /, of the position of the par- 

 ticles (which we denote as usual by /) is 



and therefore 



Jft...y?xdx l dy l ...dz K 

 X ]^...'e h xdx l dy l ...dz k 



II. Now let the system receive a small accession of heat ; SQ, 

 and let o7*, hv be the consequent increments of h and v. We 

 may suppose the alteration of volume to be effected by the 

 vessel undergoing a uniform homogeneous strain, the centre 

 remaining fixed. In that case the distance, r, between any 

 two points in it beomes after the alteration 0r, where 6 is 

 a ratio the same for every pair of points, and manifestly 



O V 



We further assume that the external forces are so adjusted 

 as to maintain the system in equilibrium in its altered state, 

 and that such adjustment takes place without altering % for 

 any given 'configuration, consequently that no change takes 



