EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 59 



greater than in any other state of the same energy, it is evidently in 

 equilibrium, as any change of state must involve either a decrease of 

 entropy or an increase of energy, which are alike impossible for an iso- 

 lated system. We may add that this is a case of stable equilibrium, as 

 no infinitely small cause (whether relating to a variation of the initial 

 state or to the action of any external bodies) can produce a finite 

 change of state, as this would involve a finite decrease of entropy or 

 increase of energy. 



We will next suppose that the system has the greatest entropy 

 consistent with its energy, and therefore the least energy consistent 

 with its entropy, but that there are other states of the same energy 

 and entropy as its actual state. In this case, it is impossible that 

 any motion of masses should take place; for if any of the energy 

 of the system should come to consist of vis viva (of sensible motions), 

 a state of the system identical in other respects but without the 

 motion would have less energy and not less entropy, which would be 

 contrary to the supposition. (But we cannot apply this reasoning to 

 the motion within any mass of its different components in different 

 directions, as in diffusion, when the momenta of the components 

 balance one another.) Nor, in the case supposed, can any conduction 

 of heat take place, for this involves an increase of entropy, as heat is 

 only conducted from bodies of higher to those of lower temperature. 

 It is equally impossible that any changes should be produced by the 

 transfer of heat by radiation. The condition which we have sup- 

 posed is therefore sufficient for equilibrium, so far as the motion of 

 masses and the transfer of heat are concerned, but to show that the 

 same is true in regard to the motions of diffusion and chemical or 

 molecular changes, when these can occur without being accompanied 

 or followed by the motions of masses or the transfer of heat, we must 

 have recourse to considerations of a more general nature. The fol- 

 lowing considerations seem to justify the belief that the condition is 

 sufficient for equilibrium in every respect. 



Let us suppose, in order to test the tenability of such a hypothesis, 

 that a system may have the greatest entropy consistent with its 

 energy without being in equilibrium. In such a case, changes in the 

 state of the system must take place, but these will necessarily be such 

 that the energy and the entropy will remain unchanged and the 

 system will continue to satisfy the same condition, as initially, of 

 having the greatest entropy consistent with its energy. Let us con- 

 sider the change which takes place in any time so short that the 

 change may be regarded as uniform in nature throughout that time. 

 This time must be so chosen that the change does not take place in it 

 infinitely slowly, which is always easy, as the change which we sup- 

 pose to take place cannot be infinitely slow except at particular 



