THERMODYNAMICAL SYSTEM OF GIBBS 73 



(i.e. which do not change the entropy at constant energy, or the 

 energy at constant entropy), while in general 



(At?), ^0, i.e. (Ae), ^0; (8) [5] 



and for unstable equilibrium there must be some variations 

 for which 



(At?), > 0, (9) [6] 



i.e. there must be some for which 



(Ae), < 0," (10) [7] 



(i.e. in respect to some variations the entropy has the properties 

 of a minimum, and the energy of a maximum), while the 

 general criteria of equilibrium: 



(577), ^ 0, i.e. (8e), ^0; (11) [8] 



are still satisfied. 



Secondly, in these criteria of equilibrium only possible varia- 

 tions are taken into account. Changes of state involving the 

 transport of matter through a finite distance are excluded from 

 consideration, so that an increase in the quantity of matter in 

 one body at the expense of that in another, is regarded as 

 possible only when the two bodies are in contact. If the system 

 consists of parts between which there is supposed to be no 

 thermal communication, the entropy of each part is regarded 

 as constant, since no diminution of entropy of any of these 

 parts is possible without the passage of heat. In this case the 

 condition of equilibrium becomes 



(56)v, ," , etc. ^0, (12) [9] 



where 77', r]", etc. denote the entropies of the various parts 

 between which there is no communication of heat. 



Otherwise, "only those variations are to be rejected as 

 impossible, which involve changes which are prevented by 

 passive forces or analogous resistances to change." It is neces- 

 sary to consider what is meant by this limitation. 



