THERMODYNAMICAL SYSTEM OF GIBBS 71 



propositions the criterion of equilibrium for a material sys- 

 tem which is isolated from all external influences: 

 I. For the equilibrium of any isolated system it is necessary and 

 sufficient that in all possible variations in the state of the 

 system which do not alter its energy, the variation of its 

 entropy shall either vanish or be negative. 

 This condition of equilibrium may be written 



(5v). ^ 0, (4) [1] 



where {8r})( denotes a variation of entropy, the energy remaining 



constant. 



II. For the equilibrium of any isolated system it is necessary and 

 sufficient that in all possible variations in the state of the 

 system which do not alter its entropy, the variation of its 

 energy shall either vanish or be positive. 



This condition may be written 



(5e), ^ 0, (5) [2] 



where (8e) „ denotes a variation of energy, the entropy remaining 

 constant. 



He proceeds to prove, that these two propositions are equiva- 

 lent to each other, that they are sufficient for equilibrium, and 

 that they are necessary for equilibrium. We shall quote largely 

 from Gibbs' own exposition, interpolating explanatory remarks 

 where they seem to be helpful. 



3. Equivalence of the Two Criteria.* "It is always possible 

 to increase both the energy and the entropy of the system, or to 

 decrease both together, viz., by imparting heat to any part of 

 the system or by taking it away. For, if condition I is 

 not satisfied, there must be some variation in the state of the 

 system for which 



5t7 > and 8e = 0." 



Therefore, by taking heat from the system in its varied state we 

 may decrease the entropy to its original value and at the same 

 time diminish the energy, so that we reach a state for which 



3?7 = and 8e < 0. 



Gibba, I, p. 56, lines 20-37. 



