CGC te. oe 
J. W. Gibbs— Equilibrium of Heterogeneous Substances. 441 
Arr. LIL—On the Equilibrium of Heterogeneous Substances ; 
by J. WILLARD Giszs.* Abstract by the author. 
The following form, which is easily shown to be equivalent 
to the preceding, is often more convenient in application : 
IL. For the equilibrium of any isolated system tt is necessary and 
sufficient that in all possible variations of the state of the system 
which do not alter its entropy, the variation of its energy shall 
ether vanish or be positive. 
If we denote the energy and entropy of the system by ¢ and 
7 respectively, the criterion of equilibrium may be expressed 
by either of the formule 
(077). 50, (1) 
2 
Again, if we assume that the temperature of the system is 
uniform, and denote its absolute temperature by ¢, and set 
pan € — tf 7, 
the remaining conditions of equilibrium may be expressed by 
the formula 
(di),=0, : 
the suffixed letter, as in the preceding cases, indicating that the 
quantity which it represents is constant. is condition, in 
Connection with that of uniform temperature, may be shown to 
equivalent to (1) or (2). The difference of the values of » 
for two different states of the system which have the same 
temperature represents the work which would be expended in 
bringing the system from one state to the other by a reversible 
Process and without change of temperature. 
* Transactions of the Connecticut Academy of Arts and Sciences, vol. iii, pp. 
108-248 and 343-524. 
