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value of which, for a material system, is the sum of its values 
for the parts of the system. 
By differentiating the energy with respect to each of these 
variables (considered as independent), we obtain a set of n-+¢ 
differential coefficients which represent the intensity of various 
properties of the substance. Thus, 
= =— p, where p is the pressure of the substance . 
o=6 where @ is the temperature on the thermodynamic : 
scale ; 
ee #, Where m, is the potential of the component (m,) with 
‘ . 
respect to the compound mass. 
Kach of the component substances has therefore a potential 
with respect to the whole mass. 
The idea of the potential of a substance is, I believe, due to 
Prof. Gibbs. His definition is as follows :-— 
If to any homogeneous mass we suppose an infinitesimal 
quantity of any substance to be added, the mass remaining 
homogeneous, and its eutropy and volume remaining unchanged, 
the increase of the energy of the mass, divided by the mass of 
the substance added, is the potential of that substance in the 
mass considered, 
The condition of the stable equilibrium of the mass is ex- 
pressed by Prof. Gibbs in either of the two following ways: . 
I. For the equilibrium of any isolated system rt 1s necessary 
and sufficient that in all possible variations of the state of the 
system which do not alter its energy, the variation of ats eutropy 
shall either vanish or be negative. 
Il. For the equilibrium of any isolated system it 1s necessary 
and sufficient that in all possible variations of the state of the 
system which do not alter its eutropy, the variation of the energy 
shall either vanish or be positive. 
