[From the Pnc*di*9 of the Cambridge Philotophical Society, Vol. II., 1876.] 



LXXVI. On the Equilibrium of Heterogeneous Substances. 



TUB thermodynamical problem of the equilibrium of heterogeneous substances 

 was first attacked by Kirchoff in 1855, who studied the properties of mixtures 

 of sulphuric acid with water, and the density of the vapour in equilibrium with 

 the mixture. His method has recently been adopted by C. Neumann in his 

 Vorksungen fiber die mechanische Theorie der Warme (Leipzig, 1875). Neither 

 of these writers, however, makes use of two of the most valuable concepts in 

 Thermodynamics, namely, the intrinsic energy and the entropy of the substance. 



It is probably for this reason that their methods do not readily give ;m 

 explanation of those states of equilibrium which are stable in themselves, but 

 which the contact of certain substances may render unstable. 



I therefore wish to point out to the Society the methods adopted by 

 Professor J. Willard Gibbs of Yale College, published in the Transactions of 

 the Academy of Sciences of Connecticut, which seem to me to throw a new- 

 light on Thermodynamics. 



He considers the intrinsic energy (c) of a homogeneous mass consisting of 

 H kinds of component matter to be a function of n + 2, variables, namely, the 

 volume of the mass v, its entropy rj, and the n masses, w,, m,...w n , of its 

 component substances. 



Each of these variables represents a physical quantity, the 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 (con- 

 sidered as independent), we obtain a set of n + 2 differential coefficients which 

 represent the intensity of various properties of the substance. Thus, 



