In the same way J.W.  Gibbs, in 1875 and 1878, then Helmholtz in 1882, and, in France, M. Duhem, from the year 1886 onward, have published works, at first ill understood, of which the renown was, however, considerable in the sequel, and in which they made use of analogous functions under the names of available energy, free energy, or internal thermodynamic potential.  The magnitude thus designated, attaching, as a consequence of the two principles, to all states of the system, is perfectly determined when the temperature and other normal variables are known.  It allows us, by calculations often very easy, to fix the conditions necessary and sufficient for the maintenance of the system in equilibrium by foreign bodies taken at the same temperature as itself.

One may hope to constitute in this way, as M. Duhem in a long and remarkable series of operations has specially endeavoured to do, a sort of general mechanics which will enable questions of statics to be treated with accuracy, and all the conditions of equilibrium of the system, including the calorific properties, to be determined.  Thus, ordinary statics teaches us that a liquid with its vapour on the top forms a system in equilibrium, if we apply to the two fluids a pressure depending on temperature alone.  Thermodynamics will furnish us, in addition, with the expression of the heat of vaporization and of, the specific heats of the two saturated fluids.

This new study has given us also most valuable information on compressible fluids and on the theory of elastic equilibrium.  Added to certain hypotheses on electric or magnetic phenomena, it gives a coherent whole from which can be deduced the conditions of electric or magnetic equilibrium; and it illuminates with a brilliant light the calorific laws of electrolytic phenomena.

But the most indisputable triumph of this thermodynamic statics is the discovery of the laws which regulate the changes of physical state or of chemical constitution.  J.W.  Gibbs was the author of this immense progress.  His memoir, now celebrated, on “the equilibrium of heterogeneous substances,” concealed in 1876 in a review at that time of limited circulation, and rather heavy to read, seemed only to contain algebraic theorems applicable with difficulty to reality.  It is known that Helmholtz independently succeeded, a few years later, in introducing thermodynamics into the domain of chemistry by his conception of the division of energy into free and into bound energy:  the first, capable of undergoing all transformations, and particularly of transforming itself into external action; the second, on the other hand, bound, and only manifesting itself by giving out heat.  When we measure chemical energy, we ordinarily let it fall wholly into the calorific form; but, in reality, it itself includes both parts, and it is the variation of the free energy and not that of the total energy measured by the integral disengagement of heat, the sign of which determines the direction in which the reactions are effected.