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.
But if the principle thus enunciated by Helmholtz as a consequence of the laws of thermodynamics is at bottom identical with that discovered by Gibbs, it is more difficult of application and is presented under a more mysterious aspect.